Abstract While performing the upper bound limit analysis, using an associated flow rule, the expressions for the power dissipation function corresponding to different forms of yield criteria for clays exhibiting shear strength anisotropy and transversely asymmetric properties (implying different strengths in compression and tension), have been derived in terms of velocities, strain rates and shear strength parameters without involving stress variables by using the concept of duality in an optimization theory. The optimization has been performed in an efficient manner by using the second order cone programming (SOCP). The problems of strip and square footings have been dealt with. The lower bound solutions have also been established for the plane strain problems, and the two bound solutions have been found to match very closely with each other. The results also match well with the different solutions reported in literature. The variations of the power dissipation function and nodal velocity patterns in the problem domain have also been studied. The proposed formulation(s) will be useful for solving different two and three-dimensional geomechanics problems in clays to account for shear strength anisotropy as well as transversely asymmetric properties.

中文翻译：

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具有各向异性和不同压缩和拉伸强度的粘土的运动学极限分析

摘要 在进行上限分析时，使用相关的流动规则，对于表现出剪切强度各向异性和横向不对称特性（意味着压缩和拉伸强度不同）的粘土，对应于不同形式的屈服准则的功率耗散函数的表达式为通过使用优化理论中的二元性概念，根据速度、应变率和剪切强度参数推导出不涉及应力变量。优化已通过使用二阶锥规划 (SOCP) 以有效方式执行。条形和方形的基础问题已经得到处理。还为平面应变问题建立了下界解，并且发现这两个界解彼此非常匹配。结果也与文献中报道的不同解决方案匹配良好。还研究了问题域中功率耗散函数和节点速度模式的变化。所提出的公式将有助于解决粘土中不同的二维和三维地质力学问题，以解释剪切强度各向异性以及横向不对称特性。