Technical Papers
Mar 8, 2024

Effects of Strength Anisotropy and Strain Softening on Soil Bearing Capacity through a Cosserat Nonlocal Finite-Element Method

Publication: International Journal of Geomechanics
Volume 24, Issue 5

Abstract

The strength anisotropy and strain softening of natural soil can significantly impact the bearing capacity of shallow foundations on clay. In this article, we present a nonlocal numerical method to study the coupled rotation of the maximum normal stress axis and strain softening on the bearing capacity of shallow foundations on clay through a Cosserat strain softening constitutive model. The strength anisotropy and strain softening characteristics were numerically implemented into a finite-element (FE) program by dynamically updating the anisotropic cohesion in global Newton–Raphson iterations. Due to its nonlocal feature, the proposed nonlocal numerical method can overcome the mesh dependence in simulating the progressive failure of clay through the classical FE method. We first validated the efficacy of this method against the results of the plane strain test and numerical results in the literature. We then study the bearing capacity of a strip footing over anisotropic and strain-softening clay through the implemented numerical method. The results indicated that the deposition angle has an important effect on the bearing capacity and failure mode. The effects of the degree of anisotropy and strain softening on the ultimate bearing capacity are quantified through the numerical method. It is found that (1) the proposed method can effectively reflect the characteristics of the maximum normal stress axis rotation on the failure surface of the footing; (2) the ultimate bearing capacity of a footing (Pu) on anisotropic clay could increase linearly with an increase in the anisotropy ratio k (i.e., k is the ratio between C1 and C2) and decreases with an increase in the softening modulus; and (3) the strength anisotropy and strain softening are strongly coupling factors impacting the bearing capacity of anisotropic clay.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all of the data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request, including all result files obtained from numerical simulations and data in Figs. 9–11, 13, 14, 20–22, and 25–28).

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant Nos. 51890912, 51979025, and 52011530189).

References

ABAQUS. 2013. Analysis user’s manual, version 2013. Providence, RI: Dassault Systemes Simulia.
Aifantis, E. C. 1987. “The physics of plastic deformation.” Int. J. Plasticity 3 (3): 211–247. https://doi.org/10.1016/0749-6419(87)90021-0.
Alkarni, A. A., and M. A. Alshamrani. 2000. “Study of the effect of soil anisotropy on slope stability using method of slices.” Comput. Geotech. 26 (2): 83–103. https://doi.org/10.1016/S0266-352X(99)00046-4.
Azami, A., S. Pietruszczak, and P. Guo. 2010. “Bearing capacity of shallow foundations in transversely isotropic granular media.” Int. J. Numer. Anal. Method Geomech. 34 (8): 771–793. https://doi.org/10.1002/nag.827.
Casagrande, A., and N. Carillo. 1944. “Shear failure of anisotropic materials.” J. Boston Soc. Civ. Eng. 31: 74–87.
Chaloulos, Y. K., A. G. Papadimitriou, and Y. F. Dafalias. 2019. “Fabric effects on strip footing loading of anisotropic sand.” J. Geotech. Geoenviron. Eng. 145 (10): 04019068. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002082.
Chang, J., X. Chu, and Y. Xu. 2015. “Finite-element analysis of failure in transversely isotropic geomaterials.” Int. J. Geomech. 15 (6): 04014096. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000455.
Chen, K., D. Zou, H. Tang, J. Liu, and Y. Zhuo. 2021. “Scaled boundary polygon formula for Cosserat continuum and its verification.” Eng. Anal. Bound. Elem. 126: 136–150. https://doi.org/10.1016/j.enganabound.2021.02.007.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Cosserat, E., and F. Cosserat. 1909. Théorie des corps déformables. Paris: Hermann.
Cramer, H., R. Findeiss, G. Steinl, and W. Wunderlich. 1999. “An approach to the adaptive finite element analysis in associated and non-associated plasticity considering localization phenomena.” Comput. Methods Appl. Mech. Eng. 176 (1–4): 187–202. https://doi.org/10.1016/S0045-7825(98)00336-3.
de Borst, R. 1991. “Simulation of strain localization: A reappraisal of the Cosserat continuum.” Eng. Comput. 8 (4): 317–332. https://doi.org/10.1108/eb023842.
de Borst, R. 1993. “A generalization of J2-flow theory for polar continua.” Comput. Method. Appl. M. 103 (3): 347–362. https://doi.org/10.1016/0045-7825(93)90127-J.
Desrues, J., R. Chambon, M. Mokni, and F. Mazerolle. 1996. “Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography.” Géotechnique 46 (3): 529–546. https://doi.org/10.1680/geot.1996.46.3.529.
Duncan, J. M., and H. B. Seed. 1966. “Anisotropy and stress reorientation in clay.” J Soil Mech Found Div. 92 (5): 21–50. https://doi.org/10.1061/JSFEAQ.0000909.
Eringen, A. C. 1968. “Theory of micropolar elasticity.” In Fracture, Vol. 1, edited by H. Liebowitz, 621–729. New York: Academic Press.
Fathipour, H., A. S. Siahmazgi, M. Payan, M. Veiskarami, and R. Jamshidi Chenari. 2021. “Limit analysis of modified pseudodynamic lateral earth pressure in anisotropic frictional medium using finite-element and second-order cone programming.” Int. J. Geomech. 21 (2): 04020258. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001924.
Foroutan Kalourazi, A., C. R. Jamshidi, and M. Veiskarami. 2020. “Bearing capacity of strip footings adjacent to anisotropic slopes using the lower bound finite element method.” Int. J. Numer. Anal. Method Geomech. 20 (11): 04020213.
Frydman, S., and H. J. Burd. 1997. “Numerical studies of bearing-capacity factor Nγ.” J. Geotech. Geoenviron. Eng. 123 (1): 20–29. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:1(20).
Galavi, V., and H. F. Schweiger. 2010. “Nonlocal multilaminate model for strain softening analysis.” Int. J. Geomech. 10 (1): 30–44. https://doi.org/10.1061/(ASCE)1532-3641(2010)10:1(30).
Gao, Z., D. Lu, and X. Du. 2020. “Bearing capacity and failure mechanism of strip footings on anisotropic sand.” J. Eng. Mech. 146 (8): 04020081. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001814.
Gao, Z., J. Zhao, and X. Li. 2021. “The deformation and failure of strip footings on anisotropic cohesionless sloping grounds.” Int. J. Numer. Anal. Method Geomech. 45 (10): 1526–1545. https://doi.org/10.1002/nag.3212.
Griffiths, D. V. 1982. “Computation of bearing capacity factors using finite elements.” Geotechnique 32 (3): 195–202. https://doi.org/10.1680/geot.1982.32.3.195.
Günther, W. 1958. “Zur statik und kinematik des cosseratschen kontinuums.” Abh. Braunschweig. Wiss.Ges. 10: 195–213.
Hicks, M. A., and C. Onisiphorou. 2005. “Stochastic evaluation of static liquefaction in a predominantly dilative sand fill.” Géotechnique 55 (2): 123–133. https://doi.org/10.1680/geot.2005.55.2.123.
Huang, M., Z. Tang, W. Zhou, and J. Yuan. 2018. “Upper bound solutions for face stability of circular tunnels in non-homogeneous and anisotropic clays.” Comput. Geotech. 98: 189–196. https://doi.org/10.1016/j.compgeo.2018.02.015.
Huang, M., H. Wang, Z. Tang, and J. Yu. 2021. “Basal stability analysis of braced excavations in anisotropic and non-homogeneous undrained clay using streamline velocity fields.” Acta Geotech. 16 (4): 1175–1186. https://doi.org/10.1007/s11440-020-01052-1.
Huang, Y., H. Gao, W. D. Nix, and J. Hutchinson. 2000. “Mechanism-based strain gradient plasticity—II. Analysis.” J. Mech. Phys. Solids 48 (1): 99–128. https://doi.org/10.1016/S0022-5096(99)00022-8.
Iordache, M.-M., and K. William. 1998. “Localized failure analysis in elastoplastic Cosserat continua.” Comput. Methods Appl. Mech. Eng. 151 (3–4): 559–586. https://doi.org/10.1016/S0045-7825(97)00166-7.
Krabbenhoft, S., L. Damkilde, and K. Krabbenhoft. 2014. “Bearing capacity of strip footings in cohesionless soil subject to eccentric and inclined loads.” Int. J. Geomech. 14 (3): 04014003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332.
Kulhawy, F. H., and P. W. Mayne. 1990. Manual on estimating soil properties for foundation design. Ithaca, NY: Cornell Univ.
Lade, P. V., J. Nam, and W. P. Hong. 2008. “Shear banding and cross-anisotropic behavior observed in laboratory sand tests with stress rotation.” Can. Geotech. J. 45 (1): 74–84. https://doi.org/10.1139/T07-078.
Li, Q., and A. W. Stuedlein. 2018. “Simulation of torsionally loaded deep foundations considering state-dependent load transfer.” J. Geotech. Geoenviron. Eng. 144 (8): 04018053. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001930.
Li, X., and H. Tang. 2005. “A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modelling of strain localisation.” Comput. Struct. 83 (1): 1–10. https://doi.org/10.1016/j.compstruc.2004.08.009.
Liang, W., S. Zhao, H. Wu, and J. Zhao. 2021. “Bearing capacity and failure of footing on anisotropic soil: A multiscale perspective.” Comput. Geotech. 137: 104279. https://doi.org/10.1016/j.compgeo.2021.104279.
Lo, K. Y. 1965. “Stability of slopes in anisotropic soils.” J. Soil. Mech. Found. Div. 91 (4): 85–106. https://doi.org/10.1061/JSFEAQ.0000778.
Mayne, P. W. 1985. “Stress anisotropy effects on clay strength.” J. Geotech. Eng. 111 (3): 356–366. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:3(356).
Menon, S., and X. Song. 2021a. “A computational periporomechanics model for localized failure in unsaturated porous media.” Comput. Methods Appl. Mech. Eng. 384: 113932. https://doi.org/10.1016/j.cma.2021.113932.
Menon, S., and X. Song. 2021b. “A stable computational nonlocal poromechanics model for dynamics analysis of saturated porous media.” Int. J. Numer. Meth. Eng. 122 (20): 5512–5539. https://doi.org/10.1002/nme.6762.
Meyerhof, G. G. 1963. “Some recent research on the bearing capacity of foundations.” Can. Geotech. J. 1 (1): 16–26. https://doi.org/10.1139/t63-003.
Meyerhof, G. G., and A. M. Hanna. 1978. “Ultimate bearing capacity of foundations on layered soils under inclined load.” Can. Geotech. J. 15 (4): 565–572. https://doi.org/10.1139/t78-060.
Mindlin, R. D. 1963. “Influence of couple-stress on stress concentrations.” Exp. Mech. 1963 (3): 1–7. https://doi.org/10.1007/BF02327219.
Pande, G. N., and S. Pieteruszczak. 1986. “Symmetric tangential stiffness formulation for non-associated plasticity.” Comput. Geotech. 2 (2): 89–99. https://doi.org/10.1016/0266-352X(86)90006-6.
Pieczyńska-Kozłowska, J. M., W. Puła, D. V. Griffiths, and G. A. Fenton. 2015. “Influence of embedment, self-weight and anisotropy on bearing capacity reliability using the random finite element method.” Comput. Geotech. 67: 229–238. https://doi.org/10.1016/j.compgeo.2015.02.013.
Pietruszczak, S., and Z. Mroz. 2000. “Formulation of anisotropic failure criteria incorporating a microstructure tensor.” Comput. Geotech. 26 (2): 105–112. https://doi.org/10.1016/S0266-352X(99)00034-8.
Rahmaninezhad, S. M., and J. Han. 2021. “Lateral facing deflections of geosynthetic-reinforced retaining walls under footing loading.” Transp. Geotech. 30: 100594. https://doi.org/10.1016/j.trgeo.2021.100594.
Song, X., and N. Khalili. 2019. “A peridynamics model for strain localization analysis of geomaterials.” Int. J. Numer. Anal. Method Geomech. 43 (1): 77–96. https://doi.org/10.1002/nag.2854.
Song, X., and S. Menon. 2019. “Modeling of chemo-hydromechanical behavior of unsaturated porous media: A nonlocal approach based on integral equations.” Acta Geotech. 14 (3): 727–747. https://doi.org/10.1007/s11440-018-0679-9.
Song, X., and S. A. Silling. 2020. “On the peridynamic effective force state and multiphase constitutive correspondence principle.” J. Mech. Phys. Solids. 145: 04161. https://doi.org/10.1016/j.jmps.2020.104161.
Sternberg, E., and R. Muki. 1967. “The effect of couple-stresses on the stress concentration around a crack.” Int. J. Solids Struct. 3 (1): 69–95. https://doi.org/10.1016/0020-7683(67)90045-5.
Tang, H. X., Z. L. Hu, and X. Li. 2013. “Three-dimensional pressure-dependent elastoplastic Cosserat continuum model and finite element simulation of strain localization.” Int. J. Appl. Mech. 5 (3): 1–33.
Tang, H., Y. Li, Z. Hu, and X. Song. 2022. “Numerical simulation of strain localization through an integrated Cosserat continuum theory and strong discontinuity approach.” Comput. Geotech. 151: 104951. https://doi.org/10.1016/j.compgeo.2022.104951.
Tang, H., W. Wei, F. Liu, and G. Chen. 2020. “Elastoplastic Cosserat continuum model considering strength anisotropy and its application to the analysis of slope stability.” Comput. Geotech. 117: 103235. https://doi.org/10.1016/j.compgeo.2019.103235.
Tang, H., W. Wei, X. Song, and F. Liu. 2021. “An anisotropic elastoplastic Cosserat continuum model for shear failure in stratified geomaterials.” Eng. Geol. 293: 106304. https://doi.org/10.1016/j.enggeo.2021.106304.
Tejchman, J., and E. Bauer. 1996. “Numerical simulation of shear band formation with a polar hypoplastic constitutive model.” Comput. Geotech. 19 (3): 221–244. https://doi.org/10.1016/0266-352X(96)00004-3.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Terzaghi, K., R. B. Peck, and G. Mesri. 1996. Soil mechanics in engineering practice. New York: Wiley.
Ukritchon, B., and S. Keawsawasvong. 2020. “Undrained lower bound solutions for end bearing capacity of shallow circular piles in non-homogeneous and anisotropic clays.” Int. J. Numer. Anal. Method Geomech. 44 (5): 596–632. https://doi.org/10.1002/nag.3018.
Ukritchon, B., A. J. Whittle, and C. Klangvijit. 2003. “Calculations of bearing capacity factor N γ using numerical limit analyses.” J. Geotech. Geoenviron. Eng. 129 (5): 468–474. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:6(468).
Vardoulakis, I. 1996. “Deformation of water-saturated sand: I. Uniform undrained deformation and shear band.” Géotechnique 46 (3): 441–456. https://doi.org/10.1680/geot.1996.46.3.441.
Veiskarami, M., C. R. Jamshidi, and A. A. Jameei. 2017. “Bearing capacity of strip footings on anisotropic soils by the finite elements and linear programming.” Int. J. Geomech. 17 (12): 04017119. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001018.
Yin, J.-H., Y.-J. Wang, and A. P. S. Selvadurai. 2001. “Influence of nonassociativity on the bearing capacity of a strip footing.” J. Geotech. Geoenviron. Eng. 127 (11): 985–989. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:11(985).
Zdravković, L., D. M. Potts, and D. W. Hight. 2002. “The effect of strength anisotropy on the behaviour of embankments on soft ground.” Géotechnique 52 (6): 447–457. https://doi.org/10.1680/geot.2002.52.6.447.
Zhao, J., and N. Guo. 2015. “The interplay between anisotropy and strain localisation in granular soils: A multiscale insight.” Géotechnique 65 (8): 642–656. https://doi.org/10.1680/geot.14.P.184.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 24Issue 5May 2024

History

Received: Mar 7, 2023
Accepted: Nov 21, 2023
Published online: Mar 8, 2024
Published in print: May 1, 2024
Discussion open until: Aug 8, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116023, P.R. China. ORCID: https://orcid.org/0009-0005-2762-6526. Email: [email protected]
State Key Laboratory of Coastal and Offshore Engineering, Dalian Univ. of Technology, Dalian 116023, P.R. China (corresponding author). ORCID: https://orcid.org/0000-0003-4618-9534. Email: [email protected]
Dept. of Civil and Coastal Engineering, Univ. of Florida, Gainesville, FL 32611. ORCID: https://orcid.org/0000-0003-0409-3761. Email: [email protected]

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.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share