Discretized Virtual Internal Bond Based Creep Fracture Model And Numerical Simulation

Creep is a very important mechanical behavior of rock.It seriously impacts the stability of rock mass engineering.The creep failure derives from the evolution of internal creep fractures in rock.Thus,it is significantly important to develop an efficient creep model to analyze the creep fracture behaviors of rock.Discretized Virtual Internal Bond(DVIB)is newly-developed lattice model,whose discrete structure is composed of lattice bond cells.Each bond cell can take any geometry with any number of bonds.One bond cell can be considered as meso grain.Thus,DVIB can capture the mesostructural characteristics of rock.The bond energy is characterized by a hyperelastic potential.The constitutive relation of the bond cell is directly derived from the bond potential.For no small deformation hypothesis is introduced,DVIB can simulate the fracture behaviors of large displacement and finite deformation.For the hyperelatical bond potential contains the micro fracturing mechanism,DVIB can simulate fracture without any separate fracture criterion.So,DVIB presents great advantages in fracture simulation.Because the original DVIB only considers the hyperelatics properties of material,it cannot simulate the creep behaviors of material.The fundamental component of DVIB is the one-dimensional bond while the conventional physical creep model is the one-dimensional combination of different physical components.Therefore,the one-dimensional combination can be considered as a one-dimensional bond,based on which the creep DVIB can be derived.Through this approach,the three dimensional transformation of the creep equation is avoided.The fracture mechanism is naturally incorporated into the creep model.Thereafter,the creep fracture can be efficiently simulated.To reflect the viscosity mechanism of rock,a viscosity component is coupled with a hyperelatic bond in parallel,forming a hyperelatic-Kelvin bond(HK).Based on the HK bond,the constitutive relation of DVIB is derived.A parameter calibration method for the micro bond viscosity is developed.And the numerical solution method for HK-DVIB is developed.The simulation examples suggest that the HK-DVIB can efficiently represent the typical three-stage feature of creep.The simulation results further indicate that the acceleration stage of creep is actually the creep fracturing stage.The reason that HK-DVIB can well simulate the typical three-stage feature of creep is that it can account for both the viscosity and micro fracture mechanisms.In addition,HK-DVIB can represent the rate-dependency of rock strength to great extent and the elastic after effect.The HK-DVIB is sensitive to bond deformation rate,leading to the over-stiff phenomenon at the initial loading stage of creep.To address this problem,an elastic bond is connected to the HK bond in series,forming a general hyperelastic Kelvin(GHK).Based on this GHK bond,the constitutive equation of DVIB is derived.The bond parameter calibration method and numerical solution method are developed.The numerical simulation results suggest that GHK-DVIB can avoid the over-stiff phenomenon.To simulate more complicated creep fracture,multiple physical components are connected together in series,forming a multistage series(MS)bond.The general constitutive equation of DVIB is derived based on the MS bond.The bond parameter calibration method and the numerical solution method are developed.To show the numerical solution method of the MS-DVIB,take the Nishihara model as example.Through this general creep model of DVIB.In the numerical implementation of the creep DVIB,it is unnecessary to derive the analytical solution of the creep component.The macro creep behaviors are the natural response of the bond assembly under the boundary condition of the macro constant stress.It provides a new creep fracture simulation method.