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三维化方法对土的平面应变强度和变形的影响分析

姚仰平, 武孝天, 崔文杰

姚仰平, 武孝天, 崔文杰. 三维化方法对土的平面应变强度和变形的影响分析[J]. 岩土工程学报, 2023, 45(3): 459-467. DOI: 10.11779/CJGE20211389
引用本文: 姚仰平, 武孝天, 崔文杰. 三维化方法对土的平面应变强度和变形的影响分析[J]. 岩土工程学报, 2023, 45(3): 459-467. DOI: 10.11779/CJGE20211389
YAO Yangping, WU Xiaotian, CUI Wenjie. Influences of 3D model generalization approach on calculation of stress and strain of soils under plane strain[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(3): 459-467. DOI: 10.11779/CJGE20211389
Citation: YAO Yangping, WU Xiaotian, CUI Wenjie. Influences of 3D model generalization approach on calculation of stress and strain of soils under plane strain[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(3): 459-467. DOI: 10.11779/CJGE20211389

三维化方法对土的平面应变强度和变形的影响分析  English Version

基金项目: 

国家重点研发计划项目 2018YFE0207100

国家自然科学基金项目 51979001

详细信息
    作者简介:

    姚仰平(1960—),男,教授,博士生导师,“973”首席科学家,主要从事岩土本构理论研究工作。E-mail: ypyao@buaa.edu.cn

    通讯作者:

    崔文杰, E-mail: wcui21@buaa.edu.cn

  • 中图分类号: TU473

Influences of 3D model generalization approach on calculation of stress and strain of soils under plane strain

  • 摘要: 临界状态本构模型需要通过三维化来反映材料在三维应力状态下的力学特性。采用不同三维化方法在描述应力罗德角和偏应力对应力应变的影响程度上具有差异性,在平面应变条件下,这种差异性对土的应力应变计算结果影响往往非常显著。以K0固结土的统一硬化(UH)本构模型和空间滑动面(SMP)强度准则为例,分别采用变换应力(TS)方法和g(θ)方法这两种常用方法对模型三维化,推导了相应的三维弹塑性刚度矩阵[Dep],阐述了不同方法在三维应力应变计算过程上的本质区别。相比g(θ)方法,TS方法可以合理描述不同K0状态下土的应力水平对偏平面上屈服曲线形状的影响规律,即由低应力比下的近圆形转变为剪切破坏时的SMP破坏准则形状,实现了土体从剪切屈服到剪切破坏的一致性。通过对一系列平面应变单元试验和边值问题的分析计算结果表明,采用TS方法三维化的UH模型预测结果与已有试验规律更为吻合。在不同K0固结条件下,由于计算得到的破坏面呈现不规则形状,采用g(θ)方法往往过高或过低地估计平面应变条件下土体的应力水平。
    Abstract: To describe the shear yield and failure behavior of soils in the generalized 3D stress space, the critical state constitutive model needs to be combined with some strength criteria. The use of various 3D model generalization approaches is frequently highly important in characterizing the impacts of stress Lode angle and deviatoric stress on stress and strain, especially under plane strain. The unified hardening (UH) constitutive model for K0 consolidated soils and the spatially mobilized plane (SMP) strength criterion are used as examples, and the transform stress (TS) and g(θ) methods are adopted for the 3D model generalization. The 3D elastoplastic stiffness matrix [Dep] associated with each model generalization approach is deduced, and the key difference between various approaches for calculating 3D stress and strain is discussed. The TS method, in comparison to the g(θ) method, is able to transform the yield curve on the π plane from a nearly circular shape under a low stress ratio to the shape of the SMP strength criterion at failure, which demonstrates the consistency from yield to failure. Predictions of a series of plane strain element tests and boundary value problems are performed with the 3D UH model generalized by the TS and g(θ) methods. The results show that the predicted results from the TS method are more consistent with the existing experimental measurements. Due to the irregular shape of the failure surface when using the g(θ) method, the estimated stress level is often either too high or too low under plane strain for K0-consolidated soils.
  • 图  1   采用TS方法三维化的K0-UH屈服面

    Figure  1.   Three-dimensional yield surface of K0-UH model using TS method

    图  2   采用g(θ)方法三维化的K0-UH屈服面

    Figure  2.   Three-dimensional yield surface of K0-UH model using g(θ) method

    图  3   采用TS方法的初始各向同性三维屈服面和破坏面(K0=1)

    Figure  3.   Three-dimensional yield surface and failure surface using TS method with initial isotropic stress status (K0=1)

    图  4   采用g(θ)方法的初始各向同性三维屈服面和破坏面(K0=1)

    Figure  4.   Three-dimensional yield surface and failure surface using g(θ) method with initial isotropic stress status (K0=1)

    图  5   采用TS方法的初始各向异性三维屈服面和破坏面(K0=0.625)

    Figure  5.   Three-dimensional yield surface and failure surface using TS method with initial anisotropic stress status (K0=0.625)

    图  6   采用g(θ)方法的初始各向异性三维屈服面和破坏面(K0=0.625)

    Figure  6.   Three-dimensional yield surface and failure surface using g(θ) method with initial anisotropic stress status (K0=0.625)

    图  7   不同罗德角下三维本构模型屈服面在p-q面形状变化的对比分析

    Figure  7.   Comparison of variation in shape of yield surface for three-dimensional constitutive model under different Lode angles in p-q plane

    图  8   应力加载路径

    Figure  8.   Stress path under loading

    图  9   平面应变单元试验的模型预测值和实测值

    Figure  9.   Predicted and measured results for plane strain element tests

    图  10   沿AB′应力路径加载时π平面应力路径

    Figure  10.   Predicted stress path on π plane when loading along AB'

    图  11   柱孔扩张模型

    Figure  11.   Sketch for modeling expansion of a cylindrical cavity

    图  12   不排水柱孔扩张的有效应力分量变化规律

    Figure  12.   Predicted variation in effective stresses for cylindrical cavity expansion under undrained conditions

    图  13   排水柱孔扩张有效应力分量和比体积变化规律

    Figure  13.   Predicted variation in effective stresses and specific volume for cylindrical cavity expansion under drained conditions

    图  14   排水柱孔扩张孔壁土体在π平面上的应力路径

    Figure  14.   Predicted stress path on π plane for cylindrical cavity expansion under drained conditions

    表  1   Boston Blue clay参数

    Table  1   Parameters for modeling Boston Blue clay

    K0 σr0/
    kPa
    σθ0/
    kPa
    σz0/
    kPa
    p0/
    kPa
    q0/
    kPa
    υ0
    1 100 100 100 100 0 2.01
    0.625 100 100 160 120 60 2.09
    0.4 100 100 250 150 150 2.13
    λ=0.15; κ=0.03; υcs=2.74
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-12-24
  • 网络出版日期:  2023-03-15
  • 刊出日期:  2023-02-28

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