Modeling of sandstone rock samples using PFC2D code
The PFC2D v. 1.10 code was used to build a numerical discrete particle model of a certain medium-grained sandstone from Jastrzebie Colliery (the Upper Silesian Coal Basin, Poland) to study the deformability and fracture phenomena of rock sample under uniaxial compression conditions. The computer simulation results were compared with the results of laboratory uniaxial compression tests. The numerical model of the dimensions 42 mm × 84 mm (width × height) consisted of about 4300 circular particles with nearly uniform distribution of radii of between 0.25 mm and 0.75 mm, and normal and shear stiffnesses 5 × 1011 Nm−1. Prior to loading there was about 9600 interparticle bonds in the sample. Bulk density and porosity of the granular aggregate was 2700 kgm−3 and 5%, respectively. The normal and shear strengths of parallel bonds were equal to 6 × 1012Pa, while normal and shear stiffnesses of the bonds were equal to 5 × 1017Pam−1. It has been found that PFC2D can reproduce in numerical tests many of the qualitative features of the Jastrzebie sandstone tested under compression. The ultimate strength was almost the same: 136 MPa for the real rock sample and 134 MPa for the numerical model. The axial strain at peak stress was the same: 0.513% and 0.523%, respectively. The secant modulus (Es50), which was measured at the strain corresponding to 50% of peak strength, was 29 GPa for the real rock and 33.5 GPa for the numerical sample. Both the real and numerical rock samples experienced shear faulting in the post-failure stage. Only one important quantitative discrepancy has been observed: the lateral (and volumetric) strain response was much greater in the numerical model than in the laboratory experiments. In general, the slope of stress–strain curves depended on many factors, and in particular on stiffness and strength of parallel bonds. Beside the results of numerical PFC2D compression tests, preliminary results of numerical simulations of the behavior of sandstone samples under uniaxial tension were introduced.