Embedded strong discontinuity finite elements for fractured geomaterials with variable friction

Abstract

SUMMARYThe strong discontinuity approach to modelling strain localization, combined with an enhanced strain element, has been used for more than a decade to model strain localization in materials including geomaterials. Most implementations of enhanced strain elements in the post-localization regime use very simple constitutive formulations along the discontinuity, such as linear softening or a constant friction coefficient. However, the softening relations can be much more complex for geomaterials. For rocks this softening is induced by micro-fractures coalescing into macroscopic cracks during a narrow time interval called 'slip weakening.' During this interval the cohesive resistance on the nucleating crack decays to zero while the frictional resistance increases. Furthermore, research has shown that the coefficient of friction for these materials is not constant, but in fact is a function both of the slip speed and the state of the material, including wear, temperature, and other factors. In this paper we augment the modelling capabilities of an enhanced strain element by incorporating a cohesive softening law and a popular rateand state-dependent friction model commonly used for describing the constitutive properties of rocks and rock-like materials sliding along the fractured surface.

An extended finite element framework for slow‐rate frictional faulting with bulk plasticity and variable friction

“…This equation predicts a nonlinear slip weakening similar to Figure 3(b) for the case of a variable t N (concave downwards or upwards depending on whether t N decreases or increases during slip weakening), and recovers a linear slip weakening for the case of a constant t N , see [21,34] for further details.…”

“…The upper block was sheared relative to the lower block, mimicking the experiment for granite with a #60 surface subjected to a 15 MPa normal stress [33]. The same experimental curve was earlier reproduced by Foster et al [21] using the assumed enhanced strain FE formulation; here we used the same parameters along with the extended FE simulation. The slip speed began at V 1 = 10 −5 m/s for 2 s, increased to V 2 = 10 −4 m/s for 2 s, and finally decreased back to V 3 = 10 −5 m/s for 2 s. Time increment used in the simulation is t = 0.002 s and the total relative displacement is 0.24 mm after 6 s. The material properties used in the simulation are listed in Table I.…”

“…Recent advances in computational plasticity, along with strong discontinuity kinematics, allow the detection of plastic deformation not only around the fault tip but also on the sliding part of the fault itself. Foster et al [21] used strong discontinuity analysis based on the assumed enhanced strain formulation and attributed the occurrence of bulk plasticity on the sliding part of a fault to locking induced by the more constrained kinematics in a curved fault. Sanz et al [46,47] utilized large deformation contact mechanics to infer the occurrence of plasticity and strain localization around the fault tip underneath an asymmetric anticline as well as to regions much farther away in front of the fault tip.…”

“…Foster et al [21] show that an enhanced FE framework for strong discontinuity based on assumed enhanced strain can handle such combined nonlinearities in the simulation of prototype boundary-value problems. The present paper aims to build upon the results of this previous work and demonstrate that a framework based on the extended FE method can handle extreme nonlinearities just as well.…”

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…The EFEM has been applied to many interesting problems [103][104][105][106] including piezoelectric materials [107], geomaterials [108], coupled formulations [109], finite strains [110], crack branching [111], and dynamic fracture [112], to name a few. Oliver et al [113] compared embedded elements with the extended finite element method (that will be discussed in the next section) (XFEM) for several selected examples and showed that embedded elements can be as accurate as XFEM.…”