基于非局部理论的瓷石矿滑坡的高阶自适应物质点法研究

数值模拟通常被作为一种预测并防护瓷石矿滑坡的重要手段，但当模拟其滑坡全过程时，经典局部理论往往面临软化带出现尺寸效应的挑战。本研究提出在物质点法中引入光滑算子减少算法的数值振荡，并利用光滑算子所含的粒子近似计算应变梯度，以结合非局部本构克服尺寸效应。采用高阶形函数解决物质点法固有的粒子穿越问题，通过室内试验确定瓷石矿的抗剪强度，以模拟瓷石矿滑坡的大变形全过程，并探究其破坏机理。显然地，光滑算子的引入将影响计算效率，本项目还将对算法进行空间自适应优化，并结合龙格库塔-切比雪夫时间积分在时域上进行优化，提高算法的精度及效率，最终建立一个在空间、时间双重自适应的高阶改进物质点法。以江西省弋阳县大型瓷石矿为研究对象，通过本算法来模拟其滑坡从产生到发展再到稳定的整个运动过程，探究其大变形破坏的诱因机理，预测将造成的破坏面和损失，揭示瓷石矿滑坡的力学演化过程，为瓷石矿的开采工程及边坡设计提供理论支撑。

Numerical simulation is usually used as an important means to predict and protect the landslide of porcelain stone mine. However, the classical local theory often face the challenges of mesh dependence for the softening zone, when simulating the whole process of the landslide. In this research, the smoothing reconstruction is introduced into the Material Point Method to reduce the unphysical oscillation. In order to overcome the mesh dependence by using the nonlocal model, the nonlocal model is adopted by use the particle approximation in the smoothing reconstruction to calculate the strain gradient. High-order shape function would be applied to overcome the inherent drawback of the Material Point Method, the particle crossing. The shear strength of porcelain stone would be determined by the laboratory test. The large deformation of the porcelain stone landslide will be simulated by the proposed algorithm, to explore the failure mechanism. Obviously, the introduction of the smoothing reconstruction would affect the computational cost. Therefore, the algorithm would be developed to be adaptively in spatial discretization to improve the efficiency. The Runge-kutta Chebyshev would be then applied to optimized the algorithm in time domain to improve the accuracy and efficiency. Finally, a high-order improved Material Point Method with time-space adaptivity would be established. Taking the large deformation of porcelain ore in the Yiyang County of Jiangxi Province as the research object, the proposed algorithm is applied to simulate the whole movement of the landslide, in order to explore the inducement mechanism of large deformation and predict the failure surface and the loss caused by flandslide. The mechanical evolution of porcelain ore slope would be reveals by applying the proposed method. In the end, theoretical support would be provided for the mining and slop design of the porcelain ore in this research.