爆炸作用下围岩稳定性样条小波三维数值模拟

摘要

Blasting load has characteristics of high pressure and transient state.Underground structure blast simulation belongs to a semi-infinite domain simulation.When using FE for its blast simulation,the computation efficiency is very low due to too many elements.The wavelet finite element method has characteristics of good numerical approach property,one element has many nodes.The 3D wavelet conversion matrix was derived.New elements of 3D interval B-spline annulus wavelet element and sector wavelet element were constructed.They were used to study the adjoining rock stability of an underground arch structure under blasting load through programming with Matlab software.The simulation results were consistent with the data collected at the blasting site.It was shown that the computation efficiency of the proposed method is improved compared with the traditional finite element method.%爆炸具有高压瞬时的特点，地下结构模拟属于半无限域，应用传统有限元模拟时单元划分较多，计算效率低。样条小波有限元具有良好的数值逼近性，一个单元具有多个节点。推导了三维小波转换矩阵，应用构造了三维区间B 样条圆环、扇形小波单元。结合工程实例通过 Matlab 软件编程，对爆炸作用地下拱形结构围岩稳定性进行了三维数值模拟，模拟结果与现场采集数据基本一致，计算效率高于传统有限元。