Structure, equipment, statue or storage cask may experience free-standing rocking on slopes because of the nonuniform settlement of the base, construction error or foundation failure. The free-standing rigid block on a slope subjected to one-sine pulse excitation and earthquake motions is examined in this paper. First, considering the free-standing rigid block on a slope, the overturning acceleration spectrum under one-sine pulse is built. The spectrum covers two overturning modes, i.e. overturning with one impact either before or after the excitation and overturning without impact. Then the influences of the slope on the overturning acceleration spectrum are discussed in depth. The analytical solution is compared with the numerical solution based on both linear and nonlinear formulations. It reveals that the safe region of the minimum overturning acceleration spectrum between mode 1 and mode 2 depends on the angle of the slope. Further, the block on a slope is subjected to the Tianjin, Kobe and Northbridge earthquake motions. By simplifying the main pulse of the motions to one-sine pulse, although the overturning acceleration spectrum fails to predict the overturning acceleration of the block subjected to real earthquake motions, it can provide some guidelines to predict the practical performance of the rocking structures.

中文翻译：

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斜坡上独立式刚性块的摇摆响应

由于基础不均匀沉降、施工错误或基础失效，结构、设备、雕像或储存桶可能会在斜坡上发生独立摇摆。本文研究了斜坡上的自支撑刚性块受到单正弦脉冲激励和地震运动。首先，考虑斜坡上的独立刚性块，建立单正弦脉冲下的倾覆加速度谱。该谱涵盖了两种倾覆模式，即激发前或激发后一次冲击翻转和无冲击翻转。然后深入讨论了坡度对倾覆加速度谱的影响。将解析解与基于线性和非线性公式的数值解进行比较。它揭示了模式1和模式2之间的最小倾覆加速度谱的安全区域取决于斜坡的角度。此外，斜坡上的地块受到天津、神户和北桥地震的影响。通过将运动的主脉冲简化为一个正弦脉冲，虽然倾覆加速度谱无法预测块体在真实地震运动下的倾覆加速度，但它可以为预测摇摆结构的实际性能提供一些指导。