ISOTROPICALLY TRANSFORMED STRESS METHOD FOR THE ANISOTROPY OF SOILS
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摘要: 在不同方向的力学参数、结构特性及应力应变关系的不同为材料的各向异性, 建立能够反映这种复杂特性的强度准则、本构模型, 对于材料本构关系的研究具有重要的理论意义. 但材料的各向异性一直是其力学特性描述的难点, 对此, 郑泉水院士提出了各向同性化定理, 为后续研究解决材料的各向异性问题提供了方向及思路. 作者等针对土的应力诱导各向异性提出了变换应力方法, 这种方法同样遵循对材料进行各向异性问题各向同性化处理的思路, 与郑泉水院士的各向同性化定理是一脉相承的, 也是对各向同性化定理的发展. 本文旨在通过分析各向同性化定理与变换应力方法明确两者间的内在联系, 并以土材料的应力诱导各向异性处理为例, 说明在具体材料的各向异性处理过程中面临的现实问题以及变换应力方法是如何解决这些问题的. 分析并给出了变换应力方法应用时的三个合理假设, 推导出了具体的变换应力数学公式, 阐明了在考虑土的应力诱导各向异性的具体函数已经给出的情况下, 在构造土的弹塑性本构模型中采用变换应力方法的必要性.Abstract: The anisotropy of the material refers to the differences in mechanical parameters, structural characteristics and stress-strain relationships of different directions. Establishment of proper strength criteria and reasonable constitutive models which can accurately illustrate this complex characteristic of materials is a huge contribution to the theoretical studies of constitutive relations of materials. However, the anisotropy of materials has always been a major difficulty for researchers in determining the mechanical properties of materials. In order to demonstrate the abstract affection of the materials’ anisotropy, professor Quanshui Zheng proposed the isotropicization theorem, providing valuable thoughts and referential ideas for subsequent researchers to deal with the anisotropy problem. Building on these ideas, the authors proposed the transformed stress (TS) method. The TS method focused on the stress-induced anisotropy of granular geotechnical materials, introduced another train of thought to describe the anisotropy of materials. The TS method followed the theory of professor Zheng about isotopicizing the anisotropy of the materials, which can be considered as a development of the isotropicization theorem. The aim of this article is to clarify the internal connection between the isotropicization theorem and the transformed stress method through the analysis of the deduction progress of transformed stress method. Also, the practical problems faced in the anisotropy treatment process of specific materials and how these problems can be solved with TS method was illustrated with an example of the stress-induced anisotropy treatment of soil materials. In this paper, three reasonable assumptions in practical application of the TS method have been raised, and the specific stress transformation formula is deduced. Also, the significance of applying the TS method even when knowing the specific functions considering the anisotropy of geotechnical materials has been delivered, and the necessity of application of TS method in the progress of constructing soil elastic-plastic constitutive models has also been proved.
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Key words:
- anisotropy /
- geotechnical materials /
- stress transformation /
- isotropicization method
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图 1 SMP准则在π平面上的屈服线/破坏线(真应力空间)
Figure 1. Yield locus/failure loci of SMP criterion in π-plane (original stress space)
图 2 SMP准则在
$ {{\tilde {\text{π}} }} $ 平面上的屈服线/破坏线(变换应力空间)Figure 2. Yield locus/failure loci of SMP criterion in
$ {{\tilde {\text{π}} }} $ -plane (transformed stress space)
图 4 SMP准则在真应力空间和变换应力空间中在π平面上的对应关系
Figure 4. The relation of original stress space and transformed space of SMP criterion in π-plane
图 6 MCC模型在
$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ 面上的屈服线及正交方向Figure 6. Yield locus of generalized MCC model and the orthogonal directions in
$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ plane
图 7 MCC模型在
$\tilde p \text{-} \left( {{{\tilde \sigma }_{\text{a}}} - {{\tilde \sigma }_{\text{r}}}} \right)$ 面上的屈服线及其对应的正交方向Figure 7. Yield locus of generalized MCC model and the orthogonal directions in
$\tilde p \text{-} \left( {{{\tilde \sigma }_{\text{a}}} - {{\tilde \sigma }_{\text{r}}}} \right)$ plane
图 8 变换应力三维化的MCC模型在
$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ 面上的屈服线及流动方向Figure 8. Yield locus and plastic strain flow directions of generalized MCC model using TS method in
$p \text{-} \left( {{\sigma _{\text{a}}} - {\sigma _{\text{r}}}} \right)$ plane
图 9 三维化MCC模型在变换应力空间内屈服面
Figure 9. Yield surface of generalized MCC model in transformed stress space
图 10 三维化MCC模型在真应力空间内屈服面
Figure 10. Yield surface of generalized MCC model in real stress space
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