ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING

Based on the layered visco-elastic soil model, according to the Terzaghi's one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained. The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. According to the results of several numerical examples, the consolidation of visco-elastic soils logs behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.

Pile foundation in alternate layered liquefiable and non-liquefiable soil deposits subjected to earthquake loading

Pile foundations are still the preferred foundation system for high-rise structures in earthquake-prone regions.Pile foundations have experienced failures in past earthquakes due to liquefaction.Research on pile foundations in liquefiable soils has primarily focused on the pile foundation behavior in two or three-layered soil profiles.However,in natural occurrence,it may occur in alternative layers of liquefiable and non-liquefiable soil.However,the experimental and/or numerical studies on the layered effect on pile foundations have not been widely addressed in the literature.Most of the design codes across the world do not explicitly mention the effect of sandwiched non-liquefiable soil layers on the pile response.In the present study,the behavior of an end-bearing pile in layered liquefiable and non-liquefiable soil deposit is studied numerically.This study found that the kinematic bending moment is higher and governs the design when the effect of the sandwiched non-liquefied layer is considered in the analysis as opposed to when its effect is ignored.Therefore,ignoring the effect of the sandwiched non-liquefied layer in a liquefiable soil deposit might be a nonconservative design approach.

Deep Penetration of Spudcan Foundation into Double Layered Soils

The spudcan foundation has been widely used in offshore engineering for jack-up rigs. However, “punch through' failure often occurs where a stronger soil layer overlays a softer soil layer. In this study, spudcan penetration into double layered soils is investigated numerically. The soil profile is set up as a stronger soil layer overlaying a softer soil layer, with the soil strength ratio (bottom soil strength / top soil strength) varied from 0.1 to 1.0 (1 means uniform soil). The bearing behaviour is discussed and the bearing capacity factors are given for various cases involving different layer thicknesses and different strength ratios of the two clay layers. The development of the plastic zones and the effect of soil self-weight on the bearing capacity are also discussed. From this study, it is found that, when a spudcan is distant from the soil layer boundary, the spudcan can be analysed with single soil layer data. However, when a spudcan becomes closer to the soil boundary layer, the influence of the lower soft soil layer is significant, and the bearing capacity of the spudcan decreases. The critical distance is an indication of the occurrence of “punch through' failure. The critical distance between the spudcan and the layer boundary is larger for a rough spudcan than the one for a smooth one, and the critical distance decreases with increasing soil strength ratio. The depth of cavity formed during initial spudcan penetration depends on the top layer soil strength, soil strength ratio and unit soil self-weight, and the cavity affects the spudcan bearing behaviour as well.

Wetting Patterns and Nitrate Distributions in Layered-Textural Soils Under Drip Irrigation

Laboratory experiments were conducted in different sequence and thickness of the soil layers to investigate the effects of layered-textural soils on wetting patterns and water and nitrate distributions from a surface point source under various combinations of application rate and applied volume. Three layered soils, including a sandy-over-sandy loam （SL）, a sandy loam-over-sandy （LS）, and a sandy loam-sandy-sandy loam （LSL）, and two uniform soils （a uniform sandy loam and a uniform sandy soil） were tested. In the experiments, the application rate was varied from 0.69 to 3.86 L h^-1 and the applied volume from 5.7 to 12.1 L. The experimental results demonstrated that the wetting patterns and water and nitrate distributions were greatly affected by the sequence and thickness of soil layers as well as the application rate and volume applied. An interface existing in the layered soils, whether a fine-over-coarse or a coarse-over-fine, had a common feature of limiting downward water movement and of increasing horizontal water movement. For the fine-over-coarse layered soils of LS and LSL, water and nitrate were uniformly distributed at a given depth in the top layer soil. For a coarse-over-fine layered soil of SL, however, water accumulated in the sublayer soil underneath the interface and a zone of lower nitrate concentration was observed. The effect of application rate on water distribution pattern was dependent upon soil layering. A minor influence of application rate on water distribution for the fine-over-coarse layered soils （LS and LSL） than for the uniform soils was found. To obtain a greater wetted depth through selecting the emitters having a smaller application rate, which is a common method in the system design for a uniform soil, may not be necessarily applied for the layered soils. Measurements of nitrate distribution showed that nitrate accumulated toward the boundary of the wetted volume for both the uniform and the layered soils. This suggests the importance of optimal management of drip fertigation because nitrate is susceptible to the movement out of the root zone by mismanagement of fertigation. The information obtained from this research is useful in the design, operation, and management of a drip fertigation system.

Three-dimensional consolidation deformation analysis of porous layered soft soils considering asymmetric effects

Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED SOILS WITH IMPEDED BOUNDARIES UNDER TIME-DEPENDENT LOADINGS

On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

Pile Running in Layered Soils

This paper presents a case study on incidents of offshore pile running in layered soils.The study provides a detailed description of the seabed soil data,pile driving records,and field surveillance video observations.Three-dimensional large deformation finite element(LDFE)analyses were conducted to retrospectively analyze the incidents,considering the remoulding of seabed soil and degradation of the pile-soil interface in the LDFE modeling.By comparing the field observations with the LDFE analysis,the mechanism of pile running was discussed,with a focus on investigating the pile penetration resistance in each layer.The study revealed that pile running in layered soils primarily resulted from a significant reduction in pile base resistance when transitioning from a strong layer to an adjacent weak layer.To further investigate the pile running mechanism in layered soils,a parametric study on the strength variation of adjacent soil layers and its influence on pile base resistance was conducted.Lastly,a simplified prediction model of pile base resistance,suitable for assessing the risk of pile running in layered soils,was proposed.

In-Situ Evaluation of Evaporation in Layered Soils （Tukulu, Sepane and Swartland）

Knowledge about the influence of soil layers on evaporation is essential for the optimization of infield rainwater harvesting （IRWH） in the semi-arid areas of the Free State province of South Africa. Among the soils earmarked for 1RWH development include the Tukulu, Sepane and Swartland soil types that have contrasting soil layers. These soils have to capture and store rainwater within the soil profile layers away from the evaporation zone. To determine how the three soils release and deliver soil water at the evaporating site, a 21-day evaporation experiment was conducted on pre-drained monoliths. Instantaneous soil water content （SWC） from in-situ and soil water characteristic curve （SWCC） from laboratory was measured. Separate soil samples of 15 mm thickness were also evaporated under the same conditions to establish the extent of drying and hydraulic gradient at the soil surface. The Darcian evaporative flux and unsaturated hydraulic conductivity （K-coefficient） were also determined. At the surface suctions of magnitude greater than 1,500 kPa were observed from all monoliths. Total contributions to evaporation from the Tukulu, Sepane and Swartland were 43, 51 and 70 mm, respectively. The low contributions were explained by the presence of the prismacutanic C-horizon in the Tukulu and Sepane at respective depths of 600 and 700 mm. This layer was associated with the steepest suction gradient that restrained further upward fluxes by subsequent lowering for the K-coefficient with more than two orders of magnitudes within a narrow range of SWC. However, the presence of the pedocutanic B-horizon at depths of 300 mm undermined this restrictive function through the appreciable capillary activity demonstrated by clays at near evaporating surfaces. The shallowness and deficiency in structure of the Swartland was consistent with the high contribution to evaporation that gave this soil a dry soil water regime. It was therefore concluded that the Tukulu offered soil profile layers that could reasonably satisfy the soil water conservation requirements for IRWH.

Analysis of Interaction Factors between Two Piles in Layered Soils

A rigorous analytical method is presented, which takes into account the pile stiffening effects, using the theory of the transfer matrix-bottom rigidity for calculating the interaction factor between two identical piles in multi-layered soils subjected to vertical loads. Following the technique proposed by Muki and Sternberg, the problem is decomposed into extended soil layers and two fictitious piles characterized respectively by Young's moduli of the layered soils and those of the differences between the piles and the layered soils. The unknown axial forces along fictitious piles are determined by solving a Fredholm integral equation of the second kind, which imposes the compatibility condition that the axial strains of the fictitious piles are equal to those corresponding to the centroidal axes of the extended layered soils. The real pile displacements can be calculated based on the determined fictitious pile forces, and finally, the desired pile interaction factors may be obtained. Selected results from parametrical studies are presented to confirm the validity of the proposed approach and portray the influence of the governing parameters on the pile interaction.

Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model

The dynamic response of pile in layered soil is theoretically investigated when considering the transverse inertia effect.Firstly, the fictitious soil-pile model is employed to simulate the dynamic interaction between the pile and the soil layers beneath pile toe. The dynamic interactions of adjacent soil layers along the vertical direction are simplified as distributed Voigt models.Meanwhile, the pile and fictitious soil-pile are assumed to be viscoelastic Rayleigh-Love rods, and both the radial and vertical displacement continuity conditions at the soil-pile interface are taken into consideration. On this basis, the analytical solution for dynamic response at the pile head is derived in the frequency domain and the corresponding quasi-analytical solution in the time domain is then obtained by means of the convolution theorem. Following this, the accuracy and parameter value of the hypothetical boundaries for soil-layer interfaces are discussed. Comparisons with published solution and measured data are carried out to verify the rationality of the present solution. Parametric analyses are further conducted by using the present solution to investigate the relationships between the transverse inertia effects and soil-pile parameters.

Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

Effects of layer thickness on desiccation cracking behaviour of a vegetated soil

The objective of this study is to explore how different layer thicknesses affect the desiccation cracking behaviour of vegetated soil.During the experiment,an electronic balance was employed to quantify water evaporation,while a digital camera was utilized to capture the initiation and progression of soil surface cracking.Results indicate that in the early drying process,the rate of evapotranspiration in vegetated soil correlates positively with leaf biomass.For soil samples with the same layer thickness,the constant rate stage duration is consistently shorter in vegetated soil samples than in their bare soil counterparts.As the layer thickness increases,both vegetated and bare soil samples crack at higher water content.However,vegetated soil samples crack at lower water content than their bare soil counterparts.Vegetation significantly reduces the soil surface crack ratio and improves the soil crack resistance.The crack reduction ratio is positively correlated with both root weight and length density.In thicker vegetated soil layers,the final surface crack length noticeably declines.

A theoretical analysis of vertical dynamic response of large-diameter pipe piles in layered soil

Considering the viscous damping of the soil and soil-pile vertical coupled vibration,a computational model of large-diameter pipe pile in layered soil was established.The analytical solution in frequency domain was derived by Laplace transformation method.The responses in time domain were obtained by inverse Fourier transformation.The results of the analytical solution proposed agree well with the solutions in homogenous soil.The effects of the shear modulus and damping coefficients of the soil at both outer and inner sides of the pipe pile were researched.The results indicate that the shear modulus of the outer soil has more influence on velocity admittance than the inner soil.The smaller the shear modulus,the larger the amplitude of velocity admittance.The velocity admittance weakened by the damping of the outer soil is more obvious than that weakened by the damping of the inner soil.The displacements of the piles with the same damping coefficients of the outer soil have less difference.Moreover,the effects of the distribution of soil layers are analyzed.The results indicate that the effect of the upper soil layer on dynamic response of the pipe pile is more obvious than that of the bottom soil layer.A larger damping coefficient of the upper layer results in a smaller velocity admittance.The dynamic response of the pipe pile in layered soil is close to that of the pipe pile in homogenous soil when the properties of the upper soil layer are the same.

Stochastic seismic response of multi-layered soil with random layer heights

This paper deals with the effect of layer height randomness on the seismic response of a layered soil. These parameters are assumed to be lognormal random variables. The analysis is carried out via Monte Carlo simulations coupled with the stiffness matrix method. A parametric study is conducted to derive the stochastic behavior of the peak ground acceleration and its response spectrum,the transfer function and the amplification factors. The input soil characteristics correspond to a site in Mexico City and the input seismic accelerations correspond to the Loma Prieta earthquake. It is found that the layer height heterogeneity causes a widening of the frequency content and a slight increase in the fundamental frequency of the soil profile,indicating that the resonance phenomenon is a concern for a large number of structures. Variation of the layer height randomness acts as a variation of the incident angle,i.e.,a decrease of the amplitude and a shift of the resonant frequencies.

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

Time-Domain Analysis of Underground Station-Layered Soil Interaction Based on High-Order Doubly Asymptotic Transmitting Boundary

Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation in complex layered soils.The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain,possessing high accuracy and good efficiency.Combining with finite element method,a coupled model is constructed for time-domain analysis of underground station-layered soil interaction.The coupled model is divided into the near and far field by the truncated boundary,of which the near field is modelled by FEM while the far field is modelled by the high-order DATB.The coupled model is implemented in an open source finite element software,OpenSees,in which the DATB is employed as a super element.Numerical examples demonstrate that results of the coupled model are stable,accurate and efficient compared with those of the extended mesh model and the viscous-spring boundary model.Besides,it has also shown the fitness for long-time seismic response analysis of underground station-layered soil interaction.Therefore,it is believed that the coupled model could provide a new approach for seismic analysis of underground station-layered soil interaction and could be further developed for engineering.

Penetration Depth of Torpedo Anchor in Two-Layered Cohesive Soil Bed by Free Fall

The penetration depth of torpedo anchor in two-layered soil bed was experimentally investigated. A total of 177 experimental data were obtained in laboratory by varying the undrained shear strength of the two-layered soil and the thickness of the top soil layer. The geometric parameters of the anchor and the soil properties(the liquid limit, plastic limit, specific gravity, undrained shear strength, density, and water content) were measured. Based on the energy analysis and present test data, an empirical formula to predict the penetration depth of torpedo anchor in two-layered soil bed was proposed. The proposed formula was extensively validated by laboratory and field data of previous researchers. The results were in good agreement with those obtained for two-layered and single-layered soil bed.Finally, a sensitivity analysis on the parameters in the formula was performed.

Axisymmetric Finite Element Method for Analysis of Plate on Layered Soil

To obtain the fundamental solution of soil has become the key problem for the semi-analytical and semi-numerical (SASN) method in analyzing plate on layered soil. By applying axisymmetric finite element method (FEM),an expression relating the surface settlement and the reaction of the layered soil can be obtained. Such a reaction can be treated as load acting on the applied external load. Having the plate modelled by four-node elements,the governing equation of the plate can be formed and solved. In this case, the fundamental solution can be introduced into the global soil stiffness matrix and five-node or nine-node element soil stiffness matrix.The existing commercial FEM software can be used to solve the fundamental solution of soil, which can bypass the complicated formula derivation and boasts high computational efficiency as well.

Numerical modeling of solute transport in deformable unsaturated layered soil

The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.