共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
A. O. Awojobi 《国际地质力学数值与分析法杂志》1984,8(1):45-55
The work presents an exact expression for the Hankel transform of the surface displacement of a rigid circular body performing harmonic vertical vibrations on a homogeneous elastic half-space of arbitrary Poissn'S ratio interrupted at some depth by a frictionless horizontal plane. The limiting case of the uninterrupted half-space is recovered in each of the extreme cases when the frictionless plane coincides with the surface or sinks to an infinite depth. Furthermore, the static case is derived in the limiting case of zero frequency and it is shown that the result agrees with the limiting case of zero gradient shear modulus variation for the static case of the incompressible non-homogeneous half-space. It is also established that Poisson'S ratio effect is linear, and the important proposition is again sustained that only surface shear modulus dominates vibrations on elastic media whereas any other factor such as the interruption of the frictionless plane as in the present case, merely constitutes a negligible secondary parameter. 相似文献
3.
Analytical solution for the problem of a surface-breaking long strike-slip fault in an elastic layer overlying an elastic
half-space is well known. The purpose of this note is to obtain the corresponding solution for a blind fault. Since the solution
is valid for arbitrary values of the fault-depth and the dip angle, the effects of these two important fault parameters can
be studied numerically. The variation of the parallel displacement and shear stress with the distance from the fault is studied
numerically for different values of the fault-depth and dip angle. 相似文献
4.
5.
假设锚杆为与周围介质相同的材料,视锚杆作用的岩土体为弹性半空间位移体;基于Mindlin位移解,求出集中力作用下周围岩土体沿锚固体的轴向位移;根据压力型锚杆锚固段的受力状态,计算锚固体在轴向荷载作用下压缩变形,利用锚固体与周围岩土体变形协调假定,推导出锚固段轴向应力和剪应力分布的理论解。经过与已有现场试验实测数据对比分析,验证了理论解的可行性,并在此基础上讨论了相关岩土参数对锚固段轴向应力和剪应力的影响。锚杆现场试验和理论分析结果表明:压力型锚杆的锚固段所受轴向应力和剪应力与锚固力成正比;压力型锚杆的锚固段所受剪应力的分布形式受周围岩土体弹模、泊松比以及锚固体与周围岩土体界面的内摩擦角等因素的影响。其中周围岩土体的弹模影响最大。 相似文献
6.
A. O. Awojobi 《国际地质力学数值与分析法杂志》1980,4(2):159-174
An exact formulation is presented for the problem of a rigid circular body performing harmonic vibrations on an elastic half-space whose shear modulus increases linearly with depth and is interrupted at some finite depth by a frictionless horizontal plane. The static case is derived in the limit of zero frequency vibrations while the known result for the uninterrupted half-space is recovered in either extreme limit of the horizontal frictionless plane coinciding with the surface or when it is pushed down to an infinite depth. It is shown that the maximum effect of the interruption occurs when the frictionless plane is at a depth where the shear modulus is about 1·6 times the surface shear modulus. Furthermore, this maximum effect is equivalent to a reduction of about 5 per cent of the surface shear modulus or a reduction of about 2½ per cent in the natural frequency of the rigid body on an uninterrupted half-space. The important conclusion, therefore, is that irrespective of the depth at which a half-space isso interrupted, the surface shear modulus is still the dominant parameter and that both the increase in shear modulus with depth and the interruption are not only secondary but also opposing effects. 相似文献
7.
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
8.
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
9.
This paper presents analytical elastic-plastic solutions for static stress loading analysis and quasi-static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far-field stresses and shear stresses along the inner cavity wall. The two-dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic-plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic-plastic boundary coincides with the direction of the maximum far-field compression stress. Furthermore, considering the internal shear stresses, an analytical large-strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi-static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated. 相似文献
10.
竖向圆形荷载作用下弹性半空间问题的位移和应力解是桩基分析的基础。利用Hankel积分变换,首先导出了弹性地基半空间位移与应力的积分形式的通解。通过适当地引入边界条件和界面位移和应力的连续条件,求得了内部作用竖向圆形荷载时弹性地基半空间位移与应力的积分形式解。在此基础上,给出了不同深度处荷载作用投影范围内竖向位移和竖向正应力的平均值。数值结果验证了解析解的正确性。 相似文献
11.
采用Green函数、保角映射等方法分析SH波上方垂直入射时弹性半空间中椭圆形弹性夹杂与任意方位裂纹的相互作用。首先,求解含椭圆形弹性夹杂的弹性半空间内任意一点承受时间谐和出平面线源荷载作用时的位移基本解,即Green函数,再结合裂纹切割法构造裂纹,得到SH波上方垂直入射时椭圆夹杂和裂纹同时存在条件下的位移场与应力场。作为算例,给出大量的数值结果,探讨不同参数情况下弹性夹杂周边动应力集中系数（DSCF）、地表位移及裂纹尖端动应力强度因子（DSIF）的分布规律,结果表明不同参数的变化会对三者的分布带来一定的影响。 相似文献
12.
研究了稳态水平剪切（SH）波作用下含有圆柱形孔洞的各向异性弹性半空间的动力响应问题,探讨介质的各向异性对孔附近动应力的影响规律。运用复变函数和多极坐标方法在变换空间中构造出各向异性弹性半空间中圆孔的散射波函数,所构造的散射波函数能够自动满足半空间水平表面上应力自由的边界条件和无穷远处的Sommerfeld辐射条件。根据圆孔表面应力自由的边界条件,采用最小二乘法求解所构造的散射波函数的系数。分析了SH波以不同角度自弹性半空间内入射时,不同介质特性、入射波数和埋深对圆孔附近动应力集中系数的影响。数值结果表明,各向异性弹性半空间中孔附近的动应力比各向同性情况有明显增高。 相似文献
13.
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
14.
Ch. Vrettos 《国际地质力学数值与分析法杂志》1990,14(9):649-662
The dynamic response of an inhomogeneous, linear-elastic half-space to a time-harmonic vertical line load on its surface is studied. The mass density and the Poisson's ratio are assumed to be constant and the shear modulus to increase continuously with depth according to a function which is bounded at infinity. This model can describe a wide range of uniformly deposited soil strata. Analytical solutions for the displacement field at the surface are obtained using the classical contour integration method by means of the residue theorem. The dependence of the displacement field on distance from the source, frequency and shear modulus variation is examined as well as the relative contribution of the higher surface wave vibration modes to the total displacement. 相似文献
15.
The quasi-static development of the force, pore pressure and displacement is obtained in the system of a circular elastic pile partially embedded in a saturated porous elastic soil, and loaded axially on the top. The porous elastic soil is governed by Biot's theory. The problem is decomposed into two systems, namely, an extended porous elastic half-space in the absence of the pile characterized by the material constants of the medium, and a fictitious pile represented by a Young's modulus equal to the difference between the Young's moduli of the real pile and the medium. The problem is found to be governed by a Fredholm integral equation of the second kind. Laplace transforms are applied to time functions involved, and Hankel transforms to the radial coordinate of which the origin is at the centre of the pile. Numerical solutions are obtained for final and initial solutions for various practical values of the parameters involved. 相似文献
16.
基于Biot多孔介质波动理论,建立孔隙率、密度、剪切模量和渗透系数相互耦合且同时沿深度变化的非均匀饱和半空间模型,引入量化的非均匀梯度表征地基非均匀程度。在柱坐标系下构建以土骨架位移和孔隙压力为基本未知量的三维动力控制方程,采用算子运算和Hankel积分变换求解控制方程,推导出简谐集中力作用下半空间地基振动响应的积分解。将所得结果分别退化到均匀饱和半空间和弹性半空间与经典Lamb解做了对比,验证了结果的正确性。利用已有研究结论,给出孔隙率、密度、剪切模量和渗透系数之间的耦合关系式,代入推导结果进行数值计算。分别对水饱和地基和气饱和（干土）地基的动力响应进行分析,给出两类地基在动力作用下的振动位移和孔隙压力分布,并对非均匀性的影响作出分析。结果表明：4参数沿地基深度耦连变化对地基的动力响应产生一定程度影响,振动位移和孔隙压力在地层中的衰减速度由此加快。由于水的黏滞性远大于气体,所以水饱和地基中的振动衰减更快。非均匀程度越高,耦合效应的影响越明显。 相似文献
17.
I. Vardoulakis 《国际地质力学数值与分析法杂志》1984,8(3):287-296
The dispersion of torsional surface waves in two types of inhomogeneous elastic media is discussed (1) in a half-space with shear modulus varying linearly with depth and with constant density (Gibson'S half-space) and (2) in a half-space with shear modulus varying with the square-root of the depth co-ordinate and with constant density. Inhomogeneous media with constant shear wave velocity are also reviewed and the obtained solutions are discussed in relation to appropriate boundary conditions. 相似文献
18.
An approximate, analytical solution is found for the gravity-induced stresses in the neighbourhood of an axisymmetric topographic feature on an elastic half-space. The solution is in the form of a perturbation expansion in powers of the characteristic slope, ?. The leading order problem, at O(1), is for a distributed normal load on a plane half-space. The O(?) correction is due to a distributed shear traction. The vertical variation of the near-surface stress perturbation and the rotation of the principal stress directions are O(?) effects, and thus include contribution s of like order from both the normal and shear loads. The method requires general solutions for axisymmetric, normal and shear tractions of arbitrary radial distribution, and these are found in terms of Hankel transforms. 相似文献
19.
This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented. 相似文献
20.
层状地基中单桩负摩擦问题积分方程解法 总被引：9，自引：1，他引：8
利用Biot固结理论和积分方程方法研究了表面有堆载的层状地基中单桩负摩擦问题。根据层状饱和土的圆形载荷基本解得出了单桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化。再结合传递和刚度矩阵传递到各个层中去,对变换域内的积分方程采用Schapery 逆变换方法得到时域内单桩的近似积分方程。求解积分方程组并进行相应的数值逆变换,就可得出层状地基中的单桩在表面圆形均布载荷作用下的位移、轴力、孔压和桩侧摩阻力随时间的变化情况。计算结果表明,桩侧剪力和孔压分层明显。 相似文献