Viscoelastic Soil Research Articles

A probabilistic analysis of the dynamic response of monopile foundations: Soil variability and its consequences

The reliability of offshore wind turbines is highly influenced by the uncertainties related to the subsoil conditions. Traditionally, the evaluation of the dynamic structural behaviour is based on a computational model with deterministic soil properties. Using this approach, however, provides limited insight into the variation of the estimate of the inherent modal properties and loads. In this paper, a comprehensive study is performed on the dynamic behaviour of an offshore wind turbine installed on a monopile foundation. Based on consistent lumped-parameter models calibrated to semi-analytical impedance functions of a monopile embedded in a stochastic linear viscoelastic soil layer, fully coupled aero-hydro-elastic simulations are conducted in the nonlinear multi-body code Hawc2. The probabilistic analysis accounts for the uncertainty of soil properties (e.g. damping and stiffness) and relies on a Monte Carlo method facilitating the derivation of the probability densities of the modal properties and the fatigue loading. The main conclusion of the presented work is that the dynamic structural behaviour of the wind turbine and its support structure is strongly affected by the stochastic soil properties. Lognormal and Gumbel distributed modal damping and accumulated side–side fatigue damage equivalent moments with a coefficient of variation of 30% and 8%, respectively, are observed.

Dynamic response sensitivity of an offshore wind turbine for varying subsoil conditions

In this paper, a comprehensive study is performed on the dynamic response of an offshore wind turbine installed on a monopile. The aim is to evaluate to what extent a change of the soil properties affects the fatigue loads for parked conditions. Based on consistent lumped-parameter models calibrated to semi-analytical impedance functions of a monopile embedded in a linear viscoelastic soil layer, fully coupled aero-hydro-elastic simulations are conducted in the nonlinear multi-body code Hawc2. Correlation of wind speeds and waves is derived on basis of wind–wave scatter diagrams from the North Sea. Changes of the soil stiffness, the soil damping and the presence of sediment transportation at seabed are shown to be critical for the fatigue damage equivalent moment at mudline that may change with more than 30% for parked wind turbine conditions.

Analytical solution of transient dynamic response of spherical cavity in viscoelastic and saturated soils

Based on the Biot's theory of wave propagation in porous media, this paper studies the transient dynamic response of spherical cavity in viscoelastic and saturated soils. The analytical solution in transformed domain is obtained by the method of Laplace transformation, and numerical results are solved through inversed Laplace transformation. The displacements, stresses and pore water pressure developed in the viscoelastic soils are analyzed and compared with those from elastic model, and some new observations are discussed and interpreted from the perspective of material's properties. The findings resulting from the current study are helpful to analyzing the transient dynamic responses of underground structures in the engineering practice.

Vertical impedance of an end‐bearing pile in viscoelastic soil

SummaryThis paper presents a new method to derive the analytical solution for the vertical impedance of an end‐bearing pile in viscoelastic soil. The soil is assumed as a homogeneous and isotropic layer, and the pile is considered as a one‐dimensional Euler rod. Considering both the vertical and radial displacements of soil and soil–pile coupled vibration, the governing equations of the soil and pile are established. The volumetric strain of soil is obtained by transformation on the equations of soil and variable separation method. Then the vertical and radial displacements of soil are obtained accordingly. The displacement response and impedance function of pile are derived based on the continuity assumption of the displacement and stress between the pile and soil. The solution is verified by being compared with an existing solution obtained by introducing potential functions. Furthermore, a comparison with two other simplified solutions is conducted. Numerical examples are presented to analyze the vibration characteristics of the pile. Copyright © 2014 John Wiley & Sons, Ltd.

Evaluation of the impact of wheel tractor velocity and other factors on its oscillations

Vertical oscillations of tractor Т-150К during operation on sandy soddy-podzolic soil prepared to sowing were investigated. As result of calculations carried out using experimental data on viscoelastic soil properties, the influence of a tractor velocity on appearance of mutually independent oscillations of its axes was shown.

Dynamic interaction numerical models in the time domain based on the high performance scaled boundary finite element method

Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method (SBFEM) is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.

Strain effects on kinematic pile bending in layered soil

The kinematic bending of single piles in two-layer soil is explored to account for soil stiffness degradation and associated damping increase with increasing levels of shear strain, a fundamental aspect of soil behaviour which is not incorporated in current simplified seismic design methodologies for pile foundations.A parametric study of a vertical cylindrical pile embedded in a two-layer soil profile to vertically-propagating S waves, carried out in the time domain by a pertinent beam-on-dynamic-Winkler-foundation (BDWF) model, is reported. Strain effects are treated by means of the equivalent-linear procedure which provides soil stiffness and damping ratio as function of shear strain level. Whereas the approach still represents a crude representation of the actual soil behaviour to dynamic loading, it is more realistic than elementary solutions based on linear visco-elasticity adopted in earlier studies.The paper highlights that soil nonlinearity may have either a detrimental or a beneficial effect on kinematic pile bending depending on the circumstances. The predictive equations for kinematic pile bending in visco-elastic soil recently developed by the Authors are extended to encompass strain effects. Numerical examples and comparisons against experimental data from case histories and shaking table tests are presented.

Analysis of Transient Dynamic Behaviour of Spherical Cavity in Viscoelastic Soil Medium

Stress, displacement, and pore pressure of a partially sealed spherical cavity in viscoelastic soil condition have been obtained in Laplace transform domain. Solutions of axisymmetric surface load and fluid pressure are derived.

An efficient model for the dynamic behaviour of a single pile in viscoelastic soil

This paper presents a novel, three-dimensional, single-pile model, formulated in the wavenumber domain and adapted to account for boundary conditions using the superposition of loading cases. The pile is modelled as a column in axial vibration, and a Euler–Bernoulli beam in lateral vibration. The surrounding soil is treated as a viscoelastic continuum. The response of the pile is presented in terms of the stiffness and damping coefficients, and also the magnitude and phase of the pile-head frequency–response function. Comparison with existing models shows that excellent agreement is observed between this model, a boundary-element formulation, and an elastic-continuum-type formulation. This three-dimensional model has an accuracy equivalent to a 3D boundary-element model, and a runtime similar to a 2D plane-strain analytical model. Analysis of the response of the single pile illustrates a difference in axial and lateral vibration behaviour; the displacement along the pile is relatively invariant under axial loads, but in lateral vibration the pile exhibits localised deformations. This implies that a plane-strain assumption is valid for axial loadings and only at higher frequencies for lateral loadings.

Axial kinematic response of end‐bearing piles to P waves

SUMMARYKinematic pile–soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady‐state kinematic response of a cylindrical end‐bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed‐form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth‐independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free‐field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications. Copyright © 2013 John Wiley & Sons, Ltd.

Horizontal Vibration of a Large-Diameter Pipe Pile in Viscoelastic Soil

An analytical solution is developed in this paper to investigate the horizontal dynamic response of a large-diameter pipe pile in viscoelastic soil layer. Potential functions are applied to decouple the governing equations of the outer and inner soil. The analytical solutions of the outer and inner soil are obtained by the method of separation of variables. The horizontal dynamic response and complex dynamic stiffnesses of the pipe pile are then obtained based on the continuity conditions between the pile and the outer and inner soil. To verify the validity of the solution, the derived solution in this study is compared with an existing solution for a solid pile. Numerical examples are presented to analyze the vibration characteristics of the pile and illustrate the effects of major parameters on the stiffness and damping properties.

ANSYS implementation of damping solvent stepwise extraction method for nonlinear seismic analysis of large 3-D structures

A three-dimensional Damping Solvent Stepwise Extraction (DSSE) method is developed and implemented in the ANSYS finite element software for nonlinear seismic analysis of large-scale structures resting on an unbounded visco-elastic soil. Given a larger introduced artificial damping and arbitrary soil–structure interface geometry, the DSSE method provides a more efficient and accurate way to calculate the interaction forces of the unbounded soil within the framework of finite elements. In order to consider the effect of the artificial damping on structures, an Interface-Coupling element established with interface nodes in generalized structure substructure is developed through the element-based partition of the damped soil elements. The Newton–Raphson iteration method is employed along with the Newmark assumptions for the nonlinear analysis of generalized structures. The Newmark algorithm for damped bounded soil is also employed to assure the accuracy and convergence of the interaction system. User Programmable Features (UPFs) available in ANSYS is used to incorporate DSSE method. Also, a complete toolkit for general seismic soil–structure interaction (SSI) analysis is created using scripting-based ANSYS Parametric Design Language (APDL) and Graphical User Interface (GUI). The proposed technique is applicable to arbitrary sophisticated structure models, irregular soil domain, and provides the selection of the artificial damping without depending on the domain size of bounded soil. Two validation examples are presented to demonstrate the accuracy and efficiency of the proposed method. Moreover, an optimal case is suggested in view of engineering practice based on the comparison among the results from several sets of computational parameters including domain size, amount of artificial damping, and extraction steps. Nonlinear seismic analysis of high arch dam in south-west China is also presented to illustrate the analysis procedure, and demonstrate the capabilities of the method.

Dynamic Winkler modulus for axially loaded piles

The problem of axial dynamic pile–soil interaction and its analytical representation using the concept of a dynamic Winkler support are revisited. It is shown that depth- and frequency-dependent Winkler springs and dashpots, obtained by dividing the complex-valued side friction and the corresponding displacements along the pile, may faithfully describe the interaction effect, contrary to the common perception that the Winkler concept is always approximate. An axisymmetric wave solution, based on linear elastodynamic theory, is then derived for the harmonic steady-state response of finite and infinitely long piles in a homogeneous viscoelastic soil stratum, with the former type of pile resting on rigid rock. The pile is modelled as a continuum, without the restrictions associated with strength-of-materials approximations. Closed-form solutions are obtained for: (a) the displacement field in the soil and the pile; (b) the stiffness and damping (‘impedance') coefficients at the pile head; (c) the actual, depth-dependent, dynamic Winkler moduli; and (d) a set of fictitious, depth-independent Winkler moduli to match the dynamic response at the pile head. Results are presented in terms of dimensionless graphs, tables and simple equations that provide insight into the complex physics of the problem. The predictions of the model compare favourably with existing solutions, while new results and simple design-oriented formulae are presented.

Vertical Vibration Amplification of a Saturated Fractional Derivative Type Viscoelastic Soil Layer

Regarding the soil skeleton as viscoelastic medium with fractional derivative constitutive behavior, the influences of the soil skeleton viscosity and the soil layer thickness of saturated fractional derivative viscoelastic soil layer on the vertical vibration amplification coefficient is studied in the frequency domain by using the theory of Biot and one dimensional wave. The analytical expressions of the displacement, stress and pore water pressure of saturated soil layer are obtained by decoupling dynamic control equations and bounding the soil layer boundary conditions. The influences of physical and geometrical parameters of the saturated soil on vertical vibration amplification are investigated, and it is revealed that the vertical vibration amplification of the saturated classic elastic, fractional derivative type viscoelastic saturated soil and saturated classic viscoelastic soil are different when the soil layer thickness are changed; the material parameters of the fractional derivative model have great influences on the vertical vibration amplification coefficient.

Dynamic Interaction of Viscoelastic Soil and Fractional Derivative Type Lining with a Circular Tunnel

Coupled harmonic vibration of viscoelastic soil and fractional derivative type lining system with a deeply buried circular tunnel is investigated in the frequency domain. Based on theory of elastic and fractional derivative, steady state response of the viscoelastic soil and lining system is studied. Regarding the lining as a medium with fractional derivative constitutive behavior, and the analytical expressins of the displacement and stress of the soil and lining are respectively obtained by the continuity conditions on the inner boundary of lining and the interface between the soil and the lining. The order of fractional derivative model has a greater influence on system dynamic response, and it dependent on the material parameters of lining. With the frequency increasing, the resonance effects of system decrease.

Evaluation of Soil Dynamic Properties in Centrifuge Tests

This paper describes a method to compute the mobilized shear modulus, G, and damping ratio, D, using the nonlinear fit of experimental transfer functions obtained at different depths in centrifuge models, with the analytical expression of the amplification function for a viscoelastic soil layer on a rigid base. The corresponding shear strain, γ, is computed as a function of the particle velocity and shear wave velocity. The sources of potential error in the determination of G, D, and γ embedded in the proposed method are identified and discussed in comparison with two other methods that have been proposed in the literature, based either on the determination of the time lag of accelerations between two accelerometers or on the evaluation of the shear stress-strain cycles from acceleration time histories recorded at different depths in the model. The performance of the three methods is evaluated using the experimental data obtained from nine centrifuge tests on dry sand. The values of G obtained by the proposed method compare well with the results of laboratory and literature data; D values are more dispersed and slightly higher than the literature data. DOI: 10.1061/(ASCE)GT.1943-5606.0000659. © 2012 American Society of Civil Engineers. CE Database subject headings: Shear modulus; Damping; Soil dynamics; Sand (soil type); Centrifuge. Author keywords: Shear modulus; Damping ratio; Soil dynamics; Sand; Centrifuge.

Torsional Dynamic Impedance of Pipe Pile Embedded in Viscoelastic Soil Considering Soil-Pile Interaction

Abstract. Based on the three-dimensional wave theory,the coupled torsion vibration of the end bearing pile embedded in viscoelastic soil is researched by using the separation of variables technique. Calculation formulas of the torsional complex stiffness and admittance of pipe pile embedded in viscoelastic soil are obtained and the influence of shear modulus ratio, viscous damping coefficient ratio and the ratio of inner and outer radius on the torsional complex stiffness and admittance of pipe pile are discussed.Finally, the following conclusions are drawn.(1) Shear modulus ratio of soil inside and outside the pile, viscous damping coefficient ratio and the ratio of inner and outer radius have no effect on dynamic damping of pipe pile. The impact of shear modulus ratio of soil inside and outside the pile and the ratio of inner and outer radius on pipe pile in low frequency range is little. With the increase of frequency, the influence is increasing. Viscous damping coefficient ratio does not cause real stiffness of pipe pile. (2) Shear modulus ratio and the ratio of inner and outer radius have a significant influence on the admittance of pipe pile top.The greater shear modulus ratio and the ratio of inner and outer radius, the amplitude of the speed admittance curve of pipe pile top is larger .

The Parameters Research on Considering the Influence of Dynamic Torsion Impedance of the Radial Inhomogeneous Viscoelastic Soil

Based on the recursion method of shearing ragidity of soil layer, dynamic torsional impedance of the radial inhomogeneous viscoelastic soil is studied.Under the certain fundamental assumption,combined with displacement basic solution of the plane axial symmetry strain question,the displacement the continuous and boundary of the soil layers, the formula of dynamic torsional impedance of the pile-soil contact surface is deduced.Degenerated into homogeneous viscoelastic model,the model is further confirmed accurate.Finally, the conclusion is obtained:(1) The bigger is G2/G1,the larger the soil body actual stiffness is. The dynamic damping presents the trend of increase;(2)In the area of the radial disturbance soil,as ‘d’increases, the soil body actual stiffness is increasing. When G2/G1 is smaller than 1,the dynamic damping is reducing along with increases of ‘d’,when G2/G1 is bigger than 1,the dynamic damping is increasing along with increases of ‘d’.(3)Actual stiffness and dynamic damping assumes the linear variation along with increasing of material damping.

1D wave propagation in saturated viscous geomaterials: Improvement and validation of a fractional step Taylor–Galerkin finite element algorithm

This paper tackles the numerical simulation of 1D wave propagation in saturated viscous porous media, and especially in soil-like geomaterials. For this purpose, an improved fractional step Taylor–Galerkin algorithm is first formulated and then validated on the basis of a new analytical solution. The algorithm, based on a stress–velocity–pressure formulation of the hydro-mechanical problem, combines an explicit Taylor–Galerkin method with a fractional time-stepping, while an accurate Runge–Kutta-type integrator is introduced to treat the viscosity of the porous skeleton. The overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables, even when the so-called “undrained incompressible limit” is approached. The accuracy and stability of the method are verified with reference to a 1D benchmark problem, concerning the propagation of P waves along a saturated viscoelastic soil stratum. For this problem, a frequency-domain analytical solution is derived, assuming incompressible interstitial fluid and soil grains. The assumption of Maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem, while the same rheology of a more realistic elasto-viscoplastic non-linear behaviour is maintained. The performance of the fractional step Taylor–Galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic, impulsive and seismic input excitations. In particular, parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses, as well as in dealing with weakly viscous materials.

Simple superposition approach for dynamic analysis of piled embedded footings

SUMMARYThe effectiveness and accuracy of the superposition method in assessing the dynamic stiffness and damping coefficients (impedance functions) of embedded footings supported by vertical piles in homogeneous viscoelastic soil is addressed. To this end, the impedances of piled embedded footings are compared to those obtained by superposing the impedance functions of the corresponding pile groups and embedded footings treated separately, with the magnitude of the relative average differences being around 10–30%. The results are presented in a set of dimensionless graphs and simple expressions that can be used to estimate the dynamic stiffness and damping of piled embedded footings, provided that the impedance functions of the two individual components are known. This is precisely the reason why the superposition approach studied here is appealing, because such impedance functions for both embedded footings and pile groups are available for a wide range of cases. How to estimate the kinematic response functions of the system when those of the individual components are known is also discussed.To address the problem, parametric analyses performed using a 3D frequency‐domain elastodynamic BEM‐FEM formulation are presented for different pile–soil stiffness contrasts, embedment depths, pile‐to‐pile separations and excitation frequencies. Vertical, horizontal, rocking, and cross‐coupled horizontal‐rocking impedance functions, together with translational and rotational kinematic response functions, are discussed. The results suggest that the superposition concept, in conjunction with a correction strategy as that presented herein, can be employed in geotechnical design. For kinematic effects, the response functions of the embedded footing are found to provide reasonable estimates of the system's behaviour. Copyright © 2011 John Wiley & Sons, Ltd.