Dependencies of Shear Wave Velocity and Shear Modulus of Soil on Saturation

Yi Dong, A.M.ASCE1; and Ning Lu, F.ASCE2

Abstract: Shear wave propagation in soil is a physical phenomenon and has been used widely for monitoring and seismic property assessment in geotechnical engineering. Shear wave velocity Vs and small-strain shear modulus G0 are the key parameters in defining material response to various dynamic loadings. To date, the dependencies of Vs and G0 on saturation, especially in high suction range, are still not well understood because of the limited testing methodology and experimental evidence. In this study, the authors present a new laboratory instrumentation of measuring shear wave propagation in different types of unsaturated soils. Low relative humidity and water mist injection environment are used for measuring shear wave velocity under both drying and wetting conditions. Bender element technique was used to measure the shear wave responses. Step function was used as excitation, and determination of a first arrival time was identified and consistently used for all shear wave measurements. Shear wave evolution and the calculated Vs and G0 with varying volumetric water content under zero total stress condition along drying and wetting are presented. The effects of different soil–water regimes on the evolution of G0 are examined. It is found that Vs or G0 depends highly on soil types, saturation, and drying/wetting state. Parameter Vs or G0 is the lowest when a soil is saturated and the highest when it is dry—varying from tens of meters per second for Vs or a few megapascals for G0 at full saturation for all soils to up to 1,800 m=sofVs or 2 GPa of G0 in clayey soil at dry state. The variability of Vs or G0 on soil type becomes more pronounced as soil has more clayey materials. It is also identified that hydraulic hysteresis of Vs or G0 is prominent only in the capillary water retention regime for all types of soil. DOI: 10.1061/(ASCE)EM.1943-7889.0001147. © 2016 American Society of Civil Engineers. Author keywords: Shear wave velocity; Small-strain shear modulus; Unsaturated soils; Bender element; Water content.

Introduction angle, and K0 parameters (Joviči´c and Coop 1998; Zeng and Ni 1998; Salgado et al. 2000; Alramahi et al. 2007; Ng and Yung Small-strain shear modulus G0 provides valuable information on 2008). soil skeleton stiffness, which is a fundamental physical property However, the accessibility of a wide range of saturation or par- relevant to liquefaction assessment, dynamic ground response ticularly high suction range becomes the obstacle for most of the analysis, and deep soil-structure design in geotechnical engineering geotechnical experimentations for unsaturated soils. The axis trans- (e.g., Kramer 1996; Clayton 2011; Yang and Gu 2013). Various lation technique, which involves high air-entry ceramic stone, is methods exist for measuring the stiffness of soil at small strain, one common approach to control the suction integrated into triaxial including, e.g., resonant column technique (Mancuso et al. 2002; test (Alramahi et al. 2007; Ng et al. 2009; Sawangsuriya 2009; Youn et al. 2008) and bender element technique (Qian et al. 1991; Ghayoomi et al. 2011; Khosravi and McCartney 2012; Heitor et al. Marinho et al. 1995; Blewett et al. 2000; Inci et al. 2003; Lee and 2013; Oh and Vanapalli 2014), but it is limited to a long time du- Santamarina 2005; Leong et al. 2009). Resonant column test is a ration of equilibrium and capability limitation of highest suction. In widely used and reliable technique for measuring small-strain shear contrast, a remarkable volume change in expansive soil during dry- modulus, but it is limited by the compatibility with other geotech- ing or wetting also increases the difficulty in good control of the nical testing apparatus such as triaxial, direct shear, odometer testing sample. A recent study by Lu and Kaya (2013) provided a (Airey and Mohsin 2013), and its inherent electromotive force in- good solution to tackle such problems. A Drying Cake method was terference (Wang et al. 2003). Over the years, the bender element established to measure the soil cake deformation and elastic modu- technique, because of its small size and nondestructive nature, has lus, and then determine the suction stress characteristic curve and become more common and has been incorporated into various soil–water retention curve. Soils can be dried under a low relative geotechnical instrumentations, combining shear wave measure- humidity environment with equivalent hundreds of MPa of suction. ment with other soil property testing such as shear strength, friction Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. A zero-loading boundary condition frees the soils to deform without crack development. 1Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, In this study, we introduce a new system of measuring shear Colorado School of Mines, 1012 14th St., Golden, CO 80401 (correspond- wave propagation and small-strain shear modulus for sandy, silty, ing author). E-mail: [email protected] and clayey soils over a wide range of saturation up to hundreds of 2Professor, Dept. of Civil and Environmental Engineering, Colorado MPa in suction without external loading. Dry air evaporation and School of Mines, 1012 14th St., Golden, CO 80401. E-mail: ninglu@ water mist adsorption were employed to provide drying and wet- mines.edu ting conditions. Bender element technique was used, and the deter- Note. This manuscript was submitted on February 4, 2016; approved on May 25, 2016; published online on July 21, 2016. Discussion period mination of wave traveling time was identified for all shear wave open until December 21, 2016; separate discussions must be submitted measurements. Shear wave velocity and small-strain shear modulus for individual papers. This paper is part of the Journal of Engineering were then calculated for analysis of their dependencies on soil Mechanics, © ASCE, ISSN 0733-9399. moisture.

J. Eng. Mech., 04016083 Measurement of Shear Wave and Determination Table 1. Basic Properties of Tested Soils and the Classifications of G0 LL PL PI Number Soil USCS Porosity Gs (%) (%) (%) Experimental Setup 1 Esperance sand SP 0.419 2.65 ——— The entire system consists of two components: (1) an environmen- 2 Hopi silt SC 0.429 2.68 36.0 23.0 13.0 3 Bonny silt ML 0.417 2.65 25.0 21.0 4.0 tal chamber that provides controlled relative humidity for drying 4 BALT silt ML 0.458 2.72 27.4 21.7 5.8 and wetting, and a digital balance that connects to a computer and 5 Missouri clay — 0.490 2.67 ——— records the change of soil weight; and (2) sensors and signal ac- 6 Denver claystone CH 0.471 2.70 44.0 26.0 18.0 quisition system that monitor the shear wave transmitted though 7 Georgia kaolinite CH 0.522 2.66 118.0 45.0 73.0 the sample. Fig. 1 provides an illustrative scheme to demonstrate the setup and connections of the system. A cylinder with a top plate seated on a bottom plate forms a chamber containing soil samples. The chamber is lifted to a certain height for soil weight evaporation rate and reduces the local relative humidity gradient monitoring. Circular openings were cut on the bottom plate with between soil sample and its surrounding air. Throughout the evapo- slightly larger size than the sample diameter, so that soil samples ration drying process, the color of the entire soil cake surface can be placed exactly on the balance through the openings and be changed uniformly, which ensured that the thin soil cakes were installed inside the chamber without touching the bottom plate and dried under a relatively homogeneous distribution of water content. disturbing the weight monitoring. Lids with adjustable openings A very thin film of Vaseline (Unilever, Englewood Cliffs, New were designed on the top plate for accelerating or decelerating Jersey) grease was spread on the surface of the sample holding the natural evaporation speed for drying. A vapor diffusor con- plate to minimize the friction between soil sample and holding nected to a humidifier was set at the center of the bottom plate plate, and to prevent the soil cracking during drying or wetting. The and provided water mist injection for the wetting process. The experimental setup was maintained at a constant room temperature entire chamber allowed two soil samples under testing separately. (25 2°C). We took advantage of the low relative humidity of 31% For simplicity, Fig. 1 shows only half capacity of the sample (10%) in local room condition, which is equivalent to a total suc- configurations. tion of approximately 123–215 MPa, based on Kelvin’s equation A pair of bender elements with 2 mm tip length was put on the (e.g., Lu and Likos 2004). This can also be achieved by using top and bottom surface of the soil specimen, respectively. The sig- desiccants or injecting dry nitrogen gas. A digital balance with nal system consisted of an oscilloscope (Tektronix MDO3012, 0.01-g accuracy was used to monitor the water content, and to Beaverton, Oregon) with a built-in signal generator module calculate the water content of soil under drying or wetting. After (MDO3AFG) for signal emission and storage, and a digital filter drying, an adjustable humidifier was used to provide water mist (Krohn-Hite 3940, Brockton, Massachusetts) for signal condition- into the chamber to gradually wet the soil cakes. Low strength of ing. The signal flow started with the signal generator sending an the mist plume was injected to prevent water droplet condensation excitation to the sender (bottom bender element). Then the shear on the specimen for wetting. One measurement needed to be taken wave was transmitted through the soil, and the receiver (top bender approximately every 12–24 h, and the duration of a single test var- element) sensed shear wave. After that the received signal filtered ied from 7 to 16 days, depending on the soil type (Dong et al. 2016; off the noise and then recorded and displayed it on the oscilloscope. Dong and Lu (2016). The measurement of shear wave velocity was accomplished by Testing Procedure similar settings in previously published papers (Truong et al. 2011; Dong et el. 2016). Because of the unknown natural frequency of the In total, seven types of soil were tested. Table 1 lists the classifi- soil-sensor system, a 50-Hz step-function signal was selected as the cations and basic properties of the soils. These soils were chosen to excitation, because step function covers the entire frequency range represent a wide range of soil type, from sandy to silty, and clayey in a frequency domain. The excitation was emitted by the sending soils. All soils were remolded and prepared as soil cakes in a mold sensor, which generated a sudden pulse of vibration (50 times in a with diameter of 76.2 mm (3 in.), and approximately 20 mm thick- second). The excitation transmitted in the manner of shear wave ness. Soil cakes were immerged in de-aired water in a desiccator through the soil skeleton. The frequency of the shear wave depends with vacuum applied for sufficient time to be saturated (usually on the soil skeleton and stiffness of the bender element and its – approximately 1 2 days). After saturation, the soil samples were mounting system (Lee and Santamarina 2005). The tiny local vi- gently transferred into the environmental chamber for drying and bration was sensed and captured by the receiver bender element and then wetting. Adjusting the opening of the lid size controls the transferred into received signal, which was then filtered through 100-Hz high-pass, 50-kHz low-pass channels, with 20 dB of gain amplification for each. The signals were digitized at a 2.5 GHz Receiving Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. Digital filter sampling rate (100,000 data points). A stack of 256 signal- Top plate acquiring permits reduced the noncoherent noise. Bender Cylinder In the literature, different methods are used to determine the Soil elements Oscilloscope/Signal generator traveling time of the shear wave: first arrival, peak to peak, cross Bottom plate correlation, wavelet analysis, phase detection analysis, and other frequency domain methods (Cho and Santamarina 2001; Bonal Vapor diffuser Sending et al. 2012; Styler and Howie 2013). The first arrival under a step- Balance Base function excitation is considered the most reliable method to determine the travel time of shear wave over the distance. The shear-wave velocity Vs can be evaluated by dividing the known Fig. 1. Experimental setup for drying and wetting of the soil sample tip-to-tip distance between the two bender elements by the travel and peripheral instruments for sensors and signals time for the first arrival t:

J. Eng. Mech., 04016083 Time [ms]

Excitation -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

=0.49

Amplitude Response 0.48 0.46

-0.5 0 0.5 1 1.5 2 2.5 3 0.44 (a) Time [ms] 0.41 0.38 0.35 First arrival 87.4 0.31 0.27 ~ 200 µs (5 kHz) 0.24 Amplitude 0.20 0.16

0 100 200 300 400 500 0.14 (b) Time [ s] 0.01

Fig. 2. Determination of first arrival of the shear wave: (a) signature (a) excitation and response of the bender element; (b) trail details in time window of approximately 0–500 μs 0.01 0.05 0.08 V ¼ðd =ΔtÞð1Þ s tt 0.10

where dtt = tip-to-tip distance between the sending and receiving 0.14 bender elements (assuming constant sample thickness as a result of 0.17 the negligible vertical deformation in a thin cake); and Δt = travel 0.21 time of the first arrival. Then the G0 values can be calculated using 0.24 2 2 G0 ¼ ρb · ðVsÞ ¼ ρb · ðdtt=ΔtÞ ð2Þ 0.28 where ρb = bulk density of soil. Specifically, Fig. 2 presents a 0.33 typical shear wave signature of one single measurement. Fig. 2(a) 0.38 shows the typical shear wave response under a step-function excitation, including the first major event of transmitted shear wave (b) – response in approximately 0 0.4 ms, and a second event of 300 reflected shear wave response in approximately 0.7–1.3 ms. The Missouri clay-drying received signal was magnified by a digital filter; therefore, the 250 Missouri clay-wetting amplitude is not on the real scale. A zoomed-in time window in Fig. 2(b) clearly shows the features of the first event, in which the 200 start of first negative deflection occurred at approximately 40 μs, 150 the first negative bump maximum at approximately 70 μs, zero after the first bump at approximately 90 μs, and first major peak 100 at approximately 125 μs. The zero recovered after first bump was 50 chosen to be the first arrival of shear wave propagation. In this μ example, the travel time was determined as 87.4 s. The major peak time [µs] travelling arrival First 0 Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. lasted approximately 200 μs, which is inconsistent with the result 0 0.1 0.2 0.3 0.4 0.5 0.6 of the fast Fourier transfer of the received signal, whose primary Volumetric water content frequency is approximately 5 kHz. (c)

Fig. 3. Typical shear wave evolution during (a) drying; (b) wetting; Results (c) time of first arrival for both drying and wetting

Wave Signature and Evolution evolution (Missouri clay) as the water content decreases under After completing one cycle of drying and wetting, the received drying, and increases afterward under wetting. Fig. 3(c) gathers signals for soil cake specimen can be collected at different water all wave traveling times of first arrival and plots its relationships contents. Figs. 3(a and b) show an example of typical shear wave with volumetric water content for both drying and wetting. In this

J. Eng. Mech., 04016083 2000 case, when the soil sample started to dry at full saturation, the first Esperance sand arrival was relatively far away from the excitation at time zero Hopi silt Bonny silt (approximately 281.8 μs), and the amplitude was very small. This 1600 BALT silt also indicates that the soil is very soft under zero total stress and in Denver claystone a full-saturation condition at water content θ ¼ 0.49. As the soil Missouri clay 1200 desaturates, the major peak starts to become prominent with higher Georgia kaolinite amplitude. In addition, the related time response turns are significantly compacted, reflecting the velocity increases and wave front 800 moving closer toward the time zero of excitation: 179.4 and 122.6 μs of the first arrivals at θ ¼ 0.48 and 0.46, respectively. 400 As the soil continues to dry, the major peak gradually moves [m/s] velocity wave Shear close to time zero of the excitation and the amplitude reaches a maximum amplitude of approximately θ ¼ 0.41, then stays at the 0 same order of magnitude but slightly decreases. At the end of 0 0.1 0.2 0.3 0.4 0.5 drying at θ ¼ 0.01, the major peak of the first wave front moves (a) Volumetric water content very close to the time zero of excitation, indicating a very fast shear 2000 wave velocity compared with that under the higher water content Esperance sand conditions. The amplitude decreases but is still discernible. After Hopi silt Bonny silt 1600 the major peak of the first event, the succeeding events such as the BALT silt second or even third arrival of the reflected shear wave—or the Denver claystone reflected p-waves by the boundary—can be identified on the trail Missouri clay 1200 of the responsive signal, because of the significantly increased soil Georgia kaolinite stiffness and propagating velocity. Therefore, more signal undula- tion can be identified on the trail in the range of approximately 800 0–0.50 ms. During the wetting process, the trend of responsive signal varia- 400 tion is reversed. As the water content increases from 0.01 to 0.10, [m/s] velocity wave Shear the reactive range signal fluctuation slightly decreases from approximately 0–0.50 to 0–0.40 ms. The composition of the multievent 0 response at θ ¼ 0.01 gradually evolves into a single major-event 0 0.1 0.2 0.3 0.4 0.5 response at θ ¼ 0.14, with a prominent major peak and a first (b) Volumetric water content – arrival in the range of approximately 0 0.15 ms and subtle re- Fig. 4. Measured shear wave velocity for selected soils under sponse of other events in the coda wave range of approximately (a) drying; (b) wetting 0.15–0.35 ms. As the water content continues to increase from θ ¼ 0.14 to 0.28, the major peak becomes dominant over the others, and the first arrival time gradually increases. During the final stage of wetting at water content 0.33 and 0.38, the major peak on the re- 1994; Sorensen et al. 2010). As the soil dries and starts to form an sponse signal starts to decay, as a result of the increased amount of air–water interface (around the water content of air entry), the shear water and soil softening. At the end of wetting at water content wave velocity has a sharp increase (e.g., Hopi silt, Missouri clay, 0.38, the signal almost recovers back to the same response signal Georgia kaolinite). When the water content is in the range of ap- at water content 0.49 of drying, but with a shorter traveling time of proximately 0.15–0.35, the shear wave velocity gradually increases the first arrival, which is considered caused by the effect of hyste- with a mild rate as the water content decreases. At the end of the resis of the capillary water, and is consistent with some previous drying stage, the shear wave velocity again significantly increases observations (Ng et al. 2009; Khosravi and McCartney 2012). and reaches the maximum values as the soil sample dries from a In Fig. 3(c), the quantitative curves clearly illustrate the varia- water content of 0.15 to 0.01. The maximum shear wave velocity tion of traveling time evolving with volumetric water content and varies from 179.2 m=s (Esperance sand) to 1,793.1 m=s (Missouri its dependency on drying or wetting paths. The step-wise charac- clay), depending on the soil type. teristics on curves of the first arrival time as the water content Under the wetting condition, the shear wave velocity decreases decreases under drying or increases under wetting indicates that in a similar pattern as its counterpart under drying. As the water different mechanisms are controlling throughout the entire soil– content increases from room-dried condition to medium degree of water regimes. The first arrival times of wetting path returns back saturation in the capillary water regime (approximately 0.3–0.4 of along the same track of drying path until the end of the first bump as water content), the shear wave velocity of wetting is equal or less

Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. the water content increases (at θ ¼ 0.33). Then, the first arrival time than that of drying. As the wetting continues to full saturation, the starts to increase significantly and deviates from the first arrivals of shear wave velocity of wetting is lower than that of drying, because drying, which suggests a hysteresis of wave propagation caused by of the effect of the capillary water hysteresis. the capillary water. Followed by the determination of traveling times of shear waves for seven soils at different water contents, shear wave velocities can G0 Variation with Water Content be calculated by Eq. (2) under both drying and wetting conditions, as shown in Fig. 4. As the water content decreases along the drying Given the shear wave velocity and bulk density of soil sample path, the shear wave velocity increases nonlinearly. When soils are at various water contents, the small-strain shear modulus can be saturated, the shear wave velocity varies from 24.4 m=s (Hopi soil) determined in terms of varying water content. Figs. 5–7 present to 72.1 m=s (Georgia kaolinite), depending on, e.g., the soil type the results of small-strain shear modulus evolution with volumetric and initial void ratio, and consolidation ratio. (Shibuya and Mitachi water content for seven tested soils. All results are categorized into

J. Eng. Mech., 04016083 10000 Esperance sand-drying Hopi silt-drying Esperance sand-wetting 10000 Hopi silt-wetting Georgia kaolinite-drying Georgia kaolinite-wetting 1000 1000

100 100

10 10 Small-strain shear modulus [MPa] Small-strain shear modulus Small-strain shear modulus [MPa] modulus Small-strain shear 1 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 Volumetric water content (a) Volumetric water content

Fig. 5. Small-strain shear modulus under drying and wetting for 10000 Bonny silt-drying Esperance sand and Georgia kaolinite Bonny silt-wetting

1000

three groups to demonstrate the dependency of G0 on water content. 100 The small-strain shear modulus of Esperance sand and Georgia kaolinite were presented in Fig. 5. Although Georgia kaolinite is classified as clay, it has a very similar pattern of small-strain shear 10 modulus development with water content as Esperance sand does, except that kaolinite has almost two orders of magnitude higher G [MPa] Small-strain shear modulus values of 0 than those of sand. Starting with drying from full 1 saturation to air entry (e.g., approximately 0.52–0.4 for kaolinite 0 0.1 0.2 0.3 0.4 0.5 and 0.42–0.38 for sand), G0 increases prominently: G0 increases (b) Volumetric water content from approximately 3 to approximately 12 MPa as θ decreases 10000 from 0.42 to 0.38 for Esperance sand; and G0 increases from 9 BALT silt-drying to 455 MPa as θ decreases from 0.52 to 0.40 for Georgia kaolinite. BALT silt-wetting G In the medium range of water content, 0 keeps a more or less 1000 constant magnitude: G0 stays at approximately 13 MPa for Esperance sand as the water content decreases from 0.35 to 0.13; G – 0 increases up to approximately 1,500 1,700 MPa and keeps 100 constant as the water content decreases from 0.35 to 0.04. In the low water content range, G0 has an obvious abrupt jump as the G soils reach the dry end: 0 increases up to 57 MPa for Esperance 10 sand at θ ¼ 0.013 and to 3,572 MPa for Georgia kaolinite at θ ¼ 0.034. For Esperance sand, a succeeding little drop of G0 Small-strain shear modulus [MPa] modulus Small-strain shear from 57 to 50 MPa as the sample drying from 0.03 to 0.01 was 1 observed. This has been considered the effect of snap-off of the 0 0.1 0.2 0.3 0.4 0.5 pendular liquid bridge at particle contacts (Cho and Santamarina (c) Volumetric water content 2001). The evolution of G0 under wetting for these two soils Fig. 6. Small-strain shear modulus under drying and wetting for basically follows the same pattern but with lower values than dry- (a) Hopi silt; (b) Bonny silt; (c) BALT silt ing, implying that a hysteresis exists on G0 evolution of this group of soils during drying and wetting. For silty and clayey soil, the results are presented in Figs. 6 and 7. Three silty soils have similar developments of small-strain 288 to 309 MPa as the water content changes from 0.04 to 0.01 for shear modulus along the drying and wetting paths. When soil starts Hopi silt; and G0 increases from 478 to 487 MPa as the water

Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. to desaturate, G0 increases around the air entry, similar to how sand content changes from 0.03 to 0.02 for BALT silt. or kaolinite does in Fig. 5. However, in the medium range of water The changed slope or increasing rate of G0 indicates that soils content in drying, instead of keeping constant such as sand or are crossing over the boundary of different soil–water regimes. kaolinite, G0 still gradually increases: G0 increases from 27 to Comparing these three soils, Hopi silt classified as clayey sand 99 MPa as θ decreases from 0.40 to 0.10 for Hopi silt, G0 increases (SC) has relatively small variation of G0 over the entire range of from 21 to 281 MPa as θ decreases from 0.41 to 0.08 for Bay Area water content (approximately 27–309 MPa), whereas the other two Landslide Tasks (BALT) silt, and G0 increases from 57 to 404 MPa silty soils (ML) have large variability in G0 for soils from wet to as θ decreases from 0.37 to 0.14 for Bonny silt. In the transition dry (approximately 21–487 MPa for BALT silt and approximately from medium water content range to low water content range, the 30–1,072 MPa for Bonny silt). Additionally, Hopi silt has a similar trajectory of G0 development changes slightly. As the soil contin- plateau on G0 in the medium range of water content from 0.2 to ues to dry, G0 increases slower in the low water content range than 0.4, which resembles the behavior of Esperance sand and Georgia in the medium water content range. For instance, G0 increases from kaolinite in Fig. 5. This observation suggests that silty soil with

J. Eng. Mech., 04016083 10000 1E+6 Missouri clay-drying Bonny silt SWRC Missouri clay-wetting Hopi silt SWRC 1E+5 1000 Claystone SWRC 1E+4

100 1E+3

1E+2 10

Matric suction [kPa] Matric suction 1E+1 Small-strain shear modulus [MPa] Small-strain shear modulus 1 1E+0 Adsorption water of 0 0.1 0.2 0.3 0.4 0.5 Bonny, Hopi, Claystone (a) Volumetric water content 1E-1 10000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Denver claystone-drying Volumetric water content Denver claystone-wetting Fig. 8. Soil–water retention curves and adsorption water contribution 1000 for Bonny silt, Hopi silt, and Denver claystone (data from Dong et al. 2016) 100

1,800 meters per second at dry conditions (e.g., Bonny silt, Denver 10 claystone, Missouri clay, Georgia kaolinite). The same trends apply to the G0 evolution with varying water content: (1) a wide range of G Small-strain shear modulus [MPa] Small-strain shear modulus variability of 0 for unsaturated soils from full saturation to dry 1 state depending on soil type; (2) different types of soil developing 0 0.1 0.2 0.3 0.4 0.5 diverse maximum G0 values at dry condition; (3) a nonlinear two- (b) Volumetric water content stage development of G0 over the entire range of saturation; and Fig. 7. Small-strain shear modulus under drying and wetting for (4) hysteresis of G0 primarily in medium and high water content (a) Missouri clay; (b) Denver claystone range. These features or variability characteristics suggest that the Vs or G0 evolution has different principles playing the roles throughout the entire range of saturation. Meanwhile, recent advancements in understanding soil–water higher fine content can develop higher G0 variation between dry retention behavior allow for better interpretation of the mechanisms and saturated states than sandy soil. behind those observations. Fig. 8 presents some typical soil–water The G0 developments for two types of clay under drying and retention curves by the Lu model (Lu 2016), which distinguishes wetting are presented in Fig. 7. Missouri clay clearly shows a different soil–water regimes based on their distinct soil–water in- second bump in the low water content range (approximately teraction mechanisms. Capillary water interaction primarily domi- 0.01–0.15) with a decreasing slope of the curve, in addition to the nates in the medium and high range of water content induced by first bump around the air entry, as the soil dries from full saturation. surface tension of the air–water interfaces. Moreover, the adsorp- The overall variation of G0 developed from saturated to dry for tion water interaction primarily governs in the low water content clay is even larger than silty soils shown in Fig. 6. Missouri clay range because of van der Waals or Coulomb forces of particle sur- and Denver claystone reach their maximum G0 of 1,793 and faces or exchangeable cations. These two soil–water regimes can 1,788 MPa, respectively. In addition, the G0 development under now be separated quantitatively by some recent soil–water reten- wetting condition follows the same curve in the low water content tion curve models (e.g., Lebeau and Konrad 2010; Revil and Lu range as the G0 development of drying. As the water content in- 2013; Lu 2016). In Fig. 8, three types of soils (Bonny silt, Hopi creases to high water content range, the G0 decreases faster, so that silt, and Claystone) with increasing amounts of maximum adsorp- G0 values of wetting are always lower than those of drying at high tion water content quantitatively determine the boundaries of water content. adsorption water interaction. Between zero and maximum adsorption water content, the adsorption water governs with capillary co-

Downloaded from ascelibrary.org by Colorado School of Mines on 07/25/16. Copyright ASCE. For personal use only; all rights reserved. existing, and beyond that limit capillarity dominates the soil–water Analysis and Discussion interaction. Furthermore, a conceptual model of the representative elemen- Generally, the S-shape nonlinear development of shear wave veloc- tary volume has been proposed (Dong et al. 2016) by applying the ity has the inverse correlation with water content: high velocity at concept of different soil–water regimes to link the stiffness property low water content and low velocity at high water content. Sandy with the hydrological property of soil–water retention, and to ex- soil has a relatively small increment on shear wave velocity from plain the mechanisms of the shear modulus dependency on water saturation to dry state (e.g., from tens of meters per second to up content for unsaturated soils. As shown in Fig. 9, the stiffness or to few hundreds of meters per second for Esperance sand, Hopi shear modulus of unsaturated soils is considered to consist of two silt, and BALT silt). For soil containing more fine content or clayey parts: the stiffness of material components in soil matrix or particle soil, however, the shear wave velocity can increase two orders of cluster (primarily responsive for the adsorption water), and the magnitude from tens of meters per second at saturation to up to effect of interparticle contact force (primarily responsive for the

J. Eng. Mech., 04016083 Contact force/ suction stress wave propagation velocity, as the water content varies under the zero total stress conditions. The measured shear wave velocity Soil matrix or changes greatly with the water content, and it varies significantly particle cluster from tens to hundreds of meters per second, or even up to a few Capillary water thousands of meters per second, as soils change from fully wet to Soil water at contacts dry. The maximum shear wave velocity of soil at dry state also hydration around alters greatly from a few hundreds of meters per second up to (a)and within the (b) 1,800 = particles m s, depending on the soil types. The small-strain shear moduli for seven soils at different water contents were determined Fig. 9. Conceptual mechanisms of contributions of capillary and along both drying and wetting paths. It is demonstrated that sandy adsorption water to small-strain shear modulus (reprinted from Dong soil has relatively small variation on G0 over the saturation, et al. 2016, © ASCE): (a) adsorption water regime; (b) capillary water whereas silty or clayey soil can develop hundreds of megapascals regime or even a few gigapascals on G0 when soil is complete dry. The Lu soil–water retention model, capable of separating the adsorption and capillary water regimes, provides insightful interpretation on the evolution characteristics of G0 with varying water capillary water). The first-part contribution to the shear modulus content. The particle-scale conceptual model based on different has been found in a power law in terms of the inverse of degree mechanisms for different soil–water regimes was employed to ex- of saturation (Lu and Kaya 2014); the second part can be repre- plain the step-wise nonlinear evolution of G0 along both drying – sented using suction stress concept and be correlated to soil water and wetting paths. In the capillary water regime, G0 keeps almost retention (Dong and Lu 2016). constant except the initial variation around the air entry, because of G Therefore, the observations of 0 development obey the same the formation of the air–water interface. Unlikely, G0 has a separate – principle of the separation of soil water regimes. As such, different nonlinear relationship with the adsorption water, in which G0 in- G – 0 development patterns indicate different soil water interaction creases with reducing water content. G0 of the adsorption regime mechanisms. Specifically, Esperance sand and Georgia kaolinite superimposes with the capillary water contribution on G0 and demonstrate a good example for G0 development primarily in the forms another bump on the curves. In the adsorption water regime, capillary water regime. Esperance sand has little fine soil content, the G0 of drying and wetting are more or less identical, whereas in and kaolinite is nonexpansive soil with only particle-surface hy- the capillary regime the G0 of wetting is always smaller than that of dration at very low water content or suction (Lu and Khorshidi drying. Therefore, the hydraulic hysteresis of G0 was found to be 2015). Hence, in the medium and high range of water content prominent in the capillary water rather than the adsorption water. (e.g., θ > 0.05), G0 shows a typical development in the capillary water as the water content varies (Fig. 5): an initial increment of G0 G around air entry followed by a barely changed plateau of 0 as soil Acknowledgments dries, and G0 of wetting always lower than G0 of drying. This feature can also be found in clayey sand Hopi silt in θ > 0.20 in This research is supported by a grant from the National Science Fig. 6(a). The G0 magnitude of Georgia kaolinite is approximately Foundation (NSF CMMI-1230544). two orders higher, because of the much smaller particle size and thus stronger capillary effect. In low water content range θ > 0 05 ( . ), Esperance sand and kaolinite have little increment of References G0 because of the gradual formation of isolated pendular liquid bridge at particle contacts. In contrast, in the medium and low water Airey, D., and Mohsin, A. K. M. (2013). “Evaluation of shear wave velocity content range, three silty soils and two expansive clays (Figs. 6 from bender elements using cross-correlation.” Geotech. Test. J., 36(4), and 7) clearly illustrate that another type of G0 evolution in the 1–9. adsorption water regime complies with the other mechanism. G0 Alramahi, B., Dante, F., Khalid, A. A., and Stephen, T. (2007). “A suction- gradually increases with a decreasing rate as the soil dries. There- control apparatus for the measurement of P and S-wave velocity in ” – fore, the G0 curve forms another bump in the range in which the soils. Geotech. Test. J., 31(1), 266 275. capillary water gradually diminishes, whereas the adsorption water Blewett, J., Blewett, I. J., and Woodward, P. K. (2000). “Phase and ampli- takes over the dominancy. 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