Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article.By constructing hydraulic potential functions of the manifold element,the element conductivity matrix and the glo...Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article.By constructing hydraulic potential functions of the manifold element,the element conductivity matrix and the global simultaneous equations for unconfined seepage analysis are derived in detail.The algorithm of locating the free surface and the formula for seepage forces are also given.Three-dimensional manifold method employs the tetrahedral mathematical meshes to cover the whole material volume.In the iterative process for locating the free surface,the manifold method can achieve an accurate seepage analysis of the saturated domain below the free surface with mathematical meshes unchanged.Since the shape of manifold elements can be arbitrary,the disadvantage of changing the permeability of transitional elements cut by the free surface in the conventional Finite Element Method（FEM） is removed,and the accuracy of locating the free surface can be ensured.Furthermore,the seepage force acting on the transitional elements can be accurately calculated by the simplex integration.Numerical results for a typical example demonstrate the validity of the proposed method.展开更多
The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. Accordin...The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.展开更多
The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture ...The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture network seepage is obtained.Through introduction of the generalized Darcy's law,conservative equations for both fracture surface and fracture interactions are established.Combined with the boundary condition of Signorini's type,a partial differential equation(PDE) formulation is presented for the whole domain concerned.To solve this problem efficiently,an equivalent variational inequality(VI) formulation is given.With the penalized Heaviside function,a finite element procedure for unconfined seepage problem in 3D fracture network is developed.Through an example in a homogeneous rectangular dam,validity of the algorithm is verified.The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems,and is effective in describing some interesting phenomenon usually encountered in practice,such as "preferential flow".展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 50725931, 50839004)the Ministry of Education of China for New Century Excellent Talents in University (Grant No. NCET-07-0632)
文摘Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article.By constructing hydraulic potential functions of the manifold element,the element conductivity matrix and the global simultaneous equations for unconfined seepage analysis are derived in detail.The algorithm of locating the free surface and the formula for seepage forces are also given.Three-dimensional manifold method employs the tetrahedral mathematical meshes to cover the whole material volume.In the iterative process for locating the free surface,the manifold method can achieve an accurate seepage analysis of the saturated domain below the free surface with mathematical meshes unchanged.Since the shape of manifold elements can be arbitrary,the disadvantage of changing the permeability of transitional elements cut by the free surface in the conventional Finite Element Method（FEM） is removed,and the accuracy of locating the free surface can be ensured.Furthermore,the seepage force acting on the transitional elements can be accurately calculated by the simplex integration.Numerical results for a typical example demonstrate the validity of the proposed method.
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProject(51178468) supported by the National Natural Science Foundation of ChinaProject(2013zzts235) supported by Innovation Fund of Central South University of China
文摘The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.
基金supported by the National Natural Science Foundation of China(Grant No.51079110)the National Basic Research Program of China("973"Project)(Grant No.2011CB013506)
文摘The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture network seepage is obtained.Through introduction of the generalized Darcy's law,conservative equations for both fracture surface and fracture interactions are established.Combined with the boundary condition of Signorini's type,a partial differential equation(PDE) formulation is presented for the whole domain concerned.To solve this problem efficiently,an equivalent variational inequality(VI) formulation is given.With the penalized Heaviside function,a finite element procedure for unconfined seepage problem in 3D fracture network is developed.Through an example in a homogeneous rectangular dam,validity of the algorithm is verified.The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems,and is effective in describing some interesting phenomenon usually encountered in practice,such as "preferential flow".
