Efficacy of Utilizing Stress-Dependent SWRC in the Analysis of a Footing Resting on an Unsaturated Soil Slope
Publication: International Journal of Geomechanics
Volume 24, Issue 12
Abstract
The response and the safety of geostructures constructed on hilly regions or sloping grounds are receiving increased attention. As the foundation of geostructures resting on slopes is often in the vadose zone, accounting for appropriate properties of partially saturated soil is essential for effective design. Moreover, changes in climatic conditions will adversely affect the load-carrying capacity and the stability of the footing resting on unsaturated slopes. Often, the soil–water retention curve (SWRC) at null stress is adopted but is expected to be affected by various factors, including the stress state of the sample. In the present study, an attempt has been made to demonstrate the effectiveness of using stress-dependent SWRC (SDSWRC) in analyzing a footing resting on a slope exposed to seasonal variations. The SDSWRC along the drying–wetting path determined experimentally was fitted using the standard SWRC model. The key parameters of the SDSWRC, hydraulic conductivity function, and shear strength of unsaturated soils are utilized in numerical modeling. Transient state flux analysis is carried out to mark the effects of SDSWRC in the development of hydraulic response. The stability of an unsaturated slope subjected to a footing load located at a chosen setback distance was assessed under various hydromechanical conditions. The results demonstrate that the seasonal variation, water table position, and net stress significantly influence the stability and the load-carrying capacity of the footing resting on an unsaturated slope.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and codes generated or used during the study appear in the published paper.
Acknowledgments
The authors express gratitude for the financial backing extended by the Science and Engineering Research Board, Department of Science and Technology, India (Grant Nos. SERB/F/4638/2013-14 and CRG/2018/004612), as well as the initial grant from IIT Kanpur (Grant No. 20110145).
Notation
The following symbols are used in this paper:
- a, m, n
- SWRC fitting parameters in the Fredlund and Xing (1994) model;
- B
- width of the footing/offset distance of footing from the crest;
- c′
- Cohesion intercept at zero matric suction;
- e
- natural number, i.e., 2.71828;
- H
- height of the slope;
- H1
- height of the domain at the crest of the slope;
- H2
- height of the domain at the toe of the slope;
- hw
- height of the water table from the base;
- k
- hydraulic conductivity;
- ks
- saturated hydraulic conductivity;
- kvd
- vapor conductivity;
- kwx, kwy
- HCF along x(horizontal) and y(vertical) directions;
- first derivative of SWRC with respect to suction;
- N
- normal force;
- R
- radius of slip circle;
- T1, T2, T3, T4, T5
- monitoring time periods;
- ua
- pore air pressure;
- uw
- pore-water pressure;
- WT
- water table;
- α
- angle of inclination of water table with horizontal plane;
- β
- angle of inclination of slope with respect to the horizontal plane;
- γw
- unit weight of water;
- Δl
- arc length of slice;
- θ
- volumetric water content;
- θ′
- first derivative of the Fredlund and Xing SWRC model;
- θr
- residual volumetric water content;
- θs
- saturated volumetric water content;
- σ
- normal stress;
- ϕ′
- angle of internal friction of soil at zero suction level;
- ϕb
- friction angle of soil obtained on the shear stress–suction plane;
- ψ
- suction; and
- ψAEV
- air entry value
References
Acikel, A. S., W. P. Gates, R. M. Singh, A. Bouazza, D. G. Fredlund, and R. K. Rowe. 2018. “Time-dependent unsaturated behaviour of geosynthetic clay liners.” Can. Geotech. J. 55 (12): 1824–1836. https://doi.org/10.1139/cgj-2017-0646.
Anand, A., and R. Sarkar. 2022. “A comprehensive investigation on bearing capacity of shallow foundations on unsaturated fly ash slopes adopting finite element limit analysis.” Eur. J. Environ. Civil Eng. 26 (14): 6914–6940. https://doi.org/10.1080/19648189.2021.1967200.
Baah-Frempong, E., and S. K. Shukla. 2018. “Stability analysis and design charts for a sandy soil slope supporting an embedded strip footing.” Int. J. Geo-Eng. 9 (1): 13. https://doi.org/10.1186/s40703-018-0082-2.
Bangheri, M., and M. Rezania. 2022. “Effect of soil moisture evaporation rate on dynamic measurement of water retention curve with high-capacity tensiometer.” Int. J. Geomech. 22 (3): 04021301. https://doi.org/10.1061/(ASCE)GM.1943-5622.000229.
Cardoso, R., G. Sarapajevaite, O. Korsun, S. Cardoso, and L. Ilharco. 2017. “Microfabricated sol-gel relative humidity sensors for soil suction measurement during laboratory tests.” Can. Geotech. J. 54 (8): 1176–1183. https://doi.org/10.1139/cgj-2016-0419.
EN (Europian Committee for Standardization). 2004 “Eurocode 7: Geotechnical design—Part 1: General rules.” EN 1997-1. Brussels, Belgium: CEN.
Choudhury, D., and K. S. Subba Rao. 2006. “Seismic bearing capacity of shallow strip footings embedded in slope.” Int. J. Geomech. 6 (3): 176–184. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:3(176).
Du, J., and F. Ye. 2021. “The bearing capacity of strip footings adjacent to the crest of unsaturated soil slopes.” Environ. Earth Sci. 80 (19): 1–20. https://doi.org/10.1007/s12665-021-09955-2.
Fredlund, D. G., N. R. Morgenstern, and R. A. Widger. 1978. “The shear strength of unsaturated soils.” Can. Geotech. J. 15 (3): 313–321. https://doi.org/10.1139/t78-029.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil-water characteristic curve.” Can. Geotech. J. 31 (4): 521–532. https://doi.org/10.1139/t94-061.
Fredlund, D. G., and H. Rahardjo. 1993. Soil mechanics for unsaturated soils. Hoboken, NJ: Wiley.
Fredlund, D. G., A. Xing., and S. Huang. 1994. “Predicting the permeability function for unsaturated soils using the soil-water characteristic curve.” Can. Geotech. J. 31 (4). 533–546. https://doi.org/10.1139/t94-062.
Garakarni, A. A., H. Sadeghi., S. Saheb., and A. Lamei. 2020. “Bearing capacity of shallow foundations on unsaturated soils: analytical approach with 3d numerical simulations and experimental validations.” Int. J. Geomech. 20 (3): 04019181.https://doi.org/10.1061/(ASCE)GM.1943-5622.000158
Georgiadis, K. 2010a. “An upper-bound solution for the undrained bearing capacity of strip footings at the top of a slope.” Geotechnique 60 (10): 801–806. https://doi.org/10.1680/geot.09.T.016.
Georgiadis, K. 2010b. “Undrained bearing capacity of strip footings on slopes.” J. Geotech. Geoenviron. Eng. 136 (5): 677–685. https://doi.org/10.1061/ASCEGT.1943-5606.0000269.
Goh, S. G., H. Rahardjo, and E. C. Leong. 2015. “Modification of triaxial apparatus for permeability measurement of unsaturated soils.” Soils Found. 55 (1): 63–73. https://doi.org/10.1016/j.sandf.2014.12.005.
Gu, X., L. Wang, Q. Ou, W. Zhang, and G. Sun. 2023. “Reliability assessment of rainfall-induced slope stability using Chebyshev–Galerkin–KL expansion and Bayesian approach.” Can. Geotech. J. 60 (12): 1909–1922. https://doi.org/10.1139/cgj-2022-0671.
Hong, L., X. Wang, W. Zhang, Y. Li, R. Zhang, and C. Chen. 2024. “System reliability-based robust design of deep foundation pit considering multiple failure modes.” Geosci. Front. 15 (2): 101761. https://doi.org/10.1016/j.gsf.2023.101761.
Hou, X., S. Qi, T. Li, S. Guo, Y. Wang, Y. Li, and L. Zhang. 2020. “Microstructure and soil-water retention behavior of compacted and intact silt loess.” Eng. Geol. 277: 105814. https://doi.org/10.1016/j.enggeo.2020.105814.
Kim, H., M. Prezzi, and R. Salgado. 2017. “Calibration of Whatman grade 42 filter paper for soil suction measurement.” Can. J. Soil Sci. 97: 93–98. https://doi.org/10.1139/cjss-2016-006.
Lee, I. M., S. G. Sung., and G. C. Cho. 2005. “Effect of stress state on the unsaturated shear strength of a weathered granite.” Can. Geotech. J. 42 (2): 624–631. https://doi.org/10.1139/t04-091.
Leong, E. C., and Z. Y. Cheng. 2016. “Effects of confining pressure and degree of saturation on wave velocities of soils.” Int. J. Geomech. 16 (6): D4016013. https://doi.org/10.1061/(asce)gm.1943-5622.0000727.
Leong, E. C., X. H. Zhang, and H. Rahardjo. 2012. “Calibration of a thermal conductivity sensor for field measurement of matric suction.” Geotechnique 62 (1): 81–85. https://doi.org/10.1680/geot.9.P.008.
Leshchinsky, B. 2015. “Bearing capacity of footings placed adjacent to c′-ϕ′ slopes.” J. Geotech. Geoenviron. Eng. 141 (6): 04015022. https://doi.org/10.1061/(asce)gt.1943-5606.0001306.
Likos, W. J., and N. Lu. 2004. Unsaturated soil mechanics. Hoboken, NJ: Wiley.
Liu, X., and Y. Wang. 2023. “Probabilistic hazard analysis of rainfall-induced landslides at a specific slope considering rainfall uncertainty and soil spatial variability.” Comput. Geotech. 162: 105706. https://doi.org/10.1016/j.compgeo.2023.105706.
Meyerhof, G. G. 1957. “The ultimate bearing capacity of foundations on slopes.” Proc. Fourth Int. Conf. Soil Mech. Found. Eng. 3a/26: 384–386.
Najdi, A., D. Encalada, J. Mendes, P. C. Prat, and A. Ledesma. 2023. “Evaluating innovative direct and indirect soil suction and volumetric measurement techniques for the determination of soil water retention curves following drying and wetting paths.” Eng. Geol. 322: 10717. https://doi.org/10.1016/j.enggeo.2023.107179.
Ng, C. W. W., and Y. W. Pang. 2000. “Influence of stress state on soil-water characteristics and slope stability.” J. Geotech. Geoenviron. Eng. 126 (2): 157–166. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:2(157).
Oh, W. T., and S. K. Vanapalli. 2013. “Interpretation of the bearing capacity of unsaturated fine-grained soil using the modified eEffective and the modified total stress approaches.” Int. J. Geomech. 13 (6): 769–778. https://doi.org/10.1061/(ASCE)GM.1943-5622.000026.
Pantelidis, L., and D. V. Griffiths. 2015. “Footing on the crest of slope: Slope stability or bearing capacity?” Eng. Geol. Soc. Territory 2: 1231–1234. https://doi.org/10.1007/978-3-319-09057-3_215.
Pham, H. Q., and D. G. Fredlund. 2008. “Equations for the entire soil-water characteristic curve of a volume change soil.” Can. Geotech. J. 45 (4): 443–453. https://doi.org/10.1139/T07-117.
Qi, S., and S. K. Vanapalli. 2018. “Simulating hydraulic and mechanical responses of unsaturated expansive soil slope to rainfall: Case study.” Int. J. Geomech. 18 (6): 05018002. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001106.
Rahardjo, H., T. H. Ong, R. B. Rezaur, and E. C. Leong. 2007. “Factors controlling instability of homogeneous soil slopes under rainfall.” J. Geotech. Geoenviron. Eng. 133 (12): 1532–1543. https://doi.org/10.1061/ASCE1090-02412007133:121532.
Rajesh, S. 2024. “Strength and deformation behavior of compacted soils under varied suction and drainage conditions.” Ind. Geotech. J. 54 (1): 284–300. https://doi.org/10.1007/s40098-023-00736-1.
Rajesh, S., S. Roy, and V. Khan. 2021. “Modelling the WRC and volume change behavior of GCLs considering net stress and temperature.” Geosyn. Int. 28 (2): 174–185. https://doi.org/10.1680/jgein.20.00032.
Rajesh, S., S. Roy, and S. Madhav. 2017. “Study of measured and fitted SWCC accounting the irregularity in the measured dataset.” Int. J. Geotech. Eng. 11 (4): 321–331. https://doi.org/10.1080/19386362.2016.1219541.
Rostami, A., G. Habibagahi, M. Azdari, and E. Nikooee. 2015. “Pore network investigation on hysteresis phenomena and influence of stress state on the SWRC.” Int. J. Geomech. 15 (5): 04014072. https://doi.org/10.1061/(ASCE)GM.1943-5622.00003.
Roy, S., and S. Rajesh. 2020. “Simplified model to predict features of soil–water retention curve accounting for stress state conditions.” Int. J. Geomech. 20 (3): 04019191. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001591.
Roy, S., and S. Rajesh. 2018. “Influence of confining pressure on water retention characteristics of compacted soil.” Ind. Geotech. J. 48 (2): 327–341. https://doi.org/10.1007/s40098-017-0265-3.
Roy, S., and S. Rajesh. 2021. “Test apparatus for rapid determination of soil-water retention curve under isotropic loading condition.” Geotech. Testing J. 44 (2): 255–273. https://doi.org/10.1520/GTJ20190416.
Schuppener, B. 2007. “Eurocode 7: Geotechnical design—Part 1: General rules—Its implementation in the European member states.” In Proc., 14th European Conf. on Soil Mechanics and Geotechnical Engineering, 279–289. Amsterdam, The Netherlands: IOS Press.
Showkat, R., H. Mohannadi, and G. L. Sivakumar Babu. 2022. “Effect of rainfall infiltration on the stability of compacted embankments.” Int. J. Geomech. 22 (7): 04022104. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002425.
Showkat, R., and G. L. Sivakumar Babu. 2023. “Deterministic and probabilistic analysis of the response of shallow footings on unsaturated soils due to rainfall.” Transp. Geotech. 43: 101150. https://doi.org/10.1016/j.trgeo.2023.101150.
Tan, M., and S. K. Vanapalli. 2021. “Performance estimation of a shallow foundation on an unsaturated expansive soil slope subjected to rainfall infiltration.” MATEC Web Conf. 337: 03009. https://doi.org/10.1051/matecconf/202133703009.
Tan, M., and S. K. Vanapalli. 2022. “Foundation bearing capacity estimation on unsaturated soil slope under transient flow condition using slip line method.” Comput. Geotech. 148: 104804. https://doi.org/10.1016/j.compgeo.2022.104804.
Thu, T. M., H. Rahardjo, and E. C. Leong. 2007. “Soil-water characteristic curve and consolidation behavior for a compacted silt.” Can. Geotech. J. 44 (3): 266–275. https://doi.org/10.1139/T06-114.
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.
Vo, T., and A. R. Russell. 2017. “Stability charts for curvilinear slopes in unsaturated soils.” Soils Found. 57 (4): 543–556. https://doi.org/10.1016/j.sandf.2017.06.005.
Wang, L., Y. Gao, L. Wang, J. Zhang, and B. Chen. 2023a. “Influence of soil suction and seismic excitation on active earth pressure.” KSCE J. Civil Eng. 27 (6): 2477–2485. https://doi.org/10.1007/s12205-023-1677-5.
Wang, L., Y. Gao, E. Zahou, J. Feng, A. Huang, and M. Xu. 2024. “Pseudo-static analysis of 3D unsaturated bench slopes stabilized by multiple rows of piles.” Transp. Geotech. 46: 101255. https://doi.org/10.1016/j.trgeo.2024.101255.
Wang, L., M. Xu, W. Hu, Z. Qian, and Q. Pan. 2023b. “3D stability of pile stabilized stepped slopes considering seismic and surcharge loads.” Geomech. Eng. 32 (6): 639–652. https://doi.org/10.12989/gae.2023.32.6.639.
Wu, C., Z. Z. Wang, S. H. Goh, and W. Zang. 2024. “Comparing 2D and 3D slope stability in spatially variable soils using random finite-element method.” Comput. Geotech. 170: 106324. https://doi.org/10.1016/j.compgeo.2024.106324.
Yang, H., H. Rahardjo, E. C. Leong, and D. G. Fredlund. 2004. “Factors affecting drying and wetting soil-water characteristic curves of sandy soils.” Can. Geotech. J. 41 (5): 908–920. https://doi.org/10.1139/T04-042.
Zhang, W., X. Gu, and Q. Ou. 2023. “Bearing capacity and failure mechanism of strip footings lying on slopes subjected to various rainfall patterns and intensities.” Geol. J. 1–12. https://doi.org/10.1002/gj.4882.
Zhou, H., Y. Shi, X. Yu, H. Xu, G. Zheng, S. Yang, and Y. He. 2023. “Failure mechanism and bearing capacity of rigid footings placed on top of cohesive soil slopes in spatially random soil.” Int. J. Geomech. 23 (8): 04023110. https://doi.org/10.1061/ijgnai.gmeng-8306.
Zhou, H., G. Zheng, X. Yin, R. Jia, and X. Yang. 2018. “The bearing capacity and failure mechanism of a vertically loaded strip footing placed on the top of slopes.” Comput. Geotech. 94: 12–21. https://doi.org/10.1016/j.compgeo.2017.08.009.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Feb 26, 2024
Accepted: Jun 12, 2024
Published online: Sep 27, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 27, 2025
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.