Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory, the solid material is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However, in VMIB, the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants, i.e. the Young's modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation, both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass, a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid, the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB, the presented paper sets up a quantitative relationship between the damage tensor and the relative distribution density of bonds. Comparison of the theoretical and the experimental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a foundation for further simulating fracture behavior of rock mass with VMIB model, and an alternative approach for modeling other multi-cracked body.