平面应力波在岩质边坡中的传播规律研究
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摘要
动荷载对岩体工程的影响本质上是应力波在岩体中传播和相互作用的过程。首先,依据弹性波几何射线理论,考虑边坡中坡顶、坡面2个自由面的影响,分析平面简谐P波自底部均匀入射时,岩质边坡中应力波场的组成,并通过叠加计算,得到坡体内质点振动速度放大系数的表达式,从理论角度揭示均质岩石边坡质点速度放大效应的机制。随后,探讨影响边坡质点速度峰值分布的关键因素,研究结果表明:P波和SV波在边坡中传播路径和传播速度不同,其到达某一质点的时间存在相位差,导致质点应力波场存在延时叠加,加之谐波振动的周期性,当边坡坡高或入射波频率大于一临界值时,坡体内质点速度放大系数呈现"节律性振荡"。临界坡高、临界频率值与岩石弹性模量成幂函数关系,临界坡高与频率、临界频率与坡高则成负幂函数关系。
Impact of dynamic load on rock mass engineering is essentially a process that stress waves propagate in rock mass and interact with each other. Firstly,based on the geometric ray theory of elastic wave transmission,the component of stress wave field in rock slope is analyzed considering the effect of slope surface and top surface,when uniform planar simple harmonic P waves normally impinge from the bottom. The expression of amplified coefficient of particle vibration velocity in slope is derived by wave field superimposition. As a result,the mechanism of velocity amplification effect in homogeneous rock slope is revealed in this way. Then the key influential factors of the distribution of peak velocity are worked out. Research shows that P and SV stress waves pass the same particle have phase difference and would superimpose with each other in time delay as different transmission pathes and velocitis in slope,so the particle velocity amplification coefficient presents "rhythmical oscillation" when the slope height or frequency of incident wave exceeds a critical value according to the regularity of harmonic wave. Additionally,the critical slope height or critical frequency presents power function relationship with the elastic modulus of rock;meanwhile the relation between critical slope height and frequency or between critical frequency and slope height is negative power function.
引文
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