Abstract
We model the fluid flow within the crack as one-dimensional flow and assume that the flow is laminar; the fluid is incompressible and accounts for the time-dependent rate of crack opening. Here, we discretise the flow equation by finite volume methods. The extended finite element methods are used for solving solid medium with crack under dynamic loads. Having constructed the approximation of dynamic extended finite element methods, the derivation of governing equation for dynamic extended finite element methods is presented. The implicit time algorithm is elaborated for the time descritisation of dominant equation. In addition, the interaction integral method is given for evaluating stress intensity factors. Then, the coupling model for modelling hydraulic fracture can be established by the extended finite element methods and the finite volume methods. We compare our present numerical results with our experimental results for verifying the proposed model. Finally, we investigate the water pressure distribution along crack surface and the effect of water pressure distribution on the fracture property.
Highlights
For hydraulic concrete structures, the external dynamic loads, such as strong earthquake, may cause cracking of these structures
Many researchers [1,2,3,4] contributed to the study of hydraulic fracturing problem and these efforts led to a progressive recognition of the multiscale nature of the hydraulic fracturing problem
We model the fluid flow within the crack as onedimensional flow and assume that the flow is laminar; the fluid is incompressible and accounts for the time-dependent rate of crack opening
Summary
The external dynamic loads, such as strong earthquake, may cause cracking of these structures. Gordeliy and Peirce (2013) [23] proposed coupled algorithms that used the XFEM to solve the elastic crack component of the elastohydrodynamic equations that governed the propagation of hydraulic fractures in an elastic medium. They (2013) [24] proposed two novel XFEM schemes for modeling fluid driven fractures both of which exploited an implicit level set algorithm for locating the singular free boundary that occurred when the fluid and fracture fronts coalesce.
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