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Half-space
Kinds of Half-space Selected AbstractsDynamic stiffness of deep foundations with inclined pilesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 12 2010L. A. Padrón Abstract The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element,finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal,rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half-space and the piles are modeled as elastic compressible Euler,Bernoulli beams. The results for different pile group configurations, pile,soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd. [source] The effect of foundation embedment on inelastic response of structuresEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2009Mojtaba Mahsuli Abstract In this research, a parametric study is carried out on the effect of soil,structure interaction on the ductility and strength demand of buildings with embedded foundation. Both kinematic interaction (KI) and inertial interaction effects are considered. The sub-structure method is used in which the structure is modeled by a simplified single degree of freedom system with idealized bilinear behavior. Besides, the soil sub-structure is considered as a homogeneous half-space and is modeled by a discrete model based on the concept of cone models. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. The soil,structure system is then analyzed subjected to a suit of 24 selected accelerograms recorded on alluvium deposits. An extensive parametric study is performed for a wide range of the introduced non-dimensional key parameters, which control the problem. It is concluded that foundation embedment may increase the structural demands for slender buildings especially for the case of relatively soft soils. However, the increase in ductility demands may not be significant for shallow foundations with embedment depth to radius of foundation ratios up to one. Comparing the results with and without inclusion of KI reveals that the rocking input motion due to KI plays the main role in this phenomenon. Copyright © 2008 John Wiley & Sons, Ltd. [source] Natural and accidental torsion in one-storey structures on elastic foundation under non-vertically incident SH-wavesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 7 2006Javier Avilés Abstract Factors , and , used in equivalent static analysis to account for natural and accidental torsion are evaluated with consideration of soil,structure interaction. The combined torsional effects of structural asymmetry and foundation rotation are examined with reference to a single monosymmetric structure placed on a rigid foundation that is embedded into an elastic half-space, under to the action of non-vertically incident SH waves. Dynamic and accidental eccentricities are developed such that when used together with the code-specified base shear, the resulting static displacement at the flexible edge of the building is identical to that computed from dynamic analysis. It is shown that these eccentricities do not have a unique definition because they depend on both the selection of the design base shear and the criterion used for separation of the torsional effects of foundation rotation from those of structural asymmetry. Selected numerical results are presented in terms of dimensionless parameters for their general application, using a set of appropriate earthquake motions for ensuring generality of conclusions. The practical significance of this information for code-designed buildings is elucidated. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical evaluation of the damping-solvent extraction method in the frequency domainEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 6 2002Ushnish Basu Abstract The damping-solvent extraction method for the analysis of unbounded visco-elastic media is evaluated numerically in the frequency domain in order to investigate the influence of the computational parameters,domain size, amount of artificial damping, and mesh density,on the accuracy of results. An analytical estimate of this influence is presented, and specific questions regarding the influence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco-elastic half-space with constant hysteretic material damping. As the domain size is increased, the results become more accurate only at lower frequencies, but are essentially unaffected at higher frequencies. Choosing the domain size to ensure that the static stiffness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artificial damping but at a slower rate as the total (material plus artificial) damping ratio ,t gets closer to 0.866. However, the results do not deteriorate significantly for the larger amounts of artificial damping, suggesting that ,t,0.6 is appropriate; a larger value is not likely to influence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping. Copyright © 2002 John Wiley & Sons, Ltd. [source] Response of unbounded soil in scaled boundary finite-element methodEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 1 2002John P. Wolf Abstract The scaled boundary finite-element method is a powerful semi-analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure,soil interface. This permits the analysis of dynamic soil,structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including the far field. The three-dimensional vector-wave equation of elasto-dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high-frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first-order ordinary differential equations numerically permits the radiation condition and the boundary condition of the structure,soil interface to be satisfied sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half-space with the results of the boundary-element method is observed. Copyright © 2001 John Wiley & Sons, Ltd. [source] A mode II weight function for subsurface cracks in a two-dimensional half-spaceFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2002A. MAZZŮ ABSTRACT The general properties of a mode II Weight Function for a subsurface crack in a two-dimensional half-space are discussed. A general form for the WF is proposed, and its analytical expression is deduced from the asymptotic properties of the displacements field near the crack tips and from some reference cases obtained by finite elements models. Although the WF has general validity, the main interest is on its application to the study of rolling contact fatigue: its properties are explored for a crack depth range within which the most common failure phenomena in rolling contact are experimentally observed, and for a crack length range within the field of short cracks. The accuracy is estimated by comparison with several results obtained by FEM models, and its validity in the crack depth range explored is shown. [source] A unified continuum representation of post-seismic relaxation mechanisms: semi-analytic models of afterslip, poroelastic rebound and viscoelastic flowGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010Sylvain Barbot SUMMARY We present a unified continuum mechanics representation of the mechanisms believed to be commonly involved in post-seismic transients such as viscoelasticity, fault creep and poroelasticity. The time-dependent relaxation that follows an earthquake, or any other static stress perturbation, is considered in a framework of a generalized viscoelastoplastic rheology whereby some inelastic strain relaxes a physical quantity in the material. The relaxed quantity is the deviatoric stress in case of viscoelastic relaxation, the shear stress in case of creep on a fault plane and the trace of the stress tensor in case of poroelastic rebound. In this framework, the instantaneous velocity field satisfies the linear inhomogeneous Navier's equation with sources parametrized as equivalent body forces and surface tractions. We evaluate the velocity field using the Fourier-domain Green's function for an elastic half-space with surface buoyancy boundary condition. The accuracy of the proposed method is demonstrated by comparisons with finite-element simulations of viscoelastic relaxation following strike-slip and dip-slip ruptures for linear and power-law rheologies. We also present comparisons with analytic solutions for afterslip driven by coseismic stress changes. Finally, we demonstrate that the proposed method can be used to model time-dependent poroelastic rebound by adopting a viscoelastic rheology with bulk viscosity and work hardening. The proposed method allows one to model post-seismic transients that involve multiple mechanisms (afterslip, poroelastic rebound, ductile flow) with an account for the effects of gravity, non-linear rheologies and arbitrary spatial variations in inelastic properties of rocks (e.g. the effective viscosity, rate-and-state frictional parameters and poroelastic properties). [source] Three-dimensional models of elastostatic deformation in heterogeneous media, with applications to the Eastern California Shear ZoneGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2009Sylvain Barbot SUMMARY We present a semi-analytic iterative procedure for evaluating the 3-D deformation due to faults in an arbitrarily heterogeneous elastic half-space. Spatially variable elastic properties are modelled with equivalent body forces and equivalent surface traction in a ,homogenized' elastic medium. The displacement field is obtained in the Fourier domain using a semi-analytic Green function. We apply this model to investigate the response of 3-D compliant zones (CZ) around major crustal faults to coseismic stressing by nearby earthquakes. We constrain the two elastic moduli, as well as the geometry of the fault zones by comparing the model predictions to Synthetic Aperture Radar inferferometric (InSAR) data. Our results confirm that the CZ models for the Rodman, Calico and Pinto Mountain faults in the Eastern California Shear Zone (ECSZ) can explain the coseismic InSAR data from both the Landers and the Hector Mine earthquakes. For the Pinto Mountain fault zone, InSAR data suggest a 50 per cent reduction in effective shear modulus and no significant change in Poisson's ratio compared to the ambient crust. The large wavelength of coseismic line-of-sight displacements around the Pinto Mountain fault requires a fairly wide (,1.9 km) CZ extending to a depth of at least 9 km. Best fit for the Calico CZ, north of Galway Dry Lake, is obtained for a 4 km deep structure, with a 60 per cent reduction in shear modulus, with no change in Poisson's ratio. We find that the required effective rigidity of the Calico fault zone south of Galway Dry Lake is not as low as that of the northern segment, suggesting along-strike variations of effective elastic moduli within the same fault zone. The ECSZ InSAR data is best explained by CZ models with reduction in both shear and bulk moduli. These observations suggest pervasive and widespread damage around active crustal faults. [source] Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading elementGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007E. Pan SUMMARY This study is motivated by a desire to develop a fast numerical algorithm for computing the surface deformation field induced by surface pressure loading on a layered, isotropic, elastic half-space. The approach that we pursue here is based on a circular loading element. That is, an arbitrary surface pressure field applied within a finite surface domain will be represented by a large number of circular loading elements, all with the same radius, in which the applied downwards pressure (normal stress) is piecewise uniform: that is, the load within each individual circle is laterally uniform. The key practical requirement associated with this approach is that we need to be able to solve for the displacement field due to a single circular load, at very large numbers of points (or ,stations'), at very low computational cost. This elemental problem is axisymmetric, and so the displacement vector field consists of radial and vertical components both of which are functions only of the radial coordinate r. We achieve high computational speeds using a novel two-stage approach that we call the sparse evaluation and massive interpolation (SEMI) method. First, we use a high accuracy but computationally expensive method to compute the displacement vectors at a limited number of r values (called control points or knots), and then we use a variety of fast interpolation methods to determine the displacements at much larger numbers of intervening points. The accurate solutions achieved at the control points are framed in terms of cylindrical vector functions, Hankel transforms and propagator matrices. Adaptive Gauss quadrature is used to handle the oscillatory nature of the integrands in an optimal manner. To extend these exact solutions via interpolation we divide the r -axis into three zones, and employ a different interpolation algorithm in each zone. The magnitude of the errors associated with the interpolation is controlled by the number, M, of control points. For M= 54, the maximum RMS relative error associated with the SEMI method is less than 0.2 per cent, and it is possible to evaluate the displacement field at 100 000 stations about 1200 times faster than if the direct (exact) solution was evaluated at each station; for M= 99 which corresponds to a maximum RMS relative error less than 0.03 per cent, the SEMI method is about 700 times faster than the direct solution. [source] Absolute S -velocity estimation from receiver functionsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2007L. Svenningsen SUMMARY We present a novel method to recover absolute S velocities from receiver functions. For a homogeneous half-space the S velocity can be calculated from the horizontal slowness and the angle of surface particle motion for an incident P wave. Generally, the calculated S velocity is an apparent half-space value which depends on model inhomogeneity and P -waveform. We therefore, suggest to calculate such apparent half-space S velocities from low-pass filtered (smoothed) receiver functions using a suite of filter-parameters, T. The use of receiver functions neutralize the influence of the P -waveform, and the successive low-pass filterings emphasize the variation of S velocity with depth. We apply this VS,app.(T) technique to teleseismic data from three stations: FUR, BFO and SUM, situated on thick sediments, bedrock and the Greenland ice cap, respectively. The observed VS,app.(T) curves indicate the absolute S velocities from the near surface to the uppermost mantle beneath each station, clearly revealing the different geological environments. Application of linearized, iterative inversion quantify these observations into VS(z) models, practically independent of the S -velocity starting model. The obtained models show high consistency with independent geoscientific results. These cases provide also a general validation of the VS,app.(T) method. We propose the computation of VS,app.(T) curves for individual three-component broad-band stations, both for direct indication of the S velocities and for inverse modelling. [source] Analytical and 3-D numerical modelling of Mt. Etna (Italy) volcano inflationGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2005A. Bonaccorso SUMMARY Since 1993, geodetic data obtained by different techniques (GPS, EDM, SAR, levelling) have detected a consistent inflation of the Mt. Etna volcano. The inflation, culminating with the 1998,2001 strong explosive activity from summit craters and recent 2001 and 2002 flank eruptions, is interpreted in terms of magma ascent and refilling of the volcanic plumbing system and reservoirs. We have modelled the 1993,1997 EDM and GPS data by 3-D pressurized sources to infer the position and dimension of the magma reservoir. We have performed analytical inversions of the observed deformation using both spheroidal and ellipsoidal sources embedded in a homogeneous elastic half-space and by applying different inversion methods. Solutions for these types of sources show evidence of a vertically elongated magma reservoir located 6 km beneath the summit craters. The maximum elevation of topography is comparable to such depth and strong heterogeneities are inferred from seismic tomography; in order to assess their importance, further 3-D numerical models, employing source parameters extracted from analytical models, have been developed using the finite-element technique. The deformation predicted by all the models considered shows a general agreement with the 1993,1997 data, suggesting the primary role of a pressure source, while the complexities of the medium play a minor role under elastic conditions. However, major discrepancies between data and models are located in the SE sector, suggesting that sliding along potential detachment surfaces may contribute to amplify deformation during the inflation. For the first time realistic features of Mt. Etna are studied by a 3-D numerical model characterized by the topography and lateral variations of elastic structure, providing a framework for a deeper insight into the relationships between internal sources and tectonic structures. [source] Surface waves in a general anisotropic poroelastic solid half-spaceGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004M. D. Sharma SUMMARY A method is introduced for studying surface waves in a general anisotropic poroelastic medium. The method is analogous to the one used for isotropic media and derives a complex secular equation to represent the propagation of surface waves at the stress-free plane surface of a non-dissipative porous medium. The point of importance is that the derived equation is, analytically, separable into real and imaginary parts and hence can be solved by iterative numerical methods. A root of this secular equation represents the existence of surface waves and calculates the apparent phase velocity along a given direction on the surface. Numerical work is carried out for the model of a crustal rock. The propagation of surface waves is studied numerically for the top three anisotropies (i.e. triclinic, monoclinic, orthorhombic). [source] On strike-slip faulting in layered mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2002Maurizio Bonafede Summary We study the effects of structural inhomogeneities on the stress and displacement fields induced by strike-slip faults in layered media. An elastic medium is considered, made up of an upper layer bounded by a free surface and welded to a lower half-space characterized by different elastic parameters. Shear cracks with assigned stress drop are employed as mathematical models of strike-slip faults, which are assumed to be vertical and planar. If the crack is entirely embedded within the lower medium (case A), a Cauchy-kernel integral equation is obtained, which is solved by employing an expansion of the dislocation density in Chebyshev polynomials. If the crack is within the lower medium but it terminates at the interface (case B), a generalized Cauchy singularity appears in the integral kernel. This singularity affects the singular behaviour of the dislocation density at the crack tip touching the interface. Finally, the case of a crack crossing the interface is considered (case C). The crack is split into two interacting sections, each placed in a homogeneous medium and both open at the interface. Two coupled generalized Cauchy equations are obtained and solved for the dislocation density distribution of each crack section. An asymptotic study near the intersection between the crack and the interface shows that the dislocation densities for each crack section are bounded at the interface, where a jump discontinuity is present. As a corollary, the stress drop must be discontinuous at the interface, with a jump proportional to the rigidity contrast between the adjoining media. This finding is shown to have important implications for the development of geometrical complexities within transform fault zones: planar strike-slip faults cutting across layer discontinuities with arbitrary stress drop values are shown to be admissible only if the interface between different layers becomes unwelded during the earthquake at the crack/interface junction. Planar strike-slip faulting may take place only in mature transform zones, where a repetitive earthquake cycle has already developed, if the rheology is perfectly elastic. Otherwise, the fault cannot be planar: we infer that strike-slip faulting at depth is plausibly accompanied by en-echelon surface breaks in a shallow sedimentary layer (where the stress drop is lower than prescribed by the discontinuity condition), while ductile deformation (or steady sliding) at depth may be accommodated by multiple fault branching or by antithetic faulting in the upper brittle layer (endowed with lower rigidity but higher stress). [source] On the use of dislocations to model interseismic strain and stress build-up at intracontinental thrust faultsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2001J. Vergne Summary Creeping dislocations in an elastic half-space are commonly used to model interseismic deformation at subduction zones, and might also apply to major intracontinental thrust faults such as the Main Himalayan Thrust. Here, we compare such models with a more realistic 2-D finite element model that accounts for the mechanical layering of the continental lithosphere and surface processes, and that was found to fit all available constraints on interseismic and long-term surface displacements. These can also be fitted satisfactorily from dislocation models. The conventional back-slip model, commonly used for subduction zones, may, however, lead to a biased inference about the geometry of the locked portion of the thrust fault. We therefore favour the use of a creeping buried dislocation that simulates the ductile shear zone in the lower crust. A limitation of dislocation models is that the mechanical response of the lithosphere to the growth of the topography by bending of the elastic cores and ductile flow in the lower crust cannot be easily introduced. Fortunately these effects can be neglected because we may assume, to first order, a stationary topography. Moreover, we show that not only can dislocation models be used to adjust surface displacements but, with some caution, they can also provide a physically sound rationale to interpret interseismic microseismicity in terms of stress variations. [source] Viscoelastic displacement and gravity changes due to point magmatic intrusions in a gravitational layered solid earthGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2001José Fernández Summary We present a method for the computation of time-dependent geodetic and geophysical signatures (deformation, potential and gravity changes) due to magmatic intrusions in a layered viscoelastic,gravitational medium. This work is an extension of a deformation model previously developed to compute effects due to volcanic loading in an elastic gravitational layered media. The model assumes a planar earth geometry, useful for near field problems, and consists of welded elastic and viscoelastic layers overlying a viscoelastic half-space. Every layer can either be considered elastic or viscoelastic. The intrusion (treated as a point source) can be located at any depth, in any of the layers or in the half-space. Several examples of theoretical computations for different media are also presented. We have found that, in line with previous results obtained by other authors, introducing viscoelastic properties in all or part of the medium can extend the effects (displacements, gravity changes, etc.) considerably and therefore lower pressure increases are required to model given observed effects. The viscoelastic effects seem to depend mainly on the rheological properties of the layer (zone) where the intrusion is located, rather than on the rheology of the whole medium. We apply our model to the 1982,1984 uplift episode at Campi Flegrei, modelling simultaneously the observed vertical displacement and gravity changes. The results clearly show that for a correct interpretation of observed effects it is necessary to include the gravitational field in the anelastic theoretical models. This factor can change the value and pattern of time-dependent deformation as well as the gravity changes, explaining cases of displacement without noticeable gravity changes or vice versa, cases with uplift and incremental gravity values, and other cases. The combination of displacement and gravity changes is found to be especially effective in constraining the possible characteristics of the magmatic intrusion as well as the rheology of the medium surrounding it. [source] The effect of inertial coupling on seismic reflection amplitudesGEOPHYSICAL PROSPECTING, Issue 5 2008Ashish Arora ABSTRACT A problem of reflection and transmission of elastic waves at a plane interface between a uniform elastic solid half-space and a porous elastic half-space containing two immiscible fluids is investigated. The theory developed by Lo, Sposito and Majer for porous media containing two immiscible fluids is employed to find out the reflection and transmission coefficients. The incident wave is assumed to propagate through the uniform elastic half-space and two cases are considered. In the first case, a beam of plane longitudinal wave is assumed to be incident and in the second case, a beam of transverse wave is assumed to be incident at the interface. By taking granite as impervious elastic medium and columbia fine sandy loam containing air-water mixture as porous medium, reflection and transmission coefficients are obtained. By neglecting the inertial coupling coefficients, these coefficients are reduced to those obtained by Tomar and Arora using the theory of Tuncay and Corapcioglu. It is found that the inertial coupling parameters significantly affect the phase speeds and the amplitude ratios of the transmitted waves. [source] Numerical modelling of complex resistivity effects on a homogenous half-space at low frequenciesGEOPHYSICAL PROSPECTING, Issue 3 2006T. Ingeman-Nielsen ABSTRACT The many different existing models describing the spectral behaviour of the resistivity of geological materials at low frequency, combined with the lack of available field data, render the interpretation of complex resistivity (CR) data very difficult. With a recent interest in CR-measurements for environmental applications and thanks to technological progress, the use of wide-band frequency equipment seems promising, and it is expected to shed light on the different results among the published solutions to the electromagnetic (EM) coupling problem. We review the theory of EM-coupling over a homogeneous half-space with CR-effects and study some aspects of the complex coupling function. We advocate the use of the CR-based coupling function in the interpretation process, in order to obtain a better understanding of the physical processes involved in CR-effects. Application of the model to real field data shows systematic good agreement in two simple cases, even over wide ranges of frequencies. Interpretation with a double Cole,Cole model is applied for comparison, and in spite of good fits to the data, large differences are observed in the interpreted low-frequency dispersion. We conclude that the use of a second Cole,Cole model to describe EM-coupling may corrupt the interpretation of the low-frequency dispersion, even when only the normal range of frequencies (<100 Hz) is considered, and that the use of the actual EM-coupling expression is essential when the goal is a better understanding of interaction between CR-effects and EM-coupling. [source] Distortions of EM transients in coincident loops at short time-delaysGEOPHYSICAL PROSPECTING, Issue 6 2000F. Kamenetsky Transient electromagnetic measurements with short time-delays of transients are used for solving different problems within the upper part of a geoelectric section. However, it is necessary to take into consideration distortions connected with self-transients within the transmitter,receiver system. From the practical point of view, it is important to estimate the minimum time-delay after which these distortions may be neglected. We present such an estimation which uses a simple approximation method for a single-loop (or coincident-loop) configuration. For common values of the loop size (10 m × 10 m to 40 m × 40 m) and of the resistivity of a homogeneous half-space (1,100 ,m), the minimum time-delay beyond which we can use a standard interpretation is in the range of 2,10 µs. This is equivalent to a minimum depth of investigation in the range of 1,30 m. [source] Axisymmetric interaction of a rigid disc with a transversely isotropic half-spaceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2010Amir Aabbas Katebi Abstract 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. [source] Vertical stress distributions around batter piles driven in cross-anisotropic mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2009Cheng-Der Wang Abstract 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. [source] Surface displacements due to batter piles driven in cross-anisotropic mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2008Cheng-Der Wang Abstract 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 ,/,,), pile inclination (,), 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. [source] Poroelastic model for pile,soil interaction in a half-space porous medium due to seismic wavesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2008Jian-Fei Lu Abstract In this paper, frequency domain dynamic response of a pile embedded in a half-space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half-space and a fictitious pile. The extended porous half-space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1-D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half-space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half-space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile,half-space system. Significant differences between conventional single-phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd. [source] The Reissner,Sagoci problem for a transversely isotropic half-spaceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2006Mohammad Rahimian Abstract A transversely isotropic linear elastic half-space, z,0, with the isotropy axis parallel to the z -axis is considered. The purpose of the paper is to determine displacements and stresses fields in the interior of the half-space when a rigid circular disk of radius a completely bonded to the surface of the half-space is rotated through a constant angle ,0. The region of the surface lying out with the circle r,a, is free from stresses. This problem is a type of Reissner,Sagoci mixed boundary value problems. Using cylindrical co-ordinate system and applying Hankel integral transform in the radial direction, the problem may be changed to a system of dual integral equations. The solution of the dual integral equations is obtained by an approach analogous to Sneddon's (J. Appl. Phys. 1947; 18:130,132), so that the circumferential displacement and stress fields inside the medium are obtained analytically. The same problem has already been approached by Hanson and Puja (J. Appl. Mech. 1997; 64:692,694) by the use of integrating the point force potential functions. It is analytically proved that the present solution, although of a quite different form, is equivalent to that given by Hanson and Puja. To illustrate the solution, a few plots are provided. The displacements and the stresses in a soil deposit due to a rotationally symmetric force or boundary displacement may be obtained using the results of this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] Stresses due to vertical subsurface loading for an inhomogeneous cross-anisotropic half-spaceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2004Cheng-Der Wang Abstract 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. [source] Steady infiltration from buried point source into heterogeneous cross-anisotropic unsaturated soilINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2004G. J. Chen Abstract The paper presents the analytical solution for the steady-state infiltration from a buried point source into two types of heterogeneous cross-anisotropic unsaturated half-spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half-space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross-anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd. [source] Elastic half-space under an oblique line impulseINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2003Moche Ziv Abstract This paper presents transient deformation of an elastic half-space under two types of line-concentrated impulsive loads applied simultaneously. One load is a sustainable normal force, while the other is a momentarily applied vector shear force. For each of the two loads the author gave the respective solution in two separate papers. Here the two solutions are superimposed to determine the response of the half-space under the combined loads. The present work is devoted to the salient wave propagation features seen in the resultant computer plots that disclose the strained half-space. Since each critical deformation is explicitly indicated in the plots by a wave front, the interpretation of the response of the half-space to the applied load is readily available at a glance. A comparison is then presented that identifies those deformation traits and wave fronts, among the nineteen here, that are more closely related to those found in previous works. Copyright © 2003 John Wiley & Sons, Ltd. [source] Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2003James P. Doherty Abstract The scaled boundary finite-element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power-law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half-space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non-homogeneous half-space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. [source] The response of an elastic half-space under a momentary shear line impulseINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2003Moche Ziv Abstract The response of an ideal elastic half-space to a line-concentrated impulsive vector shear force applied momentarily is obtained by an analytical,numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half-space, while being normal to that line as well as to the axis of symmetry of the half-space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half-space; in this sense, the source configuration is exact. For the transient boundary-value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half-space. A numerical integration of these extended differential equations is then carried out in a three-dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half-space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd. [source] A study of ground-structure interaction in dynamic plate load testingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2002Bojan B. Guzina Abstract A mathematical treatment is presented for the forced vertical vibration of a padded annular footing on a layered viscoelastic half-space. On assuming a depth-independent stress distribution for the interfacial buffer, the set of triple integral equations stemming from the problem is reduced to a Fredholm integral equation of the second kind. The solution method, which is tailored to capture the stress concentrations beneath footing edges, is highlighted. To cater to small-scale geophysical applications, the model is used to investigate the near-field effects of ground-loading system interaction in dynamic geotechnical and pavement testing. Numerical results indicate that the uniform-pressure assumption for the contact load between the composite disc and the ground which is customary in dynamic plate load testing may lead to significant errors in the diagnosis of subsurface soil and pavement conditions. Beyond its direct application to non-intrusive site characterization, the proposed solution can be used in the seismic analysis of a variety of structures involving annular foundation geometries. Copyright © 2002 John Wiley & Sons, Ltd. [source] Source signature and elastic waves in a half-space under a sustainable line-concentrated impulsive normal forceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2002Moche Ziv Abstract First, the response of an ideal elastic half-space to a line-concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature,the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress-free surface of the half-space to three points located on the other two boundaries of the solution domain. These four wave-arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface-axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface-axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint-Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line-concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||