Bonded Particle-Finite Element Simulation of Rock in Split Hopkinson Pressure Bar Test

ABSTRACT: Dynamic uniaxial compressive strength of Pennsylvania blue sandstone was investigated using split Hopkinson pressure bar both physically and numerically. A hybrid finite-discrete element code called CA3 was employed to simulate the physical tests. The incident and transmitted bars were modeled using finite elements while the rock specimen was represented by a bonded particle discrete system. The incident stress pulse measured in the physical test was utilized as the input for the numerical simulation and was applied to the free end of the incident bar. Analysis of the numerical results suggests an underestimation of the dynamic rock strength; the effect of axial and circumferential inertia of the specimen didn’t manifest the strength value consistent with the physical observation. Therefore, a parameter called rock strength enhancement coefficient was introduced which increases the bond strength between the particles as a function of the relative velocity of particles at the contact points. A much better match between the physical and numerical results is observed if this coefficient is applied in the numerical simulation.

1. INTRODUCTION

Most of the operations on the rock like materials from mining and road structures to dam foundations usually include the dynamic application of the load to the rock. Rocks are pressure sensitive and rate-dependent materials and show a drastically different behavior under dynamic loading. Since the dynamic loading of rocks is applied in a variety of loading rates, it is essential to study the dynamic strength parameters of the rocks and fracture properties over a wide range of loading rates.

There are three main methods for testing the rock materials under dynamic loading conditions which have been suggested by the International Society for Rock Mechanics [1]. These methods include dynamic compression test, dynamic Brazilian test, and dynamic notched semi-circular bend (NSCB) test. All these tests are performed using the split Hopkinson pressure bar (Kolsky bar).

The split Hopkinson pressure bar (SHPB) was first designed for testing of ductile materials such as metals [2]. In the last couple of decades, SHPB has been widely used for evaluating various parameters for brittle materials like rock, concrete, and ceramics [3, 4].

Along with the physical tests, many numerical methods have been utilized to investigate the characteristics of quasi-brittle materials such as rock and concrete in dynamic loading. Various constitutive models were used in ABAQUS to study different parameters which affect the dynamic strength of rock like materials in the FEM method [5, 6, 7]. As previous studies show, discrete element method (DEM) provides an alternative and reliable solution for discontinuum materials like rocks [5, 8, 9]. However, this method is computationally time-consuming when it comes to large scale domains.