Layered Half-space Research Articles

Dynamic Responses of Pile Groups Embedded in a Layered Poroelastic Half-Space to Harmonic Axial Loads

The dynamic responses of a pile group embedded in a layered poroelastic half-space subjected to axial harmonic loads is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in the layered poroelastic half-space is derived via the transmission and reflection matrix (TRM) method. Utilizing Muki’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile group is constructed. The proposed methodology was validated by comparing the results of this paper with a known result. Numerical results show that in a two-layered half-space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has different influences on the central pile and the corner piles, while for the sparse pile group, it has almost the same influence on all the piles. For a three-layer half-space, the presence of a stiffer middle layer in the layered half-space will enhance the impedance of the pile group significantly, while a softer middle layer will reduce the impedance of the pile group.

Circular surface loading on a layered multiferroic half space

By introducing the cylindrical system of vector functions and the correspondingpropagating matrix, we present a semi-analytical solution for a layered multiferroic halfspace under a uniform vertical circular load on its surface. A two-layered system made ofBaTiO3 andCoFe2O4 is analyzed by the proposed method. The coupling feature among the elastic, electric, andmagnetic fields and the interplay between the adjacent layers are investigated. Inparticular, we find that the interfacial elastic, electric, and magnetic fields are very sensitiveto the thickness of the surface layer. Consequently, a critical thickness is found for eachfield quantity when it reaches its extreme value for varying thickness of the surface layer.This striking feature could be very useful as a theoretical reference for the optimal designof surface coatings.

The Effect on Scattering of SH-Wave in a Layered Half-Space with the Subsurface Circular Cavities

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method and wave functions expansion method. The solution of scattering of SH-wave was given by using circular boundary of large radius to approximate straight boundary of surface elastic layer. According to boundary conditions, we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around circular cavities were discussed in numerical examples.

The one-bit noise correlation: a theory based on the concepts of coherent and incoherent noise

Waveforms emerging from correlations of long seismic noise records are extensively used to investigate the crustal and upper-mantle structure of the Earth. To remove the non-stationary events that inevitably lie in seismic records, the so-called one-bit normalization is commonly applied to the noise data. This processing consists of replacing each sample of a record by its sign. Although it is a strong non-linear operation, it preserves the phase of the signal emerging from correlation. Some recent studies show that information can also be extracted from the amplitude of such correlations. In this paper, we develop a theory to understand these non-intuitive results. A statistical approach is used to get an expression of the one-bit noise correlation. This expression involves the standard deviations of coherent and incoherent noise. These two kinds of noise are precisely defined, and explicit expressions of their standard deviations are given in the case of a uniform distribution of noise sources generating surface waves on a layered half-space. In this case, we show that the one-bit noise correlation has the same phase and relative amplitude as the raw noise correlation. This is true in both elastic and anelastic media. Numerical simulations are performed to support our theory.

Consistent transmitting boundary with continued-fraction absorbing boundary conditions for analysis of soil–structure interaction in a layered half-space

A continued-fraction absorbing boundary condition (CFABC) is combined with a consistent transmitting boundary and applied to an analysis of soil–structure interaction in a layered half-space. In order to be a perfect absorber for in-plane waves with an arbitrary horizontal wavenumber in a layered half-space, it is proposed that the CFABC be used in the form of a 2-layer. A method for determination of parameters of the 2-layers was proposed for evanescent waves as well as propagating waves. Combined with consistent transmitting boundaries, the 2-layers of CFABC are applied to problems of dynamics of rigid strip and circular foundations on a layered half-space. The results demonstrate that the proposed 2-layers of the CFABC can represent a layered half-space accurately in the entire frequency range and absorb both evanescent and propagating P and S waves effectively.

A model for seismicity rates observed during the 1982–1984 unrest at Campi Flegrei caldera (Italy)

We consider the space–time distribution of seismicity during the 1982–1984 unrest at Campi Flegrei caldera (Italy) where a correlation between seismicity and rate of ground uplift was suggested. In order to investigate this effect, we present a model based on stress transfer from the deformation source responsible for the unrest to potential faults. We compute static stress changes caused by an inflating source in a layered half-space. Stress changes are evaluated on optimally oriented planes for shear failure, assuming a regional stress with horizontal extensional axis trending NNE-SSW. The inflating source is modeled as inferred by previous studies from inversion of geodetic data with the same crustal model here assumed. The magnitude of the regional stress is constrained by imposing an initial condition of “close to failure” to potential faults. The resulting spatial distribution of stress changes is in agreement with observations. We assume that the temporal evolution of ground displacement, observed by a tide-gauge at Pozzuoli, was due mainly to time dependent processes occurring at the inflating source. We approximate this time dependence in piecewise-linear way and we attribute it to each component of average stress-change in the region interested by the observed seismicity. Then we evaluate the effect of a time dependent stressing rate on seismicity, by following the approach indicated by Dieterich (1994) on the basis of the rate- and state-dependent rheology of faults. The seismicity rate history resulting from our model is in general agreement with data during the period 1982–1984 for reasonable values of unconstrained model-parameters, the initial value of the direct effect of friction and the reference shear stressing rate. In particular, this application shows that a decreasing stressing-rate is effective in damping the seismicity rate.

DETERMINATION OF THE FRESNEL REFLECTION COEFFICIENT OF A HALF-SPACE FOR MEDIUM ESTIMATION PURPOSES

A novel procedure for estimating the Fresnel re∞ection coe-cient of a transversally homogeneous half-space medium is introduced. GPR multistatic measurements are exploited as data whereas the Fresnel coe-cient (as a function of the incidence angle) is retrieved by inverting a linear integral equation. Having estimated the re∞ection coe-cient it can be exploited to determine the medium electromagnetic parameters. Numerical examples are used to show the procedure efiectiveness for difierent types of homogeneous half-space media within a two-dimensional scalar geometry. The case of a layered half-space is also discussed.

G010014 表面および界面の力学的特性を考慮した薄膜を有する半無限異方性弾性体の接触解析([G01001]計算力学部門一般セッション(1):固体力学の基礎的な数値解析)

In this paper, contact analysis for anisotropic elastic layered half-space is performed using surface Green function considering surface and interface property. The discrete convolution and fast Fourier transform (DC-FFT) method and conjugate gradient (CG) method were used for conducting the contact analysis. The contact analysis was conducted for investigating the effect of thickness of thin films and material of substrate on the penetration depth for the rigid spherical indenter.

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method (IBEM). A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

Characterization of Films with Thickness Less than 10 nm by Sensitivity-Enhanced Atomic Force Acoustic Microscopy.

We present a method for characterizing ultrathin films using sensitivity-enhanced atomic force acoustic microscopy, where a concentrated-mass cantilever having a flat tip was used as a sensitive oscillator. Evaluation was aimed at 6-nm-thick and 10-nm-thick diamond-like carbon (DLC) films deposited, using different methods, on a hard disk for the effective Young's modulus defined as E/(1 - ν2), where E is the Young's modulus, and ν is the Poisson's ratio. The resonant frequency of the cantilever was affected not only by the film's elasticity but also by the substrate even at an indentation depth of about 0.6 nm. The substrate effect was removed by employing a theoretical formula on the indentation of a layered half-space, together with a hard disk without DLC coating. The moduli of the 6-nm-thick and 10-nm-thick DLC films were 392 and 345 GPa, respectively. The error analysis showed the standard deviation less than 5% in the moduli.

Application of a second-order paraxial boundary condition to problems of dynamics of circular foundations on a porous layered half-space

A half-space finite element and a consistent transmitting boundary in a cylindrical coordinate system are developed for analysis of rigid circular (or cylindrical) foundations in a water-saturated porous layered half-space. By means of second-order paraxial approximations of the exact dynamic stiffness for a half-space in plane-strain and antiplane-shear conditions, the corresponding approximation for general three-dimensional wave motion in a Cartesian coordinate system is obtained and transformed in terms of cylindrical coordinates. Using the paraxial approximations, the half-space finite element and consistent transmitting boundary are formulated in a cylindrical coordinate system. The development is verified by comparison of dynamic compliances of rigid circular foundations with available published results. Examination of the advantage of the paraxial condition vis-á-vis the fixed condition shows that the former achieves substantial gain in computational effort. The developed half-space finite element and transmitting boundary can be employed for accurate and effective analysis of foundation dynamics and soil–structure interaction in a porous layered half-space.

Poroelasticity: Finite element modelling of anomalous tilt and pore pressure caused by pumping in a sedimentary half space with fault

Extraction of groundwater or hydrocarbons causes pore pressure gradients and soil deformation due to poroelastic coupling. Recent studies show that high-resolution engineering tiltmeters installed at shallow depth between 2 and 10 m resolve this deformation. Models using poroelasticity can describe the relationship between fluid extraction, pore pressure gradients and induced tilt for homogeneous and layered sedimentary half spaces. Faults intersecting a stack of sedimentary layers, for example in the Lower-Rhine-Embayment, are of fundamental impact to the groundwater flow system of an area. However, the fault’s hydromechanical effect on pump induced tilt and the pore pressure regime is still poorly investigated. We chose a comparatively simple approach to quantify anomalous pump induced tilt and pore pressure observed near a fault and close to the surface in a sedimentary subsoil. A PC-based Finite Element software is used to model poroelastic deformation, i.e. modelling vertical tilt and excess pore pressure in response to fluid extraction through a singular well. We compare numerical solutions for models with and without faults and show that a fault can modify symmetry and amplitude of the deformation field by more than a magnitude. We conclude that tilt and pore pressure measurements also at shallow depth can thus be biased by large subsurface structures like faults. Vice versa, these measurements may provide means to quantify hydromechanical effects caused by subsurface structures. However, depending on the geological setting, i.e. if pathways are established by a fault, the anomaly caused by the fault can also be small and hard to detect. Therefore, faults and geological structures like material boundaries have to be considered in poroelastic models carefully. For tilt surveys with a limited number of instruments in geologically well constrained areas these models allow the preselection of potential positions for tiltmeters where prominent field anomalies are expected.

Efficient Reformulation of the Thomson-Haskell Method for Computation of Surface Waves in Layered Half-Space

This paper presents an efficient and effective scheme for reforming the original Thomson–Haskell transfer matrix method for the stable modeling of surface waves in a layered half-space. The proposed scheme splits the layer propagator matrix and then determines the interface stiffness instead of directly building the propagator matrix as the original Thomson–Haskell method does. For the Love wave, an explicit solution for the interface stiffness is obtained. The reformulation of the Thomson–Haskell method keeps the simplicity of the original method but naturally excludes its exponential growth terms. Hence, the modified Thomson–Haskell method is computationally stable for high frequency and increasing layer thickness. Moreover, both analytical and numerical results indicate the modified Thomson–Haskell method is the most efficient of all the complex arithmetic algorithms available, including the original Thomson–Haskell method and generated reflection and transmission matrix method. The computational speed of the modified Thomson–Haskell method rises by more than 15% for the Love and Rayleigh waves. Furthermore, a discussion of the effect of frequency and layer thickness on the phase velocity of Gutenberg Earth model indicates the modified Thomson–Haskell method is a powerful candidate for efficiently and effectively simulating surface waves in a layered half-space.

Implementation of a second-order paraxial boundary condition for a water-saturated layered half-space in plane strain

A half-space finite element and a transmitting boundary are developed for a water-saturated layered half-space using a paraxial boundary condition. The exact dynamic stiffness of a half-space in plane strain is derived and a second-order paraxial approximation of the stiffness is obtained. A half-space finite element and a transmitting boundary are then formulated. The development is verified by comparison of the dynamic stiffness of impermeable and permeable rigid strip foundations with other published results. The advantage of using the paraxial boundary condition in comparison with the rigid boundary condition is examined. It is shown that the paraxial boundary condition offers significant gain and the resulting half-space finite element and transmitting boundary can represent the effects of a water-saturated layered half-space with good accuracy and efficiency. In addition, the numerical method described herein maintains the strengths and advantages of the finite element method and can be easily applied to demanding problems of soil–structure interaction in a water-saturated layered half-space. Copyright © 2010 John Wiley & Sons, Ltd.

Influence of sliding interfaces on the response of a layered viscoelastic medium under a moving load

This article presents a method to compute the response of a viscoelastic layered half-space to a moving load when interlayer slip is considered. The Navier equations of equilibrium are solved for each layer in the frequency domain. The solution in the spatial coordinate system is subsequently obtained by means of Fast Fourier Transform and quadrature rules applied to integrable singularities. Following the global solution technique, the developed method compiles all the interface and the boundary conditions within a global matrix and it solves a unique linear system per couple of wave numbers. This method proves to be effective and is validated in an elastic case by comparison with the ALIZE-LCPC software that implements the Burmister axisymmetric solution. The influence of the interface sliding condition on the response of a layered viscoelastic medium is studied through an application to pavement structures. In this application, the effect of the load speed on vertical and horizontal profiles of the longitudinal strain and the normal stress is analyzed. It is shown, inter alia, that the maximum extension in the medium is not systematically observed at the location of an interface and that, as expected, low speeds and interlayer slip are more damaging to the structure when either a strain or a stress criterion is considered.

A 2.5D coupled FE-BE model for the prediction of railway induced vibrations

Ground vibrations induced by railway traffic at grade and in tunnels are often studied by means of two-and-half dimensional (2.5D) models that are based on a Fourier transform of the coordinate in the longitudinal direction of the track. In this paper, the need for 2.5D coupled finite element-boundary element models is demonstrated in two cases where the prediction of railway induced vibrations is considered. A recently proposed novel 2.5D methodology is used where the finite element method is combined with a boundary element method, based on a regularized boundary integral equation. In the formulation of the boundary integral equation, Green's functions of a layered elastic halfspace are used, so that no discretization of the free surface or the layer interfaces is required. In the first case, two alternative models for a ballasted track on an embankment are compared. In the first model, the ballast and the embankment are modelled as a continuum using 2.5D solid elements, whereas a simplified beam representation is adopted in the second model. The free field vibrations predicted by both models are compared to those measured during a passage of the TGVA at a site in Reugny (France). A very large difference is found for the free field response of both models that is due to the fact that the deformation of the cross section of the embankment is disregarded in the simplified representation. In the second case, the track and free field response due to a harmonic load in a tunnel embedded in a layered halfspace are considered. A simplified methodology based on the use of the full space Green's function in the tunnel–soil interaction problem is investigated. It is shown that the rigorous finite element-boundary element method is required when the distance between the tunnel and the free surface and the layer interfaces of the halfspace is small compared to the wavelength in the soil.

Modeling elasto-plastic indentation on layered materials using the equivalent inclusion method

This paper develops a fast semi-analytical model for solving the three-dimensional elasto-plastic contact problems involving layered materials using the Equivalent Inclusion Method (EIM). The analytical elastic solutions of a half-space subjected to a unit surface pressure and a unit subsurface eigenstrain are employed in this model; the topmost layer is simulated by an equivalent inclusion with fictitious eigenstrain. Accumulative plastic deformation is determined by a procedure involving an iterative plasticity loop and an incremental loading process. Algorithms of the fast Fourier transform (FFT) and the Conjugate Gradient Method (CGM) are utilized to improve the computation efficiency. An analytical elastic solution of layered body contact ( O’Sullivan and King, 1988) and an indentation experiment result involving a layered substrate ( Michler et al., 1999) are used to examine the accuracy of this model. Comparisons between numerical results from the present model and a commercial FEM software (Abaqus) are also presented. Case studies of a rigid ball loaded against a layered elasto-plastic half-space are conducted to explore the effects of the modulus, yield strength, and thickness of the coating on the hardness, stiffness, and plastic deformation of the composite body.

Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half Space

Abstract An elastic contact model for three-dimensional layered or coated materials under coupled normal and tangential loads, with consideration of partial slip effects, has been developed in this paper. The response functions for calculating the displacements and stresses were determined in the frequency domain by using the Papkovich–Neuber potentials. The partial slip contact problem was solved by a numerical procedure based on the conjugate Gradient method and fast Fourier transform technique. The contact pressure, surface shear tractions, stick ratios, rigid body displacements, and subsurface stresses are analyzed under different conditions with variations in the material properties and coating thickness. Results show that stiffer coatings tend to decrease the stick ratios and the rigid ball tangential displacements in comparison to those with compliant coatings under the same contact conditions. For stiffer coatings, the values of the von Mises stress and compressive surface stress increase and the positions of maximum von Mises stress move up to the surface; meanwhile, the distributions of the compressive stress become asymmetric due to the action of the tangential load.

2.5D scattering of incident plane SH waves by a canyon in layered half-space

This paper presents 2.5D scattering of incident plane SH waves by a canyon in layered half-space by the indirect boundary element method (IBEM). The free field response is carried out to give the displacements and stresses on the line which forms boundary of the canyon. The fictitious uniform moving loads are applied to the same line to calculate the Green’s functions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The displacements due to the free field and from the fictitious uniform moving loads have to be added to obtain the whole motion. The numerical results are carried out for the cases of a canyon in homogenous and in one layer over bedrock. The results show that the 2.5D wave scattering problem is essentially different from the 2D case, and there exist distinct differences between the wave amplification by a canyon in layered half-space and that in homogeneous half-space. The reasons for the distinct difference are explored, and the effects of the thickness and stiffness of the layer on the amplification are discussed.

A 2.5D coupled FE–BE methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace

This paper presents a general 2.5D coupled finite element–boundary element methodology for the computation of the dynamic interaction between a layered soil and structures with a longitudinally invariant geometry, such as railway tracks, roads, tunnels, dams, and pipelines. The classical 2.5D finite element method is combined with a novel 2.5D boundary element method. A regularized 2.5D boundary integral equation is derived that avoids the evaluation of singular traction integrals. The 2.5D Green’s functions of a layered halfspace, computed with the direct stiffness method, are used in a boundary element method formulation. This avoids meshing of the free surface and the layer interfaces with boundary elements and effectively reduces the computational efforts and storage requirements. The proposed technique is applied to four examples: a road on the surface of a halfspace, a tunnel embedded in a layered halfspace, a dike on a halfspace and a vibration isolating screen in the soil.