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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.
In this article, we present the solutions for the stresses induced by four different loads associated with an axially loaded pile in a continuously inhomogeneous cross‐anisotropic half‐space. The planes of cross‐anisotropy are parallel to the horizontal surface of the half‐space, and the Young's and shear moduli are assumed to vary exponentially with depth. The four loading types are: an embedded point load for an end‐bearing pile, uniform skin friction, linear variation of skin friction, and non‐linear parabolic variation of skin friction for a friction pile. The solutions for the stresses due to the pile load are expressed in terms of the Hankel integral and are obtained from the point load solutions of the same inhomogeneous cross‐anisotropic half‐space which were derived recently by the authors (Int. J. Rock Mech. Min. Sci. 2003; 40 (5):667–685). A numerical procedure is proposed to carry out the integral. For the special case of homogeneous isotropic and cross‐anisotropic half‐space, the stresses predicted by the numerical procedure agree well with the solutions of Geddes and Wang (Geotechnique 1966; 16 (3):231–255; Soils Found. 2003; 43 (5):41–52). An illustrative example is also given to investigate the effect of soil inhomogeneity, the type and degree of soil anisotropy, and the four different loading types on the vertical normal stress. The presented solutions are more realistic in simulating the actual stratum of loading problem in many areas of engineering practice. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

3.
This work presents analytical solutions for determining lateral force (force per unit length) and centroid location caused by horizontal and vertical surcharge surface loads acting on a cross‐anisotropic backfill. The surcharge loading types are point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load, and downward nonlinear‐varying strip load. The planes of cross‐anisotropy are assumed parallel to the backfill ground surface. The proposed solutions, derived by integrating the lateral stress solutions (Int. J. Numer. Anal. Meth. Geomech. 2005; 29 :1341–1361), do not exist in literature. Clearly, the type and degree of material anisotropy, loading distance from the retaining wall, and loading types markedly impact the proposed solutions. Two examples are utilized to illustrate the type and degree of soil anisotropy, and the loading types on the lateral force and centroid location in the isotropic/cross‐anisotropic backfills generated by the horizontal and vertical uniform, upward linear‐varying and upward nonlinear‐varying strip loads. The parametric study results demonstrate that the lateral force and centroid location accounting for soil anisotropy, loading distance from the retaining wall, dimension of the loading strip, and loading directions and types differ significantly from those estimated using existing isotropic solutions. The derived solutions can be added to other lateral pressures, such as earth pressure or water pressure, required for stability and structural analysis of a retaining wall. Additionally, they can simulate realistically actual surcharge loading problems in geotechnical engineering when backfill materials are cross‐anisotropic. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

4.
This study derives analytical solutions for estimating the lateral stress caused by horizontal and vertical surcharge strip loads resting on a cross‐anisotropic backfill. The following loading types are employed in this work: point load, line load, uniform strip load, upward linear‐varying strip load, upward nonlinear‐varying strip load, downward linear‐varying strip load and downward nonlinear‐varying strip load. The cross‐anisotropic planes are assumed to be parallel to the horizontal surface of the backfill. The solutions proposed herein have never been mentioned in previous literature, but can be derived by integrating the point load solution in a Cartesian co‐ordinate system for a cross‐anisotropic medium. The calculations by the presented solutions are quick and accurate since they are concise and systematized. Additionally, the proposed calculations demonstrate that the type and degree of material anisotropy and the horizontal/vertical loading types decisively influence the lateral stress. This investigation presents examples of the proposed horizontal and vertical strip loads acting on the surface of the isotropic and cross‐anisotropic backfills to elucidate their effects on the stress. The analytical results reveal that the stress distributions accounting for soil anisotropy and loading types are quite different from those computed from the available isotropic solutions. Restated, the derived solutions, as well as realistically simulating the actual surcharge loading circumstances, provide a good reference for the design of retaining structures for the backfill materials are cross‐anisotropic. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

5.
This work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

6.
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   

7.
A complete formulation and implementation for assessment of the response to dynamic loads of cylindrical rigid structures embedded in transversely isotropic elastic half‐spaces is presented. The analysis is performed in the frequency domain and the steady‐state structure response is obtained. The method is based on a non‐singular version of the indirect boundary element method which uses influence functions, instead of Green's functions, as fundamental solutions. These influence functions are the response of an elastic half‐space to distributed, internally applied loads. The proposed method imposes full bonding contact between the foundation and the surrounding soil. Numerical results for displacement (vertical and horizontal) and rotation (twisting and rocking) impedances, showing the influence of the soil anisotropy, are presented. Results for the soil–structure interface tractions and for the displacement field throughout the half‐space are also shown. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

8.
An analytical investigation of a half‐space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape‐ and rigidity‐ induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point‐load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half‐space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two‐dimensional adaptive‐gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
A method is presented for coupling cubic‐order quadrilateral finite elements with the finite side of a new coordinate ascent hierarchical infinite element. At a common side shared by a hierarchical infinite element and an arbitrary number of finite elements, the displacements are minimized in the least square sense with respect to the degrees‐of‐freedom of the finite elements. This leads to a set of equations that relate the degrees‐of‐freedom of the finite and hierarchical infinite elements on the shared side. The method is applied to a non‐homogeneous cross‐anisotropic half‐space subjected to a non‐uniform circular loading with Young's and shear moduli varying with depth according to the power law. A constant mesh constructed from coupled finite and hierarchical infinite elements is used and convergence is sought simply by increasing the degree of the interpolating polynomial. The displacements and stresses produced by conical and parabolic circular loads applied on the surface are obtained. The efficiency of the proposed method is demonstrated through convergence and comparison studies. New results produced by a frusto‐conical circular load applied on the surface of a half‐space made up of heavily consolidated London clay are provided. The non‐homogeneity parameter and degree of anisotropy are shown to influence the soil response. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

10.
In the framework of elastostatics, a mathematical treatment is presented for the boundary value problem of the interaction of a flexible cylindrical pile embedded in a transversely isotropic half‐space under transverse loadings. Taking the pile region as a stiffened subdomain of an extended half‐space, the formulation of the interaction problem is reduced to a Fredholm integral equation of the second kind. The necessary set of Green's functions for the transversely isotropic half‐space is obtained by means of a method of potentials. The resulting Green's functions are incorporated into a numerical procedure for the solution of the integral equation. The theoretical response of the pile is presented in terms of bending moment, displacement and slope profiles for a variety of transversely isotropic materials so that the effect of different anisotropy parameters can be meaningfully discussed. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

11.
This work presents analytical solutions for displacements caused by three‐dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed toyield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (?), (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (Px, Py, Pz). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22 (6):425–447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three‐dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

12.
A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

13.
Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

14.
A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

15.
This article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
A boundary integral equation method is presented for a rigid cylindrical pipe‐pile of finite length embedded in a transversely isotropic half‐space under lateral loads. In the framework of three‐dimensional elastostatics, the complicated soil‐structure interaction problem is shown to be reducible to three coupled Fredholm integral equations. Through an analysis of the associated Cauchy singular kernels, the intrinsic singular characteristics of the radial, angular, and vertical interfacial load transfers are rendered explicit. By means of a complicated numerical procedure, detailed results on the three‐dimensional load–transfer process are provided for benchmark comparison and practical applications. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

17.
In this paper, forced rocking vibration of a rigid circular disc placed in a transversely isotropic full‐space, where the axis of material symmetry of the full‐space is normal to the surface of the plate, is analytically investigated. Because of using the Fourier series and Hankel integral transforms, the mixed boundary‐value problem is transformed into two separate pairs of integral equations called dual integral equations. The dual integral equations involved in this paper are reduced to Fredholm integral equations of the second kind. With the aid of contour integration, the governing integral equation is numerically evaluated in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly determined, and it is shown that the pressure in between the plate and the full‐space and the compliance function reduced for isotropic half‐space are identical to the previously published solutions. The dynamic contact pressure in between the disc and the space and also the related impedance function are numerically evaluated in general dynamic case and illustrated. It is shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. To show the effect of material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

18.
王俊林  祝彦知  张天航 《岩土力学》2007,28(7):1315-1322
在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。  相似文献   

19.
半无限横观各向同性介质中多裂纹相互作用分析   总被引：2，自引：0，他引：2  
王炳军  肖洪天  岳中琦 《岩土力学》2012,33(8):2527-2535
为评估含矩形裂纹的半无限横观各向同性介质的局部强度和稳定性,采用基于双横观各向同性材料基本解的对偶边界元数值方法,分析了在沿裂纹面法向和切向均布力分别作用下矩形裂纹的应力强度因子及两个共面或平行的矩形裂纹的相互作用问题。通过数值计算考察了自由面对应力强度因子值的影响,以及裂纹间距、边长比及自由面对共面或平行双裂纹相互作用效应的影响。结果表明,自由面的存在引起该类裂纹应力强度因子值大于无限域情况;裂纹形状和裂纹间距对共面或平行双裂纹相互作用效应均有较明显的影响,但自由面对共面或平行双裂纹的相互作用效应均影响较小。  相似文献   

20.
Numerical solutions have been obtained for stresses and displacements in a linear elastic half space due to distributed loads of circular, rectangular and elliptical shapes. The technique primarily involves use of a multi-dimensional numerical integration technique to integrate point load solutions over the distributed loading after discretizing the area into a finite number of elements. Both uniform vertical and shear loads have been considered as well as vertical conical loads and inward shear loads. The technique evolved facilitates the determination of stresses and displacements by the use of mini-computers and is neither as tedious and cumbersome as the use of tables and charts nor as costly as FEM solutions. A detailed comparison has been presented between the results obtained by the numerical solutions and those of the existing analytical solutions wherever they are available. It is found that the agreement between the two is within one per cent for displacements at all depths for the different cases studied. The matching is also good in the case of stresses, except at shallow depths.  相似文献   

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