光滑数值流形法研究及其在岩石动态破坏分析中的应用

In rock engineering, such as blasting, rockburst and earthquake engineering, rocks may fail dynamically due to dynamic loads. It is of great importance to study the dynamic response of rock for the safety evaluation in geotechnical engineering. Numerical manifold method, characterized by both continuity and discontinuity, has got many achievements in the simulation of rock mass failure. But in traditional numerical manifold method, calculation accuracy is poor due to the use of constant strain triangle, which in turn limits the further application of numerical manifold method in rock dynamic failure problems.. The strain smoothing technique in smoothed finite element method is introduced into the framework of the numerical manifold method to combine the continuity and discontinuity of manifold method and the high precision of smoothed finite element method. Then the smoothed numerical manifold is established for the whole process simulation of rock dynamic failure. Using SHPB as loading system, plate impact under different loading rates is designed to study the rate dependence of rock. The ultra-high speed camera is utilized to observe the failure process. Rate-dependent dynamic failure criterion can be obtained from the experiment. At last, the smoothed numerical manifold together with the new dynamic failure criterion is applied to the analysis of rock dynamic failure, providing technical support for revealing rock dynamic failure mechanism.

岩石在动力载荷作用下往往发生动态破坏，这一情况普遍存在于爆破、岩爆、地震防护等工程问题中，因此研究岩石在动力载荷作用下的响应对评价岩土工程的安全性具有重要意义。兼具连续和非连续特性的数值流形法在岩体破坏的全过程响应中已经取得不少成果。但常见的数值流形法采用的是三角形插值，属于常应变单元，精度很差，这限制着数值流形法在动力破坏问题中的进一步应用。. 本项研究拟在数值流形法的框架下，引入光滑有限元中的“应变光滑”技术，将流形法的连续、非连续特性同光滑有限元的高精度结合起来，建立模拟岩石动力破坏全过程的光滑数值流形法。同时利用SHPB和超高速摄影技术开展不同加载率下的平板撞击实验，并由此建立率相关的岩石动态破坏准则。最后将岩石动态破坏准则加入光滑数值流形法，用于模拟岩石动态破坏全过程响应，并尝试解释岩石动态破坏的率相关性，为探索岩石动态破坏机理提供技术支撑。

岩石中往往包含大量裂纹、节理等不连续线。裂纹的萌生、扩展和贯通引起岩石的破坏，最终引发工程事故。因此研究岩石在静、动荷载下的破坏过程，具有重要的现实意义。. 常规数值流形法基于三角形插值，精度很差，限制着数值流形法的进一步应用。本项目首先将光滑有限元中的边光滑技术引入数值流形法，建立了高精度的光滑数值流形法。紧接着将光滑数值流形法用于裂纹扩展问题中，建立考虑混合单元影响的修正的扩展光滑数值流形法，大大提高了数值流形法的精度和求解效率。基于四叉树网格，建立了规则网格下的h自适应数值流形法，并将其应用于弹性力学问题和裂纹扩展问题。另外建立了基于三角形网格快速有效的颗粒堆积方法，为颗粒型离散元方法提供了一种新的建模方法。最后为块体DDA建立了一套前处理程序，并将其用于动态裂纹分叉问题。. 本项目显著提高了数值流形法的精度，有助于数值流形法进一步应用于岩石力学问题里。针对块体DDA的研究，扩宽了DDA方法的应用范围，使得DDA方法能更好地模拟完整岩石的破坏，为相关岩石工程问题提供技术支撑。