Numerical Simulation of the Rock SHPB Test with a Special Shape Striker Based on the Discrete Element Method

Abstract

A split Hopkinson pressure bar (SHPB) system with a special shape striker has been suggested as the test method by the International Society for Rock Mechanics (ISRM) to determine the dynamic characteristics of rock materials. In order to further verify this testing technique and microscopically reveal the dynamic responses of specimens in SHPB tests, a numerical SHPB test system was established based on particle flow code (PFC). Numerical dynamic tests under different impact velocities were conducted. Investigation of the stresses at the ends of a specimen showed that the specimen could reach stress equilibrium after several wave reverberations, and this balance could be maintained well for a certain time period after the peak stress. In addition, analyses of the reflected waves showed that there was a clear relationship between the variation of the reflected wave and the stress equilibrium state in the specimen, and the turning point of the reflected wave corresponded well with the peak stress in the specimen. Furthermore, the reflected waves can be classified into three types according to their patterns. Under certain impact velocities, the specimen deforms at a constant strain rate during the whole loading process. Finally, the influence of the micro-strength ratio (s c =r c ) and distribution pattern on the dynamic increase factor (DIF) of the strength DIF were studied, and the lateral inertia confinement and heterogeneity were found to be two important factors causing the strain rate effect for rock materials.Keywords SHPB Á Special shape striker Á Discrete element method Á Strain rate effect Micro-strength ratio (ratio of contact-bond shear to normal strength) n Time-step N Current time-step DTðnÞ Interval time under time-step n(s) l Frictional coefficient at the specimen/bar interface

Dynamic Fracturing Behavior of Layered Rock with Different Inclination Angles in SHPB Tests

“…Besides, the lengths of transmitted bar and incident bar were set to 0.75 m and 1.5 m. The density of bars particles and striker particles is 7810 kg/m 3 , and the contact bond strength was selected to be high enough to avoid damage during the impact test. The previous studies have been revealed that these settings are feasible [27,28]. Because the impact velocity of striker in laboratory test was 9.4∼10.2 m/s, and the impact velocity of analogue striker was set to be 10 m/s.…”

“…Cylindrical specimens (7283 particle, 50 mm × 50 mm) were produced, and the particle radius of specimen is in the range of 0.3 mm∼0.6 mm. Special particles with radius of 1 mm were aligned to the end of striker, incident bar, specimen, and transmitted bar to improve the contact condition [27]. The features of layered rock were modeled by two steps.…”

An Experimental and Numerical Study on Cracking Behavior of Brittle Sandstone Containing Two Non-coplanar Fissures Under Uniaxial Compression

“…12). Although PFC 2D is only twodimensional, it can be used to simulate many scientific problems in rock mechanics and rock engineering, including laboratory experiments on the failure mechanical behavior of rock material (Debecker and Vervoort 2013;Jia et al 2013;Zhang and Wong 2013), crack initiation, propagation, and coalescence in rock specimens containing pre-existing fissures Zhang and Wong 2012), split Hopkinson pressure bar (SHPB) dynamic test problems (Li et al 2014), large-scale slope failure (Behbahani et al 2013), etc. In PFC 2D , there are two kinds of micro-bond models (Cho et al 2007): one is a contact bond model (CBM) and the other is a parallel bond model (PBM).…”

Numerical Investigation of Dynamic Rock Fracture Toughness Determination Using a Semi-Circular Bend Specimen in Split Hopkinson Pressure Bar Testing

“…Compared with substantial static researches regarding rock fracture toughness determination in recent decades however, studies associated with rock dynamic fracture were fewer in number, resulting in a limited understanding of dynamic fracturing characteristics of rocks. Due to the transient nature of loading and the complexity of rock mass, rock dynamic fracture tests remain challenging and to be improved in the following problems: (1) some vital micromechanisms, such as wave propagation, failure process, force equilibrium, and so on, are still unclear; (2) although numerous detecting techniques have been developed, the time to fracture remains challenging to capture because of the three-dimensional failure process of specimens with complex configurations; (3) the measurement on energy partitions is far from consummate and, thus, the propagation fracture toughness based on the energy analysis is only roughly determined due to the lack of sophisticated monitoring techniques under high-speed loading (Zhang et al 2000;Chen et al 2009;Li et al 2014;Zhang and Zhao 2014).…”

“…Among commonly used numerical methods to simulate dynamic problems, e.g., finite element analysis (FEA) (Li et al 2009), discrete element method (DEM) (Li et al 2014), distinct lattice spring method (DLSM) (Zhao et al 2011), numerical manifold method (NMM) (Wu et al 2014), DEM features: (1) reproducing fracturing of brittle materials, since microcracks initiate, coalesce, and form macrofractures as a result of breakage of bonds cemented between particles; (2) bypassing the development of sophisticated constitutive laws and simulating the physical micromechanisms directly; (3) generating the actual dynamic impact process due to the application of Newton's second law and the real-time tracking of contact forces (Cundall and Strack 1979;Potyondy and Cundall 2004). Indeed, DEM is believed to be an efficient tool for simulating the dynamic failure process of rocks (Li et al 2014).…”