基于广义非线性统一强度理论的隧道塌落拱分析

Tunnel collapse arch analysis based on generalized nonlinear unified strength theory

基于广义非线性统一强度的剪切破坏理论,在平面应变状态下,根据极限上限定理和隧道顶部的围岩塌落机制,在耗散能中引入了包含曲线型破裂面方程的目标函数,建立了围岩中任意断面的隧道顶部围岩的塌落机制。基于塑性位势理论,考虑塑性应变增量与塑性势函数的应力梯度成正比,由此得出了在速度间断线上任意点内能的耗散率;再运用虚功原理,建立内能耗散率和外力做功相等的关系式,从而通过变分原理得出了隧道顶部塌落面的解析表达式,由该表达式计算出隧道顶部塌落面的形状。以圆形断面隧道为例,对影响塌落拱形状的隧道半径和中间主剪应力系数等相关参数进行了讨论分析。由此得出:在平面应变状态下,隧道顶部围岩塌落体的宽度和高度随着中间主剪应力系数的不断增大而减小;塌落面的高度随着广义非线性统一强度参数的不断增大而增大,而塌落面的宽度则不断减小;塌落宽度和塌落高度随隧道半径的增大而增大。

Based on the shear failure theory of generalized nonlinear unified strength,under the plane strain state,according to the collapsing mechanism of surrounding rock and the upper bound theorem,the collapse mechanismsin tunnels with arbitrary cross sections are studied.Firstly,the objective function including the equation of curvilinear fracture surface is introduced,and the collapse mechanism of tunnel top surrounding rock with arbitrary cross section in surrounding rock is established.Based on the plastic potential theory,the increment of plastic strain is proportional to the stress gradient of the plastic potential function,and the dissipation rate of energy consumption at any point on the discontinuous line of velocity can be obtained.By using the principle of virtual work,the relationship between the power of external force and the dissipation rate of internal energy consumption can be established.Then the variational method is used to calculate the extreme value and the analytical expression of the collapse surface of tunnel top is calculated.The shape of the collapsed arch can be obtained by using the expression.Finally,taking circular section tunnel as an example,the parameters affecting the shape of collapsed arch,such as the coefficient of intermediate principal shear stress and the radius of tunnel,are analyzed and discussed.