Single Soil Layer Research Articles

Energy-Based Approach: Analysis of a Laterally Loaded Pile in Multi-Layered Non-Linear Elastic Soil Strata

Several studies have been reported in published literature on analytical solutions for a laterally loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. The present study describes a new continuum-based analysis or energy-based approach for predicting the pile displacement responses subjected to static lateral loads and moments considering the soil non-linearity. This analytical analysis treats the pile as an elastic Euler–Bernoulli beam and the soil as a three-dimensional (3D) continuum in which the non-linear elastic properties are described by a modulus degradation relationship. The principle of virtual work was applied to the energy equation of a pile–soil system in order to obtain the governing differential equation for the pile and soil displacements. An iterative procedure was adopted to solve the equations numerically using a finite difference method (FDM). The pile displacement response was obtained using the software MATLAB R2021a, and the results from the energy-based method were compared with those obtained from the field test data as well as the finite element analysis (FEA) based on the software ANSYS Workbench 2021R1. The present study investigated the effect of explicit incorporation of soil properties and layering through a parametric study in order to understand the importance of predicting appropriate pile displacement responses in a linear elastic soil system. The responses indicated that the effect of soil layers and their thicknesses, pile properties and the variation in soil moduli have a direct impact on the displacements of piles subjected to lateral loading. Hence, a proper emphasis has to be given to account for the soil non-linearity. Considering the effect of soil non-linearity, it is observed that the results obtained from the energy-based method agreed well with the field measured values and those obtained from the FEA. The results indicated a difference of approximately less than 7% between the proposed method and the FEA. The approach presented in this study can be further extended to piles embedded in multi-layered soil strata subjected to the combined action of axial loads, lateral loads and moments. Furthermore, the same approach can be extended to study the response of the soil to group piles.

Energy-Based Approach: Analysis of a Vertically Loaded Pile in Multi-Layered Non-Linear Soil Strata

Numerous studies have been reported in the published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an analytical model based on the energy-based approach to obtain displacements in an axially loaded pile embedded in multi-layered soil considering soil non-linearity. The developed analytical model incorporating Euler-Bernoulli beam theory proved to be an effective way in estimating the load-displacement responses of piles embedded in multi-layered non-linear elastic soil strata. The differential equations are solved analytically and numerically using the variational principle of mechanics. A parametric study investigated the effect of explicit incorporation of soil properties and layering in order to understand the importance of predicting appropriate pile displacement responses in linear elastic soil system. It is clear from the results that the analyses which consider the soil as a single homogeneous layer will not be able to produce an accurate estimation of the pile stiffnesses. Therefore, it is highly important to account for the effect of soil layering and the non-linear response. The pile displacement response is obtained using the software MATLAB R2019a and the results from the energy-based method are compared with those obtained from the field test data as well as the Finite Element Analysis (FEA) based on the software ANSYS 2019R3. The non-linear elastic constitutive relationship which described the variation of secant shear modulus with strain through a power law has shown reasonably accurate predictions when compared to the published field test data and the FEA. The developed mathematical framework is also more computationally efficient than the three-dimensional (3D) FEA.

Influence of Groundwater Depth on Pile–Soil Mechanical Properties and Fractal Characteristics under Cyclic Loading

The analysis of the behavior of soil and foundations when the piles in offshore areas are subjected to long-term lateral loading (wind) is one of the major problems associated with the smooth operation of superstructure. The strength of the pile-soil system is influenced by variations in the water content of the soil. At present, there are no studies carried out analyzing the mechanical and deformational behavior of both the material of the laterally loaded piles and soil with groundwater level as a variable. In this paper, a series of 1-g model tests were conducted to explore the lateral behavior of both soil and monopile under unidirectional cyclic loading, based on the foundation of an offshore wind turbine near the island. The influence of underground water level and cyclic load magnitude on the performance of the pile–soil system was analyzed. To visualize the movements of soil particles during the experimental process, particle image velocimetry (PIV) was used to record the soil displacement field under various cyclic loading conditions. The relationship curves between pile top displacement and cyclic steps, as well as the relationship curves between cyclic stiffness and cyclic steps, were displayed. Combined with fractal theory, the fractal dimension of each curve was calculated to evaluate the sensitivity of the pile–soil interaction system. The results showed that cyclic loading conditions and groundwater depth are the main factors affecting the pile–soil interaction. The cyclic stiffness of the soil increased in all test groups as loading progressed; however, an increase in the cyclic load magnitude decreased the initial and cyclic stiffness. The initial and cyclic stiffness of dry soil was higher than that of saturated soil, but less than that of unsaturated soil. The ability of the unsaturated soil to limit the lateral displacement of the pile decreased as the depth of the groundwater level dropped. The greater the fluctuation of the pile top displacement, the larger the fractal dimension of each relationship curve, with a variation interval of roughly 1.24–1.38. The average increment of the cumulative pile top displacement between each cycle step following the cyclic loading was positively correlated with fractal dimension. Based on the PIV results, the changes in the pile–soil system were predominantly focused in the early stages of the experiment, and the short-term effects of lateral cyclic loading are greater than the long-term effects. In addition, this research was limited to a single soil layer. The pile–soil interaction under layered soil is investigated, and the results will be used in more complex ground conditions in the future.

Computation of total soil organic carbon stock and its standard deviation from layered soils

To assess carbon sequestration in the agricultural and natural systems, it is usually required to report soil organic carbon (SOC) as mass per unit area (Mg ha-1) for a single soil layer (e.g., the 0-0.3 m ploughing layer). However, if the SOC data are reported as relative concentration (g kg-1 or %), it is required to compute the SOC stock and its standard deviation (SD) for a given layer as the product of SOC concentration and bulk density (BD). For a proper computation, it is required to consider that these two variables are correlated. Moreover, if the data are already reported as SOC stock for multiple sub-layers (e.g., 0-0.15 m, 0.15-0.3 m) it is necessary to compute the SOC stock and its SD for a single soil layer (e.g., 0-0.3 m). The correlation between stocks values from adjacent and non-adjacent soil sub-layers must be accounted to compute the SD of the single soil layer.The present work illustrates the methodology to compute SOC stock and its SD for a single soil layer based on SOC concentration and BD also from multiple sub-layers. An Excel workbook automatically computes the means of stocks and SD saving the results in a ready-to-use database.•Computation of a carbon (SOC) stock and its standard deviation (SD) from the product between SOC concentration and bulk density (BD), being correlated variables.•Computation of a SOC stock and its SD from the sum of SOC stocks of multiple correlated sub-layers.•An Excel workbook automatically computes the means of SOC stocks and SD and saves the results in a ready-to-use database.

The rainwater retention mechanisms in extensive green roofs with ten different structural configurations.

Rainfall infiltration, rainwater retention, runoff and evapotranspiration (ET) are important components of the water balance in green roofs. These components are expected to be influenced by variations in the structural configurations (i.e., substrate layers) of green roofs. This study explores the influence of layered soil and green roof configurations on the rainwater retention capacity (RRC) of the roofs as compared to conventional improvements (i.e., soil conditioning and enhanced substrate depth). Ten different extensive green roof modules were designed by varying the substrate materials, substrate depths, storage/drainage layers and vegetation layers. For all modules, the RRCs ranged from 34 to 59%. The RRCs of layered soil were 1-4% higher than that for single-layer soil. The RRC increased by 13% in the presence of a water storage module. It can be concluded that highest RRC corresponds to a combination of high-permeability soil in the upper layer along with a relatively large water holding capacity in the deep layer. Water storage layer and layered soil could significantly delay the water stress in vegetation. The importance of wick irrigation, vegetation types, back-to-back rain events and the ET rate on the RRC were also discussed.

A Unified Model for Analyzing Comprehensive Behaviors of Deepwater Anchors

Anchors may exhibit various complicated behaviors in the seabed, especially for deepwater anchors including gravity installed anchors (GIAs) and drag embedment plate anchors (drag anchors), stimulating the development of an efficient analytical tool that applies to a variety of anchors. The present paper introduces a unified model for analyzing different anchor behaviors in both clay and sand, consisting of unified concepts, mechanical models, and analytical procedure. The kinematic behaviors of the anchors are classified uniformly as three types, i.e., diving, pulling out, and keying. By utilizing the least-force principle, various anchor properties, such as the ultimate pullout capacity (UPC), failure mode, movement direction, embedment loss, and kinematic trajectory, can all be determined by the combination and analysis of the three behaviors. Applications of the model are demonstrated summarily, by solving the UPC and the failure mode of anchor piles and suction anchors, the kinematic trajectory of drag anchors in a single soil layer or layered soils, the maximum embedment loss (MEL) of suction embedded plate anchors (SEPLAs) and OMNI-Max anchors, and the kinematic behavior of OMNI-Max anchors. Compared to existing theoretical methods, this unified model shows strong applicability and potentiality in solving a variety of behaviors and properties of different anchors under complicated seabed conditions.

Study on negative friction of pile foundation in single homogeneous soil layer in collapsible loess area of Northwest China

Study on negative friction of pile foundation in single homogeneous soil layer in collapsible loess area of Northwest China

Accounting for field-scale heterogeneity in the ecohydrological modeling of large arid river basins: Strategies and relevance

It remains a great challenge to represent field-scale (e.g., meters to tens of meters) heterogeneity in the ecohydrological modeling of large river basins due to the tradeoff between spatial resolution and computational cost. This study improved an existing ecohydrological model, HEIFLOW, by introducing the subgrid structure of land cover, multilayer soil water simulation and accurate spatial coverage of irrigation within the grid. These improvements enable the model to provide reliable simulations over a wide spectrum of spatial scales, from the field scale to the large-basin scale (i.e., 104 to 105 km2). The new model was implemented in the Heihe River Basin, the second largest endorheic river basin in China, with a grid size of 1 km by 1 km for a modeling domain of approximately 90,589 km2. The major study findings include the following. First, in arid areas with sparse vegetation, ignoring the subgrid characteristics of land surfaces will lead to significant errors that may be further propagated when the modeling results are used to support management or scaled up for larger-scale climate modeling. Second, the multilayer soil structure can improve ecohydrological simulations in terms of temporal variations, and it is necessary to separate a thin surface layer from the soil zone in arid areas. In the case study, a single-layer soil structure would introduce greater than 10% error in simulating the annual maximum leaf area index (LAI). Third, considering the accurate spatial coverage of irrigation within the grid cell is critical for successful simulations of ecohydrological processes in arid areas. In the case study, accurate spatial coverage would lead to −31%, +46%, and +13% changes in the simulated average soil evaporation, transpiration and LAI, respectively, over the entire area with irrigation. Overall, this study provides a unique perspective to address the scale issue in ecohydrological modeling and reveals the importance of field-scale heterogeneity to the management of water resources and ecosystems based on ecohydrological modeling.

Slope stability evaluation using neural network optimized by equilibrium optimization and vortex search algorithm

A dependable evaluation of the stability of slopes is a prerequisite in many construction projects. Although machine learning models have been satisfactorily used for this purpose, combining them with metaheuristic optimizers has resulted in a larger accuracy. This study, therefore, suggests the use of equilibrium optimization (EO) and vortex search algorithm (VSA) for optimizing a multi-layer perceptron neural network (MLPNN) employed to anticipate the factor of safety of a single-layer soil slope. Two hybrid models, as well as the regular MLPNN, are fed by a total of 630 data acquired from finite element simulations. The results, first, showed the applicability of artificial intelligence in this field. Next, reducing the training root mean square error (RMSE) of the MLPNN (from 0.4715 to 0.3891 and 0.4383 by the EO and VSA, respectively) revealed the efficiency of the used algorithms in remedying the computational weaknesses of this model. Moreover, the testing RMSE declined from 0.5397 to 0.4129 and 0.5155, which indicates a higher generalization ability of the hybrid models. Furthermore, due to the larger accuracy of the EO-based ensemble, this algorithm outperformed the VSA in optimizing the MLPNN.

Effects of Soil Profile on the Transient Performance of Substation Grounding System

<table width="593" border="1" cellspacing="0" cellpadding="0"><tbody><tr><td valign="top" width="387"><p>Lightning transient characteristic of the grounding grid is fundamental for optimum performance of lightning protection of a substation. In order to design an appropriate grounding system for such substation, it is important to study its transient characteristics because the high impulse current is significantly different compared to power frequency current. In this paper, substation grounding grid model was developed using CDEGS software to analyze the grid transient performance in terms of ground potential rise (GPR), touch voltage and step voltage when the grounding system is struck by a lightning impulse current. Several parameters, such as lightning current amplitude, feed point and the number of sub-grids, were altered to study their relationship with the transient performance. The maximum transient GPR, touch voltage, and step voltage increase as the lightning current amplitude increase. The maximum transient GPR and step voltage are the highest at the corner of the grounding grid while the maximum touch voltage is the highest at the centre of the grounding grid. In addition, the maximum transient GPR and step voltage decrease when the number of sub-grid increases. In contrast, the touch voltage slightly increases as the number of sub-grid increases. The maximum transient GPR, and step voltage are the highest at the 2-layer and the lowest at the uniform soil or single-layer soil.</p></td></tr></tbody></table>

Metaheuristic-hybridized multilayer perceptron in slope stability analysis

This research is dedicated to slope stability analysis using novel intelligent models. By coupling a neural network with spotted hyena optimizer (SHO), salp swarm algorithm (SSA), shuffled frog leaping algorithm (SFLA), and league champion optimization algorithm (LCA) metaheuristic algorithms, four predictive ensembles are built for predicting the factor of safety (FOS) of a single-layer cohesive soil slope. The data used to develop the ensembles are provided from a vast finite element analysis. After creating the proposed models, it was observed that the best population size for the SHO, SSA, SFLA, and LCA is 300, 400, 400, and 200, respectively. Evaluation of the results showed that the combination of metaheuristic and neural approaches offers capable tools for estimating the FOS. However, the SSA (error = 0.3532 and correlation = 0.9937), emerged as the most reliable optimizer, followed by LCA (error = 0.5430 and correlation = 0.9843), SFLA (error = 0.8176 and correlation = 0.9645), and SHO (error = 2.0887 and correlation = 0.8614). Due to the high accuracy of the SSA in properly adjusting the computational parameters of the neural network, the corresponding FOS predictive formula is presented to be used as a fast yet accurate substitution for traditional methods.

Behaviors of drag embedment anchor in layered clay profiles

Layered soil profiles can complicate the installation of an offshore foundation and affect its performance. The goal of this study is to further understand the drag trajectory and capacity of a drag embedded plate anchor in layered clay profiles. Drag embedment tests using a model anchor were performed in various test beds made of marine clay with different profiles of undrained shear strength. The trajectory and orientation of the anchor during drag embedment were captured by a magnetometer. This innovative instrument is capable to measure the six-degree-of-freedom movements for buried objects in soil. A prediction model based on the simplified plasticity theory was calibrated against experimental results. The calibrated model can well predict anchor capacity, trajectory and pitch in single-layer soil profiles, including the constant and the linearly increasing shear strength profiles. For the layered clay profiles with a stiff layer interbedded in soft clay, one key factor determining whether or not the anchor can penetrate into the stiff layer is the pitch of the fluke when approaching the stiff layer, and a flattened pitch may be favorable for penetration. The stiff layer depth and the mooring line thickness significantly affect the pitch angle. Moreover, a lower undrained shear strength ratio of the stiff layer over surrounding soft soil facilitates the anchor to penetrate into the stiff layer.

Estimation of the soil hydraulic properties from field data by solving an inverse problem

Estimating unsaturated soil hydraulic properties to predict water dynamics through a vertical soil profile under the effects of irrigation, drainage and evapotranspiration is imperative for managing soils in the arid regions. The aim of this work was to determine the soil water retention curve and the hydraulic permeability function of a bare soil profile in a Tunisian oasis threatened by salinization. The developed model combines a numerical inversion of the unsaturated flow equation with the BOBYQA optimisation algorithm. The direct model solved the Richards equation using a cell-centred finite difference model. Hydraulic properties were described by van Genuchten-Mualem models. Input data for the inverse problem are the infiltration flow, soil water contents and pressure heads measured during ponded infiltration and internal drainage tests. Numerical simulations of these two tests were performed considering a homogeneous single-layer soil profile but a better fitting between measured and simulated water contents was obtained when the soil profile was divided into five sub-layers. The hysteresis phenomenon was highlighted from the soil water retention and the relative permeability curves corresponding to the ponded infiltration and internal drainage tests.

Semi-analytical prediction for tunnelling-induced ground movements in multi-layered clayey soils

This paper develops a semi-analytical method to calculate the ground movements due to tunnelling in multi-layered clayey soils which are usually encountered in urban areas. The proposed method is based on the modified Loganathan-Poulos formula combined with the elastic equivalent theory. The key issue disposed in current study is the transformation of the boundary of excavation and the boundary after convergence from multi-layered soil system into single layer soil system. The proposed method is verified through the comparisons with previous associated studies associated with the field measurements from five well-documented cases. A parametric study based on the situation that the interlayer is arranged between the upper and lower soil layer is conducted to explore the effects of the mechanical properties and dimensional variables of the interlayer on ground settlements. The results indicate that the soil stratification has a significant impact on ground movements induced by tunnelling in multi-layered clayey soils.

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.

Study on the integrated distribution coefficient of ammonium N migration in layered soil.

Adsorption is an important mechanism for contaminant transport in groundwater, which results in retardation of contaminant migration. Different types of soils have different amounts of ammonium N adsorption, and ammonium N will experience different types of soil as it migrates through the actual soil environment. To better explore the integrated adsorption effect of ammonium N as it moves through the soil, layered soil was considered as a whole in this study. Under the condition that ammonium N is not transformed, the relationship between the distribution coefficient of ammonium N in layered soil and that in a single soil layer was explored through batch and column experiments. The results showed that the integrated distribution coefficient of ammonium N in mixed soil was in good agreement with the linear superposition relationship between the distribution coefficient and mass of each single soil layer. In the one-dimensional column simulation experiment, a mathematical model of pollutant migration in soil was used to simulate the migration of ammonium N in the soil and verify parameters of the model. The model-fitted ammonium N concentration values were in good agreement with the measured values. The overall retardation factor of layered soil was linearly sum up of the retardation factor of a single soil layer by the thickness of each layer. The distribution coefficient of ammonium N in layered soil was integrated to the cumulative value of the product of the distribution coefficient and the thickness ratio of each single soil layer. When the difference in the density of the soil layers was small, the relationship between the integrated distribution coefficient of the layered soil and the distribution coefficient of a single layer could be adequately described by using the linear superposition relationship of the layered distribution coefficient and thickness.

Analytical Solutions for Thermomechanical Soil Structure Interaction in End-Bearing Energy Piles

Analytical solutions for axial displacement, strain, and stress in an end-bearing energy pile subjected to a thermal load and a combined thermal and mechanical load have been derived and validated against full-scale in situ pile tests. The pile is embedded into a single layered and multilayered soil underlain by stiff bedrock. The thermoelastic constitutive law has been used to describe pile behavior, while soil–pile interface has been characterized by a linear elastic load-transfer function. In the case of thermal load, the solutions for a single-layered soil show that both the absolute minimum magnitude of axial strain and the absolute maximum magnitude of axial stress develop at the pile tip. Thus, the maximum compressive and maximum tensile stress develops at the pile tip for net heating and cooling scenarios, respectively. When subjected to combined thermal and mechanical load, the shapes of the corresponding displacement and strain and stress response curves are dominated by either the response to thermal or the response to mechanical load, depending on the ratio of the magnitudes of the temperature change and the axial force applied at the pile head. The analytical solutions provide not only a quick quantitative assessment, but also an in-depth qualitative understanding of the thermomechanical soil structure interaction in energy piles.

Behavior of Geotextile-Encased Single Stone Column in Soft Soils

Stone columns have become a widely used method of increasing bearing capacity of soft soils. This study investigates floating stone columns with and without encasement in soft soils. Although the stone columns in single-layered soil have been studied extensively, stone columns constructed in a base of varying soil layers are not fully understood. In the present study, the behavior of both single-layered soft soil and layered soil consisting of loose sand overlaying the soft soil was investigated by using small-scale laboratory pilot tests. The bearing capacity of soft soil was improved in all cases of stone column application. The contribution of stone columns on the bearing capacity of soft soil was presented by the term bearing improvement ratio (BIR). With a non-encased stone column in single-layered soft soil, the BIR was about 3.3-fold and with geotextile encasement in the same soil, the improvement ratio increased to 3.4-fold. For a non-encased stone column in layered soils, the BIR was about 2.0-fold and with geotextile enhancement in the same soil, this improvement ratio increased to 4.0-fold. The inclusion of geotextiles resulted in improved bearing capacity by distributing the induced stresses over larger areas. The maximum bulging of non-encased stone column in single-layered soft soil was observed at the depth of 1.5 times the original diameter of the stone column from the top, whereas for encased stone column in single-layered soft soil, the maximum bulging was transferred to a depth of 3.0 times the original diameter of the stone column.

Cross validation of analytical solutions against the computational model predictions of the response of end bearing energy pile

Predictions of responses of a single energy pile to a combined mechanical and thermal loading are presented. They were obtained from computational and analytical models. The former model provided predictions based on a coupled thermal hydro-mechanical finite element analysis while the predictions of the latter were obtained from the recently derived analytical solutions. The energy pile is surrounded by a single uniform soil layer underlain by a very stiff bedrock. Two scenarios of temperature history were considered. In the first scenario the pile remained in a net heated state while the second one induced a net cooled state. In both loading scenarios a compressive axial load was applied at the pile head prior to the thermal loading. The net heating induced an upward axial displacement, tensile strain and compressive stress while the net cooling induced a downward vertical pile displacement, compressive strain and tensile stress. In spite of different methods of obtaining the soil stiffness for computational and analytical models the predictions of the axial pile displacement, stress and strain show a very good agreement.

Cross validation of analytical solutions against the computational model predictions of the response of semi floating energy pile

In this study, responses of a single semi floating energy pile to a combined thermal and mechanical load are predicted by analytical and computational models. The axial compressive load applied at the pile head comprises the mechanical load while the thermal load is applied by prescribing the temperature difference history to the pile. The temperature difference is the difference between the temperatures of the pile and the surrounding soil. The energy pile is surrounded by a single uniform soil layer underlain by the bedrock, which is flush with the pile tip. A selected combination of thermal and mechanical loads resulted in an upward displacement, tensile strain and compressive stress in the case of heating. In the case of cooling the load combination resulted in a downward displacement, compressive strain and tensile stress. In spite of different methods of obtaining soil stiffness parameters for analytical and computational models the predictions of both methods are in a very good agreement.