巷道围岩状态的等效应力等效应变表述

Expression on equivalent stress and equivalent strain of wall rock state of tunnel

在体积应变为零的条件下,根据巷道围岩属简单加载的特性得到围岩中同时关联三向应力σθ,σz,σr和三向应变εθ,εz,εr的,用等效应力σi和等效应变εi表示的对围岩加载-形变关系式。严格地论证了巷道围岩的弹性、硬化、软化和流动区的应力应变状态分别与围岩的等效应力-等效应变曲线各阶段的应力应变状态相对应。以等效应力、等效应变为中间变量可以简化围岩弹性分析,简捷地写出巷道围岩偏应力应变能的计算公式。等效剪应力τi是围岩中的最大剪应力τmax,等效剪应力单元受正应力和剪应力作用,但其上只有剪切应变,这突出了巷道围岩形变破坏是由于最大剪应力和偏应力应变能所致的实质。根据等效剪应力概念确定的滑移线,可适用于材料应变硬化和软化阶段,不要求刚塑性假定条件。

Abstract： Under the condition of no cubic strain, the loading-deformation relational expressions of wall rock are obtained according to simple loading characteristics of wall rock of tunnel. The relational expressions are simultaneously related with triaxial stress （δθ,δz,δr） and triaxial strain （εθ,εz and εr） in wall rock, and they are expressed by equivalent stress, δr, and equivalent strain, εi. The stress or strain state of elastic zone, hardening zone, softening zone and flowing zone of wall rock of tunnel are respectively corresponded with the stress or strain state of different stages of equivalent stress-strain curve, and they have strictly been demonstrated. Supposing equivalent stress, δi, and equivalent strain, εi, are regarded as middle variables, can the elastic and plastic analysis of surrounding rock be simplified, and can the calculation expression of deviatoric stress-strain energy generation of tunnel surrounding rock is written forthright. Equivalent sheafing stress, τi, is the most sheafing stress, τmax, in wall rock. Equivalent sheafing stress unit is acted on by the direct stress and sheafing stress, but it only has sheafing strain. This emphasizes an essence that the deformation and fracture of wall rock of tunnel are resulted from the most sheafing stress and biased stress-strain energy. The determined slipping line based on equivalent sheafing stress conception can be applied to strain hardening and softening stages of the materials and needn＇t require the supposition condition of rigidity-plasticity.