梯度塑性理论及其在地质灾害预测研究中的应用

Application prospect of gradient-dependent plasticity in forecasting geological hazards

岩石结构稳定性问题是岩土工程实践中迫切需要解决的重要课题之一。文章以地震为例,讨论了地质灾害的局部化特征,介绍了经典弹、塑性理论的某些缺陷及梯度塑性理论的几点优越性:(1)控制方程总是适定的;(2)病态网格依赖性消失;(3)局部化带宽度由材料的内部长度完全确定;(4)可对岩石结构的尺寸效应及失稳回跳进行合理解释和预测;(5)对预测宏观及微观问题均比较有效。介绍了基于梯度塑性理论的岩石变形、破坏及稳定性研究进展。梯度塑性理论可用于研究单轴压缩条件下,岩石试件发生剪切破坏时全程应力-应变曲线、尺寸效应、剪切带倾角尺寸效应及失稳回跳等问题,它们对土木工程及岩土工程均十分重要。若将单轴压缩岩样比拟为矿柱,则该失稳判据即为矿柱岩爆准则。梯度塑性理论可用于研究韧性断层带内部应变、应变率分布规律、断层带错动位移及带内孔隙度分布规律,为韧性断层带定量分析提供了新的手段。此外,该理论还可对直剪试验机———岩样系统不稳定性进行分析,系统失稳可比拟为断层岩爆。发展基于梯度塑性理论尺度律及失稳判据等解析解一方面可加深对岩石变形、破坏的理解;另一方面,还可用来检验数值结果的正确性。

The problem of stability on rock structure is one of particularly important objects in geo-engineering. The characteristics of strain localization of earthquake were discussed firstly. Then,several defects of classical elastoplastic theory were analyzed and advantages of gradient-dependent plasticity were introduced:(1)governing equation is always well posed; (2)pathological mesh dependence vanishes; (3)the size of localization band is determined strictly according to internal length parameter; (4)it is possible for one to explain and predict the size effect and the snap-back behavior and (5) it is valid for macroscopic and microscopic problems. Then,the analytical progress of deformation,failure and instability of rock structure based on gradient-dependent plasticity is discussed. For uniaxial compression quasi-brittle materials subjected to shear failure,gradient-dependent plasticity can be used to investigate the complete stress-strain curve,size effect,size effect of inclination angle of shear band and snap-back instability criterion etc,which are especially important for civil engineering and geotechnical engineering. If the uniaxial compression specimen is seen as the pillar, the instability criterion is that of pillar rock burst. The theory can be used to study the distributed strain, strain rate, porosity and plastic shear displacement in fault band, which presents a new method for quantitative analysis of ductile shear zone. In addition, the stability of the system composed for shear band ('specimen') and elastic rock mass outside the band ('testing machine') can be analyzed based on the theory. Losing stability of the system means that fault rock burst occurs. Developing the analytical solutions for size effect and instability criterion etc. will enrich the understanding of deformation and failure of rock on one hand. On the other hand, the analytical solutions can be used to check the validity of the numerical results. Finally, further objects of research were proposed.