Analysis Of Dynamic Response Of Underground Structures With Consideration Of Rotation Under The Seismic Excitation

After the Kobe earthquake in 1995,domestic and foreign seismic experts and scholars have come to realize that the earthquake-resistance of underground structures is a problem which needs to be solved urgently.At present,the construction of underground structures in China is in the golden period of development,and more and more second-tier cities have begun to build underground structures,so it is necessary for us to make systematic theory study of the earthquake-resistance of underground structures.However,since the founding of China,the static force method has always been used to calculate the internal force of the structure in the code.Despite advances in the anti-seismic research,the numerical analysis is still a commonly used means,and the systematic theoretical analysis of the anti-seismic structures is in lack.At the same time,due to simplify the theoretical analysis model,the scholars always ignore the rotation of structure and only pay attention to the translation under seismic action.Therefore,in this assumption,the structure may be unsafe sometimes.In this paper,the dynamic response of underground tunnel structure under horizontal seismic action is studied,with the consideration of rotation of the structure.Subsequently,the internal force of the structure is calculated.Two kinds of calculation methods are expounded systematically: A pseudo-static analysis method is presented to consider the rotation of the structure,and the other is the pseudo-static analysis method without consideration of rotation of the structure.The main research results are as follows:(1)The motion equations of underground structures are derived with consideration of translation and rotation of the structure under horizontal seismic excitation by using the Lagrange equation.In order to simplify the analysis,the underground structure is viewed as a rectangular rigid body and the Winkler elastic foundation model is adopted.The damping effect exerted by structure-soil interaction is neglected.After the determination of kinetic energy and potential energy of the structure-soil interaction,the motion equations is obtained by using Lagrange's equation.Numerical example is given to demonstrate the effect of the rotation on the earth pressure on the structure.(2)It is unrealistic to use the theory of structural mechanics to calculate the underground structure's internal force in practical engineering.Therefore,this paper presents a new improved method to calculate the underground structure's internal force.At first,the local elastic foundation beam model is proposed based on the Winkler hypothesis.Secondly,the calculation method of the internal force of the underground structure with consideration of translation is obtained by using the motion equations.Finally,a numerical example is given to demonstrate the feasibility of the method.And the results are compared with the structural internal forces calculated by the continuous beam theory.(3)A simplified method to analysis the dynamic interaction of soil and underground structure is optimized.The soil is modeled as Winkler ground.The primary unknowns of the problem are structure joint rotations,and the axial deformation of the members of the structure is neglected.As for the selection of seismic wave,only shear sine seismic action component is considered.And the rotation of the model is ignored.In terms of load,the side wall's dynamic soil pressure under the seism adopt the Davis dynamic pressure distribution.And the equivalent nodal load of the structure is obtained by using the elastic foundation beam theory.The global stiffness matrix of the structure is obtained by the basic principle of the matrix displacement method.The joint rotations of structure are acquired through governing equation.Finally,the bending moment of structure are obtained.