DISEÑO METODOLÓGICO Tipo de estudio:

1.3.1 Background on interface element models

Cohesive interface elements have been widely used to model nucleation or propagation of cracks in composite materials (e.g. delamination of fiber-reinforced composite laminates (Balzani and Wagner, 2008), cross-ply composite laminates (Aymerich et al., 2008, 2009), and polymer ma- trix composite (Corigliano and Ricci, 2001)), rock failure (e.g. fault slip (Aagaard et al., 2013)), soil-structure interaction (e.g. soil-wall and soil-pile) (Cai et al., 2000; Hu and Pu, 2004), and soil-reinforcement analysis (Gens et al., 1989). Desai et al. (1984) proposed a thin-layer interface element for soil-structure interaction with special constitutive law to model cracks under opening and shearing modes. Given the same constitutive parameters, the performance of the interface element can be affected by the thickness of the thin-layer. This effect was discussed by Sharma and Desai (1992) through an extensive parametric study; certain guidelines were provided to em- pirically determine the element thickness under various conditions. Different approaches have been proposed for the constitutive model of discontinuity including penalty method (Papadopoulos and Taylor, 1992; Xie and Waas, 2006), Lagrange multipliers (Aagaard et al., 2013). Numerical per- formance of different interface laws (or stress-displacement curves), e.g.bilinear, linear-parabolic, exponential, and trapezoidal, for debonding problems was studied using pure-mode problems (Al- fano, 2006); it was reported that the choice of softening curve depended greatly on ratio between

the interface toughness and the stiffness of the bulk material. In geomechanics, several categories of finite elements that have been proposed to model the soil-structure interaction, soil-reinforcement interaction, and rock joints (Goodman et al., 1968; Beer, 1985; Griffiths, 1985; Pande and Sharma, 1979; Gens et al., 1989). Some examples are: Gens et al. (1989) used zero-thickness solid inter- face elements to analyze the soil-reinforcement interaction in a pull-out test; softening behavior of the interface was observed. Carol et al. (1997) proposed a general normal/shear cracking model for quasi-brittle materials, which was used for discrete crack analysis. Katona (1983) introduced a contact-friction interface element to simulate the frictional slippage, separation and re-bonding between two bodies along the interface and the subsequent deformation due to an arbitrary static loading. Zong-Ze et al. (1995) explored the constitutive law using a direct shear test and proposed an interface element model with small thickness. Day and Potts (1994) numerically investigated the effects of stiffness matrix and stress gradients on the stability of zero-thickness interface ele- ments in practical applications. Some research work related to mesh free method (Dolbow and Belytschko, 1999; Sukumar and Belytschko, 2000; Wells and Sluys, 2001; Remmers et al., 2003) have been developed based on partition-of-unity property of finite element shape functions Melenk and Babuˇska (1996). The key feature is to capture the crack initiation/propagation in an arbitrary direction independent of mesh structure. Therefore, mesh bias can be avoided and remeshing is not necessary during the crack propagation.

1.3.2 Multiphase flow and heat transfer in fractured porous media

Fluid flow in saturated fracture has been studied by many researchers. Fractures saturated with liquid in geomaterials act as main flow paths. Noorishad et al. (1982) studied the coupled stress and fluid flow in a fracture-closing problem due to fluid withdraw in a saturated fractured medium. Ge (1997) proposed a generalized equation to predict fluid flow behavior in a saturated fracture with nonparallel and nonsmooth geometry surfaces under steady state conditions. Segura and Carol (2004) presented a double-noded zero-thickness flow interface model to account for both longitudinal and transversal fluid flows in a single discontinuity. The model was further extended

to a coupled hydro-mechanical interface model for geomaterials with existing or developing frac- tures by Segura and Carol (2007a,b, 2010). In contrast to saturated fractures, multiphase flow and transport processes in partially saturated fractures are theoretically more complex and practically more significant. For partially saturated fractures with two phases (gas and liquid) coexisting, and the presence of one phase produces various degrees of resistance to the flow of the other phase, depending on phase saturation. With the flow paths distorted, the fractures may act as barriers for the phase under low saturation. Several mathematical models have been proposed to describe the multiphase flow in fractured porous media under partially saturated condition (Therrien and Sudicky, 1996; Pruess and Tsang, 1990; Persoff and Pruess, 1995). Recently, coupling between flow and mechanical response in cracks of geomaterials has gained increasing attention. A typ- ical application is related to geomechanical analysis of geological sequestration of CO2, which is

broadly considered as a challenging but promising technology to mitigate climate change. Reservoir failure or fault slip may happen due to increased fluid pressure during geological sequestration of CO2, and earthquake may be induced by the fault-instability processes (Rutqvist et al., 2007, 2008,

2010; Cappa and Rutqvist, 2011a,b). Fluid flow and chemical transport in fractured porous me- dia under non-isothermal conditions have received increasing attention due to various geotechnical applications. A number of numerical simulations have been reported to predict the more com- plex interaction between multiphase flow, chemical transport, and heat transfer processes (Pruess et al., 1990; Xu and Pruess, 2001). Rutqvist et al. (2002) developed a coupled thermo-hydrologic-

mechanical-chemical simulator by combining two existing computer codes TOUGH2 and FLAC3D.

The so-called “coupling” between flow and mechanical responses in the analysis are based on linking the multiphase flow simulator TOUGH2 (Pruess et al., 1999) and commercial geomechanical code FLAC3D.