推导出了二维对称刚性块体在水平地面加速度的全正弦波作用下的振动和倾覆响应的解析解。我们用此解估算了致使开往旧金山的列车颠覆的1906年旧金山地震期间加利福尼亚州雷斯角火车站的峰值地面加速度的下限。对单个正弦波在3％阻尼比的条件下,我们得到1,1.5和2Hz的最小颠覆加速度分别为0.35g,0.5g和1.05g。对较真实的加速度图,颠覆加速度约为1.1g(综合数据)和0.76g(1992年兰德斯地震时卢塞恩的记录)。 The analytic solution of vibration and overturning response of two-dimensional symmetric rigid block under the action of full sine wave of horizontal ground acceleration is deduced. We use this solution to estimate the lower limit of peak ground acceleration at the station at Cape Cleas, California, during the 1906 San Francisco earthquake that caused the overturning of the train bound for San Francisco. For a single sine wave at 3% damping ratio, we obtain the minimum subsidence accelerations of 1, 1.5 and 2 Hz of 0.35 g, 0.5 g and 1.05 g, respectively. For more realistic acceleration plots, the subversion acceleration is about 1.1 g (composite data) and 0.76 g (Lucerne’s record at the time of the 1992 Landes earthquake).