Analytical Method For MechanicalAnalysis Of The Bolt-LiningJoint Support In Underground Tunnels

In tunnel support engineering,bolt and lining are widely used in national defense engineering,water conservancy engineering and mining engineering because of their good support effect,convenient construction and low cost.They have been proved to be economic and reliable roadway support methods.However,compared with the wide application of support technology,the mechanism research,design theory and calculation method of bolt and lining support are not perfect.In particular,the theoretical analysis of the simultaneous existence of bolt and lining support is rare.The focus of this paper is to analyze the mechanical transfer mechanism among surrounding rock,anchor bolt and lining in tunnel excavation engineer ing by establishing a reasonable theoretical model.Based on the existing support theory,aiming at the different combined engineering conditions of surrounding rock,rock bolt and lining,this paper will study the axial force of anchor bolt,shear stress distribution of anchor interface,stress distribution of lining and surrounding rock.In this paper,the support problem of deeply buried tunnel is simplified as a plane strain problem in infinite domain.It is considered that the surrounding rock,lining and rock bolt are all elastic materials,and the three are in complete contact.Using the Cauchy integral method and conformal mapping method in the complex function method,the accurate analytical solutions of stress and displacement of circular hole in infinite domain under the action of concentrated force at any point in the domain is obtained.Using this analytical solution and the accurate analytical solutions of stress and displacement of lined circular tunnel,the mechanical model of the interaction between surrounding rock,lining and anchor bolt is established,the mechanical transfer law between the three is solved,and the influence of various parameters is analyzed,which is compared and verified by ANSYS numerical simulation.The research results obtained in this paper are as follows:(1)When the circular tunnel is excavated and the point anchored rock bolt is installed for support,the effect of the point anchored rock bolt on the surrounding rock can be simplified as a pair of concentrated forces with equal size and opposite direction,which act on the edge of the hole and the midpoint of the anchorage section respectively.Using the analytical solution of stress and displacement with concentrated force acting on any point in the infinite domain of circular hole,based on the displacement coordination condition between surrounding rock and point anchored rock bolt,the axial force of bolts can be obtained by solving corresponding linear equations.The results show that the greater the ratio of Young’s modulus between bolt and surrounding rock,the greater the axial force of bolts,which indicates that the softer the surrounding rock,the greater the axial force borne by bolts;The axial force of the bolt arranged along the direction of the maximum in-situ stress is the largest,and the axial force of the bolt arranged along the direction of the minimum in-situ stress is the smallest.No matter how large the lateral pressure coefficient is,there is a specific length for each bolt to maximize the axial force of the bolt.In other words,if the length of the anchor bolt is too long or too short,the rock bolt can not bear greater axial force.The greater the preload applied to each bolt,the greater the final axial force of the bolt after the deformation of the surrounding rock is completed,and the final axial force of the bolt has a linear relationship with the preload.On the premise that the final axial force of each bolt is the same,the preload required by each bolt is different.The bolt arranged along the direction of maximum in-situ stress needs the least preload,and the bolt arranged along the direction of minimum in-situ stress needs the most preload.After the bolt is installed in the tunnel,the stress distribution of surrounding rock can be improved to a certain extent,but the degree of improvement is not large.The existence of bolt increases the stress in the radial direction and reduces the stress in the circumferential direction.Compared with no bolt,it increases the minimum principal stress and reduces the maximum principal stress,making it easier for the surrounding rock to remain stable.(2)When excavating a circular tunnel and installing a full-length bonded bolt for support,the effect of the bolt on the surrounding rock can be simplified as the shear distribution force along the length of the bolt.Similar to the point anchored rock bolt,the analytical solution of stress and displacement with concentrated force acting on any point in the infinite domain of circular hole is used,and the integral equation for solving the surface shear stress of bolt is established based on the deformation coordination condition of their interaction.The shear stress distribution with high accuracy can be obtained by solving the integral equation by numerical method.The contact shear stress distribution and axial force distribution of the full-length bonded bolt are deduced,and the results accord with the neutral point theory.The shear stress near the end point of the tunnel anchor is the largest,and the possibility of sliding between the anchor and the surrounding rock is the greatest in this area.(3)When the circular tunnel is excavated and supported by pointed anchored rock bolt and lining,the installation of point anchored rock bolts changes the stress distribution of the lining,and reduces the tangential stresses for the most of points within the lining(not significant),but there exit different behaviors for the points in the direction of the bolts:tangential stresses at the inner boundary of the lining shapely increases and even exceed the value without bolts,while tangential stresses at the outer boundary of the lining shapely drop.As for the radial displacement,it decreases no matter where the point is,especially in the direction of bolts installation.With the increase of the Young’s modulus of the lining,the axial forces of the bolts and displacement at the inner boundary of the lining decrease,while the tangential stresses for the points at the inner boundary of the lining increase,which means bearing more loads.