Shear Strength–Based Determination of the Effective Stress Parameter in Unsaturated Compacted Clayey Soils: Experimental Investigation and Microstructural Interpretation - 2026
Shear Strength–Based Determination of the Effective Stress Parameter in Unsaturated Compacted Clayey Soils: Experimental Investigation and Microstructural Interpretation
[en] The χ parameter in the generalized effective stress formulation for unsaturated soils aims at weighting the contribution of suction
on the magnitude of effective stress. It is usually expressed as a function of the degree of saturation. This paper presents a comprehensive
methodology to calibrate this χ parameter, based on ensuring a unique shear failure criterion when the stresses are represented in terms of
generalized effective stress. The method requires knowing the intrinsic strength parameters (effective cohesion and friction angle) from triaxial
compression tests upon saturated conditions, and the uniaxial compression strength at various suction levels. The effectiveness of the
proposed methodology is verified by applying it to three different compacted clayey soils. Then, the microstructural significance of the obtained
relationship between the χ parameter and the degree of saturation is discussed from pore size distribution analyzed from a bimodal perspective.
The macroscopic effective stress is primarily governed by the water residing in macropores (interaggregate region), while the water
retained within micropores (intra-aggregate region) has a negligible effect on the χ parameter.
Disciplines :
Civil engineering
Author, co-author :
Ebrahimisadr, Hesam ; Université de Liège - ULiège > Urban and Environmental Engineering
Lanckohr, Sophie ; Université de Liège - ULiège > Urban and Environmental Engineering
François, Bertrand ; Université de Liège - ULiège > Urban and Environmental Engineering
Language :
English
Title :
Shear Strength–Based Determination of the Effective Stress Parameter in Unsaturated Compacted Clayey Soils: Experimental Investigation and Microstructural Interpretation
Original title :
[en] hear Strength–Based Determination of the Effective Stress Parameter in Unsaturated Compacted Clayey Soils: Experimental Investigation and Microstructural Interpretation
Alonso, E. E., J.-M. Pereira, J. Vaunat, and, S. Olivella. 2010. " A microstructurally based effective stress for unsaturated soils." Géotechnique 60 (12): 913-925. https://doi.org/10.1680/geot.8.P.002.
Alonso, E. E., N. M. Pinyol, and, A. Gens. 2013. " Compacted soil behaviour: Initial state, structure and constitutive modelling." Géotechnique 63 (6): 463-478. https://doi.org/10.1680/geot.11.P.134.
Arlabosse, P., E. Rodier, J. H. Ferrasse, S. Chavez, and, D. Lecomte. 2003. " Comparison between static and dynamic methods for sorption isotherm measurements." Drying Technol. 21 (3): 479-497. https://doi.org/10.1081/DRT-120018458.
ASTM. 2010. Standard test method for measurement of soil potential (suction) using filter paper. ASTM D5298-10. West Conshohocken, PA: ASTM.
Bishop, A. W. 1959. " The principle of effective stress." Teknisk Ukeblad 39: 859-863.
Bishop, A. W., I. Alpan, G. E. Blight, and, I. B. Donald. 1960. " Factors controlling the strength of partly saturated cohesive soils." In Proc., Research Conf. on Shear Strength of Cohesive Soils 503-532. Reston, VA: ASCE.
Cao, T. D., and, L. Sun. 2025. " Temperature-dependent elastoplastic behavior of low plasticity unsaturated soils." Acta Geotech. 20: 2889-2909. https://doi.org/10.1007/s11440-025-02554-6.
Delage, P., M. D. Howat, and, Y. J. Cui. 1998. " The relationship between suction and swelling properties in a heavily compacted unsaturated clay." Eng. Geol. 50 (1-2): 31-48. https://doi.org/10.1016/S0013-7952(97)00083-5.
Ebrahimisadr, H., S. Lanckohr, and, B. Francois. 2025. " A methodology for the calibration of the effective stress parameter: From macroscopic considerations to microstructural validation." E3S Web Conf. 642: 02003. https://doi.org/10.1051/e3sconf/202564202003.
Gallipoli, D., P. Grassl, S. Wheeler, and, A. Gens. 2018. " On the choice of stress-strain variables for unsaturated soils and its effect on plastic flow." Geomech. Energy Environ. 15: 3-9. https://doi.org/10.1016/j.gete.2018.02.002.
Gallipoli, D., S. J. Wheeler, and, M. Karstunen. 2003. " Modelling the variation of degree of saturation in a deformable unsaturated soil." Géotechnique 53 (1): 105-112. https://doi.org/10.1680/geot.53.1.105.37249.
Gens, A., M. Sánchez, and, D. Sheng. 2006. " On constitutive modelling of unsaturated soils." Acta Geotech. 1 (3): 137-147. https://doi.org/10.1007/s11440-006-0013-9.
Gerard, P., M. Mahdad, A. R. McCormack, and, B. François. 2015. " A unified failure criterion for unstabilized rammed earth materials upon varying relative humidity conditions." Constr. Build. Mater. 95: 437-447. https://doi.org/10.1016/j.conbuildmat.2015.07.100.
Ghorbani, J., and, J. Kodikara. 2024. " Thermodynamically consistent effective stress formulation for unsaturated soils across a wide range of soil saturation." Comput. Mech. 73 (5): 1077-1094. https://doi.org/10.1007/s00466-023-02401-z.
Gray, W. G., B. A. Schrefler, and, F. Pesavento. 2009. " The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition." J. Mech. Phys. Solids 57 (3): 539-554. https://doi.org/10.1016/j.jmps.2008.11.005.
Haeri, S. M., S. S. Borujerdi, and, A. A. Garakani. 2023. " Effects of initial shear stress on the hydromechanical behavior of collapsible soils." Acta Geotech. 18 (11): 6051-6076. https://doi.org/10.1007/s11440-023-02034-9.
Haeri, S. M., A. A. Garakani, A. Khosravi, and, C. L. Meehan. 2014. " Assessing the hydro-mechanical behavior of collapsible soils using a modified triaxial test device." Geotech. Test. J. 37 (2): 190-204. https://doi.org/10.1520/GTJ20130034.
Haeri, S. M., A. Khosravi, A. A. Garakani, and, S. Ghazizadeh. 2017. " Effect of soil structure and disturbance on hydromechanical behavior of collapsible loessial soils." Int. J. Geomech. 17 (1): 04016021. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000656.
Jennings, J. E. B., and, J. B. Burland. 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.
Khalili, N., and, M. H. Khabbaz. 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.
Khalili, N., R. Witt, L. Laloui, L. Vulliet, and, A. Koliji. 2005. " Effective stress in double porous media with two immiscible fluids." Geophys. Res. Lett. 32 (15): L15309. https://doi.org/10.1029/2005GL023766.
Khoshghalb, A., and, B. Shahbodagh. 2025. " Discussion of 'Indefinability of effective stress for unsaturated soils'." J. Geotech. Geoenviron. Eng. 151 (9): 07025010. https://doi.org/10.1061/JGGEFK.GTENG-13624.
Kim, B.-S., S. Shibuya, S.-W. Park, and, S. Kato. 2010. " Application of suction stress for estimating unsaturated shear strength of soils using direct shear testing under low confining pressure." Can. Geotech. J. 47 (9): 955-970. https://doi.org/10.1139/T10-007.
Kohgo, Y., M. Nakano, and, T. Miyazaki. 1993. " Theoretical aspects of constitutive modelling for unsaturated soils." Soils Found. 33 (4): 49-63. https://doi.org/10.3208/sandf1972.33.4_49.
Likos, W. J. 2014. " Effective stress in unsaturated soil: Accounting for surface tension and interfacial area." Vadose Zone J. 13 (5): 1-12. https://doi.org/10.2136/vzj2013.05.0095.
Lu, N., J. W. Godt, and, D. T. Wu. 2010. " A closed-form equation for effective stress in unsaturated soil." Water Resour. Res. 46 (5): W05515. https://doi.org/10.1029/2009wr008646.
Lu, N., and, D. V. Griffiths. 2004. " Profiles of steady-state suction stress in unsaturated soils." J. Geotech. Geoenviron. Eng. 130 (10): 1063-1076. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1063).
Lu, N., and, W. J. Likos. 2006. " Suction stress characteristic curve for unsaturated soil." J. Geotech. Geoenviron. Eng. 132 (2): 131-142. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131).
Mohyla, T., J. Boháč, and, D. Mašín. 2021. " Small-strain behaviour of unsaturated silty clay: Experiments and model interpretation." Acta Geotech. 16 (9): 2837-2849. https://doi.org/10.1007/s11440-021-01204-x.
Morvan, M., and, D. Perić. 2025. " Discussion of 'Indefinability of effective stress for unsaturated soils'." J. Geotech. Geoenviron. Eng. 151 (9): 07025011. https://doi.org/10.1061/JGGEFK.GTENG-13629.
Nikooee, E., G. Habibagahi, S. M. Hassanizadeh, and, A. Ghahramani. 2013. " Effective stress in unsaturated soils: A thermodynamic approach based on the interfacial energy and hydromechanical coupling." Transp. Porous Media 96 (2): 369-396. https://doi.org/10.1007/s11242-012-0093-y.
Nuth, M., and, L. Laloui. 2008. " Effective stress concept in unsaturated soils: Clarification and validation of a unified framework." Int. J. Numer. Anal. Methods Geomech. 32 (7): 771-801. https://doi.org/10.1002/nag.645.
Öberg, A. L., and, G. Sällfors. 1997. " Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve." Geotech. Test. J. 20 (1): 40-48. https://doi.org/10.1520/GTJ11419J.
Pham, T. A. 2022. " Micromechanical-based shear strength equation considering the stress-state effect for unsaturated soils." Int. J. Geomech. 22 (9): 06022022. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002495.
Rojas, E. 2025. " Discussion of 'Indefinability of effective stress for unsaturated soils'." J. Geotech. Geoenviron. Eng. 151 (9): 07025012. https://doi.org/10.1061/JGGEFK.GTENG-13630.
Schmitz, R. M., C. Schroeder, and, R. Charlier. 2004. " Chemo-mechanical interactions in clay: A correlation between clay mineralogy and Atterberg limits." Appl. Clay Sci. 26 (1-4): 351-358. https://doi.org/10.1016/j.clay.2003.12.015.
Schrefler, B. A. 1984. " The finite element method in soil consolidation (with applications to surface subsidence)." Ph.D. thesis, Dept. of Civil Engineering, Univ. College of Swansea.
Tarantino, A., and, G. El Mountassir. 2013. " Making unsaturated soil mechanics accessible for engineers: Preliminary hydraulic-mechanical characterisation & stability assessment." Eng. Geol. 165: 89-104. https://doi.org/10.1016/j.enggeo.2013.05.025.
Tarantino, A., and, S. Tombolato. 2005. " Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay." Géotechnique 55 (4): 307-317. https://doi.org/10.1680/geot.2005.55.4.307.
Terzaghi, K. 1936. Theoretical soil mechanics. New York: Wiley.
Vanapalli, S. K., and, D. G. Fredlund. 2000. " Comparison of different procedures to predict unsaturated soil shear strength." In Advances in Unsaturated Geotechnics,. Geotechnical Special Publication 99, edited by C. D. Shackelford, S. L. Houston, and N.-Y. Chang., 195-209. Reston, VA: ASCE.
van Genuchten, M. T. 1980. " A closed-form equation for predicting the hydraulic conductivity of unsaturated soils." Soil Sci. Soc. Am. J. 44 (5): 892-898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Vaunat, J., and, F. Casini. 2017. " A poromechanical framework to model soil fabric evolution and its effect on material hydromechanical response." In Proc., 6th Biot Conf. on Poromechanics, 1443-1450. Reston, VA: ASCE.
Wang, J., D. Zhang, N. Wang, and, T. Gu. 2019. " Mechanisms of wetting-induced loess slope failures." Landslides 16 (5): 937-953. https://doi.org/10.1007/s10346-019-01144-4.
Zhan, T. L. T., R. Chen, and, C. W. W. Ng. 2014. " Wetting-induced softening behavior of an unsaturated expansive clay." Landslides 11 (6): 1051-1061. https://doi.org/10.1007/s10346-013-0449-6.
Zhang, C., and, N. Lu. 2018. " What is the range of soil water density? Critical reviews with a unified model." Rev. Geophys. 56 (3): 532-562. https://doi.org/10.1029/2018RG000597.
Zhang, C., and, N. Lu. 2019. " Unitary definition of matric suction." J. Geotech. Geoenviron. Eng. 145 (2): 02818004. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002004.
Zhang, C., and, N. Lu. 2020. " Unified effective stress equation for soil." J. Eng. Mech. 146 (2): 04019135. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001718.
Zhang, X., and, S. Houston. 2024. " Indefinability of effective stress for unsaturated soils." J. Geotech. Geoenviron. Eng. 150 (8): 04024064. https://doi.org/10.1061/JGGEFK.GTENG-12435.
Zhang, X., and, S. Houston. 2025. " Closure to 'Indefinability of effective stress for unsaturated soils'." J. Geotech. Geoenviron. Eng. 151 (9): 07025013. https://doi.org/10.1061/JGGEFK.GTENG-13965.
Zhou, Y. F., L. G. Tham, W. M. Yan, F. C. Dai, and, L. Xu. 2014. " Laboratory study on soil behavior in loess slope subjected to infiltration." Eng. Geol. 183: 31-38. https://doi.org/10.1016/j.enggeo.2014.09.010.