SH波斜入射时有阻尼成层介质自由场的一维化时域算法

A 1D time-domain method for free field motion in layered media with damping under obliquely incident SH wave

在进行大型大跨结构抗震设计时,需要考虑地震波斜入射的影响。在刘晶波等提出的一维化时域算法基础上,采用有限差分方法,推导建立了SH波斜入射情形下、考虑阻尼影响的水平成层弹性介质出平面自由场求解的显式数值逐步法公式,并采用Fortan程序语言编制了相应的数值计算程序。综合采用有限元法和数值逐步法,进行SH波斜入射下单层土和双层土的算例分析。结果表明:土层介质阻尼仅影响到SH波斜入射下自由场的位移幅值,而对位移时程的波形没有影响;SH波斜入射下有阻尼与无阻尼情形相比位移幅值有明显衰减,对单层土,30°斜入射下衰减幅度可达40.5%;对双层土,最大衰减幅度可达39.7%;有阻尼土层位移幅值的衰减幅度从底部边界向自由表面逐渐增大。

The influence of obliquely incident seismic wave on the seismic responses of large and long-span structures need to be considered in seismic design. Based on a 1D time-domain method for the out-of-plane wave motion of the free field in a layered half space proposed by Liu and Wang, formulas of an explicit time-stepping method to solve the out-of-plane wave motion of the free field in layered media with damping under obliquely incident SH wave were established by using the finite difference method, and its numerical program was developed with Fortran programming language. A cases study of out-of-plane wave motions of the free field in one-layer soil and two-layer soil with damping under obliquely incident SH wave were carried out respectively. The results show that ： soil damping only has effect on the peak displacements of free field motions, and has no effect on the waveforms of the displacement time histories; the displacement amplitudes in layered soil with damping reduce significantly compared with that of without damping under obliquely incident SH wave, and the displacement amplitudes can be reduced by 40. 5% and 39. 7% for one-layer soil and two-layer soil, respectively. The case study also indicates that the attenuation of displacement amplitudes in layered soil with damping gradually increased from the bottom boundary to the free surface.