A numerical method based on a damage-viscoplasticity model for rock implemented with the polygonal finite element method is presented in this paper. As many rocks display polygonal mineral texture, polygonal elements are naturally suited for modelling these rocks. A heterogeneity description based on random clusters of elements representing the constituent minerals of the rock is included. The numerical simulations of dynamic indentation of rock with a spherical indenter are carried out to demonstrate the method. The effect of surface roughness is accounted for in the simulation showing that it adds to the reliability of the results.

1 Introduction

The basic problem to be tackled in numerical modelling of purely percussive drilling is the dynamic indentation of rock by a single indenter (Saadati et al., 2014; Saksala, 2011). A numerical method with predictive capabilities in modelling this problem provides a valuable tool for the drill bit design. Therefore, this is the problem where a numerical model for percussive drilling is to be first tested.

In the two studies cited above, the continuum approach based on finite elements and damage-plasticity type of rock modelling were chosen. However, they used conventional hexahedral (Saadati et al. 2014) and axisymmetric triangular (Saksala, 2011) finite elements. In the present study, the polygonal finite elements are employed in numerical modelling of rock failure under dynamic indentation with a spherical tool.

Polygonal finite elements are rarely used in numerical analyses of rock failure. However, as many rocks exhibit polygonal mineral texture, it is natural to used polygonal elements to describe rock mineral mesostructure. Saksala (2018) used polygonal elements in numerical simulation of rock fracture under dynamic loading. The rock heterogeneity was described at the mesolevel by random clusters of elements representing the rock constituent minerals with their respective material properties.

Compared to the usual triangular and quadrilateral elements, polygonal elements offer, in many cases, greater flexibility in meshing arbitrary geometries, better accuracy in the numerical solution, better description of certain materials, and less locking-prone behavior under volume-preserving deformation (Sukumar & Tabarraei, 2004). However, due to the rational basis functions, the numerical integration is more involved.

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