Numerical Simulation Of The Meta-instability Stage Of The Fault Based On The Rate And State Dependent Friction Law By Use Of The Continuum-Discontinuum Method

The unstable slip of the fault can easily lead to the rock burst of the fault and the mining earthquake.In view of the fact that the traditional Coulomb friction law cannot be used to simulate the stick-slip of the fault,the rate and state dependent friction law is introduced into the developed continuum-discontinuum method in which the Lagrangian element and deformational discrete element are combined together.The proposed method is verified through a numerical simulation of the slide-hold-slide test under direct shear.A numerical simulation of the stick-slip of a straight strike-slip fault under biaxial compression is carried out.Evolution of the absolute value of the averaged difference stress acting at the upper end of the rock specimen at a stick-slip with timestep can be divided into the approximately linear stage,the deviated linear stage and the softening stage.The softening stage can be divided into the meta-instability stage I,the meta-instability stage II and the instability slipping stage.At the deviated linear stage,the shear stress of the monitored element at the upper part of the fault begin to release firstly.At the meta-instability stage I,all monitored elements have completed the transformation from stress accumulation to stress release;the displacement value of each monitored point tends to synergize.At the meta-instability stage II,all monitored elements have completed the transformation from slow stress release to rapid stress release;the synergism of the displacement value of each monitored point is strengthened.A numerical simulation of the stick-slip of a straight strike-slip fault with different dip angles is carried out,and the distribution of the friction coefficient at the meta-instability stage is investigated.With the increase of the fault dip angle,the stress drop changes from regular to irregular,the timesteps when the first stick-slip occurs decreases,the averaged stress drop decrease,the period of the stick-slip decreases.The fault is prone to the stick-slip,and the energy released by each stick-slip decreases.At the approximate linear growth stage before the stick-slip,distributions of shear stress and friction coefficient on the fault plane tend to be uniform gradually.At the meta-instability stage,the averaged value of friction coefficient on the fault plane decreases rapidly,which can be regarded as a characteristic of the meta-instability stage.Based on the geological conditions of the 6303 working face in 3-rd Jisan coal mine,a numerical model is established,and a numerical simulation of the fault slipping process induced by mining is carried out.The reason for different displacements based on the rate and state dependent friction law and the Coulomb friction law is discussed.At the slow growth stage,the displacements based on the two friction laws are almost the same;at the rapid growth stage,the averaged displacements based on the rate and state dependent friction law are small,and the averaged displacements have two sudden increases(when the working face is 40 m away from the fault,the first unstable slip occurs;When the working face is 10 m away from the fault,the second unstable slip occurs).The rate and state dependent friction law can be used to simulate the unstable slip of the fault induced by mining.When the distance between the working face and the fault is less than or equal to 40 m,the roof control should be strengthened.Under mining,the displacement based on the rate and state dependent friction law is smaller than that based on the Coulomb friction law.This is due to the fact that after the rate and state dependent friction law is introduced,the fault is in states of rate strengthening and stick for a long time.This is different from results obtained under direct shear.Under direct shear,the displacement value based on the rate-state dependent friction law is greater than that based on the Coulomb friction law.This is due to the fact that after the rate and state dependent friction law is introduced,the fault is in the state of rate weakening,and the friction coefficient on the fault plane decreases.There are 37 figures,2 tables and 89 references in this thesis.