An Upper Bound Formulation for Stability Assessment of Variably Saturated Reinforced Soils
Publication: International Journal of Geomechanics
Volume 24, Issue 8
Abstract
A novel unified numerical limit analysis method is proposed to study variably saturated soils reinforced by flexible inclusions. An effective stress-based criterion is utilized to determine the shearing resistance of variably saturated soil-reinforcement interfaces, which is verified through available experimental results. Soils are then treated as single-phased materials and equivalent forces are respectively established within the soil mass and along the interface. In this way, the role of matric suction profiles in stabilizing the reinforced soils under different hydraulic conditions can be analyzed in a more efficient way. To represent the limited tensile strength and negligible compressive strength of the flexible reinforcement, a strategy is proposed to calculate its plastic dissipation rate without the incorporation of stress variables. Plastic dissipation rates of the soil, the reinforcement, and their interfaces are computed using only kinematic variables. The solution domains of the soil, the reinforcement, and the interface are discretized using linear and constant strain finite elements, respectively. Finally, numerical examples are provided to discuss the effect of matric suction on the stability of reinforced structures made of marginal soils.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The present investigation was performed with the support of the National Natural Science Foundation of China (No. 51908053), the China Postdoctoral Science Foundation (2022M722436), the Yingcai Project of Shaanxi Railway Institute (2023KYYC-06), and the Fundamental Research Funds for the Central Universities (300102213105).
References
Abu-Farsakh, M., J. Coronel, and M. Tao. 2007. “Effect of soil moisture content and dry density on cohesive soil–geosynthetic interactions using large direct shear tests.” J. Mater. Civ. Eng. 19 (7): 540–549. https://doi.org/10.1061/(ASCE)0899-1561(2007)19:7(540).
Bouazza, A., J. Zornberg, J. S. McCartney, and R. M. Singh. 2013. “Unsaturated geotechnics applied to geoenvironmental engineering problems involving geosynthetics.” Eng. Geol. 165: 143–153. https://doi.org/10.1016/j.enggeo.2012.11.018.
Bushra, I., and R. Robinson. 2012. “Shear strength behavior of cement treated marine clay.” Int. J. Geotech. Eng. 6 (4): 455–466. https://doi.org/10.3328/IJGE.2012.06.04.455-465.
Chakraborty, D., and J. Kumar. 2014a. “Bearing capacity of strip foundations in reinforced soils.” Int. J. Geomech. 14 (1): 45–58. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000275.
Chakraborty, M., and J. Kumar. 2014b. “Bearing capacity of circular foundations reinforced with geogrid sheets.” Soils Found. 54 (4): 820–832. https://doi.org/10.1016/j.sandf.2014.06.013.
Clarke, S. D., C. C. Smith, and M. Gilbert. 2013. “Modelling discrete soil reinforcement in numerical limit analysis.” Can. Geotech. J. 50 (7): 705–715. https://doi.org/10.1139/cgj-2012-0387.
Esmaili, D., K. Hatami, and G. A. Miller. 2014. “Influence of matric suction on geotextile reinforcement-marginal soil interface strength.” Geotext. Geomembr. 42 (2): 139–153. https://doi.org/10.1016/j.geotexmem.2014.01.005.
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.
Hamid, T. B., and G. A. Miller. 2009. “Shear strength of unsaturated soil interfaces.” Can. Geotech. J. 46 (5): 595–606. https://doi.org/10.1139/T09-002.
Hatami, K., and D. Esmaili. 2015. “Unsaturated soil–woven geotextile interface strength properties from small-scale pullout and interface tests.” Geosynth. Int. 22 (2): 161–172. https://doi.org/10.1680/gein.15.00002.
Hatami, K., J. E. Granados, D. Esmaili, and G. A. Miller. 2013. “Reinforcement pullout capacity in mechanically stabilized earth walls with marginal-quality soils.” Transp. Res. Rec. 2363 (1): 66–74. https://doi.org/10.3141/2363-08.
Huang, C.-C., C.-L. Lo, J.-S. Jang, and L.-K. Hwu. 2008. “Internal soil moisture response to rainfall-induced slope failures and debris discharge.” Eng. Geol. 101 (3–4): 134–145. https://doi.org/10.1016/j.enggeo.2008.04.009.
Khoury, C. N., G. A. Miller, and K. Hatami. 2011. “Unsaturated soil–geotextile interface behavior.” Geotext. Geomembr. 29 (1): 17–28. https://doi.org/10.1016/j.geotexmem.2010.06.009.
Koerner, R. M., and T.-Y. Soong. 2001. “Geosynthetic reinforced segmental retaining walls.” Geotext. Geomembr. 19 (6): 359–386. https://doi.org/10.1016/S0266-1144(01)00012-7.
Kumar, J., and J. P. Sahoo. 2013. “Bearing capacity of strip foundations reinforced with geogrid sheets by using upper bound finite-element limit analysis.” Int. J. Numer. Anal. Methods Geomech. 37 (18): 3258–3277. https://doi.org/10.1002/nag.2189.
Li, S., C. Zhang, T. Zhang, W. Li, and P. Jia. 2023. “Experimental study on the strength, collapsibility, and microstructure of cement and micro-silica-stabilized saline soil under freeze-thaw cycles.” Case Stud. Constr. Mater. 19: e02518.
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): 567–573.
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).
Makrodimopoulos, A., and C. M. Martin. 2007. “Upper bound limit analysis using simplex strain elements and second-order cone programming.” Int. J. Numer. Anal. Methods Geomech. 31 (6): 835–865. https://doi.org/10.1002/nag.567.
Mancarella, D., A. Doglioni, and V. Simeone. 2012. “On capillary barrier effects and debris slide triggering in unsaturated layered covers.” Eng. Geol. 147–148,: 14–27. https://doi.org/10.1016/j.enggeo.2012.07.003.
Mehrjardi, G. T., A. Ghanbari, and H. Mehdizadeh. 2016. “Experimental study on the behaviour of geogrid-reinforced slopes with respect to aggregate size.” Geotext. Geomembr. 44 (6): 862–871. https://doi.org/10.1016/j.geotexmem.2016.06.006.
Mehrjardi, G. T., and F. Motarjemi. 2018. “Interfacial properties of geocell-reinforced granular soils.” Geotext. Geomembr. 46 (4): 384–395. https://doi.org/10.1016/j.geotexmem.2018.03.002.
Portelinha, F. H. M., B. S. Bueno, and J. G. Zornberg. 2013. “Performance of nonwoven geotextile-reinforced walls under wetting conditions: Laboratory and field investigations.” Geosynth. Int. 20 (2): 90–104. https://doi.org/10.1680/gein.13.00004.
Portelinha, F. H. M., and J. G. Zornberg. 2017. “Effect of infiltration on the performance of an unsaturated geotextile-reinforced soil wall.” Geotext. Geomembr. 45 (3): 211–226. https://doi.org/10.1016/j.geotexmem.2017.02.002.
Sargent, P., and M. Rouainia. 2023. “A new framework for quantifying the structure of undisturbed and artificially cemented alluvium.” Géotechnique 73 (2): 143–164. https://doi.org/10.1680/jgeot.21.00059.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–571. https://doi.org/10.1680/geot.12.RL.001.
Smith, C. C., and A. Tatari. 2016. “Limit analysis of reinforced embankments on soft soil.” Geotext. Geomembr. 44 (4): 504–514. https://doi.org/10.1016/j.geotexmem.2016.01.008.
Subramaniam, P., and S. Banerjee. 2020. “Dynamic properties of cement-treated marine clay.” Int. J. Geomech. 20 (6): 04020065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001673.
Tang, Y., H. A. Taiebat, and A. R. Russell. 2016. “Bearing capacity of shallow foundations in unsaturated soil considering hydraulic hysteresis and three drainage conditions.” Int. J. Geomech. 17 (4): 04016142.
Thuo, J. N., K. H. Yang, and C. C. Huang. 2015. “Infiltration into unsaturated reinforced slopes with nonwoven geotextile drains sandwiched in sand layers.” Geosynth. Int. 22 (6): 457–474. https://doi.org/10.1680/jgein.15.00026.
Vahedifard, F., K. Mortezaei, B. A. Leshchinsky, D. Leshchinsky, and N. Lu. 2016. “Role of suction stress on service state behavior of geosynthetic-reinforced soil structures.” Transp. Geotech. 8: 45–56. https://doi.org/10.1016/j.trgeo.2016.02.002.
Vanapalli, S. K., D. G. Fredlund, D. E. Pufahl, and A. W. Clifton. 1996. “Model for the prediction of shear strength with respect to soil suction.” Can. Geotech. J. 33 (3): 379–392. https://doi.org/10.1139/t96-060.
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.
Wang, J.-Q., L.-L. Zhang, J.-F. Xue, and Y. Tang. 2018. “Load-settlement response of shallow square footings on geogrid-reinforced sand under cyclic loading.” Geotext. Geomembr. 46 (5): 586–596. https://doi.org/10.1016/j.geotexmem.2018.04.009.
Xu, C., C. Liang, and P. Shen. 2019. “Experimental and theoretical studies on the ultimate bearing capacity of geogrid-reinforced sand.” Geotext. Geomembr. 47 (3): 417–428. https://doi.org/10.1016/j.geotexmem.2019.01.003.
Yang, K.-H., T. S. Nguyen, Y.-H. Li, and B. Leshchinsky. 2019. “Performance and design of reinforced slopes considering regional hydrological conditions.” Geosynth. Int. 26 (5): 451–473. https://doi.org/10.1680/jgein.19.00031.
Yang, X. L., and J. H. Chen. 2019. “Factor of safety of geosynthetic-reinforced slope in unsaturated soils.” Int. J. Geomech. 19 (6): 04019041. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001399.
Yu, H. S., and S. W. Sloan. 1997. “Finite element limit analysis of reinforced soils.” Comput. Struct. 63 (3): 567–577. https://doi.org/10.1016/S0045-7949(96)00353-7.
Yuan, S. 2021. “A rigorous numerical formulation for upper bound analysis of reinforced soils using second order cone programming.” Geotext. Geomembr. 49 (5): 1294–1311. https://doi.org/10.1016/j.geotexmem.2021.05.002.
Yuan, S., and J. Du. 2018. “Effective stress-based upper bound limit analysis of unsaturated soils using the weak form quadrature element method.” Comput. Geotech. 98: 172–180. https://doi.org/10.1016/j.compgeo.2018.02.008.
Yuan, S., and J. Du. 2020. “A lower-bound formulation for unsaturated soils.” Géotechnique 70 (2): 123–137. https://doi.org/10.1680/jgeot.18.P.103.
Yuan, S., X. Si, and S. Zhang. 2020. “Shakedown analysis of unsaturated soils considering the variation of hydraulic states.” Int. J. Geomech. 20 (9): 04020151. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001760.
Zhang, C., S. Liu, D. Zhang, F. Lai, T. Lu, and Y. Liu. 2022. “A modified equal-strain solution for consolidation behavior of composite foundation reinforced by precast concrete piles improved with cement-treated soil.” Comput. Geotech. 150: 104905. https://doi.org/10.1016/j.compgeo.2022.104905.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 8 • August 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 11, 2023
Accepted: Feb 13, 2024
Published online: Jun 7, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 7, 2024
ASCE Technical Topics:
- Compressive strength
- Effective stress
- Environmental engineering
- Geomechanics
- Geotechnical engineering
- Material mechanics
- Material properties
- Materials engineering
- Pollution
- Saturated soils
- Soft soils
- Soil analysis
- Soil dynamics
- Soil mechanics
- Soil pollution
- Soil properties
- Soil stabilization
- Soil suction
- Soil treatment
- Soils (by type)
- Strength of materials
- Stress (by type)
- Structural analysis
- Structural engineering
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.