土石坝地震响应的非线性剪切条模型与对比分析

对一维剪切条计算模型进行改进，提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系，建立了各层的振动控制方程及其边值条件，进而采用数学物理方程方法进行了求解，确定了体系的振动特性，并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质，通过对线弹性地震响应的反复迭代计算，使得各层土的模量和阻尼比与其相应的剪应变水平相协调，确定出与非线性坝体系统相等效的线性解答，并将所得到的地震响应作为非线性地震响应的近似解。最后，以均质坝和心墙坝作为算例进行了具体的数值计算，将所得结果与有限元数值解进行对比分析，论证了所提方法的适用性和合理性。

Nonlinear shear slice model and comparative studies for seismic response analysis of earth and rock-fill dams

As a simplified analytical procedure, the shear-beam or shear-slice model is widely employed for evaluating dynamic response of earth dams or embankments. In order to improve the accuracy or extend the range of this simplified model, many efforts have been made in past several decades. Presented in this paper is a modified equivalent linear technique for analysis of seismic response of embankments which is based on one-dimensional shearslice model. In the proposed method, the discrete shear-slice model is developed to consider the layered distribution of shear moduli and damping ratios of soils along depth. The differential equations for governing the vibration behavior of embankment are solved mathematically under the assumption of that the soils of embankment display visco-linear-elastic behavior and the closed-form solutions for the natural characteristics and seismic response of the embankment are obtained. The resulting linear solutions are incorporated with equivalent linearization technique for seismic response of embankment or soil strata. A series of trial-and-error iterations are performed in order to make the moduli and damping ratios of all individual layers be compatible with their strain amplitudes. Then a linear system which is overall equivalent to nonlinear embankment system is achieved and the seismic response for this equivalent linearization system can be taken as a good approximation of nonlinear seismic response of embankment. Finally, example studies are performed for both homogeneous embankment and clay-core dam and the numerical results are compared with the solutions obtained by the finite element method to illustrate the rationality and applicability of the orooosed method.