Discretized Virtual Internal Bond Model And Its Application In Dynamic Fracture Simulation Of Rock

Discretized Virtual Internal Bond(DVIB) is a newly-developed lattice model. The distinct difference from the conventional model is that the DVIB consists of unit bond cell. Each cell contains finite number of cells and bonds, and can have any geometry. The interatomic potential is introduced to describe the bond energy and the force-displacement relationship of a unit cell is directly derived from the potential, bypassing so-called stress-strain constitutive law. This makes the DVIB model capable of simulating large deformation and large displacement problems without separate fracture criterion. To account for the heterogeneity, the modulus of unit cell is assumed to be random number, complying with the Weibull distribution law. The simulation results suggest that with increasing the loading rate, the dynamic fracture path deviates from that predicted under the static load. With the loading rate further increasing, the branching behavior is observed. These phenomena agree with the experimental results. The simulation results suggest that the heterogeneity has significant effect on the fracture propagation. When the rock is strongly heterogeneous, the fracture path deviates seriously from that predicted in homogenous case.Structural anisotropy of triangle cell may have influence on the crack trajectory in fracture simulation. So the regular hexagon unit cell is chosen as the unit cell of the present study. The reason to adopt the regular hexagon unit cell is two-fold. One is that the hexagon has a fully symmetrical geometry. Thus, the geometry of unit cell has no influence on the crack trajectory. Another is that rocklike materials consist of polygon grains. So, the hexagonal cell is proper to represent a grain. By the hexagonal DVIB model, some phenomena in classic dynamic fracture tests such as different fracture mode due to different location of initial notch in impact beam tests and branching are reproduced. The simulation examples show that DVIB is an effective and simple model in dynamic fracture simulation.Although the DVIB can simulate most of dynamic fracture behaviors of material, it cannot well simulate the compressive and shear failure behaviors of geomaterials, which limits its application to geotechnical engineering. To solve this problem, the present paper adopts the idea of effective stress and introduces the Mohr-Coulomb criterion to DVIB model at micro scale. The relationship between micro frictional angle, cohesive strength and the corresponding macro parameters is established. Simulation results show the improved DVIB model can reproduce the characteristic of rock strength under triaxial compression.Another problem in lattice model is that the Poisson ratio of mateiral it represents is fixed. The present papers firstly modified the Stillinger-Weber(SW) potential, and expanded it to other materials than silicon. The modified SW potential is used to characterize the energy of the unit cell of DVIB. Simulation results show that the model can reproduce the variable Poisson ratios. The simulation results also show that the effect of Poisson ratio is non-negligible and the model can well simulate the dynamic fracture behaviors of rock-like material. The present thesis provides a new lattice method for the dynamic fracture simulation of geomaterials.