悬臂式刚性墙动力响应解析研究  

Analytical study on dynamic response of cantilever underground rigid wall

作　　者：赵爽 余俊[1] 刘新源 胡钟伟 ZHAO Shuang;YU Jun;LIU Xin-yuan;HU Zhong-wei(School of Civil Engineering,Central South University,Changsha,Hunan 410075,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075

出　　处：《岩土力学》2022年第1期152-159,168,共9页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.51978671)。

摘　　要：从水平简谐振动作用下二维土-悬臂式刚性墙计算模型出发,基于波动力学理论,同时考虑土层的竖向应力和竖向位移,对二维场地中悬臂式刚性墙的动力响应特性进行了解析研究。首先对土层振动方程进行变换,得到关于体积应变θ的方程,通过分离变量法进行求解,再回代振动方程得到关于位移运动方程的非齐次方程,结合墙与土层的相互作用条件及远场边界条件得到振动方程定解,进而得到地下刚性墙墙上土压力、墙底剪力及弯矩的更为严格的解析解。将所得解与忽略竖向应力解、忽略竖向位移解进行了对比。研究表明,所得解能多反映出一个共振频率,且当土体泊松比大于0.45时,忽略竖向位移解失去意义。通过参数分析,表明激励频率与土体阻尼因子对墙体动力响应影响较大,考虑的振动模态阶数对墙体动力响应影响较小。Starting from the calculation model of the two-dimensional soil-cantilever rigid wall under horizontal simple harmonic resonance action,and based on the theory of wave mechanics,the dynamic response characteristics of two-dimensional soil-cantilever rigid wall were studied considering the vertical stress and vertical displacement of soil layer.Firstly,the vibration equation of the soil layer was transformed to obtain the equation of the volumetric strain θ,which was solved by the method of separation of variables.Then,the inhomogeneous equation of the displacement motion equation was obtained by substituting the solution back to the vibration equation.The definite solution of the vibration equation was obtained by combining the interaction conditions between the wall and the soil layer as well as the far-field boundary conditions.Then more strict analytical solutions of the earth pressure on the wall,the shear force at the bottom of the wall and the bending moment of the rigid underground wall were obtained.Compared with the vertical stress-neglected solution and the vertical displacement-neglected solution,it is shown that the obtained solution can reflect one more resonance frequency,and when the Poisson’s ratio of soil is greater than 0.45,the vertical displacement-neglected solution is meaningless.Through parameter analysis,it is shown that the excitation frequency and soil damping factor have great influence on the dynamic response of the wall,whereas the vibration mode order considered has less impact.

关 键 词：地下结构抗震分析 简谐振动 动力响应 分离变量法 解析解 

分 类 号：TU435[建筑科学—岩土工程]