In this study, a theoretical approach is used to investigate the scattering problem of circular holes under a scalene triangle on the surface. The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables. Based on the complex function, multi-polar coordinate method, and region-matching technique, algebraic equations are established at auxiliary boundaries and free boundaries conditions in a complex domain. The auxiliary circle is used to solve the singularity of the reflex angle at the triangle corner. Then, according to sample statistics, the least squares method is used instead of the Fourier expansion method to solve the undetermined coefficient of the algebraic equations by discrete boundary. Numerical results show that the continuity of the auxiliary boundaries and the accuracy of the zero-stress boundaries are adequate, and the displacement of the free surface and the stress of the circular hole are related to the shape of the triangle, the position of the circular hole, the direction of the incident wave, and the frequency content of the excitation. Finally, time-domain responses are calculated by FFT based on the frequency domain theory, and the results reveal the wave propagation mechanism in a complicated structure.
Rock mass in the fault fracture zone has some characteristics such as low strength and poor self-stability, so the control mechanism of stability has been a difficulty in the research of underground engineering. A set of laboratory simulation method of fault fractured rock mass is developed to reflect the natural forming process of fault fracture zone. Compared with intact rock mass, the fault fractured rock mass has an obvious degradation in strength and deformation parameters, and the degradation index is between 22.79 and 84.06%. The bolt has a certain supporting effect on the fault fractured rock mass, and in the situation of end anchoring, the greater the pretightening force is, the better the enforcement effect will be. The stress field produced by high pretightening force can relieve the stress concentration around the bolt hole and make the initial cracks of rock mass away from the bolt plate. The evolution curve of bolt axial force in the process of uniaxial compression of large-scale specimen shows four stages, which are the initial compression stage, pre-peak joint load-bearing stage, post-peak joint load-bearing stage and the residual stage. Research results could provide some theory reference for the stability control of rock mass in the fault fracture zone. 相似文献