同震断层三维裂纹扩展波动时域超奇异积分法

3D CRACK PROPAGATION MECHANISM ON CO-SEISMIC SLIP UNDER P-AND S-WAVES BY WAVE TIME-DOMAIN HYPERSINGULAR INTEGRAL METHOD

应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题;定义了广义应力强度因子,得到裂纹前沿广义奇异应力增量解析表达式;应用波动时域有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以三维矩形裂纹扩展问题为例,通过典型算例,研究了广义应力强度因子随裂纹位置变化规律;分析了同震断层裂纹扩展中力、磁、电场辐射规律.

This work presents a wave time-domain hypersingular integral equation（WTD-HIE） method proposed by the authors for modeling 3D crack propagation problem on co-seismic slip under fully coupled electromagnetothermoelastic P-and S-wave fields through theoretical analysis and numerical simulations. First,the general extended incremental displacement wave solutions are obtained by wave time-domain Green＇s function method.Then,based on the nonlinear boundary element method,the problem is reduced to solving a set of WTD-HIEs coupled with nonlinear boundary integral equations,in which the unknown functions are the general extended displacement discontinuity waves.The behavior of the general extended singular stress indices around the crack front terminating at the slip surface is analyzed by the time-domain main-part analysis method.The general extended incremental singular stress waves and the extended stress intensity factors are obtained by closed-form solutions.In addition,a numerical method for the problem is put forward with the extended incremental displacement discontinuity waves approximated by the product of time-domain basic density functions and polynomials.Finally,extended stress intensity factors radiation distribution for P-and S-waves at the crack surface are calculated,and the results are presented to demonstrate the applicability of the proposed method.