SUMMARYThis paper presents a damage-viscoplastic cap model for rocks with brittle and ductile behavior under low-velocity impact loading, which occurs, e.g. in percussive drilling. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept. This approach does not suffer from ill posedness-caused by strain softening-of the underlying boundary/initial-value problem since viscoplasticity provides a regularization under dynamic loading by introducing an internal length scale. The model uses the Drucker-Prager (DP) yield function with the modified Rankine criterion as a tension cut-off and a parabolic cap surface as a compression cut-off. The parabolic cap is smoothly fitted to the DP cone. The strain softening law in compression is calibrated with the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle-to-ductile transition and hardening behavior of geomaterials under highly confined compression, which is the prevailing stress state under a bit-button in percussive drilling. Rock strength heterogeneity is characterized statistically at the structural level using the Weibull distribution. An explicit time integrator is chosen for solving the FE-discretized equations of motion. The contact constraints due to the impact of an indenter are imposed with the forward increment Lagrange multiplier method that is compatible with explicit time integrators. The model is tested at the material point level with various uniaxial and triaxial tests. At the structural level confined compression, uniaxial tension tests and a rock sample under low-velocity impact are simulated.

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SUMMARYIn this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi-brittle failure phenomena. The model is capable of describing the rate-dependent behavior in dynamics and the three phases in failure of quasi-brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture-process zone creation, represented with rate-dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate-dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time-stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption.

SUMMARYThis paper presents a numerical method for continuum modelling of the dynamic bit-rock interaction process in percussive drilling. The method includes a constitutive model based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. The interaction between the drill bit and rock is modelled using contact mechanics by treating the bit as a rigid body. As the bit-rock interaction in percussive drilling is a transient event, the method is implemented in explicit dynamics FEM. The rock strength heterogeneity is characterized at the mesoscopic level statistically using the Weibull distribution. The bit-rock interaction is simulated under axisymmetric conditions using cylindrical and hemispherical buttons. The choice of the quite complex constitutive model accounting, e.g. for plastic compaction, viscoplastic shear and tensile failure along with induced damage and rate dependency is justified by numerical simulations. Moreover, the quasi-static and dynamic cases are compared in plane strain simulations. Finally, some results clarifying the discrepancy of opinions found in the literature concerning the side (lateral) crack formation are obtained.

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Regrettably, the author noticed an error in the code used to compute all the results in the original paper. Namely, the ordering of the last two shear components of the strain/stress vector (6Â1 vector in the Voigt notation) was not consistent. When this error was fixed, the results changed notably. Consequently, the analyses of the results in the original paper are not fully correct.In what follows, the re-computed results are presented along with their corrected analyses as well as the other errors or misprints found in the original manuscript.In the second paragraph in Section 4 (Numerical simulations), the Weibull distribution parameters should read x u = 5 MPa, x u = 50 MPa, not x u = 6 MPa, x u = 60 MPa.In Figure 2a in Section 4.1 (Single-button bit case: simulations with different button geometries), the radius of the button should read R = 5 mm, not R = 10 mm.