The extended finite element method (XFEM) is a new numerical method for modeling discontinuity. Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored. By building the virtual work principle of the fracture problem considering water pressure on the crack surface, the governing equations of XFEM for hydraulic fracture modeling are derived. Implementation of the XFEM for hydraulic fracturing is presented. Finally, the method is verified by two examples and the advan- tages of the XFEM for hydraulic fracturing analysis are displayed.
In the paper,the added tangential nonlinear springs are introduced to represent the effects of one-way and two-way shear keys. The added tangential stiffness coefficient is relative to the joint opening and the relative tangential movement and determined numerically by using a refined model of shear keys.The user subroutine of nonlinear spring elements has been implemented into ABAQUS program.The seismic responses of an arch-gravity dam are mainly examined.It is shown by the results that a significant increase of about 17%-30%in joint opening can be observed for the dam with one-way shear keys;the two-way shear keys are beneficial to restrain the sliding displacement along both the radial and vertical directions,whereas the one-way shear keys mainly restrain the displacement along the radial direction;for the dam with shear keys,the maximum arch stress is increased,the cantilever stress is reduced,and the location of the maximum cantilever stress is also moved from the dam heel to the midheight of the cantilever.
JIANG ShouYan 1,DU ChengBin 1 &YUAN JuWei 2 1 Department of Engineering Mechanics,Hohai University,Nanjing 210098,China
The extended finite element method (XFEM) is a new numerical method for modeling discontinuity.Research about numerical modeling for concrete hydraulic fracturing by XFEM is explored.By building the virtual work principle of the fracture problem considering water pressure on the crack surface,the governing equations of XFEM for hydraulic fracture modeling are derived.Implementation of the XFEM for hydraulic fracturing is presented.Finally,the method is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed.
The paper is devoted to proposing a constitutive model based on micromechanics. The joints in rock masses are treated as penny-shaped inclusion in solid but not through structural planes by considering joint density, closure effect, joint geometry. The mechanical behavior of the joints is represented by an elasto-plastic constitutive law. Mori-Tanaka method is used to derive the relationship between the joint deformations and macroscopic strains. The incremental stress-strain relationship of rock masses is formulated by taking the volume average of the representative volume element. Meanwhile, the behavior of joints is obtained. By using implicit integration algorithms, the consistent tangent moduli are proposed and the method of updating stresses and joint displacements is presented. Some examples are calculated by ABAQUS user defined material subroutine based on this model.
