准静态加载条件下的岩石破裂过程动态分析

Dynamic Analysis of Rock Failure Process Under Quasi-static Loading

自然界所有的物质都处于由空间和时间构成的四维时空之中,任何力学过程都是与空间和时间相关的过程。但准静态加载条件下的时间维度往往为人们所忽略。文章通过数值计算,解释了准静态力学问题简化为静态问题的合理性,证明了准静态加载条件下动态分析的正确性,讨论了其时间步长的选取原则。研究表明:动力问题和静力问题(准静态问题)具有统一性,在准静态加载条件下选择动态求解器计算是可行的,应力波的传播、透射和反射对计算结果没有影响;在动力计算中,时间步长选取不但与单元尺寸和波速有关,而且与加载速率相关,在准静态加载条件下,选择较大的时间步长依然可以保证计算精度;时间步长对岩石的应力应变曲线和损伤与破裂模式影响较大。为保证岩石应力应变曲线和破裂模式的稳定性和可重复性,时间步长应小于0.03tp。

All substances in nature are in a four-dimensional space-time composed of manifold.Any mechanical process is a process related to space and time.However,the time dimension of quasi-static mechanical problems is often ignored.By means of the numerical method,the validity of rock dynamic analysis under the quasi-static loading is testified,and the selecting principle of time step is analyzed.The results are as follows.The dynamic problem and static(quasi-static)problem are unified.The dynamic analysis under the quasi-static loading is viable.The numerical results are irrelevant to the propagation,transmission and reflection of the stress wave.In the dynamic calculation,the time step is not only related to the element size and wave velocity,but also associated with the loading rate.The time step can be larger under the quasi-static loading which also can meet the calculation precision.The time step has a significant impact on the stress-strain curve and failure mode.The time step should be less than 0.03tp in order to guarantee their stability and repeatability.