离散元-有限元-有限体积法并发型多尺度流固耦合模型研究

The concurrent multiscale fluid solid coupling model for discrete element-finite element-finite volume methods is an essential tool to reproduce the progressive failure process of saturated rock and soil masses. The keys to improving its computational accuracy and efficiency are constructing a coupling strategy that maintains stress continuity between the macroscopic and mesoscopic models and establishing a model adaptivity strategy that makes the sizes of substituted randomly distributed discrete element assembly and replaced finite element matched. Based on the generalized bridging domain method, a concurrent multiscale fluid solid coupling model is proposed in this project. The stresses obtained by statistically averaging the contact forces of discrete elements are applied at the numerical integration points of the finite elements while the displacements interpolated from finite elements are imposed on the artificial boundary of discrete elements. Navier-Stokes equations, which are discretized by finite volume method, are consistently adopted to describe both the macroscopic and mesoscopic pore fluids flows. The relationship between the viscous drag force and the relative pore fluid velocity with respect to rock or soil skeleton is correlated by Ergun, Wen and Yu’s empirical formulas. The Mohr-Coulomb strength condition is chosen as the model adaptivity criterion, the finite element that reaches the adaptive criterion is replaced by discrete element assembly that is randomly generated according to the granular graduation. The proposed concurrent multiscale fluid solid coupling model is used to simulate the progressive failure process of saturated rock and soil masses, cone penetration process in saturated and layered sand is taken as an example. Cone penetration test is performed to validate the established concurrent multiscale fluid solid coupling model.

离散元-有限元-有限体积法并发型多尺度流固耦合模型是再现饱和岩土体渐进破坏过程的重要手段。构建能够保持宏细观模型间应力连续的耦合策略及使替换的随机离散元颗粒集合与被替换的有限单元大小相匹配的模型自适应策略是提高其计算精度和效率的关键。本项目基于广义桥域法构建并发型多尺度流固耦合模型，在有限元的数值积分点上施加由离散元接触力统计平均的应力，在离散元的截断边界上施加有限单元的插值位移。采用由有限体积法离散的Navier-Stokes方程统一描述宏细观孔隙流体的流动，粘性拖拽力与孔隙流体-岩土骨架相对运动速度的关系由Ergun，Wen和Yu经验公式关联。选取摩尔-库伦强度条件作为模型自适应准则，采用按颗粒级配随机生成的离散元颗粒集合替换达到自适应准则的有限单元。多尺度数值模拟饱和岩土体的渐进破坏过程（以饱和成层砂土的静力触探过程为例），并通过静力触探试验验证所构建的并发型多尺度流固耦合模型。

岩土体的渐进破坏过程严重威胁着我国人民的生命和财产安全。准确地模拟岩土体的渐进破坏过程是当前国民经济发展的迫切需求。本项目研究一种离散元-有限元-有限体积法并发型多尺度流固耦合模型并开发相应的软件平台来再现饱和岩土体的渐进破坏过程。构建能够保持宏细观模型间应力连续的耦合策略及使替换的随机离散元颗粒集合与被替换的有限单元大小相匹配的模型自适应策略是提高其计算精度和效率的关键。本项目首先基于广义桥域法构建并发型多尺度流固耦合模型，在有限元的数值积分点上施加由离散元接触力统计平均的应力，在离散元的截断边界上施加有限单元的插值位移。采用由有限体积法离散的Navier-Stokes方程统一描述宏细观孔隙流体的流动，粘性拖拽力与孔隙流体-岩土骨架相对运动速度的关系由Ergun，Wen和Yu经验公式关联。选取摩尔-库伦强度条件作为模型自适应准则，采用按颗粒级配随机生成的离散元颗粒集合替换达到自适应准则的有限单元。提出基于快速傅里叶变换的改进均化分析方法关联岩土体的宏细观参数。在此基础上，开发岩土体渐进破坏过程的离散元-有限元-有限体积法并发型多尺度流固耦合分析平台及岩土体宏细观参数的均化分析程序。对岩土体的细观多孔结构开展均化分析获得宏观等效参数，结果表明改进的均化分析方法能够很好地关联岩土体的宏细观参数。多尺度数值模拟岩土体的渐进破坏过程，结果表明本项目所提出的基于广义桥域法的离散元-有限元-有限体积法并发型多尺度流固耦合模型能够保持宏细观不同尺度模型间的应力连续。岩土体的渐进破坏过程，尤其是宏细观模型参数的演化规律，关心区域的细观演变规律，得到了有效地预测。

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