Cross-anisotropic Soil Research Articles

The mechanical response of energy pile groups in layered cross-anisotropic soils under vertical loadings

The mechanical response of energy pile groups in layered cross-anisotropic soils under vertical loadings is studied with the aid of the coupled finite element method - boundary element method (FEM-BEM). The single energy pile is simulated based on the finite element theory, which then is extended to energy pile groups. The global flexibility matrix for soils is obtained by considering the coupling effects of vertical and thermal loadings. The coupled FEM-BEM equation for the interaction between energy pile groups and soils is derived based on the displacement compatibility condition at the pile-soil interface. According to the displacement coordination condition and force balance in the rigid cap, the displacement of the cap and axial forces of pile groups can be solved. The presented theory is validated by comparing the calculated results with numerical simulations and field test results in existing literature. Finally, effects of the thermal loading, pile-soil stiffness ratio, pile spacing, cross-anisotropy of Young's modulus and the stratification are discussed.

A two-stage based model for partially-buried pile group response in cross-anisotropic saturated media adjacent to moving harmonic loads

The pile foundations are frequently affected by adjacent traffic loads except for general active loads. However, the dynamic responses of the pile groups under moving loads have been rarely reported before. In addition, the influence of material anisotropy is often neglected. In this paper, a three-dimensional (3D) analytical model for the dynamic analysis of partially buried pile groups in stratified saturated cross-anisotropic media under adjacent moving harmonic loadings is developed. Specifically, a 3D Bernoulli–Euler beam theory is adopted to simulate the monopile and then superimposed into the finite element (FE) formulation for the partially embedded pile groups. Subsequently, the basic solutions of layered saturated cross-anisotropic soils are derived by the analytical layer-element approach (ALEA). By combination with ALEA, the two-stage based boundary element (BE) equations for the pile-soil interface are obtained. Finally, by coupling the FE and BE formulations, the dynamical response equation of pile-soil is established. Based on the verification of the accuracy of the proposed methodology by comparisons with existing solutions and FE results from ABAQUS, the impacts of material anisotropy, pile buried length, loading velocity, and pile stiffness on the time-domain dynamic behavior of pile groups are analyzed. The results show that increasing the pile-buried ratio or pile stiffness reduces the magnitude of the dynamic response. Moreover, with the increase of material anisotropic parameters, the peak pile response decreases. And the peak dynamic response first increases and then reduces as the loading velocity increases.

Time-dependent transient response of piles partially embedded in layered viscoelastic saturated cross-anisotropic soils using a fractional-order Merchant model

A 3D analytical method is proposed for the lateral time-dependent response of monopiles partially embedded in stratified saturated viscoelastic cross-anisotropic soils under horizontal transient loads. Nevertheless, previous studies on ocean engineering have rarely considered the rheological properties of seabed materials. In this study, depending upon Biot's dynamical formulation, the linear elastic solution of the layered cross-anisotropic saturated soils due to lateral transient and vertical loads is solved using the analytical layer-element method (ALEM). The fractional-order Merchant model is adopted to describe the rheological deformation of the seabed, and the viscoelastic solution of the laminar cross-anisotropic saturated soils is derived by combining the elastic-viscoelastic transformation theory. Using the consolidation solution of the seabed as the kernel function, the pile-soil boundary problem is analyzed by the boundary element method (BEM) to obtain the BE equation of the viscoelastic saturated soils. The Timoshenko beam is employed to simulate the monopile, and based on the finite element method (FEM), the monopile is discretized into pile units to derive the FE matrix equation. Finally, the dynamic response formulation of the partially embedded offshore monopile is obtained by coupling the BE and FE equations through the coordination conditions of close contact between the Timoshenko beam and the seabed. The accuracy of the methodology is verified by comparing with the existing solutions and the numerical results from ABAQUS. And the effects of the transient load type, seabed viscosity, and pile properties on the horizontal response of partially embedded monopiles are explored.

Thermo-mechanical analysis of energy piled raft foundations in layered cross-anisotropic soils

The pile-soil-raft interaction and thermo-mechanical effects lead to broad attention in the analysis of the energy piled raft foundations. Natural soils are generally anisotropic and show obvious stratification. Influences of the cross-anisotropy and stratification on the performance of energy piled raft foundations are investigated in this paper. The raft and energy piles are modelled as a flexible plate and one-dimensional bars, respectively. Stiffness matrix equations of the raft and energy piles considering the thermal and mechanical loads are established based on the finite element method. The soils are modelled as the layered cross-anisotropic elastic media. The force-deformation relationships of nodes at the raft-soil and pile-soil interfaces are acquired based on the boundary element method. Then, displacement variables of the pile-soil interface onto the raft are condensed and the pile-soil-raft interaction is further simplified into the raft-soil interaction. The comparison with in-situ tests is made to verify the proposed method. Parametric analyses show that the top axial force of the center pile increases by approximately 5 % in the cooling condition and 12 % in the heating condition with the increase of the cross-anisotropic parameter m*, while it makes a negligible contribution to that of the corner and side pile.

An Anisotropic Failure Criterion for Cross-anisotropic Soils

Strength anisotropy is an important feature closely related to soil microstructure characteristics. A new anisotropic failure criterion, extended from the Ogawa failure criterion, was developed to describe the strength anisotropy of cross-anisotropic soils. Nonlinearization of the failure curves of the Ogawa failure criterion was introduced to account for the nonlinear failure of cross-anisotropic soils in the meridian plane. Meanwhile, an anisotropic strength function based on fabric tensor was theoretically proposed to modify the failure strength under different loading directions and depositional angles. The evolution of the new anisotropic failure criterion in the deviatoric plane was investigated through a series of parametric studies. All of the undetermined parameters in the new criterion can be readily determined in laboratory tests. Compared with experimental results on several types of soils, the new anisotropic failure criterion showed good performance in strength prediction in the deviatoric plane, as well as predicting the peak friction angle. Finally, a linear theoretical relationship on construction of the anisotropic strength function was also elucidated and discussed. The new anisotropic failure criterion proposed in this paper can effectively predict the strength anisotropy of cross-anisotropic soils under different loading directions and depositional angles.

Thermo-mechanical analysis of pipe energy piles in layered cross-isotropic soils

This paper aims to propose a method for the thermo-mechanical analysis of pipe energy piles in layered cross-anisotropic soils. Firstly, the pipe pile is modelled as a bar and the stiffness matrix equation considering thermo-mechanical loads is established based on the finite element method (FEM). The soils are considered to be layered cross-anisotropic and the boundary element method (BEM) is employed to obtain the deformation-force relationship of the soil-pile nodes. Afterwards, the coupled BEM-FEM equation is developed according to soil-pile deformation coordination conditions. The proposed method is verified with responses of pipe piles, solid energy piles and pipe energy piles. Parametric analyses show that the performance of the pipe energy pile induced by heating needs considering in the design of the pipe pile thickness, and the induced tensile stress should be taken into account in the design in hard soils. Besides, the influence of cross-anisotropy on the performance of the pile under cooling is larger than that under heating, and a softer surface soil layer yields a smaller axial force of the pipe energy pile for layered soils.

Combined load bearing capacity of rigid piles embedded in a cross-anisotropic clay deposit using 3D finite element lower bound

In this study, an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition. The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium, equilibrium of shear and normal stresses along discontinuities, boundary conditions, yield function, and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure. A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment (V–H–M) space. The results of this study are compared and validated against three different cases including an isotropic lateral loading, anisotropic end bearing capacity, and a pile embedded in an isotropic soil deposit under general loading condition. A parametric study is conducted to evaluate the impact of different influencing factors. It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads, whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

The performance analysis of energy piles in cross-anisotropic soils

Energy piles possess two important properties – structural load-bearing and ground heat exchangers, which is a cost-effective building energy-saving solution. Besides, natural soils generally exhibit anisotropic properties which impact the overall performance of energy piles. Therefore, the performance of energy piles in layered cross-anisotropic soils is investigated in this paper. Firstly, based on the basic equations of elasticity and heat transfer theory, the extended precise integration method (EPIM) is applied to acquire the thermo-elastic fundamental solution of layered cross-anisotropic soils, which will be utilized as the kernel function of the boundary element method (BEM). Then, the stiffness matrix equation of the energy pile considering the thermal strain and mechanical loads is derived with the aid of the finite element method (FEM). Afterwards, according to soil-pile deformation coordination conditions, the coupled BEM-FEM formulation to represent the soil-pile interaction is developed. Compared with in-situ tests and numerical simulations, the accuracy of the proposed method is verified. Finally, parametric analyses are conducted on the performance of energy piles subjected to the mechanical and temperature load simultaneously, and influences of pile-soil stiffness ratio, length-diameter ratio and soil cross-anisotropy on energy pile responses are discussed.

An Investigation on the Settlement of Shallow Foundations Resting on Cross-Anisotropic Soil Deposits

Natural soil deposition process results in formation of anisotropic planes with different properties along different directions, and hence, such natural deposits possess inherent anisotropy. On the other hand, an estimate of the elastic settlement of surface foundations placed on such anisotropic deposits is very important. In this research, the effect of anisotropy (in fact, cross-anisotropy) on the elastic settlement of shallow foundations resting on anisotropic granular soils, often sands, has been investigated. The most important properties in this work, in addition to the geometry of the footing, are the soil modulus of elasticity, Poisson’s ratio and the ratio of these moduli along anisotropic planes in a cross-anisotropic medium. The governing equations of deformation in such media are first presented. Then, the elastic settlement of shallow foundations resting on such media has been estimated using the finite difference method, and then, some influence factors are presented. The factors are useful in estimating the elastic settlement of shallow foundations on cross-anisotropic soils, when the soil properties along two perpendicular directions are known. A series of design charts are provided in non-dimensional form so as to avail their practical use in a general form.

Case-wise investigation of body-wave propagation in a cross-anisotropic soil with multiple inhomogeneity coefficients

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material. The material properties such as Young’s moduli, shear modulus, and density have been assumed to vary as a function of depth. These functions have been considered as the possible combinations of a polynomial function, exponential function, and trigonometric function. A suitable mathematical formulation of the physical problem has been developed (an eigenvalue problem) with displacement components as fundamental variables. With the help of separation of variables, appropriate substitution, and applicable mathematical treatment, displacement components have been deduced. Furthermore, employing intrinsic boundary conditions, the closed-form expressions for quasi-wave velocities have been derived. Numerical examples have been investigated, and the dependency of phase velocity on phase angle and inhomogeneity coefficients have been shown graphically. It has been observed that the increment and decrement in the degree of material anisotropy disturb the magnitude of phase velocity to a great extent.

Seismic analysis of rigid walls retaining a cross-anisotropic soil by the differential quadrature method

Many construction projects such as bridges, barriers, road construction, etc. use rigid or flexible retaining walls. Seismic behaviour analysis of such structures is difficult and complex due to the complexity of the relationships governing wall behaviour. Three methods of field observation, laboratory simulation and numerical modelling can be used for this purpose. In this study, dynamic behaviour of pair of rigid smooth and rough retaining walls assuming transverse anisotropic soil in frequency domain is evaluated. The Differential Quadrature Method (DQM) is used for analysis. For solving the problem, a computer code is provided. The obtained results for the displacements, horizontal normal stress at the soil-wall interface, base shear force and corresponding bending moment are very close to the previous published results. The effects of the surcharge pressure are also considered in the analysis.

A general failure criterion for soil considering three-dimensional anisotropy

Abstract This paper proposes a generalized three-dimensional (3D) failure criterion for cross-anisotropic soils based on the spatially mobilized plane (SMP) criterion. In the proposed criterion, the anisotropic property of soil is considered by introducing a novel modification stress tensor, in which the angle between the principal stress and the soil depositional direction serves as a basic variable. Taking advantage of the SMP criterion, the proposed anisotropic criterion is subtly extended into a 3D version. The proposed criterion only involves two friction angles, φ v and φ h , which are determined by triaxial compression test along and perpendicular to the depositional direction, respectively. To account for the effects of the depositional direction, two special modification stress tensors regarding different depositional conditions (vertical and inclined) are discussed in this study. Comparisons between the predictions from the proposed strength criterion and the observations of the true triaxial tests on four cross-anisotropic soil samples show that the proposed generalized failure criterion can well capture both the cross-anisotropic behaviors and the 3D strength of cross-anisotropic soils.

Site response analysis in cross-anisotropic alluvial deposits subjected to inclined incident SH wave

Elastic site response analysis in cross-anisotropic deposits has been elaborated due to incidence of inclined SH wave front. A site consisting of a single cross-anisotropic soil layer rested on a half-space representing the bedrock is examined, subjected to inclined SH wave and the out-of-plane displacement amplitude is obtained by assembling the dynamic stiffness matrices of the layer and the underlying bedrock. The effects of the cross-anisotropy substantiated in form of different horizontal and vertical shear moduli were investigated and discussed accordingly. Results showed that anisotropy has great effect on the site response; however, this effect becomes immaterial when the incidence angles are almost sub-horizontal.

Numerical simulation of the nonlinear wave-induced dynamic response of anisotropic poro-elastoplastic seabed

In this paper, a 2D poro-elastoplastic model for wave-induced dynamic response in an anisotropic seabed is derived analytically. The seabed is treated as a porous medium and characterized by Biot’s consolidation equations. The soil plasticity and wave non-linearity are included in the model and both the pore fluid and the soil skeleton are assumed to be compressible. The nonlinear ocean waves are respectively considered as progressive and standing waves. The previous experimental data is used to validate the proposed model. Numerical results demonstrate that the influence of nonlinear wave components should not be ignored without committing substantial error. A significant difference between progressive and standing waves is also observed for the development of residual pore pressure, as well as the distribution of liquefied zone. A detailed parametric investigation reveals that the nonlinear wave-induced seabed response is also affected significantly by cross-anisotropic soil parameters.

Effects of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of pipeline buried in elasto-plastic seabed foundations

In this paper, a two-dimensional integrated numerical model is developed to examine the influences of cross-anisotropic soil behaviour on the wave-induced residual liquefaction in the vicinity of a pipeline buried in a porous seabed. In the wave model, the RANS (Reynolds Averaged Navier–Stokes) equation is used to govern the wave motion. In the seabed model, the residual soil response in the vicinity of an embedded pipeline is considered with the 2-D elasto-plastic solution, where the phase-resolved shear stress is used as a source for the build-up of residual pore pressure. Classical Biot׳s consolidation equation is used for linking the solid-pore fluid interaction. The validation of the proposed integrated numerical model is conducted by the comparisons with the previous experimental data. Numerical examples show that the pore pressures can accumulate to a large value, thus resulting in a larger area of liquefaction potential in the given anisotropic soil compared to that with isotropic solution. The influences of anisotropic parameters on the wave-induced residual soil response in the vicinity of pipeline are significant. A high rate of pore pressure accumulation and dissipation is observed and the liquefaction potential develops faster as the anisotropic parameters increase. Finally, a simplified approximation based on a detailed parametric investigations is proposed for the evaluation of maximum liquefaction depth (zL) in engineering application.

Assessment of anisotropic elastic parameters of saturated clay measured in triaxial apparatus: Appraisal of techniques and derivation procedures

Recent developments in laboratory techniques adopting highly precise local instrumentation have made possible the determination of all five independent elastic parameters necessary for describing the small-strain stiffness in cross-anisotropic soils. However, the techniques and the derivation procedures are not necessarily straightforward, and different processes sometimes lead to apparently inconsistent sets of parameters, revealing their complex and sensitive nature. This paper firstly reports a new fully-instrumented triaxial system that was optimised to test Japanese standard-sized (∅70–75mm) clay samples. The testing techniques and procedures to obtain the five cross-anisotropic elastic parameters, defined in this paper for recoverable strain smaller than 0.001%, are reviewed. Some updates, including notes on how to deal with creep in soft clays and the optimisation of drained probe rates, are described. A simplified procedure is proposed for completing the parameter determination, without actually measuring the radial displacement, by inverting the relationship between the undrained Young׳s modulus and the drained elastic parameters in saturated soils. The validity of this approach is demonstrated by comparing the parameters of sedimentary clays obtained with and without radial measurements. By eliminating the need for complex radial instrumentation, this approach will make the quantification of stiffness anisotropy more accessible in less-equipped laboratories.

A failure criterion for cross-anisotropic soils considering microstructure

Strength anisotropy is an important soil behavior which is closely related to the microstructural characteristics in soil. Proper consideration of the microscopic properties of a soil is key to accurate description of its strength anisotropy. This paper presents a failure criterion for cross-anisotropic soils based on the Spatially Mobilized Plane (SMP) criterion. In the new criterion, the shear-normal stress ratio defined in the SMP is related to the relative orientation of the loading direction with respect to the axes of material anisotropy through a microstructure-based tensor. The formulation includes only two parameters which can be easily calibrated by conventional triaixal tests. By comparison with tests data, the criterion is shown to offer good characterization of the strength anisotropy for a variety of geomaterials with cross-anisotropy.

The Onset of Strain Localization in Cross-Anisotropic Soils Under True Triaxial Condition

ABSTRACT The influences of inherent cross-anisotropy on soil strength on the homogeneous deformation and bifurcation characteristic of the stress-strain relationship are studied. By neglecting the cohesion term and employing an elliptical shape function in Mohr-Coulomb failure criterion, a 3D anisotropic failure criterion is proposed to describe the strength of cross-anisotropic sands under true triaxial conditions. Based on the proposed failure criterion, the influence of the anisotropic parameter on the failure curve on the deviatoric plane and the relationship between the peak friction angle and the intermediate principal stress ratio are obtained. The suitability of the criterion is justified by comparing with a series of true triaxial tests on sands without strain localization. The proposed failure criterion is adopted to build a three dimensional anisotropic elasto-plastic model, which allows the bifurcation analysis to be incorporated with the non-coaxial flow rule for the purpose of studying the onset of strain localization. Compared with the true triaxial tests under several intermediate principal stress ratios conditions in the literature, the proposed model and bifurcation analysis is shown to be capable of predicting the influence of inherent cross-anisotropy on the onset of strain localization.

Failure Criterion for Cross-Anisotropic Soils

Experimental evidence and analyses of results of three-dimensional (3D) tests show that the shape of the failure surface for soils is influenced by the intermediate principal stress, shear banding, and cross anisotropy. Presented here is a formulation of a general 3D failure criterion for cross-anisotropic soils for both nonrotating and rotating stresses. The formulation relates the loading direction to the principal directions of the cross-anisotropic microstructure of the soil. The criterion is based on a function of stress, previously used as the 3D failure criterion for isotropic frictional materials, which is set equal to a scalar that varies over a sphere. The formulation is specialized for true triaxial tests and torsion shear tests and determination of material parameters is demonstrated. The failure criterion for cross-anisotropic soils is compared with experimental results from the literature to show that it is able to capture the conditions obtained in true triaxial tests without stress rotations as well as the conditions in torsion shear tests performed to study effects of stress rotation. Sets of data from some classic true triaxial tests are reinterpreted to show their true cross-anisotropic behavior.

Modeling failure in cross-anisotropic frictional materials

Three-dimensional test results for frictional materials such as soils, concrete, and rock show that the shapes of their failure surfaces are influenced by the intermediate principal stress, shear banding, and cross-anisotropy (transverse isotropy). A general 3D failure criterion for cross-anisotropic soils for both non-rotating and rotating stresses is presented and compared with experimental results for sand, clay, and sea ice. The formulation relates the loading direction to the principal directions of the cross-anisotropic microstructure of the material. The criterion is based on a function of stress, previously used as the 3D failure criterion for isotropic frictional materials, which is set equal to a scalar that varies over a sphere. The formulation is specialized for true triaxial tests and torsion shear tests and determination of material parameters is demonstrated. The failure criterion is compared with experimental results from the literature to show that it is able to capture the conditions obtained in three-dimensional experiments without and with stress rotations. The limitations of the criterion are demonstrated by its failure to capture the behavior of some cross-anisotropic materials with particular micro-structures, and the reasons for the shortcomings are discussed.