School of Geosciences and Surveying Engineering, China University of Mining and Technology-Beijing, Beijing, P. R. China.
State Key Laboratory Coal Resources and Safe Mining, China University of Mining and Technology-Beijing, Beijing, P. R. China.
PLoS One. 2022 Jun 24;17(6):e0270400. doi: 10.1371/journal.pone.0270400. eCollection 2022.
Numerical simulation is very important to solve geotechnical problems. However, it is difficult to obtain required comprehensive and accurate information such as parameters, boundary conditions, and etc. In this paper, a grey distributed parameter model, which integrates the finite element method (FEM) with the grey system theory, was proposed to address the issue. The analysis of grey properties on rock and soil system was performed. The equilibrium equations, geometric equations, physics equations and related differential equations were obtained, each of the equations contains grey parameters and variables. And the discretization and solution methods of the FEM with the grey variables were discussed. An example of deep-buried circular mining tunnel was applied to test the proposed model. The calculation results were compared with those of the exact solution (analytical solution) and the classical FEM, respectively, through which the rationality of the proposed model was demonstrated. For the first time, grey variables and grey parameters are defined in geotechnical numerical simulation. The expressions of basic equations with grey variables are given respectively. A grey distributed parameter model which integrates the FEM with the grey system theory is proposed to solve geotechnical problems, and the optimal solution to the proposed model is determined through calculation and comparison of an application example. The proposed numerical model with grey variables not only has the advantage of grey system theory, but also greatly improves the adaptability and application effect of the model, which contributes to the prediction and evaluation problems in geological engineering, geotechnical engineering, water conservancy engineering and civil engineering with complex structures.
数值模拟对于解决岩土工程问题非常重要。然而，要获得所需的综合和准确信息（如参数、边界条件等）却非常困难。在本文中，提出了一种灰色分布参数模型，该模型将有限元法（FEM）与灰色系统理论相结合，以解决这一问题。对岩土系统的灰色特性进行了分析。得到了平衡方程、几何方程、物理方程和相关微分方程，每个方程都包含灰色参数和变量。并讨论了具有灰色变量的 FEM 的离散化和求解方法。应用深埋圆形采矿隧道的实例来测试所提出的模型。通过计算和比较，将计算结果分别与精确解（解析解）和经典 FEM 的结果进行了比较，验证了所提出模型的合理性。本文首次在岩土数值模拟中定义了灰色变量和灰色参数，并分别给出了具有灰色变量的基本方程的表达式。提出了一种将有限元法与灰色系统理论相结合的灰色分布参数模型来解决岩土工程问题，并通过应用实例的计算和比较确定了该模型的最优解。所提出的具有灰色变量的数值模型不仅具有灰色系统理论的优点，而且极大地提高了模型的适应性和应用效果，有助于解决地质工程、岩土工程、水利工程和土木工程中具有复杂结构的预测和评价问题。
