Abstract
The experimental data dealing with the so-called small strain stiffness of soils are indispensable in developing and calibrating advanced numerical models. A literature review revealed a lack of such data for unsaturated soils. In this study, the laboratory measurements of very small and small strain stiffness are carried out in a double-walled triaxial cell using bender elements and LVDT transducers. The tested soil is a reconstituted silty clay, representing a typical soil encountered in engineering practice. A so-called effective stress for unsaturated soil is used in interpreting and numerically simulating the effects of suction magnitude, net stress magnitude and suction history on the initial elastic shear modulus, and on its decrease with increasing strain. The increase of both net stress and suction leads to increase in stiffness. This is observed by both elastic shear modulus and shear modulus reduction curve measurements. The “overconsolidation” by suction leads to the increase of stiffness, too. The experimental data are used for calibrating constitutive parameters and for assessing the capabilities of an advanced hypoplastic model for unsaturated soils. The model predictions are consistent with the laboratory measurements and the model can capture the increase of stiffness with respect to the increase of suction and net stress reasonably well. Moreover, the model is able to predict the increase of stiffness due to suction “overconsolidation”.
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References
Alonso EE, Pereira JM, Vaunat J, Olivella S (2010) A microstructurally based effective stress for unsaturated soils. Géotechnique 60(12):913–925. https://doi.org/10.1680/geot.8.P.002
Atkinson JH (2000) Non-linear soil stiffness in routine design. Géotechnique 50(5):487–508. https://doi.org/10.1680/geot.2000.50.5.487
Biglari M, Jafari MK, Shafiee A, Mancuso C, d’Onofrio A (2011) Shear modulus and dumping ratio of unsaturated kaolin measured by new suction-controlled cyclic triaxial device. Geotech Test J 34(5):525–536. https://doi.org/10.1520/GTJ103635
Biglari M, Mancuso C, d’Onofrio A, Jafari MK, Shafiee A (2011) Modelling the initial shear stiffness of unsaturated soils as a function of the coupled effects of the void ratio and the degree of saturation. Comput Geotech 38(5):709–720. https://doi.org/10.1016/j.compgeo.2011.04.007
Biglari M, d’Onofrio A, Mancuso C, Jafari MK, Shafiee A, Ashayeri I (2012) Small-strain stiffness of Zenoz kaolin in unsaturated conditions. Can Geotech J 49(3):311–322. https://doi.org/10.1139/t11-105
Bishop AW (1959) The principle of effective stress. Tekniske Ukeblad 39:859–863
Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Hydrology papers 3, Colorado State University, Fort Collins
Cabarkapa Z, Cuccovillo T (2006) Automated triaxial apparatus for testing unsaturated soils. Geotech Test J 29(1):21–29. https://doi.org/10.1520/GTJ12310
Cabarkapa Z, Cuccovillo T, Gunn M (1998) A new triaxial apparatus for testing unsaturated soils. In: Proceedings of the second international conference on unsaturated soils UNSAT'98, vol 2. Beijing, China, pp 194–195
Clayton CRI (2011) Stiffness at small strain: research and practice. Géotechnique 61(1):5–37. https://doi.org/10.1680/geot.2011.61.1.5
Coop MR, Jovičić V, Atkinson JH (1997) Comparisons between soil stiffness in laboratory tests using dynamic and continuous loading. In: Proceedings of the fourteenth international conference on soil mechanics and foundation engineering, vol. 1. Hamburg, Germany, pp 267–270
Costa Filho LM (1985) Measurement of axial strains in triaxial tests on London clay. Geotech Test J 8(1):3–13. https://doi.org/10.1520/GTJ10851J
Cuccovillo T, Coop MR (1997) The measurement of local axial strains in triaxial tests using LVDTs. Géotechnique 47(1):167–171. https://doi.org/10.1680/geot.1997.47.1.167
Gallipoli D, Gens A, Sharma R, Vaunat J (2003) An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53(1):123–135. https://doi.org/10.1680/geot.2003.53.1.123
Gasparre A, Hight DW, Coop MR, Jardine RJ (2014) The laboratory measurement and interpretation of the small-strain stiffness of stiff clays. Géotechnique 64(12):942–953. https://doi.org/10.1680/geot.13.P.227
Gens A (1996) Constitutive modelling: application to compacted soil. In: Alonso EE, Delage P (eds) Proceeding of the 1st International Conference on Unsaturated Soils, Paris, France, vol 3. Balkema, Rotterdam, pp 1179–1200
Gens A, Sánchez M, Sheng D (2006) On constitutive modelling of unsaturated soils. Acta Geotech 1:137–147. https://doi.org/10.1007/s11440-006-0013-9
Hasan A, Wheeler S (2016) Interpreting measurements of small strain elastic shear modulus under unsaturated conditions. In Proceedings of the 3rd European Conference on Unsaturated Soils (E-UNSAT 2016), Paris, France.
Hoyos LR, Suescún-Florez EA, Puppala AJ (2015) Stiffness of intermediate unsaturated soil from simultaneous suction-controlled resonant column and bender element testing. Eng Geol 188:10–28. https://doi.org/10.1016/j.enggeo.2015.01.014
Jardine RJ, Symes MJ, Burland JB (1984) The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3):323–340. https://doi.org/10.1680/geot.1984.34.3.323
Jennings JEB, Burland JB (1962) Limitations to the use of effective stresses in partly saturated soils. Géotechnique 12(2):125–144. https://doi.org/10.1680/geot.1962.12.2.125
Jovičić V, Coop MR (1997) Stiffness of coarse-grained soils at small strains. Géotechnique 47(3):545–561. https://doi.org/10.1680/geot.1997.47.3.545
Jovičić V, Coop MR, Simić M (1996) Objective criteria for determining Gmax from bender element tests. Géotechnique 46(2):357–362. https://doi.org/10.1680/geot.1996.46.2.357
Khalili N, Khabbaz MH (1998) A unique relationship for χ for the determination of the shear strength of unsaturated soils. Géotechnique 48(5):681–687. https://doi.org/10.1680/geot.1998.48.5.681
Leong EC, Cahyadi J, Rahardjo H (2006) Stiffness of a compacted residual soil. In: Proceedings of the fourth international conference on unsaturated soils. Carefree, Arizona, United States, pp 1169–1180
Lu N, Khalili N, Nikooee E, Hassanizadeh SJ (2014) Principle of effective stress in variably saturated porous media. Vadose Zone J 13(5):1–4. https://doi.org/10.2136/vzj2014.04.0038
Mancuso C, Vassallo R, d’Onofrio A (2002) Small strain behavior of a silty sand in controlled-suction resonant column torsional shear tests. Can Geotech J 39(1):22–31. https://doi.org/10.1139/t01-076
Mašín D (2005) A hypoplastic constitutive model for clays. Int J Numer Anal Meth Geomech 29(4):311–336. https://doi.org/10.1002/nag.416
Mašín D (2010) Predicting the dependency of a degree of saturation on void ratio and suction using effective stress principle for unsaturated soils. Int J Numer Anal Meth Geomech 34(1):73–90. https://doi.org/10.1002/nag.808
Niemunis A, Herle I (1997) Hypoplastic model for cohesionless soils with elastic strain range. Mech Cohes Frict Mater 2(4):279–299. https://doi.org/10.1002/(SICI)1099-1484(199710)2:4%3c279::AID-CFM29%3e3.0.CO;2-8
Ng CWW, Xu J (2012) Effects of current suction ratio and recent suction history on small-strain behaviour of an unsaturated soil. Can Geotech J 49(2):226–243. https://doi.org/10.1139/t11-097
Ng CWW, Kaewsong R, Zhou C, Alonso EE (2017) Small strain shear moduli of unsaturated natural and compacted loess. Géotechnique 67(7):646–651. https://doi.org/10.1680/jgeot.16.T.013
Ng CWW, Baghbanrezvan S, Sadeghi H, Zhou C, Jafarzadeh F (2017) Effect of specimen preparation techniques on dynamic properties of unsaturated fine-grained soil at high suctions. Can Geotech J 54(9):1310–1319. https://doi.org/10.1139/cgj-2016-0531
Rahardjo H, Melinda F, Leong EC, Rezaur RB (2011) Stiffness of a compacted residual soil. Eng Geol 120:60–67. https://doi.org/10.1016/j.enggeo.2011.04.006
Shao L, Guo X, Liu S, Zheng G (2017) Effective stress and equilibrium equation for soil mechanics. CRC Press, Taylor & Francis Group. doi:https://doi.org/10.1201/9781315107554
Shao L, Guo X, Zhao B (2018) On effective stress and effective stress equation. In: Wu W, Yu HS (eds), Proceedings of China-Europe conference on geotechnical engineering, SSGG. Springer, Cham, pp 65–68. doi:https://doi.org/10.1007/978-3-319-97112-4_15
Sheng D, Sloan SW, Gens A (2004) A constitutive model for unsaturated soils: thermomechanical and computational aspects. Comput Mech 33:453–465. https://doi.org/10.1007/s00466-003-0545-x
Sivakumar R, Sivakumar V, Blatz J, Vimalan J (2006) Twin-cell stress path apparatus for testing unsaturated soils. Geotech Test J 29(2):175–179. https://doi.org/10.1520/GTJ14014
Vasallo R, Mancuso C, Vinale F (2007) Effects of net stress and suction history on the small-strain stiffness of a compacted clayey silt. Can Geotech J 44(4):447–462. https://doi.org/10.1139/t06-129
Vasallo R, Mancuso C, Vinale F (2007) Modelling the influence of stress-strain history on the initial shear stiffness of an unsaturated compacted silt. Can Geotech J 44(4):463–472. https://doi.org/10.1139/t06-130
Viggiani G, Atkinson JH (1995) Stiffness of fine-grained soil at very small strains. Géotechnique 45(2):249–265. https://doi.org/10.1680/geot.1995.45.2.249
Vucetic M, Dobry R (1991) Effect of soil plasticity on cyclic response. J Geotech Eng 117(1):89–107. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:1(89)
Wheeler SJ, Sharma RS, Buisson MSR (2003) Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils. Géotechnique 53(1):41–54. https://doi.org/10.1680/geot.2003.53.1.41
Wong KS, Mašín D (2014) Coupled hydro-mechanical model for partially saturated soils predicting small strain stiffness. Comput Geotech 61:355–369. https://doi.org/10.1016/j.compgeo.2014.06.008
Wong KS, Mašín D, Ng CWW (2014) Modelling of shear stiffness of unsaturated fine grained soils at very small strains. Comput Geotech 56:28–39. https://doi.org/10.1016/j.compgeo.2013.10.005
Acknowledgements
The financial support by the Project 17-21903S of the Czech Science Foundation (GAČR) is acknowledged. The third author is grateful for the financial support by a research grant LTACH19028 of the Czech Ministry of Education, Youth and Sports and for the institutional support by Center for Geosphere Dynamics (UNCE/SCI/006).
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Mohyla, T., Boháč, J. & Mašín, D. Small-strain behaviour of unsaturated silty clay: experiments and model interpretation. Acta Geotech. 16, 2837–2849 (2021). https://doi.org/10.1007/s11440-021-01204-x
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DOI: https://doi.org/10.1007/s11440-021-01204-x