Abstract
Strength anisotropy is an important feature closely related to soil microstructure characteristics. A new anisotropic failure criterion, extended from the Ogawa failure criterion, was developed to describe the strength anisotropy of cross-anisotropic soils. Nonlinearization of the failure curves of the Ogawa failure criterion was introduced to account for the nonlinear failure of cross-anisotropic soils in the meridian plane. Meanwhile, an anisotropic strength function based on fabric tensor was theoretically proposed to modify the failure strength under different loading directions and depositional angles. The evolution of the new anisotropic failure criterion in the deviatoric plane was investigated through a series of parametric studies. All of the undetermined parameters in the new criterion can be readily determined in laboratory tests. Compared with experimental results on several types of soils, the new anisotropic failure criterion showed good performance in strength prediction in the deviatoric plane, as well as predicting the peak friction angle. Finally, a linear theoretical relationship on construction of the anisotropic strength function was also elucidated and discussed. The new anisotropic failure criterion proposed in this paper can effectively predict the strength anisotropy of cross-anisotropic soils under different loading directions and depositional angles.
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Abbreviations
- A:
-
Anisotropic variable
- b:
-
Intermediate principal stress coefficient
- C 1 ,C 2 :
-
Model variables of g(θ)
- e 1, e 2, e 3 :
-
Unit vector of material coordinate system
- e ′1 ,e ′2 ,e ′3 :
-
Unit vector of reference coordinate system
- f(A):
-
Anisotropic strength function
- Fij :
-
Fabric tensor
- g(θ):
-
Shape function
- I 1, I 2 I 3 :
-
First, second and third stress invariants
- k, ξ :
-
Constants of the Ogawa failure criterion
- M 0 :
-
Critical state stress ratio
- Mf :
-
Failure stress ratio
- n:
-
Model constant of the new failure criterion
- p:
-
Mean principal stress (p = (σ1 + σ2 + σ3)/3)
- p 0 :
-
Intercept on the p-axis
- pr :
-
Reference pressure
- q:
-
Deviatoric stress
- sij :
-
Deviatoric stress tensor
- Tij :
-
Transform matrix
- α:
-
Model constant
- β:
-
Model constant of f(A)
- Δ:
-
Statistical scalar of fabric anisotropy
- δ:
-
Depositional angle
- φ 0 :
-
Friction angle
- φp :
-
Peak friction angle
- η:
-
Stress ratio
- ηp :
-
Peak stress ratio
- γ:
-
Angle of the σ1 with respect to the z-axis
- θ:
-
Lode angle
- σij :
-
Stress tensor
- σ 1 σ 2 σ 3 :
-
Major, intermediate and minor principal stresses
References
Abelev AV, Lade PV (2004) Characterization of failure in crossanisotropic soils. Journal of Engineering Mechanics 130(5):599–606, DOI: https://doi.org/10.1061/(ASCE)0733-9399(2004)130:5(599)
Dafalias YF, Papadimitriou AG, Li XS (2004) Sand plasticity model accounting for inherent fabric anisotropy. Journal of Engineering Mechanics 130(11):1319–1333, DOI: https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1319)
Dao L-Q, Delage P, Tang AM, Cui YJ, Pereira JM, Li XL, Sillen X (2014) Anisotropic thermal conductivity of natural Boom Clay. Applied Clay Science 101:282–287, DOI: https://doi.org/10.1016/j.clay.2014.09.003
Gao ZW, Zhao JD, Yao YP (2010) A generalized anisotropic failure criterion for geomaterials. International Journal of Solids and Structures 47(22–23):3166–3185, DOI: https://doi.org/10.1016/j.ijsolstr.2010.07.016
Haruyama M (1981) Anisotropic deformation-strength characteristics of an assembly of spherical particles under three dimensional stresses. Soils and Foundations 21(4):41–55, DOI: https://doi.org/10.3208/sandf1972.21.4_41
Hattab M, Hammad T, Fleureau JM, Hicher, P.Y. (2013) Behaviour of a sensitive marine sediment: Microstructural investigation. Géotechnique 63(1):71–84, DOI: https://doi.org/10.1680/geot.10.P.104
Jiang MJ, Zhang A, Fu C (2018) 3-D DEM simulations of drained triaxial tests on inherently anisotropic granulates. European Journal of Environmental and Civil Engineering 22(sup1):37–56, DOI: https://doi.org/10.1080/19648189.2017.1385541
Jin YF, Yin ZY (2020) Enhancement of backtracking search algorithm for identifying soil parameters. International Journal for Numerical and Analytical Methods in Geomechanics 44:1239–1261, DOI: https://doi.org/10.1002/nag.3059
Kirkgard MM, Lade PV (1993) Anisotropic three-dimensional behavior of a normally consolidated clay. Canadian Geotechnical Journal 30(5):848–858, DOI: https://doi.org/10.1139/t93-075
Kong YX, Zhao JD, Yao YP (2013) A failure criterion for cross-anisotropic soils considering microstructure. Acta Geotechnica 8:665–673, DOI: https://doi.org/10.1007/s11440-012-0202-7
Kumruzzaman M, Yin JH (2012) Influence of the intermediate principal stress on the stress-strain-strength behaviour of a completely decomposed granite soil. Géotechnique 62(3):275–280, DOI: https://doi.org/10.1680/geot.8.P.025
Lade PV, Duncan JM (1973) Cubical triaxial tests on cohesionless soil. International Journal of Rock Mechanics and Mining Sciences &Geomechanics Abstracts 11(3):50, DOI: https://doi.org/10.1016/0148-9062(74)91579-4
Lade PV, Nam J, Hong WP (2008) Shear banding and cross-anisotropic behavior observed in laboratory sand tests with stress rotation. Canadian Geotechnical Journal 45(1):74–84, DOI: https://doi.org/10.1139/T07-078
Lade PV, Van Dyck E, Rodriguez NM (2014) Shear banding in torsion shear tests on cross-anisotropic deposits of fine Nevada sand. Soils and Foundations 54(6):1081–1093, DOI: https://doi.org/10.1016/j.sandf.2014.11.004
Lam W, Tatsuoka F (1988) Effects of initial anisotropic fabric and σ2 on strength and deformation characteristics of sand. Soils and Foundations 28(1):89–106, DOI: https://doi.org/10.3208/sandf1972.28.89
Li X, Yu HS, Li XS (2009) Macro-micro relations in granular mechanics. International Journal of Solids and Structures 46(25–26):4331–4341, DOI: https://doi.org/10.1016/j.ijsolstr.2009.08.018
Liu MD, Indraratna BN (2011) General strength criterion for geomaterials including anisotropic effect. International Journal of Geomechanics 11(3):251–262, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000082
Liu YM, Xu CM, Xu GF, Mao HJ, Xiao ZQ (2021) Macro-micro mechanical behavior of crushable granular materials under generalized stress conditions. KSCE Journal of Civil Engineering 25(5):1634–1644, DOI: https://doi.org/10.1007/s12205-021-1035-4
Lü XL, Huang MS, Andrade JE (2016) Strength criterion for cross-anisotropic sand under general stress conditions. Acta Geotechnica 11:1339–1350, DOI: https://doi.org/10.1007/s11440-016-0479-z
Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc JSCE 232:59–70, DOI: https://doi.org/10.2208/jscej1969.1974.232_59
Mortara G (2010) A yield criterion for isotropic and cross-anisotropic cohesive-frictional materials. International Journal for Numerical and Analytical Methods in Geomechanics 34:953–977, DOI: https://doi.org/10.1002/nag.846
Oboudi M, Pietruszczak S, Razaqpur AG (2016) Description of inherent and induced anisotropy in granular media with particles of high sphericity. International Journal of Geomechanics 16(4):04016006, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000635
Ochiai H, Lade PV (1983) Three-dimensional behavior of sand with anisotropic fabric. International Journal of Geotechnical Engineering 109(10):1313–1328, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1983)109:10(1313)
Oda M (1972) Deformation mechanism of sand in triaxial compression tests. Soils and Foundations 12(4):45–63, DOI: https://doi.org/10.3208/sandf1972.12.4_45
Oda M, Koishikawa I, Higuchi T (1978) Experimental study of anisotropic shear strength of sand by plane strain test. Soils and Foundations 18(1):25–38, DOI: https://doi.org/10.3208/sandf1972.18.25
Oda M, Nakayama H (1989) Yield function for soil with anisotropic fabric. Journal of Engineering Mechanics 115(1):89–104, DOI: https://doi.org/10.1061/(ASCE)0733-9399(1989)115:1(89)
Ogawa S, Mitsui S, Takemure O (1974) Influence of the intermediate principal stress on mechanical properties of a sand. Proc. 29th Annual Meeting of JSCE, Part 3:49–50
Olalla JC, Winkels TG, Ngan-Tillard DJM, Heimovaara TJ (2022) Geophysical tomography as a tool to estimate the geometry of soil layers: Relevance for the reliability assessment of dikes. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 16(4):678–698, DOI: https://doi.org/10.1080/17499518.2021.1971252
Pietruszczak S, Guo P (2013) Description of deformation process in inherently anisotropic granular materials. International Journal for Numerical and Analytical Methods in Geomechanics 37:478–490, DOI: https://doi.org/10.1002/nag.1106
Rabczuk T, Zi G, Bordas SPA, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 199(37–40):2437–2455, DOI: https://doi.org/10.1016/j.cma.2010.03.031
Reynolds JM (2011) An Introduction to Applied and Environmental Geophysics, 2nd edition. John Wiley & Sons, Inc., Hoboken, NJ, USA, 225–228
Rodriguez NM, Lade PV (2013) Mean normal stress on failure criterion for cross-anisotropic sand. Journal of Engineering Mechanics 139(11): 1592–1601, DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000595
Santos RAD, Esquivel ER (2018) Saturated anisotropic hydraulic conductivity of a compacted lateritic soil. Journal of Rock Mechanics and Geotechnical Engineering 10(5):986–991, DOI: https://doi.org/10.1016/j.jrmge.2018.04.005
Shapiro S, Yamamuro JA (2003) Effects of silt on three-dimensional stress-strain behavior of loose sand. Journal of Geotechnical and Geoenvironmental Engineering 129(1):1–11, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2003)129:1(1)
Tian Y, Yao YP (2017) A simple method to describe three-dimensional anisotropic failure of soils. Computers and Geotechnics 92:210–219, DOI: https://doi.org/10.1016/j.compgeo.2017.08.004
Tong ZX, Fu PC, Zhou SP, Dafalias YF (2014) Experimental investigation of shear strength of sands with inherent fabric anisotropy. Acta Geotechnica 9:257–275, DOI: https://doi.org/10.1007/s11440-014-0303-6
Wang S, Zhong ZL, Liu XR (2020) Development of an anisotropic nonlinear strength criterion for geomaterials based on SMP criterion. International Journal of Geomechanics 20(3):04019183, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001588
Yang LT, Li X, Yu HS, Wanatowski D (2016) A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding. Acta Geotechnica 11:1111–1129, DOI: https://doi.org/10.1007/s11440-015-0423-7
Yao YP, Lu DC, Zhou AN, Zou B (2004) Generalized nonlinear strength theory and transformed stress space. Science in China. Series E, Technological Sciences 47(6):691–709, DOI: https://doi.org/10.1360/04ye0199
Yao YP, Tian Y, Gao Z (2017) Anisotropic UH model for soils based on a simple transformed stress method. International Journal for Numerical and Analytical Methods in Geomechanics 41:54–78, DOI: https://doi.org/10.1002/nag.2545
Yao YP, Wang ND (2014) Transformed stress method for generalizing soil constitutive models. Journal of Engineering Mechanics 140(3): 614–629, DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000685
Yin ZY, Jin YF, Shen JS, Hicher PY (2018) Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement. International Journal for Numerical and Analytical Methods in Geomechanics 42:70–94, DOI: https://doi.org/10.1002/nag.2714
Zamanian M, Mollaei-Alamouti V, Payan M (2020) Directional strength and stiffness characteristics of inherently anisotropic sand: The influence of deposition inclination. Soil Dynamics and Earthquake Engineering 137:106304, DOI: https://doi.org/10.1016/j.soildyn.2020.106304
Zhang YM, Gao ZR, Wang XY, Liu Q (2022) Predicting the porepressure and temperature of fire-loaded concrete by a hybrid neural network. International Journal of Computational Methods 19(8): 2142011, DOI: https://doi.org/10.1142/S0219876221420111
Zhang YM, Gao ZR, Wang XY, Liu Q (2023) Image representations of numerical simulations for training neural networks. Computer Modeling in Engineering & Sciences 134(2):821–833, DOI: https://doi.org/10.32604/cmes.2022.022088
Zhang YM, Huang JG, Yuan Y, Mang HA (2021a) Cracking elements method with a dissipation-based arc-length approach. Finite Elements in Analysis and Design 195:103573, DOI: https://doi.org/10.1016/j.finel.2021.103573
Zhang YM, Yang XQ, Wang XY, Zhuang XY (2021b) A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements. Theoretical and Applied Fracture Mechanics 113:102930, DOI: https://doi.org/10.1016/j.tafmec.2021.102930
Acknowledgments
This work was supported by the National Natural Science Foundation of China [Grant No.41572255], and Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology [Grant No. 2021B1212040003].
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Wang, H., Sun, H., Ge, X. et al. An Anisotropic Failure Criterion for Cross-anisotropic Soils. KSCE J Civ Eng 27, 3808–3823 (2023). https://doi.org/10.1007/s12205-023-2253-8
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DOI: https://doi.org/10.1007/s12205-023-2253-8