761

i) Technical Engineer, Ocean and Coastal Consultants Inc. a COWI Company, USA (msravisharma＠yahoo.com).ii) Associate Professor, Department of civil/ocean engineering, The University of Rhode Island, USA (baxter＠oce.uri.edu).iii) Previously Graduate Student, ditto (michaeljander＠gmx.de).

The manuscript for this paper was received for review on July 7, 2010; approved on April 14, 2011.Written discussions on this paper should be submitted before May 1, 2012 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

761

SOILS AND FOUNDATIONS Vol. 51, No. 4, 761–771, Aug. 2011Japanese Geotechnical Society

RELATIONSHIP BETWEEN SHEAR WAVE VELOCITY ANDSTRESSES AT FAILURE FOR WEAKLY CEMENTED

SANDS DURING DRAINED TRIAXIAL COMPRESSION

RAVI SHARMAi), CHRISTOPHER BAXTERii) and MICHAEL JANDERiii)

ABSTRACT

Small strain shear modulus (Gmax) has been a parameter of choice used to assess the strength and deformation behav-ior of cemented and other sensitive soils. The in‰uence of density, eŠective conˆning stress, stress anisotropy, and ce-ment content on shear wave velocity (vs)/shear modulus has been studied extensively and published. There are,however, very few studies on the eŠects of cement/strength degradation during shear on the shear wave velocity/shearmodulus, which may be important for reliable and accurate prediction of mechanical behavior of cemented sands. Theobjective of this study is to evaluate the eŠect of cement degradation on shear wave velocity/shear modulus by measur-ing continuously the shear wave velocity during shear. A laboratory testing program was performed using samples ofsilty sand artiˆcially cemented with Ordinary Portland Cement (OPC). Shear wave velocity was measured continuous-ly within the triaxial cell during the shear phase using torsional ring transducers. Gmax was calculated using the shearwave velocity and the corresponding density during shear. Results from this study suggest that Gmax reaches a peakvalue before s?1 reaches a failure stress and this behavior is believed to be an indicator of bond breakage or destructur-ing. Gmax calculated at various stages during shear showed that the cement and modulus degradation can be representedby a simple index using Gmax. The results of this study suggest that there may be a unique relationship between smallstrain shear modulus and eŠective stresses at failure for dilative soils implying that in situ shear wave velocity measure-ments may be used to estimate eŠective stress strength parameters or as a precursor to failure in weakly cemented soils.

Key words: cement degradation, cemented sands, shear wave velocity, small strain shear modulus, triaxial compres-sion, vertical stress at failure (IGC: D6/D7/D10)

INTRODUCTION

The assessment of the drained shear strength of soils isnecessary for the analysis of a number of geotechnicalproblems including bearing capacity, slope stability, andthe evaluation of lateral earth pressures. The drainedstrength is generally applicable when the rate of loading isslow relative to the soils‘ability to dissipate excess porewater pressures that are generated during shear, or whensu‹cient time has been allowed for the soil to dissipateexcess pore water pressures. In some cases the critical de-sign condition exists under drained conditions, and there-fore the ability to design safe and cost-eŠective structuresand earthworks depends on an accurate prediction of thedrained strength of soils.

Undisturbed sampling of cemented and other sensitivesoils is both expensive and extremely di‹cult. To over-come this di‹culty, the strength and mechanical behaviorof such soils is often obtained using in situ methods, in-cluding penetration tests (e.g., Standard Penetration

Test, Cone Penetration Test) and shear wave velocitymeasurements. Shear wave velocity tests are increasinglybeing used to assess a wider range of soil properties in-cluding strength. The shear wave velocity (vs) is theoreti-cally related to the shear modulus and therefore is a directmeasurement of the small strain shear modulus (Gmax).For this reason, shear wave velocity is commonly used inengineering practice to obtain stiŠness properties forearthquake site response analyses (Kramer, 1996).However, shear wave velocity has also been correlated tolarge strain properties such as undrained shear strength inclays and cyclic strength in sands (Andrus and Stokoe,2000) with success. Unlike the SPT or CPT the major ad-vantage of using the shear wave velocity measurement isthat it is non-destructive, i.e., it does not alter the proper-ties of the soil during testing.

The small strain shear modulus (Gmax) is an importantelastic parameter and is being used increasingly in theanalysis and design of geotechnical structures (e.g., Tat-suoka et. al., 1994; Yun and Santamarina, 2005). Gmax is

762

Fig. 1. Grain size distribution of the tested soil

762 SHARMA ET AL.

calculated from the shear wave velocity using the follow-ing relationship:

Gmax＝rv2s (1)

where r is the mass density and vs is the shear wave veloc-ity. Gmax, and thus vs, is known to be a function of severalparameters including eŠective conˆning stress, void ratio(Hardin and Richart, 1963; Hardin and Drnevich, 1972),cement content (Acar and El-Tahir, 1986) and stressanisotropy (Roesler, 1979).

In order to evaluate strength and deformations in theˆeld during loading, the eŠect of shear stress on the smallstrain shear modulus has been studied by many resear-chers for various soil types with contradictory ˆndings.For granular soils, Yu and Richart (1984) and Tatsuoka(1985) showed that the small strain shear modulusdecreases with increasing shear stresses for principaleŠective stress ratios (s?1/s?3) greater than 3. For clayeysoils, Rampello et al. (1997) reported that the modulus(and likewise the shear wave velocity) is dependent on thedeviator stress ratio (q/p?) whereas Teachavorasinskunand Akkarakun (2004) reported that deviator stress hadno eŠect on vs for normally consolidated clay loaded un-der undrained conditions but had a signiˆcant eŠect onoverconsolidated clay.

Recently, Hoque and Tatsuoka (2004) showed thatsmall strain elastic stiŠness, E (Young's modulus, whichis theoretically related to Gmax through Poisson's ratio),measured from local strain measurements during triaxialshear, in a given direction is a function of the principaleŠective stress in that direction, and is independent ofstress path. They found that the elastic stiŠness of agranular soil increases under applied shear stress until theprincipal stress ratio reaches a value of 3–4; beyond thisratio, stiŠness decreases signiˆcantly due to plastic defor-mation. Yun and Santamarina (2005) studied the eŠect ofstress state on small strain shear modulus of cementedsands during 1-D consolidation. They concluded that forcemented sands in a contractive state, a stiŠness reduc-tion occurs at relatively low strain levels (0.002–0.004)due to decementation, and beyond this level, the stiŠnessincreases with vertical eŠective stress and then convergeswith the trend of uncemented soils. For dilative cementedsoils, however, they did not observe a decrease in stiŠ-ness.

Kongsukprasert and Tatsuoka (2007) highlighted thatthe small strain stiŠness (Young's modulus) of cementedgravelly sand measured from the stress-strain relation-ship, using high precision local strain measurements, isin‰uenced by the visco-plastic strains at close proximityto peak stress state, strain amplitude, and strain rate. Infact they termed the small strain stiŠness thus obtained asquasi-elastic stiŠness.

Given the variability in the ˆndings of published stu-dies, the objective of this study was to evaluate therelationship between strength and small strain shearmodulus of a weakly cemented sand. To achieve this, 24isotropically consolidated drained triaxial compressiontests (CID) were performed on artiˆcially cemented sam-

ples of silty sand at three diŠerent densities (1.8 g/cm3,2.1 g/cm3 and 2.25 g/cm3), three eŠective conˆningstresses (50 kPa, 100 kPa, and 300 kPa) and four levels ofcement content (0.0z, 1.0z, 2.5z and 5.0z). OrdinaryPortland Cement (OPC) was used as the cementingagent. Shear wave velocity was measured within the triax-ial apparatus during the shear phase and the corre-sponding small strain shear modulus was calculated. Thisstudy suggests a potentially useful correlation betweensmall strain shear modulus and major principal stress atfailure. The degradation of small strain shear modulusduring shear is also analysed and reported.

EXPERIMENTAL PROGRAM

Soil TestedThe soil used in this study was blended from quartz

sand and non-plastic silt from Rhode Island, USA, and isclassiˆed as a silty sand (SM) according to the UniˆedSoil Classiˆcation System (USCS). The grain size distri-bution of the soil is shown in Fig. 1. Approximately 5zof the soil consists of clay-sized particles. The D50 of thesoil was found to be 0.074 mm and the uniformitycoe‹cient (Cu) and coe‹cient of curvature (Cc) were 20and 1.25 respectively. The speciˆc gravity (Gs) of the soilwas found to be 2.66.

Sample PreparationSamples used in this study were prepared using a modi-

ˆed moist tamping method (Ladd, 1978; Bradshaw andBaxter, 2007). A 3 kg hammer was used to tamp the soilin 5 layers within a cylindrical mold. Using the under-compaction procedure, the drop height of the hammerwas calculated for each layer to vary the energy applied toeach layer to achieve a uniform initial target densitythroughout the length of the sample. The uniformity wasevaluated by making local bulk density measurements at5 mm increments using a multi-sensor core logger(MSCL). The MSCL is often used in the oŠshore industryto obtain sediment properties that includes bulk density,P-wave velocity, magnetic susceptibility, and electricalresistivity (e.g., Schultheiss and Weaver, 1992). The bulkdensity of the soil was estimated by measuring the gammaradiation that penetrated through the samples, similar inprinciple to a nuclear density gage (Bradshaw and Baxter,2007). The average variation in the density of the tested

763

Fig. 2. Triaxial and shear wave measurement test setup

Fig. 3. Example of transmitted and received signals obtained duringthe shear phase of a CID triaxial compression test on a 2.1 g/cm3

bulk density and 2.5% OPC cemented sample. The received signalswere obtained at diŠerent eŠective stress levels from the start ofshear (top most signal) to the failure of sample (bottom most sig-nal)

Table 1. Testing matrix used in this study

Initial bulk density(g/cc)

z OPCcement content

Initial eŠectiveconˆning stress (kPa)

1.8 0, 1, 2.5, 5 100, 3001.8 5 502.1 0, 1, 2.5, 5 100, 3002.25 0, 1, 2.5, 5 100

763GMAX VS s?IF

samples was found to be less than 2z (0.04 g/cc). Thesamples were 5 cm in diameter and 10 cm in length.

Cemented samples were prepared by mixing a givenpercentage (by weight) of OPC with dry soil prior to theaddition of any water. Enough water was added to thesamples to hydrate the OPC (30z of the dry weight ofthe OPC ) and to achieve a molding water content of 8z,which corresponds to the optimum moisture content de-termined by the standard proctor method. After compac-tion, the cemented samples were kept in the mold at roomtemperature for a period of approximately 12 hours. Thesamples were then removed from the mold and cured for14 days at room temperature before they were tested. Themass of the sample was monitored every day during thecuring period, and it was found to decrease during theˆrst 4–5 days and then remained constant. At the time oftesting, the water content of the samples was typically lessthan 1z. Uncemented samples were tested soon aftercompaction. The densities reported herein refer to the ini-tial bulk density of the samples measured immediately af-ter the samples were compacted.

Triaxial Compression TestsTriaxial compression tests were performed using a fully

automated triaxial apparatus manufactured by the Ge-ocomp Corporation. All samples were fully saturatedprior to shearing by ˆrst ‰ushing the samples with carbondioxide, then inundating the samples with de-aired water.The back pressure was increased to 750 kPa while main-taining constant eŠective stress. For the cemented sam-ples, the back pressure was maintained for at least 12hours. This procedure ensured that a B-value of at least0.95 and 0.9 was achieved for uncemented and cementedsamples, respectively. The lower values of B for cementedsamples are due to the increased stiŠness of the soil skele-ton, and are consistent with values from the literature(Black and Lee, 1973; Schnaid et al., 2001; Karg andHaegeman, 2009). Following consolidation to the desiredeŠective stress, the samples were sheared at an axial strain(ea) rate of 0.005z/min under drained condition. A totalof 24 drained triaxial tests were conducted and the testingmatrix is shown in Table 1.

Shear Wave Velocity MeasurementsThe triaxial and shear wave measurement test setup is

illustrated in Fig. 2. The shear wave velocity of the sam-ples was measured continuously throughout the shearphase using torsional ring transducers mounted in the endcaps of the triaxial apparatus (Wang et al., 2006). Thesetransducers have been shown to yield the same shear wave

velocities as those obtained with bender elements(Nakagawa et al., 1996; Hanchar, 2006; Wang et al.,2006) and have an added beneˆt in that they do not pene-trate into the samples. In addition to the torsional trans-ducers, the shear wave velocity measurement system con-sisted of a Wavetek 500 MHz function generator, a Stan-ford Instrument pre-ampliˆer and a National Instru-ments data acquisition card (PCI-6110) interfaced with adesktop computer. A Matlab script was used to generatea single sine wave of 10 kHz frequency with a burstperiod of 0.1 s and peak-to-peak voltage of 20 V, trig-gered at every 5 minutes which corresponds to ¿0.025zaxial strain interval during shear. The received signal wasampliˆed before sampling at a frequency of 1 MHz.

The travel time was estimated from the ˆrst peak of thetransmitted and received signals. It has been shown thatthe interpretation of arrival time using the peak-to-peak

764

Fig. 4. Shear wave travel time versus eŠective vertical stress for brasssample

Fig. 5. Stress-dependent travel time correction for the presence ofporous stones

Fig. 6. Comparison of a test with porous stone correction and a testperformed without porous stones (Sample Speciˆcations: rb＝2.1g/cc, OPC＝0%, s?3＝300 kPa)

764 SHARMA ET AL.

method is truly valid if the frequency of the transmittedand received signals are almost same (i.e., non-dispersivematerials), and therefore this method yields a slightlylower estimate (¿3z) of shear wave velocity in soilscompared to zero crossing method (Yamashita et al.,2007; Jander, 2009). A typical waveform of transmittedand received signals is shown in Fig. 3. The shear wavevelocity was calculated using the instantaneous samplelength and the travel time. Appropriate corrections weremade for instrumental and analog ˆltering delays in theestimation of travel time (Fam and Santamarina, 1995;Sharma, 2010) and a correction for the use of porousstone during the test was also made as explained below.

Stress-dependent Travel Time Correction for thePresence of Porous Stones

Porous stones were used at the bottom and the top ofthe sample to facilitate saturation and consolidation ofthe samples which increased the travel distance of theshear wave and therefore aŠect the travel time and shearwave velocity (Fig. 2). Thus, a correction for the shearwaves travel time through the porous stones had to be in-cluded. Since shear wave velocity is a function of eŠectivestress, the correction also needed to be related to the ap-plied stresses. To derive this correction, a test was per-formed on a solid brass specimen. Brass is an isotropicmaterial which can withstand much higher stresses thanthe tested sand. The maximum vertical stress applied tothe sand was less than 3000 kPa, which is still in the elas-tic range for the brass. Therefore, the shear wave traveltime for the same brass specimen was practically constantfor this range of stresses. To measure the time delaycaused by the porous stones, tests were performed withand without the porous stones. The two data sets werematched for the same vertical eŠective stresses and thenplotted against the shear wave travel time as shown inFig. 4. The diŠerence between the two graphs is the timedelay caused by the porous stones.

This diŠerence in travel time for diŠerent values of ver-tical eŠective stress is shown in Fig. 5. A regression linewas ˆtted to the graph with a power law relationship toobtain an equation for the correction. The trend linematches the data quite well, as shown by a R2-value of0.9517. The resulting equation for the correction of thewave travel time for the porous stones is:

Dt＝249.2826 s1?－0.4262 for s?1Æ100 kPa (2)Dt＝37 for s?1º100 kPa (3)

where s?1 is the vertical eŠective stress and Dt is the timedelay due to the porous stones in micro seconds. Usingthis correction, the appropriate time diŠerence, Dt, wassubtracted from the measured travel times to obtain thecorrect shear wave velocity.

Figure 6 shows shear wave velocity measurements dur-ing shear for two identically prepared specimens. Theˆrst specimen was tested without porous stones and thesecond specimen was tested with porous stones and ana-lyzed with the porous stone travel time correction. Thegood agreement between the two tests conˆrms the

applicability of the correction.

Repeatability TestThe reproducibility of samples was evaluated based on

measurements of the Unconˆned Compressive Strength(UCS). UCS tests on cemented samples were conductedon three identically prepared samples prepared to an ini-tial bulk density of 1.8 g/cc, 2.1 g/cc, and 2.25 g/cc,cured for 13 days at room temperature and then soakedfor at least 24 hours to ensure saturation prior to testing.Uncemented samples were tested at the molding watercontent in order to avoid disintegration of samples by

765

Table 2. Average and standard deviation values of unconˆned com-pressive strength (UCS) based on three tests for each level of den-sity and cement content. Note: No UCS tests for 5% cement con-tent were conducted

Density [g/cm3] z cement Average UCS [kPa] std dev [kPa]

2.25 0 116 8

2.25 1 859 47

2.25 2.5 1807 83

2.1 0 201 12

2.1 1 411 29

2.1 2.5 1016 79

1.8 0 64 5

1.8 1 128 7

1.8 2.5 275 29

Fig. 7. Results for identically prepared samples (rb＝1.8 g/cm3, OPC＝5%, s?3＝50 kPa) illustrating the repeatability of test results. (Note: p?＝(s?1＋s?3)/2)

765GMAX VS s?IF

soaking. The average and standard deviation of UCSvalues thus obtained for 0, 1 and 2.5z cemented samplesare shown in Table 2. The low values of standard devia-tion (average coe‹cient of variation is ¿7z) for theUCS suggests that the sample preparation was highlyreproducible.

To check the repeatability of the tests with shear wavevelocity measurements, two identically prepared samples

were tested under the same conditions. The results forboth tests are shown in Fig. 7. The deviatoric stresses aswell as the measured shear wave velocities are almostidentical for both samples. The small strain shear modu-lus (Gmax) was calculated using Eq. (1), and the variationof bulk density due to volume change during shear wastaken into account. Values of Gmax diŠered by approxi-mately 10z (¿40 MPa) which may be practically negligi-ble considering the inherent variations in the cementedsamples, measurement techniques, etc. This variabilitywas consistent with the measured variation in unconˆnedcompressive strength shown in Table 2.

Figure 8 shows transmitted and received signals atdiŠerent mean eŠective stresses (p?＝s?1＋s?3)/2) for thesetwo samples. It can be seen that the signals are almostsimilar, which supports the assertion that the results arerepeatable and that the sample preparation methodologyyielded similar samples.

DRAINED BEHAVIOR OF CEMENTED SANDS

The results of eight drained triaxial tests with shearwave velocity measurements during shear on samples attwo diŠerent densities (1.8 g/cm3 and 2.1 g/cm3) areshown in Fig. 9. These are representative of the results ofall 24 tests. In all cases, the peak deviator stress increasedconsistently with increasing conˆning stress, density andcement content. The failure mechanism was relatively

766

Fig. 8. Signal traces for identically prepared samples (rb＝1.8 g/cc, OPC＝5%, s?3＝50 kPa) illustrating the repeatability of test results

766 SHARMA ET AL.

brittle (i.e., exhibited dilatant behavior) for all the sam-ples tested except for the 1.8 g/cc samples at low levels ofcement content (0z and 1z), which exhibited contrac-tive behavior ( see Fig. 9(a)). The volumetric strainresponse for the 22 dilative samples exhibited initial con-traction followed by signiˆcant dilation, and the amountof initial contraction increased with cement content for agiven density and conˆning stress. In general the ob-served behavior of these samples during drained shear isconsistent with other published results on cemented soils(e.g., Clough et al., 1981; Huang and Airey, 1998;Malandraki and Toll, 2001).

Figures 9(a) and (b) also show that the shear wave ve-locity, vs, and Gmax increased during shear to a peak valueand then it decreased gradually with strain. However, thisincrease in shear modulus was observed at principal stressratios varying from 2 to 21 with cement content levelsranging from 0–5z (Fig. 10), in contrast to principalstress ratios of 3–4 observed by Hoque and Tatsuoka(2004) for granular soils. The observation of increasingGmax with cement content, density and eŠective conˆningstress is consistent with other published results (e.g., Acarand El-Tahir, 1986; Chang and Woods, 1992; Huang andAirey, 1998).

Gmax as a Possible Indicator of DestructuringThe general behavior of both the deviator stress and

small strain shear modulus during shear shown in Fig. 9is illustrated in Fig. 11, which shows the relative positionsof the initial (Gmax, i) and maximum small strain shearmodulus (G*max) relative to the eŠective vertical stress atfailure (s?1f). EŠective vertical stress was plotted insteadof deviator stress or principal stress ratio to clearly showthat the shear wave velocity was in‰uenced by changes ins?1, as s?3 remained constant throughout shearing. Thisbehavior of increasing elastic stiŠness (or vs) with s?1 dur-ing triaxial compression is consistent with the ˆnding ofHoque and Tatsuoka (2004) who reported the same basedon local strain measurement. It should be noted that thestiŠness measurement obtained from wave propagationtechnique is essentially equal to the stiŠness measuredfrom stress-strain relationship, only if the stress condi-tions and the induced strain amplitude are same. Con-sidering the typical wave length of the signals used in thisstudy (¿40 cm) and the inherent in-homogeneity scale ofthe cemented soils, the stiŠness reported in our papermay be considered as an average stiŠness of the sample.

In 22 of the 24 tests (i.e., the dilative samples), thesmall strain shear modulus reached a clear peak prior tofull mobilization of the shear strength which is evident

767

Fig. 9. Typical results of CID triaxial tests with shear wave velocity measurements for weakly cemented sands. (a). Results for rb＝1.8 g/cc, s?3＝100 kPa. (b) Results for rb＝2.1 g/cc, s?3＝300 kPa

767GMAX VS s?IF

from the plot of axial strain at failure and axial strain atG*max (Fig. 12). It is clear that most of the points fall wellbelow the 459line, which indicates that G*max was mobi-lized prior to failure. The two exceptions that lie on the459line are low density, uncemented samples which ex-hibited contractive behavior. It is hypothesized that atG*max, which occurred at ¿2z axial strain, the cementbonds begin to break and further straining results in the

formation of shear bands. It can also be seen from Fig. 9,that at G*max, the volumetric strain transformed from con-traction to dilation, which is similar to the behaviorfound in dense sands including Toyoura sand (Kuwano etal., 2005). However, well developed shear planes werevisible only after the stress reached a peak value.

The authors hypothesize that this phenomenon is an in-dicator of bond breakage and destructuring in the sam-

768

Fig. 10. Variation of small strain shear modulus during shear withprincipal stress ratio

Fig. 11. Typical behavior observed in all dilative samples tested show-ing how small strain shear modulus ˆrst increased during shear to amaximum value prior to full mobilization of the shear strength.Figure 11 also identiˆes diŠerent notations used in this study fordeˆning Gmax at diŠerent stages during shear

Fig. 12. Comparison of axial strains at failure and G*max for all the 24tests. Note: For samples sheared at s?3＝300 kPa, the legendremains same as indicated above except a larger circle out scribedthe symbol

768 SHARMA ET AL.

ples. Similar ˆndings have been reported by Feda (1995)for naturally cemented clay specimens and Ayling et al.(1995) for porous rocks. However, this behavior is diŠer-ent from the behavior observed for Ko loading of weaklycemented sands by Yun and Santamarina (2005). UnderKo loading the stiŠness loss occurred before bond break-age, at relatively low strain levels (º0.004) and beyondthis strain levels stiŠness increased with vertical stress.

RELATIONSHIP BETWEEN Gmax AND s?1f

Figure 13 shows the relationship between small strainshear moduli at various stages during shear. Figure 13(a)shows the function between the initial small strain shearmodulus, Gmax, i, and the maximum small strain shearmodulus, G*max, for 24 samples of varying densities andcement content. Figure 13(b) shows a similar relationship

between the maximum small strain shear modulus, G*max,and the small strain shear modulus at failure, Gmax, f.

769

Fig. 13. Relationship between: (a) Gmax, i and G*max. Gmax, i (b) G*max andGmax, f. Gmax, f. (Refer Fig. 11 for deˆnitions and Fig. 12 for legendnote)

Fig. 14. Relationship between G*max and s?1f. This relationship was de-veloped using data from 3 levels of densities, 4 levels of cementcontent and 2 levels of eŠective conˆning stresses. (Refer Fig. 12for legend note)

769GMAX VS s?IF

These results show that the shear modulus increased by30z due to the applied load before signiˆcant cementdegradation; beyond this the modulus at failure decreasesto 80z of G*max as shown in Fig. 13(b). This suggests thatthe value of shear modulus is greater than the value ob-served at the isotropic conˆning stress until failure. Thisis consistent with recent ˆndings by LeBlanc et al (2010)who found that soil stiŠness increased during cyclic load-ing of model piles rather than decreasing with shear.

In addition, there was a strong relationship betweenthe initial small strain shear modulus (Gmax, i) and themajor principal eŠective stress at failure. Figure 14 showsthe relationships between G*max and s?1f. Figure 13(a) andFig. 14 result in the following equations:

G*max＝1.306 Gmax, i (4)s?1f＝0.004 G*max (5)

Combining the above two equations results in the follow-ing relationship between Gmax, i and s?1f:

Gmax, i/s?1f＝constant§190 (6)

The authors believe that the stiŠness measured fromthe wave propagation technique inherently captured thevisco-plastic strains if any, which might have occurredunder the application of shear stress/strain, as observedby Kongsukprasert and Tatsuoka (2007) in cementedgravelly sand. In other words, our proposed equationshave not explicitly addressed this issue but believe that itcaptured the large strain behavior (i.e., s?1f) to a certainextent (at least up to failure) as is evident from thestatistical ˆt of data.

Based on these ˆndings, the authors hypothesize thatthere may be a unique relationship between the initialsmall strain shear modulus and eŠective stresses at failure(i.e., Go/s?1f is constant) for a given dilative or structuredsoil. It would mean that in situ shear wave velocity mea-surements, for example from cross-hole or seismic conepenetration tests, could be used as an early warning sys-tem for the onset of failure in cemented, structured, orsensitive soils during staged construction of embank-ments and foundations. This idea is consistent with thework of Yun and Santamarina (2005), who showed in1-D consolidation tests on cemented sand that shear wavevelocity decreases (i.e., stiŠness loss occurs) with applica-tion of vertical stress and reaches the path of uncementedsand at higher stress levels. They indicated that this be-havior could be used as an indicator of collapse due to thebreaking of cement content bonds.

This concept of using small strain shear modulus or

770

Fig. 15. Results of a drained multistage triaxial test on weakly cemented sand (r＝2.1 g/cm3) in which shear wave velocity was used as a precursorto failure and the termination criterion for advancing to the next loading stage; (a.) the variation of shear wave velocity and deviator stress forintermediates stages (1–3) and the ˆnal stage (4) of loading; (b.) the variation of shear wave velocity with vertical eŠective stress for all stages ofloading suggests that for a given vertical eŠective stress the velocity varied within a narrow range of 5–6% indicating negligible amount of des-tructuring occurred during the intermediate loading stages (Sharma et al., 2011)

770 SHARMA ET AL.

shear wave velocity as a precursor to failure has alreadybeen utilized by the authors to develop a new methodolo-gy for drained multistage triaxial testing of weaklycemented sands (Sharma et al., 2011). Figure 15 showsthe results of four loading stages from a multistage teston sample cemented with 2.5z Ordinary Portland Ce-ment (OPC); the ˆrst three intermediate stages were ter-minated when the shear wave velocity reached a maxi-mum and before bond breakage occurred. Only thefourth stage was loaded to failure. This methodologyyielded eŠective stress strength parameters, f? and c?,that were in excellent agreement with the results of singlestage triaxial tests.

Another possible application of this concept would bethe estimation of eŠective stress strength parameters di-rectly from in situ shear wave velocity measurements.Given a known Gmax/s?1f ratio for particular soil (analo-gous to Su/s?v ratios for cohesive soils), the variation ofs?1f can be estimated with depth. Combined with esti-mated or measured values of horizontal eŠective stressesin the ˆeld, the eŠective stress strength parameters, f?and c?, can be estimated. This approach might be particu-larly useful for soils in which undisturbed sampling, suchas dense sands and silts or sensitive clays, is very di‹cult.

CONCLUSION

Small strain shear modulus calculated from the shearwave velocity has been a parameter of choice to assess theproperties (including strength) of soils, in particularcemented and other sensitive soils. The objective of thisstudy was to evaluate the relationship between strengthand small strain shear modulus of weakly cemented sand.To achieve this, 24 isotropically consolidated drainedtriaxial compression tests (CID) were performed on arti-

ˆcially cemented samples of silty sand at three diŠerentdensities, two eŠective conˆning stresses and four levelsof cement content. Shear wave velocity was measured wi-thin the triaxial apparatus during the shear phase and thecorresponding small strain shear modulus was calculated.

Results from this study shows that small strain shearmodulus reaches a peak value before fully mobilizing theshear strength. This phenomenon suggests that shearwave velocity could be used as an early warning systemfor the onset of failure in cemented, structured, or sensi-tive soils during staged construction of embankments andfoundations. Careful observation of Gmax at variousstages during shear showed that the cement and modulusdegradation can be represented by a simple index relatingGmax measured at diŠerent stages during shear, and it wasfound that the ratio of Gmax, i/s?1f was constant for all thedilative samples tested.

ACKNOWLEDGEMENTS

This research was supported by a grant from the Na-tional Science Foundation grant No. CMMI 1031135.

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