On Calculation Of Settlement Of Shield Tunnel Structures With Axial Force And Shear Effect Considered

In order to investigate the law of settlement of shield tunnels and to improve accuracy and applicability of the method to calculate the settlement,a mechanical model and a calculation method considering axial force and nonlinear shear effect were established,based on theoretical analysis,local prototype test,numerical simulation,and in-situ monitoring.The main research results are as follows:(1)The shield tunnel was taken as a Timoshenko beam with equivalent stiffness.With consideration of axial force and shear-deformation-caused subgrade reaction,a governing differential equation was derived,which was solved by Fourier series method and finite difference method.(2)Influencing factors to the settlement of shield tunnels were analyzed using the established mechanical model.Calculation shows that,the shear deformation of shield tunnels can account for more than 20% of the total settlement.Shear deformation increases with decrease of shear stiffness.As the shear deformation is added,the whole settlement gets larger,while the bending deformation and bending moment are smaller than that as shear deformation is not counted.Assembling-caused axial force enlarges bending deformation and bending moment,but the enlargement is limited.(3)Based on the bilinear elastic-plastic model of longitudinal bolt and considering the preload of the bolt,theoretical calculation formulae to equivalent tensile stiffness and equivalent shear stiffness of the circumferential joint was derived.The equivalent tensile stiffness is divided into three stages according to the preload and the tensile force at elastic limit of the bolt,while the equivalent shear stiffness is divided into four stages in the light of the friction force between adjacent rings,the gap size between the bolt and the hole,and the total shear force at elastic limit of the bolts.(4)In accordance with different axial loads on the segments,local prototype tests on shear mechanical properties of circumferential joints were carried out.Three tests were performed on bent-bolt-connected segments which were taken from lining rings of6.0m diameter,while another three tests were done on slant-bolt-connected segments which were from lining rings of 8.8m diameter.Tests show that,the process of deformation of specimens can be divided into three stages: static friction stage between adjacent segments,gap closing stage between the bolt and the hole,and shear strengthening stage of the bolt.In stage 3,cracks appeared on the concrete surface and penetrated into the segments quickly.The cracks grew radially around the bolt hole.The bolt yielded obviously but did not break.Increment of shear force in stage 2 was small.When the specimen broke,more than 60% of the shear force came from the friction between adjacent segments.The step of 6.0m diameter specimen in stage 2 accounted for 83% of the total step,while the proportions of 8.8m diameter specimen in stage 2and stage 3 were 42% and 49%,respectively.(5)Refined finite element meshes were used to model shear behavior of circumferential joints,upon which the equivalent shear and tensile stiffness of circumferential joints were calculated,respectively.The stiffness of circumferential joints by three means of theoretical formulae,FEM simulation and local prototype tests were compared.The load-displacement curves from three ways were consistent with each other.Then equivalent nonlinear shear stiffness of the circumferential joints and nonlinear shear and tensile stiffness of the longitudinal bolts were determined.(6)In-situ monitoring on the settlement of shield tunnel structures was conducted at two construction sites.Monitored settlement of the tunnel structure were compared with that by theoretical formulae and finite element simulation.The comparison shows that,results by theoretical calculation are of higher consistency with that by numerical simulation and in-situ monitoring.Overall,the results by three methods go well enough with each other,which proves the effectiveness and practicability of the proposed theoretical method.