V形河谷中非均匀土石坝振动的简化分析

Simplified analysis of transverse vibration for inhomogeneous earth-rock dams in triangular canyons

本文提出了一种分析V形河谷中三维非均匀土石坝横向振动及其地震反应的近似解析方法 .在考虑坝体的剪切模量随深度呈指数变化的情况下 ,运用三维剪切楔理论 ,导出了土石坝横向振动的控制微分方程 ,并采用分离变量法和伽辽金逼近方法 ,得到了计算土石坝横向振动前三阶振型自振频率的代数公式 .然后 ,应用反应谱技术 ,给出了相应的估计土石坝横向地震反应的最大位移、最大速度、最大加速度以及最大应力的计算公式 .最后 ,给出了地震反应分析的算例 .

An approximate method is proposed for evaluating the transverse earthquake responses of inhomogeneous earth rock dams in triangular canyons. Assuming the shear modulus is varied with depth as an exponential function and based on the 3-D shear wedge theory, the control differential equation of transverse vibration for earth rock dams is derived. Using the variable separation and Bubnov Galerkin method, the algebraic formulas for calculating the free frequencies of the first, second and third mode are deduced. On the basis of technique for response spectrum, the formulas for calculating the maximum values of earthquake response such as maximum dynamic displacement, maximum velocity, maximum acceleration and maximum stress are obtained. An example is given for demonstration.