ANALYTICAL SOLUTION OF HYDRODYNAMIC PRESSURE WITH REFLECTIVE CONDITION AT RESERVOIR BOTTOM DURING EARTHQUAKES
ANALYTICAL SOLUTION OF HYDRODYNAMIC PRESSURE WITH REFLECTIVE CONDITION AT RESERVOIR BOTTOM DURING EARTHQUAKES
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地震时库底反射条件下水动力压力的解析解
DOI：
10.2208/jscej1969.1974.229_119
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
T. Hatano
中科院分区：
文献类型：
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作者：
T. Nakagawa;T. Hatano
这里，x表示沿静止水库自由表面向上沿着的水平方向，j表示沿静止壁向上沿着的垂直方向，水深为h。假设壁是刚性的，并作2 sin wt的谐运动。常数k 0，km '，jo，jm和j2'的确定如下：ko是满足kotanh koh=w2/g，ko>0的唯一实数; km'（m=1，2，.）是满足km'tankm' h =-w2/g，0<k11<k2 '<k3'<.的那些真实的数; r是指数m的最大整数，使得c2> km 2; j 02 =c2+ k 02; jm 2 =c2-km 2;以及jm 2 =km/2-C2，其中c2= Wow 2/gK，其中Wo是水的单位重量，K是水的体积模量。这个解在某些方面被认为是韦斯特加德的结果的改进，韦斯特加德首先指出了地震中存在动水压力。然而，它似乎不够令人满意，因为它固有的强烈共振引起的水的弹性。后来，其中一位作者观察到，在真实的大坝的振动实验和实验室实验中，共振频率下的压力并没有显著上升3）。此外，这些实验甚至表明，在水库底部被细沙等压力吸收材料覆盖的情况下，根本没有共振。这些结果表明，（1.2）中的边界条件（i）是不适当的，因为它导致了水库底部动水压力的完全反映。为了克服这一困难，提出了以下取自声学理论的条件来代替（1.2）中的（i）：
Here, x denotes the horizontal direction upstream along the free surface of reservoir at rest, and j the vertical direction upward along the wall at rest with the depth h of water. The wall is assumed to be rigid and in harmonic motion of a 2 sin wt. The constants k0, km', jo, jm, and j2' are determined as follows: ko is the unique reall number satisfying ko tanh koh=w2/g, ko>0; km' (m=1, 2,...) are those real numbers satisfying km' tankm'h=-w2/g, 0<k11<k2'<k3'<...; r is the largest integer of indices m such that c2> km'2; j02=c2+ko2; jm2=c2-km'2; and jm'2=km/2-C2, where c2=Wow2/gK in which Wo is the unit weight of water and K the bulk modulus of water. The solution was claimed to be an improvement of the result by Westergaard2) in some respects, who first pointed out the existence of hydrodynamic pressure during earthquakes. However, it seemed to be not enough satisfactory because of a strong resonance inherent to it caused by the elasticity of water. Later, one of the authors observed that in vibration experiments of real dams and in laboratory experiments the pressure at resonance frequencies did not rise significantly3). Furthermore, these experiments even revealed no resonance at all in those cases when the reservoir bottom was covered by pressure-absorbing materials such as fine sand. These results suggested that the boundary condition (i) of (1.2) was not adequate since it caused a complete reflection of hydrodynamic pressure at the reservoir bottom. In order to overcome this difficulty, the following condition taken from the theory of acoustics was proposed to replace (i) of (1.2):