基于双剪统一强度理论应变退化模型的隧道结构稳定性分析

STABILITY ANALYSIS OF TUNNEL STRUCTURES BASED ON THE TWIN-SHEAR UNIFIED STRENGTH THEORY WITH STRAIN-SOFTENING EFFECT

论文基于双剪统一强度准则应变软化模型对圆形隧道稳定性的分析,提出一种简单的数值计算方法来对围岩进行弹塑性分析。该文采用差分法,基于广义形式的双剪应力屈服准则,并采用相关联流动法则,建立本构方程。对于应变软化模型,该文选定塑性应变增量作为软化参数,并且假设强度参数随软化参数成线性函数关系。弹性区的解答引用拉梅解答,而求解塑性区的解答时,将塑性区分成很多微元圆环,并假设每个圆环的径向应力?r沿半径向内均匀递减;其次,建立每个微元圆环的平衡微分方程、本构方程、几何方程及相邻两微元之间的应力增量和应变增量的关系。从弹塑性交界面处的塑性区最外一个圆环开始,求解出每一个微元圆环的解答。并且利用MATLAB进行编程求解出最终的结果:应力场、应变场、径向位移场的数值解。此外还分析讨论了中间主应力影响系数b、软化参数临界值η*对解答的影响,并分析了影响塑性区半径的因素。

This paper focuses on the analysis of the stability behavior of tunnel structures with circular openings based on the twin-shear unified strength theory with strain-softening model. A simplified numerical approach is proposed for analyzing elasto-plastic behavior of surrounding rocks. Modifying the difference method, this paper proposes a constitutive equation associated with flow rule based on the generalized unified failure criterion. For the strain-softening behavior, plastic strain increment is chosen as the softening parameter, and it is assumed that all the strength parameters are linearly correlated to the softening parameter. The solution of the elastic zone is imposed by Lamé solution. The solution in plastic zone is achieved by subdividing it into infinitesimal annuli, in which the radial stresses are assumed to decrease monotonically along each annulus. Then, equilibrium, constitutive and geometrical equations are established to determine the relationship of the increment of stresses and strains between the adjacent two annuli. The numerical solution of each annulus is calculated from the outmost annulus at the elastic-plastic interface. The stress, strain, and radial displacement results are obtained by programming in MATLAB environment. In addition, the impact of intermediate principal stress factor and the critical softening parameter on the solution are investigated, and the factors influencing plastic radius are discussed.