Two-layer Soil Research Articles

Numerical Evaluation of Geogrid-Reinforced Two-Layer Soil System with Plate Load Test

Numerical Evaluation of Geogrid-Reinforced Two-Layer Soil System with Plate Load Test

Drained Bearing Capacity of Strip Footings on Two-Layered Sand Soil Slope

Drained Bearing Capacity of Strip Footings on Two-Layered Sand Soil Slope

Torsion of end-bearing pile foundations in layered anisotropic geomaterials

ABSTRACT An analysis for the torsional dynamic response of end-bearing pile foundations embedded in a layered transversely isotropic geomaterial (soil/rock) is presented. The deformation of the transversely isotropic soil or rock is described by the method of separation of variables. The elasticity theory for a viscoelastic medium with frequency independent hysteretic material damping, and the Extended Hamilton’s Principle are utilised to derive the differential equations describing pile and soil motions. The differential equations are solved analytically in an iterative algorithm. The accuracy of the analysis is verified with existing studies reported in the literature for pile foundations embedded in a homogeneous and layered soil deposit. The effect of the degree of anisotropy on the pile-soil response – dynamic pile-head stiffness, distribution of pile rotation and torque with depth, dimensionless soil displacement function for various values of pile slenderness and pile-soil stiffness ratios in a homogenous soil deposit is investigated. Design charts of static pile-head stiffness in a homogeneous soil deposit for a wide range of pile-soil stiffness and pile slenderness ratios, and degree of anisotropy are also reported. The effect of soil layering for a pile embedded in a two-layered soil deposit is also studied.

Surface acoustic waves in porous soils with two-layered infiltration

Abstract Two stage mathematical and computer models based on the finite element solution of Richards’ equation for water infiltration in two-layered fluid-saturated soil and modal analysis using a semi-analytical approach for vertically stratified soils are presented and briefly described. Dispersion curves of surface waves in the layered poroelastic half-space are computed and studied. The features of porous water infiltration effect on the characteristics of surface elastic waves are discussed.

Three-dimensional numerical analysis of twin tunnelling in two-layered soil strata

Tunnelling induces stress change and displacement in the ground. The excavation of a new tunnel in stratified soil can trigger different patterns of stress redistribution, which may adversely influence nearby tunnels. Research on multi-tunnel interaction has mainly been performed on the assumption of a uniform ground. The effects of different soil stratifications on tunnelling interaction remain poorly understood. In this paper, three-dimensional numerical parametric studies verified by previous centrifuge tests were carried out to analyse the twin tunnelling effects in two-layered soil. An advanced hypoplastic constitutive model that can capture stress-, path-, and strain-dependency of soil behaviour is adopted. Numerical cases investigated include perpendicular twin tunnelling in two sand layers with different relative densities and the location of the interface between the two sand layers. It is revealed that larger settlements and a wider surface settlement trough occur when tunnelling in two-layered soil strata than in a uniform ground. This is because of the wider and larger soil arch induced in two-layered soil strata. The structural response including tunnel deformation, induced bending moment, and induced hoop stress of the existing tunnel can be greater when tunnelling in layered soil strata than in a uniform ground owing to larger stress relief. Moreover, the combination of bending moment and hoop stress can exceed the M−N failure envelope of the structure in layered soil. A conventional simplified assumption of a uniform ground can underestimate of the influence of new tunnel excavation on existing tunnels, resulting in unsafe designs.

Seismic wave amplification in a weakly nonlinear two-layered soil deposit

Based on numerous observations, local soil site conditions can significantly affect the formation of seismic responses. In this paper, we examine seismic responses caused by shear waves propagating through a two-layered soil deposit. The aim of the research is to study the phenomenon of amplification of shear waves due to the resonant properties of the soil deposit and the nonlinear characteristics of partial layers, which are assumed to be the cubically nonlinear continuous media. The target problem relates to a nonlinear boundary value problem, the solution of which is carried out using a semi-analytical approach. According to the approach, the problem’s solution is sought using the method of separation of variables, while the solution to the corresponding spectral problem is derived in the form of a power series. Additionally, good agreement is shown between theoretical studies and numerical simulations. The developed approach allows one to evaluate the amplification factor for a nonlinear two-layered soil deposit and to detect changes in the shape of amplification factor profiles when the frequency of an incident wave on a rigid bedrock is varied.

Numerical Analysis of the Ultimate Bearing Capacity of Strip Footing Constructed on Sand-over-Clay Sediment

This paper analyzes the bearing capacity of two-layered soil medium using finite element (FE) software ABAQUS/CAE 2023. Although geotechnical engineers design foundations for layered soil, majorly current geotechnical studies emphasize single homogenous soil. So, this research has significant novelty as it focuses on layered soil and adds to the current literature. A nonlinear FE model was prepared and analyzed to determine the ultimate bearing capacity of two-layered soil (sandy soil over clayey soil). The Drucker–Prager and Mohr–Coulomb models were used to represent sandy soil and clayey soil layers, respectively. Strip footing material properties were considered isotropic and linearly elastic. This study performed parametric studies to understand the effects of thickness, unit weight, and the modulus of the elasticity of sandy soil on the ultimate soil bearing capacity. Additionally, it also analyzed the effect of the cohesive strength of clayey soil on layered soil bearing capacity. Results showed that an increase in sandy soil layer thickness strengthens the layered soil, and thus, improves the bearing capacity of soil. Increasing the sandy soil layer thickness over footing width (h1/B) ratio from 0.15 to 2.0 improved the ultimate bearing capacities with elastic settlements of 350 mm and 250 mm by 145.62% and 101.66%, respectively. Additionally, for a thicker sandy soil layer, an increase in the unit weight and modulus of the elasticity of sandy soil led to higher ultimate bearing capacity. Furthermore, it was concluded that an increase in clayey soil’s cohesive strength from 20 kPa to 30 kPa resulted in a 24.31% and 3.47% increase in soil bearing capacity for h1/B = 0.15 and h1/B = 2.0, respectively. So, the effect of cohesion is prevalent in the case of a thicker clayey soil layer.

Deformation of layered soil

One of the consequences of the aggression of the russian federation in Ukraine is a change in the properties of the surface layers of some regions of the soil. Construction of structures in such areas must be carried out considering the above. In order to create prerequisites for taking into account the artificially created layering of the soil, an algorithm for analytical determination of the stress-strain state of a two-layered soil was developed in a linear setting within the limits of plane deformation. Layers are considered as linear elastic bodies of limited dimensions in the plan. The algorithm is based on the Ery stress function with arbitrary coefficients, on the dependence of the indicators of the stress-strain state of the soil layers on it and on the mechanical indicators of the material of the layers, the thickness of the artificially formed surface layer. The algorithm provides for the formulation of the load conditions by the normally distributed force of part of the soil surface, the conditions of the interaction of the layers, and the unlimited thickness of the main soil layer.The listed conditions and features of the layers constitute a system of linear algebraic equations. The solution of the system of levels provides an opportunity to determine the coefficients of the stress function and, accordingly, to determine the indicators of the stress-strain state of the two-layer soil support. The generalization of the results, carried out by planning the experiment for the selected limits of possible realizations of the mechanical properties of the soil layers, allows for determining the deflections of the surfaces of the layers depending on individual factors.The following is established. The characteristics of the dependences of the deflections of the layer surfaces on other parameters are similar. Maximum deflections decrease with increasing surface layer thickness. Deflections of the interaction surface of the soil layers are linearly dependent on the Poisson ratio of the main soil layer and decrease as the ratio increases. The results obtained within the limits of the linear formulation can be considered sufficiently reliable because they are obtained analytically and generalized by the methods of the linear theory of elasticity and the method of planning the experiment.

Integrated machine learning for modeling bearing capacity of shallow foundations

Analyzing the stability of footings is a significant step in civil/geotechnical engineering projects. In this work, two novel predictive tools are suggested based on an artificial neural network (ANN) to analyze the bearing capacity of a footing installed on a two-layered soil mass. To this end, backtracking search algorithm (BSA) and equilibrium optimizer (EO) are employed to train the ANN for approximating the stability value (SV) of the system. After executing a set of finite element analyses, the settlement values lower/higher than 5 cm are considered to indicate the stability/failure of the system. The results demonstrated the efficiency of these algorithms in fulfilling the assigned task. In detail, the training error of the ANN (in terms of root mean square error—RMSE)) dropped from 0.3585 to 0.3165 (11.72%) and 0.2959 (17.46%) by applying the BSA and EO, respectively. Moreover, the prediction accuracy of the ANN climbed from 93.7 to 94.3% and 94.1% (in terms of area under the receiving operating characteristics curve—AUROC). A comparison between the elite complexities of these algorithms showed that the EO enjoys a larger accuracy, while BSA is a more time-effective optimizer. Lastly, an explicit mathematical formula is derived from the EO-ANN model to be conveniently used in predicting the SV.

An uncoupled approach for estimating seismic-induced pore water pressures in liquefiable sandy soils

Proper evaluation of seismic-induced excess pore water pressures in saturated sandy soils is still an open issue, which can be tackled with fully coupled to uncoupled approaches. The former are more accurate but computationally onerous, while the latter require seismic demand and pore pressure build-up to be computed in two successive steps, typically employing simple constitutive assumptions.Starting from the work by Seed et al. (1975), this paper presents a novel uncoupled procedure to compute excess water pressures developing in a 1D soil column under partially drained conditions, when subjected to horizontal seismic excitations. Fundamental modifications are introduced to account for: non-uniform distribution of equivalent loading cycles; soil stiffness degradation; and modification of the frequency content of ground motion due to pore pressure build-up.The approach was implemented in Matlab via the Finite Difference Method and validated against both fully-coupled Finite Element analyses and one centrifuge test. An extensive parametric study was also performed for a two-layer soil column, by varying the thickness and hydraulic conductivity of the shallow layer, as well as the seismic input. The good agreement with both numerical and experimental data demonstrates that key features of liquefaction are well-captured by the proposed uncoupled approach.

Train-earth-grid coupling DC magnetic bias model for stray current diffusion

The DC magnetic bias phenomenon in transformers can result in increased noise and harmonic components. This study focuses on the DC magnetic bias generated by stray currents in the DC traction power supply system of neutral grounding transformers under multiple train operation conditions. A two-layer soil model is utilized to calculate geodetic potential, with rail potentials from both mainline and depot serving as sources for stray current within the model. Two paths of stray current intrusion into the transformer via the grounding network and cable armor layer from the Main substation have been modeled and analyzed. A simulation test has been designed to verify that the maximum error between experimental data and model calculation data is 8.87%. The implementation of a blocking connection device between the depot and mainline, as well as a change in grounding strategy for the metal protective layer, can effectively reduce DC bias magnetic current in the substation.

A simulation on soil structure interaction with ABAQUS; effect on the behavior of a concrete building of soil layers and earthquake properties

In this article, the effect of soil properties and earthquakes on a structure built in a multi-layer foundation soil is studied using Abaqus/СAЕ. Single foundations are one of the most common types of foundations traditionally required to support buildings in earthquake-prone regions. Most researchers work on the dynamic interaction between the foundation and the soil, which can affect the response of the building during earthquakes due to the type of earthquake and the properties of the soil layer. In this paper, four different earthquakes were applied to a reinforced concrete building constructed in two-layer soils with very different soil properties, and a discussion on soil-structure interaction was opened using Abaqus software. In the analysis, a layered soil is simulated with 4 different models (soft-hard, hard-soft). Through these analyses, the influence of the different soil layers (soft and hard), the building displacement and the frequency content of the earthquake were studied. According to the result of the analysis, it is important to consider the earthquake characteristics, the soil properties, and the type of foundation in the dynamic soil-structure interaction.

Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth

In the common hydrogeologic scenarios of horizontal groundwater flow and a water table below the surface, the steady-state 2D thermal field resulting from the coupling between water flow and heat flow and transport gives rise to a vertical temperature profile that develops progressively over a finite extent of the domain. Beyond this region, the temperature profiles are linear and independent of horizontal position. Such profiles are related to the groundwater velocity so they can be usefully used to estimate this velocity in the form of an inverse problem. By non-dimensionalization of the governing equations and boundary conditions, this manuscript formally derives the precise dimensionless groups governing the main unknowns of the problem, namely, (i) extent of the profile development region, (ii) time required for the steady-state temperature profile solution to be reached and (iii) the temperature–depth profiles themselves at each horizontal position of the development region. After verifying the mathematical dependencies of these unknowns on the deduced dimensionless groups, and by means of a large number of accurate numerical simulations, the type curves related to the horizontal extension of the development of the steady-state profiles, the characteristic time to develop such profiles and the dimensionless vertical temperature profiles inside the characteristic region are derived. These universal graphs can be used for the estimation of groundwater horizontal velocities from temperature–depth measurements.

Calculation of the Bearing Capacity of a Two-Layer Soil Base Under an Inclined Load

Calculation of the Bearing Capacity of a Two-Layer Soil Base Under an Inclined Load

Elastic–Plastic Analysis of Rigid Passive Piles in Two-Layered Soils

The paper analyses the behavior of a rigid passive pile embedded in a soil profile consisting of a stable layer underlying an unstable layer subjected to a uniform soil displacement. Pile-soil interaction is considered by modeling the soil by a series of elastic–plastic springs along the pile shaft. The modulus of horizontal subgrade reaction is assumed to linearly increase with depth in the unstable layer and constant in the stable one. The ultimate soil resistance is assumed increasing with depth in both layers. The results of analysis are presented in dimensionless form in terms of shear force developed at the slip surface as a function of the pile embedment into the stable layer and the distribution of soil characteristics over depth. The method allows capturing pile response not only at the soil ultimate state but also at the intermediate states. Specifically, the governing equations for the elastic, elastic–plastic and plastic cases are discussed and, whenever possible, a set of closed-form expressions is provided to estimate the maximum bending moment along the shaft and the pile head deflection, so that for an assigned value of the required stabilizing force both ultimate and serviceability limit state of the pile can be checked. A numerical example is given to illustrate the application of the proposed procedure.

Kinematic response of floating piles in two-layered soils subjected to vertically incident S-waves

A rigorous solution is proposed for the kinematic transverse response of a single floating pile in the two-layered soil by vertically propagating S-waves. The soil displacements of the two layers are solved by Helmholtz decomposition and the method of separation of variables. The soil mode functions with a series of eigenvalues are calculated and satisfy the weighted orthogonality. The unknown coefficients in the solution functions are obtained in light of the boundary conditions. An infinite series of algebraic equations with unknown coefficients can be solved by truncating the series number. The cutoff frequency, soil reaction factor, and pile curvature along the shaft are investigated for different properties of the adjacent soil. For the pile in the soil with soft upper and stiff lower layers, the dimensionless cutoff frequency is smaller than that of homogeneous soil, but it follows opposite rules when the upper layer is rigid.

Kinematic response of the single floating piles in the two-layered soil subjected to vertically incident P-waves

An analytical model for the kinematic response of a single floating pile in a two-layered soil under vertically propagating P-waves is proposed by elastodynamics. A Heaviside step function is introduced to simulate the variability of the layered soil. The continuity of the pile and the fictitious soil column are considered based on Tajimi’s theory. The main contribution of the present solution is that the model of the fictitious soil column for the floating pile in the homogeneous soil under vertically propagating P-waves is extended to the two-layered soil with the simulation of the depth-dependent soil mode function. The effect of the properties of the soil layer and the shaft on the vibration of the soil–pile system is investigated. For the soil with the upper softer layer, the dimensionless cutoff frequency of the two-layered soil is smaller than that of homogeneous soil and the opposite trend is for the soil with an upper stiffer layer. For the soil with upper stiff and lower soft layers, the axial pile strain decreases with the decrease of the soil modulus ratio and the effect of soil modulus ratio on the soil resistance at the lower part of the shaft is negligible.

A study on soil propagation mechanism of traffic-induced vibration based on numerical analysis and theoretical approach

In order to clarify soil propagation mechanism of traffic-induced vibration, soil surface responses excited by vertical and horizontal force focused on the frequency characteristics are examined based on numerical analyses, theory of surface wave, and field observations. Relationships between natural frequency of surface soil and frequency at which wave with large amplitude propagates at distant points are examined. In the case of two-layer soil, vertical displacement amplitude excited by vertical point force becomes the largest at twice the natural frequency at distant points. Horizontal displacement amplitude excited by horizontal point force becomes the largest at the natural frequency at distant points.

Numerical Study on Effect of Axial Loading on Rock-Socketed Piles in Two-Layered Soil Slope

Numerical Study on Effect of Axial Loading on Rock-Socketed Piles in Two-Layered Soil Slope

An analytical solution for the filtering effect of piles in two-layer soil

The aim of this work is to investigate the kinematic response of a floating pile (either free- or fixed-head) embedded in a two-layer soil subjected to upward-propagating seismic waves. Closed form analytical solutions are provided for the kinematic interaction factors, based on a Beam-on-Dynamic-Winkler-foundation (BDWF) model properly adjusted for the problem at hand. For the fixed-head pile case, a simplified solution to assess the pile-to-soil acceleration ratio is provided adopting the concept of average soil motion over an effective pile length. The proposed solutions compare well with rigorous elastodynamic Finite-Element analysis. Insight is given into the interpretation of the mechanisms regulating the reduction of design spectra as function of structural period. Finally, as an outcome of a wide parametric study, ready-to-use formulae are proposed for a rapid assessment of the pile-induced spectral reduction.