Saturated Soil Layer Research Articles

The use of R code for modeling and simulation of 2-D contaminant migration through a soil for the pulse source

<p>In this study, based on an existing analytical solution for the two-dimensional transport of contaminants in a saturated soil layer, for the pulse source, the R program code was developed. The simulation is used to obtain the profiles of contaminant concentration, for a steady groundwater velocity, as a function of distance from the source and time. The problem is analytically solved by leveraging the similarity between the Gaussian (normal) distribution and contaminant concentration distribution, the development of the analytical model (i.e., solution of partial differential equation) by using this similarity is explained step by step since it may be of interest to researchers. Contaminant propagation is modeled using R software, which helps to understand how contaminants migrate through a saturated soil layer. This approach aids in comprehending the mechanisms and spatial dynamics of contaminant dispersion, facilitating the prediction and management of soil and groundwater contamination. The provided R code can be altered for different parameters and time intervals.</p>

The use of R code for modeling and simulation of 2-D contaminant migration through a soil for the pulse source

<p>In this study, based on an existing analytical solution for the two-dimensional transport of contaminants in a saturated soil layer, for the pulse source, the R program code was developed. The simulation is used to obtain the profiles of contaminant concentration, for a steady groundwater velocity, as a function of distance from the source and time. The problem is analytically solved by leveraging the similarity between the Gaussian (normal) distribution and contaminant concentration distribution, the development of the analytical model (i.e., solution of partial differential equation) by using this similarity is explained step by step since it may be of interest to researchers. Contaminant propagation is modeled using R software, which helps to understand how contaminants migrate through a saturated soil layer. This approach aids in comprehending the mechanisms and spatial dynamics of contaminant dispersion, facilitating the prediction and management of soil and groundwater contamination. The provided R code can be altered for different parameters and time intervals.</p>

Coupled finite element analysis of the dynamics of poroelastic media considering the relative fluid acceleration

AbstractThis paper mainly discusses the dynamics of poroelastic media using the finite element analysis based on the u‐v‐p full formulation, where , , and p denote the solid displacement, relative fluid velocity with respect to solid velocity, and pore fluid pressure. It incorporates the effect of relative fluid acceleration with respect to solid acceleration on soil dynamic response. The ‐‐p formulation is first verified through the comparison with the analytical solution. After that, the response of one‐dimensional saturated soil column and two‐dimensional partially saturated soil layer subjected to vertical loading with different combinations of soil permeability and loading frequency are investigated using the analyses with the ‐‐p and ‐p formulations, based on which the effect of relative pore fluid motion is discussed and the differences in the soil response between two kinds of analysis approaches are examined. Results reveal that the rapid fluid flow has a pronounced effect on soil dynamics and the soil with a greater degree of saturation is more sensitive to the increase of loading frequency and soil permeability. The soil dynamic response can basically be divided into two main categories that represent insignificant and significant flow motion depending on loading frequency and soil permeability. Furthermore, despite vertical loading, horizontal soil response can also be affected by the large relative pore fluid flow when loading frequency and soil permeability are large. In addition, the simplified formulation can still be applicable to predict dynamics of poroelastic media in cases with high loading frequency and low soil permeability.

Analysis of Surface Vibration Response Induced by PHC Piles Driven into Non-Uniform Saturated Soil Layer

Analysis of Surface Vibration Response Induced by PHC Piles Driven into Non-Uniform Saturated Soil Layer

Analytical solution for horizontal vibration of partially embedded pipe pile group in layered saturated soil

AbstractBased on Biot's dynamic wave theory and Novak's plane strain model (PSM), an analytical model for the horizontal vibration of a partially embedded pipe pile group (PEPPG) in layered saturated soil (LSS) that considers the soil‐plugging effect was established: First, the frequency‐domain analytical expressions of the saturated surrounding soil (SSS) and soil plug were obtained by introducing operator decomposition theory and the variable separation method. Second, the analytical solution of the horizontal impedance of a partially embedded pipe pile in the LSS is derived using the coupled condition of the pile–soil interface and transfer matrix method. Finally, an analytical solution for the horizontal impedance of PEPPG in LSS was derived by introducing the horizontal dynamic interaction factor of piles and the superposition method. The derived solution is then reduced and compared with existing theoretical solutions to verify its rationality. In addition, further parametric analysis was conducted to investigate the influences of pile spacing, embedment ratio, properties of layered SSS, and soil‐plugging on the horizontal vibration characteristics (HVCs) of PEPPG.

Propagation Behavior of P1-Wave Passing through Fluid-Saturated Porous Continuous Barrier in Layered Saturated Soil

The fluid-saturated porous continuous barrier has a better vibration isolation effect than the single-phase solid continuous barrier, and layer-forming saturated soils will have an impact on the vibration isolation effect of the barriers due to their irregular layer-forming distribution. Based on Biot’s theory of saturated porous media and Snell’s law, a dynamic model of a fluid-saturated porous continuous barrier in layered saturated soil is established in this study. By introducing the potential function and using the continuous boundary condition of the interface between the saturated soil and the barrier, the analytical solution of the inverse transmission amplitude ratio of a P1-wave passing through the fluid-saturated porous continuous barrier in stratified saturated soil is obtained. The rationality of the proposed method is verified by comparing the solution of the P-wave model at the interface between the elastic medium and the saturated coarse particle interlayer. The differences in the propagation characteristics of fluid-saturated porous continuous barriers in layered saturated soils, homogeneous saturated soils, and layered single-phase soils are analyzed via numerical examples, and the influence of changes in the physical and mechanical parameters of the fluid-saturated porous continuous barriers on the reflectance amplitude ratios under the conditions of a layered saturated soil foundation are also analyzed. The results show that the presence of fluid in the stratified saturated soil model changes the trend of the reflection amplitude ratio with the incidence angle. The reflection amplitude ratio of the P2-wave and the SV-wave increases first and then decreases with the increase in the incident angle, while the reflection amplitude ratio of P1-wave decreases first and then increases. Barrier thickness and porosity change the energy distribution relationship at the interface; a relatively thicker barrier thickness and a higher porosity would result in a higher amplitude of barrier reflections.

Lower-bound shakedown solutions for transportation infrastructures subjected to moving harmonic loads: A focus on saturated subgrade support

As a valuable tool, the shakedown analysis technique can be used to evaluate the long-term resilience of transportation infrastructures subjected to dynamic vehicular loads. In this paper, we introduce a 3-D analytical model that faithfully replicates the geometric complexities inherent in real-world transportation systems. Rather than utilizing the total stress field, modifications to the existing shakedown limit determination methods are executed by focusing on the effective stress field within saturated subsoil. This refined methodology is specifically designed for multi-layered transportation infrastructures like road pavements and rail tracks built over saturated subgrade soils. Upon validation of both the analytical model and the enhanced method for calculating shakedown limits, a systematic investigation into the role of various parameters is conducted. These include the strength ratio, embankment height, and dynamic loading characteristics such as speed and frequency. Subsequent numerical analyses reveal that both the strength ratio and embankment height markedly influence shakedown limits within defined boundaries. Additionally, a comprehensive consideration of load speed and frequency is imperative for an accurate shakedown behavior assessment of the infrastructure in question. The findings validate that the proposed approach offers a more rigorous framework for the optimized design and safety evaluation of transportation systems comprising saturated soil layers.

Thermal consolidation of layered saturated soil under time‐dependent loadings and heating considering interfacial flow contact resistance effect

AbstractDue to the presence of tiny gaps at the interface of two layers of saturated soil, water seepage occurs at a slower rate within these gaps, resulting in laminar flow at the interface. Based on the Hagen‐Poiseuille law, a general imperfect flow contact model was established for layered saturated soil interfaces by introducing the flow contact transfer coefficient Rω and the flow partition coefficient ηω. The investigation focused on the thermal consolidation behavior of layered saturated soil foundations under variable loadings considering the flow contact resistance effect at the interface. By employing the Laplace transform and its inverse transform, a semi‐analytical solution for the thermal consolidation of layered saturated soil foundations was derived. In the context of a two‐layer soil system, the effects of Rω, ηω, and permeability coefficient k on the consolidation process were examined. The obtained results were then compared with three other interfacial contact models, thereby confirming the rationality of the presented model. The study findings revealed that the flow contact resistance effect leads to a clear jump in the pore water pressure. Furthermore, an increase in Rω and a decrease in ηω were found to significantly enhance displacement and pore water pressure, while having minimal impact on the temperature increment. These insights contribute to a more comprehensive understanding of the thermal consolidation behavior of layered saturated soil foundations and underscore the significance of accounting for the flow contact resistance effect in such analyses.

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.

Investigation on the Damping Effect of FST System under Moving Load Using the Track–Tunnel-Layered Saturated Ground Model

In this paper, a single-tier beam-spring-damping system and a two-tier beam-spring-damping system are adopted to simulate the FT (fixed track) and FST (floating slab track) system, respectively. The tunnel is modeled as an infinitely long Euler—Bernoulli beam embedded in the layered saturated soil. By solving the governing equations of the saturated soil and employing the TRM (transmission and reflection matrices) method, the frequency response function of the tunnel-layered saturated soil model is obtained. Making use of the interaction between the tunnel and track systems, the track system is coupled with the tunnel-layered saturated ground model. The solutions for the dynamic response of the track system–tunnel-layered saturated ground model under moving loads in the time–space domain are obtained using the inverse Fourier integral transform. To evaluate the damping effect of the FST system on the vibration of tunnel and soil, four damping coefficients are defined and the vibration results of the FT system–tunnel-layered saturated soil model are compared with those of the FST system–tunnel-layered saturated soil under different moving loads and soil conditions. The numerical results show that both the vibration displacement and acceleration amplitude are attenuated after using the FST system, and the damping coefficient of acceleration is about 30% greater than that of the displacement. In addition, the damping effect of the FST system on the ground surface vibration is associated with the embedded depth of the tunnel and the soil stiffness.

Evaluation of the storage and evapotranspiration terms of the water budget for an agricultural watershed using local and remote-sensing measurements

The understanding of the water budget components, especially evapotranspiration and the amount of water stored in the watershed, is key to water resources management and hydrological modeling in general. In this work, we present the analysis of 13 hydrological years’ measurements of discharge, precipitation, evapotranspiration, and soil moisture over two agricultural watersheds in Eastern Nebraska, United States. These data were used to investigate several facets of the hydrological water budget: water- and energy-balance closures, water budget residues (here, the water budget residue is the remaining imbalance after all water budget terms have been considered; see Eq. (13)), storage in the unsaturated and saturated soil layers, and the evapotranspiration derived from the water budget. Remote-sensing data were also used to assess the spatial variability of net radiation and soil moisture over the basins. Adjusting the eddy-covariance measured evapotranspiration to close the energy budget agreed, in the long term, with the water budget evapotranspiration estimates. The evapotranspiration estimated with storage calculated with soil moisture measurements and recession analysis presented the best agreement with the (adjusted) measured evapotranspiration, but considering only either the vadose zone or the saturated zone for storage estimates still produced reasonable results. We found considerable variability in soil moisture over the basins in the final period of the growing season, coinciding with the time of the year when water budget residues were largest.

Lateral dynamic response of single floating piles in saturated soil layer

AbstractA closed‐form formulation for the dynamic analysis of lateral response of floating piles in a saturated finite‐thickness soil layer is presented in this paper. Governing equations of the saturated soil are established on the basis of Biot's poroelastic theory, solution to which results in the lateral resistance of surrounding saturated soil to pile deflection. Closed‐form expressions of the lateral deformations of pile along depth and the dynamic compliances at pile head are obtained by solving a system of linear equations from the boundary and continuity conditions, instead of solving sophisticated integral equations in existing boundary integral methods. The parametric study focuses on exploring the sensitivity of pile compliances and deformations to the main problem parameters, including pile‐soil modulus ratio and soil permeability.

Kinematic response of floating piles in a saturated soil layer subjected to seismic S-wave propagation

A mathematical formulation for the seismic analysis of floating piles embedded in a saturated soil layer to vertically propagating S waves is presented in this paper. Pivotal to the formulation is the establishment of a closed-form expression for the lateral soil reaction to pile displacement, and results from expressions for the free-field and scattered soil displacements obtained from Biot’s governing equations. Subsequently the pile is analysed as Euler-Bernoulli beam and the soil column between the pile tip and the bedrock is analysed as one-dimensional shear beam. This results in expressions for the kinematic response factors, that provide the frequency-dependent pile head displacement and rotation as function of the free-field soil movement. Validation of the developed model is followed by a discussion on the sensitivity of pile response to the two-phase nature of soil, focused on informing researchers and practitioners on the uncertainties introduced in conventional seismic analysis, where the foundation soil is modelled as single-phase medium.

Hydrological setting controls 137Cs and 90Sr concentrations in a headwater catchment in the Chornobyl Exclusion Zone

Concentration-discharge relationships are widely used to understand the hydrological processes controlling river water chemistry. This study investigates how hydrological processes affect radionuclide (137Cs and 90Sr) concentrations in surface water in headwater catchments within the Chornobyl Exclusion Zone (ChEZ) in Ukraine. In the flat wetland catchments, the depth of the saturated soil layer changes little throughout the year, but changes in the saturated soil surface area during snowmelt and immediately after rainfall affect water chemistry by changing the opportunities for contact between the surface water and the soil surface. On the other hand, in the slope catchments where there are few wetlands, the water chemistry of river water is governed by changes in the relative contributions of “shallow water” and “deep water” due to changes in the catchment water supply pathways feeding the rivers. In this study, no correlations were observed between dissolved or suspended 137Cs concentrations and either discharge rates or competitive cations, but the solid-liquid ratio of 137Cs was found to be significantly and negatively correlated with water temperature. However, 90Sr concentrations in surface water were found to be strongly related to the water pathways for each of the catchments. Moreover, contact between the surface water and the soil surface and changes in the relative contributions of shallow and deep waters to stream water were correlated with changes in 90Sr concentrations in surface water in wetland and slope catchments, respectively. The study concludes that 90Sr in rivers inside the ChEZ are strongly affected by the water pathways in headwater catchments. Additional studies will be necessary to clarify the details of sorption/desorption reactions.

A Wave Based Method for the analysis of a fully and partially saturated halfspace under harmonic loading

The dynamic response of a fully or partially saturated halfspace due to vibrations from traffic or rotating machinery can significantly be influenced by water and air phases within the pores. An extension of the Wave Based Method (WBM) is presented to consider these influences and to propose an efficient numerical method for the dynamic analysis of fully and partially saturated soil layers. Biot’s theory for the low frequency range and the Berryman-Thigpen-Chin model (BTC model) are introduced and a transmitting boundary condition is implemented to approximate the Sommerfeld radiation condition. Moreover, coupling conditions for dry, fully and partially saturated soil layers are formulated and involved into a weighted Galerkin approach. The accuracy of the WBM is evaluated for a fully saturated and a layered halfspace with different degrees of saturation. For this, numerical examples are compared with reference solutions from literature. It is shown that the WBM delivers adequate field responses and succeeds in modeling different types of system behaviour, which are characteristic for a fully saturated and layered halfspace.

Validity of Local Thermal Equilibrium Assumption for Heat Transfer in a Saturated Soil Layer

The assumption of local thermal equilibrium (LTE) between solid and fluid phases commonly is used for studies of heat transfer in saturated soil and is valid for a wide range of conditions. However, for certain conditions, the heat transfer process may give rise to local thermal nonequilibrium (LTNE) in which adjacent solid and fluid phases have different temperatures. This note presents the results of a numerical study of the validity of the LTE assumption for one-dimensional heat transfer in a saturated soil layer with fluid flow. For the conditions investigated, the LTE assumption holds for soil with particle sizes smaller than the gravel range. For soil with particles sizes in the gravel range and larger, the LTE assumption may be valid or invalid, depending primarily on fluid discharge velocity, with higher fluid velocity values more likely to produce LTNE conditions.

Vertical dynamic response of single floating piles in poroelastic soil

This paper presents a closed-form formulation for the time-harmonic response of single floating piles that are embedded in a saturated soil layer of finite thickness. The frictional force of surrounding soil to pile vertical motion is first established, considering the soil layer as homogeneous isotropic poroelastic medium that obeys Biot’s governing equations. The pile and the soil column underlying the pile tip are modelled using one-dimensional rod theory, and then closed-form solution is obtained from the boundary and continuity conditions, instead of numerically solving complicated integral equations that are used in the common boundary integral methods. Finally, we use arithmetic examples to identify the sensitivity of the dynamic pile impedance and of the soil reactions to the main geometrical and material problem parameters.

Soil arching evolution caused by shield tunneling in deep saturated ground

Shield tunneling is accompanied by variations of stress and displacement in soil, which could induce the soil arching effect. Although there have been many studies on the soil arching effect caused by shield tunneling, the research on deep-buried and saturated conditions is still lacking. In this study, a finite element model was firstly built and verified by field data. Then, two hypothetical finite element models were established with two different strata to investigate the stress transfer mechanisms, the development law of excess pore water pressure, and the soil arching evolution of deep-buried tunnel. The methods to determine the arch zone and loosened zone were proposed and verified, which were adopted to compare the differences of soil arching effect between saturated sandy and clayey soil layers. The results show that the heights of the arch zone and loosened zone in the saturated sandy soil layer are both higher than those in the saturated clayey soil layer after the shield tunneling. The subsequent strata consolidation resulted in a 36% reduction in the arch zone height in clayey soil, which means that time effect for the soil arching is significant. Compared with Terzaghi's loosening earth pressure theory, in deep ground, the theoretical overburden pressure is only 5.0% larger than the numerical results for sandy soil but 18.3% less than that for clayey soil. The numerical results can bring new sights about the soil arching evolution caused by shield tunneling and the corresponding tunnel overburden pressure in deep saturated ground.

Transient analysis of monopiles embedded in layered saturated soils under vertical excitations

This paper investigates the transient dynamic response of vertical loaded monopiles embedded in layered saturated soils. Firstly, the piles are modeled as the one-dimensional rods, which are solved by the finite element method (FEM). Then the analytical layer-element solutions of layered saturated soils are used as the kernel functions of the boundary element method (BEM), and the boundary integral equation of the soils are further acquired. By introducing the pile-soil interface conditions, the transient response of the pile-soil system is obtained with the aid of the FEM-BEM coupled method. The proposed method is verified by comparing the results with those in existing literature and ABAQUS. Finally, parametric studies are conducted to determine the effects of the length-diameter ratio, pile-soil modulus ratio, stratification and permeability.

Simplified mathematical modeling to plane strain consolidation considering unsaturated and saturated conditions for ground with anisotropic permeability

Road embankment where the unsaturated soil layer lies above the saturated soil layer is often encountered in geotechnical engineering, but the analytical models for evaluating the plane stain consolidation characteristics of an unsaturated–saturated ground are limited. With a combination of the consolidation theories for saturated and unsaturated soils, this paper thus develops a plane strain consolidation model for exploring the transient behavior of unsaturated–saturated soils subjected to instantaneous loading. A semi-analytical solution, which is a simple tool for assessing unsaturated–saturated soil consolidation, is proposed by making use of decoupling strategy, Fourier expansion as well as Laplace transformation. Further, the proposed solution in this paper is validated by the published analytical or semi-analytical solutions in some specific cases. By implementing the proposed solution into a computation, the consolidation behavior of an unsaturated–saturated subgrade is presented, and the effects of important factors, including the anisotropic permeability ratio and interlayer permeability ratio, are studied. The anisotropic permeability ratio and interlayer permeability ratio are significant indexes to change the consolidation rate of lower soils so that the prefabrication of lateral drainage boundary on both sides of the unsaturated–saturated subgrade would accelerate its consolidation.