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采用间接边界元法研究了层状场地中凸起地形对斜入射Rayleigh波的三维响应问题.该间接边界元方法结合层状半空间中移动斜线均布荷载动力格林函数基本解,克服了传统边界元法中的奇异性问题,刚度矩阵运算的引入则避免了对土层交界面和自由地表的离散,使得该方法具有很高计算精度的同时对复杂边界有着很好的适应性.通过与已有结果的比较验证了方法的正确性,并以均匀半空间和基岩上单一土层中凸起地形为例,分别在频域和时域内进行了计算分析,研究了Rayleigh波的斜入射角度、入射频率、凸起的截面形状、凸起的高度、特别是Rayleigh波的频散和多模态特性对地面动力响应的影响.研究表明层状场地中由于Rayleigh波存在频散和多模态特性,使得凸起表面的动力放大效应与均匀场地情况存在明显的差别,层状场地高阶模态(二阶以上模态)凸起水平位移幅值放大谱与第一阶模态存在很大差异,呈现窄频放大,峰值频率处凸起顶部附近位移幅值非常大,且峰值频率与对应有效阻尼比峰值频率一致.
The indirect boundary element method is used to study the three-dimensional response of the convex topography to the oblique incident Rayleigh waves in the layered terrain. The indirect boundary element method overcomes the basic solution of moving ramp uniform dynamic Green’s function in layered half-space and overcomes the traditional boundary The singularity problem in the meta-law and the introduction of the stiffness matrix operation avoid the discretization of the interface between the soil and the free surface, so that the method has high computational precision and has good adaptability to complex boundaries. The comparison of the results verifies the correctness of the method. Taking the uniform half-space and the convex topography of a single soil layer on a bedrock as an example, the calculation and analysis are carried out in the frequency and time domains respectively. The oblique incident angles of the Rayleigh wave are studied, The influence of the incident frequency, the convex cross-sectional shape, the height of the convexity, especially the dispersion and multi-modal properties of the Rayleigh wave on the ground dynamic response are studied.The results show that the Rayleigh wave has the characteristics of dispersion and multi- , So that there is a clear difference between the dynamic amplification effect on the convex surface and the uniform field. The horizontal displacement amplitude of the high-order mode (second-order mode) Large spectrum and first-order mode are very different, presenting narrowband amplification, peak displacement amplitudes at frequencies near the top of the projection is very large, and the peak frequency corresponding to the effective damping consistent than the peak frequency.