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1.
Mete Oner 《国际地质力学数值与分析法杂志》1990,14(9):613-629
Vertical and horizontal deformations of surface footings have been studied for an inhomogeneous elastic half-space in which the shear modulus increases with an arbitrary power of depth, n, and Poisson's ratio is constant. A general solution for displacements has been obtained first for point loads applied in vertical and horizontal directions. These are then used in obtaining closed-form solutions for displacements of uniformly loaded circular and rectangular footings. Finally, a numerical method is described that can be used to analyse a rigid footing of an arbitrary shape, and results for rigid rectangular footings are given. 相似文献
2.
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
3.
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
4.
The transfer matrix approach is used to solve the problem of static deformation of an orthotropic multilayered elastic half-space
by two-dimensional surface loads. The general problem is decoupled into two independent problems. The antiplane strain problem
and the plane strain problem are considered in detail. Integral expressions for displacements and stresses at any point of
the medium due to a normal line load and a shear line load, acting parallel to a symmetry axis, are obtained. In the case
of a uniform half-space, closed form analytic expressions for displacements and stresses are derived. The procedure developed
is quite easy and convenient for numerical computations. 相似文献
5.
Arching in Inclined and Vertical Mine Stopes 总被引：2，自引：1，他引：1
Shailesh Singh Sanjay Kumar Shukla Nagaratnam Sivakugan 《Geotechnical and Geological Engineering》2011,29(5):685-693
Hydraulic fills are one of the most common backfills used by mining industries to backfill the stopes (voids) created after
extracting the ore. It is important to estimate the stresses within to the stope to design the drainage and barricades. Most
of the existing analytical models for the estimation of stresses within the stopes consider flat rectangular elements to include
the effects of arching, although a continuous compression catenary arch of principal stresses using intersections of shear
lines is the reality in field situations. In this paper, a circular compression arch of principal stresses has therefore been
used to derive a general expression for stress within the inclined stopes. The results have been compared with the existing
analytical and numerical models for vertical stopes as well as inclined stopes. A methodology has been presented to determine
the vertical stress variation along the width of stope at different depths. The variation of stresses along the width of stope
is also presented graphically. 相似文献
6.
Analytical stress and displacement due to twin tunneling in an elastic semi‐infinite ground subjected to surcharge loads 
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下载免费PDF全文 The construction of twin tunnels at shallow depth has become increasingly common in urban areas. In general, twin tunnels are usually near each other, in which the interaction between tunnels is too significant to be ignored on their stability. The equivalent arbitrarily distributed loads imposed on ground surface were considered in this study, and a new analytical approach was provided to efficiently predict the elastic stresses and displacements around the twin tunnels. The interaction between 2 tunnels of different radii with various arrangements was taken into account in the analysis. We used the Schwartz alternating method in this study to reduce the twin‐tunnel problem to a series of problems where only 1 tunnel was contained in half‐plane. The convergent and highly accurate analytical solutions were achieved by superposing the solutions of the reduced single‐tunnel problems. The analytical solutions were then verified by the good agreement between analytical and numerical results. Furthermore, by the comparison on initial plastic zone and surface settlement between analytical solution and numerical/measured results of elastoplastic cases, it was proven that the analytical solution can accurately predict the initial plastic zone and its propagation direction and can qualitatively provide the reliable ground settlements. A parametric study was finally performed to investigate the influence of locations of surcharge load and the tunnel arrangement on the ground stresses and displacements. The new solution proposed in this study provides an insight into the interaction of shallow twin tunnels under surcharge loads, and it can be used as an alternative approach for the preliminary design of future shallow tunnels excavated in rock or medium/stiff clay. 相似文献
7.
In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
8.
The numerical predictions obtained with the Melanie and MIT-E3 models are compared. Firstly, the performance of the constitutive models is checked against undrained triaxial tests. The models are then used to replicate the behaviour of an embankment built on soft clay. The numerical results are compared with the field data in terms of settlements, lateral displacements and excess pore pressures. Additionally, the numerical predictions are also analysed in terms of yield area, contours of vertical effective stresses, horizontal effective stresses and shear stresses and in terms of effective stress paths. 相似文献
9.
利用弹性矩形板与多层地基表面的竖向位移协调条件与光滑接触条件,由横观各向同性多层地基应力与位移非耦合的传递矩阵解,推导出弹性矩形板下竖向应力和位移的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明：矩形板刚度对板底竖向位移及板中心下的竖向应力有着较为显著的影响;板底竖向位移及板中心下的竖向应力随着板刚度的增加而减小,相同荷载作用下横观各向同性地基与均匀各向同性地基模型的计算结果差异较大,实际工程中很有必要采用更符合土体性质的横观各向同性地基模型 相似文献
10.
This paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a finite depth below the free surface of a poroelastic medium. Biot's elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic fields are obtained by using Hankel integral transforms. Analytical solutions for influence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the influence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully flexible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for different depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
11.
基于实测资料,假设列车轮载经钢轨传递下来的荷载由5根枕木承担。根据分担比,获得了道渣层表面非均布荷载的表达式。将道渣层视为单相弹性介质,软土地基被看成是考虑水土耦合作用的饱和多孔介质。借助势函数,利用Helmholtz矢量分解法及Fourier变换技术分别对弹性土体和饱和半空间土体进行求解,得到非均布移动荷载作用下软土地基位移、应力及孔压响应在变换域内的精确解答。利用FFT算法得到了数值结果,详细分析了荷载分布形式、观察点位置、道渣性质以及软土地基渗透系数对动力响应的影响。研究结果表明：高速情况下动力响应与低速情况有很大不同;对于软土路基,应特别注意列车高速运行时路基浅层范围内产生的孔压响应。 相似文献
12.
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
13.
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
14.
A numerical technique is presented for the analysis of surface displacements of a non-homogeneous elastic half-space subjected to vertical and/or horizontal surface loads uniformly distributed over an arbitrarily shaped area. The non-homogeneity considered is a particular form of power variation of Young's modulus with depth. Since the exponent which determines the degree of non-homogeneity may vary from zero to unity, both the homogeneous half-space and the Gibson soil may be included as limiting cases in a single numerical scheme. In order to account for the arbitrary shape of the loading, the boundary of the loaded area is linearized piecemeal. This enables the modeling of any load pattern according to the desired degree of accuracy. Special attention is focused on the integration scheme, since the singularity associated with the Green's function becomes progressively more pronounced the greater the non-homogeneity parameter gets. The performance of the numerical procedure is studied using analytical solutions for rectangular shaped areas. Further comparisons with well-known solutions based on integral transform techniques for a uniformly distributed load acting on a circular area of the non-homogeneous soil mass show excellent agreement as well. © 1997 John Wiley & Sons, Ltd. 相似文献
15.
Pushpendra Sharma Amit Kumar Verma Anil Negi Manish Kumar Jha Pradeep Gautam 《Arabian Journal of Geosciences》2018,11(15):431
Thermoelastic deformation of rock significantly affects the stability of rock slope because thermoelastic strains may cause fracture propagation under favorable condition of failure. Rock slope stability depends on the balance between shear stress and shear resistance along the plane of weakness. Due to warming of rock slopes by heat transfer phenomena, viz. conduction and convection, considerable change in induced stresses (normal and shear) and resistance takes place which further causes instability in rock slope. In this paper, a two-dimensional finite element model has been used to simulate the stability of jointed rock slope containing crack in its upper surface. Four different cases have been simulated on the basis of infilling material (air, water, ice, water and ice) in the crack. Stability of rock slope is examined in terms of shear displacement and factor of safety for different thermal conditions of slope surface. A comparative study has been done for the four cases of infilling material in the crack. The various affecting parameters, viz. shear displacement, factor of safety, shear strength along the joint, and different surface temperature conditions, are illustrated by means of graphs. It has been found that the values of horizontal and vertical displacements are in the range of millimeters. The maximum values of horizontal and vertical displacements are 2.17 mm. Moreover, the maximum values of vertical compressive and tensile stresses are 15.4 MPa and 4.45 MPa respectively for the said four cases. According to the infilling material in the crack, the stability of the rock slope for the given geometry of slope is found in the following order: crack filled with ice < crack filled with ice and water < crack filled with water < empty crack. Validations of numerical results have been done from previous studies, and it has been found that the trends of normal stress, shear strength, and shear displacement along the joint are well matched. 相似文献
16.
The influence of the consolidation on a strutted excavation in soft soil is analysed using a computer code based on the finite element method. A base jet-grout slab is considered in order to improve stability against bottom heave failure and minimize wall displacements. The numerical model incorporates the Biot consolidation theory (coupled formulation of the flow and equilibrium equations) with soil constitutive relations simulated by the p–q–θ critical state model. Special emphasis is given to the analysis, during and after the construction period, of the pore pressures, shear stresses, stress levels and displacements in the ground, as well as strut compression loads, wall displacements and bending moments, earth pressures on the wall faces and compression loads and bending moments on the jet-grout slab. The safety factor against bottom heave is also evaluated from the finite element analysis considering formulations of the critical state soil mechanics, and also compared to values obtained with traditional methods that use limit equilibrium approach and bearing capacity fundamentals. 相似文献
17.
The construction of quasirectangular tunnels at shallow depths is becoming increasingly common in urban areas to efficiently utilize underground space and reduce the need for backfilling. To clarify the mechanical mechanism of the stresses and displacements around the tunnels, this study proposes analytical solutions that precisely account for quasirectangular tunnel shapes, the ground surface, the tunnel depth, and the ground's elastic/viscoelastic properties. The Schwarz alternating method combined with complex variable theory is employed to derive the elastic solution, and convergent and highly accurate solutions are obtained by superposing the solutions in the alternating iterations. Based on the solution and the extended corresponding principle for the viscoelastic problem, the time-dependent analytical solutions for the displacement are obtained for the ground assuming any viscoelastic model. The analytical solutions agree well with the finite element method (FEM) numerical results for models that are completely consistent, and qualitatively agree with field data. Furthermore, based on the stress solution combined with the Mohr-Coulomb failure criterion, the predicted initial plastic zone and propagation directions around the tunnels are qualitatively consistent with those determined by the limit analysis. A parametric study is performed to investigate the influences of the rectangular/quasirectangular tunnel shape, burial depth, and supporting pressure on the ground stresses and displacements. 相似文献
18.
利用间接边界元方法,在频域内求解了层状场地中局部不均体对平面P波的散射。利用精确的土层动力刚度矩阵进行自由场反应分析,求得位移和应力响应。通过计算虚拟分布荷载的格林影响函数,求得相应位移和应力;根据边界条件确定虚拟分布荷载,最终得到问题的解答。研究了入射P波时,不均体宽度、埋深、厚度、入射角、入射频率度等参数对地表位移幅值的影响,并与相应自由场的结果进行了比较。不均体对P波散射有重要影响,在工程场地地震安全性评价中,应合理考虑局部不均体对场地设计地震动参数确定的影响。 相似文献
19.
20.
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