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Soil Dynamics and Earthquake Engineering

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Centrifuge tests to assess seismic site response of partially saturated sandlayers

Morteza Mirshekari, Majid Ghayoomi⁎

Department of Civil and Environmental Engineering, University of New Hampshire, 33 Academic Way, Durham NH 03824, United States

A R T I C L E I N F O

Keywords:Seismic site responseUnsaturated soilsCentrifuge modeling

A B S T R A C T

Seismic response of unsaturated soil layers may differ from that of saturated or dry soil deposits. A set ofcentrifuge experiments was conducted to study the influence of partial saturation on seismic response of sandlayers under scaled Northridge earthquake motion. Steady state infiltration was implemented to control andprovide uniform degree of saturation profiles in depth. The amplification of peak ground acceleration at the soilsurface was inversely proportional to the degree of saturation, especially in low period range. The cumulativeintensity amplification of the motion was also higher in unsaturated soils with higher suctions. The lateraldeformation and surface settlement of partially saturated sand with higher stiffness were generally lower thanthat in dry soil. Although neglecting the effect of partial saturation in sand layers might be conservative withrespect to seismic deformations, it may result in underestimating the surface design spectra.

1. Introduction

Seismic waves generated by earthquakes often travel through soilswith different mechanical and hydraulic characteristics where they canbe dramatically altered in terms of intensity, frequency content, andduration. This transition is commonly evaluated using “Site ResponseAnalysis”, which is a crucial step toward seismic design of soil-structuresystems. Applications of site response analysis include development ofdesign response spectra for surface structures, estimating seismicallyinduced stresses, strains, and settlements, and liquefaction hazardassessment. Local site conditions such as soil density, plasticity index,stiffness, and damping can significantly affect seismic site response [1–8]. Thus, ignoring the effects of changes in the site conditions may leadto inaccurate assessment of the site response.

The role of local site condition and the intensity of rock motion inthe site response have been highlighted using fully monitored andinstrumented sites during past earthquakes [1,4–15]. In general, lowersite amplification factors were observed during earthquakes withhigher bedrock motion intensities [8,11–15]. This could be attributedto the nonlinear stress-strain behavior of soils and higher dampingvalues as a result of higher induced strain levels. The motionamplification was, also, found inversely proportional to the squareroot of shear wave velocity as a representative measure of local siteconditions [1,4–7,16]. Data obtained from instrumented sites understrong ground motions (e.g. [17,18]) as well as physical modelingexperiments (e.g. [19,20]) can be used to develop guidelines for site

response assessment. Traditionally, different methods have beenemployed to consider the effects of local site conditions and motionintensity in the surface motion evaluation, ranging from simplifiedprocedures regulated by seismic provisions [21–23] to more complexsite-specific ground response analysis for sensitive seismic designsusing available software [24–29]. In current seismic provisions thelocal site condition is reflected through site classification system usingan average shear wave velocity of the top 30 m of the soil profile (Vs)(Table 1).

Degree of water saturation is among the parameters that influencethe seismic response of soil layers [30]. Inter-particle suction inpartially saturated soils increases the effective stresses on the grainskeleton [31]. This, in turn, yields to different soil dynamic propertiesincluding small-strain and strain-dependent shear modulus and damp-ing [32–43]. As a result, seismic wave propagation mechanisms mayvary in partially saturated soil layers [44] that would lead to a differentseismic site response [30,45–49]. Soils in either dry or fully saturatedconditions have been believed to result in more conservative solutionsbecause matric suction in unsaturated soils increases the groundstiffness. Therefore, partial saturation has not been directly consideredin the state-of-the-practice site response analysis. However, recentinvestigations on the site response in unsaturated soils showed that thisassumption might not be always reasonable [47–49]. Further, theinfluence of the degree of saturation on seismic response analysis isoften considered by incorporating the in-situ measured shear wavevelocity of shallow unsaturated soil layers. However, the extent of this

http://dx.doi.org/10.1016/j.soildyn.2017.01.024Received 9 August 2016; Received in revised form 28 November 2016; Accepted 11 January 2017

⁎ Corresponding author.E-mail address: majid.ghayoomi@unh.edu (M. Ghayoomi).

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0267-7261/ © 2017 Elsevier Ltd. All rights reserved.

MARK

influence might be beyond the suction-dependency of the dynamic soilproperties where the wave propagation mechanisms may vary [45]. Inaddition, soil properties may differ between the time of the construc-tion and prior to the earthquake due to the seasonal fluctuation ofwater table. Thus, recognizing this difference would be essential inassessing the uncertainty in projected site response.

Yang [45] analytically studied the frequency-dependent amplifica-tion of inclined vertically propagated shear waves (SV waves) in soillayers overlying bedrock. The results indicated that a slight decrease inthe degree of saturation of fully-saturated soil layers causes a dramaticdifference in vertical amplification of the SV waves. Specifically, forregular earthquake frequencies, unsaturated soils may lead to a highervertical amplification than saturated soil layers. D’Onza et al. [46]implemented the small-strain shear modulus and damping obtainedfrom suction-controlled resonant column tests in a series of numericalsite response analyses. Suction was found to significantly affect thenatural frequency and Peak Ground Acceleration (PGA) amplificationfactor in clayey silt and silty sand layers. According to their numericalstudy, the natural frequency of the soil layers increased in highersuction values whereas PGA amplification factor was reduced.Ghayoomi et al. [30] studied seismically induced settlements inpartially saturated sand by applying sinusoidal cyclic loads to sandlayers in a set of suction-controlled centrifuge tests using steady-stateinfiltration technique [50]. The least amount of surface settlementoccurred in middle range degrees of saturation due to the increase inshear modulus. Moreover, they observed a maximum 20% increase inPGA amplification factor in unsaturated sand with respect to the one indry condition [47].

Recently, Ghayoomi and Mirshekari [48] and Mirshekari andGhayoomi [49] numerically studied the seismic response of partiallysaturated sand and silt layers using site response software DeepSoil[24]. In the absence of any available numerical procedure to accountfor partial saturation, this influence was investigated by adjusting thesoil unit weight and effective stress for any given degree of saturation.Changes of the effective stress in unsaturated soils, in turn, altered soildynamic properties including small-strain and strain-dependent shearmodulus and damping. Accordingly, partial saturation in the soil layersappeared to considerably influence the site response, where the extentof this effect was a function of soil type as well as induced motioncharacteristics. For example, partial saturation in sandy soils with low-range suction level (e.g. 10 kPa) resulted in higher amplifications andlateral deformations whereas in silty soils with high suction range (e.g.70 kPa) led to lower amplifications and lateral deformations incomparison with those of dry soil layers.

Despite the proven influence of the degree of saturation on thedynamic soil properties and the site response, well-documented field orlaboratory seismic site response data in partially saturated soils are stillneeded. Centrifuge physical modeling of free-field seismic groundresponse using a “degree of saturation-controlled” system is of a greatvalue to validate this effect and to calibrate future numerical andanalytical predictive models. This paper describes the adaptation andmodification of an experimental setup to control the degree of

saturation in a geotechnical centrifuge and its application to studyseismic site response of partially-saturated soil layers. Furthermore,the effect of partial saturation on the site response of a sand layer isinvestigated and discussed in terms of different motion characteristicsincluding PGA amplification factor (FPGA), low-period and mid-periodamplification factors (Fa and Fv, respectively), 5% damped spectralacceleration, Arias intensity (Ia), lateral deformation, and seismicallyinduced settlements.

2. Suction control in geotechnical centrifuge

Modeling unsaturated soils under high gravitational acceleration isa challenging task where controlling suction or the degree of saturationis the key to any systematic investigation involving partially saturatedsoils. Centrifuge modeling of unsaturated fine-grained soils could beaccomplished by using methods such as compacting soils with a targetdegree of saturation [51] or in-flight free drainage of an initiallysaturated specimen [52]. For sand layers, however, centrifugationalong with free drainage leads to very low degrees of saturation dueto their relatively higher permeability values. To address this problem,steady state infiltration was implemented in this study to generateuniform degree of saturation profiles inside a geotechnical centrifuge.This approach was devised from centrifuge permeameters [53–55],mainly used to streamline measurements of hydraulic parameters inunsaturated soils. Recently, similar steady state infiltration method wassuccessfully incorporated in a laminar container inside a large armcentrifuge to study seismically induced settlements in partially satu-rated sand layers [50].

Dell’Avanzi et al. [56] analytically solved Richards' equation ofwater flow in unsaturated soils [57] for steady state infiltration, underhigher gravitational field inside a geotechnical centrifuge. The suctionprofile along the depth of the specimen during steady state infiltrationcan be estimated using the following equations [56]:

⎡⎣⎢⎢

⎤⎦⎥⎥

⎛⎝⎜

⎞⎠⎟ψ

aln e v

N kif v

N ke=− 1 − + >0

ln vN k e aρ z ω r z

m

r sat

m

r sat

aψ( + − ( − 2 )) −mr sat

aψw m

m− 0 2 0 0

(1a)

⎡⎣⎢⎢

⎤⎦⎥⎥

⎛⎝⎜

⎞⎠⎟ψ

aln e v

N kif v

N ke=− 1 − − + <0

ln vN k e aρ z ω r z

r sat

m

r sat

aψ( + − ( − 2 )) −mr sat

aψw m

m− 0 2 0 0

(1b)

where a is the Gardner's hydraulic conductivity parameter in kPa−1

[58], e is the natural base of logarithms, vm is the discharge velocity inm/s, zm is height of any location in the specimen from its bottom in m,Nr is the g-level depending on zm parameter, ksat is the soil hydraulicconductivity in saturated condition, ψ0 is suction at the bottom of thespecimen defining the boundary conditions, and ρw is the density ofwater in kg/m3. Then, the degree of saturation profiles could beobtained using hydraulic constitutive models relating the degree ofsaturation and matric suction; Soil Water Retention Curves (SWRC)(e.g. van Genuchten [59]). Applying steady state infiltration in higherg-levels results in a uniform suction with height with small transitionzones. For example, profiles of the degree of saturation are illustratedin Fig. 1(a) and (b) for different discharge velocities and g-levels,respectively, during the centrifugation of a 22.86 cm of model Ottawasand.

Dell’Avanzi et al. [56], also, determined suction scaling factor forsteady state flow condition where a prototype infiltration is to berepresented by a model with the length and discharge velocity scalingfactors of 1/N and N, respectively. Comparison of prototype and modelinfiltration equations led to a suction scaling factor of unity forrelatively uniform acceleration fields (i.e. ratio of centrifuge arm'slength to the length of specimen is greater than 10). For the case ofsmaller centrifuges, however, the suction scaling factor becomes

Table 1Site classification (after NEHRP Provisions [21]).

NEHRPcategory

Description Time-weighted average

shear wave velocity (V )s

A Hard rock > 1500 m/sB Firm to hard rock 760–1500 m/sC Dense soil, soft rock 360–760 m/sD Stiff soil 180–760 m/sE Soft clays < 180 m/sF Special study soils, e.g. liquefiable

soils, sensitive clays, organic soils,soft clays > 36 m thick

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slightly different leaning toward lower values within the upper portionof the profile (this is observed in the analytical solutions in Fig. 1(b)).This scaling factor is solely for an infiltration problem, where the sameprototype suction profile would be achieved in a model (in largecentrifuges) undergoing a N-times increased discharge velocity. Thisconcept, however, should not be considered when mechanical behaviorof soils is studied. When suction stresses that were measured in themodel should be projected to prototype values, matric suction in thecentrifuge has to be scaled using the conventional pressure scalingfactor (i.e. Nσ=1). However, in this study matric suction was indirectlyobtained from the measured degrees of saturation, so the interchange-able application of soil water retention in model and prototype wascarefully considered. Since SWRC is not a function of g-level [60,61]measured degrees of saturation in centrifuge experiments can be linkedto matric suction using 1-g SWRC.

3. Experimental program

3.1. Experimental setup

3.1.1. Centrifuge, shaking table, and containerThe recently renovated 5 g-ton centrifuge at the University of New

Hampshire was used in this investigation [62]. The arm radius is 1 mfrom the center of rotation to the platform in its fully extendedposition. The centrifuge is equipped with an in-flight shaking tablethat is capable of imposing harmonic or seismic displacement timehistories. A hydraulic servo valve controlled by National Instrumentssystem operates the table. Due to servo valve limitations, the currentsystem has an analog displacement threshold of 10-mm. Four fluidsupply lines, two devoted to the hydraulic fluid and two to theinfiltrating water, were passed through the centrifuge slip ring. Alaminar container was used herein to avoid adverse boundary effects onthe shear wave propagation [63]. The container consists of 19rectangular aluminum laminates, each 12.7 mm thick, which areseparated using cylindrical bearing with negligible frictional resistance[64]. The inner dimensions of the box are 35.5 cm in length, 17.7 cm inwidth, and 25.4 cm in height with the ratio of length to width as 2. Aschematic of the container is shown in Fig. 2. In order to allow for freedrainage of water, the container base plate was replaced with anoutflow control aluminum plate with a network of 14 drainage ports.

3.1.2. Infiltration setupThe basic procedure to apply steady-state infiltration inside the

laminar container in this study is similar to Ghayoomi et al. [50].

Inflow water was supplied from an 80-gallons pressurized tank locatedoutside the centrifuge. An inlet slip-ring port was deployed to route thewater to 8 fog-spray nozzles. Three sets of BETE nozzles were utilizedin this investigation to obtain various discharge rates and, therefore,different degree of saturation profiles. 1/8 PJ10, 1/8 PJ20, and 1/8PJ40 nozzles were used for degrees of saturation lower than 45%,between 45% and 60%, and higher than 60%, respectively. In order tocontrol the inflow rate, a solenoid valve was employed in conjunctionwith an ultra-precision needle valve ahead of the nozzles. The solenoidvalve was used to open the water flow during the centrifugation whilethe needle valve was in charge of controlling the inflow rate. Drainagewas conducted through four of the outflow ports opened by miniaturesolenoid valves. The outflow water was guided to four drainage tanksmounted on the front, back, and bottom of centrifuge platform (Fig. 2).

3.1.3. InstrumentationInstrumentation setup comprises of dielectric sensors, acceler-

ometers, and LVDTs to measure volumetric water content, accelera-tion, and displacement, respectively. Four EC-5 dielectric sensors fromDecagon Devices were placed at different depths (i.e. 1.6, 6.3, 12.4, and18.1 cm in model scale from the top of the soil surface). Several PCBPiezoelectronics accelerometers were used to record acceleration timehistories along the depth of the specimen (i.e. at surface, bottom anddepths of 5.7, 11.4, and 17.1 cm in model scale from the top of thespecimen as shown in Fig. 2). Two accelerometers were placed apartfrom each other at some levels to ensure the uniformity of motionacross the container. In addition, one accelerometer was mounted tothe base plate of the container to measure the actual applied motion.Two MHR500 LVDTs and three MHR250 LVDTs were mounted on thetop and side of the specimen to measure the vertical and lateraldeformations, respectively.

3.2. Material

F-75 Ottawa sand was used in this study as it is fine-enough to holdsuctions up to 10 kPa and yet permeable-enough to permit the steady-state infiltration. The grain size distribution of the sand is illustrated inFig. 3(a). The sand was dry-pluviated in the container to reach thetarget void ratio of 0.66. Soil Water Retention Curve (SWRC) of thissand measured by Mirshekari and Ghayoomi [49] and Le andGhayoomi [43] are shown in Fig. 3(b) alongside fitted curves for bothdrying and wetting paths using van Genuchten's equation [59].Geotechnical physical and hydraulic properties of the sand are sum-marized in Table 2. The Hydraulic Conductivity Function (HCF) fitting

Fig. 1. Analytical degree of saturation profiles during steady-state infiltration (after Dell’Avanzi et al. [56]): (a) for different discharge velocities; (b) for different g-levels.

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parameter (αG) necessary for steady state infiltration solution wasfound to be 2.5 kPa−1 using van Genuchten-Mualem model [59].

3.3. Testing procedures

3.3.1. Sample preparationLoose specimens were prepared inside the laminar container while

a plastic membrane was glued to the base plate in order to preventleakage of sand and water from the gaps between laminates. Inaddition, a gravel layer was placed at the bottom of the sand specimento provide a saturated boundary condition, separated from the sandlayer using geotextile filters. The final specimen height was 22.86 cm inmodel scale with an approximate relative density of 45%.Accelerometers and dielectric sensors were placed at different depthsof the soil layer when needed (Fig. 2). Upon completing the pluviation,spray nozzles and vertical LVDTs were mounted on the sensor racksatop the container sitting on the in-flight shaking table. Moreover,horizontal LVDTs were placed on a side frame measuring the displace-ments of the laminates. The specimen was, then, saturated (forsaturated and unsaturated tests) by passing de-aired water throughtwo drainage ports on the base plate. A completely prepared andmounted specimen is shown in Fig. 4. A slight negligible change in therelative density was measured due to the saturation and centrifugation.

The centrifuge was spun up to 50-g acceleration measured at themiddle of the soil layer. Upon reaching the target g-level, the inflow andoutflow solenoid valves were opened to generate a steady-stateinfiltration within the specimen. Different discharge rates were ob-

tained in this study by varying the types of nozzles and opening of theneedle valve (i.e. vm/ksat between 1.5×10−4 to 2.4×10−3).Consequently, various uniform degree of saturation profiles wereobtained ranging from 32% to 68% (corresponding to matric suctionsfrom 3.9 to 4.9 kPa) within a short time span after starting theinfiltration (e.g. about 1 min for all the specimens). Some of the

Fig. 2. Instrumentation in the laminar container modified for steady-state infiltration: (a) Side-view Schematic (b) Front-view Schematic.

Fig. 3. Properties of F-75 Ottawa sand: (a) Grain size distribution; (b) SWRC.

Table 2Physical and hydraulic properties of F-75 Ottawa sand.

Parameter Value

Coefficient of curvature, Cc 1.71Coefficient of uniformity, Cu 1.01Specific gravity, Gs 2.65D50 (mm) 0.182Dry density limits, ρD-min, ρD-max (kg/m

3) 1469, 1781Void ratio limits, emin, emax 0.49, 0.80Relative density, Dr 0.45Friction angle (deg) 40Poisson's ratio, υ 0.38Saturated Hydraulic Conductivity, ks (cm/s) 6×10−4

van Genuchten's avG parameter for Drying Path (kPa−1) 0.25van Genuchten's NvG parameter for Drying Path 9Residual volumetric water content for Drying Path, θr 0.07Saturated volumetric water content for Drying Path, θs 0.392van Genuchten's avG parameter for Wetting Path (kPa−1) 0.7van Genuchten's NvG parameter for Wetting Path 5Residual volumetric water content for Wetting Path, θr 0.07Saturated volumetric water content for Wetting Path, θs 0.322

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achieved degrees of saturation and their corresponding dischargevelocities are shown in Fig. 5 along with the corresponding analyticalsolutions (Eq. (1)). Although a somewhat uniform degree of saturationprofile was reached across the height of the specimen, the bottommostsection (about 5% in length) still had a transient degree of saturationvarying from the fully saturated boundary condition to the targetdegree of saturation. This length was aimed to become minimal byincreasing the g-level (Fig. 1b). The transition zone has to beconsidered when interpreting and applying the results of this study.After a constant degree of saturation was achieved throughout thespecimen, the scaled earthquake motion was applied to the sand layerand the response was captured. Conventionally, a more viscous porefluid with similar mechanical properties with water has been imple-mented to address the time scaling conflicts between dynamic anddiffusion problems in the centrifuge [65]. However, the mechanisms ofdynamic suction variations mainly rely on distortions of water menisciduring seismic events and differ from those of excess pore waterpressure generation and dissipation. The unsaturated tests in this study

were performed in degrees of water saturation much lower than one(for fully saturated) to avoid the time scaling conflict for dynamicproblems in the centrifuge models. In addition, the steady stateinfiltration technique leverages the accelerated flow of the water inthe soil in high g-level, which would not be the case for fluids withhigher viscosity.

3.3.2. Input earthquake motionNorthridge earthquake motion, 1994, captured at WPI station was

selected as the desired motion in this investigation, as it encompasses awide range of frequency contents. The acceleration time history of theoriginal recorded motion was scaled down to meet the shaking tablelimits (i.e. PGA was scaled from 0.42g to 0.3g in prototype scale). Thefrequencies higher than 8 Hz in prototype scale were filtered from this“desired” motion to obtain the “target” motion for this investigation. Asa common practice, in-flight shaking tables are calibrated for a specificearthquake motion by matching the target and the “achieved” motionson the shaking table [66,67]. The method introduced by Mason et al.[67] was used through which the “command” motion sent to theshaking table was modified using a set of frequency response analysis,so the achieved motion becomes approximately similar to the targetmotion. Different characteristics of the final achieved motion includingacceleration time history, Arias intensity, Fourier amplitude, and 5%damped spectral acceleration are illustrated in Fig. 6. Although thesame motion was imposed to all the specimens with different degrees ofsaturation, the input motions recorded at the bottom accelerometerwere slightly different. This could be due to the different specimenweights and nonlinear shaking table performance.

4. Results and discussion

The centrifuge experiments were performed on three dry specimens(D1, D2, and D3), eleven unsaturated specimens (specified with theletter U followed by the degree of saturation) with degrees of saturationvarying between 32% and 68%, and one saturated (S) specimen. Thecaptured acceleration and displacement time histories were post-processed to obtain various motion characteristics. Then, the influence

Fig. 4. Fully assembled experimental setup.

Fig. 5. Experimentally developed profiles of degree of saturation along with theanalytical solutions (after Dell’Avanzi et al. [56]).

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of the degree of saturation on the seismic response was investigated interms of different motion parameters including PGA, frequency-dependent motion amplification, cumulative intensity amplification,lateral deformation, and seismic settlement. The following results areall presented in prototype scale unless specified.

4.1. Peak ground acceleration amplification

PGA amplification factor (FPGA) was calculated at different depthsusing the following equation:

F PGAPGA

=PGAbase (2)

where PGA and PGAbase are the maximum accelerations at a givendepth and at the bottom of the specimen (considered as bedrockmotion herein), respectively.

As previously mentioned, PGAbase slightly varied among differenttests that, in turn, influenced the FPGA values. In order to eliminate thiseffect, a relationship was formulated to normalize all the base motionsto a reference one. To find such a correlation, FPGA values were graphedover PGAbase for tests with approximately similar degrees of saturation;e.g. D1, D2, and D3 and U48, U49, and U50; shown in Fig. 7. Knowingthe expected trend from previous studies [8,11–15], FPGA was setinversely proportional to PGAbase for the given limited range ofacceleration. The following linear correlation was developed wherethe slope of the line was similar for dry and partially saturated cases:

F PGA d= −5. 75 × +PGA base (3)

where the parameter d indicates the influence of degree of saturation.The FPGA values were modified by moving along the same slope suchthat a reference base PGA of 0.3g was achieved for all the tests basedon the abovementioned linear relationship:

Fig. 6. Applied scaled Northridge earthquake motion characteristics: (a) Acceleration time history; (b) Arias intensity; (c) Fourier amplitude; (d) 5% damped spectral acceleration.

Fig. 7. Correlation of PGA amplification factor (FPGA) and base peak ground acceleration(PGAbase).

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F F PGA= −5. 75 × (0. 3− )PGA Mod PGA base, . (4)

This modification could increase or decrease the FPGA depending onthe values of PGAbase (e.g. for the test U66 with PGAbase of 0.2828 theFPGA was modified from 1.212 to 1.1131). Modified surface FPGA valuesfor different degrees of saturation are shown in Fig. 8(a). While theamplification factors for dry tests were approximately one, the un-saturated soil condition led to higher amplification factors at surfaceespecially at lower degrees of saturation (with an average increase of16%). The amplification factor for the case of fully saturated sand layerwas expectedly lower than the ones in dry and unsaturated sand layersdue to the de-amplification of motion in possibly fully- or partially-liquefied ground (the liquefaction occurrence was not assured due tothe absence of pore water pressure transducers). Therefore, the focus ofthis paper has been mainly on comparing the response of dry andunsaturated sand layers.

Amplification factor at the soil surface was shown to be inverselyproportional to the degree of saturation with a nonlinear pattern. Theamplification factor is somewhat constant for mid-level degrees ofsaturation where the change in suction is almost negligible (i.e.between 45% and 70% degrees of saturation). In addition, the code-based [21,22] amplification factor is demonstrated in Fig. 8(a) wherethe weighted-average shear wave velocity,Vs , was calculated using thefollowing formula:

∫V H

dz=s H

v01s (5)

where H is the soil layer thickness, z is the depth, and vs is the depth-dependent shear wave velocity resulted from small-strain shear mod-ulus values at each depth. The site class, thereafter, was estimatedusing Table 1 where regardless of the choice of the small-strainmodulus formula (i.e. [40,68,69]), a Class D was assigned. Also,estimating an average shear wave velocity for 30-m soil layer assuggested by the code or for 11.43-m soil layer in this study wouldyield to the same site class. Although partial saturation increased thePGA amplification, the code-suggested FPGA value for this case isconservatively higher than nearly all the experimental values. Thevalues suggested by seismic provisions were developed based upon alarge number of recorded data from the past earthquakes in differentsite conditions [70] while this study limited the testing conditions (e.g.uniform degree of saturation profiles; one type of sand, and oneearthquake motion) to evaluate the effect of partial saturation.

The observed higher amplification in unsaturated sand layer incomparison with the one in the dry condition is consistent with theones from simplified numerical site response analysis [48,49] andcentrifuge physical modeling under cyclic loads with equivalent PGA of0.55g and 0.65g [47]. However, Ghayoomi and McCartney [47] foundthe code-based amplification factors to be lower than the measuredFPGA values. This difference could be either a result of simulatingseismic motions using cyclic loads in Ghayoomi and McCartney [47] ordifferent suction-dependent site response mechanisms in very strongground motions such as continuous full cycles of dynamic loads.

Parameters influencing the site response could be simplisticallyexplored by inspecting the analytical solution to a linear Single Degreeof Freedom (SDOF) system under cyclic motion. This SDOF systemcould represent a uniform soil layer overlying bedrock. The maximumacceleration amplification ratio in such a system would be approxi-mated as follows [71]:

aa β

( ) ≈ 1( )+( )

surface

bedrockmax

Iπ

S1

2 (6)

where βS is the soil damping ratio and I is the rock/soil impedanceratio equal to γrVr/γsVs, in which γr and γs are the unit weights and Vr

and Vs are the shear wave velocities of the rock and soil, respectively.As the ratio of γr/γs is between 1.1 and 1.4 for majority of sites [70], the

Fig. 8. PGA amplification factor (FPGA) for sand layers with different (a) degrees ofsaturation; (b) matric suction; and (c) suction stress.

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amplification ratio becomes a function of the shear wave velocity anddamping where both are influenced by motion intensity and local siteconditions. However, for sands, the shear wave velocity is mainly afunction of local site conditions while the damping is predominantlyaffected by the motion intensity [70]. Despite the useful insights gainedfrom the analytical solution to the dynamic response of the SDOFsystem, this simplified equation might not be used in real applicationswhere soil becomes nonlinear under relatively intense earthquakesespecially in layered grounds; e.g. Northridge region during the 1994earthquake [72]. Eq. (6), however, might be used to shed light ondifferent aspects of the effect of partial saturation on site responsewhere both parameters affecting the SDOF response (i.e. shear wavevelocity and damping) vary by changes of the degree of saturation.Shear wave velocity or small-strain shear modulus are increased inpartially saturated soils as a function of matric suction [38,40,73]. Onthe contrary, damping decreases while matric suction increases [41].Given the inversely proportional relations between the amplificationfactor and both shear modulus and damping in Eq. (6), the increase inshear wave velocity of unsaturated soils yields to lower amplificationwhereas the decrease in damping leads to higher amplification. As aresult, the influence of partial saturation on the site response should beholistically explored considering the interaction between the change inshear modulus and damping.

Shear modulus and damping are functions of their small-strainvalues and induced level of strain in soils. Small-strain shear modulusis proportional to the square root of effective stress in dry or saturatedsoils [68,69] while small-strain damping is correlated to the effectivestress raised to a much lower power (e.g. −0.08 according to Menq[74]). Therefore, the influence of the effective stress is more pro-nounced on shear wave velocity in comparison with damping, resultingin a general trend of lower amplification factors for stiffer sites [21].The presence of suction in unsaturated soils increases the effectivestress, however, the variations of small-strain dynamic properties fordifferent degrees of saturation might not only depend on the effectivestress [73]. Dong et al. [73] discussed that water can soften the soilmatrix in unsaturated soils by reducing the inter-particle friction thatcontradicts the added stiffness caused by the matric suction. Hence, theinfluence of damping and shear modulus on the site response maybecome comparable. Also, the extent of the influence of partialsaturation on the site response could vary in depth depending on thedominance of variations in either damping or shear modulus.

Further, the seismically induced strain level in soil layers plays animportant role in interpreting the acceleration amplification factors.Basically, higher intensity earthquake motion leads to higher strain-dependent damping and lower strain-dependent shear modulus. Then,the amplification factor decreases [11,12] as a result of the interactionof these two parameters. In unsaturated soil conditions, however, theinduced shear strains are affected not only by the intensity of themotion but also by the soil stiffening and lower damping. Depending onthe induced level of shear strain, the mobilized shear modulus anddamping in soil layers may vary and, consequently, alter the amplifica-tion factor.

Since matric suction increases the contact effective stresses inunsaturated soils, more insights might be gained by illustrating FPGA

versus matric suction, shown in Fig. 8(b). In addition, Lu et al. [75]discussed that it is the combined effect of the matric suction and thedegree of saturation that influence the behavior of unsaturated soils.They synthesized experimental data from shear or tensile strength testsand proposed “suction stress” parameter that could be practicallyresponsible for the mechanical behavior of unsaturated soils; asfollows:

σ = u − u(1+[α(u − u )] )

s a w

a wn 1− 1

n (7)

whereσs is the suction stress, ua and uw are pore air and pore waterpressures, respectively, and α and n are the parameters for the van

Genuchten [59] SWRC model. FPGA values are shown versus suctionstress in Fig. 8(c). Although the performed tests cover a wide range ofdegree of saturation, only a slight variation occurred in terms of matricsuction (i.e. from 3.9 to 4.9 kPa) while the suction stress expands therange from 0.8 to 2.3 kPa. The suction stress might be a betterpredictor of seismic soil behavior while the amplification factor wasnot coherently linked to the change in matric suction. Overall,unsaturated specimens showed a higher amplification factor at surface,however, FPGA decreases as suction stress increases.

In order to understand the variations of amplification factor alongthe depth, FPGA profiles are shown over the height of the sand layer fordifferent degrees of saturation in Fig. 9 (only for the tests with fiveaccelerometers in the middle array); where an average FPGA ispresented for the tests with similar degrees of saturation. The degreeof saturation imposed a depth-dependent influence on PGA amplifica-tion factor. Despite the observed trend at the soil surface, shown inFig. 8, FPGA values in depth of unsaturated sand layers were mostly(except for the lowest degree of saturation) lower than the ones of drysand. This difference can be associated with the coupled effects ofdepth-, strain-, and suction-dependent damping and shear modulus onmotion amplification pattern. For example, the suction stress results ina higher increase in the effective stress in shallow soils where totalstresses are low. Further, the inconsistent amplification profiles inunsaturated soil layers would imply more complex wave propagationmechanisms in unsaturated soils [45].

4.2. Frequency-dependent motion amplification

Surface to bedrock amplification of response spectra or Fourierspectra could be used to investigate the frequency-dependent amplifi-cation of seismic motions. Low-period and mid-period amplificationfactors are commonly evaluated as average values of Ratio of ResponseSpectra (RRS) or the ratio of Fourier spectra within a period orfrequency range; e.g. between 0.1–0.5 s and between 0.4 and 2 s forFa and Fv for the recorded data of Loma Prieta earthquake 1989,respectively [5]. An average value of RRS between 0.1–0.5 s and 0.6–2 s were used herein to calculate Fa and Fv, respectively, since for thespecific case of this study the values of RRS at 0.4 s do not representamplification at mid-term periods; as shown in Fig. 10. Fa and Fv

variations for different degrees of saturation and suction stresses areshown in Fig. 11. Both amplification factors were significantly higher atsoil surface in partially saturated specimens than the ones in drycondition. This clarifies that unsaturated condition yields to higheramplification at surface regardless of the period range. An average

Fig. 9. Profiles of PGA amplification factors (FPGA) for sand layers with different degreesof saturation.

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increase of 19% and 6% were observed in Fa and Fv values ofunsaturated specimens than dry ones, respectively. This indicates amore significant influence of unsaturated condition on motion ampli-fication at low-period range. Since no strong correlation between the Fa

and Fv and PGAbase was found for the tests with similar degree of

saturation, the frequency-dependent amplification factors were notmodified with respect to the base motion. This explains the reason thatthe data was more scattered in terms of Fa and Fv in comparison withthe FPGA. In order to better compare the response of dry and

Fig. 10. Period range selection procedure for low- and mid-period amplification factors.

Fig. 11. Low-period amplification factors (Fa) for different: (a) degrees of saturation; and (b) suction stress. Mid-period amplification factors (Fv) for different: (c) degrees of saturation;and (d) suction stress.

Fig. 12. Ratio of Reponses Spectra (RSS) for selected tests for sand layers with differentdegrees of saturation.

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unsaturated sand layers in terms of frequency-dependent amplifica-tion, 5% damped smoothed surface-to-base RRS graphs for selectedtests are shown in Fig. 12. The general higher motion amplification inunsaturated soil, more substantial in low period range, is discernable.

4.3. Cumulative intensity amplification

Arias intensity [76], a well-known cumulative intensity character-istic, was selected to represent the accumulated energy buildup duringa shaking event in sites with different degrees of saturation. Ratio of themaximum Arias intensity at the soil surface over the maximum Ariasintensity at the base was used to quantify the change in energy level ofthe motions. The variation of Arias Intensity ratio with the degree ofsaturation is shown in Fig. 13, enabling a comparison between theresponse of dry and unsaturated sand layers. To avoid misinterpreta-tion of the results only the tests with bedrock Arias intensity within a ±5% offset from the reference dry motion were shown. The presentedresults show an overall 6% increase in Arias Intensity amplification forunsaturated specimens where the acceleration was amplified differentlyin different frequency ranges.

4.4. Lateral deformation

Lateral deformations were obtained using direct measurements ofthe side LVDTs as well as double integration of acceleration timehistories followed by baseline correction of the obtained displacementtime histories [77]. Maximum lateral deformation profiles of selectedtests based on accelerometer and LVDT measurements are shown inFig. 14(a) and (b), respectively. Maximum lateral deformation at thesoil surface measured by both methods are illustrated against degree ofsaturation in Fig. 14(c). Overall, the lateral deformation of unsaturatedsoils obtained from both LVDTs and accelerometers were lower thanthat of dry soils by the ratio of 10% and 8% for LVDT andaccelerometer measurements, respectively. This can be attributed tothe higher shear modulus and stiffness in unsaturated sand resulted inlower induced shear strain and lateral deformations. The acceleration-based lateral deformation values were lower than those of LVDTmeasurements that could be due to the double integration processthat involved base line correction. This difference in deformationsobtained from the two methods is consistent with previous work byHashash et al. [20].

Fig. 13. Surface-to-base ratio of Arias intensity for sand layers with different degrees ofsaturation.

Fig. 14. Maximum lateral deformation profiles for selected tests with different degreesof saturation based on (a) LVDT measurements; and (b) accelerometer measurements.(c) Maximum surface deformation of sand layers with different degrees of saturation.

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4.5. Seismic settlement

Seismically induced surface settlements were estimated by anaverage value of the middle and side LVDTs' measurements aftershaking shown in Fig. 15. Seismic settlements were generally lower forpartially saturated sand layers as a result of stiffer response ofunsaturated sand. A minimum settlement at a middle range degreeof saturation, e.g. at about 38% in this case, is consistent withGhayoomi et al. [30] for seismically induced settlements under cyclicloads. Ghayoomi et al. [30] attributed this trend to the collective effectsof seismic compression and post shaking consolidation.

5. Summary and conclusion

The implementation process of a steady state infiltration system ina laminar container inside a geotechnical centrifuge was presented inthis paper, which was successfully deployed to control degree ofsaturation and, consequently, matric suction in scaled physical models.Seismic excitation simulating scaled Northridge earthquake motionwas applied to 11.43 m-thick dry, saturated, and unsaturated speci-mens of loose Ottawa sand with uniform degrees of saturation in depth.The recorded data were used to assess the seismic site response underdifferent water saturation profiles.

The effect of partial saturation on PGA amplification factor wasshown to be a function of depth as well as the degree of saturation.Despite the commonly-practiced assumption that neglects the seismicresponse of unsaturated soil layers in order to be conservative, a higherPGA amplification at soil surface was observed as a result of partialsaturation with an average increase of 16%. Amplification factors at soilsurface decreased as the degree of saturation increased (i.e. lowermatric suction and higher suction stress) where it became somewhatconstant between the degrees of saturation of 45% and 70%. Suctionstress correlated properly with the amplification factor, demonstratinga potentially promising parameter in evaluating the seismic behavior ofunsaturated soils. The PGA amplification factors proposed by seismicprovisions were conservatively higher than the ones for the appliedrange of the degree of saturation in this study with limited soil andmotion conditions.

The spectral acceleration in both low- and mid-period ranges weremore amplified at soil surface as a consequence of partial saturationshowing a more substantial change in the low-period amplificationfactor. The accumulated energy was more intensified within theunsaturated soil layers indicated by a 6% increase in the surface tobedrock Arias intensity ratio, compared with the dry sand layer.Despite higher intensity amplification in unsaturated soils, their lateral

deformations were generally lower than the dry specimens with anaverage of 10% reduction. Seismically induced settlement reduced inunsaturated sand layers comparing with the dry ones, with a minimumsettlement at a degree of saturation about 38% due to the higherstiffness.

Albeit unsaturated soils are stiffer than those of dry or saturatedwhere it resulted in lower lateral deformation and surface settlement,partial saturation may trigger more intensity amplification as a result ofthe interaction between different soil characteristics such as shearmodulus, damping, and mobilized shear strain within the soil layers.The novel testing procedures and findings of this study highlighted thesignificance of the degree of saturation in the seismic site response.Further, in order to capture different aspects of this effect, morecomprehensive investigation on seismic behavior of variety of soil typesin unsaturated state under a wide suite of earthquake motions isneeded along with developing numerical procedures to account forpartial saturation.

Acknowledgment

The authors would acknowledge funding of this project by theNational Science Foundation through the NSF CMMI grant No.1333810.

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