Combined Viscoplasticity-Embedded Discontinuity Model for 3D Description of Rock Failure Under Dynamic Loading

Abstract

This paper presents a combined viscoplasticity-embedded discontinuity model for 3D analyses of rock failure processes under dynamic loading. Capabilities of a rate-dependent embedded discontinuity model, implemented with the linear tetrahedral element, for mode I (tension) loading induced fractures is extended to compressive (shear) failure description by viscoplastic softening model with the Drucker–Prager yield criterion. The return mapping update formulas are derived for the corner plasticity case exploiting the consistency conditions for both models simultaneously. The model performance is demonstrated in 3D numerical simulations of uniaxial tension and compression test on a heterogeneous rock at various loading rates. These simulations corroborate the conception that the rate sensitivity of rock is a genuine material property in tension while structural (inertia) effects play the major role in compression at high loading rates (up to 1000 s−1). Finally, the model is validated with predicting the experiments of dynamic Brazilian disc test on granite.

A 3D grain‐based reconstruction method from a 2D surface image for the Distinct Lattice Spring Model

“…Generally, only 2D volume fractions of each mineral composition can be obtained from a 2D digital image, which differs from their corresponding 3D contents. Referring to the previous works of Artemieva et al 41 and Saksala, 42 the compositions of each mineral of granite are collected. Since it is difficult to distinguish the difference between feldspar and plagioclase from colours alone and they have almost the same mechanical properties, they are treated as having the same composition.…”

“…Taking Beishan granite as an example, scaled reconstructed GBMs are shown in Figure 19, and the mechanical parameters of each composition are modified from previous works, as listed in Table 1. 38,42,50 As shown in Figure 20, a quantitative comparison of strengths between experimental data and numerical results under compression tests is presented. The numerical results match well with the experimental data.…”

Effect of Grain Level Anisotropy on Numerical Rock Fracture Behaviour under Dynamic Loading

“…As the displacement jump is assumed elementwise constant, ∇ ≡ and thus (2) follows from taking gradient from (1). It should be noted that the term containing the Dirac's delta function, Γ ( ⊗ ) , in (2), is nonzero only when ∈ Γ . This term is zero outside the discontinuity, i.e.…”

“…It is, however, interesting to test the effect of crystal anisotropy in numerical simulation of rock fracture at the laboratory sample level of scale. For this end, the fracture model based on the embedded discontinuity finite element method by Saksala [2] is applied here in simulations of uniaxial tension test on granitic rock. The rock material, consisting of Quartz (trigonal), Feldspar (triclinic) and Biotite (taken hexagonal here) minerals, is described as a linear elastic (up to fracture) heterogeneous and anisotropic material, which fails upon reaching the tensile strength of the individual constituent minerals.…”