Longitudinal Seismic Response And Shock Absorption Mechanism Analysis For Tunnels Based On Timoshenko Beam Model

The anti-seismic and shock absorption for tunnels should not be ignored in seismic zone with the frequently high intensity earthquake.Generally,Shear wave?namely S wave?has a pivotal effect on seismic damage of tunnels.This dissertation treats a tunnel as a Timoshenko beam laid on elastic foundation,and herein S wave acting as an external excitation is simplified to be a harmonic load in the lateral direction,then,the high order governing differential equation of a beam at the state of dynamic equilibrium shall been achieved based on equilibrium equations of the internal force?bending moment and shear force?of a small element.As referring to Green's function method for solving the basic dynamic problems of a Timoshenko beam,the explicit formulation of dynamic response of tunnel liner will be derived in order to analyze the dynamic response,anti-seismic and shock absorption effectiveness of a shallow embedded tunnel.Upon a series of simplified precondition for the mechanics model,the basic method and deriving procedure provided in the dissertation,can not only present an explicit formulation of dynamic response of tunnel liner to assess the efficiency of anti-seismic and shock absorption measures,but also contribute to form a new metholody for seismic analysis of tunnel.The study can enrich the theory research for seismic analysis of tunnel and dedicate to draw the more attention and interesting for further and deeper exploration of this field,moreover,the results and datas obtained here can partially support the similar engineering practices.?1?The solution of the basic dynamic response of Timoshenko beam based on Green's function method.The Green's function of dynamic response of an axially loaded Timoshenko beam will be unified by introducing a transition parameter?regarding the two different assumption of the contribution of axial force to vertical force of element.With the aid of Laplace transformation and its invert transformation,the closed explicit form of Green's function for dynamic response of a Timoshenko beam can be deduced,which offers the theoretic support and deriving procedure for the analytical solution of dynamic response of the same beam on elastic foundation.Considering the effect of P wave in analyzing the longitudinal seismic reponse of a tunnel,the transverse response will be amplified due to the essence of the weakened material property caused by axial compression.?2?The shear coefficient of typical cross section of tunnel liner.According to the classic stress-strain relationship,the shear coefficient?can be deduced,and the validation of?is verified by comparing with the result from some references.When the inner radius is adequate and the wall is quite thin,then,a liner of tunnel can be deemed as a thin-wall structure,which results in that?is independent with radius.Besides,the dissertation has listed the some?for some typical liner cross sections treated as thin-wall structures corresponding with the classification of ground varying from type?to type?for railway tunnel and expressway tunnels.?3?The Green's function of dynamic response for the liner section nearby tunnel portal.Introducing the resistant coefficient of elastic foundation into the governing equations of dynamic equilibrium state for a Timoshenko beam,the solution of dynamic response of the liner section nearby tunnel portal can be regarded as that of a Timoshenko beam under a harmonic external excitation by employing Green's function method to get the response of the liner section.The evolving trend of dynamic internal force response of a Timoshenko beam under the free–free boundary condition almost is identical with that has been discovered in the existing literature:the internal force?bending moment,shear force?rises from zero to a peak value,then gradually goes down.The trend under the free-free boundary condition matches that of dynamic response of liner during the actual earthquake.As far as the anti-seismic measure of shallow embedded tunnel liner is concerned,the appropriately improving ratio of portal slope can effectively curb the dynamic response of liner section nearby tunnel portal.The peak of internal force response?bending moment,shear force?arises accompanying with the increasement of the resistant coefficient of elastic foundation.Therefore,the high magnitude of the resistant coefficient of some sound surrounding rock is adverse to anti-seismic effect for shallow embedded tunnel portal.?4?The dynamic response of tunnel liner passing through transition zone of surrounding ground.Importing the conception of a flexible joint?the equivalent model of the torsional spring?into the Green's function of an axial loaded Timoshenko beam on elastic foundation,the dynamic response of liner with the flexible joint will be tackled by the transfer matrix method and superposition technology.In the view of the dynamic response for displacement and internal force,during a earthquake,the dynamic characteristic of a liner with flexible joint passing through transition zone of anisotropic ground,shall be dissected in detail.The weaker ground corresponding with the lower grade of surrounding ground?generally,the resistant coefficient of elastic foundation of the weaker ground is less than that of ordinary ground?,shall lead to the higher level of dynamic response varying with the longer transition zone section.The resistant coefficient of elastic foundation can be increased by improving the quality of surrounding ground by grouting reinforcement,and the optimum shock-absorption effectiveness shall be acquired at k_c2=20×10⁶N/m².When the flexible joint degenerate to absorbing joint?completely disconnecting between liner sections?,the dynamic response of displacement will go up,oppositely,the dynamic response of internal force will decline.The lower internal force response means the better shock absorption effect.?5?The mechanism study of absorption layer based on double-beam system.Using double-beam system to simulate a composite liner system with absorption layer?surrounding ground--preliminary liner--absorption layer--secondary liner?,the Green's function of dynamic response of the composite liner system will be got by solving the governing differential equation of double-beam system.Depending on Green's function of the double-beam system,it has been revealed definitely that the composite liner system can effectually reduce the dynamic response of internal force?bending moment,shear force?.The internal force of the composite liner system arises with the rising of the resistant coefficient of elastic foundation.Moreover,the internal force of secondary liner is rather small by comparing with that of preliminary liner,which illustrates truth that preliminary liner suffers the main earthquake excitation while the secondary liner undertakes a small additional internal force caused by earthquake due to the existing of absorption layer.The internal force of secondary liner shall gradually increase as the stiffness coefficient of absorption layer increasing,however,the internal force is still small.Stemming from that essence that the preliminary liner bears a large portion of the additional load triggered by earthquake,it is quietly clear that the distinct shock mitigation for the secondary liner has been achieved from the perspective of fairly low level of internal force of secondary liner.