颗粒土中剪切带临界状态数学描述及其完全解

Mathematical Description and Complete Solution of the Critical State in the Shear Band of Granular Soil

为正确模拟土体涉及剪切带演化的后失效力学响应,需采用包含细观特征长度的高阶连续介质力学模型.笔者利用前期所建立的微极亚塑性模型,对颗粒土中剪切带的发展过程进行了分析推导,得到了剪切带临界状态条件下关键变量所满足的非线性微分方程.该文展示了上述非线性微分方程的简要推导,重点讨论了该非线性微分方程的主要性质、主要参数变化范围和求解途径;通过对剪切带进一步的力学分析补充建立了一个能量方程,使问题具有确定解.在此基础上,应用数值积分求出了剪切带厚度因子和剪切内应力、变形率分布及剪切速度分布的完全解.其中剪切带厚度因子对于微极亚塑性模型细观参数的确定具有重要作用.

High-order continuum models are needed for properly capturing the post-failure mechanical respon-ses of soils involving shear bands.Through analysis on the evolution of shear band in granular soils based on a previously proposed micropolar hypoplastic model,a governing equation for the shear band in the critical state was obtained,which is a special nonlinear ordinary differential equation satisfied by the Cosserat angular veloc-ity.A concise derivation of the governing equation was conducted.The properties of the governing equation,the range of the chief parameter and the approach to the solution were mainly discussed.An energy balance equa-tion was formulated as a complementary condition for the determinant of the problem through analysis on the mechanical properties of the shear band.Then,the complete solutions,including the shear-band thickness fac-tor,the stress distribution,the strain rate components,and the shear velocity,were obtained through numeri-cal integration.The shear band thickness factor is particularly useful in determination of the micro-strength pa-rameter of the constitutive model.