The validity of dynamic block displacement prediction using DDA
The validity of dynamic block displacement prediction using DDA
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DOI：
10.1016/s1365-1609(01)00026-0
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发表时间：
2001-06
影响因子：
7.2
通讯作者：
Y. Hatzor;A. Feintuch
中科院分区：
文献类型：
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作者：
Y. Hatzor;A. Feintuch
1965年，纽马克发表了他的经典兰金讲座“地震对水坝和水坝的影响”。在他的论文中，Newmark提出了在地震荷载作用下质量块沿沿着圆形或平面滑动面的位移解。纽马克假设质量块作为一个单一的刚体移动，阻力沿着滑动面移动。纽马克进一步考虑了仅持续时间间隔t0的幅度为Ag的单个脉冲，认为正弦脉冲的引入将不必要地使表达式复杂化。因此，所谓的“纽马克法”提供了在恒定幅度和给定持续时间的地面加速度下预期的质量位移量的估计。纽马克承认，他的方法通常会高估实际位移，因为它忽略了相反方向的地震脉冲。Goodman和Seed [2]通过实验研究了砂土对循环荷载的抗剪性，并提出了剪切强度退化作为位移函数的表达式。他们使用数值积分来求出斜坡上的块体的速度和位移，该块体受到形式为<$A sinuso ωt <$θ 1的正弦加速度函数，其中θ是满足滑动开始时刻（t <$0）的初始条件a <$Ay所需的相位角，其中Ay定义为屈服加速度。Goodman和Seed指出，仅对于摩擦滑动，其中沿滑动面的粘聚力沿着为零，水平向下的坡度产生了位于倾斜度为a的平面上的块体的加速度，摩擦角φ由ay/tanj φeq@ aerg; φ 2 eq给出，其中φeq是与位移相关的摩擦角，在岩石力学中，对于所有实际目的，可以用φ代替。类似地，可以表明，对于上坡滑动，水平屈服加速度由下式给出：在图1中，以g为单位的水平屈服加速度被绘制为滑动表面的摩擦角和倾角的函数。很明显，上坡运动需要明显更高的加速度，因此纽马克只处理下坡运动似乎是合理的。
In 1965, Newmark [1] published his classic Rankine lecture on ‘‘effects of earthquakes on dams and embankments’’. In his paper, Newmark presented solutions for displacement of a mass along circular or planar sliding surface under earthquake loading. Newmark made the assumption that the mass moves as a single rigid body with resistance mobilized along the sliding surface. Newmark further considered only a single pulse of magnitude Ag lasting for a time interval t0, arguing that introduction of a sinusoidal pulse would complicate the expressions unnecessarily. Thus, the socalled ‘‘Newmark method’’provided an estimate for the amount of mass displacement to be expected under ground acceleration of constant magnitude and given duration. Newmark admitted that his approach would generally overestimate the actual displacement because it ignores the earthquake pulse in the opposite direction. Goodman and Seed [2] studied experimentally the shear resistance of sand to cyclic loading and suggested an expression for shear strength degradation as a function of displacement. They used numerical integration to find the velocity and displacement of a block on an incline subjected to a sinusoidal acceleration function of the form at ¼ A sinðωt þ θÞ ð1Þ in which θ is the phase angle required to satisfy the initial condition a ¼ ay at the instant sliding begins (t ¼ 0), where ay is defined as the yield acceleration. Goodman and Seed showed that for frictional sliding only, where cohesion along the sliding surface is zero, the down slope, horizontal, yields acceleration for a block resting on a plane with inclination a and friction angle φ is given by ay ¼ tanðφeq@ aÞg; ð2Þ where φeq is a displacement dependent friction angle, which for all practical purposes in rock mechanics could be replaced by φ. Similarly, it can be shown that for up slope sliding the horizontal yield acceleration is given by ay ¼ tanða þ φÞg: ð3ÞIn Fig. 1 horizontal yield acceleration in units of g is plotted as a function of friction angle and inclination of the sliding surface. It is apparent that up slope motions require significantly higher accelerations, and therefore Newmark’s treatment of downhill motions only, seems justified.