Research On Contact Problems And Stability Evaluation And Reinforcement In Block System

At present,many large-scale underground projects under construction and completed in China are located in the southwest region.These projects are large in scale and complex in structure,so the construction of the projects is very difficult.At the same time,the terrain conditions in southwestern China are very complex and there are many geological faults.The unstable block formed by the fault cutting surrounding rock will directly affect the stability of the surrounding rock of the cavern.The instability of surrounding rock caused by unstable blocks is one of the most common failure forms in underground engineering,so the study of block stability is crucial.These projects are often directly related to the national economy,people's livelihood and national energy security.Once the blocks are destabilized,these projects will be destroyed,which will cause great harm to safety of construction and operation of the project and will have a major impact on our country.From this point of view,it is very important to study the block stability of large-scale underground engineering,and the contact problem of block system is an crucial part of block stability research.Therefore,it is an important issues to search for an efficient and stable contact algorithm of block system and to put forward the corresponding evaluation and reinforcement method of unstable surrounding rock,which needs to be studied urgently and has great research significance.This paper focuses on several key issues related to contact problem of block system and stability reinforcement of surrounding rock,including the DDA method coupled with finite element method and the improvement of pre-processing,the explicit solution of contact state of block system,the solution of block system considering contact force,the study on the damping properties of blocks and the study on the evaluation method of block stability and corresponding reinforcement measures.The main research contents are as follows:(1)According to the basic theory of DDA coupled with finite element method,an improved modeling method of DDA coupled with finite element is proposed,and a DDA calculation program coupled with finite element is preliminarily developed.Based on the theory of the traditional DDA method and the finite element method,the displacement mode of the DDA method coupled with the finite element is analyzed,and the corresponding form of the element sub-matrix is derived with the displacement mode,and the complexity of the contact problem in the case of dividing elements within blocks is analyzed.At the same time,several key issues related to programming are studied,including grid coordinate description and selection,numerical integration within elements and structured programming design.With specific engineering examples,the improved modeling method and the DDA calculation program coupled with finite element are verified.(2)The approximate step function is used to simulate the contact state of blocks,and based on Lagrange interpolation and variable metric method,the minimum potential energy of block system is obtained,and the explicit solution to obtain the contact state of block system is formed.The hyperbolic tangent function is used to approximate the step function,and the step function with block displacement is used to describe the contact state of the blocks,so as to replace the open-close iteration,to avoid the problem that the open-close iteration is difficult to get converged.Based on the block contact constraint states described by the step function,the potential energy function of block system only containing block displacements as unknown quantity is derived with the Lagrange interpolation.The variable metric method is used to obtain the extremum of the total potential energy function in order to get the displacement of blocks.The displacement of blocks is substituted into the approximated step function to obtain the contact state of blocks.With the sliding block and the multi-block tunnel model,the calculation accuracy and the calculation speed of the explicit solution are analyzed to verify the correctness and the stability of the explicit solution method for obtaining the contact state of the block system.(3)The explicit DDA equation considering contact force is derived,and with the contact constraint equations of the block system,the solution to obtain the contact force of is formed.Considering the interaction between blocks as the point load acting on a single block,the corresponding contact submatrix is calculated and the basic equations of the block system are integrated.The center difference method is used to obtain the explicit expression of block displacement containing contact force.Based on the contact complementarity theory,the constraint relationship between contact force and displacement is derived,and the contact constraint equations are smoothed and converted into derivable equations.The explicit basic equation and contact constraint equation of block system are simultaneously solved by Newton method,and the block displacement and the contact force between blocks are obtained.With the sliding block and the block impacting on a bar,the accuracy and the speed of explicit DDA solution considering contact force are analyzed to verify the correctness and the stability of the explicit DDA solution.(4)Symmetric motion equation of block system considering viscoelastic damping is derived,and based on the Newmark integral,the oscillation characteristics of the block and the final stable state under the action of the external load are analyzed.The convolutional non-viscous damping model is analyzed and substituted into the motion equation of block system,and the motion equation of block system with non-viscous damping is obtained.By introducing auxiliary variables and auxiliary coefficient matrix,the motion equation of block system with non-viscous damping becomes symmetrical in order to make it convenient to solve.Newmark integral is introduced to discrete the motion equation of block system with non-viscous damping,and the velocity and the acceleration are transformed into the expression with displacement;the constant force and resonant excitation are respectively applied on the block to study the final stable state under the action of non-viscous damping.With the underground cavern model,the displacement of the blocks formed by the fault cutting the bottom part of cavern and the stable surrounding rock is monitored.The variation of displacement before and after excavation is analyzed,which verifies the correctness of the motion equations of block system with non-viscous damping.(5)The block stability evaluation method based on strength reduction method of structural plane is studied,and the block reinforcement system is formed.Summarizing the failure modes of block instability,based on the principle of strength reduction of structural plane,a method for evaluating the block stability is proposed,and the criterion of instability is put forward,and it is compared with the rigid body limit equilibrium method.The reinforcement effect of "consolidation grouting of structural plane" and "application of prestressed anchor" to the stability of underground caverns are studied,and the design concept of reinforce unstable blocks of underground caverns is put forward.With the model of underground cavern,the two reinforcement effect of "consolidation grouting of structural plane" and"application of prestressed anchor" are discussed.