Double-layered Soil Research Articles

Analytical solutions for thermal–mechanical coupling of energy piles in double-layer soil

Energy piles have gained a lot of attention in recent years as an environmentally responsible way to use renewable energy. The aim of this research is to analyze the behavior of energy piles in double-layer soil when subjected to mechanical and thermal loads, as well as combined thermomechanical loads. To achieve this, the study proposes analytical solutions for axial stress, strain, and displacement, which are based on principles such as equilibrium, kinematics, thermoelastic constitutive relationships, and elastic constitutive relationships of the pile-soil interface. These analytical solutions have been proven to accurately predict the behavior of energy piles under various loads. This paper analyzes several factors that affect the thermal–mechanical coupling analytical solutions for the energy pile, including soil lateral restraint, soil depth, pile end restraint, thermal expansion coefficient of the pile and mechanical load. In conclusion, the analytical solutions presented in this paper make us better understand the pile-soil interaction behavior and load transfer mechanism of semi-floating energy piles rather than ideally end-bearing piles nor ideally fully floating piles, thus can be used as a simple tool for the design and construction of energy piles in double-layer soil.

A One-Dimensional Nonlinear Consolidation Analysis of Double-Layered Soil with Continuous Drainage Boundary

Based on the soil nonlinearity assumptions proposed by Mesri, the one-dimensional nonlinear consolidation of double-layered soil is investigated. To better align with engineering reality, a continuous drainage boundary is introduced, bolstering the reliability of the derived solution through comparison against existing findings. Subsequently, the consolidation behavior of double-layered soil is analyzed for the soil permeability, compressibility, nonlinear parameters, and interface parameters. The outcomes elicit a positive correlation between the consolidation rate of the double-layered soil and both the ratio of permeability coefficient from the lower to upper soil layers and the value of the interface parameter. Furthermore, it is observed that a lower compressibility coefficient ratio between the lower and upper soil layers, along with a reduced ratio of compression index to penetration index, both contribute to an increased consolidation rate within the context of double-layered soil. The one-dimensional nonlinear consolidation of double-layered soil is intricate, intertwined with the relative permeability and compressibility of soil layers, and the influence of nonlinear parameters and drainage boundary configuration. Integrating these factors is crucial for analyzing the consolidation traits of double-layered soil, leading to a more precise portrayal of the consolidation behavior of coastal soft soils.

Semi-analytical solution for two-dimensional electro-osmotic consolidation of double-layered soil

This study proposed a semi-analytical solution for 2D electro-osmotic consolidation of double-layered soil. The method of Laplace transform is employed to derive the solution in the frequency domain. Then the numerical approach of inverse Laplace transform is used to obtain the explicit solution in the time domain. A finite element simulation is conducted to validate the proposed solution's accuracy. The verification example shows excellent agreement between the two methods. Based on the parametric study, it is found that the value of soil parameters in the second layer has significant influences on the behaviour of electro-osmotic consolidation. The larger the electro-osmosis coefficient in the second layer, the smaller the excess pore pressure at a given time. Additionally, a higher coefficient of volume compressibility in the second layer results in higher excess pore pressure. Compared with the 1D case, the distribution of excess pore pressure at the steady state is non-linear with depth in the 2D electro-osmotic consolidation, rather than a linear distribution. Furthermore, the dissipation rate and steady-state excess pore pressure could be underestimated if the electro-osmotic consolidation is modelled as a 1D case.

Measured Rainfall Infiltration and the Infiltration Interface Effect on Double-Layer Loess Slope

It is of great theoretical and engineering significance to carry out field rainfall tests and research on double-layer soil slopes in loess areas. Based on the developed rainfall simulation system with slow-moving injection, field rainfall tests were carried out on a natural double-layer loess slope. The characteristics of volumetric water content were monitored, and the rainfall infiltration characteristics and infiltration effect at the interface of the soil layer were analyzed by numerical simulation. The results showed the fastest infiltration at the top platform of the slope, followed by that at the upper surface of the slope, and the slowest infiltration at the lower surface of the slope during rainfall. Under various rainfall intensities, the erosion of the upper silty loess slope was greater than that of the lower clay loess slope, and the erosion patterns were quite different at the end of rainfall. During the infiltration process in the double-layer loess slope, a stagnant transition area was formed near the interface of the soil layer. The equipotential line of water content in the stagnant transition area of the upper region was roughly parallel to the slope surface, and the equipotential line in the lower region was roughly parallel to the interface of the soil layer. With an increase in rainfall intensity, the upper transition area at the interface of the soil layer continued to extend from the slope surface inward, showing the interface infiltration effect that became increasingly significant with the intensification of rainfall. The infiltration effect at the soil layer interface could provide an evaluation basis for rainfall infiltration analyses of multi-layer soil slopes.

Analysis of One-Dimensional Consolidation for Double-Layered Soil with Non-Darcian Flow Based on Continuous Drainage Boundary

The boundary drainage performance controls the rate of pore water discharge in the soil and plays an important role in the prediction of soil consolidation and settlement. Based on a continuous drainage boundary that can reflect the change of boundary drainage performance with time, a one-dimensional consolidation model of double-layered soil considering non-Darcian flow is established. The finite-difference method and semianalytical method are used to solve the consolidation equation, and the reliability of the two methods is verified by comparing with existing solutions. Based on the proposed solution, the consolidation behaviors of the double-layered soil are explored in depth through a systematic parametric study. The results show that, if the time effect of drainage boundary and the influence of non-Darcian flow are ignored, the estimated consolidation rate is relatively fast in the whole consolidation stage. The non-Darcian flow has a greater influence on soil consolidation under the continuous drainage boundary condition compared with that under the traditional drainage boundary condition. The consolidation rate of the foundation can be improved by appropriately increasing the permeability of the underlying soil layer or decreasing the compressibility of the underlying soil layer.

SUBSTITUTIONAL MODEL OF THE SOIL BASED ON ARTIFICAL NEURAL NETWORKS

This paper presents an interpretation of the results of measurement of specific soil resistivity by means of artificial neural networks. The model based on artificial neural networks replaces the soil which can be physically considered a two-layer medium with a vertical change of the specific electric resistivity and a horizontal boundary line between the layers. Learning of the neural network was performed under supervision using the input dataset obtained by means of a very accurate theoretical model of the double-layer soil. The proposed algorithm that approximates non-linear soil properties using the artificial neural network is reliable in assessment of the soil parameters and specific electric soil resistivity. Application of the substitutional model of the soil based on neural networks is demonstrated by a realistic example, determination of parameters of the double-layer soil from the measured data obtained by the Wenner technique for measuring the specific soil resistivity. For simplicity of presentation and model comparability, the current probes (poles) are replaced by the ball electrodes, i.e. spot fi eld sources. The results obtained are analytically and graphically presented and discussed.

Double-layered granular soil modulus extraction for intelligent compaction using extended support vector machine learning considering soil-structure interaction

Intelligent Compaction (IC) has been acquiring a growing interest in real-time quality control of compacted soil layers because of its high efficiency and full-area coverage. The current intelligent compaction technology allows the determination of the uniformity level of compaction over large areas according to the dynamic response of the roller. However, accurate real-time determination of the soil modulus during compaction based on roller acceleration has been challenging due to the multi-layered composite nature of the soil and the nonlinearities of the governing dynamic equations of motion and soil response. This study adopts a double-layered soil profile, and a three-dimensional finite element model, accounting for soil-drum interaction, is utilised for the analysis. The isotropic hardening elastoplastic hysteretic model was implemented to simulate the soil behaviour subjected to cyclic loading ranging from small to large strain amplitudes and account for stiffness degradation. The comprehensive dataset composed of the roller acceleration response and ground characteristics is then used to correlate the predicted soil modulus via an advanced machine learning approach. The adopted machine learning method incorporating Gaussian Kernel and Generalised Gegenbauer Kernel functions can reasonably predict the double-layered soil modulus during roller compaction. Additional analyses were conducted to observe the proper training size and number of iterations to achieve real-time quality control to be used by site engineers. Furthermore, the influences of the relative modulus ratio, drum length and top layer modulus on the soil surface dynamic displacement are discussed.

Analysis of heat pulse measurements in double-layered soils with the heating probe positioned at the layer interface

In the case where a heat-pulse (HP) sensor installed in a layered soil with the heating and sensing probes positioned at different layers, the HP measurement violates the underlying assumption of soil homogeneity for the cylindrical perfect conductors (CPC) theory that is used to interpret the HP data. In this study, laboratory and numerical studies were performed to evaluate the heat transfer patterns and models to analyze HP measurement data when heating probe was positioned at the interface of a double-layered soil with different upper- and lower-layer properties. A parameterized hetero-CPC model was proposed to describe temperature-by-time curves at the sensing probes in the upper and lower soil layers. The hetero-CPC estimates matched well with the simulated values, and its accuracy relied on the thermal property differences between the soil layers. The heat distributions caused by heat pulse inputs in the layered soils showed semi-circular isotherms with different radii centered on the heating source, therefore showing discrepancies in heat fluxes for the upper and lower soil layers. The proposed hetero-CPC model was able to accurately describe the combined effects of finite probe properties and heterogeneous soil thermal property values on the HP data in a double-layered soil system with the heating probe positioned at the layer interface.

Analytical Solution for One-Dimensional Nonlinear Consolidation of Saturated Double-Layered Soil Subjected to Cyclic Loadings

Cyclic loading-induced consolidation behavior of soft soil is of great interest for the analysis of offshore and onshore structures. In this study, an analytical solution for one-dimensional (1D) nonlinear consolidation of saturated double-layered soil under various types of cyclic loadings such as trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading was derived. The proposed solution was subsequently degenerated into solutions for special cases and compared to the existing solutions. The degenerate solutions show good agreement with the existing results, which proves that the proposed solutions are more general ones for 1D nonlinear consolidation of saturated soils under time-dependent loading. Finally, a comprehensive parametric study was conducted to investigate the influences of different layer parameters, drainage conditions, and loading parameters on nonlinear consolidation of saturated double-layered soil under cyclic loadings.

Inner soil heave of stiffened caisson during installation in soft-over-stiff clay

The identification of soil heaves inside a caisson during installation is important for the caisson’s design length, since the inner soil heave during the caisson installation affects the final effective caisson penetration depth, hence caisson capacity. This paper reports an extensive parametric study of stiffened caissons penetrating in double-layer of soft-over-stiff clay using large deformation finite element (LDFE) analyses. The LDFE analysis was first validated against the existing results from centrifuge tests and numerical analyses. Then the parametric study was carried out to explore the inner soil movements during stiffened caisson installations with various influencing factors, such as caisson diameter, caisson stiffener width, top-layer soil strength, double-layer soil strength ratio, and roughness of soil-caisson interface. It is found that the caisson diameter, stiffener width, and top-layer soil strength have significant influences on the inner soil behaviors. Besides, the movements of both soil surface and soil layer interface were also investigated. Based on the LDFE results, design formulas are proposed to estimate the inner soil heaves for soft-over-stiff clay. A design formula to estimate the movement of the soil layer interface for soft-over-stiff clays is also reported.

Consolidation theory of homogeneous multilayer treatment by air-boosted vacuum preloading

Air-boosted vacuum preloading, composed of anticlogging vertical drains and an outer booster system, is a new foundation treatment method that is beneficial to accelerating soil consolidation by applying different pressures between soil and vertical drains. Based on the assumption of equal strain, the present paper has simplified the calculation model of the air-boosted vacuum preloading method. Combined with the Newman-Carroll equation, the analytical solution for the consolidation of the double-layer soil foundation is proposed using separation of variables. Moreover, the theoretical solutions of consolidation without well resistance and ideal wells were given, and a chart convenient for engineering practice was acquired. Results show that the setting of well diameter ratio should not be more than 10 in engineering practice. At present, the consolidation theory of air-boosted vacuum preloading is imperfect and only focuses on the reinforcement mechanism of single-layer foundation. Therefore, it is of great significance to perfect the consolidation theory of air-boosted vacuum preloading with multiple layers.

Analysis of one-dimensional rheological consolidation of double-layered soil with fractional derivative Merchant model and non-Darcian flow described by non-Newtonian index

Analysis of one-dimensional rheological consolidation of double-layered soil with fractional derivative Merchant model and non-Darcian flow described by non-Newtonian index

Unsaturated seepage and stability of double-layer slope under rainfall infiltration

Taking a homogeneous double-layer soil slope as an example, the SEEP/W module and SLOPE/W module in the finite element analysis software GeoStudio were used in this paper. Then, the changes of pore water pressure and stability under different rainfall patterns and soil parameters were studied. Finally, the variation curves of pore water pressure and slope safety factor with rainfall time were obtained. The results show that: Soil parameters a and m are directly proportional to the slope safety factor, while n is inversely proportional to the slope safety factor. Under the condition of continuous rainfall, the decreasing rate of slope safety factor is directly proportional to the rainfall intensity.Under different rainfall patterns, the continuous rainfall in the advanced and normal rainfall patterns will cause the slope stability to decline and then gradually recover, while delayed and averaged rainfall patterns rainfall will cause the slope stability to decline continuously.In addition, there is a lag period in the change of slope safety factor, and the whole lag period lasts about 6 hours. During the lag period, the pore water pressure inside the soil began to decrease, while the slope safety factor continued to decrease. The safety factor starts to recover after the lag period ends.

Poroelastic theory of consolidation for a two-layer system with an upper unsaturated soil and a lower saturated soil under fully permeable boundary conditions

Soils are naturally present in the form of stratified layers, each being distinguishable from adjacent layers by a distinctive set of hydraulic and elasticity properties. Lo et al. (2020) have recently presented a theoretical model of poroelasticity that provides a detailed description of simultaneous solid framework deformation and immiscible fluid flow in a two-layer soil system that is made up of upper unsaturated and lower saturated zones caused by a vertical constant surface load under semi-permeable boundary drainage conditions. Due to the existence of different moisture contents (partial and full saturations) in the upper and lower layers, excess pore fluid pressure does not exhibit a symmetric distribution with respect to depth. Therefore, an exact, analytical solution for fully permeable boundary drainage conditions cannot be determined readily by applying scaling transformations and spatial translations from our recent result even though the coupled model equations possess an invariance feature.In this paper, a well-defined boundary-value problem based on the decoupled model equations of poroelasticity generalized for a two-fluid system is rigorously formulated for a double-layer (unsaturated-saturated) soil profile that allows water drainage at both top and bottom surfaces. Using Laplace time transformation, we derive the closed-form, exact-analytical solution accounting for the intricate interaction between deformable solid matrix and compressible interstitial fluids in such a two-layer system. The solution takes a more complicated form than that for the semi-permeable case. Boundary drainage conditions indeed affect the development of excess pore water and air pressures along with the time evolution of total settlement. We show that when the bottom boundary of the saturated layer overlain by the unsaturated layer with a lower hydraulic conductivity is impervious, the curve describing the relationship between the depth and excess water pressure at the interface has a negative slope, whereas the slope is positive when the boundary is pervious. The total settlement in the lower saturated layer would thus achieve an equilibrium state faster.

Analytical solution for one-dimensional nonlinear consolidation of double-layered soil with improved continuous drainage boundary

Following the assumptions proposed by Davis and Raymond, an analytical solution for one-dimensional nonlinear consolidation of double-layered soil under constant loading is derived by introducing an improved continuous drainage boundary condition. The effectiveness of the present solution is assessed by comparing against other existing analytical solutions and laboratory consolidation test results. A parametric study is then conducted to investigate the consolidation behaviour of double-layered soil for different interface parameters or stress ratios (i.e. final effective pressure over initial effective pressure, Nσ ). The results show that, the average consolidation degree defined by soil settlement U s increases with the increase of N σ, and the average consolidation degree defined by excess pore water pressure U p decreases with the increase of Nσ . The magnitude of U s is always larger than U p, and the difference between U s and U p increases with the increase of Nσ . Compared with the Xie's solution, the stress ratio Nσ has little effect on U p in the solution with continuous drainage boundary condition.

Analytical solution for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading

This paper presents analytical solutions for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading. Analytical solutions are derived for one-dimensional nonlinear consolidation of multi-layered soil subjected to constant loading and ramp loading. The proposed solutions are verified through the comparison with the existing solutions for double-layered soil and single-layered soil, which shows the proposed solutions are more general ones for one-dimensional nonlinear consolidation of saturated soils subjected to time-dependent loading. Based on the proposed solutions, nonlinear consolidation behavior of saturated multi-layered soil under time-dependent loading is investigated.

Rainfall Infiltration Characteristics of Double-Layered Soil Slope Covered by a Highly Permeable Stratum

Rainfall Infiltration Characteristics of Double-Layered Soil Slope Covered by a Highly Permeable Stratum

Investigation of the torsional behaviour of circular piles in double-layered nonhomogeneous soil

Response of piles subjected to torsional loading is significantly affected by soil profile and the interaction between soil and pile, which has not yet been fully understood. This paper describes a new analytical method for predicting the nonlinear response of torsional loaded piles in a double-layer soil profile, which considers the effect of elastoplastic behaviour of soil and the nonlinear variation of soil profile. The results from the new method have been compared with experimental and other published data, with good agreement obtained. Finally, an illustrative example has been carried out to explain how the new method can be applied to a practical situation.

Analytical solution for one-dimensional electro-osmotic consolidation of double–layered system

Abstract Electro-osmotic consolidation can be used as a valid and innovative technique for ground improvement. Considering the limitation of previous studies that layered soil heterogeneity was not taken into account, this paper presented an analytical model for one-dimensional(1D) electro-osmotic consolidation of double-layered soil, and a computer program of fully explicit solutions for excess pore pressure and degree of consolidation was developed. In order to validate its accuracy, a series of verification examples were conducted using analytical approach and the finite difference method. Comparison results demonstrated excellent accuracy of the proposed solutions. Furthermore, parametric studies were conducted to investigate the influence of relative permeability and compressibility relationship on the consolidation behavior. It can be found that the differences of hydraulic conductivities and electro-osmosis conductivities in the two layers will lead to a sharp change of the excess pore pressure profiles at the interface of two layers. A larger value of coefficient of volume compressibility in the second layer will slow down the dissipation process of excess pore pressure. A thicker layer with higher compressibility will result in a slower the rate of dissipation of the excess pore pressure, and a thicker layer with higher permeability causes a smaller value of the excess pore pressure, while in the layer of lower permeability, the opposite occurs.

Flow through Double Layered Porous Media Perpendicular to Bedding Plane: An Experimental & Simulation Work

Permeability (k) is an essential property of soil and has its importance in various fields of soil mechanics and geotechnical engineering. It is the ease with which water can percolate through the interconnected voids in a soil mass. To determine the permeability of soil samples, experimentation work needs to be carried out. The permeability analysis of layered soil samples, i.e., double-layered or triple-layered soil samples, much more time is consumed to achieve accurate results. So, to bypass this time consumption and laborious physical work, Computational Fluid Dynamics (CFD) analysis proves to be beneficial. ANSYS Fluent 14 software is a powerful tool which works on CFD technique seems to provide accurate results for permeability analysis as compared to laboratory results. In the present study, CFD analysis of double-layered soil samples is carried out using ANSYS Fluent 14 software, and the results obtained by this technique are compared with the laboratory results. Experimental as well as a numerical study was carried out to determine permeability and pressure drop variation for double layer combinations developed using the five soil types namely gravel (G), coarse sand (CS), fine sand (FS), fly ash (FA) and silt (S), and a formulation was proposed to calculate viscous resistance factor experimentally which was validated through simulation results. The permeable soil layer was modeled as porous media obeying Forchheimer's law.