材料界面迁移问题的SPH大规模精细模拟方法及应用研究

The phenomena of dynamic change in the material interfaces and mechanical properties are often involved in geotechnical engineering such as shield tunneling and foundation penetration, which is usually defined as the Problem with Moving Material Interfaces. Due to the extremely large deformation introduced by material cutting and soil flow, the numerical simulations using conventional methods for these problems are quite difficult, especially when the problems-scale is much large, which seriously reduces the design quality and tends to produce engineering accidents. Therefore, it is urgent to develop new theories and effective numerical methods. The SPH is a kind of mesh-free method which discretizes the governing equations with arbitrarily distributed particles, so it can handle the complicated deformation behavior in a natural way with sufficient computational efficiency; therefore it is a potential powerful tool to solve these challenging problems. The goal of this program is to apply SPH method to solving large geomechanic problems with moving material interfaces with sufficient accuracy and efficiency by adopting radom cutting and multi-resolution computation strategy. The core idea of this program is to establish an adaptive particle reconstruction method, in which the error characteristic of the reconstruction process and the error minimization technique as well as the influence on computational stability will be analyzed; particularly, special efforts will be put on conquering the difficulties of random nonuniform splitting of the SPH particles for the modeling of the meso-mechanical behavior of material cutting. At the same time, the GPU parallel-computation is adopted to improve the computing speed. Finally, experiments of foundation punch-through will be carried out to verify the proposed methods and algorithms, and the research findings will be applied to the numerical simulation for some large engineering projects.

岩土工程分析时（如盾构掘进、基础贯入等）常涉及不同材料交界面及相关力学特性的动态变化，即材料界面迁移。由于这类问题涉及岩土体的切削和流动大变形，常规数值方法求解难度较大，在大规模计算中则受到更为艰巨的挑战，影响了工程设计水平并易引发事故。因此，亟需发展新的理论和方法。SPH无网格法通过任意分布的粒子来离散控制方程，能够以一种自然的方式模拟复杂变形行为，计算效率高，极具发展潜力。本项目以实现大规模岩土力学材料界面迁移问题的SPH高效求解为目标，以随机分割、多分辨率分析为手段，探索自适应粒子重构方法，研究重构的误差特征和控制策略及其对计算稳定性的影响，并重点攻克切削过程中细观力学模拟的SPH粒子随机非均匀分割难题；同时，引入GPU并行计算策略，有效提高大规模计算的速度；最后，开展基础刺入破坏模型试验来验证算法的有效性，并将成果应用于沉井渗蚀助沉的施工仿真。

岩土工程分析常涉及因材料界面迁移引起的土体切削及水—土—结构耦合大变形，常规方法求解难度大，大规模计算更是巨大的挑战。本项目在SPH框架下，提出上述耦合大变形的计算理论和算法，并用于实际工程计算。提出了由切削行为驱动的非对称分布形式的自适应粒子剖分算法，在不显著增加计算量的基础上，提高了计算分辨率和精度，能够精细化模拟迁移材料界面的土体细观切削行为，且子粒子的分布是以最小化侵蚀深度为依据的，可有效减轻接触力振荡，进一步提高计算稳定性，对材料界面迁移问题的模拟起到了重要推动作用。基于两相混合物理论研究，将土体浮密度作为分析对象提出了一种SPH改进水-土耦合算法，有效解决了淹没土与水交界面位置因边界缺陷导致的一系列数值不稳定问题，也可以作为一种有效手段处理土颗粒由于核近似被交界面截断所引起的受拉行为。改进的SPH水土耦合算法可以作为一种潜在的有效工具，为沉井下沉、盾构掘进等涉水实际工程问题提供理论支持和技术支撑。分别建立了笛卡尔坐标系以及轴对称条件下柱坐标系中的土-水-结构耦合SPH算法，在SPH框架下首次实现了土-水-结构三者之间耦合作用，开发了相应的计算程序并采用OpenACC加速器编程语言编制了基于GPU的并行版本，显著提高了计算效率。将虚拟裂缝模型的概念引入SPH，利用弹塑性断裂力学的最小应变能密度因子理论对裂缝扩展的方向进行判定，提出一种基于虚拟裂缝边界的SPH支持域模型，可解决非连续介质计算SPH裂缝问题出现的不稳定问题，为岩土工程中土体大变形裂缝、土石坝心墙水力劈裂等现象的研究提供理论依据。应用上述研究成果及所开发的程序，分别对轴对称条件下纺锤形桩靴基础连续贯入问题以及大型沉井施工下沉问题进行了模拟分析。结果证明算法有效可靠，可作为材料界面迁移问题以及具有大变形特征的土-水-结构耦合作用实际工程问题的有效计算方法。