Research ArticleQuantitative Research and Characterization of the LoessMicrostructure in the Bai Lu Tableland Shaanxi Province China

Longsheng Deng 123 Wen Fan 123 Shaopeng Liu1 Yupeng Chang1 Yan Dai1

and Yubo Li4

1School of Geological Engineering and Geomatics Changrsquoan University Xirsquoan 710054 China2Key Laboratory of Western China Mineral Resources and Geological Engineering Xirsquoan 710054 China3Key Laboratory of Mine Geological Hazards Mechanism and Control Xirsquoan China4China Railway First Survey and Design Institute Group Co Ltd Xirsquoan China

Correspondence should be addressed to Longsheng Deng dlshchdeducn and Wen Fan fanwenchdeducn

Received 30 October 2019 Revised 27 April 2020 Accepted 1 May 2020 Published 10 June 2020

Academic Editor Rafael J Bergillos

Copyright copy 2020 Longsheng Deng et al -is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Loess is a special geotechnical material with strong structural properties and the microstructural characteristics of loess significantlyinfluence its macroscopic physical features mechanical properties and catastrophic behavior In this paper serial samples wereextracted from the continuous loess and paleosol strata of the Bai Lu tableland with these samples the optical microscopy-basedserial sectioning method was adopted to study the quantitative characterization and variation in the loess microstructure -ree-dimensional characteristics and quantitative parameters of the particles pores and throats of the loess were obtained -e resultsindicate that the volume Eq-Radius and major-minor axis ratio of the loess particles satisfy third-order third-order and second-order Gaussian distributions respectively -e Eq-Radius of the loess pores and throats satisfies a first-order Gaussian distributionand the throat channel length satisfies a gamma distributionWith increasing stratum depth the particles becomemore flattened thethroat radii become larger and the pore channels become slenderer -e variation in fitting parameters and the correlations betweenthe macrophysical and mechanical properties of loess were then explored -e study of the microstructure of loess contributes to abetter understanding of the catastrophic behavior of loess and the physical mechanism of geologic hazards in this area

1 Introduction

Loess generally shows a high strength when dry but underconditions of soaking the skeleton of loess weakens rapidlywhich would result in the collapse of loess settlement ofloess ground and instability of a loess slope [1ndash3] As aspecial geotechnical material loess is known for its strongstructure water sensitivity and seismic vulnerability amongwhich the water sensitivity and seismic vulnerability es-sentially originate from its structural properties Micro-structural characteristics are the most dominant factorscontrolling the structural properties of loess and can directlyinfluence the engineering properties and macroscopic me-chanical behavior of loess [4 5] As a granular material thedeformation and failure of loess begins with shear

deformation and slippage among particles on the otherhand themechanical properties of loess are dominated by itsmicrostructure [4 6 7] -e microstructure of loess mainlyconsisted of pores particles and connections which controlthe contact system and force chains in the loess and thendominate the macrophysical and mechanical properties ofloess [8]-e study of themicrostructure of loess contributesto a better understanding of the catastrophic behavior andphysical mechanism of loess geologic hazards

Scientists and engineers have long noticed the impor-tance of microstructure for the determination of loess en-gineering properties [9 10] and considerable efforts havebeen made to explore the microstructure of loess -esestudies mainly focus on the following aspects (1) investi-gation of loess microstructural characteristics and variations

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 3681382 14 pageshttpsdoiorg10115520203681382

among different regions and geological ages (2) classifica-tion of loess microstructure and determination of the cor-responding microstructural parameters (3) evolution ofloess microstructure under specific conditions and (4)microscopic mechanism of typical loess geologic hazards

Due to the variation in material provenance sedimen-tary geological environment and history the microstruc-tural characteristics and parameters vary from loess to loess-e structural characteristics of Malan loess in the mid-stream area of the Yellow River which were studied usingthe oil immersion method were described earlier in terms ofthe loess microstructure [9 11] Subsequently increasinglymore studies have been presented Loess samples fromvarious regions depths and geological ages were extractedto study the pore sizes particle characteristics and ce-mentations as well as the types of loess microstructures[2 12ndash18] Mercury intrusion porosimetry (MIP) andscanning electron microscopy (SEM) are the most widelyadopted techniques in such studies and the investigationshave mainly concentrated on the determination of the planemorphology two-dimensional characteristics of the loesspores and particles and corresponding microstructuralparameters [19]

Determination of loess microstructure types couldprovide more insight into the catastrophic characteristicsand mechanical behavior of loess On the basis of micro-scopic observations a widely used classification of pores inloess was proposed according to pore size Four types ofpores macropores mesopores fine pores and microporeswere proposed and the division thresholds were pore di-ameters of 0032mm 0008mm and 0002mm respectively[20 21] Loess microstructure was divided into 12 categoriesby Gao [22 23] mainly considering the forms of grainsmodes of arrangement and types of connection and dividedinto 6 categories by Lei considering the cementationstrengths and pore types [20 21] -e influence of micro-structure types on the stability of loess has been properlystudied [24] and many conceptual microstructure modelshave been proposed to explore the mechanism of loessdeformation and failure [14 25ndash27] which has a greatsignificance for the assessment of loess engineering

-e engineering properties of loess are fundamentallycontrolled by their microstructure Many scholars havedevoted their work to exploring the relationship between themicrostructural parameters and mechanical properties ofloess and a combination of microtests and macrophysical-mechanical experiments has been carried out [5 28ndash32]-eachievements demonstrated that the variation in loessstrength is directly related to the changes in microstructureand that cementation bonds play an important role in thestrength and deformation behavior of loess [30] -esestudies paved the way for the establishment of disastertheory of loess on multiple scales of analysis

-e importance of loess microstructure for the under-standing of loess collapse and corresponding geohazards hasbeen demonstrated by many recent efforts [3 33ndash39] Basedon microstructure tests and analyses the formation anddevelopment of loess microstructures during collapse weredivided into five stages [1] Many conceptual models have

been proposed to elucidate the origin of loess collapsibility[25] -e contribution of the microstructure to the strengthof compacted loess after soaking was explored [40] and therelationship of the collapse potential versus the micro-structural parameters of the loess was qualitatively studied[41] -e relationship between loess microstructure andseismic subsidence and the relationship between micro-structure and shear strength under freezing conditions werestudied [42ndash45] However despite these efforts the currentunderstanding of the cause of collapsibility and the un-derlying mechanisms controlling loess collapse behaviorremain controversial or incomplete

Notably the research quality and image resolution havebeen improving gradually with the development of newobservation apparatuses and processing technologies andthe achievements reflect the shift from qualitative analysis toquantitative research Most of these achievements areconcentrated around the characterization of two-dimen-sional (2D) morphology and very few researchers havestudied the three-dimensional (3D) microstructural char-acteristics of loess To date optical and electron microscopynuclear magnetic resonance (NMR) and X-ray computedtomography (CT) are the most commonly used techniquesused to obtain microscopic images of soil among whichoptical and electron microscopy are generally used to obtaintwo-dimensional images [46ndash48] NMR is more suitable fordetecting pores in materials filled with water and high-energy X-ray CTscanning can be used to obtain images withhigher resolutions but is expensive and not easily accessibleto most researchers in geotechnical engineering With theadvent of serial sectioning microscopy-based image analysiscan be used to create 3Dmicrostructures [49] It is feasible toobtain the 3D microstructure of loess by combining opticalmicroscope scanning serial sectioning and 3D image re-construction Although the method of optical microscopy-based serial sectioning has the disadvantage of being time-consuming and laborious it is inexpensive and easy to followyet produces large high-resolution area images which cancapture both short-range features (particles) and long-rangefeatures (localized zones) to enable a more comprehensivecharacterization of the soil microstructure

-e Bai Lu tableland is located in the southern Wei HeBasin Shaanxi Province China and is covered by a greatthickness of loess with continuous loess-paleosol inter-bedded strata Due to the approximate flat geography thetypical microstructural characteristics of aeolian loess in thetableland were preserved well In this paper Di Zhai villagewas chosen as the research site Data collection and fieldinvestigation were performed to determine the geologicalconditions of the site Engineering drilling was carried out toexplore the loess and paleosol strata Serial samples fromvarious loess and paleosol strata were extracted Field andlaboratory tests were conducted to obtain the physical andmechanical parameters of the loess -e optical microscopy-based serial sectioning method was adopted the experimentmethod included sample preparation observation imageprocessing structure reconstruction and quantitative indexanalysis -e characteristics of the loess particles and poresand the microstructural parameters were systematically

2 Advances in Civil Engineering

studied -is work could provide a scientific basis for thestudy of loess catastrophic mechanics theory and the con-struction of projects in this area

2 Experimental Method and Scheme

-e Bai Lu tableland is located in the southernWei He Basinadjacent to the northern Qin Ling Mountains which is astrip terrain oriented southeast-northwest and divides the Baand Chan rivers According to the geological tectonicbackground and evolution history the Bai Lu tableland wasformed on river terraces with aeolian loess covers and wasaffected by fault activity and fluviatile erosion -e geologicconditions of the study area are presented in Figure 1According to the strata data the loess in the Bai Lu tablelandhas been depositing since the early Pleistocene accumu-lating a thickness of approximately 65ndash126m of a contin-uous loess-paleosol strata sequence-e Bai Lu tableland is asuitable site for studying the variation in microstructuralcharacteristics of the loess-paleosol sequence

An 80m deep geological borehole was drilled in Di Zhaivillage from which 8 layers of loess and 7 layers of paleosolwere explored -e depth and thickness of every layer arepresented in Figure 1 Samples were extracted from everylayer with which the physical parameters were tested and arepresented in Table 1

-e optical microscopy-based serial sectioning methodwas adopted to study the 3D microstructure of the loess -eexperiment and image reconstruction process mainly in-volved the following steps (1) Sample preparation a subcubicsample with a side length less than 10 cm was extracted fromthe loess sample and then saturated in a vacuum environmentusing a special liquid -e liquid is a mixture of epoxy resinacetone ethane diamine and dibutyl phthalate with constantvolume ratios of 200ml 100ml 4ml and 2ml Acetone has alow consistency and can be easily volatilized the mixed liquidwas diluted and could easily infiltrate into the pores of theloess sample Ethane diamine and dibutyl phthalate acceleratethe solidification process and improve the hardness of thesample Finally the sample was prepared via secondarycasting for polishing and observation (2) Image capture thesample was polished to obtain a smooth plane using Multi-prep equipment with which the polishing process could becontrolled to a precision of 01 μm -e planar image of thesample with the resolution of 04 μmpixel was observed usinga Leica DM6000M microscope -e sample was thenrepolished to remove approximately 2 μm which was con-trolled using the vertical displacement laser monitor and thepolishing duration A series of 2D images with a spacing of2 μm were then obtained (3) -ree-dimensional (3D)structure reconstruction all the slices were aligned andconverted to extract the particles and pores adopting theappropriate threshold via the changes of gray scale Generallythe point of inflection for the colormap of gray intensity isselected as the threshold value -e 2D images were cali-brated and the 3D particle and pore morphologies were thenreconstructed using Avizo software (4) Quantitative analysisthemicrostructural characteristics parameters and variationsof various layers of loess were then analyzed using the

statistical indexes of particles throats and pores -e ex-periment and image reconstruction processes are presented inFigure 2 Since the undisturbed samples of strata L7 and L8were not extracted successfully the microstructure studymainly focused in strata L1-S6

3 Three-Dimensional QuantitativeCharacteristics of Loess Particles

-e morphological characteristics of loess particles could bedepicted by adopting the parameters volume (V) Eq-Radius(Eq-R

(6 times V)π3

1113968) orientation and major-minor axis

ratio among which the orientation was described byadopting the angles phi and theta and the major-minor axisratio was defined asWL-e definitions of the characteristicparameters of a loess particle are presented in Figure 3

Figures 4(a) and 4(b) present the distribution ofquantitative probability versus the corresponding volume ofthe loess particle in which the test data fitting curve andcumulative probability curve of loess L1 and paleosol S1 arepresented respectively According to the figures the ex-perimental data could be fitted well by applying the third-order Gaussian distribution function -e fitting functioncan be expressed as formula (1) in which xPminusV represents theparticle volume and α1 α2 α3 b1 b2 b3 c1 c2 and c3 arethe fitting parameters According to the fitting condition thecorrelation coefficient of fitting is approximately equal to 10For loess L1 60 of the loess particles have a volume smallerthan 35 μm3 70 of the particles are smaller than 65 μm3and 80 of the particles are smaller than 215 μm3 forpaleosol S1 the thresholds of 60 70 and 80 correspondto 70 μm3 150 μm3 and 415 μm3 respectively Conse-quently it is obvious that the loess L1 of the Bai Lu tablelandis finer than the paleosol S1

f x(PminusV)1113872 1113873 α1 times eminus1times x(PminusV)minus b1( )c1( )

2

+ α2 times eminus 1times x(PminusV)minus b2( )c2( )

2

+ α3 times eminus 1times x(PminusV)minus b3( )c3( )

2

(1)

Figure 4(c) presents a comparison of the fitting curves ofvarious layers of loess and paleosol indicating that thedeeper layer generally involves a larger proportion of smallparticles while layer L3 shows a finer particle characteristicFigure 4(d) shows the variation in the fitting parameters ofthe loess and paleosol layers Although the fitting parameterα1 varies from layer to layer the value of α1 for the paleosolis generally greater than that of the adjacent loess layer -evalues of b and c tend to increase with increasing depth

Figures 5(a) and 5(b) show the distribution character-istics of particle Eq-Radius for L1 and S1 and the experi-mental data also satisfy the third-order Gaussiandistribution well Figure 5(c) presents the variation in thefitting curves for various loess and paleosol layers -edistribution of the curves depicted that finer particles aregenerally enriched in the upper layers except L3 Figure 5(d)gives the variation in fitting parameters which shows thatthe values of the parameters b3 and c3 generally decreasewith the increase in depth

Advances in Civil Engineering 3

Figures 6(a) and 6(b) show the distributions of themajor-minor axis ratio for loess particles from L1 and S1these distributions exactly satisfied the second-orderGaussian distribution with a correlation coefficient up to098-e probability density function in the distribution canbe represented by adopting formula (2) where x(AminusR)

represents the major-minor axis ratio of the loess particlesand α1 α2 b1 b2 c1 and c2 are the fitting parametersAccording to the figures the parameters α1 α2 b1 b2 c1and c2 are regressed by applying the least squares methodand are determined to be 01062 011139 1837 2334 0337and 06536 for loess L1 and 01283 005716 1902 259904602 and 08863 for paleosol S1 Figure 6(c) presents the

variation in fitting curves for various loess layers andpaleosol layers -e ratios of the major-minor axis length fallin the range of 10 to 40 for layers L1 S1 L2 S2 and L4 therange of 10 to 60 for layers L5 and S5 and the range of 10 to80 for L6 and S6 Consequently with increasing stratadepth loess particles generally become increasinglyflattened

f x(AminusR)1113872 1113873 α1 times eminus 1times x(AminusR)minusb1( )c1( )

2

+ α2 times eminus 1times x(AminusR)minus b2( )c2( )

2

(2)

Figures 7(a) and 7(b) show the distribution of the proba-bility density of loess particle quantity versus the corresponding

Holocene

(Scale 1 200000)

Holocene alluvial (1)

Holocene alluvial (2)

Pleistocene aeolian

Qh

Qh1al

γ5

P

Qh2al

Qp3eol

Qp2eol

Qp3eol

Jurassic

L1

L2

L3

L4

L5

L6

L8

S1

S2

S3

S4

S5

Strata of the sampling site

2356

79

80

Thic

knes

s

96

12

168

24

52

86

3864

AnnotationL loess S paleosoilUnit of thickness m

Permian

Fault

River

Figure 1 Location and geological condition of the study area

Table 1 Physical parameters of the experimental samples

Stratum Depth d(m)

-ickness h(m)

Unit mass c

(gcm3)Water

content w ()Liquid limit

LL ()Plastic limitPL (）

Permeabilitycoefficient k (ms)

Shear wavevelocity Vs (ms)

L1 56 56 181 194 320 237 612times10minus5 2229S1 79 23 172 226 310 221 571times 10minus5 2967L2 158 79 174 258 345 226 417times10minus5 4166S2 238 80 178 243 327 253 271times 10minus5 3942L3 334 96 183 261 307 203 354times10minus5 4644S3 346 12 182 274 298 205 305times10minus5 4045L4 514 168 180 237 295 207 472times10minus5 5048S4 538 24 184 239 291 212 272times10minus5 5345L5 612 52 187 244 311 190 152times10minus5 6058S5 698 86 179 233 341 214 127times10minus5 7573L6 736 38 185 221 296 219 118times10minus5 6853S6 745 09 183 212 301 198 106times10minus5 6163L7 764 19 182 224 312 201 292times10minus5 6604S7 777 13 181 237 320 202 277times10minus5 7291L8 800 23 186 240 338 219 331times 10minus5 7112

4 Advances in Civil Engineering

value of loess particle orientation -e values of phi mainly fallin the ranges of 0ndash30deg and 85ndash90deg which indicates that most ofthe loess particles were deposited with a gentle inclination and

near-vertical orientation According to Figure 7(a) the value ofphi for the upper layer of soil is generally smaller when0degltphilt30deg and larger when 85degltphilt90deg which indicatesthat particles in the deeper layers of loess weremore prone to bedeposited horizontally According to Figure 7(b) all the curvesincrease sharply near the angle theta 90deg which indicates thatthe loess deposited with a predominantly eastward orientationand the directionality characteristics are more obvious for thesoil of the upper layer

4 Three-Dimensional QuantitativeCharacteristics of Loess Voids

-e characteristics of loess voids are one of the mostdominant factors controlling loess microstructure -emorphological features size distribution and connectivity

Epoxy resin (200ml) + acetone (100ml) +ethanediamine (4ml) + dibutyl

phthalate (2ml)

Extractlyophilization

Liquid nitrogen

Loess sample

Series 2D image observedwith spacing as 2microm

Align

Subvolume Image convert Thresholding

slices

2D image observation(Leica DM6000M)

2D image calibrate

Quantitative analysis

3D particle Pore throats 3D pore

3D structure reconstruction

Polish equipment(Multiprep)

Vacuum saturation

Vacuum

Sample preparation

Image capture

3D structure reconstruction

Circle

2microm

Casting mold

Mixedliquid

Figure 2 -e experiment and image reconstruction process

z

y

x

PhiTheta

W widthx y plane

L length

Figure 3 Definition of characteristic parameters for loess particles

Advances in Civil Engineering 5

Gaussian distribution (R = 10)α1 = 1178 b1 = 1231 c1 = 1723α2 = 007022 b2 = 1971 c2 = 7982α3 = 002338 b3 = 3909 c3 = 2834

50 100 150 2000Particle volume of L1 (μm3)

000

020

040

060

080

100

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

025Q

uant

ity p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(a)

Gaussian distribution (R = 10)α1 = 05279 b1 = 1196 c1 = 1766α2 = 006708 b2 = 1973 c2 = 8225α3 = 002498 b3 = 4177 c1 = 3088

50 100 150 2000Particle volume of S1 (μm3)

000

005

010

015

020

Qua

ntity

pro

babi

lity

000010020030040050060070080090

Cum

ulat

ive p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(b)

Gaussiandistribution curves

20 40 60 80 1000Particle volume of loess (microm3)

000

005

010

015

020

025

030

Prob

abili

ty fi

tting

curv

es

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

20 70

60

50

40

30

20

10

0

15

10

05

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 4 Distribution characteristics of particle volume (a) L1 (b) S1 (c) comparison of fitting curves for various layers (d) variation infitting parameters

Gaussian distribution (R = 099)α1 = 02438 b1 = 3007 c1 = 04349α2 = 007404 b2 = 4012 c2 = 1205α3 = 001128 b3 = 9812 c3 = 7621

200 400300 500 60000 100Particle Eq-Radius of L1 (μm)

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

030

025

Qua

ntity

pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01429 b1 = 3009 c1 = 05175α2 = 007154 b2 = 4106 c2 = 1265α3 = 001955 b3 = 8544 c3 = 5602

200 300 400 500 60000 100Particle Eq-Radius of S1 (μm)

00

02

04

06

08

000

005

010

015

020

Qua

ntity

pro

babi

lity

10Cu

mul

ativ

e pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(b)

Figure 5 Continued

6 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

studied -is work could provide a scientific basis for thestudy of loess catastrophic mechanics theory and the con-struction of projects in this area

2 Experimental Method and Scheme

-e Bai Lu tableland is located in the southernWei He Basinadjacent to the northern Qin Ling Mountains which is astrip terrain oriented southeast-northwest and divides the Baand Chan rivers According to the geological tectonicbackground and evolution history the Bai Lu tableland wasformed on river terraces with aeolian loess covers and wasaffected by fault activity and fluviatile erosion -e geologicconditions of the study area are presented in Figure 1According to the strata data the loess in the Bai Lu tablelandhas been depositing since the early Pleistocene accumu-lating a thickness of approximately 65ndash126m of a contin-uous loess-paleosol strata sequence-e Bai Lu tableland is asuitable site for studying the variation in microstructuralcharacteristics of the loess-paleosol sequence

An 80m deep geological borehole was drilled in Di Zhaivillage from which 8 layers of loess and 7 layers of paleosolwere explored -e depth and thickness of every layer arepresented in Figure 1 Samples were extracted from everylayer with which the physical parameters were tested and arepresented in Table 1

-e optical microscopy-based serial sectioning methodwas adopted to study the 3D microstructure of the loess -eexperiment and image reconstruction process mainly in-volved the following steps (1) Sample preparation a subcubicsample with a side length less than 10 cm was extracted fromthe loess sample and then saturated in a vacuum environmentusing a special liquid -e liquid is a mixture of epoxy resinacetone ethane diamine and dibutyl phthalate with constantvolume ratios of 200ml 100ml 4ml and 2ml Acetone has alow consistency and can be easily volatilized the mixed liquidwas diluted and could easily infiltrate into the pores of theloess sample Ethane diamine and dibutyl phthalate acceleratethe solidification process and improve the hardness of thesample Finally the sample was prepared via secondarycasting for polishing and observation (2) Image capture thesample was polished to obtain a smooth plane using Multi-prep equipment with which the polishing process could becontrolled to a precision of 01 μm -e planar image of thesample with the resolution of 04 μmpixel was observed usinga Leica DM6000M microscope -e sample was thenrepolished to remove approximately 2 μm which was con-trolled using the vertical displacement laser monitor and thepolishing duration A series of 2D images with a spacing of2 μm were then obtained (3) -ree-dimensional (3D)structure reconstruction all the slices were aligned andconverted to extract the particles and pores adopting theappropriate threshold via the changes of gray scale Generallythe point of inflection for the colormap of gray intensity isselected as the threshold value -e 2D images were cali-brated and the 3D particle and pore morphologies were thenreconstructed using Avizo software (4) Quantitative analysisthemicrostructural characteristics parameters and variationsof various layers of loess were then analyzed using the

statistical indexes of particles throats and pores -e ex-periment and image reconstruction processes are presented inFigure 2 Since the undisturbed samples of strata L7 and L8were not extracted successfully the microstructure studymainly focused in strata L1-S6

3 Three-Dimensional QuantitativeCharacteristics of Loess Particles

-e morphological characteristics of loess particles could bedepicted by adopting the parameters volume (V) Eq-Radius(Eq-R

(6 times V)π3

1113968) orientation and major-minor axis

ratio among which the orientation was described byadopting the angles phi and theta and the major-minor axisratio was defined asWL-e definitions of the characteristicparameters of a loess particle are presented in Figure 3

Figures 4(a) and 4(b) present the distribution ofquantitative probability versus the corresponding volume ofthe loess particle in which the test data fitting curve andcumulative probability curve of loess L1 and paleosol S1 arepresented respectively According to the figures the ex-perimental data could be fitted well by applying the third-order Gaussian distribution function -e fitting functioncan be expressed as formula (1) in which xPminusV represents theparticle volume and α1 α2 α3 b1 b2 b3 c1 c2 and c3 arethe fitting parameters According to the fitting condition thecorrelation coefficient of fitting is approximately equal to 10For loess L1 60 of the loess particles have a volume smallerthan 35 μm3 70 of the particles are smaller than 65 μm3and 80 of the particles are smaller than 215 μm3 forpaleosol S1 the thresholds of 60 70 and 80 correspondto 70 μm3 150 μm3 and 415 μm3 respectively Conse-quently it is obvious that the loess L1 of the Bai Lu tablelandis finer than the paleosol S1

f x(PminusV)1113872 1113873 α1 times eminus1times x(PminusV)minus b1( )c1( )

2

+ α2 times eminus 1times x(PminusV)minus b2( )c2( )

2

+ α3 times eminus 1times x(PminusV)minus b3( )c3( )

2

(1)

Figure 4(c) presents a comparison of the fitting curves ofvarious layers of loess and paleosol indicating that thedeeper layer generally involves a larger proportion of smallparticles while layer L3 shows a finer particle characteristicFigure 4(d) shows the variation in the fitting parameters ofthe loess and paleosol layers Although the fitting parameterα1 varies from layer to layer the value of α1 for the paleosolis generally greater than that of the adjacent loess layer -evalues of b and c tend to increase with increasing depth

Figures 5(a) and 5(b) show the distribution character-istics of particle Eq-Radius for L1 and S1 and the experi-mental data also satisfy the third-order Gaussiandistribution well Figure 5(c) presents the variation in thefitting curves for various loess and paleosol layers -edistribution of the curves depicted that finer particles aregenerally enriched in the upper layers except L3 Figure 5(d)gives the variation in fitting parameters which shows thatthe values of the parameters b3 and c3 generally decreasewith the increase in depth

Advances in Civil Engineering 3

Figures 6(a) and 6(b) show the distributions of themajor-minor axis ratio for loess particles from L1 and S1these distributions exactly satisfied the second-orderGaussian distribution with a correlation coefficient up to098-e probability density function in the distribution canbe represented by adopting formula (2) where x(AminusR)

represents the major-minor axis ratio of the loess particlesand α1 α2 b1 b2 c1 and c2 are the fitting parametersAccording to the figures the parameters α1 α2 b1 b2 c1and c2 are regressed by applying the least squares methodand are determined to be 01062 011139 1837 2334 0337and 06536 for loess L1 and 01283 005716 1902 259904602 and 08863 for paleosol S1 Figure 6(c) presents the

variation in fitting curves for various loess layers andpaleosol layers -e ratios of the major-minor axis length fallin the range of 10 to 40 for layers L1 S1 L2 S2 and L4 therange of 10 to 60 for layers L5 and S5 and the range of 10 to80 for L6 and S6 Consequently with increasing stratadepth loess particles generally become increasinglyflattened

f x(AminusR)1113872 1113873 α1 times eminus 1times x(AminusR)minusb1( )c1( )

2

+ α2 times eminus 1times x(AminusR)minus b2( )c2( )

2

(2)

Figures 7(a) and 7(b) show the distribution of the proba-bility density of loess particle quantity versus the corresponding

Holocene

(Scale 1 200000)

Holocene alluvial (1)

Holocene alluvial (2)

Pleistocene aeolian

Qh

Qh1al

γ5

P

Qh2al

Qp3eol

Qp2eol

Qp3eol

Jurassic

L1

L2

L3

L4

L5

L6

L8

S1

S2

S3

S4

S5

Strata of the sampling site

2356

79

80

Thic

knes

s

96

12

168

24

52

86

3864

AnnotationL loess S paleosoilUnit of thickness m

Permian

Fault

River

Figure 1 Location and geological condition of the study area

Table 1 Physical parameters of the experimental samples

Stratum Depth d(m)

-ickness h(m)

Unit mass c

(gcm3)Water

content w ()Liquid limit

LL ()Plastic limitPL (）

Permeabilitycoefficient k (ms)

Shear wavevelocity Vs (ms)

L1 56 56 181 194 320 237 612times10minus5 2229S1 79 23 172 226 310 221 571times 10minus5 2967L2 158 79 174 258 345 226 417times10minus5 4166S2 238 80 178 243 327 253 271times 10minus5 3942L3 334 96 183 261 307 203 354times10minus5 4644S3 346 12 182 274 298 205 305times10minus5 4045L4 514 168 180 237 295 207 472times10minus5 5048S4 538 24 184 239 291 212 272times10minus5 5345L5 612 52 187 244 311 190 152times10minus5 6058S5 698 86 179 233 341 214 127times10minus5 7573L6 736 38 185 221 296 219 118times10minus5 6853S6 745 09 183 212 301 198 106times10minus5 6163L7 764 19 182 224 312 201 292times10minus5 6604S7 777 13 181 237 320 202 277times10minus5 7291L8 800 23 186 240 338 219 331times 10minus5 7112

4 Advances in Civil Engineering

value of loess particle orientation -e values of phi mainly fallin the ranges of 0ndash30deg and 85ndash90deg which indicates that most ofthe loess particles were deposited with a gentle inclination and

near-vertical orientation According to Figure 7(a) the value ofphi for the upper layer of soil is generally smaller when0degltphilt30deg and larger when 85degltphilt90deg which indicatesthat particles in the deeper layers of loess weremore prone to bedeposited horizontally According to Figure 7(b) all the curvesincrease sharply near the angle theta 90deg which indicates thatthe loess deposited with a predominantly eastward orientationand the directionality characteristics are more obvious for thesoil of the upper layer

4 Three-Dimensional QuantitativeCharacteristics of Loess Voids

-e characteristics of loess voids are one of the mostdominant factors controlling loess microstructure -emorphological features size distribution and connectivity

Epoxy resin (200ml) + acetone (100ml) +ethanediamine (4ml) + dibutyl

phthalate (2ml)

Extractlyophilization

Liquid nitrogen

Loess sample

Series 2D image observedwith spacing as 2microm

Align

Subvolume Image convert Thresholding

slices

2D image observation(Leica DM6000M)

2D image calibrate

Quantitative analysis

3D particle Pore throats 3D pore

3D structure reconstruction

Polish equipment(Multiprep)

Vacuum saturation

Vacuum

Sample preparation

Image capture

3D structure reconstruction

Circle

2microm

Casting mold

Mixedliquid

Figure 2 -e experiment and image reconstruction process

z

y

x

PhiTheta

W widthx y plane

L length

Figure 3 Definition of characteristic parameters for loess particles

Advances in Civil Engineering 5

Gaussian distribution (R = 10)α1 = 1178 b1 = 1231 c1 = 1723α2 = 007022 b2 = 1971 c2 = 7982α3 = 002338 b3 = 3909 c3 = 2834

50 100 150 2000Particle volume of L1 (μm3)

000

020

040

060

080

100

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

025Q

uant

ity p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(a)

Gaussian distribution (R = 10)α1 = 05279 b1 = 1196 c1 = 1766α2 = 006708 b2 = 1973 c2 = 8225α3 = 002498 b3 = 4177 c1 = 3088

50 100 150 2000Particle volume of S1 (μm3)

000

005

010

015

020

Qua

ntity

pro

babi

lity

000010020030040050060070080090

Cum

ulat

ive p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(b)

Gaussiandistribution curves

20 40 60 80 1000Particle volume of loess (microm3)

000

005

010

015

020

025

030

Prob

abili

ty fi

tting

curv

es

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

20 70

60

50

40

30

20

10

0

15

10

05

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 4 Distribution characteristics of particle volume (a) L1 (b) S1 (c) comparison of fitting curves for various layers (d) variation infitting parameters

Gaussian distribution (R = 099)α1 = 02438 b1 = 3007 c1 = 04349α2 = 007404 b2 = 4012 c2 = 1205α3 = 001128 b3 = 9812 c3 = 7621

200 400300 500 60000 100Particle Eq-Radius of L1 (μm)

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

030

025

Qua

ntity

pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01429 b1 = 3009 c1 = 05175α2 = 007154 b2 = 4106 c2 = 1265α3 = 001955 b3 = 8544 c3 = 5602

200 300 400 500 60000 100Particle Eq-Radius of S1 (μm)

00

02

04

06

08

000

005

010

015

020

Qua

ntity

pro

babi

lity

10Cu

mul

ativ

e pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(b)

Figure 5 Continued

6 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

Figures 6(a) and 6(b) show the distributions of themajor-minor axis ratio for loess particles from L1 and S1these distributions exactly satisfied the second-orderGaussian distribution with a correlation coefficient up to098-e probability density function in the distribution canbe represented by adopting formula (2) where x(AminusR)

represents the major-minor axis ratio of the loess particlesand α1 α2 b1 b2 c1 and c2 are the fitting parametersAccording to the figures the parameters α1 α2 b1 b2 c1and c2 are regressed by applying the least squares methodand are determined to be 01062 011139 1837 2334 0337and 06536 for loess L1 and 01283 005716 1902 259904602 and 08863 for paleosol S1 Figure 6(c) presents the

variation in fitting curves for various loess layers andpaleosol layers -e ratios of the major-minor axis length fallin the range of 10 to 40 for layers L1 S1 L2 S2 and L4 therange of 10 to 60 for layers L5 and S5 and the range of 10 to80 for L6 and S6 Consequently with increasing stratadepth loess particles generally become increasinglyflattened

f x(AminusR)1113872 1113873 α1 times eminus 1times x(AminusR)minusb1( )c1( )

2

+ α2 times eminus 1times x(AminusR)minus b2( )c2( )

2

(2)

Figures 7(a) and 7(b) show the distribution of the proba-bility density of loess particle quantity versus the corresponding

Holocene

(Scale 1 200000)

Holocene alluvial (1)

Holocene alluvial (2)

Pleistocene aeolian

Qh

Qh1al

γ5

P

Qh2al

Qp3eol

Qp2eol

Qp3eol

Jurassic

L1

L2

L3

L4

L5

L6

L8

S1

S2

S3

S4

S5

Strata of the sampling site

2356

79

80

Thic

knes

s

96

12

168

24

52

86

3864

AnnotationL loess S paleosoilUnit of thickness m

Permian

Fault

River

Figure 1 Location and geological condition of the study area

Table 1 Physical parameters of the experimental samples

Stratum Depth d(m)

-ickness h(m)

Unit mass c

(gcm3)Water

content w ()Liquid limit

LL ()Plastic limitPL (）

Permeabilitycoefficient k (ms)

Shear wavevelocity Vs (ms)

L1 56 56 181 194 320 237 612times10minus5 2229S1 79 23 172 226 310 221 571times 10minus5 2967L2 158 79 174 258 345 226 417times10minus5 4166S2 238 80 178 243 327 253 271times 10minus5 3942L3 334 96 183 261 307 203 354times10minus5 4644S3 346 12 182 274 298 205 305times10minus5 4045L4 514 168 180 237 295 207 472times10minus5 5048S4 538 24 184 239 291 212 272times10minus5 5345L5 612 52 187 244 311 190 152times10minus5 6058S5 698 86 179 233 341 214 127times10minus5 7573L6 736 38 185 221 296 219 118times10minus5 6853S6 745 09 183 212 301 198 106times10minus5 6163L7 764 19 182 224 312 201 292times10minus5 6604S7 777 13 181 237 320 202 277times10minus5 7291L8 800 23 186 240 338 219 331times 10minus5 7112

4 Advances in Civil Engineering

value of loess particle orientation -e values of phi mainly fallin the ranges of 0ndash30deg and 85ndash90deg which indicates that most ofthe loess particles were deposited with a gentle inclination and

near-vertical orientation According to Figure 7(a) the value ofphi for the upper layer of soil is generally smaller when0degltphilt30deg and larger when 85degltphilt90deg which indicatesthat particles in the deeper layers of loess weremore prone to bedeposited horizontally According to Figure 7(b) all the curvesincrease sharply near the angle theta 90deg which indicates thatthe loess deposited with a predominantly eastward orientationand the directionality characteristics are more obvious for thesoil of the upper layer

4 Three-Dimensional QuantitativeCharacteristics of Loess Voids

-e characteristics of loess voids are one of the mostdominant factors controlling loess microstructure -emorphological features size distribution and connectivity

Epoxy resin (200ml) + acetone (100ml) +ethanediamine (4ml) + dibutyl

phthalate (2ml)

Extractlyophilization

Liquid nitrogen

Loess sample

Series 2D image observedwith spacing as 2microm

Align

Subvolume Image convert Thresholding

slices

2D image observation(Leica DM6000M)

2D image calibrate

Quantitative analysis

3D particle Pore throats 3D pore

3D structure reconstruction

Polish equipment(Multiprep)

Vacuum saturation

Vacuum

Sample preparation

Image capture

3D structure reconstruction

Circle

2microm

Casting mold

Mixedliquid

Figure 2 -e experiment and image reconstruction process

z

y

x

PhiTheta

W widthx y plane

L length

Figure 3 Definition of characteristic parameters for loess particles

Advances in Civil Engineering 5

Gaussian distribution (R = 10)α1 = 1178 b1 = 1231 c1 = 1723α2 = 007022 b2 = 1971 c2 = 7982α3 = 002338 b3 = 3909 c3 = 2834

50 100 150 2000Particle volume of L1 (μm3)

000

020

040

060

080

100

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

025Q

uant

ity p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(a)

Gaussian distribution (R = 10)α1 = 05279 b1 = 1196 c1 = 1766α2 = 006708 b2 = 1973 c2 = 8225α3 = 002498 b3 = 4177 c1 = 3088

50 100 150 2000Particle volume of S1 (μm3)

000

005

010

015

020

Qua

ntity

pro

babi

lity

000010020030040050060070080090

Cum

ulat

ive p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(b)

Gaussiandistribution curves

20 40 60 80 1000Particle volume of loess (microm3)

000

005

010

015

020

025

030

Prob

abili

ty fi

tting

curv

es

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

20 70

60

50

40

30

20

10

0

15

10

05

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 4 Distribution characteristics of particle volume (a) L1 (b) S1 (c) comparison of fitting curves for various layers (d) variation infitting parameters

Gaussian distribution (R = 099)α1 = 02438 b1 = 3007 c1 = 04349α2 = 007404 b2 = 4012 c2 = 1205α3 = 001128 b3 = 9812 c3 = 7621

200 400300 500 60000 100Particle Eq-Radius of L1 (μm)

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

030

025

Qua

ntity

pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01429 b1 = 3009 c1 = 05175α2 = 007154 b2 = 4106 c2 = 1265α3 = 001955 b3 = 8544 c3 = 5602

200 300 400 500 60000 100Particle Eq-Radius of S1 (μm)

00

02

04

06

08

000

005

010

015

020

Qua

ntity

pro

babi

lity

10Cu

mul

ativ

e pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(b)

Figure 5 Continued

6 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

value of loess particle orientation -e values of phi mainly fallin the ranges of 0ndash30deg and 85ndash90deg which indicates that most ofthe loess particles were deposited with a gentle inclination and

near-vertical orientation According to Figure 7(a) the value ofphi for the upper layer of soil is generally smaller when0degltphilt30deg and larger when 85degltphilt90deg which indicatesthat particles in the deeper layers of loess weremore prone to bedeposited horizontally According to Figure 7(b) all the curvesincrease sharply near the angle theta 90deg which indicates thatthe loess deposited with a predominantly eastward orientationand the directionality characteristics are more obvious for thesoil of the upper layer

4 Three-Dimensional QuantitativeCharacteristics of Loess Voids

-e characteristics of loess voids are one of the mostdominant factors controlling loess microstructure -emorphological features size distribution and connectivity

Epoxy resin (200ml) + acetone (100ml) +ethanediamine (4ml) + dibutyl

phthalate (2ml)

Extractlyophilization

Liquid nitrogen

Loess sample

Series 2D image observedwith spacing as 2microm

Align

Subvolume Image convert Thresholding

slices

2D image observation(Leica DM6000M)

2D image calibrate

Quantitative analysis

3D particle Pore throats 3D pore

3D structure reconstruction

Polish equipment(Multiprep)

Vacuum saturation

Vacuum

Sample preparation

Image capture

3D structure reconstruction

Circle

2microm

Casting mold

Mixedliquid

Figure 2 -e experiment and image reconstruction process

z

y

x

PhiTheta

W widthx y plane

L length

Figure 3 Definition of characteristic parameters for loess particles

Advances in Civil Engineering 5

Gaussian distribution (R = 10)α1 = 1178 b1 = 1231 c1 = 1723α2 = 007022 b2 = 1971 c2 = 7982α3 = 002338 b3 = 3909 c3 = 2834

50 100 150 2000Particle volume of L1 (μm3)

000

020

040

060

080

100

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

025Q

uant

ity p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(a)

Gaussian distribution (R = 10)α1 = 05279 b1 = 1196 c1 = 1766α2 = 006708 b2 = 1973 c2 = 8225α3 = 002498 b3 = 4177 c1 = 3088

50 100 150 2000Particle volume of S1 (μm3)

000

005

010

015

020

Qua

ntity

pro

babi

lity

000010020030040050060070080090

Cum

ulat

ive p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(b)

Gaussiandistribution curves

20 40 60 80 1000Particle volume of loess (microm3)

000

005

010

015

020

025

030

Prob

abili

ty fi

tting

curv

es

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

20 70

60

50

40

30

20

10

0

15

10

05

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 4 Distribution characteristics of particle volume (a) L1 (b) S1 (c) comparison of fitting curves for various layers (d) variation infitting parameters

Gaussian distribution (R = 099)α1 = 02438 b1 = 3007 c1 = 04349α2 = 007404 b2 = 4012 c2 = 1205α3 = 001128 b3 = 9812 c3 = 7621

200 400300 500 60000 100Particle Eq-Radius of L1 (μm)

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

030

025

Qua

ntity

pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01429 b1 = 3009 c1 = 05175α2 = 007154 b2 = 4106 c2 = 1265α3 = 001955 b3 = 8544 c3 = 5602

200 300 400 500 60000 100Particle Eq-Radius of S1 (μm)

00

02

04

06

08

000

005

010

015

020

Qua

ntity

pro

babi

lity

10Cu

mul

ativ

e pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(b)

Figure 5 Continued

6 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

Gaussian distribution (R = 10)α1 = 1178 b1 = 1231 c1 = 1723α2 = 007022 b2 = 1971 c2 = 7982α3 = 002338 b3 = 3909 c3 = 2834

50 100 150 2000Particle volume of L1 (μm3)

000

020

040

060

080

100

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

025Q

uant

ity p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(a)

Gaussian distribution (R = 10)α1 = 05279 b1 = 1196 c1 = 1766α2 = 006708 b2 = 1973 c2 = 8225α3 = 002498 b3 = 4177 c1 = 3088

50 100 150 2000Particle volume of S1 (μm3)

000

005

010

015

020

Qua

ntity

pro

babi

lity

000010020030040050060070080090

Cum

ulat

ive p

roba

bilit

y

Quantity probability fitting curveQuantity probability of the experiment dataCumulative probability curve

(b)

Gaussiandistribution curves

20 40 60 80 1000Particle volume of loess (microm3)

000

005

010

015

020

025

030

Prob

abili

ty fi

tting

curv

es

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

20 70

60

50

40

30

20

10

0

15

10

05

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 4 Distribution characteristics of particle volume (a) L1 (b) S1 (c) comparison of fitting curves for various layers (d) variation infitting parameters

Gaussian distribution (R = 099)α1 = 02438 b1 = 3007 c1 = 04349α2 = 007404 b2 = 4012 c2 = 1205α3 = 001128 b3 = 9812 c3 = 7621

200 400300 500 60000 100Particle Eq-Radius of L1 (μm)

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

030

025

Qua

ntity

pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01429 b1 = 3009 c1 = 05175α2 = 007154 b2 = 4106 c2 = 1265α3 = 001955 b3 = 8544 c3 = 5602

200 300 400 500 60000 100Particle Eq-Radius of S1 (μm)

00

02

04

06

08

000

005

010

015

020

Qua

ntity

pro

babi

lity

10Cu

mul

ativ

e pro

babi

lity

Quantity probability of the experiment dataQuantity probability of fitting curveCumulative probability curve

(b)

Figure 5 Continued

6 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

Gaussian distribution (R = 098)α1 = 01062 b1 = 1837 c1 = 0337α2 = 01139 b2 = 2334 c2 = 06536

20 40 60 80 10000Ratio of major-minor axis length for loess particle of L1

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

000

005

010

015

020

Prob

abili

ty d

ensit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(a)

Gaussian distribution (R = 098)α1 = 01283 b1 = 1902 c1 = 04602α2 = 005716 b2 = 2599 c2 = 08863

20 40 60 80 10000Ratio of major-minor axis length for loess particle of S1

000

005

010

015

020

Prob

abili

ty d

ensit

y

00

02

04

06

08

10

Cum

ulat

ive p

roba

bilit

y

Probability density of fitting curveProbability density data of experimentCumulative probability curve

(b)

20 40 60 80 10000Ratio of major-minor axis length for loess particle

000

005

010

015

020

Prob

abili

ty d

ensit

y of

fittin

g cu

rves

L2L3L4

L1

S1S2

L5L6

S3S4S5S6

(c)

Figure 6 Distribution characteristics of the major-minor axis ratio of loess particles (a) L1 (b) S1 (c) variation in fitting curves for variouslayers of loess and paleosol

Gaussiandistribution curves

5 10 15 200Particle Eq-Radius of loess (microm)

000

005

010

015

020

025

030Q

uant

ity p

roba

bilit

y

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(c)

08 15

12

9

6

3

0

06

04

02

00

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (α

)

Para

met

er o

f Gau

ssia

ndi

strib

utio

n (b

c)

S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6L1Loess strata

α1b1c1

α2b2c2

α3b3c3

(d)

Figure 5 Distribution characteristics of Eq-Radius (a) L1 (b) S1 (c) comparison of fitting curves of various layers (d) variation in fittingparameters

Advances in Civil Engineering 7

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

of voids control the structural physical and mechanicalproperties of loess as well as its collapsibility seismicsubsidence and other disaster-related behaviors Based onthe variation and influence of void morphology we definedthroats and pores to depict the void characteristics of loessquantitatively -e throat is defined as a narrow passagethrough loess pores and connects adjacent pores -e poresin loess could be generalized as a sphere with equal volumewith which the Eq-Radius of the pore was defined as theradius of the sphere and the throat channel length wasdefined as the distance between adjacent pore centers -edefinitions of the loess void characteristic parameters arepresented in Figure 8 in which the chromatic aberrations aredue to the visual effect induced by the shadow of three-dimensional pores

According to the experimental results we extractedvoids from images to build a 3D pore network and thenetwork was separated into many pores by throats -edistribution characteristics of the throat dimension generallydirectly dominated the connectivity and permeability ofloess -e dimension of the throat could be described byadopting the parameter throat Eq-Radius which was definedas the radius of a circle with equal area -e distribution ofthroat Eq-Radius in the loess is presented in Figure 9 -erelationship of throat Eq-Radius and the correspondingquantity probability density satisfied a first-order Gaussiandistribution well -e probability density function can beexpressed as formula (3) in which x(TminusR) represents thethroat Eq-Radius and α1 b1 and c1 are the fitting pa-rameters Figures 9(a) and 9(b) show a comparison of thefitting curves versus the experimental data of layers L1 andS1 depicting that the parameters α1 b1 and c1 are 0071913677 and 4166 respectively for loess L1 and 008427 3836and 34 respectively for paleosol S1 and that the correlationcoefficient R is close to 10 in both cases

f x(TminusR)1113872 1113873 α1 times eminus 1times x(TminusR)minus b1( )c1( )

2

(3)

Figure 9(c) gives the distribution characteristics of throatEq-Radius of various layers -e figure depicts that the

values of throat Eq-Radius are less than 125 μm 110 μm130 μm 150 μm 120 μm 140 μm 160 μm 180 μm190 μm 200 μm 210 μm and 220 μm for L1 to S6 re-spectively and that the maximum throat Eq-Radius gen-erally increases gradually with increasing stratum depthAccording to the shape of the fitting curves the curve of adeeper stratum tends to be wider and the curve of a shallowstratum falls into a relatively tight bound which indicatesthat the loess at a great depth has large pore throatsFigure 9(d) represents the variation in fitting parameters forvarious layers of soil which depicted that the parameter α1decreases with increasing stratum depth and that the pa-rameters b1 and c1 show a contrary characteristic

According to the definition the throat channel lengthrepresents the distribution of the average pore length in theloess and is one of the most important structural parametersthat can reflect the uniqueness of loess -e distribution ofthroat channel length versus the probability density is givenin Figure 10 among which Figures 10(a) and 10(b) depict

Throat Eq-Radius

Equivalent sphere of poreCentroid

Pore

Throat

Pore Eq-Radius

Chromatic aberration

Thro

at ch

anne

l len

gth

Figure 8 Definition of the characteristic parameters of loess voids

000

015

030

045

060Pr

obab

ility

den

sity

0 15 30 45Phi (deg)

60 75 90

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(a)

0

003

006

009

012

015

Prob

abili

ty d

ensit

y

ndash180 ndash120 ndash60 0Theta (deg)

60 120 180ndash150 ndash90 ndash30 30 90 150

S2L4S5

L1

S4L6

S1L3

L2S3L5S6

(b)

Figure 7 Orientation characteristics of loess particles (a) phi (b) theta

8 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of L1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 007191 b1 = 3677

c1 = 4166 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

00 50 100 150 200 250Distribution of throats Eq-Radius of S1 (μm)

Cum

ulat

ive p

roba

bilit

y08

06

04

02

10

00

Gaussian distributionα1 = 008427 b1 = 3836

c1 = 34 R = 096

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

010

008

006

004

002

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 105 15 20 25Throats Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

010

008

006

004

002

000

Para

met

er o

f Gau

ssdi

strib

utio

n (α

1)

Para

met

er o

f Gau

ssdi

strib

utio

n (b

1 c1

)

L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6Loess strata

90

70

50

30

b1c1α1

(d)

Figure 9 Eq-Radius of loess throats (a) probability density versus throat Eq-Radius of L1 (b) probability density versus Eq-Radius of S1 (c)distribution characteristics of Eq-Radius for various layers (d) variation in fitting parameters for various layers of soil

Gamma distributionα = 392611 β = 584606μ = 229523 σ = 13418

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of L1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y080

060

040

020

100

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Gamma distributionα = 377738 β = 562399μ = 212439 σ = 119476

005

004

003

002

001

0000 10 20 30 40 50 60 70

Throat channel length of S1 (μm)80 90 100

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

Prob

abili

ty d

ensit

y

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(b)

Figure 10 Continued

Advances in Civil Engineering 9

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

the comparison of the experimental data and fitting curves ofthe loess L1 and paleosol S1 respectively According to thefigures the distribution of throat channel length satisfies thegamma function well -e density function of the gammadistribution can be expressed as follows

f x(TminusL)1113872 1113873 βα

Γ(α)x

(αminus1)(TminusL)e

minus βx(TminusL) x(TminusL) gt 0 (4)

where x(TminusL) represents the throat channel length α is ashape parameter and β is a scale parameter -e Γ(α)

function is a generalization of a factorial on a real number-e mean value μ and variance σ of the gamma distributionare given by the following formula

μ αβ

σ2 αβ2

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(5)

-e fitting parameters are determined by adopting theleast squares method According to the results the pa-rameters α β μ and σ are respectively determined to be392611 585606 229523 and 13418 for loess L1 and377738 562399 212439 and 119467 for paleosol S1

Figure 10(c) shows the distribution of channel length forvarious loess and paleosol layers -e curve of the upper layergenerally shows a narrower and higher coverage area as well asa larger peak with a smaller abscissa which indicates that thepore channel becomes slenderer with increasing stratum depthFigure 10(d) presents the variation in fitting parameters forvarious loess strata According to the figure the parameters αβ and μ increase gradually with increasing stratum depth

Similar to the determination of the quantitative mi-crostructural parameters for throats those for pore size

could be described by adopting the parameter Eq-Radius of asphere with an equal volume Figure 11 gives the distributioncharacteristics of the pore Eq-Radius for the loess -ecomparison of experimental data and fitting curves is pre-sented in Figures 11(a) and 11(b) which shows that therelationship of pore Eq-Radius and probability density alsosatisfies the first-order Gaussian distribution well -e pa-rameters α1 b1 and c1 could be regressed by adopting theleast squares method and are respectively given as 010156256 and 5689 for loess L1 and 01532 671 and 3587 forpaleosol S1 -e corresponding correlation coefficient Rresults are high Figure 11(c) shows the distribution char-acteristics of the pore Eq-Radius for various layers andFigure 11(d) gives the variation in the fitting parameters forvarious layers of loess and paleosol -e variations in thefitting curves and parameters for the pore size are similar tothose for the throat

5 Discussion

-e correlation of the physical parameters (such as unitmass water content liquid limit plastic limit permeabilitycoefficient and shear wave velocity) and fitting parametersof the distribution function of the particles pores andthroats of the loess was studied -e values of the perme-ability coefficient and shear wave velocity have obviouscorrelations with the fitting parameters of the loess poresand throats -e relationship between the physical prop-erties and the fitting parameters is presented in Figure 12According to the figures the fitting parameters b1 and c1 ofthe Eq-Radius of the throats and pores and the fitting pa-rameters of throat channel length decrease linearly with theincrease in permeability coefficient and increase with theincrease in shear wave velocity meanwhile the fitting pa-rameter α1 of the Eq-Radius of the throats and pores shows

0 20 40 60 80 100Throat channel length of loess (μm)

005

004

003

002

001

000

Prob

abili

ty d

ensit

y

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

100

80

60

40

20

00L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

αβμ

35

30

25

20

15

10

5

0

Para

met

er o

f gam

ma

distr

ibut

ion

(α β

)

Para

met

er o

f gam

ma

distr

ibut

ion

(μ)

(d)

Figure 10 Distribution characteristics of throat channel length (a) probability density versus channel length of L1 (b) probability densityversus channel length of S1 (c) distribution characteristics of channel length for various layers (d) variation in fitting parameters for variouslayers of loess

10 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

012

010

008

006

004

002

000

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

0000 10 20

Pore Eq-Radius of L1 (μm)30 40 50

Gaussian distribution (R = 092)α1 = 01015 b1 = 6256

c1 = 5689

Probability density data of experimentProbability density of fitting curveCumulative probability curve

(a)

Prob

abili

ty d

ensit

y

Cum

ulat

ive p

roba

bilit

y

100

080

060

040

020

000

018

015

012

009

006

003

0000 10 20

Pore Eq-Radius of S1 (μm)30 40 50

Probability density data of experimentProbability density of fitting curveCumulative probability curve

Gaussian distribution (R = 098)α1 = 01532 b1 = 671

c1 = 3587

(b)

018

015

012

009

006

003

000Prob

abili

ty d

ensit

y fit

ting

curv

e

0 5 10 15 20 25 30Pore Eq-Radius of loess (μm)

L1L2L3L4L5L6

S1S2S3S4S5S6

(c)

020

015

010

005Para

met

er o

f Gau

ss d

istrib

utio

n (α

1)

Para

met

er o

f Gau

ss d

istrib

utio

n(b

1 c1

)

130

110

90

70

50

30L1 S1 L2 S2 L3 S3 L4 S4 L5 S5 L6 S6

Loess strata

b1c1α1

(d)

Figure 11 Distribution characteristics of pore Eq-Radius for loess (a) probability density versus pore Eq-Radius of L1 (b) probabilitydensity versus pore Eq-Radius of S1 (c) distribution characteristics of pore Eq-Radius for various layers (d) variation in fitting parametersfor various layers of loess

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

300 000002 000004 000006 000008

Permeability coefficient k (ms)α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(a)

200 400 600 800Shear wave velocity Vs (ms)

012

010

008

006

004

002

000

Para

met

ers o

f thr

oat

Eq-R

adiu

s (α1

)

Para

met

ers o

f thr

oat

Eq-R

adiu

s (b1

c1)

90

70

50

30

α1c1Fitting line for b1

b1

Fitting line for c1Fitting line for α1

(b)

Figure 12 Continued

Advances in Civil Engineering 11

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

the reverse variation Based on the above description wepropose that the macrophysical-mechanical properties ofloess are quantitatively dominated by certain microstruc-tural parameters of loess and the quantitative correlationwould be the next focus of our research -e microstructureof loess is mainly controlled by the parameters of the par-ticles pores and cementation as well as the structure modelAlthough the research method used in this study is availableto analyze the three-dimensional quantitative character-ization of particles and pores it is difficult to investigate thecementation of particles Consequently the microstructure-based structure model of loess still needs to be generalized inthe future

6 Conclusion

-e loess of the Bai Lu tableland involves a series of loess-paleosol interbedding strata and the microstructuralcharacteristics physical features and mechanical propertiesof this loess vary from layer to layer As a special geotechnicalmaterial with strong structural properties the

microstructural characteristics significantly influence themacroscopic mechanical properties and catastrophic be-havior of this loess -e study of the microstructure of loesscontributes to a better understanding of the catastrophicbehavior and physical mechanism of loess geologic hazards-e main conclusions can be summarized as follows

(1) -e volume and Eq-Radius of the loess particlessatisfy a third-order Gaussian distribution and themajor-minor axis ratio of the loess particles satisfies asecond-order Gaussian distribution In the Bai Lutableland the loess deposited with a predominantlyeastward orientation and the directionality char-acteristics are more obvious for the soil in the upperlayer With increasing stratum depth the loessparticles generally become increasingly flattened

(2) -e Eq-Radius of the loess pores and throats satisfiesa first-order Gaussian distribution and the throatchannel length satisfies a gamma distribution Withincreasing stratum depth the loess throat radii in-crease and the pore channels become slenderer

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

0 000002 000004 000006 000008Permeability coefficient k (ms)

400

300

200

100

0

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(c)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f thr

oat c

hann

elle

ngth

(μ)

400

300

200

100

0

Para

met

ers o

f thr

oat c

hann

elle

ngth

(α b

)

80

60

40

20

00

μbFitting line for α

α

Fitting line for bFitting line for μ

(d)

0 000002 000004 000006 000008Permeability coefficient k (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

02

015

01

005

0

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

120

100

80

60

40

20

00

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(e)

200 400 600 800Shear wave velocity Vs (ms)

Para

met

ers o

f por

eEq

-Rad

ius (α1

)

Para

met

ers o

f por

eEq

-Rad

ius (b1

c1)

02

015

01

005

0

120

100

80

60

40

20

00300 500 700

b1α1Fitting line for c1

c1

Fitting line for α1Fitting line for b1

(f )

Figure 12 -e relationships between the physical properties and the fitting function parameters of the loess (a) permeability coefficientversus fitting function parameters of throat Eq-Radius (b) shear wave velocity versus parameters of fitting function of throat Eq-Radius (c)permeability coefficient versus coefficient of fitting function of throat channel length (d) shear wave velocity versus fitting functioncoefficient of throat channel length (e) permeability coefficient versus fitting function coefficient of throat of pore Eq-Radius (f ) shear wavevelocity versus fitting function coefficient of pore Eq-Radius

12 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

(3) -e fitting parameters of the distribution functionobviously depend on the variation in the loess andpaleosol strata and the macrophysical-mechanicalproperties of the loess were controlled by certainmicrostructural parameters

(4) -e quantitative correlation of the microstructuralparameters and the physical and mechanical prop-erties of loess will be the focus of our future work

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is study was sponsored by the National Natural ScienceFoundation of China (grant nos 41877245 and 41630634)and Open Foundation of China Railway First Survey andDesign Institute Group Co Ltd (SPS-D-04)

References

[1] Z Lin and W Liang ldquoEngineering properties and zoning ofloess and loess-like soils in Chinardquo Canadian GeotechnicalJournal vol 19 no 1 pp 76ndash91 1982

[2] G Gao ldquoFormation and development of the structure ofcollapsing loess in Chinardquo Engineering Geology vol 25no 2ndash4 pp 235ndash245 1988

[3] E Derbyshire and T W Mellors ldquoGeological and geotech-nical characteristics of some loess and loessic soils from Chinaand Britain a comparisonrdquo Engineering Geology vol 25no 2ndash4 pp 135ndash175 1988

[4] F Zhang R Kong and J Peng ldquoCompositional structuraland physicochemical properties of loess under laboratoryconditionsrdquo Applied Clay Science vol 152 no 1 pp 259ndash2662018

[5] J Wang P Li Q Gu Y Xu and T Gu ldquoChanges in tensilestrength andmicrostructure of loess due to vibrationrdquo Journalof Asian Earth Sciences vol 169 no 1 pp 298ndash307 2019

[6] F Zhang G Wang K Toshitaka W Chen D Zhang andJ Yang ldquoUndrained shear behavior of loess saturated withdifferent concentrations of sodium chloride solutionrdquo Engi-neering Geology vol 155 no 14 pp 69ndash79 2013

[7] F Zhang G Wang T Kamai and W Chen ldquoEffect of pore-water chemistry on undrained shear behaviour of saturatedloessrdquo Quarterly Journal of Engineering Geology andHydrogeology vol 47 no 3 pp 201ndash210 2014

[8] Y Li T Zhang Y Zhang and Q Xu ldquoGeometrical ap-pearance and spatial arrangement of structural blocks of theMalan loess in NW China implications for the formation ofloess columnsrdquo Journal of Asian Earth Sciences vol 158 no 1pp 18ndash28 2018

[9] H Zhu F Gao and J Pei ldquoAnalysis of loess particles undermicroscoperdquo Sciential Geological Sinica vol 3 no 1pp 90ndash92 1959 in Chinese

[10] H Zhu ldquoSome properties of particle and structure of Malanloess in middle stream of the Yellow Riverrdquo Sciential Geo-logical Sinica vol 2 no 1 pp 88ndash101 1963 in Chinese

[11] Z Zhang ldquoA study on the microtexture of the Chinese loessrdquoActa Geologica Sinica vol 44 no 1 pp 357ndash366 1964 inChinese

[12] J Cegla T Buckley and I J Smalley ldquoMicrotextures ofparticles from some European loess depositsrdquo Sedimentologyvol 17 no 1-2 pp 129ndash134 1971

[13] Y Wang and Z Teng ldquoMicrostructure characteristics andvariation with ages and regions of loess in Chinardquo ChineseScience Bulletin vol 27 no 2 pp 102ndash105 1982 in Chinese

[14] Y Zhang and Y Qu ldquoCements of sand loess and the ir ce-mentation in north Shaanxi and west Shanxirdquo Journal ofEngineering Geology vol 13 no 1 pp 18ndash28 2005 inChinese

[15] R G Gimenez R V de la Villa and J A G MartınldquoCharacterization of loess in central Spain a microstructuralstudyrdquo Environmental Earth Sciences vol 65 no 7pp 2125ndash2137 2012

[16] X A Li and L Li ldquoQuantification of the pore structures ofMalan loess and the effects on loess permeability and envi-ronmental significance Shaanxi province China an experi-mental studyrdquo Environmental Earth Sciences vol 76 no 15pp 523ndash533 2017

[17] A A Velichko T D Morozova V P Nechaev et al ldquoLoesspaleosolcryogenic formation and structure near the northernlimit of loess deposition East European Plain RussiardquoQuaternary International vol 152-153 no 1 pp 14ndash30 2006

[18] T Gu J Wang L Guo D Wu and K Li ldquoStudy of Q3 loessmicrostructure changes based on image processingrdquo ChineseJournal of Rock Mechanics and Engineering vol 30 no 1pp 3185ndash3192 2011 in Chinese

[19] B G Olszewska ldquoSEM analysis of microstructures of loessdepositsrdquo Bulletin of the International Association of Engi-neering Geology vol 11 no 1 pp 45ndash48 1975

[20] X Lei ldquoType of the loess microtextures in Xirsquoan districtrdquoJournal of Northwest University (Natural Science Edition)vol 4 no 1 pp 34ndash39 1983 in Chinese

[21] L Xiangyi ldquo-e relationship between microtexture types andindices of fhysico-mechanical properties of loess in ChinardquoActa Geologica Sinica-English Edition vol 2 no 4 pp 433ndash443 1989

[22] G Gao ldquoMicrotexture type and collapsibility of loess soilrdquoScience in China vol 12 no 1 pp 1203ndash1208 1980 inChinese

[23] G Gao ldquoClassification of microstructures of loess in Chinaand their collapsibilityrdquo Scientia Sinica vol 24 no 7pp 962ndash973 1981

[24] B G Olszewska ldquoSkeletal microstructure of loessesmdashitssignificance for engineering-geological and geotechnicalstudiesrdquo Applied Clay Science vol 4 no 4 pp 327ndash336 1989

[25] Z Liu F Liu F Ma et al ldquoCollapsibility composition andmicrostructure of loess in Chinardquo Canadian GeotechnicalJournal vol 53 no 4 pp 673ndash686 2016

[26] T Miao Z Liu and Y Liu ldquoUnified catastrophic model forcollapsible loessrdquo Journal of Engineering Mechanics vol 128no 5 pp 595ndash598 2002

[27] Q Sun X-K Zhang and H-E Li ldquoResearch on micro-structural catastrophe model of deformation of collapsibleloessrdquo Rock and Soil Mechanics vol 29 no 3 pp 663ndash6672008 in Chinese

[28] R VMatalucci M Abdel-Hady and JW Shelton ldquoInfluenceof microstructure of loess on triaxial shear strengthrdquo Engi-neering Geology vol 4 no 4 pp 341ndash351 1970

[29] N Wang D Luo Y Yong X Chen and J Yang ldquoDynamicstrength and microstructure change of Malan loess undertriaxal cycle loadingrdquo Journal of Engineering Geology vol 19no 5 pp 467ndash471 2011 in Chinese

Advances in Civil Engineering 13

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering

[30] M Jiang F Zhang H Hu Y Cui and J Peng ldquoStructuralcharacterization of natural loess and remolded loess undertriaxial testsrdquo Engineering Geology vol 181 no 1pp 249ndash260 2014

[31] R L Hu M R Yeung C F Lee and S J Wang ldquoMechanicalbehavior and microstructural variation of loess under dy-namic compactionrdquo Engineering Geology vol 59 no 3-4pp 203ndash217 2001

[32] J Xia and A-M Han ldquoCyclic variability in microstructureand physio-mechanical properties of the XiashuLoessndashpalaeosol sequence in Nanjing Chinardquo EngineeringGeology vol 104 no 3-4 pp 263ndash268 2009

[33] M Wang Study on Structure of Collapsible Loess in ChinaTaiyuan University of Technology Taiyuan China 2010 inChinese

[34] P Li W Xie R Y S Pak and S K Vanapalli ldquoMicro-structural evolution of loess soils from the Loess Plateau ofChinardquo Catena vol 173 no 1 pp 276ndash288 2019

[35] L-X Gao M-T Luan and Q Yang ldquoEvaluation of loesscollapsibility based on principal components of microstruc-tural parametersrdquo Rock and Soil Mechanics vol 33 no 7pp 1921ndash1926 2012 in Chinese

[36] G Gao ldquoStudy of the microstructures and the collapsemechanism in loess soil from Lanzhourdquo Journal of LanzhouUniversity (Natural Science Edition) vol 1972 no 1 pp 1ndash131979 in Chinese

[37] G Gao ldquo-e distribution and geotechnical properties of loesssoils lateritic soils and clayey soils in Chinardquo EngineeringGeology vol 42 no 1 pp 95ndash104 1996

[38] R Li Z Wu Q Liang S Xu and T Zhao ldquoInfluence factorsof dynamic characteristics of loess considering the micro-structure propertiesrdquo Journal of Engineering Geology vol 26no 4 pp 905ndash914 2018 in Chinese

[39] L-S Deng W Fan Y-P Yin and Y-B Cao ldquoCase study of acollapse investigation of loess sites covered by very thickloessndashpaleosol interbedded stratardquo International Journal ofGeomechanics vol 18 no 11 Article ID 05018009 2018

[40] F Ma J Yang and X Bai ldquoWater sensitivity and micro-structure of compacted loessrdquo Transportation Geotechnicsvol 11 no 1 pp 41ndash56 2017

[41] W-l Xie P Li M-s Zhang T-e Cheng and Y WangldquoCollapse behavior and microstructural evolution of loesssoils from the Loess Plateau of Chinardquo Journal of MountainScience vol 15 no 8 pp 1642ndash1657 2018

[42] W Ni and H Shi ldquoInfluence of freezing thawing cycles onmicrostructure and shear strength of loessrdquo Journal of Gla-ciology and Geocryology vol 36 no 4 pp 922ndash927 2014 inChinese

[43] Y Shi L Li and H Liu ldquoStudy on the relation of loess seismicsubsidence and its microstructure charactersrdquo NorthwesternSeismological Journal vol 24 no 2 pp 129ndash134 2002 inChinese

[44] Y Shi and G Qiu ldquoConstitutive relation of seismic subsidenceof loess based on microstructurerdquo Chinese Journal of Geo-technical Engineering vol 33 no 1 pp 7ndash11 2011 in Chinese

[45] S Lei and W Tang ldquoAnalysis of microstructure change forloess in the process of loading and collapse with CTscanningrdquoChinese Journal of Rock Mechanics and Engineering vol 23no 24 pp 4166ndash4169 2004

[46] Q Xiao X ZhaoW Lin X Huang and Z Song ldquoApplicationof NMR to test sandstone stress sensitivity of the dongfang Xgas field Chinardquo IEEE Access vol 7 pp 95212ndash95223 2019

[47] W Lin X Li Z Yang S Xiong Y Luo and X ZhaoldquoModeling of 3D rock porous media by combining X-ray CT

and Markov chain Monte Carlordquo Journal of Energy ResourcesTechnology vol 142 no 1 Article ID 013001 8 pages 2020

[48] W Lin X Li Z Yang et al ldquoMultiscale digital porous rockreconstruction using template matchingrdquo Water ResourcesResearch vol 55 no 8 pp 6911ndash6922 2019

[49] Y Lu Reconstruction Characterization Modeling and Visu-alization of Inherent and Induced Digital Sand Microstruc-tures Georgia Institute of Technology Atlanta Georgia 2010

14 Advances in Civil Engineering