SH波对浅埋圆柱形弹性夹杂附近多个半圆形凸起的散射

利用复变函数及移动坐标法建立了多个半圆形凸起及附近浅埋弹性夹杂对SH波散射问题的解析方法.求解时将整个求解模型进行分区,区域I为包括多个半圆形凸起在内的多个圆形区域;区域II包括多个半圆形凹陷和1个圆柱形弹性夹杂.然后在两个区域内分别构造满足边界条件的位移解.最后,根据连接面的契合条件,利用移动坐标法将两个区域在公共边界上装配起来,同时考虑弹性夹杂的边界条件,建立起求解该问题的无穷代数方程组.通过算例,讨论了凸起间距,夹杂埋深等参数对地表位移幅值的影响.     

SH波在多个浅埋圆形孔洞附近的多个含孔半圆形凸起地形处的散射

为研究地震时局部地形与附近浅埋结构的作用,文中使用"分区"思想,复变函数法和移动坐标的方法,建立多个浅埋圆形孔洞附近的多个含孔半圆形凸起地形对SH波的散射的数学模型,并通过算例给出含孔半圆形凸起地形的地表位移,讨论了浅埋圆孔的深度、含孔半圆形凸起间距及浅埋圆孔间距对地表位移影响。     

SH波入射时多个含孔半圆形凸起附近的多个浅埋圆孔的动应力分析

文中使用"契合"、复变函数法和移动坐标的方法,给出了SH波入射条件下多个含孔半圆形凸起地形附近多个浅埋圆形孔洞动力分析问题的解答.将模型分成两个区域,在区域Ⅰ和区域Ⅱ中分别构造波函数,最后在两个区域的公共边界上实施"契合",即满足两个区域的公共边界上位移、应力的连续条件.通过算例给出了浅埋圆孔动应力与入射波数、入射波角度的变化规律.     

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波入射时等腰三角形与半圆形凸起地形的地震动

利用复变函数和移动坐标研究了等腰三角形凸起和半圆形凸起地形对SH波的散射.首先将求解区域分为三个部分,区域I为一个带有半圆形弧线的等腰三角形区域,区域II为含有两个半圆形凹陷的弹性半空间,区域III为包括半圆形凸起在内的圆形区域.在区域I中构造满足在腰三角形斜边上应力自由的驻波函数WA,在区域II中分别构造两个半圆形凹陷的散射波WB和WC,且两者均预先满足水平界面上应力为零的边界条件,在区域III构造一个上半部边界应力为零,而其余部分位移、应力任意的驻波函数.将所研究的问题转换成一个求解满足在"公共边界"上位移应力连续的问题.可利用坐标移动方法,通过傅立叶级数展开,建立该问题代数方程组,并采用截断有限项的方法对其进行求解.最后,给出了一个算例.     

线源荷载对半圆形凸起圆形夹杂附近浅埋圆孔的动力作用

采用复变函数法和Green函数法研究了在水平界面承受出平面线源荷载时弹性半空间内半圆形凸起的圆柱形弹性夹杂对浅埋圆孔的动力作用.该问题采用“分区”、“契合”思想求解.首先,将整个求解区域分割成两部分,其一为含半圆形凹陷和圆孔的弹性半空间,其二为圆柱形弹性夹杂;其次,构造满足含半圆形凹陷半空间水平界面应力自由和圆孔边界应力自由的散射波,构造满足圆形夹杂上半表面应力自由下半表面应力连续条件的驻波和散射波;最后,在两个区域的“公共边界”上实施“契合”,满足公共边界处位移和应力的连续性条件,同时满足圆孔边界应力自由的边界条件,建立起求解该问题的无穷代数方程组,并就具体算例分析讨论了浅埋圆孔边缘动应力集中系数(DSCF)的数值结果.结果表明:圆柱形弹性夹杂的“软”、“硬”对浅埋圆孔孔边动应力集中系数有不同的影响.     

SH波入射时半圆形凸起地形附近浅埋圆形衬砌结构的动应力分析

本文给出了地下圆形衬砌结构与地面上的半圆形凸起地形对垂直于地面入射的SH波散射问题的解答。方法是将求解区域分割成两部分。其一为包含半圆形凸起地形在内的圆形区域Ⅰ，其二为带有一个半圆形凹陷和一个圆形衬砌结构的弹性半空间Ⅱ，半圆形凹陷部分为其公共边界，在区域Ⅰ和Ⅱ中分别构造其位移解，然后再通过移动坐标，使其满足“公共边界”上的条件和地下衬砌的边界条件，建立起求解该问题的无穷代数方程组。最后，本文给出了算例，并讨论了数值结果，给出了圆形衬砌结构周边上的动应力集中系数变化规律。     

SH波冲击下浅埋任意形孔洞的动力分析

求解了稳态SH波垂直弹性半空间水平表面入射时,浅埋任意形孔洞的动力响应。采用复变函数和多极坐标方法构造了一个能够自动满足水平表面上应力自由边界条件的散射波函数。应用这一波函数,将半空间中的问题转化为求解一个全空间中任意形孔洞的散射问题,最终将问题归结为对一组无穷代数方程组的求解。作为对抗爆问题的研究,给出了浅埋椭圆孔和方孔附近的动应力集中系数的数值结果,并对算例进行了讨论。     

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。     

双等腰三角形凸起地形在SH波入射时的地表位移函数

利用"分区、辅助函数"思想,将求解的区域分为三部分,区域Ⅰ为一个带有半圆形弧线的等腰三角形区域,区域Ⅱ也为一个带有半圆形弧线的等腰三角形区域,区域Ⅲ为两个带有半圆形凹陷的弹性半空间,并利用波函数展开法分别在区域Ⅰ、Ⅱ和区域Ⅲ中构造满足等腰三角形在其斜面上应力自由和在弹性半空间中满足水平面上应力自由的驻波函数,以此为基础,通过区域Ⅰ、Ⅱ和区域Ⅲ的"公共边界"位移应力连续条件,建立对该问题进行求解的无穷代数方程组,并采用截断有限项的方法对其进行求解。     

On terrain corrections in terrestrial heat flow

The theory of heat-flow variation over a Lees-type hill is well known for evaluating terrain effects on terrestrial heat flow. However, a hill cannot be converted into a valley by simply changing the sign of one of the terrain-defining parameters, nor can several Lees' hills be superposed to simulate a series of hills and valleys for correcting a terrain-induced disturbance of heat flow. The proper derivations for a Lees-type valley are presented and the superposition is compared with analytic solutions for two parallel semi-cylindrical valleys and two semi-spherical basins embedded in an otherwise planar ground. Generally, heat flux climaxes over central valleys or basins, and dips toward their margins where rapid change in topography occurs. Variation of heat flux induced by a three-dimensional terrain is relatively large, as compared to two-dimensional features, but its areal extent is relatively limited. The two-dimensional effects also extend relatively deeper. In applying two-dimensional algorithms to a three-dimensional terrain, the correction may be over- or underestimated depending on the distance from a borehole to prominent terrain features in the surrounding area.     

Isotopic study of alluvial groundwaters,south-west lockyer valley,queensland, australia

The isotopic chemistry of alluvial groundwaters from two adjacent valleys are described and hydrological processes within related aquifers are identified as evidenced by oxygen-¹⁸, deuterium, tritium and chloride data. A plot of δ¹⁸O against δD values reveals isotopic enrichment of the groundwater by the recycling of spray irrigation water. A plot of tritium versus chloride concentrations displays separate linear correlations for alluvial groundwaters within the two valleys. The salinity has a common source, therefore the separate correlations are interpreted as the past transfer of low salinity groundwater from the alluvial aquifers in one valley to the underlying sandstone aquifers.     

Dynamic stress concentration of an elliptical cavity in a semi-elliptical hill under SH-waves

The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.     

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.     

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。     

圆弧状多层沉积谷地在平面P波入射下稳态响应的解析解

利用波函数的FourierBessel级数展开法,给出了含任意多个圆弧状沉积层的谷地在平面P波入射下稳态动力响应的解析解.并以具有三个沉积层的谷地为例,在宽频范围内,利用稳态地面运动幅值的空间分布,讨论了谷地中沉积介质的成层性对地面运动的影响.     

Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach

In this paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve the exterior Helmholtz problems with alluvial valleys. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals by locating the null-field point exactly on the real boundary. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. Image concept and technique of decomposition are utilized for half-plane problems. After moving the null-field point to the real boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples including single and successive alluvial valleys are given to test our program. Limiting cases of a single canyon and two successive canyons are also addressed. Amplification of soft basin is also observed in this study. The validity of the semi-analytical method is verified. Our advantages, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence and mesh-free, by using the present method are achieved.     

Impact of geometrical and mechanical characteristics on the spectral response of sediment-filled valleys

A comprehensive numerical analysis of the seismic response and site period of curved alluvial valleys was performed by taking into account the characteristics of sedimentary materials. This study presents a criterion as a combination of the three following geometrical and geotechnical characteristics of curved valleys in order to provide a simple method for code implementation of complex site effects: depth ratio, filling ratio and impedance ratio. The parametric studies were performed by a HYBRID program combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The amplification patterns under above-mentioned characteristics were determined at the central point of valleys. The results are shown in the form of response spectra. Different impedance coefficients of materials were considered to evaluate effects resulting from combination with filling ratio and geometrical parameters. Finally, a criterion is proposed in terms of engineering applications to assess the spectral response at the surface of curved alluvial valleys.