考虑土颗粒微细观运动的多尺度耦合有限元分析方法

A multi-scale coupling finite element method based on the microscopic soil particle motions

土体是一种多相碎散性颗粒材料,具有显著的非均匀非连续力学特性。建立在单一宏观尺度上的经典弹塑性有限元法忽略了土体微细观尺度上的控制机制,不能模拟和预测土体跨尺度层次演化的变形-破坏过程。为研究土体微细观尺度上的物理细节和运动特征对宏观力学响应的影响规律,基于多尺度分层次的土体胞元模型,建立考虑土颗粒转动自由度的多尺度耦合颗粒微转动理论,并编制相应的颗粒微转动理论多尺度耦合有限元程序,对地基塑性区的开展深度进行模拟和预测。结果表明:颗粒微转动理论能有效地实现土颗粒微细观运动细节与土体宏观力学响应的跨尺度耦合关联,且可有效地克服经典有限元法的病态网格依赖性问题;土颗粒的转动位移主要集中在地基塑性区范围内,颗粒转动位移最大值为4°;地基塑性区的开展深度随地基土的颗粒粒径和弹性模量的增加而增大。地基塑性区跨尺度演化的微细观物理机制可解释为:土颗粒的微观转动削弱了颗粒之间应变的传递能力,进而形成塑性应变的集中和发展,最终导致地基的塑性区贯通而发生破坏。

Soil is a multi-phase and multi-scale geomaterial that exhibits dramatically inhomogeneous and discontinuous physical nature.Conventional finite element method,which is conceptualized at a single macroscale and ignores the control mechanism of soil at the micro and meso scales,cannot reproduce and predict the multi-scale and hierarchical failure of soil.In order to investigate the influence of the physical details and kinematic characteristics of soil at the microscale associated with the global mechanical responses,a multi-scale particle micro-rotation theory is established according to the concept of the soil cell element model.The method is implemented into a multi-scale finite element code,and is used to reproduce and predict the depth of foundation plastic zone.The numerical simulation results show that the multi-scale coupling finite element model can relate the motion feature of soil particles at the microscale to the mechanical response of soil at the macroscale;the rotation displacements of soil particles concentrate upon the plastic zone and has an average value of 4°;the depth of foundation plastic zone increases as the size of soil particle and elasticity modulus of soil increases respectively.The concentration and development of plastic deformation,which is caused by the particle rotation leading to a degradation of the ability of strain transmission,are the micro-mesoscale physical mechanism of the trans-scale evolution of foundation plastic zone.