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A graphical method for undrained analysis of cavity expansion in Mohr–Coulomb soil
Géotechnique ( IF 5.8 ) Pub Date : 2022-12-12 , DOI: 10.1680/jgeot.22.00088
Sheng-Li Chen 1 , Xu Wang 1
Affiliation  

A rigorous analytical solution is developed for undrained cavity expansion problems in non-associated Mohr–Coulomb soil, based on a novel graphical analysis approach and on the Lagrangian description through tracking only the responses of a soil particle at the cavity surface. The mathematical difficulties involved with the flow rate calculation when the stress state lies on the corner/edge of two adjacent (Mohr–Coulomb) yield surfaces, for both cylindrical and spherical cases, are tackled by using the generalised Koiter theory for non-associated plasticity. In particular, through the unique geometrical formulation, the effective stress path pertaining to the cylindrical cavity problem can be very conveniently directly determined, and is found to consist of simple, piecewise straight lines in the deviatoric stress plane with the orientations dependent of the relative magnitude of Poisson's ratio and the friction angle. This thus renders possible the removal of the stringent intermediacy assumption for the vertical stress that is commonly adopted in previous formulations, and hence the development of a complete cylindrical cavity expansion solution in Mohr–Coulomb soil under undrained loading conditions. The stress and deformation responses of the cavity, including the typical pressure–expansion curves and limiting cavity pressure, are finally analytically obtained along with the Lagrangian form of the radial equilibrium equation in completely explicit forms. The closed-form solution provided in this paper is the first rigorous one of its kind, thus completing the analytical analysis of the cavity expansion problem with the classical Mohr–Coulomb model; this is deemed to be essential for the interpretation of in situ test results pertaining to cohesive-frictional soils.

中文翻译:

Mohr-Coulomb 土壤空洞膨胀不排水分析的图解法

基于新颖的图形分析方法和拉格朗日描述,通过仅跟踪土壤颗粒在空腔表面的响应,针对非相关莫尔-库仑土壤中的不排水空腔膨胀问题开发了严格的解析解。当应力状态位于两个相邻 (Mohr-Coulomb) 屈服面的拐角/边缘时,对于圆柱形和球形情况,流量计算所涉及的数学困难通过使用非关联塑性的广义 Koiter 理论来解决. 特别是,通过独特的几何公式​​,可以非常方便地直接确定与圆柱形腔体问题有关的有效应力路径,并且发现由简单的,偏应力平面中的分段直线,其方向取决于泊松比和摩擦角的相对大小。因此,这使得消除以前公式中通常采用的垂直应力的严格中介假设成为可能,因此可以在不排水加载条件下开发 Mohr-Coulomb 土壤中的完整圆柱形空腔膨胀解。腔体的应力和变形响应,包括典型的压力-膨胀曲线和极限腔体压力,最终以完全显式的形式与径向平衡方程的拉格朗日形式一起解析获得。本文提供的封闭形式的解决方案是同类中第一个严格的解决方案,从而完成了用经典Mohr-Coulomb模型对空腔膨胀问题的解析分析;这被认为对于解释与粘性摩擦土有关的现场测试结果至关重要。
更新日期:2022-12-12
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