Dynamic analysis of pile foundations in time-domain using Lanczos vectors

An analytical procedure to obtain the response of pile-group in time domain is described. The procedure makes use of large domain for discretization along with coordinate transformation using Lanczos vectors. The responses are obtained in time domain using an adaptive direct integration method. The scheme has the ability of error estimation due to temporal discretization and coordinate transformation. The procedure has been applied to three dimensional pile-group foundations. The compliance functions of the foundations have been obtained for all modes of vibration. The computational scheme has also been used to analyze the response of a machine foundation transmitting non-harmonic but periodic forces. The present method has all the advantages of time domain scheme which is local in space and time with small computational effort.     

The influence of tunnel excavation on the hydraulic head

In this paper an alternative method is proposed for computing the effect of tunnelling on the piezometric head field during construction. The seepage flow equations, usually formulated in a fixed co-ordinate system are here reformulated within a frame of reference that advances together with the tunnel heading. The governing equations contain the advance rate as an additional parameter, and are solved by the finite-element method. The quasi-steady state (i.e. the steady state in the moving frame of reference) can then be computed in a single step. Selection of a marching scheme in the time domain is, therefore, rendered unnecessary. Thanks to the economy of the proposed method, it has been possible to carry out comprehensive parametric studies, the results of which are presented in a dimensionless form. The applicability of the computational method to poroelastic problems is also addressed.     

Analysis of stone-column reinforced foundations

A numerical model is proposed to analyse elastic as well as elastoplastic behaviour of stone-column reinforced foundations. The stone-columns are assumed to be dispersed within the in situ soil and a homogenization technique is invoked to establish equivalent material properties for in situ soil and stone-column composite. The difficulties encountered in carrying out elastoplastic analyses of composite materials are overcome by adopting a separate yield function for each of the constituent materials and a sub-iteration procedure within an implicit backward Euler stress integration scheme. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenization procedure are satisfied for both elastic as well as elastoplastic stress states. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model circular footings resting on stone-column reinforced foundations. This prediction indicates good agreement with experimental observation. Finally, a new scheme in which the length of stone-column is variable is proposed and its behaviour is examined through a numerical example. © 1998 John Wiley & Sons, Ltd.     

Seepage flow problems by variational inequalities: Theory and approximation

The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h^1.25-δ), 0 < δ < 0.25, respectively, if the permeability is constant.     

Isogeometric analysis for unsaturated flow problems

Unsaturated flow problems in porous media often described by Richards’ equation are of great importance in many engineering applications. In this contribution, we propose a new numerical flow approach based on isogeometric analysis (IGA) for modeling the unsaturated flow problems. The non-uniform rational B-spline (NURBS) basis is utilized for spatial discretization whereas the stable implicit backward Euler method for time discretization. The nonlinear Richards’ equation is iteratively solved with the aid of the Newton–Raphson scheme. Owing to some desirable features of an efficient numerical flow approach, major advantages of the present formulation involve: (a) numerical oscillation at the wetting front can be avoided or facilitated, simply by using either an h-refinement or a lumped mass matrix technique; (b) higher-order exactness can be obtained due to the nature of the IGA features; (c) the approach is straightforward to implement and it does not need any transformation, e.g., Kirchhoff transformation or filter algorithm; and (d) in contrast to the Picard iteration scheme, which forms linear convergences, the proposed approach can however yield quadratic convergences by using the Newton–Raphson method for solving resultant nonlinear equations. Numerical model validation is analyzed by solving a three-dimensional unsaturated flow problem in soil, and its derived results are verified against analytical solutions. Numerical applications are then studied by considering three extensive examples with simple and complex configurations to further show the accuracy and applicability of the present IGA.     

Improving resolution of gravity data with wavelet analysis and spectral method

Gravity data are the results of gravity force field interaction from all the underground sources. The objects of detection are always submerged in the background field, and thus one of the crucial problems for gravity data interpretation is how to improve the resolution of observed information. The wavelet transform operator has recently been introduced into the domain fields both as a filter and as a powerful source analysis tool. This paper studied the effects of improving resolution of gravity data with wavelet analysis and spectral method, and revealed the geometric characteristics of density heterogeneities described by simple shaped sources. First, the basic theory of the multiscale wavelet analysis and its lifting scheme and spectral method were introduced. With the experimental study on forward simulation of anomalies given by the superposition of six objects and measured data in Songliao plain, Northeast China, the shape, size and depth of the buried objects were estimated in the study. Also, the results were compared with those obtained by conventional techniques, which demonstrated that this method greatly improves the resolution of gravity anomalies. Translated from Progress in Geophysics, 2007, 22(1): 112–120 [译自: 地球物理学进展]     

Optimal estimation of in-situ ground stresses from displacement measurements

This paper presents a study on the optimal estimation of initial in-situ stresses, in which the in-situ stresses may be constant or linearly changing along a co-ordinate axis, from a set of relative measurements between adjacent measuring points utilized for monitoring the stability of tunnels. Displacements occurring before installation of measuring devices can be taken into account. The approach may be used for a variety of models used to simulate the ground media through which the tunnels are being excavated and has the advantage of being easy to implement on the computer and having both good precision and calculation stability. Finally, an analysis is carried out on the stability of the algorithm and computational time for different numerical examples.     

Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method

A finite element algorithm for frictionless contact problems in a two‐phase saturated porous medium, considering finite deformation and inertia effects, has been formulated and implemented in a finite element programme. The mechanical behaviour of the saturated porous medium is predicted using mixture theory, which models the dynamic advection of fluids through a fully saturated porous solid matrix. The resulting mixed formulation predicts all field variables including the solid displacement, pore fluid pressure and Darcy velocity of the pore fluid. The contact constraints arising from the requirement for continuity of the contact traction, as well as the fluid flow across the contact interface, are enforced using a penalty approach that is regularised with an augmented Lagrangian method. The contact formulation is based on a mortar segment‐to‐segment scheme that allows the interpolation functions of the contact elements to be of order N. The main thrust of this paper is therefore how to deal with contact interfaces in problems that involve both dynamics and consolidation and possibly large deformations of porous media. The numerical algorithm is first verified using several illustrative examples. This algorithm is then employed to solve a pipe‐seabed interaction problem, involving large deformations and dynamic effects, and the results of the analysis are also compared with those obtained using a node‐to‐segment contact algorithm. The results of this study indicate that the proposed method is able to solve the highly nonlinear problem of dynamic soil–structure interaction when coupled with pore water pressures and Darcy velocity. Copyright © 2015 John Wiley & Sons, Ltd.     

Sampling design optimization for spatial functions

A new procedure is presented for minimizing the sampling requirements necessary to estimate a mappable spatial function at a specified level of accuracy. The technique is based on universal kriging, an estimation method within the theory of regionalized variables. Neither actual implementation of the sampling nor universal kriging estimations are necessary to make an optimal design. The average standard errorand maximum standard error of estimationover the sampling domain are used as global indices of sampling efficiency. The procedure optimally selects those parameters controlling the magnitude of the indices, including the density and spatial pattern of the sample elements and the number of nearest sample elements used in the estimation. As an illustration, the network of observation wells used to monitor the water table in the Equus Beds of Kansas is analyzed and an improved sampling pattern suggested. This example demonstrates the practical utility of the procedure, which can be applied equally well to other spatial sampling problems, as the procedure is not limited by the nature of the spatial function.     

Coupled boundary element/finite element analysis in geomechanics including body forces

A coupling scheme for boundary and finite elements using joint elements is proposed which includes the consideration of body forces. In this scheme the boundary and joint elements are formulated in a similar way as finite elements (i.e., the equivalent FE procedure). These joint elements are efficiently used to combine different BE regions. For the evaluation of a body forces, two methods are compared on computational efficiency and it is found that the method using Galerkin tensor is more efficient than the method dividing the problem domain into several internal cells. Two main geotechnical problems considering self weight are numerically examined using this coupling procedure.     

Steady‐state solution for cylindrical penetrometers

This paper suggests a new method for obtaining steady‐state solutions for ‘full‐flow’ penetrometers. The method is based on the numerical solution of the small strain plastic‐flow problem (i.e. rigid plastic material) with an inhomogeneous strength field, which is determined by converting changes of material properties over time in a stationary frame of reference into spatial distribution of strength in a moving frame of reference. Rather than building streamlines from back integration of soil element distortion, as previous methods have suggested, the method treats the domain as continuous with the associated field equations. The method employs an upstream weighting technique for the determination of information flow within the domain. The execution order for the calculation is based on topological ordering. This results in the calculation having a complexity of O(N), as compared with O(N^1.5) for the strain path or streamline methods (N is the number of discretized points), which significantly reduces the calculation time. The formulation is presented for the cylindrical (T‐bar) penetrometer, and includes aspects of soil strength degradation, strain rate effects, strength anisotropy, and interface strength law. Comparison to previously published values, based on large displacement finite element simulations with remeshing, showed good agreement, indicating on the correctness of the suggested approach. Investigation into the soil rigid‐body rotation and the remolding effect on anisotropy characteristics showed an interesting behavior, where the decrease of strength anisotropy due to remolding has a greater influence when the soil strength is higher in the vertical direction. Copyright © 2009 John Wiley & Sons, Ltd.     

Boundary element approach to the dynamic stiffness functions of circular foundations

A boundary element approach for time harmonic axisymmetric problems using the complete space point load fundamental solution is presented. The fundamental solution is integrated numerically along the azimuthal co-ordinate of each axisymmetric element. To increase the accuracy of the numerical integration a simple co-ordinate transformation is proposed. The approach is applied to the computation of the dynamic stiffness functions of rigid circular foundations on layered viscoelastic soils. Three different sites are considered: a uniform half-space, a soil layer on a half-space, and a soil consisting of four horizontal layers and a compliant half-space. The numerical results obtained by the proposed approach for surface circular foundations are very close to corresponding published results obtained by different procedures.     

Particle shape: a review and new methods of characterization and classification

Shape is a fundamental property of all objects, including sedimentary particles, but it remains one of the most difficult to characterize and quantify for all but the simplest of shapes. Despite a large literature on the subject, there remains widespread confusion regarding the meaning and relative value of different measures of particle shape. This paper re‐examines the basic concepts of particle shape and suggests a number of new and modified methods which are widely applicable to a range of sedimentological problems; it is shown that the most important aspects of particle form are represented by the I/L ratio (elongation ratio) and S/I ratio (flatness ratio). A combination of these two ratios can be used to classify particles in terms of 25 form classes. A method of obtaining a quantitative measure of particle roundness using simple image analysis software is described, and a new visual roundness comparator is presented. It is recommended that measurements of both roundness and circularity (a proxy measure of sphericity) are made on grain images in three orthogonal orientations and average values calculated for each particle. A further shape property, irregularity, is defined and a classification scheme proposed for use in describing and comparing irregular or branching sedimentary particles such as chert and coral.     

Efficient solution for matrix-fracture flow with multiple interacting continua

An efficient numerical procedure for implementing the multiple interacting continua (MINC) method for fractured porous media in a general-purpose multiphase simulator is presented. This procedure is substantially faster, requires less memory, is amenable to any n-component, multiphase non-isothermal package, and is readily adaptable for parallel processing computers. The present procedure results in a reduction of the computing time by a factor of the order of NMINC³ as compared to the band algorithm, where NMINC is the number of nested continua into which each matrix block is further discretized. The memory requirement approaches a reduction factor of the order of NMINC² for larger problems compared to the band algorithm. The code for the algorithm was structured so as to set up the time consuming, but independent, computations for each matrix block in a subroutine that was parallelized and tested using a Sequent machine accessed under a UNIX environment. For NMINC=10, total computing time was reduced by 33 per cent for the use of two versus one processor, with the savings increasing for increasing NMINC. The proposed procedure can be implemented with the same ease and efficiency in conjunction with any iterative or direct method, and the grid-blocks can be ordered in any non-standard manner such as in D-4, D-2, and others. Copyright © 1999 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

An unconditionally stable explicit and precise multiple timescale finite element modeling scheme for the fully coupled hydro-mechanical analysis of saturated poroelastic media

An unconditionally stable, fully explicit and highly precise multiple timescale finite element modeling scheme is described for a fully coupled hydro-mechanical (FCHM) analysis of saturated poroelastic media. The finite element method (FEM) is used for the discretization of the FCHM differential equation in the space domain. Direct integration is performed based on the precise time step integration method (PTSIM) for the time derivatives. Two configurations for the proposed scheme are constructed (abbreviated as PTSIM-f1 and -f2, respectively). The stability and convergence of the PTSIM-f1 and -f2 are proved using a matrix-based spectral analysis in the time domain. It is demonstrated that the explicit scheme proposed in this paper is unconditionally stable and independent of the time-step size. The algorithmic error estimation results indicate that the numerical modeling performed using PTSIM-f1 and -f2 in the time domain match the computer precision. Theoretically, the algorithmic error is caused by only the mesh discretization. Therefore, the proposed modeling scheme is a semi-analytical scheme. The applicability and accuracy of the proposed scheme are examined using sample calculations. By comparing with the analytical solutions, it is indicated that the modeling results have significant advantages over the standard FEM in terms of precision and computational efficiency for large timescales.     

Identification of karst features with spectral analysis on the seismic reflection data

The use of high-resolution seismic tools to investigate karst terrain has had limited success due to the ambiguous seismic events caused by lateral heterogeneities of the sedimentary cover, as well as the superimposition of surface waves. To address these problems, a spectral analysis scheme is proposed on the seismic reflection data to characterize karst features in this paper. First, the S-transform is applied to suppress the ground roll. As a type of time–frequency transform, the S-transform provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. Application of a filter based on the S-transform attenuates ground roll in a time–frequency domain. Then, the continuous wavelet transform is employed for the time–frequency mapping of potential karst features, which are featured as frequency differentiation anomalies. Synthetic model and real-data example validate the efficiency of the spectral analysis scheme for the detection of karst features.     

Adaptive isogeometric finite element analysis of steady‐state groundwater flow

Numerical challenges occur in the simulation of groundwater flow problems because of complex boundary conditions, varying material properties, presence of sources or sinks in the flow domain, or a combination of these. In this paper, we apply adaptive isogeometric finite element analysis using locally refined (LR) B‐splines to address these types of problems. The fundamentals behind isogeometric analysis and LR B‐splines are briefly presented. Galerkin's method is applied to the standard weak formulation of the governing equation to derive the linear system of equations. A posteriori error estimates are calculated to identify which B‐splines should be locally refined. The error estimates are calculated based on recovery of the L₂‐projected solution. The adaptive analysis method is first illustrated by performing simulation of benchmark problems with analytical solutions. Numerical applications to two‐dimensional groundwater flow problems are then presented. The problems studied are flow around an impervious corner, flow around a cutoff wall, and flow in a heterogeneous medium. The convergence rates obtained with adaptive analysis using local refinement were, in general, observed to be of optimal order in contrast to simulations with uniform refinement. Copyright © 2015 John Wiley & Sons, Ltd.