Explicit solutions for the ground displacement of a sliding model simulating both the frictional and rotational effects under idealized acceleration pulses
Angelos L. Protopapas, Constantine A. Stamatopoulos
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引用次数: 0
Abstract
For the first time, the present work derives explicit equations predicting the downward ground displacement of a sliding model simulating both the frictional and rotational effects under idealized acceleration pulses, in the form of simple formulas. Explicit equations allow not only accurate predictions in all cases, but also analysis of the solutions and derivation of expressions for limit cases. Half and full cycles of (i) rectangular, (ii) triangular, (iii) trapezoidal, and (iv) sinusoidal pulses and slopes both under static stability and instability are considered. For this purpose, for pulse cases (i)–(iii) recently proposed implicit analytical solutions are used, while for case (iv), first the analytical equations predicting the sliding displacement and velocity of a sinusoidal pulse in terms of time are obtained and then the time duration of motion is estimated, by using the Bhaskara approximation of the sine and cosine functions. Then, from these, solutions for the particular limit cases corresponding to the “conventional” sliding-block model (Case A) and the post-failure run-off movement without any applied pulse (Case B) are derived. The results for Case A provide a useful tabulation of sliding-block solutions, some of which are not reported in the literature. The results for Case B provide novel predictions of the time duration of motion in the case of post-failure movement. The general solutions are analyzed graphically and the deviation from the solutions of Cases A and B is illustrated. Finally, the explicit solutions are compared to solutions of actual accelerograms.
本研究首次以简单公式的形式,推导出模拟理想化加速度脉冲下摩擦和旋转效应的滑动模型地面向下位移的明确预测方程。显式方程不仅可以准确预测所有情况,还可以分析解法并推导出极限情况的表达式。考虑了 (i) 矩形、(ii) 三角形、(iii) 梯形和 (iv) 正弦脉冲的半周期和全周期,以及静态稳定和不稳定情况下的斜坡。为此,对于脉冲情况(i)-(iii),采用了最近提出的隐式解析解,而对于情况(iv),首先利用正弦和余弦函数的巴斯卡拉近似法,得到预测正弦脉冲滑动位移和速度的解析方程,然后估算运动的持续时间。然后,根据这些结果,得出与 "传统 "滑动块模型(情况 A)和无任何施加脉冲的故障后径流运动(情况 B)相对应的特定极限情况的解决方案。情况 A 的结果提供了一个有用的滑块解法列表,其中一些解法在文献中没有报道过。情况 B 的结果对失效后运动的持续时间进行了新的预测。对一般解法进行了图形分析,并说明了与案例 A 和案例 B 的解法之间的偏差。最后,将显式解法与实际加速度图的解法进行比较。
期刊介绍:
Earthquake Engineering and Structural Dynamics provides a forum for the publication of papers on several aspects of engineering related to earthquakes. The problems in this field, and their solutions, are international in character and require knowledge of several traditional disciplines; the Journal will reflect this. Papers that may be relevant but do not emphasize earthquake engineering and related structural dynamics are not suitable for the Journal. Relevant topics include the following:
ground motions for analysis and design
geotechnical earthquake engineering
probabilistic and deterministic methods of dynamic analysis
experimental behaviour of structures
seismic protective systems
system identification
risk assessment
seismic code requirements
methods for earthquake-resistant design and retrofit of structures.