Analytical solutions of combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam-Clay

IF 3.4 2区工程技术 Q2 ENGINEERING, GEOLOGICAL

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-08-07 DOI:10.1002/nag.3821

Chong Jiang, Yaolong Ma, Li Pang, Zhao Chen

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Abstract

This paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam-Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first-order differential equations by using the axisymmetric condition, equilibrium equations, and elastic-plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress-strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.

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未排水改良型 Cam-Clay 中圆柱形空腔的垂直和扭转联合剪切加载的分析解决方案

本文提出了未排水改性 Cam-Clay 中圆柱形空腔的垂直和扭转联合剪切载荷的分析解决方案。在极坐标下建立了圆柱形空腔的控制偏微分方程。利用轴对称条件、平衡方程和弹塑性构成关系，将问题表述为一组一阶微分方程。在塑性状态下，考虑了第二次剪切加载对初始剪切应变的影响。然后，通过对空腔周围的弹性区和塑性区进行积分，可以计算出应力应变分布。为了验证所提出的方法，建立了空腔在组合剪切加载下的有限元法模拟，结果与所提出的分析方案十分吻合。对不同加载路径和加载比下粘土过固结率和原位应力系数的影响进行了参数分析。结果表明，空腔壁上的组合剪切荷载对周围土壤的应力分布有显著影响，加载路径的影响不容忽视。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal for Numerical and Analytical Methods in Geomechanics 工程技术-材料科学：综合

CiteScore

6.40

自引率

12.50%

发文量

160

审稿时长

9 months

期刊介绍： The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.