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1.
Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
2.
The Biot linearized quasi-static theory of fluid-infiltrated porous materials is used to formulate the problem of the two-dimensional
plane strain deformation of a multi-layered poroelastic half-space by surface loads. The Fourier-Laplace transforms of the
stresses, displacements, pore pressure and fluid flux in each homogeneous layer of the multi-layered half-space are expressed
in terms of six arbitrary constants. Generalized Thomson-Haskell matrix method is used to obtain the deformation field. Simplified
explicit expressions for the elements of the 6 × 6 propagator matrix for the poroelastic medium are obtained. As an example
of the possible applications of the analytical formulation developed, formal solution is given for normal strip loading, normal
line loading and shear line loading. 相似文献
3.
The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase
medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly
elastic half-space caused by a two-dimensional source in the elastic half-space. The integral expressions for the displacements
and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic
medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail.
The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency
limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for
the drained case (ω → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically.
Diffusion of the pore pressure with time is also studied. 相似文献
4.
J. A. Hemsley 《国际地质力学数值与分析法杂志》1991,15(11):759-783
In the idealised modelling of ground distortion induced by a freely deposited heap of granular material, consideration is given to a fundamental problem in classical elasticity whereby an axisymmetric distribution of vertical conical loading is applied to the surface of a half-space. Closed-form expressions are derived for the deformed shape of the surface, and three variations of the integral transform method are described for determining stresses and displacements within the half-space. Extensive numerical results are presented in graphical form. 相似文献
5.
Closed form analytical expressions of stresses and displacements at any field point due to a very long dip-slip fault of finite
width buried in a homogeneous, isotropic elastic half-space, are presented. Airy stress function is used to derive the expressions
of stresses and displacements which depend on the dip angle and depth of the upper edge of the fault. The effect of dip angle
and depth of the upper edge of the fault on stresses and displacements is studied numerically and the results obtained are
presented graphically. Contour maps for stresses and displacements are also presented. The results of Rani and Singh (1992b)
and Freund and Barnett (1976) have been reproduced. 相似文献
6.
This paper treats the dynamic response of a multilayered transversely isotropic fluid saturated poroelastic half-space under surface time-harmonic traction. The governing system of partial differential equations is uncoupled with the use of a set of physically meaningful and complete potential functions that decompose different body waves in a saturated poroelastic transversely isotropic medium. After expressing the equations in the Hankel-Fourier domain, a proper algebraic factorization is applied to generate reflection and transmission matrices for decomposed waves. All responses including displacements, stresses, and pore fluid pressure for both general patch load and point load are presented in the form of semi-infinite line integrals. The verification of the method is confirmed with the degeneration of the solutions presented here to the existing solutions for dried both homogeneous and multilayered elastic half-spaces as well as poroelastic half-space. Selected numerical results are depicted to investigate the effects of layering and pore pressure on responses of a transversely isotropic poroelastic medium. The load distribution effects are studied by comparison of the patch and point load responses. Also, resonance notion and effective parameters on this phenomenon such as layering system and anisotropy contrast are discussed. Significant influence of materials and layering configuration on number and amplitude of resonances depicted through the numerical evaluation. 相似文献
7.
借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。 相似文献
8.
In practical engineering, an applied rectangular area load is not often horizontally or vertically distributed but is frequently inclined at a certain angle with respect to the horizontal and vertical axes. Thus, the solutions of displacements and stresses due to such a load are essential to the design of foundations. This article yields the analytical solutions of displacements and stresses subjected to a uniform rectangular load that inclines with respect to the horizontal and vertical axes, resting on the surface of a cross‐anisotropic geomaterial. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The procedures to derive the solutions can be integrated the modified point load solutions, which are represented by several displacement and stresses elementary functions. Then, upon integrations, the displacement and stress integral functions resulting from a uniform inclined rectangular load for (1) the displacements at any depth, (2) the surface displacements, (3) the average displacements in a given layer, (4) the stresses at any depth, and (5) the average stresses in a given layer are yielded. The proposed solutions are clear and concise, and they can be employed to construct a series of calculation charts. In addition, the present solutions clarify the load inclinations, the dimensions of a loaded rectangle, and the analyzed depths, and the type and degree of geomaterial anisotropy profoundly affect the displacements and stresses in a cross‐anisotropic medium. Parametric results show that the load inclination factor should be considered when an inclined rectangular load uniformly distributed on the cross‐anisotropic material. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面SV波的散射问题。通过自由场反应分析,求得假想洞室边界上各点位移和各单元应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面SV波的放大作用。结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。 相似文献
10.
The problem of the coseismic deformation of an earth model consisting of an elastic layer of uniform thickness overlying an
elastic half-space due to a very long tensile fault in the layer is solved analytically. Integral expressions for the surface
displacements are obtained for a vertical tensile fault and a horizontal tensile fault. The integrals involved are evaluated
approximately by using Sneddon’s method of replacing the integrand by a finite sum of exponential terms. Detailed numerical
results showing the variation of the displacements with epicentral distance for various source locations in the layer are
presented graphically. The displacement field in the layered half-space is compared with the corresponding field in a uniform
half-space to demonstrate the effect of the internal boundary. Relaxed rigidity method is used for computing the postseismic
deformation of an earth model consisting of an elastic layer of uniform thickness overlying a viscoelastic half-space. 相似文献
11.
We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd. 相似文献
12.
埋置简谐扭转荷载作用下广义Gibson饱和地基动力响应 总被引：1，自引：0，他引：1
考虑地基为饱和半空间,研究了广义Gibson饱和地基内作用简谐扭转动荷载时地基的动力响应问题。从Biot饱和地基固结理论出发,结合扭转振动的特点,建立了剪切模量随深度线性变化的饱和地基扭转振动的动力微分方程,通过Hankel变换求解此微分方程,给出了Hankel变换域内的切向位移和剪应力关于待定系数的表达式。根据饱和地基表面为自由表面,荷载作用面位移连续、剪应力差等于动荷载大小,波的辐射条件等边界条件求解出待定系数,借助Hankel逆变换给出地基内的位移和应力的表达式。通过数值算例研究发现:在同一水平面内,地基内的切向位移和剪应力曲线的实部和虚部都呈现出非常明显的波动变化规律;在竖向平面内,动荷载作用面上部区域内随深度逐渐增大时,地基内切向位移和剪应力曲线的实部逐渐增大,而在动荷载作用面下部区域则正好相反;扭转动荷载的影响范围主要是荷载作用面上下2倍半径区域。 相似文献
13.
为分析列车引起的地基动应力特性,用移动荷载作用下的弹性地基Euler-Bernoulli梁模型计算得到地基表面与路堤之间的反力。将其视为作用于地基表面的移动面荷载,以单位移动荷载引起的半空间地基内部应力解为基础,对反力在作用空间上进行积分,得到了列车速度小于地基中Rayleigh波速时列车荷载在地基中引起的稳态应力响应解答。给出了应力随空间坐标和时间的变化,分析了应力的特性及分布规律。发现列车经过时在地基中产生的动应力是循环应力,具有明显的偏移应力。竖向动应力的影响范围随着列车速度的增大而不断增大。 相似文献
14.
The calculation of the deformation caused by shear and tensile faults is necessary for the investigation of seismic and volcanic
sources. The solution of the two-dimensional problem of a long inclined shear fault in two welded half-spaces is well known.
The purpose of this note is to present the corresponding solution for a tensile fault. Closed-form analytical expressions
for the Airy stress function for a tensile line source in two welded half-spaces are first obtained. These expressions are
then integrated analytically to derive the Airy stress function for a long tensile fault of arbitrary dip and finite width.
Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. These
expressions are suitable for computing the displacement and stress fields around a long inclined tensile fault near an internal
boundary. 相似文献
15.
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17.
Summary This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic
half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse
isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented
by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior
of the half-space. Then, by setting z=0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These
charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level
of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for
interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation;
however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the
use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped
load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence
charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable
accuracy. 相似文献
18.
George Maurice Iskander 《国际地质力学数值与分析法杂志》2012,36(3):344-351
The analysis of earth pressure resulting from an applied point load behind a retaining wall is to be carried out in three dimensions as the earth pressure distribution varies both in vertical and horizontal directions. In this research, the semi‐empirical expressions developed by Terzaghi [Trans. ASCE 1954; 119 ] for earth pressure due to point load are integrated and a correction factor is introduced to develop equivalent equations for two‐dimensional analyses. A new parameter referred to as the design width, which is the horizontal distance retained by the individual vertical retaining element is introduced. The used procedure and the resulted equations are tested and verified by adopting different design width values covering the practical range. The resulted equations together with the semi‐empirical expressions of earth pressure due to line load developed by Terzaghi [Trans. ASCE 1954; 119 ] can be easily used for two‐dimensional analysis of the effect of point load. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
The closed-form analytic expressions for the displacement and stresses at any point of an elastic layer lying over a base
due to a very long vertical strike-slip dislocation are obtained. The interface between the layer and the base is assumed
to be either ‘smooth-rigid’ or ‘rough-rigid’ or ‘welded’. The variations of displacement and stresses with the horizontal
distance from the fault for different types of coupling of the layer with the base have been studied. It is found that the
displacement for ‘welded interface’ lies between the displacements due to ‘smooth rigid’ and ‘rough-rigid’ interfaces for
different positions of the observer and different values of the ratio of rigidities of the layer and half-space. 相似文献
20.
The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant. 相似文献