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Tensile Strength of Compacted Clayey SoilChao-Sheng Tang1; Xiang-Jun Pei2; De-Yin Wang3; Bin Shi4; and Jian Li5
Abstract: Tensile strength of soil plays an important role in controlling the cracking and tensile failure of many earth structures. In thisinvestigation, a direct tensile test apparatus was developed to determine the tensile strength of compacted clayey soil over a broad range ofwater contents (4.3–28.5%) and with different dry densities (1.5–1.7 Mg=m3). The results show that the tensile strength of compacted clayeysoil significantly depends on water content. The tensile strength characteristic curve (TSCC) exhibits one peak value occurring at the criticalwater content wc around 11.5%.With increasing water content, the tensile strength increases at the dry side of wc and then decreases at the wetside of it. Generally, with the increase of dry density, the tensile strength also increases. Moreover, a modified model is proposed to describethe tensile strength characteristics of compacted clayey soil, and it is validated by the obtained test data. DOI: 10.1061/(ASCE)GT.1943-5606.0001267. © 2014 American Society of Civil Engineers.
Author keywords: Tensile strength; Compacted clayey soil; Direct tensile test; Water content; Dry density; Soil suction.
Introduction
Tensile strength of soil is a major mechanical parameter controllingthe development of tensile cracking, which is commonly encoun-tered in many earth structures (e.g., dams, hydraulic barriers,slopes, runway subgrades, river banks, highway and railway em-bankments), especially when subjected to desiccation, differentialsettlement, or other external loads (Morris et al. 1992; Konrad andAyad 1997). As reported, deep desiccation cracks appeared in morethan 1,200 reservoir dams in Chongqing (China) in 2007 becauseof severe drought (Tang et al. 2011). In Hungary, a persistent periodof severe droughts from 1989 to 1993 resulted in serious crackingof flood prevention dikes on the River Tisza (Lazanye et al. 1998).The presence of tensile cracks in soil can significantly affect itsmechanical and hydraulic properties. For example, the overallstrength and bearing capacity of a soil containing cracks are oftenmuch less than those of intact soil (Morris et al. 1992). The crackscan also create preferential flow paths that may significantly in-crease soil hydraulic conductivity (Albrecht and Benson 2001).As a result, the performance of soil involved in various engineeringdisciplines (geotechnical, geological, and environmental engineer-ing) could be significantly affected by cracks (Morris et al. 1992;
Konrad and Ayad 1997; Albrecht and Benson 2001; Péron et al.2009; Tang et al. 2010). There is evidence that cracking at the crestarea of the slopes usually triggers the initiation of slope failure(Take 2003). Progressive failures that take place in UK’s extensivedyke system (extending up to 35,000 km with an annual mainte-nance budget of $720 million) are also triggered commonly bydesiccation cracking (Dyer et al. 2009). To prevent such effectsof tensile cracking and reveal the relevant cracking mechanisms,a comprehensive understanding of soil tensile strength characteris-tics is essential.
There are two categories of methods that can be used to measuresoil tensile strength, namely indirect and direct methods. Theindirect method allows developing correlations between variousparameters for determining the soil tensile strength, includingthe Brazilian tensile test (Ghosh and Subbarao 2006), flexure beamtest (Ajaz and Parry 1975), double punch test (Kim et al. 2007), andunconfined penetration test (Kim et al. 2012). In these tests, spec-imens are split under point or linear compression loads. Varioushypotheses are proposed to calculate the tensile strength. Particu-larly, the tensile strength is essentially determined by assuming thattensile stress distributes uniformly on the failure plane. As a result,these methods are more suitable for brittle and elastic materials(stiff, highly compacted, or chemical stabilized soils) than forductile materials (soft and wet clayey soils).
For the direct method, the tensile strength of soil is usually de-termined by uniaxial tensile tests. The tensile load is directly appliedto the two ends of a soil specimen. Such tests are generally preferred,as the tensile stress and strength can be directly obtained. Both thetensile load and displacement can be controlled, depending on testdevice. However, it has been shown that direct tensile tests aredifficult to perform due to problems of specimen preparation andspecimen fixing during tension. Development of new test setupsand methodologies are therefore needed to improve the efficiencyof these direct tests (Tang and Graham 2000; Nahlawi et al. 2004;Tamrakar et al. 2005; Lu et al. 2005; Lakshmikantha et al. 2012).
In this study, a direct tensile test apparatus was developed forbetter measurement and understanding of the tensile strengthcharacteristics of compacted clayey soil, following the techniquesproposed by Mikulitsch and Gudehus (1995), but with some mod-ifications to simplify the test procedures and improve test repeat-ability. Using the developed apparatus, a series of direct tensile testswere then carried out on specimens compacted to different dry
1Associate Professor, School of Earth Sciences and Engineering,Nanjing Univ., 22 Hankou Rd., Nanjing 210093, China; and VisitingScholar, Key Laboratory of Geohazard Prevention and GeoenvironmentProtection, Chengdu Univ. of Technology, Chengdu 610059, China(corresponding author). E-mail: [email protected]
2Professor, Key Laboratory of Geohazard Prevention and Geoenviron-ment Protection, Chengdu Univ. of Technology, Chengdu 610059, China.E-mail: [email protected]
3Research Scholar, School of Earth Sciences and Engineering, NanjingUniv., 22 Hankou Rd., Nanjing 210093, China. E-mail: [email protected]
4Professor, School of Earth Sciences and Engineering, Nanjing Univ.,22 Hankou Rd., Nanjing 210093, China. E-mail: [email protected]
5Research Scholar, School of Earth Sciences and Engineering, NanjingUniv., 22 Hankou Rd., Nanjing 210093, China. E-mail: [email protected]
Note. This manuscript was submitted on October 17, 2013; approved onNovember 18, 2014; published online on December 15, 2014. Discussionperiod open until May 15, 2015; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, © ASCE, ISSN 1090-0241/04014122(8)/$25.00.
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densities (1.5–1.7 Mg=m3) and with a broad range of water con-tents (4.3–28.5%). The effects of compaction conditions on soiltensile strength are discussed. Based on the tensile strength theoryand model of granular soil presented by Lu et al. (2009), a modifiedmodel was proposed to interpret the tensile strength of compactedclayey soil.
Test Apparatus
The test apparatus developed for direct tensile test consists of aload frame and a newly designed tensile mold. The load frameis driven by a motor that can apply compressive or tensile forceto the specimen at a given displacement rate (ranging from 0 to10 mm=min with a precision of 0.01mm=min), and consists ofthree systems: load and displacement controlling and measuringsystem (control box, control panel, load transducer, and displace-ment transducer); platen positioning system (platen and positionadjuster); and data collecting, transferring, and storing system (datalogger and computer).
The tensile mold comprises two halves of a wedge-shaped splitmold that holds the specimen firmly (80 mm long and 10 mmthick). In order to allow specimen failure to take place at thegap between the wedge-shaped molds, a neck at the center sectionof the specimen is formed, reducing the specimen width from 40 to20 mm. The lower part of the tensile mold was clamped to theplaten of the testing machine. The upper part of the tensile moldwas connected to the top crossbeam through the load transducer(with a capacity of 100 N and a resolution of 0.001 N). A displace-ment transducer with a capacity of 50 mm and a resolution of0.01 mm was also mounted on the platen.
Materials and Methods
Materials
The clayey soil used in this study was collected from the Nanjingarea of eastern China. It widely distributes in the middle and lowerreaches of the Yangtze River and is commonly used in differentconstruction applications. It has also been proposed as a potentialliner material for landfills. Before the test, the collected clayey soilwas air-dried, crushed, and sieved at 2 mm in the laboratory. Itsphysical properties are listed in Table 1.
Specimen Preparation and Installation
To prepare the soil specimens, the crushed air-dried soil powderwas mixed with the required amount of distilled water to the desired
water content. Eight groups of mixtures were prepared at a largerange of water contents, i.e., 4.3 (air-dried state), 7.0, 10.5,12.5, 14.5, 16.5, 18.5, 20.5, 22.5, 24.5, 26.5, and 28.5%, respec-tively. The prepared mixtures were stored and sealed in plastic bagsfor 2 days to allow water to distribute uniformly within the material.
In order to prepare the necked specimen, a special compactionmold and piston with a neck section were designed. The requiredquantity of soil mixture was put in the compaction mold and stati-cally compacted by the piston to the target height (10 mm) andpredetermined dry densities (ρd ¼ 1.5, 1.6, and 1.7 Mg=m3). Allthe specimens were compacted in one layer. After compaction,the specimen was extruded from the compaction mold and placedinto the tensile mold. The tensile mold holding the specimen wasthen transferred to the load frame. The lower part of the tensilemold was clamped to the platen of the load frame. The upper partof the tensile mold was connected to the top crossbeam through theload transducer. Good alignment was ensured by using the positionadjuster, which is connected to the platen.
Test Procedures
Tensile tests were conducted at a constant rate (0.5 mm=min) ofvertical displacement, i.e., the load plate moved downwards toapply the axial load on the specimen. During the tests, the axialload and displacement were continually measured by the loadtransducer and displacement transducer, respectively. They werealso simultaneously recorded by the data logger and transferredto the computer. The tensile load T acting on the specimen is de-termined by subtracting the weight W of the upper halves of boththe tensile mold and the specimen from the measured axial load N.The tensile stress σ was then computed by dividing the tensile loadby the cross-sectional area A at the specimen’s neck, which is equalto width × height (20 × 10 mm)
σ ¼ TA¼ N −W
Að1Þ
The peak tensile stress is defined herein as the tensile strength σtof the specimen at failure, which is related to the maximum tensilestress necessary to counterbalance the whole interparticle contactforce along the failure plane.
A total of 32 groups of direct tensile tests were conducted. Forthe specimens at each dry density and water content, tests wererepeated at least three times and in some cases five times, thuschecking the repeatability of the tests. To prevent moisture evapo-ration, the exposed surface of the specimen was covered withadhesive tape during the tests. The water contents of specimensafter testing were measured and compared with the initial values.Very slight variation (<0.15%) was observed and could be assumednegligible.
Results and Discussion
Overall Tensile Characteristics
Fig. 1 shows the typical tensile curves (tensile load-displacement)of the specimens compacted at a water content of 16.5% and drydensity of 1.5 Mg=m3. The results of repeated tests are also pre-sented. As can be seen, the tensile patterns of the parallel specimens(T1 and T2) are similar, indicating good consistency of specimenpreparation and test procedures. The tensile load increases mono-tonically with increasing displacement before the peak load isreached. After that, the tensile load decreases sharply, indicatingthat tensile cracking has occurred at the specimen neck, as shown
Table 1. Physical Properties of Soil
Soil properties Value
Specific gravity 2.73Consistency limit
Liquid limit (%) 37Plastic limit (%) 20Plasticity index (%) 17
USCS classification CLCompaction study
Optimum moisture content (%) 16.5Maximum dry density (g=m3) 1.7
Grain size analysisSand (%) 2Silt (%) 76Clay (%) 22
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in Fig. 1. According to the maximum tensile loads determined fromthe tensile curves, the average tensile strength of each test groupwas calculated.
One of the explanations given for the existence of the tensilestrength in soil is the cohesion between particles (Lambe andWhitman 1979). The physical mechanisms attributing to the cohe-sion of soil include the following: (1) van der Waals attraction at ornear particle contacts; (2) electrical double-layer repulsion betweenplaty clay particles and attraction near face-to-edge contacts; (3) ce-mentation due to solute precipitation; and (4) capillary attractiondue to the existence of water bridges or bodies between particles(Lu et al. 2007). Currently, the quantitative understanding of theroles and magnitudes of each of the first three mechanisms intensile behavior of soils is not well established (Lu et al. 2007).Most of the research in recent decades has mainly focused onthe quantitative understanding of the relationship between capillaryattraction and tensile strength of unsaturated soils by examiningwater retention mechanisms or mechanical interactions betweentwo particles (Orr et al. 1975; Schubert 1975; Lian et al. 1993;Lu and Likos 2006; Lu et al. 2007, 2009).
In recent years, the suction stress characteristic curve has beenproposed to represent the state of stress in unsaturated soil, andsuction stress was considered as the dominant parameter control-ling soil tensile strength (Lu and Likos 2006; Lu et al. 2009). Me-chanically, suction stress originates from the available interactionenergy at the soil solid surface that can be conceptualized to exist inthe forms of van der Waals and double-layer forces, surface tension,and tensile pore water pressure (Lu et al. 2010). As indicated by Luet al. (2010), a macroscopic continuum representation of suctionstress is the tensile stress that can be simply determined fromthe direct tensile test. According to the Mohr-Coulomb (M-C) shearfailure criterion, if it is assumed that the ratio of shear stress to nor-mal stress in the tensile stress regime remains the same in the com-pressive stress regime, i.e., tanϕ, then the uniaxial tensile strengthmeasured by the direct tensile test can be logically considered as themobilization of isotropic bonding stress (cohesion) when the maxi-mum principal stress remains zero (Lu et al. 2009). In other words,failure occurs not because the applied stress reaches the bondingstrength, but because the ratio of shear stress to normal stress ata point reaches tanϕ. In the case of homogeneous and isotropicsoil, no shear stress develops at any point in any direction whensoil fails under isotropic tensile stress. The isotropic tensile strengthof soil is independent of the internal friction angle. Lu and Likos(2006) and Lu et al. (2009) defined the isotropic tensile strength as
a part of suction stress, and they developed a theory for describingthe tensile strength of unsaturated granular media derived by con-sidering the suction stress. More details about the theoretical rela-tionships between and among suction stress, isotropic tensilestrength, cohesion, and uniaxial tensile strength can be found inLu et al. (2009).
Effect of Water Content
For soils that are either completely dry or saturated, tensile strengthis often considered as a material constant or part of the shearstrength. For soils under partially saturated conditions, tensilestrength is known as a function of suction and significantly dependson water content (Lu et al. 2007). In the past several decades,although the tensile strength of compacted soil has been quantita-tively investigated by either the indirect or direct methods dis-cussed, the water contents of the test specimens were usuallyconcentrated in a narrow range around the optimum value deter-mined from the Proctor curve (Tang and Graham 2000; Nahlawiet al. 2004; Kim et al. 2007; Wang et al. 2007). Information onthe tensile strength within a broader range of compaction watercontents is relatively limited.
Herein according to the measured tensile strength σt at differentwater contents w or degrees of saturation S, the tensile strengthcharacteristic curves (TSCC, σt versus w or S) were determinedfor the specimens compacted at different dry densities ρd (1.5,1.6, and 1.7 Mg=m3) as shown in Figs. 2(a and b), respectively.Three distinct curves can be seen for the three different dry den-sities, but all the curves show similar features and peak valuescan be observed. The results indicate that the σt depends signifi-cantly on w or S at a given dry density. With the increase of w or S,the σt increases quickly before a critical water content wc or criticaldegree of saturation Sc is reached, which corresponds to the peakvalue of σt. As shown in Fig. 2, both the wc and Sc are only slightlyinfluenced by dry density and can be assumed negligible. The aver-age value of wc (11.5%) and Sc (45.2%) will be used in the follow-ing discussion sections. Beyond this point, a decreasing trend in σtis observed with further increases in w or S. For example, the aver-age σt of the specimens compacted at a dry density of 1.5 Mg=m3
increases from 12.93 to the peak value of 33.77 kPa as the watercontent increases from 4.3 to 12.5%, and then decreases graduallyto 17.90 kPa at a water content of 28.5% (about 96% saturation).Generally, the increase rate of σt at the dry side (w lower than wc) ishigher than the decrease rate at the wet side (w larger than wc).Moreover, the decrease rate of σt drops gradually with further in-crease of water content, showing that the tensile strength at highdegree of saturation (i.e., S > 80%) is not significantly sensitiveto the variation of water content, while tends to reach a residualtensile strength at saturation.
The preceding observation shows an important conceptualchange to the previous theories or findings wherein the tensilestrength decreases monotonically with a decrease in suction orincrease in water content or degree of saturation (Towner 1987;Morris et al. 1992; Tang and Graham 2000; Ávila 2004; Nahlawiet al. 2004; Wang et al. 2007), because this is only true for soilwithin the wet side, where the corresponding degree of saturationis relatively high [Fig. 2(b)]. However, for the soil within the dryside of wc, the tensile strength increases with an increase in watercontent or degree of saturation (or decrease in suction) until a peakvalue is reached. This significant dependence of tensile strength onwater content or degree of saturation for compacted clayey soil canbe explained by considering both the microstructure and the capil-lary bonding forces between the particles.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00
1
2
3
4
5
T1 T2
Ten
sile
load
(T),
N
Tensile displacement (l), mm
w = 16.5%
ρd = 1.5 Mg/m3
tensile load
tensile load
tensile crack
Fig. 1. Typical tensile curves of two repeated soil specimens, T1 andT2 (w ¼ 16.5%, ρd ¼ 1.5 Mg=m3)
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Over the past few decades, the microstructure of compacted soilhas been thoroughly studied with the application of scanning elec-tron microscopy (SEM) and mercury intrusion porosimetry (MIP)techniques (Delage et al. 1996; Romero and Simms 2008). It is wellknown that the arrangement and distribution of particles, particleassemblies, and pores and their contacts and connectivity signifi-cantly depend on compaction water content. Generally, clayey soilcompacted at low water content, i.e., at dry of optimum (Proctorcurve), presents a well-developed aggregate structure. The pore sizedistribution (PSD) curve usually shows typical bimodal pore dis-tribution characterized by interaggregate and intraaggregate poros-ity (Romero et al. 1999). Clayey soil compacted at high watercontent, i.e., at wet of optimum (Proctor curve), naturally has a dis-persed structure with less or no obvious interaggregate pores. Basedon the two types of porosity, Alonso et al. (2010) described twotypes of degree of saturation in compacted soil, namely macro-scopic degree of saturation (referring to the interaggregate poresor macropores) and microscopic degree of saturation (referringto the intraaggregate pores or micropores). They indicated thatthe macroscopic degree of saturation is greatly affected by variationof water content, because water trapped in interaggregate pores isconsidered as capillary water and is dominated by capillary forces.
The microscopic degree of saturation is not affected so much by theexternal or internal loads (suction changes due to variation of watercontent), because water trapped in intraaggregate pores is predomi-nantly controlled by particle surface forces and the internal cohe-sion is usually very strong.
As a result of the soil structure described, a conceptual model onsoil water retention regimes is employed in Fig. 3 to illustrate thedevelopment of tensile strength of compacted clayey soil as a func-tion of water content or degree of saturation. Taking the typicalaggregate structure into consideration, it is reasonable to assumethat, at low water content, the overall tensile strength is determinedby forces that can be transmitted from aggregate to aggregate, sincethe tensile strength of the aggregates themselves are usually veryhigh due to the relatively strong internal cohesion, and the tensioncannot entirely break them down. Therefore, the tensile strength ofa compacted clayey soil at relatively low water content is domi-nated by the contact forces between aggregates, which could bedescribed by the tensile strength of an equivalent granular soil con-sisting of particles of the same size and shape as the aggregates;thus, the capillary theory and suction stress can be used to interpretthe dependence of tensile strength on water content (Schubert1975; Lu et al. 2007, 2009).
0 5 10 15 20 25 30 35
10
20
30
40
50
60
70
80
90(a)
wc = 11.5%
d = 1.5 Mg/m3
d = 1.6 Mg/m3
d = 1.7 Mg/m3
Ten
sile
str
engt
h (
t), k
Pa
Water content (w), %
d = 1.5 Mg/m3
d = 1.6 Mg/m3
d = 1.7 Mg/m3
dry side wet side
0 20 40 60 80 100 120
10
20
30
40
50
60
70
80
90
d = 1.7 Mg/m3
d = 1.6 Mg/m3
d = 1.5 Mg/m3
d = 1.6 Mg/m3
d = 1.7 Mg/m3
Ten
sile
str
engt
h (
t), k
Pa
Degree of saturation (S), %
Sc = 45.2% d = 1.5 Mg/m3
(b)
dry side wet side
(a) (b)
Fig. 2. Measured tensile strength characteristic curves of specimens as a function of (a) water content; and (b) degree of saturation
TSCC of sand (by Lu et al., 2009)
Ten
sile
str
engt
h
Water content (w) or degree of saturation (S)
TSCC of compacted clayey soil
SWCC
capillary regimefunicular regime
Suct
ion
wc/S
c
pendular regime
aggregate structure aggregate-dispersed structure dispersed structure
Fig. 3. Conceptual illustration of soil water retention states, microstructure features, and tensile strength characteristics of compacted clayey soil andsand (the boundaries between different regimes are estimated)
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At low water contents (on the dry side of wc, Fig. 2), most ofthe water is trapped in intraaggregate pores, while small amountsof water form a limited number of water-bridges at the aggregate-aggregate contact points (Fig. 3). These bridges result in capillarybonding forces between the aggregates, giving rise to bothcohesion and tensile strength. According to the results of Romeroet al. (1999), the compacted specimens at this stage are locatedin the region of intraaggregate governing suction. Although thesoil suction is high, it contributes less to the interaggregate forceas well as tensile strength. Moreover, the water trapped ininteraggregate pores (water-bridges) is disconnected and charac-terized as a pendular regime (Schubert 1975), where suctionstress increases with an increase in degree of saturation (Lu et al.2009, 2010).
As the water content increases, more and more water-bridgesare developed in the contact points. After water-bridges residein all the possible contact points among the aggregates, suctionstress and tensile strength may reach its maximum value, whichcorresponds to the critical water content wc or critical degree ofsaturation Sc (Figs. 2 and 3).
With a further increase in water content, a decreasing trend intensile strength is observed after its peak value (wet side of wc,Fig. 2). This phenomenon can be explained by considering the fol-lowing factors: (1) the size and number of interaggregate pores insoil specimens decrease because the aggregate structure at lowwater content changes gradually to an aggregate-dispersed struc-ture (Fig. 3); (2) capillary bonding forces developed by the bridgesystem gradually disappear because the trapped pore water betweenaggregates starts to transform from disconnected to a connectedstate, and this regime is known as the funicular regime (Schubert1975); and (3) suction and cohesion between clay particles alsodecrease concurrently. The tensile strength of soil at this stage isprobably dominated by both the cohesions between aggregatesand between clay particles (Fig. 3).
As the specimen nears full saturation, the aggregates are subdi-vided into individual small clay particles and the interaggregatepores disappear (Delage et al. 2006). The specimen shows an evi-dent dispersed structure, where the pores are almost filled withwater and only few disconnected air bubbles are trapped (Fig. 3).This stage is known as the capillary regime (Schubert 1975), wheresuction is very low and does not contribute much to the tensilestrength. As indicated by Lu et al. (2009), suction stress and tensilestrength of sand in a capillary regime generally reduce to zerowhen the sand is sufficiently wet. However, for compacted clayeysoil, a residual tensile strength was observed (Fig. 2). The measuredtensile strength within this regime is mainly dominated by cohesionbetween clay particles such as van der Waal forces, particlesurface forces, etc., which are unlike the capillary bonding forcesdeveloped at the dry side of wc and not sensitive to variation ofwater content.
It should be noted that, especially if the specimen is saturatedor near saturation, pore water pressure is likely to develop duringthe tension test due to two processes: dilatancy and applicationof the tensile force itself. Both processes would cause negativepore water pressure generation, and also an increase in suctionas the specimen is stretched (Ávila 2004). Consequently, themeasured tensile strength would be overestimated, and dependon tensile rate accordingly. In this investigation, only one tensilerate (0.5 mm=min) was employed. The effect of the tensile rateon suction and tensile strength is beyond the scope of thisstudy. In the future, the design of a new tensile test apparatusequipped with suction control or measurement devices shouldbe encouraged.
Effect of Dry Density
From the results shown in Fig. 2, it can also be seen that tensilestrength is significantly affected by dry density ρd. With the in-crease in ρd, there is an increase in σt even though the specimenswere compacted at the same water content. For example, at awater content of 4.3%, the average tensile strength increasesby 73.2 and 200.5% as ρd increases from 1.5 to 1.6 and from1.5 to 1.7 Mg=m3, respectively. Blazejczak et al. (1995) alsoreported that a high dry density had a positive effect on tensilestrength. This is because higher ρd leads to more contacts be-tween soil aggregates and particles, hence increasing the numberof water-bridges, which causes higher measured tensile strength.This phenomenon is more pronounced at low water content.Fig. 4 shows the average increase percent of σt at different watercontents as the specimen’s dry density increases from 1.5 to1.6 Mg=m3 and from 1.6 to 1.7 Mg=m3, respectively. The in-crease percent at the dry side of wc (w lower than 11.5%) isgenerally higher than that at the wet side. This is expectedsince the water is mainly trapped in intraaggregate pores atlow compaction water content. Soil specimens are located inthe intraaggregate governing suction region, where the waterretention state and capillary bonding force is slightly affectedby mechanical effects except the number of water-bridges(Romero et al. 1999). However, as the specimen is compactedat high water content, the increase of ρd can result in boththe rise of macroscopic degree of saturation and the decreaseof suction levels (Alonso et al. 2010), and consequently counter-balance part of the contribution of dry density to the tensilestrength.
Application of the Lu et al. Model
As discussed previously, Lu et al. (2009) developed a theory for thetensile strength of unsaturated sands derived by considering thesuction stress of Lu and Likos (2006), defined as the isotropic ten-sile stress that can be conceptualized as the isotropic tensilestrength. According to the relationships between suction stressand equivalent degree of saturation, and isotropic tensile strengthand uniaxial tensile strength, Lu et al. (2009) proposed the follow-ing two expressions for estimating the uniaxial tensile strength ofunsaturated sand in terms of soil suction and equivalent degree ofsaturation, respectively:
σt ¼ 2 tanϕt tan
�π4− ϕt
2
�ðua − uwÞf1þ ½αðua − uwÞ�ng1=ðn−1Þ
ð2aÞ
5 10 15 20 25 3030
40
50
60
70
80
90
100
d increases from 1.5 to 1.6 Mg/m3
d increases from 1.6 to 1.7 Mg/m3
Incr
ease
per
cent
of
(t),
%
Water content (w), %
11.5%
Dry side Wet side
Fig. 4. Variation of increase percentage of σt with water content asspecimen dry density increases
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σt ¼ 2 tanϕt tan
�π4− ϕt
2
�Seα½Sn=ð1−nÞe − 1�1=n ð2bÞ
where σt = uniaxial tensile strength; ϕt = internal friction angledetermined at low normal stress level, i.e., less than 1 kPa; ua =pore air pressure; uw = pore water pressure; α = inverse valueof the air-entry pressure; n = pore size spectrum number;and Se = equivalent degree of saturation, which is defined asdegree of saturation S normalized by the residual saturation Sras follows:
Se ¼S − Sr1 − Sr
ð3Þ
Thus, Eq. (2) may be used to predict the uniaxial tensile strengthof unsaturated sands as a function of suction or degree of saturationif the parameters ϕt, α, and n are known. Generally, the latter twoparameters, α and n, can be determined by the soil water character-istic curve (SWCC). The preceding model has been shown to bevalid for different sands, and accorded well with experimentalwater retention and tensile strength data (Lu et al. 2009). Becausethe SWCC was not measured in this investigation, only the relation-ship between tensile strength and degree of saturation will be dis-cussed in the following sections.
Generally, for unsaturated sand, the tensile strength presentsa nonlinear relationship with saturation or soil suction (Lu et al.2009). Dry sand usually has minimal tensile strength close to zero.As sand progressively wets toward full saturation, tensile strengthwill first increase up to a peak value, which is followed by a re-duction to zero near saturation or the sand is sufficiently wet(Fig. 3). Apparently, the TSCC of sand is significantly differentfrom that of compacted clayey soil, which presents evidentresidual tensile strength near saturation (Figs. 2 and 3). This isbecause, as illustrated by Lu et al. (2010), the suction stress ofclayey soil is not zero at saturated condition due to the presenceof van der Waals and double-layer forces. Meanwhile, the suctionstress of sand at saturated condition is zero due to the disappear-ance of tensile pore water pressure. For this reason, the tensilestrength model proposed by Lu et al. (2009), mainly based onthe suction stress state of sand, would not be directly appliedto estimate the tensile strength of clayey soil at a relatively highdegree of saturation.
In this study, a modification is made when applying the Lu et al.model to fit the obtained tensile strength data of compacted clayeysoil (Fig. 2). Rather than using a single expression [Eq. (2b)] todescribe the tensile behavior of sand as introduced by Lu et al.(2009), herein two separate expressions are proposed for thetwo distinct TSCC phases of compacted clayey soil, separatedby Sc. As the degree of saturation S is less than Sc, the compactedclayey soil has a typical aggregate structure. Its tensile strengthbehavior is generally equivalent to granular soil as mentioned.Eq. (2b) can be therefore directly used to estimate the tensilestrength of compacted clayey soil at relatively low saturation(S ≤ Sc). As the degree of saturation S is larger than Sc, the com-pacted clayey soil has an aggregate-dispersed or dispersed struc-ture. If it is assumed that the influence of structure change onthe model parameters (ϕt, α, and n) is insignificant during thisrange of saturation, Eq. (2b) can, in theory, also be adopted to es-timate the corresponding tensile strength. However, considering thecontributions of van der Waals attractive forces and electric double-layer forces between clay particles to suction stress or the overalltensile strength of clayey soil, the Lu et al. model is modified byadding a residual tensile strength σtr corresponding to the fully sa-turated state. Therefore, the two expressions can be written as
σt ¼8<:
2 tanϕt tan�π4− ϕt
2
�Seα
�Sn=ð1−nÞe − 1
�1=n0 ≤ S ≤ Sc
σtr þ 2 tanϕt tan�π4− ϕt
2
�Seα
�Sn=ð1−nÞe − 1
�1=n Sc ≤ S ≤ 100%
ð4Þ
For simplicity, the residual saturation of the clayey soil tested inthis investigation is assumed to be 8%, and the internal friction an-gle is assumed to be 25° by referring to Lu et al. (2010) and Cui andDelage (1993). Because no attempt is made for soil water retentionmeasurement, the measured tensile strength data at different de-grees of saturation [average values, Fig. 2(b)] are used directlyto calibrate the α, n, and σtr parameters using the two expressionsin Eq. (4). The resulting curves for specimens compacted at differ-ent dry densities are shown as dashed curves in Fig. 5, and the best-fit α, n, and σtr values are presented in Table 2. It is found that thecurves with two phases agree well with the measured data. Thespecimens compacted at higher dry density generally have higherair-entry values as well as a slightly smaller spectrum of pore sizes.As expected, the residual tensile strength σtr also increases with anincrease of dry density. These are consistent with the fact that soilcompacted at higher dry density has a lower porosity, thus higherair-entry pressure, narrower pore-size distribution, and closer ar-rangement of soil particles. For comparison, the measured tensilestrength data were also fitted by the single expression [Eq. (2b)] ofLu et al. (2009) in the full range of saturation, as the solid linesshown in Fig. 5. The results indicate that the proposed model withtwo expressions is more suitable than the single expression to fit themeasured tensile strength of compacted clayey soil.
It is worthwhile noting that, due to the presence of clay minerals,the mechanisms involved in tensile behavior of unsaturated clayeysoil are much more complex than that of unsaturated sand or othergranular geomaterials. The evolution processes of microstructure,pore size distribution, water retention characteristics, cohesion,solid-liquid interactions, interparticle forces, and other physico-chemical forces are highly complicated with varying water content.However, most existing theories and models related to tensilestrength are derived by considering interparticle forces or capillarymechanisms for idealized two-particle systems featuring smoothspheres, rough spheres, parallel plates, and other such geometries(Schubert 1982; Likos and Lu 2004; Lu and Likos 2004; Lechmanet al. 2006). This is much different than natural geomaterials.The idealizations and assumptions involved in the models signifi-cantly limit their theoretical and practical applications (Lu et al.2009). Undoubtedly, there is still a long way go to accurately de-scribe and predict tensile strength of compacted clayey soils andother geomaterials under various conditions. More comprehensive
Fig. 5. The comparisons of measured tensile strength and fitted TSCCsby the Lu et al. (2009) model and the modified Lu et al. model
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experimental and theoretical studies should be conducted by con-sidering the coupled effects of the discussed processes on tensilestrength.
Conclusions
A direct tensile apparatus was developed and a series of directtensile tests were performed on compacted clayey soil. The effectsof compaction water content and dry density on tensile strengthcharacteristics were examined. The following conclusions canbe drawn:1. The developed direct tensile apparatus and method offers a
simple but effective means for investigating the tensile char-acteristics of compacted clayey soil at different water contentsand dry densities.
2. The tensile strength of compacted clayey soil depends signif-icantly on compaction water content. The tensile strength gen-erally increases with increasing water content and eventuallyreaches a maximum value at the critical water content wcaround 11.5%, and then it decreases. The increase rate of ten-sile strength at the dry side of wc is higher than the decreaserate at the wet side of wc. This is especially true when the spe-cimens are nearly saturated, where the tensile strength is nolonger sensitive to the variation of water content.
3. With an increase in dry density, the tensile strength also in-creases. The contribution of dry density at low water contentis more pronounced than that at relatively high water content.It is found that the increase of dry density from 1.5 to1.7 Mg=m3 does not significantly influence the value of wc.
4. The proposed model, which is based on the Lu et al. (2009)model, with two separate expressions provides a more accurateapproach to estimate the tensile strength characteristic curve ofcompacted clayey soil.
A better understanding of the tensile strength characteristics ofcompacted clayey soils is essential for improving risk assessmentof tension-induced cracks in earth structures, such as cover barriersand bottom liners of landfills, slopes, earth-filled dams, runwaysubgrades, and highway and railway embankments. However,extensive studies should be still conducted to consider the coupledmicrostructural-hydromechanical effects on tensile behavior inthe future.
Acknowledgments
The authors would like to give special thanks for Dr. Sue Struthersfor improving this paper. This work was gratefully supported bythe National Science Foundation for Excellent Young Scholars(Grant No. 41322019), Key Project of National Natural ScienceFoundation of China (Grant No. 41230636), Opening fund ofState Key Laboratory of Geohazard Prevention and Geoenviron-ment Protection (Chengdu University of Technology) (Grant No.
SKLGP2013K010), National Basic Research Program of China(973 Program, No. 2011CB710605), and Natural Science Founda-tion of Jiangsu Province (Grant No. BK2011339). Also, the authorsextend their thanks to Mr. Zhang Qi, Mr. Liu Bao-Sheng, Mr. TangWei, and Mr. Zhu Kun at Nanjing University for their contributionsto the work.
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Table 2. Model Parameters Determined from the Best-Fitting Curves
Model parameters(Mg=m3)
Two separate expressions, Eq. (4) Single expression, Eq. (2b)
0 ≤ S ≤ Sc Sc ≤ S ≤ 100% 0 ≤ Sc ≤ 100%
Lu et al. (2009) model Modified Lu et al. model Lu et al. (2009) model
α (kPa−1) n α (kPa−1) n σtr (kPa) α (kPa−1) n
ρd ¼ 1.5 0.004 4.61 0.09 1.38 15.43 0.009 2.43ρd ¼ 1.6 0.003 4.52 0.07 1.29 24.20 0.005 2.42ρd ¼ 1.7 0.002 3.99 0.02 1.43 42.43 0.003 2.57
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