基于摩尔库伦准则考虑渗流影响的孔扩张理论

MohrCoulomb Criterionbased Theoretical Solutions of Spherical Cavity Expansion Considering Seepage

摘要:

通过球对称问题的应变协调方程、渗流理论、统一强度准则和相关联流动法则分析了球孔扩张问题.首先，根据渗流理论推导出了球对称状态下的球孔扩张的超孔隙水压力分布公式，确定了考虑渗流影响的球形孔扩张问题的应力场、应变场和位移场的基本公式.利用位移公式，结合塑性区球孔孔壁位移，推导了球孔初始半径a0，扩孔半径a和对应的塑性区半径rp三者的理论关系式.利用该关系式和其他相关公式给出了求解球孔扩张问题的具体求解方法.通过该方法求得具体问题的应力场、应变场和位移场.总之，通过扩孔压力p、初始孔径a0和扩孔孔径a这三者中的任意两者可求得具体问题的扩孔压力、应力场和位移场等.最后分析了一个计算实例的主要参量、应力场、位移场.

Abstract:

An analysis was made of the cavity expansion based on the unified strength theory, seepage theory, strain compatibility equations in spherical coordinates and the associative flow rule. First, the excess pore water pressure formula was derived by the seepage theory in spherical coordinates and the basic formulas of stresses, strains, displacements in the elastic and plastic regions were obtained with the excess pore water pressure formula. Then the formula of displacements，boundary conditions of plastic zone were used to derive the theoretical relationship formula among the initial radius a0, expanded radius a and radius of plastic zone rp of the spherical bore. The solution method of the spherical cavity expansion considering seepage was obtained based on the abovementioned formula and some other relative formulas. The closedform solutions of stresses, strains, displacements in the elastic and plastic regions could be obtained in concrete problems of cavity expansion. In summary, the expansion pressure, stresses, strains, displacements in concrete problems could be directy obtained. Finally, a case study was made of the main parameters, the distributions of stresses, strains and displacements.