Canadian Geotechnical Journal. Dynamic modulus characteristics of saturated clays under variable confining pressure

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1 Dynamic modulus characteristics of saturated clays under variable confining ressure Journal: Canadian Geotechnical Journal Manuscrit ID cgj r1 Manuscrit Tye: Note Date Submitted by the Author: 23-Nov-216 Comlete List of Authors: Gu, Chuan; Wenzhou University, College of Civil Engineering and Architecture Gu, Zhiqiang; Wenzhou University, College of Civil Engineering and Architecture Cai, Yuanqiang; Zhejiang University, Wang, Jun; Wenzhou University, College of Architecture and Civil Engineering Ling, Dao-Sheng; Zhejiang University, College of Civil Engineering and Architecture Keyword: Shear modulus, Dynamic roerties, Cyclic confining ressure, Triaxial tests, Clays

2 Page 1 of 3 Canadian Geotechnical Journal Dynamic modulus characteristics of saturated clays under variable confining ressure Chuan Gu 1, Zhiqiang Gu 2, Yuanqiang Cai 3, Jun Wang 4 *, Daosheng Ling 5 1 Associate Professor, College of Civil Engineering and Architecture, Wenzhou University, Wenzhou 32535, P.R. China. single_k@163.com 2 Master student, College of Civil Engineering and Architecture, Wenzhou University, Wenzhou 32535, P.R. China @qq.com 3 Professor, Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 3158, P.R. China. caiyq@zju.edu.cn 4 Professor, College of Civil Engineering and Architecture, Wenzhou University, Wenzhou 32535, P.R. China. cleg198628@163.com (corresonding author), Tel: , Fax: Professor, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 3158, P.R. China. dsling@zju.eud.cn 1

3 Page 2 of 3 Abstract: Dynamic loadings, induced by earthquakes and other causes, will lead to the cyclic variation of both shear stress and normal stress comonents on the soil elements. A series of cyclic triaxial tests with and without variable confining ressure were carried out to investigate the couling effects of cyclic shear stress and cyclic normal stress on the G/G max characteristics of saturated clays. Results indicated that both the hase differences and ratios between the cyclic deviatoric stress and cyclic confining ressure exerted a constant and ronounced influence on the G/G max, indicating that the G/G max roerties under combined loadings will be more reresentative of actual field conditions than from single-loading conditions. A modified hyerbolic model considering the effects of cyclic confining ressure was further roosed. Key words: Shear modulus; Dynamic roerties; Cyclic confining ressure; Triaxial tests; Clays 2

4 Page 3 of 3 Canadian Geotechnical Journal Introduction Water-saturated, fine-grained soil deosits can be subjected to undrained cyclic loads induced by earthquakes, ile driving, exlosions, ocean wave storms and other causes. The dynamic resonse under such loads deends to a large extent on the cyclic stress-strain characteristics of the soil in shear. Relationshis between the secant shear modulus G and the cyclic shear strain amlitude γ, tyically exressed as a curve of G/G max versus γ, are usually emloyed to show the modulus characteristics of soils at moderate to high strains under cyclic loadings. Substantial research has been undertaken to elucidate the influence of soil tye, void ratio, the initial state of effective stresses, overconsolidation ratio, geologic age, degree of saturation, and grain characteristics on the G/G max characteristics of saturated soils (e.g., Hardin and Drnevich 1972b; Iwasaki et al. 1978; Kokusho et al. 1982; Seed et al. 1986; Vucetic 1988; Vucetic and Dobry 1991; Ishibashi and Zhang 1993; Rollins et al. 1998; Stokoe et al. 1999; Stokoe et al. 24; Zhang et al. 25). For examle, in their summary of the effects of different factors on G/G max with a secific focus on the lasticity index (PI), Vucetic and Dobry (1991) concluded that the PI correlates well with all imortant arameters and asects of the cyclic behavior. Similarly, Stokoe et al. (24) and Zhang et al. (25) argued that that the effect of PI on dynamic soil behavior was not as significant as reviously thought and suggested the confining stress and geologic age should be considered when selecting G/G max curves for design. However, none of these revious studies considered the couling of different dynamic stress comonents. 3

5 Page 4 of 3 Of the studies undertaken to study these coulings, Aggour and Zhang (26) indicated that dynamic loadings induced by earthquakes were comosed of very comlex combinations of various waves such as comressive waves and shear waves, among others. They then used a resonant column device to simulate the combinations of different seismic waves by the combined action of cyclic axial and shear strains. Results indicated a greater reduction of the modulus under combined loadings as oosed to a single excitation. As suggested by Gu et al. (212) and Qian et al (216), the combined roagation of comressive waves and shear waves would lead to the cyclic variation of both shear stress comonents and normal stress comonents on the soil elements. This combined action of cyclic shear stress and cyclic normal stress comonents can be simulated through the couling of cyclic deviatoric stress and cyclic confining ressure in cyclic triaxial tests with variable confining ressure (VCP tests). In comarison with the resonant column device emloyed by Aggour and Zhang (26), both stress controlled and dislacement controlled cyclic loadings are used in the VCP tests. It is also ossible to vary the ratios and hase differences between the cyclic deviatoric stress and cyclic confining ressure, to consider more comlicated conditions of the combinations of comressive and shear waves. It should be noted that although multi-directional simle shear tests have also been emloyed by some researchers (e.g., Kammerer et al. 22, 24; Rutherford 212) to simulate the multi-directional shaking due to earthquakes and other sources, there are many differences between the VCP tests and multi-directional simle shear tests. For examle, the multi-directional simle shear tests are mainly used to simulate the couling of different shear waves rather than the couling of comressive waves and shear waves. 4

6 Page 5 of 3 Canadian Geotechnical Journal While very few studies have been undertaken to elucidate the G/G max behavior of saturated soils under the couling of cyclic deviatoric stress and cyclic confining ressure, the influences of different static stress aths in -q lane (i.e., the couling of deviatoric stress and mean rincial stress) on the stress-strain resonses of saturated soils have been studied (e.g., Gasarre et al. 27, Cho and Finno 21; Finno and Cho 211). For examle, based uon their substantial testing of drained static stress aths on Chicago glacial clays over a wide strain range, Cho and Finno (21) observed that the secant shear and bulk moduli obtained at strain levels greater than.2% deended strongly uon the loading direction and strain level. Further, they also observed a decrease in the deendence of these moduli on the stress ath direction with an increasing strain for both the shearing and volumetric behaviors. It is seculated that the G/G max behavior of saturated soils under cyclic loadings may also be related to the dynamic stress aths in the -q lane. In this study, a series of stress-controlled and staged cyclic triaxial tests with and without variable confining ressure were conducted on two different remolded saturated clays, in which two hase differences and several ratios between the cyclic deviatoric stress and cyclic confining ressure were emloyed. Test results show that both the hase differences and ratios influence the G/G max characteristics greatly and regularly, imlying that the G/G max relationshis under combined loadings cannot be determined simly by conventional tests that only aly a single cyclic loading. A modified hyerbolic model considering the effects of cyclic confining ressure is therefore roosed. 5

7 Page 6 of 3 Test Aaratus, Test Materials and Exerimental Program The tests in this study were conducted using a combination device of a iezoelectric-ceramic bender element system and an advanced cyclic triaxial aaratus (Gu et al. 214), which was designed and manufactured by the GDS Cororation in Great Britain. The bender elements are set into the to and bottom latens of the triaxial cell. The advanced cyclic triaxial aaratus can control both the amlitudes of the cyclic deviator stress and cyclic confining ressure, and indeendent hase difference between the two. The vertical stress is alied by a servo-loading system, while the confining ressure is sulied through an oil ressure tye iston. The measurement of axial dislacement had an accuracy of aroximately.5 µm, resulting a strain accuracy of aroximately.5% at a height of 1 mm. To facilitate the investigation into the couling effects of cyclic deviator stress and cyclic confining ressure, the arameter η aml was introduced, using a rocedure develoed by Gu et al. (212) and Sun et al. (215). As shown in Fig. 1, q aml is the amlitude of cyclic deviator stress, aml and σ 3 is the amlitude of cyclic confining ressure. aml is the amlitude of cyclic mean rincial stress, which is calculated by aml = ( σ aml σ aml 3 ) / 3 = σ aml aml 3 + q / 3. η aml is defined as aml /q aml. In cyclic triaxial tests with constant confining ressure (CCP tests), η aml =1/3. In VCP tests, the two reresentative values of the hase angle θ, i.e., θ= and θ=18 were emloyed to study the influence of hase differences on the G/G max characteristics. aml aml aml aml aml aml When θ=, η = 1/ 3 + σ 3 / q, and when θ=18, η = 1/ 3 σ 3 / q. In Fig. 1, the inclinations of the stress aths in -q-lane signify the η aml values. 6

8 Page 7 of 3 Canadian Geotechnical Journal In order to remove the influences of initial soil fabric and overconsolidation on G/G max characteristics, remolded clays were selected as the test materials. The original clays used for the rearation of remolded samles were obtained from 6-9 meters beneath the ground surface, from two sites in Wenzhou city, which is in eastern coastal China and well-known for its soft clay deosits. The soft clays in Wenzhou city are mostly marine deosits and can reach a deth of 15 m. One site is in the camus of Wenzhou University and the other is close to the Oujiang River. In this study, the two clays are named WZU clay and WZO clay, resectively, the rimary hysical index roerties of which are summarized in Table 1. According to the USCS classification method, both the WZU and WZO clays are classified as CH. A standard routine samle rearation rocedure was emloyed to guarantee the consistency of the samle quality (Gu et al. 212 and Cai et al. 213). First, the original clay was dried in an oven and then ground to a owder followed by the rearation of a samle of clay slurry with water content equal to the liquid limit w L. After being mixed and de-aired thoroughly, the slurry was re-consolidated in a large consolidation vessel under a vertical ressure of 5 kpa for a month. Finally, cylindrical secimens with a diameter of 5 mm and a height of 1 mm were trimmed from the consolidated blocks and then mounted in the triaxial cell. Subsequently, a back ressure of 3 kpa with an effective stress of 1 kpa was alied, until B values greater than.97 were achieved. The secimens were then isotroically consolidated under selected effective confining ressures. After consolidation, the bender element test was first conducted to obtain the small-strain shear modulus G max. A combined action of cyclic deviator stress and cyclic confining ressure 7

9 Page 8 of 3 was then alied in stages. For each loading stage, 11 cycles were alied on the secimen under undrained conditions, followed by a eriod of ore-ressure equalization. The next 11 cycles with larger amlitudes of both cyclic deviatoric stress and cyclic confining ressure were then subsequently alied with the same arameter of η aml. This rocess was reeated until the cyclic axial strain amlitude reached aroximately 2%. The numbers of loading stages for all tests are set at 11. It should be noted that the amlitudes of cyclic loadings (including both cyclic deviatoric stress and cyclic confining ressure) at the same loading stage but among different secimens are varied to otimize according to the results of reliminary tests. Following a rocedure develoed by Tatsuoka et al. (21) and Yamada et al. (28), the dynamic roerties were calculated from the 1th cycle data of each loading stage. The detailed test rogram is summarized in Table 2, including 7 tests on WZU clay and 12 tests on WZO clay. Two values of effective confining ressure ( =1 kpa and 2 kpa) and seven values of η aml (η aml = 1/3, 1., 1.5, 2, -1., -1.5, and -2.) were emloyed. Tests were conducted at a low frequency of.1 Hz for WZU clay and.1 Hz for WZO clay, resectively. These slow loading frequencies were selected because of their lack of effect on the initial shear modulus (Shibuya et al. 1995) and can make the alication of cyclic confining ressure more accurate. 8

10 Page 9 of 3 Canadian Geotechnical Journal G/G max versus γ relationshis under variable confining ressure The time-history curves of cyclic deviatoric and cyclic confining ressure from three tyical tests are resented in Fig. 2a (WZO clay, =1 kpa, η aml =1/3) and Fig.4a (WZO clay, =1 kpa, η aml =1.5), Fig. 3a (WZO clay, =1 kpa, η aml =-1.5), resectively, while the hysteresis loos from the same three tests are shown in Fig. 2(b) and Fig. 3(b) and Fig. 4(b), resectively. Both the time-history curves and hysteresis loos include all loading cycles in every loading stage. The cyclic deviatoric stress and cyclic confining ressure were alied at the same hase (θ= ), the results of which are shown in Fig. 2(a). The condition of the oosite hase (θ=18 ) is shown in Fig. 4(a) and the constant confining ressure is shown in Fig. 3(a). Although there were no significant visible differences between the three hysteresis loos, the calculations based on the whole test data indicated that the ratio of the maximum comression strain to the maximum tension strain at the same loading cycle decreased gradually with an increase in η aml values. This decrease indicates that the tension strain is roduced faster than the comression strain does with an increase in η aml values. The mechanism resulting from this henomenon has been carefully elucidated by Gu et al. (212), which indicated that in the effective stress aths of tests under η aml >, the effective stresses in the tensile half cycle (i.e., q<) are lower than those in the comressive half cycle (i.e., q>), and this trend is reversed gradually when the η aml value is decreasing. In cyclic triaxial tests, the dynamic elastic modulus is determined by E=q/ε a, in which ε a is the amlitude of cyclic axial strain in a hysteresis loo and q is the amlitude of cyclic 9

11 Page 1 of 3 deviatoric stress corresonding to ε a. Considering that most studies on the dynamic secant modulus behavior used the arameters of shear modulus G and shear strain γ, E and ε a were transformed to G and γ for our uroses here. Further, as the Poisson ratio ν is.5 for saturated soils, the modulus is exressed as: E E G= = 2(1 + ν ) 3 (1) γ = (1 + ν ) ε = 1.5ε a (2) The reliminary tests indicated that the average densities ρ of samles after the consolidation under =1 kpa and 2 kpa were 1.72 g/cm 3 and 1.79 g/cm 3 for WZU clay and 1.74 g/cm 3 and 1.8 g/cm 3 for WZO clay, resectively. The results of the bender element tests showed that the average shear wave velocities V s under =1 kpa and 2 kpa were 97.2 m/s and m/s for WZU clay and 12.1 m/s and m/s for WZO clay, resectively. As the small-strain shear modulus G max can be calculated based on G = ρv, the average max 2 s G max under =1 kpa and 2 kpa was 16.3 MPa and 26.8 MPa for the WZU clay and 18.1 MPa and 32.4 MPa for the WZO clay, resectively. The G/G max versus γ relationshis for the WZU and WZO clays are shown in Figs. 5 and 6, resectively. Note the effects of cyclic confining ressure on the G/G max roerties in which the increase of η aml values causes a decrease in the G/G max curves. Comared to the results of CCP tests at the same shear strain, the couling of cyclic deviatoric stress and cyclic confining ressure at the same hase (i.e., θ= ) will reduce the G/G max values. This decrease will in turn exand with an increase in the ratios of the cyclic confining ressure amlitude to the cyclic 1

12 Page 11 of 3 Canadian Geotechnical Journal deviatoric stress amlitude. Conversely, for the VCP tests at the oosite hase (i.e., θ=18 ), the G/G max values increase gradually with an increase in the corresonding ratios. Take Fig. 6(a) as an examle (WZO clay, =1 kpa), the stress ath under η aml =2. and η aml =-2. delivers an aroximate -14% and +16% increment of the G/G max value, resectively, comared with that obtained in the CCP test (η aml =1/3). These results indicate that the G/G max relationshis under combined loadings, which are more reresentative of actual field conditions, cannot be determined simly by conventional tests that only aly a single loading. Within the strain range of aroximate.7% to 2% measured in this study, the differences of G/G max values between every two stress aths changed greatly with a variation of shear strains. At large shear strains, as the shear strain increases the change in the shear modulus reduction curve for different η aml values decreases, eventually becoming negligible. Gu et al. (212) indicated that although the couling of cyclic deviatoric stress and cyclic confining ressure has little effect on the residual excess ore water ressure of saturated clays, it has comlicated influences on the develoment of axial strain and the shaes of effective stress aths. The ratio of the maximum comression strain to maximum tension strain during a single loading cycle is also related to the cyclic confining ressure. It is seculated that all these changes of dynamic roerties under the couling of cyclic deviatoric stress and cyclic confining ressure may lead to the behavior of dynamic modulus. 11

13 Page 12 of 3 Hyerbolic model considering the effects of variable confining ressure Hyerbolic models, such as that develoed by Harden and Drnevich (1972a), have been used to describe the nonlinear soil behavior under cyclic loadings. In this articular model, a hyerbola asymtotic to the maximum shear stress is used to reresent the stress strain curve of the soil. Unfortunately, the single curve-fitting variable of this simle hyerbolic model makes it a oor fit for the test data. In this study, the authors used a hyerbolic model modified from rocedures develoed by Stokoe et al. (1999) and Zhang et al. (25) to fit the G/G max versus γ relationshis under cyclic confining ressure, which is exressed as: G G = 1 γ ) α γ max 1+ ( r (3) Unlike the reference strain used in the single curve fitting model develoed by Hardin and Drnevich (1972a), two curve-fitting variables are used here; γ r is the reference strain that corresonds to the shear strain when G/G max =.5, with α serving as the fitting arameter. The test data of both clays under =1 kpa was used to fit Eq. (3), while the test results under =2 kpa was used for the verification of the fitting equation. Multile regression was then used to determine the α values that rovide the closest fit to the comiled test data. Table 3 resents all of the γ r and α values, and shows that there is a general increase in the values of both γ r and α with a corresonding decrease in the η aml values. The comarison between the fitting curves based on Eq. (3) and the measured test data are shown in Fig. 7, in which Fig. 7(a) and Fig. 7(b) are the results of WZU clay and WZO clay, resectively. The values of γ r and α for every test and the values of adjusted R 2 for every fitting 12

14 Page 13 of 3 Canadian Geotechnical Journal curve are also lotted in the figures. It can be seen that almost all R 2 values are above.99, imlying that Eq. (3) can well reflect the influences of cyclic confining ressure on the G/G max characteristics, through varying α values. The increase of the η aml values causes a gradual decrease of the fitting curves. The relationshis between α and η aml for both clays are show in Fig. 8, indicating a linear relationshi between all of them regardless of different soil tyes and loading frequencies. This close correlation also clearly indicates a simle formula can be used to quantitatively exress the effects of cyclic confining ressure on the G/G max curves. These findings will be of use in elucidating and determining the G/G max characteristics of saturated soils under combined loadings. However, the limitations of the test data means that extensive research is still needed to determine the factors affecting the G/G max curves under variable confining ressures. The fitted linear equation is exressed as: aml α = η (4) The γ r and α values of the 7 tests under =2 kpa are resented in Table 4, in which all the α values are calculated by Eq. (4). A comarison between the test data and the rediction by Eq. (3), resented in Fig. 9, shows that the redicted results closely agree with the measured test data, articularly within the shear strain range of.1% to.5%. These results indicate a good rediction quality for the G/G max characteristics under the comlex stress aths of cyclic deviatoric stress and cyclic confining ressure. 13

15 Page 14 of 3 Conclusions In this study, a series of stress-controlled and staged cyclic triaxial tests both with and without variable confining ressure were conducted on two remolded saturated clays, to investigate the couling effects of cyclic deviator stress and cyclic confining ressure on the G/G max characteristics. The major conclusions from these tests are summarized as follows: (1) Both the hase differences and ratios in the couling of cyclic deviatoric stress and cyclic confining ressure had a ronounced and significant influence on the G/G max characteristics, imlying that conventional tests alone, which use only a single loading, are inadequate for determining the G/G max relationshis under combined loadings. (2) A roosed modified hyerbolic model considering the effects of cyclic confining ressure was used, in which the fitting arameter α was linear to the η aml. The modified hyerbolic model was also closely verified through the use of other test data. Acknowledgements The work was suorted the National Key Research and Develoment Program of China (No. 216YFC823), the National Natural Science Foundation of China (No ), the National Basic Research Program (973 Program) of China (No. 214CB475), and the Provincial Nature Science Foundation of Zhejiang (No. LY17E811). 14

16 Page 15 of 3 Canadian Geotechnical Journal References Aggour, M. S., and Zhang, J. X. 26. Degradation of Sands due to Combined Sinusoidal Loading. J. Geotech. Geoenviron. Eng., 132(12), Cai, Y. Q., Gu, C., Wang, J., Juang, C. H., Xu, C. J., and Hu, X. Q One-Way Cyclic Triaxial Behavior of Saturated Clay: Comarison between Constant and Variable Confining Pressure. J. Geotech. Geoenviron. Eng., 139(5), Cho, W., and Finno, R. J. 21. Stress-Strain Resonses of Block Samles of Comressible Chicago Glacial Clays. J. Geotech. Geoenviron. Eng., 136(1), Finno, R. J., and Cho, W Recent Stress-History Effects on Comressible Chicago Glacial Clays. J. Geotech. Geoenviron. Eng., 137(3), Gasarre, A., Nishimura, S., Minh, N. A., Coo, M. R., and Jardine, R. J. 27. The stiffness of natural London clay. Geotechnique, 571, Gu, C., Wang J., Cai, Y. Q., and Guo, L Influence of cyclic loading history on small strain shear modulus of saturated clays. Soil Dynamics and Earthquake Engineering, 66, Gu, C., Wang, J., Cai, Y. Q., Yang, Z. X., and Gao, Y. F Undrained cyclic triaxial behavior of saturated clays under variable confining ressure. Soil Dynamics and Earthquake Engineering, 4, Hardin, B. O., and Drnevich, V. P. 1972a. Shear modulus and daming in soils. J. Soil Mech. Found. Div., 98(7),

17 Page 16 of 3 Hardin, B. O., and Drnevich, V. P. 1972b. Shear modulus and daming in soils: Measurement and arameter effects (Terzaghi Lecture). J. Soil Mech. Found. Div., 98(6), Ishibashi, I., and Zhang, X. J Unified dynamic shear moduli and daming ratios of sand and clay. Soils Found., 33(1), Iwasaki, T., Tatsuoka, F., and Takagi, Y Shear moduli of sands under cyclic torsional shear loading. Soils Found., 18(1), Kammerer, A. M., Pestana J. M., and Seed, R. B.22. "Undrained Resonse of Monterey /3 Sand Under Multidirectional Cyclic Simle Shear Loading Conditions." Geotechnical Engineering Research Reort No. UCB/GT/2-1, University of California, Berkeley. Kammerer, A. M., Wu J., Riemer M., Pestana J. M., and Seed, R. B. 24. "Shear shears strain develoment in liquefiable soil under bi-directional loading conditions." In roceeding of 13th World Conference on Earthquake Engineering, Paer 281, Vancouver, B.C., Canada. Kokusho, T., Yoshida, Y., and Esashi, Y Dynamic roerties of soft clay for wide strain range. Soils Found., 22(4), Qian J. G., Wang Y. G., Yin Z. Y., and Huang, M. S Exerimental identification of lastic shakedown behavior of saturated clay subjected to traffic loading with rincial stress rotation." Engineering Geology, 214, Rollins, K. M., Evans, M. D., Diehl, N. B., and Daily, W. D., III Shear modulus and daming relationshis for gravels. J. Geotech. Geoenviron. Eng., 124(5),

18 Page 17 of 3 Canadian Geotechnical Journal Rutherford C. J Develoment of a multi-directional direction simle shear testing device for characterization of the cyclic shear resonse of marine clays." Ph.D. thesis, Texas A&M University, Texas. Seed, H. B., Wong, R. T., Idriss, I. M., and Tokimatsu, K Moduli and daming factors for dynamic analysis of cohesionless soils. J. Geotech. Eng., 112(11), Shibuya, S., Mitachi, T., Fukuda, F., and Degoshi, T Strain rate ffect on the shear modulus and daming of normally consolidated clay. Geotech. Test. J., 183, Stokoe, K. H., II, Darendeli, M. B., Andrus, R. D., and Brown, L. T Dynamic soil roerties: Laboratory, field and correlation studies. Proc., 2nd Int. Conf. on Earthquake Geotechnical Engineering, Vol. 3, Lisbon, Portugal, Stokoe, K. H., II, Darendeli, M. B., Gilbert, R. B., Menq, F. Y., and Choi, W. K. 24. Develoment of a new family of normalized modulus reduction and material daming curves. Proc., NSF/PEER Int. Worksho on Uncertainties in Nonlinear Soil Proerties and their Imact on Modeling Dynamic Soil Resonse, Univ. of California at Berkeley, Berkeley, Calif. Sun, L., Gu, C., and Wang, P Effects of cyclic confining ressure on the deformation characteristics of natural soft clay. Soil Dynamics and Earthquake Engineering, 78, Tatsuoka, F., Shibuya, S., and Kuwano, R. 21. Advanced laboratorystress-strain testing of geomaterials. Balkema, Rotterdam, The Netherlands,

19 Page 18 of 3 Vucetic, M Normalized behavior of offshore clay under uniform cyclic loading. Can. Geotech. J., 25(1), Vucetic, M., and Dobry, R Effect of soil lasticity on cyclic resonse. J. Geotech. Eng., 117(1), Yamada S., Hyodo M., Orense R. P., and Dinesh, S. V. 28. Initial Shear Modulus of Remolded Sand-Clay Mixtures. J. Geotech. Geoenviron. Eng.,134(7), Zhang, J. F., Andrus, R. D., and Juang, C. H. 25. Normalized shear modulus and material daming ratio relationshis. J. Geotech. Geoenviron. Eng., 131(4),

20 Page 19 of 3 Canadian Geotechnical Journal Figures cations Fig. 1. The stress aths emloyed in this study Fig. 2. (a) Time-history curves of the cyclic deviatoric stress and the cyclic confining ressure and (b) the hysteresis loos for WZO clay, =1 kpa and η aml =1.5 Fig. 3. (a) Time-history curves of the cyclic deviatoric stress and the cyclic confining ressure and (b) the hysteresis loos for WZO clay, =1 kpa and η aml =1/3 Fig. 4. (a) Time-history curves of the cyclic deviatoric stress and the cyclic confining ressure and (b) the hysteresis loos for WZO clay, =1 kpa and η aml =-1.5 Fig. 5. G/G max versus γ relationshis for WZU clay: (a) Fig. 6. G/G max versus γ relationshis for WZO clay: (a) =1 kpa; (b) =1 kpa; (b) =2 kpa =2 kpa Fig. 7. Comarison between the fitting curves based on Eq. (3) and measured test data for: (a) WZU clay; (b) WZO clay Fig. 8. Relationshis between α and η aml Fig. 9. Comarison between the test data and the redicted results for: (a) WZU clay; (b) WZO clay 19

21 Page 2 of 3 Table 1. The hysical index roerties of the two remolded clays used in this study Soil tye G s a w b (%) w c (%) WZU clay ~ WZO clay ~ Note: a G s = secific gravity; b w=water content; c w =lasticity limit; d w L =liquid limit; e I = lasticity index; f Pc= clay content; g Fc= fines content. w L d (%) I e Pc f (%) Fc g (%) Soil tye Table 2. Summary list of the resent tests Loading Number of η = frequency loading stages / q aml aml aml (kpa) WZU clay 1.1 Hz 11 1/3; 1.5; -1.5; 2.; -2. WZU clay 2.1 Hz ; 2. WZO clay 1.1 Hz 11 1/3; 1.; -1.; 1.5; -1.5; 2.; -2. WZO clay 2.1 Hz 11 1/3; 1.; -1.; 1.5; -1.5 Table 3. The values of γ r and α under =1 kpa WZU clay WZO clay η aml γ r (%) α η aml γ r (%) α / /

22 Page 21 of 3 Canadian Geotechnical Journal Table 4. The values of γ r and α under =2 kpa WZU clay WZO clay η aml γ r (%) α η aml γ r (%) α /

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