单面边坡高程放大效应的射线理论解

利用平面射线理论和方法,推导出单面边坡地震的高程放大效应理论解,可用于描述边坡临空面对地震波的反射,反映边坡的高程放大效应.边坡的高程放大效应是由于边坡自由面的反射作用形成的;动弹性模量、泊松比、坡度及入射波频率的综合作用导致高程放大系数稀疏相间、节律变化,入射频率越高,节律性越明显,极值点也越多;自然边坡由于受自由面反射、岩体界面的折反射作用,其值可能远大于坡脚的振动效应.

Ray theory solution of the elevation amplification effect on a single-free-face slope

Planar ray theory is used to deduce the analytic solution of the elevation amplification effect on a single-free-face slope in seismic engineering.It is proved that the solution can describe the reflection effect of seismic waves on the free face of the slope and reflect the elevation amplification effect.It is shown that the surface reflection induces the amplification effect.Dynamic Young's modulus,Poisson's ratio,gradient and incident wave frequency are all contributing factors of the elevation amplification coefficient,which has intervals of rough and fine contour and rhythmic variation.Rhythmicity and the number of extreme points increases with the increase of the incident frequency.A natural slope is under reflection of free faces,refraction and reflection of rock interfaces,and the elevation amplification effect may be greater in single-free-face slope than at the foot of the slope.