E. Haghighat

A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique

In this paper, the crack growth simulation is presented in saturated porous media using the extended finite element method. The mass balance equation of fluid phase and the momentum balance of bulk and fluid phases are employed to obtain the fully coupled set of equations in the framework of

Characterizing the mechanical behaviour of the Tournemire argillite

u{-}p

Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique

u-p formulation. The fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well-known cubic law. The spatial discritization is performed using the extended finite element method, the time domain discritization is performed based on the generalized Newmark scheme, and the non-linear system of equations is solved using the Newton–Raphson iterative procedure. In the context of the X-FEM, the discontinuity in the displacement field is modeled by enhancing the standard piecewise polynomial basis with the Heaviside and crack-tip asymptotic functions, and the discontinuity in the fluid flow normal to the fracture is modeled by enhancing the pressure approximation field with the modified level-set function, which is commonly used for weak discontinuities. Two alternative computational algorithms are employed to compute the interfacial forces due to fluid pressure exerted on the fracture faces based on a ‘partitioned solution algorithm’ and a ‘time-dependent constant pressure algorithm’ that are mostly applicable to impermeable media, and the results are compared with the coupling X-FEM model. Finally, several benchmark problems are solved numerically to illustrate the performance of the X-FEM method for hydraulic fracture propagation in saturated porous media.

On modeling of discrete propagation of localized damage in cohesive‐frictional materials

Abstract In this paper, the problem of modeling of mixed mode cracking in concrete structures is addressed within the context of a constitutive law with embedded discontinuity (CLED). This approach, which was originally developed for describing the propagation of localized deformation in a “smeared” sense, is enhanced here to model a discrete nature of crack propagation. The latter is achieved by coupling the CLED approach with the level-set method, which is commonly used within the framework of Extended Finite Element (XFEM). Numerical simulations of experimental tests conducted at Delft University, which involve four-point bending of a notched concrete beam under the action of two independent actuators, are presented. The results based on enhanced CLED approach are directly compared with XFEM simulations. The predictions from both these methodologies are quite consistent with the experimental data, thereby giving advantage to CLED scheme in view of its simplicity in the numerical implementation.

Modeling of deformation and localized failure in anisotropic rocks

Abstract A laboratory programme of uniaxial, triaxial, cyclic and Brazilian tests was conducted to investigate the anisotropic mechanical behaviour of the Tournemire argillite, with different axial loading orientations with respect to the bedding planes (i.e. loading orientation angle, θ=0°, 30°, 45°, 60° and 90°). The experimental results show that both strength and deformation of the argillite are direction-dependent. Failure occurs in a brittle manner with a sudden collapse of the material strength. The failure mode exhibits localization along distinct failure planes and also depends on the loading orientation. This paper summarizes the experimental results and describes constitutive relationships that were developed in order to simulate the stress–strain behaviour of the Tournemire argillite. A microstructure tensor approach is adopted in order to take into account the anisotropic behaviour of the argillite. The identification procedure for material function and parameters is outlined, and the model is applied to simulate the set of triaxial tests performed at different levels of confining pressure and orientation of the bedding planes. It is demonstrated that the model adequately reproduces the anisotropy, the pre-peak stress–strain response and the onset of material collapse in those tests.