A Simple Generalized Method for Unified Constitutive Model of Clay and Sand
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摘要:
为统一描述砂土和黏土在广义应力路径下的力学响应，在具有状态参数的砂黏统一本构模型CASM的基础上，结合次加载面理论和变换应力法，提出一种适用于广义加载条件的统一临界状态本构模型（CASM-SG模型）. 该模型基于原始CASM模型，结合次加载面概念建立一种与土体初始状态相关的塑性内变量，并利用变换应力法成功将原先由三轴压缩实验确定的二维屈服包面拓展到三维应力空间；构建广义应力条件下CASM-SG模型的应力剪胀关系和硬化准则等完整本构框架，并基于一致性条件推导出其塑性模量与弹塑性刚度矩阵的显式表达式；采用新提出的模型对Hostun砂土和Fujinomori黏土在排水与不排水三轴压缩及拉伸条件下的力学行为进行模拟. 模拟结果显示：CASM-SG模型能够较为准确地捕捉砂土和黏土在不同应力路径下的力学行为；对于Fujinomori黏土，三轴拉伸强度相对三轴压缩强度降低了24%左右，CASM-SG模型能够精确捕捉这一特征；相比原始CASM模型，该模型仅增加了2个具备明确物理意义的材料参数，但体现出良好的精度与简洁性兼顾的建模优势.
Abstract:To consistently describe the mechanical response of sand and clay under generalized stress paths, a unified critical state constitutive model (CASM-SG) applicable to generalized loading conditions was proposed based on the unified constitutive clay and sand model (CASM) with state parameters and by employing the subloading surface theory and the transformed stress method. In the model based on the original CASM model, a plastic internal variable associated with the initial state of the soil was established by using the concept of subloading surface, and the original two-dimensional yield surface determined from triaxial compression tests was transformed into the three-dimensional stress space through the transformed stress method. A complete constitutive framework was constructed for the CASM-SG model under generalized stress conditions, including the stress dilatancy relationship and the hardening rule. Explicit expressions for the plastic modulus and the elastoplastic stiffness matrix were derived based on the consistency condition. Finally, the proposed model was employed to simulate the mechanical behavior of Hostun sand and Fujinomori clay under drained and undrained triaxial compression and extension conditions. The simulation results indicate that the CASM-SG model can accurately capture the mechanical behavior of both sand and clay under various stress paths. For Fujinomori clay, the triaxial extension strength decreases by approximately 24% compared with the triaxial compression strength, and the CASM-SG model captures this characteristic. Compared to the original CASM model, the CASM-SG model introduces two additional material parameters with clear physical interpretations, demonstrating a favorable balance between modeling accuracy and simplicity.
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Key words:
- generalized stress space /
- sand /
- clay /
- constitutive model /
- transformed stress method
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图 1 状态参数，参考状态参数在e-ln p空间中的示意[18]
Figure 1. State and reference state parameters in e-ln p space
图 3 CASM模型和CASM-SG模型在广义应力空间中的屈服面 （r = 50, n = 2, M = 1.2）
Figure 3. Yield curves of CASM and CASM-SG models in generalized stress space （r = 50, n = 2, M = 1.2）
图 4 Hostun砂土在不排水TC/TE条件下的有效应力路径
Figure 4. Effective stress paths of Hostun sand under undrained TC/TE conditions
图 5 Hostun砂土在不排水TC/TE条件下的应力-应变关系
Figure 5. Stress–strain relationship of Hostun sand under undrained TC/TE conditions
图 6 正常和超固结Fujinomori黏土在排水TC条件下的应力-应变及体变-应变曲线
Figure 6. Stress–strain and volumetric strain–strain curves of normally and over-consolidated Fujinomori clay under drained TC conditions
图 7 正常固结Fujinomori黏土在排水TE条件下的应力-应变及体变-应变曲线（Δp = 0）
Figure 7. Stress–strain and volumetric strain–strain curves of normally consolidated Fujinomori clay under drained TE conditions （Δp = 0）
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