含峭壁V形峡谷对地震SH波散射的解析解

地表地形常引起地震动的局部放大,这是由于地震波传播至局部地形时产生了散射现象.本文利用波函数展开方法和区域匹配技术,提出了含峭壁V形峡谷对平面SH波散射问题的解析解,并进行了退化验证.通过频域内的参数分析,揭示了峭壁深度、入射波频率和角度等因素对峡谷场地地面运动的影响规律,发现上部峭壁会增强峡谷对地震动的地形放大效应.研究结果不仅为数值方法提供了验证基准,还可为含峭壁峡谷周边建筑物的抗震设计提供顺河向地震动输入.

     

Scattering of SH waves by a scalene triangular hill

<正>The influence of local landforms on ground motion is an important problem.The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function,moving coordinates and auxiliary functions.First,the model is divided into two domains:a scalene triangular hill with a semi-circular bottom;and a half space with a semi-circular canyon.Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains.Then,considering the displacement continuity and stress equilibrium, algebraic equations are established.Finally,numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.     

风化半圆形河谷对柱面SH波的散射解析解

风化河谷地震效应对建在此类场地上工程结构(如大坝、桥梁)的动力稳定性具有潜在的威胁,为揭示河谷风化层对地面运动的影响,利用波函数展开法推导风化半圆形河谷对线源柱面SH波散射问题的解析解。计算不同震源位置条件下风化半圆形河谷的地表位移反应和地面运动放大因子,分析地面运动的幅值和形态,发现随着震源距离的增大,在河谷附近地震动的放大和衰减的交替更频繁。     

Rayleigh波在浅圆凹陷地形附近的散射:高频解答

利用波函数展开法给出了Rayleigh波在浅圆凹陷地形附近散射的一个高频解析解，并分析了入射频率、凹陷地形宽度和深度等因素对波散射的影响。数值结果表明，由于Rayleigh波幅值随深度而衰减，凹陷地形表面位移幅值整体上较小，且随着凹陷地形深度的增加而减小；由于Rayleigh波幅值还随频率而衰减，随着入射频率的升高，凹陷地形表面位移幅值逐渐减小；由于凹陷地形的屏障作用，在人射波的近端，地表位移分布变得相对复杂，地表位移峰值出现在左角点附近，而在入射波远端，地表位移分布相对简单，地表位移峰值出现在距凹陷地形较远的地方。     

SV波入射情况下V型河谷地形对地震动的影响分析

基于局部人工边界的显式有限元方法,给出了二维V型河谷地形在SV波垂直人射下地面运动数值解,并分析其地震动分布规律以及两侧不同的边坡角度对于地震动分布规律的影响.数值结果表明:谷底的角点、两岸靠近河谷的点、两侧谷坡靠近谷底的点以及靠近两岸的点,对地表位移有放大作用,而对其邻近区域地表位移有抑制作用.这是由于角点处存在面的...     

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free ...     

Antiplane response of two scalene triangular hills and a semi-cylindrical canyon by incident SH-waves

Antiplane response of two scalene triangular hills and a semi-cylindrical canyon by SH-waves is studied using wave function expansion and complex function method. Firstly, the analytical model is divided into three parts, and the displacement solutions of wave fields are constructed based on boundary conditions in the three regions. Three domains are then conjoined to satisfy the "conjunction" condition at shared boundary. In addition, combined with the zero-stress condition of semi-cylindrical canyon, a series of infinite algebraic equations for the problem are derived. Finally, numerical examples are provided and the influence of different parameters on ground motion is discussed.     

Scattering of plane P waves by a semi-cylindrical hill： analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.     

浅埋圆柱形弹性夹杂附近等腰三角形凸起地形引起的SH波的散射

文章利用“契合”思想,给出了地下弹性夹杂与地面上的等腰三角形凸起地形引起的SH波散射问题的解析解答。利用复平面下坐标移动,通过区域Ⅰ和区域Ⅱ以及区域Ⅱ和区域Ⅲ的“公共边界”位移应力连续条件,建立起求解该问题的无穷代数方程组并截断有限项进行求解,最后通过具体算例及结果分析得出相应结论。     

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fic...     

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.     

SH波作用下浅埋裂纹附近半圆形凸起的地震动

利用Green函数、复变函数及多极坐标法研究了浅埋裂纹附近的半圆形凸起地形对SH波的散射问题。首先求解出适合本问题的Green函数,即含有半圆形凸起的弹性半空间内任意一点承受时间谐和的出平面线源荷载作用时位移场的解答。然后,从半圆形凸起地形对SH波的散射问题出发,利用本问题的Green函数在基体内构造裂纹。最后给出了浅埋裂纹附近的半圆形凸起地形对SH波散射的位移场。通过算例讨论了裂纹对地表位移幅值的影响,结果表明裂纹在一定情况下具有减震作用。     

SH波在浅埋可移动圆柱形刚性夹杂处的散射与地震动

采用复函数、多极坐标法研究了含有可移动圆柱形刚性夹杂的弹性半空间对SH波的散射问题。构造一个能自动满足含可移动刚性圆柱的弹性半空间自由表面上应力为零的边界条件的散射波,应用可移动圆柱形刚性夹杂的运动条件来确定该散射波。最终则可将求解问题归结为求解一个无穷代数方程组,采用截断有限项的方法对其进行求解。给出了地表位移幅值的数值结果,并讨论了各种参数对它的影响。     

SH波入射时半圆形凸起与凹陷地形的地震动

研究了弹性半空间中半圆形凸起与凹陷相连地形对SH波的散射问题。将整个求解区域分割为2部分,在其中分别构造满足边界条件的位移解,通过移动坐标使之满足“公共边界”以及半圆形凹陷表面上的边界条件,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移幅值的数值结果以及凸起地形顶点和凹陷地形最低点处位移幅值的反应谱并进行了讨论。     

SH波在含圆形孔洞的半圆形凸起处的散射

采用复变函数法研究了含有圆形孔洞的半圆形凸起地形对SH波的散射问题。第一步将所研究的域分为两个域，相应地构造出了所论问题的两组解：一组是在凸起边界上满足应力为零、而其余边界应力待定的圆环域中的级数解，另一个组为含有半圆形凹陷的半空间的解。第二步，通过上述两个域(两组解)在“公共边界”上实施“契合”，建立起求解该问题的无穷代数方程组。第三步，对有限个方程进行数值求解，给出了地表位移幅值和圆形孔洞的表面位移及周边上的动应力集中的数值结果，并讨论了波数及凸起和圆孔半径比等的影响。     

Scattering of plane P waves by canyons containing multiple circular-arc-shaped layers

By expressing the wave functions in the form of Fourier-Bessel series,the analytical solution for the two-dimension scattering problem of plane P waves by the cylindrical canyon topography that contains arbitrary number of circular-arc-shaped layers is presented firstly.And then,the convergence of the proposed series solution with the truncation number of terms is discussed,which demonstrates that the analytical solution can converge even for very high frequencies of the incident P wave.Finally,using this solution,the influences that are imposed on the stationary ground motion by the number and the sequence of alluvial layers,as well as the stiffness of soft interlayer contained in the canyon,are studied.     

Scattering of plane P waves by circular-arc layered alluvial valleys: An analytical solution

IntroductionThe site effect of local inhomogeneity and irregularity on seismic wave propagation is one of the most attractive topics in seismology. The problem may be resolved by either analytical method or numerical method. Here, the analytical method is the wave function expansion method; numerical methods include the finite difference, finite element, boundary integration equation, and discrete wave number method, etc. Although these numerical methods can be applied for sites of arbitrary s…     

Anti-plane （SH） waves diffraction by cavity： analytical an underground semi-circular solution

Diffraction of a two-dimensional (2D) semi-circular cavity in a half-space under incident SH-waves is studied using the classic wave function expansion method with a new de-coupling technique. This so-called “improved cosine halfrange expansion” algorithm exhibits an excellent performance in reducing displacement residual errors at two rim points of concern. The governing equations are developed in a manner that minimizes the residues of the boundary conditions. Detailed derivation and analysis procedures as well as truncation of infinite linear governing equations are presented. The semi-circular cavity model presented in this paper, due to its simple profile, is expected to be used in seismic wave propagation studies as a benchmark for examining the accuracies of various analytical or numerical methods for mixed-boundary wave propagation problems.     

地下夹塞断面形状随机性对平面SH波散射的影响

采用波函数展开法及边界离散的方法给出了任意断面形状的地下夹塞对平面SH波散射的半解析解; 利用蒙特卡罗方法随机模拟产生了30组夹塞断面样本, 通过对该样本在平面SH波入射下地表位移幅值的统计分析, 研究了夹塞断面形状随机性对平面SH波散射的影响. 结果表明, 夹塞断面形状随机性对平面SH波的散射具有重要影响. 以圆形夹塞为例, 当断面半径的变异系数为0.1时, 地表位移响应幅值变异系数可达0.71. 随着入射频率的升高, 变异系数逐渐增大; 随着夹塞刚度的降低, 变异系数逐渐增大; 随着夹塞埋深的增加, 变异系数逐渐减小.     

饱和层状场地中任意凹陷地形对入射SV波的散射

利用饱和土层的精确动力刚度矩阵和动力格林(Green)函数,采用间接边界元法,在频域内求解了层状饱和场地中任意凹陷地形对入射SV波的散射问题.通过自由场反应分析,求得凹陷地形表面各点的位移和各单元的应力响应;同样计算了虚拟分布荷载的格林影响函数,求得相应的位移和应力响应;根据边界条件确定虚拟分布荷载,将自由场位移响应和...