Investigation On Friction Contact Model Of Cushion And Concrete And Its Application In Shield Tunneling

Contact and friction is prevalent in engineering practice,which belongs to the nonlinear problem,and has always been an important and relatively difficult research topic.It is vital to correctly analyze the mechanism of the deformation of the contact surface,the location of the shear failure,the stress-strain relationship of the contact surface,the transfer process of the load,and the accurate calculation of these for the study of contact and friction problems.In the current shield tunnel,the shield tunnel segments are composed of a few pieces of prefabricated reinforced concrete blocks,and there are circumferential joints between the block and the block and ring joints between the rings and rings.The contact and friction between tunnel segment have an important effect on the stability of the shield tunnel under the action of the surrounding soil.And the rubber cushion attached to segments in joints is super-elastic material,which lead to more complex response of contact and friction between the tunnel segments in joints.The contact and friction characteristics of interface between rubber cushion and concrete are studied by direct shear test in this paper,which is descried by PPR potentialbased cohesive zone model to simulate the shear tests.In addition,the 3D FEM is combined with the cohesive theory to study the failure form of tunnel lining,and the numerical results is compared with full scale tests of tunnel lining.And the distribution and propagation of cracks and the failure form of tunnel lining is analyzed based on this model.Moreover,based on the idea of hierarchical model,the 2D hierarchical model and the 3D discontinuous model of shield tunnel are established with stratigraphic-structure method and contact theory to study the effect of contact and friction in joints on the stability of shield tunnel segments.(1)The process of shear stress via shear displacement can be divided into the elastic stage and the plastic phase when the interface is between concrete and concrete.And the contact surface is still in the high stress state after the shear stress reaches the shear peak stress.However,when the concrete specimen is affixed with the rubber cushion,the process of the shear stress and the shear displacement produce softening phenomenon based on the material properties of the rubber cushion.Although the rubber cushion is very thin,it is a typical flexible material,which can play a good buffering response between concrete and release the stress concentration.The shear peak stress is increase with the axial stress for two interface conditions,and the relation between shear stress and axial stress is described by revised Archard's nonlinear friction power law.The parameters m and n of the two kinds of interfaces are 1.37,0.99 and 4.55,0.33 respectively,which provide the basis for the estimation and prediction of the shear stress peak of similar interfaces.When the interface without separation,the normal and tangential contact stiffness of the interface between concrete are 28.95 MPa / mm,12.77 MPa / mm,respectively;and the normal and tangential contact stiffness is 35.85 MPa / mm,2MPa / mm respectively for the interface of concrete with cushion,which provide reference for the analysis and calculation of contact and friction characteristics of joints in shield tunnel.(2)The PPR cohesive model has advantage on describe failure problems because of its macroscopic fracture parameters are represented by the fracture boundary conditions and can be obtained from tests.The contact and friction of above tests are described by the PPR cohesive model,and the results are in good agreement with the tests.The revised PPR cohesion model can accurately reflect the response of relation between shear stress and shear displacement,which can be used to describe similar shear failure problems.(3)The failure mode of tunnel lining under loading has been represented by the 3D FEM combined with the cohesive theory,and the relationship between the displacement and loading,the crack distribution and crushing of the tunnel lining are identify with fullscale tests.It is reliable to analyze and describe the crack propagation and process of failure of tunnel lining.Under local bias conditions,the bias load and relative displacement of tunnel lining are decrease and increase respectively with the range of bias load increase.The main crack firstly produces in the inside of tunnel lining when the range of bias load is smaller,and the failure mode of tunnel lining represents crushing failure at the center of the bias range.With the increase of the bias range,the inside of the tunnel lining at both ends of the bias range crushes,and the failure mode represents the crushing failure of tunnel lining at the end of the bias range.With smaller range of loose pressure,the firstly penetrating crack appear at the inside of tunnel lining,and the failure mode of the tunnel lining presents a crushing failure on the outside of the top of the lining.The local crushing generates at the both sides and the crown of tunnel with the increase of loose pressure range,and the tunnel lining is crushing finally at the both ends of tunnel lining.Larger loose pressure range makes it easier to crushing the tunnel lining.When void exists behind tunnel lining,the main cracks firstly generate at the crown of tunnel lining.Then fracturing fracture produce at the inside of two sides of tunnel lining,and the tunnel lining finally crushing at the outside in the crown of tunnel lining.The load and displacement is same at different void range when the tunnel lining is crushing,and the void area behind the lining has little effect on the cracks and failure forms of the tunnel lining.(4)The beam theory with assumptions and using conditions can't really reflect the stress distribution of the end section,and there is a large error during the internal force calculation of tunnel segment and can't accurately reflect the stress behavior of tunnel segment.The bending moment calculated by the beam element exist larger error and the axial force is larger compared with hierarchical model.The deformation of tunnel segment for hierarchical model and homogeneous ring model are similar,but there are significant differences in the deformation of the tunnel segment near the circumferential joints.The rotation and dislocation between the segments of the circumferential joint are significantly larger than those at the other positions of the segment,which makes the mechanical properties of tunnel segment near the circumferential joint appear complex non-linear distribution.The deformation of the segment is related to the position of the circumferential joint in the tunnel segment lining,and the detail structures in joint plays an important role in the stress predictions for joint sections in the tunnel segment.The cushions involved in the lining structure played an accommodated role in the mechanical behaviours of concrete segments.The launching and break through zones are the relatively weakest positions in the lining system,which must be reinforced by various effective engineering measures to guarantee the service-life of lining structure.(5)The deformation of tunnel segment lining for discontinuous model is similar to that of the homogeneous ring model,but the deformation of the tunnel segment near to joints is significant in the discontinuous model.Under the loading of soil,the deformation between tunnel segment in circumferential joints present relative displacement and rotation;while the deformation between tunnel segment in rings joints mainly present relative displacement,and The deformation of the segment is related to the position of the circumferential joint in the tunnel segment lining.The existence of the circumferential and rings joints of the tunnel segments causes relative dislocation and rotation between tunnel segments,which lead to the deformation of tunnel segment near to joint are significantly larger and are discontinuously distributed.In the two models,the inside and outside of the tunnel segments are compressed and tensile respectively on the both sides of the tunnel;while the inside of and inside of the tunnel segment are tensile and compressed respectively at the crown and bottom of tunnel.There is a relative dislocation and rotation between the tunnel segments in the discontinuous model,which result in the stress concentration in the local position of the joint.At the same time,the stress of the local tunnel segment is released and the stress value and the force range are obviously reduced,and the stress distribution of tunnel segment is also discontinuous.Under the local load,the contact and friction between tunnel segments has a significant effect on the stress deformation of the tunnel segments.The local loading is mainly suffered by the load-ring and its local deformation is larger in the discontinuous model.The influence of the local loading on the tunnel segment is larger than that on the homogeneous ring model,and the local position of the tunnel segment is more likely to produce large deformation and damage that threatening the overall stability of the tunnel segment lining.