Research and application of precise PFC numerical calculation method based on Voronoi diagram
Macro-mechanical behavior of rocks depends on their micro-structural characteristics.That means the accuracy of discrete element based modeling is closely related to the efficiency of numerical model in representing complex micro-structure of rocks.In order to improve the adaptability of discrete element based modeling to mining engineering,a precise PFC numerical calculation method based on Voronoi diagram is proposed accordingly.The convex polyhedron involved in the Voronoi diagram,which commonly used to divide the space,has the advantages of randomness and variety in variation,which makes it similar to rock micro-structure.The identification number and position of the point,edge,plane and polyhedron are extracted from the Voronoi diagram and imported into PFC as geometry data with the help of Fish language embedded in PFC.Two kinds of methods for developing irregular particle are established,including VCPM and VBPM models and the referred models are used to simulated intact rock and broken rock,respectively.Monte-Carlo method is utilized to produce pseudo random numbers complying Weibull distribution,which are assigned to characterize the micromechanical parameters of rocks and achieve simulation of rock heterogeneity.The number of contacts surrounding single irregular particle is defined as coordination number(CN).The volume and CN of irregular particle present Weibull distribution and normal distribution,respectively,realizing simulation of micro-structural complexity.The VCPM model reproduces strength variation,pre-peak hardening behavior,post-peak softening behavior and volumetric dilation behavior of rock under uniaxial and triaxial compression conditions.According to modeling results,the uniaxial compressive strength and elastic modulus are equal to 221 MPa and 64 GPa,respectively,and the predicted internal cohesion and friction angle are 34 MPa and 55°,respectively,which are consistent with experimental data.The large friction angle means the shear inter-locking effect is strengthened in the proposed model.Besides,the modeling results indicate rock failure mode transmits from axial splitting to shear faulting and then to plastic flowing due to increase in the confining pressure.The VBPM model reproduces compression process and load-bearing capacity variation of broken rock in horizontal constrained compression test.In the initial loading stage,the slope of deformation curve is small duo to large porosity of broken rock.The increase in axial load cause close of the pore,leading to continuous growth in the slope of the curve.The simulation results of the stress-strain curve are consistent with the experimental results.Due to great differences in the freedom between different irregular particles,the distribution of contact force in the VBPM model shows non-uniform distribution during the compression process.
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