Anisotropic Super-Subloading Surface Constitutive Model Considering Small Strain Stiffness of Soil

  • Wang Zhichao ,
  • Lin Yanghao ,
  • Tian Yinghui ,
  • Zhang Chunhui ,
  • Luo Guangcai
Expand
  • 1. Hunan Key Laboratory of Geomechanics and Engineering Safety, Xiangtan University, Xiangtan, Hunan 411105, P. R. China;
    2. College of Civil Engineering, Xiangtan University, Xiangtan, Hunan 411105, P. R. China;
    3. Department of Infrastructure Engineering, University of Melbourne, Victoria, 3010 Australia;
    4. School of Civil Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, P. R. China;
    5. China Construction Fifth Engineering Bureau Co., Ltd., Changsha 410000, P. R. China

Received date: 2025-07-20

  Online published: 2026-06-23

Abstract

To overcome the limitations of the conventional super-subloading surface constitutive model in capturing soil stress-induced anisotropy and the nonlinear degradation of shear modulus at small strains, this study presents an enhanced model. By incorporating the g(θ) method and integrating classical small-strain stiffness theory, the proposed model offers improved representation of both anisotropic behavior and the nonlinear shear modulus reduction under small-strain conditions. The new model was subsequently applied to predict triaxial shear test results for Shanghai soft clay, Fukakusa clay, and Hefei slightly expansive clay, as well as to simulate the deep excavation of the Huifu Road Station in Hefei Metro. The results demonstrate that the proposed model effectively captures the high initial shear modulus and its nonlinear attenuation under small-strain conditions, unifies the application of four yield criteria (von Mises, Mohr-Coulomb, Matsuoka-Nakai, and Lade-Duncan) to characterize stress-induced anisotropy, and successfully describes both the structural shear-shrinkage softening of soft clay and the shear-dilation softening of overconsolidated soil. The improved model not only effectively characterizes complex mechanical behaviors of natural soil but also accurately predicts deformation patterns of retaining piles during excavation processes.

Cite this article

Wang Zhichao , Lin Yanghao , Tian Yinghui , Zhang Chunhui , Luo Guangcai . Anisotropic Super-Subloading Surface Constitutive Model Considering Small Strain Stiffness of Soil[J]. Chinese Journal of Underground Space and Engineering, 2026 , 22(3) : 780 -787 . DOI: 10.20174/j.JUSE.2026.03.04

References

[1] Burland J B. Ninth Laurits Bjerrum Memorial Lecture: “Small is beautiful”—the stiffness of soils at small strains[J]. Canadian Geotechnical Journal, 1989, 26(4): 499-516.
[2] Atkinson J H,Sallfors G. Experimental determination of stress-strain-time characteristics in laboratory and in situ tests[J]. Proceedings of the International Conference on Soil Mechanics and Foundation Engineering, 1991, 3: 915-956.
[3] Benz T. Small-strain Stiffness of Soils and its Numerical Consequences[D]. Stuttgart: University of Stuttgart, 2007.
[4] Asaoka A, Nakano M, Noda T. Super loading yield surface concept for the saturated structured soils[J]. Proceedings of the 4th European Conference on Numerical Methods in Geotechnical Engineering- NUMGE98, Udine, 1998: 233-242.
[5] Asaoka A, Nakano M, Noda T. Superloading yield surface concept for highly structured soil behavior[J]. Soils and Foundations, 2000, 40 (2): 99-110.
[6] He H, Li S,Senetakis K, et al. Influence of anisotropic stress path and stress history on stiffness of calcareous sands from Western Australia and the Philippines[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14 (1): 197-209.
[7] Nakai T, Matsuoka H. A generalized elastoplastic constitutive model for clay in three-dimensional stresses[J]. Soils and Foundations, 1986: 26 (3): 81-98.
[8] Yao Y, Zhou A, Lu D. Extended transformed stress space forgeomaterials and its application[J]. Journal of Engineering Mechanics, 2007, 133 (10): 1115-1123.
[9] Xu B, Chen K, Pang R. A bounding surface model for overconsolidated clays with unified plastic potential function in triaxial and general stress state[J]. Computers and Geotechnics, 2024, 172: 106429.
[10] Zienkiewicz O. Some useful forms of isotropic yield surface for soil and rock mechanics[M]. Finite elements in geomechanics, G. Gudehus, ed., Wiley, London, 1977: 179-190.
[11] Crouch R, Wolf J. On a three-dimensional anisotropic plasticity model for soil[J]. Geotechnique, 1995, 45 (2): 301-305.
[12] Yao Y, Wang N. Transformed stress method for generalizing soil constitutive models[J]. Journal of Engineering Mechanics, 2014, 140 (3): 614-629.
[13] Panteghini A, Lagioia R. A single numerically efficient equation for approximating the Mohr-Coulomb and the Matsuoka-Nakai failure criteria with rounded edges and apex[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38 (4): 349-369.
[14] Panteghini A, Lagioia R. On the existence of a unique class of yield and failure criteria comprising Tresca, von Mises, Drucker-Prager, Mohr-Coulomb, Galileo-Rankine, Matsuoka-Nakai and Lade-Duncan[J]. Proceedings of the Royal Society A, 2016, 472(2185): 20150713.
[15] Panteghini A, Lagioia R. Accounting for specific failure criteria in the slip-line method for plane strain problems[J]. Geotechnique Letters, 2017, 7 (2): 184-189.
[16] Panteghini A, Lagioia R. A micropolar isotropic plasticity formulation for non associated flow rule and softening featuring multiple classical yield criteria[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2022, 46(4): 674-696.
[17] 王智超, 彭乙芹, 秦云, 等. 基于统一屈服准则超固结土的应力诱导各向异性下负荷面模型[J]. 岩土力学, 2023, 44(7): 1891-1900. (Wang Zhichao, Peng Yiqin, Qin Yun, et al. Stress-induced anisotropy Subloading surface model for overconsolidated soil based on unified yield criterion[J]. Rock and Soil Mechanics, 2023, 44(7): 1891-1900. (in Chinese))
[18] Hashiguchi K.Subloading surface model in unconventional plasticity[J]. International Journal of Solids and Structures, 1989, 25 (8): 917-945.
[19] Asaoka A, Nakano M, Noda T, et al. Delayed compression/consolidation of natural clay due to degradation of soil structure[J]. Soils and Foundations, 2000, 40 (3): 75-85.
[20] Hardin B O. The nature of stress strain behavior of soils[C]. Proceedings of the ASCE Geotechnical Engineering Division Specialty Conference. Pasadena, CA: ASCE, 1978:3-90.
[21] Santos J A,Correia A G. Reference threshold shear strain of soil its application to obtain a unique strain-dependent shear modulus curve for soil[A]//15th International Conference on Soil Mechanics and Geotechnical Engineering[C]. Istanbul, Turkey: ASCE, 2001: 267-270.
[22] Casagrande A. The determination of the pre-consolidation load and its practical significance[J]. Proceedings of the 1st International Conference on Soil Mechanics, 1936: 3-60.
[23] Ye G, Ye B. Investigation of theoverconsolidation and structural behavior of Shanghai clays by element testing and constitutive modeling[J]. Underground Space, 2016, 1 (1): 62-77.
[24] Vucetic M, Dobry R. Effect of soil plasticity on cyelic responsel[J]. Journal of Geotechnical Engineering, 1991, 117(1): 89-107.
[25] 尹振宇, 顾晓强, 金银富. 土的小应变刚度特性[M]. 上海: 同济大学出版社, 2017. (Yin Zhenyu, Gu Xiaoqiang, Jin Yinfu. Small strain stiffness of soils[M]. Shanghai: Tongji University Press, 2017. (in Chinese))
[26] 张硕, 叶冠林, 甄亮, 等. 考虑小应变下刚度衰减特征的软土本构模型[J]. 上海交通大学学报, 2019, 53(5): 535-539. (Zhang Shuo, Ye Guanlin, Zhen Liang, et al. Constitutive model of soft soil after considering small strain stiffness decay characteristics[J]. Journal of Shanghai Jiao Tong University, 2019, 53(5): 535-539. (in Chinese))
[27] Ye G, Ye B, Zhang F. Strength anddilatancy of overconsolidated clays in drained true triaxial tests[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2014, 140 (4): 06013006.
Outlines

/