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The horizontal drainage layer is widely used in blow-filling and road foundation-filling projects. Due to the change in the groundwater table and horizontal drainage layer, the double-layer ground sometimes shows two states of unsaturated and saturated. Meanwhile, the two-layered unsaturated–saturated soil system ground is very widely distributed in nature. In this paper, based on the soil consolidation theory, semi-analytical solutions of excess pore pressures and the settlement of a two-layered unsaturated–saturated soil system containing a horizontal drainage layer under different drainage layer boundary are obtained by using the Laplace transform technique and decoupling method. And the model in this paper can be well degraded to two classic soil consolidation ones and presents an excellent agreement with references, showing excellent accuracy and reliability of the solutions obtained in this paper. Further, by selecting parameters to analyze their effects on the consolidation of the modelling in this paper. The results show that the horizontal drainage layer can provide additional drainage channels to accelerate the consolidation of two-layered ground in an unsaturated–saturated soil system, while the location of the horizontal drainage layer at 0.3 H -0.5 H can most efficiently accelerate the ground consolidation process. When drainage conditions are poor, the settlement completion time is prolonged. [ABSTRACT FROM AUTHOR]

Bentonite and bentonite mixtures are used as buffer material for deep geological radioactive waste repositories. The proper determination of bentonite maximum swelling pressure is important as it influences the long-term stability and sealing characteristics of the barrier system. We developed a constrained machine learning model based on extreme gradient boosting (XGBoost) algorithm tuned with grey wolf optimization (GWO) to determine the maximum swelling pressure of bentonite and bentonite mixtures. We integrated a penalty term into the XGBoost algorithm's loss function to constrain the model during the training phase ensuring meaningful predictions. To this end, we compiled a dataset containing 305 experimental data of bentonite maximum swelling pressure and other relevant soil properties including montmorillonite content, liquid limit, plastic limit, plasticity index, initial water content, and soil dry density to develop the model. The performance of the hybrid GWO-XGBoost model was benchmarked against feed-forward and cascade-forward neural network models. The GWO-XGBoost model showed a better performance in estimating the experimental values comparing to the other models, thereby demonstrating its effectiveness and reliability in determining the maximum swelling pressure of bentonite and bentonite mixtures. [ABSTRACT FROM AUTHOR]

Soil curling, a natural phenomenon in thin soil fragments induced by desiccation cracks, exacerbates the potential threats of soil cracking. Analyzing soil curling, especially in conjunction with soil desiccation cracking, poses challenges in existing numerical investigations due to factors such as inadequate knowledge of the soil curling mechanism, complex soil characteristics with diverse parameters, moving boundary conditions during deformation, and crack initiation and growth. This study aims to uncover the soil curling mechanism using a fully coupled hygro-mechanical ordinary state-based peridynamic (OSB PD) model and its corresponding monolithic solutions. Specifically, the PD form of the moisture diffusion equations for saturated and unsaturated states are derived by employing the variational principle with nonconservative Lagrangian action and peridynamic differential operator (PDDO). Also, the PD bond force is derived by considering the energy equivalent principle for a fully coupled hygro-mechanical model. A model of soil strip desiccation deformation and curling is constructed while considering realistic moving boundaries of moisture and displacement with relevant parameters, and soil characteristics evolution from saturated to unsaturated states. It successfully captures the entire curling process, including concave-up and concave-down curling. Furthermore, this study explores the influencing factors of liquid limit, extra evaporation surface, and thickness on the curling performance. • Peridynamic form of moisture diffusion equation for saturated and unsaturated soil. • Coupled multi-dimensional hygro-mechanical ordinary state-based peridynamic model. • A monolithic implicit solution of coupled equations for soil desiccation analysis. • Complete curling behavior due to the consideration of unsaturated characteristics in soil. • Soil curling mechanism induced by differential shrinkage and multiple influence factors. [ABSTRACT FROM AUTHOR]

Analytical expressions are presented for the determination of the pore air and pore water pressure parameters in unsaturated soils under undrained conditions. The kinematic constraints governing the volumetric alterations of the soil skeleton and fluid phases, in conjunction with the effective stress principle, are utilised to derive the pore pressure parameters. The effect of hydraulic hysteresis on the effective stress parameter and the soil water characteristic curve is considered in the solutions. The expressions derived are validated against the experimental data available in the existing literature. It is demonstrated that: − with an increase in the degree of saturation of the soil, both pore pressure parameters increase and approach unity; − the change in the pore water pressure in an unsaturated soil under undrained compression is greater than the change in the pore air pressure; − the pore pressure parameters are strongly dependent on the compressibility of the soil skeleton; − the hydraulic hysteresis has a substantial influence on the pore water pressure parameter; − the pore air pressure parameter is slightly affected by the hydraulic hysteresis and it is mostly influenced by the compressibility of the air phase; − an increase in the degree of saturation leads to a reduction in the instantaneous settlement; and − the hydraulic state has a significant impact on the instantaneous settlement of unsaturated soil. [ABSTRACT FROM AUTHOR]

Based on the motion theory of three-phase poroelastic medium, the torsional vibration of a pile in unsaturated soil is investigated contemplating the impact of construction disturbance. The soil is segregated into a series of vertical annular zones, with the soil parameters of each zone varied to simulate its radial inhomogeneity. Subsequently, the governing equations for pile-soil interaction are formulated and solved, leading to the derivation of an analytical solution for torsional vibration in the frequency domain. Following a validation process, the proposed solution underwent parametric analysis to scrutinize the influence of soil saturation degree and construction disturbance on the torsional vibration characteristics of the pile. [ABSTRACT FROM AUTHOR]

Prefabricated vertical drains (PVDs) are an established ground improvement method. Mimicking drinking straws, PVDs are installed to convey vacuum pressure in the ground and lift groundwater. However, the dewatering performance is suboptimal in consolidating fine-grained layers. Practical applications have shown that better dewatering performance is achieved through aiding the vacuum dewatering with an air-booster. Air-boosters are installed in an alternating pattern adjoining PVDs, increasing pore pressures and unclogging pores. This study presented a numerical model for this vacuum and air-booster combined dewatering solution. Taking account of the large strain deformation, this model used the Lagrangian-convective coordinate to track the global and local deformation of the soil layer separately, thus enabling accurate determination of consolidation. This model also considered air-booster induced unsaturated conditions and the associated effects on water flow. The numerical model was verified against field test results and laboratory measurements. [ABSTRACT FROM AUTHOR]

Land and groundwater pollution is increasingly threatening public health and ecological safety. Vertical drain is recognised as an effective solution to clean up contaminated lands. Clean-ups often involve complicated hydro-chemical transport processes and are difficult to manage. This study presents a consolidation–solute transport model to assist with clean-up management. The model can predict coupled consolidation and chemical transport in diverse ground conditions, e.g., fully or partially saturated, less to highly deformable, or permeable to impermeable layers. To factor in the varied ground conditions, the model integrates the unsaturated flow characteristics, finite deformation theory and finite difference method into a set of governing equations and numerical solutions. The model was experimentally verified and then applied to examine effects of soil saturation conditions, solute transport conditions, and consolidation efforts on solute transport. The results show that the dispersion process contributes to the chemical clean-up, whereas the contribution becomes less noticeable in unsaturated conditions. The solute sorption process counteracts the solute transport and delays the clean-up. The consolidation accelerates the transport of reactive chemicals but shows limited effects on transport of non-reactive chemicals. [ABSTRACT FROM AUTHOR]

Water level rise and fall can lead to changes in seepage flow in the bank slopes of reservoirs. Cyclic seepage flow can result in the redistribution and even loss of fine particles in the slope, which eventually influences the slope stability. In this study, numerical simulations were conducted based on a multispecies transport finite element method (FEM) to investigate the influence of periodic water level fluctuations on the reservoir bank slope. The unsaturated soil was treated as a five-constituent mixture, by which erosion and deposition behaviours were captured by phase transition between deposited and fluidized fines. A constitutive model for suffusion considering the hydraulic fluctuation effect was employed to quantify the erosion process. The change in the seepage field and the corresponding evolution of the erosion rate and fines eroded ratio in the slope during the fluctuation period were investigated. The influence of the water level fluctuation frequency on the fines redistribution in the slope was analysed. Furthermore, the evolution patterns of the slope stability under different fluctuation frequencies were compared. The numerical results indicated that a higher fluctuation frequency could promote fine particle loss in the zones near the slope surface, consequently inducing greater deterioration in the slope stability. [ABSTRACT FROM AUTHOR]

A generalized water retention curve (WRC) model in a wide suction range considering the initial void ratio is presented in this paper. Both capillary and adsorbed water in soil pores are considered. Based on the experimental results that the adsorbed water content w a is not dependent on the initial void ratio, a new degree of saturation equation of adsorbed water is established. Meanwhile, a new degree of saturation equation of capillary water at various initial void ratios is proposed with a void ratio-related expression of the air entry value. Compared to Lu's model, only one parameter b is introduced in the established model, which can be easily calibrated using WRCs under two initial void ratios. The measured WRC results of 5 soils are used to verify the proposed model in comparison with the other 3 widely used WRC models. The soil used in the model validation covers a wide range of soil types from sandy soil to clay soil, including clayey silty sand, sandy clay till, clayey silt, expansive soil and lateritic soil. The proposed model is well verified for its ability to describe soil water retention characteristics in a wide suction range at various initial void ratios. [ABSTRACT FROM AUTHOR]

Pre-existing (open) cracks at slope crests, especially tension cracks, are a significant factor in the transition from shallow to deep-seated landslides in unsaturated soil slopes induced by rainfall. This paper presents an analytical framework to assess the stability of unsaturated soil slopes for deep-seated rotational failure considering arbitrary crack depths and unsteady infiltration, and its effectiveness is verified by previous literature and finite element analysis. A closed-form formula is proposed for the maximum depth of cracks in unsaturated soils by the stability of the vertical crack boundary. A parametric study is performed to investigate the impact of some key parameters on the stability of unsaturated soil slopes with cracks. Dimensionless stability charts are developed, which can calculate the factor of safety for the slopes with cracksof any depth and can reflect that the potential slip surfaces through or without passing through the crack tip. In addition, given the existence of a critical crack depth and maximum crack depth, with a ratio ranging from 0.5 to 0.6 based on the stability charts, deep-seated rotational failure is more likely to occur than failure caused by a crack boundary. [ABSTRACT FROM AUTHOR]

Periodic wave barriers have been widely used to mitigate ambient vibration. However, almost all the studies on the performance of periodic wave barriers are conducted under the assumption that soil is a single-phase or saturated medium. In fact, soil often consists of three phases: solid, liquid and gas, and it is more reasonable to be considered as an unsaturated soil. Existing research demonstrates that the dynamic properties of unsaturated soil have been significantly changed by gas phase, or the dynamic performance of unsaturated soil is completely different from that of single-phase soil and saturated soil. Especially, the dynamic performances of unsaturated soil cannot be approximated by the two extremes (saturated soil and single-phase soil). In this paper, the feasibility of vibration mitigation in unsaturated soil by periodic pile barriers is numerically validated. Firstly, based on the periodic theory, the complex band structures of P-SV waves in the periodic pile-unsaturated soil system are calculated. The influence of the saturation on the complex band structures is also investigated. Secondly, a numerical model for analyzing ambient vibration isolation is established. The responses of the numerical model are carried out in both frequency and time domains. The results indicate that periodic wave barriers in unsaturated soil can be designed with a wide attenuation zone covering the dominant frequencies of P1 waves, which is just a dream in saturated soil. Furthermore, S waves can also be greatly shielded in the target band. The present study removes the obstacles for the vibration mitigation in unsaturated soil by periodic pile barriers. [ABSTRACT FROM AUTHOR]

A multi-exponential function (ME) is proposed to depict the highly nonlinear soil water retention curve and hydraulic conductivity function. Then, semi-analytical solution of pore-water pressure in an unsaturated infinite slope at steady state is derived using ME to depict soil hydraulic properties. The solution is verified with experimental and numerical results. It is found that ME can better describe the highly nonlinear hydraulic properties of soil than the single exponential function (SE), which is commonly-used previously. At steady state, the adoption of SE results in overestimating negative pore-water pressure (PWP; i.e., matric suction) by about 25 kPa and slope's factor of safety (FOS) by 100% under rainfall, but underestimating negative PWP by about 50 kPa under evaporation. The difference between PWP and FOS calculated by using SE and ME becomes more significant for soil with bimodal hydraulic conductivity function than that with unimodal one. This difference reduces at a larger slope angle and deeper depth. Moreover, this difference generally increases at a lower S ME /S SE , where S ME and S SE represent the suction at which the unsaturated hydraulic conductivity expressed by ME and SE equals the applied rainfall intensity or evaporation rate, respectively. When S ME /S SE is greater than 0.1, the difference basically diminishes. [ABSTRACT FROM AUTHOR]

The settlement has been reported to regularly be a fundamental factor in controlling the stability of geotechnical structures. Because the theory of elasto-plasticity is widely employed to predict the settlement, the elastic modulus is a vital parameter that is regularly utilized for theoretical calculation. Moreover, thermomechanical behaviour of unsaturated soils has recently received considerable attention because its importance in various energy geostructures applications, as well as in relation to climate change. This paper presents a coupled thermo-hydro-mechanical model of the elastic modulus characteristic curve (EMCC) that was developed based on the effective stress theories of unsaturated soils. The proposed model uses the soil–water characteristic curve (SWCC) and the modulus of elasticity under saturated conditions to predict the variation of modulus of elasticity with matric suction for unsaturated soils. The successful prediction performance of the proposed model is demonstrated by the comparison of measured and predicted outcomes for various published data sets in the literature related to different soil types. The proposed method was then used to present a parametric study considering the coupled impact of some important parameters on SWCC and EMCC. The analysis results indicated that the normalized elastic modulus rate increases with increasing matric suction, hydraulic conductivity, soil density, and with decreasing flow rates, temperatures, and normal stresses. [ABSTRACT FROM AUTHOR]

Expansive soils exhibit excessive volume increases upon contact with water, which can pose a serious threat to stability of structures and foundations. Therefore, it is essential to determine the swelling properties, e.g. maximum swelling pressure, of these problematic soils. We employed a feed-forward neural network algorithm trained with Levenberg–Marquardt, Bayesian regularization, scaled conjugate gradient, and genetic algorithm to build a network model capable of determining the maximum swelling pressure of clayey soils over a wide range of conditions. The models were developed based on a sufficiently large experimental dataset that takes into account key factors that influence the soil swelling. The results show that the feed-forward neural network algorithm trained with Bayesian regularization has the highest overall accuracy, as its predictions agree well with the experimental data. Besides, a simplified network model was developed to be used in cases of limited data availability. The developed model provides accurate predictions over a wide range of conditions and can serve as a valuable tool for researchers and engineers dealing with expansive soils. [ABSTRACT FROM AUTHOR]

The bimodal characteristic of water retention curves of dual-porosity soils has been fully recognized, however, the excessive number of fitted parameters in the existing models limits their application. This study develops a simple water retention model for dual-porosity soils that considers the self-similar characteristics of the pore size distribution (PSD) between macropore and micropore regions. In the model, we simulate the macropore PSD by differential VG model, which is then shifted and scaled to capture micropore PSD. It is hypothesized that the bimodal PSD can be obtained by superimposing the PSDs of macropore and micropore regions to derive the bimodal water retention curve (BWRC). The mercury intrusion porosimetry (MIP) tests and water retention tests are conducted on Nanyang clay with three different dry densities to evaluate the proposed BWRC. The results show that the new parameter can be determined by the MIP dataset and then used to predict the water retention behavior of dual-porosity soils well. Finally, we also explore the application of the proposed BWRC in predicting the hydraulic conductivity of dual-porosity soils without adding any extra parameters. [ABSTRACT FROM AUTHOR]

The analytical representation of the dynamic interaction between a strength composite (SC) pile and unsaturated soil under lateral excitations at the pile head is studied using three-dimensional continuum modelling. The fractional standard line solid (FSLS) model is utilized in the governing equation of unsaturated soil to characterize the flow-independent viscosity of the soil skeleton. Timoshenko beam theory is employed to describe the horizontal dynamic behaviour of SC piles composed of cement-soil mixing (CM) piles and precast high-strength concrete (PHC) pipe piles. A closed series form solution of the horizontal dynamic behaviour for an SC pile embedded in unsaturated soil under lateral excitation at the pile head is deduced theoretically. The solutions of the proposed model are compared with those captured from existing solutions. Finally, the effects of physical parameters in the SC pile-unsaturated soil system on the horizontal dynamic behaviour of the SC pile are evaluated with analytical examples and parametric study. The results indicate that the radius and elastic modulus of the SC pile have a critical influence on the horizontal dynamic behaviour of the SC pile, the FSLS model parameters are the key factors influencing the horizontal dynamic behaviour of the SC pile, and the horizontal dynamic behaviour of the SC pile varies with the change in liquid saturation of unsaturated soil. The research results provide theoretical references for the anti-vibration design and safe operation of SC piles. [ABSTRACT FROM AUTHOR]

Soils surrounding energy piles are often subjected to high overburden pressure. So far, the stress effects on the thermal conductivity of soils and hence the thermal performance of energy piles have not been well investigated. This study proposed a new model for the stress-dependent thermal conductivity of saturated and unsaturated soils. It was validated using the data from a series of new tests and the literature and is able to capture stress-induced variations of thermal conductivity. Then, it was applied to finite element analysis of energy piles' heat transfer efficiency. The numerical results reveal that ignoring stress effects on thermal conductivity, as in the conventional analysis, underestimates the heat exchange rate between energy piles and ground. The underestimation is more significant for piles with a larger aspect ratio and a faster pipe flow velocity, especially when the ground is drier and more compressible. For example, when the pile is 0.6 m in diameter and 50 in aspect ratio, the underestimation is up to 18%, 15% and 4% for the clay, silt and sand, respectively. These results suggest that stress effects on thermal conductivity should be considered for better assessing the heat transfer efficiency of energy piles and other thermal geostructures. [ABSTRACT FROM AUTHOR]

Modeling the time-dependent behavior of unsaturated soil is a topic that is poorly addressed by the current literature. This paper presents a novel elastic-viscoplastic constitutive model for reproducing the time-dependent behavior of unsaturated soil. The model is established using the theoretical framework of the Unified Hardening (UH) model and the Barcelona Basic Model (BBM) combined with Perzyna's overstress theory. A unified hardening parameter is introduced to modify the elastic-viscoplastic constitutive model to consider the effect of the loading history. A new expression for the secondary consolidation coefficient considering the effect of suction is presented, and the state variables related to the void ratio of unsaturated soil considering the time effect are derived. Combined with the one-dimensional viscoplastic hardening parameter, the viscoplastic scalar multiplier in overstress theory is presented, and a three-dimensional elastic-viscoplastic constitutive model is then constructed. With 17 parameters, the proposed model can describe the effects of time and suction on the shear, dilatancy, and compression behaviors of unsaturated soil with various initial void ratios and stresses. Comparisons between the model predictions and experimental data are employed to validate the capability of the proposed model in terms of reproducing the time-dependent behavior of unsaturated soil or soft rock. [ABSTRACT FROM AUTHOR]

Abstract Tsunamis attack coastal areas and cause significant damage to coastal buildings and infrastructure. Many coastal areas are dominated by fine, poorly-graded sands, and in many cases, the upper portion of the nearshore sand bed is unsaturated before tsunami attack. During tsunami runup, inundation of water into the unsaturated sand bed occurs, and the sand bed can eventually become pressurised under the correct conditions. During tsunami drawdown, the total stress is relieved from the sand bed surface, and excess pore water pressure dissipation process can cause sediment instability via fluidisation. The foregoing physical description is complicated by the large bed shear stress caused by tsunami loading, which can motivate significant sediment transport and scour around coastal structures. Herein, we present a coupled seepage-deformation model to estimate the temporal and spatial pore water pressure changes in sand beds during tsunami loading. The numerical formulation is described in detail, and then numerical experimentation is performed to demonstrate modelling capabilities. The results of the numerical experimentation show that tsunami drawdown can induce large pore water pressure head gradients and the speed of the infiltration front is important for examining the potential for tsunami-induced sediment instability. [ABSTRACT FROM AUTHOR]

Abstract Seismic stability analyses of soil slopes are routinely performed with dry and/or saturated assumptions under two-dimensional (2D) conditions. However, in practice, soils are often unsaturated and slopes usually fail in 3D fashion. Three-dimensional (3D) effect and suction-induced effect are essential to be considered to produce more realistic solutions in the slope stability analyses. In this regard, an analytical framework is developed in this paper for assessing the 3D seismic stability of unsaturated soil slopes. A semi-analytical method including the simplified method (SM) and the layer-wise summation method (LSM) is developed to deal with the highly variable nature of suction. The validity of the analytical framework in assessing the soil slope stability is checked with published solutions. Examples are given to illustrate the 3D effect and the effect of suction on the slope seismic stability. The described framework allows the user to quantify the effect of changes in moisture content on effective stress distribution and effective unit weight distribution in the slope and thus, changes in the slope stability. [ABSTRACT FROM AUTHOR]

Abstract Considering engineering practices in terms of decrease in the matric suction of unsaturated soil with increasing embedded depth, this study, employing a new global optimization algorithm on the basis of radial movement optimization (RMO), focused on investigating the critical slip surface and ultimate bearing capacity of a rough strip footing on unsaturated soil subjected to vertical load. Based on upper-bound limit analysis theorem, an equation for calculating the ultimate bearing capacity of unsaturated soil has been established. The data structure of RMO was improved by considering self-feedback of the particles. The results show that the improved radial movement optimization can be successfully applied to accurately and stably search the critical slip surface and subsequently calculate the ultimate bearing capacity on unsaturated soil. It also found that, compared with no matric suction, the critical slip surface determined considering the matric suction of unsaturated soil is larger and deeper, and the corresponding ultimate bearing capacity is also significantly improved. [ABSTRACT FROM AUTHOR]

Abstract This paper presents semi-analytical solutions of two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading using Fourier sine series and Laplace transform. The consolidation equations in form of two-order partial differential equations with three variables are firstly converted to that with two variables. Then four-order ordinary differential equations about excess pore-air and pore-water pressures are presented, and the semi-analytical solutions of excess pore-air and pore-water pressures and settlement are achieved in the Laplace transform domain. Two comparisons are performed to verify the exactness of the obtained solutions, and the consolidation behavior involving three time-dependent loadings is illustrated and discussed. [ABSTRACT FROM AUTHOR]

Abstract Unsaturated soil is a three-phase discontinues system, and microscopic analysis can provide an intrinsic understanding for macroscopic mechanical behavior of the soil. Discontinuous Deformation Analysis (DDA) has the advantage for analyzing the material like granular aggregates. Based on capillary mechanics, a newly developed algorithm is applied in conventional DDA code, which treats a DDA element as an ideal soil particle and exerts capillary force among elements. Then, to validate the extended method, an ideal microscopic soil model is established, and the simulation results are in good agreement with typical analytical solutions. It indicates that the developed DDA is reliable and applicable to explore unsaturated soil behaviors microscopically. [ABSTRACT FROM AUTHOR]

Abstract Evaporation from unsaturated soil is characterized by vapor transfer in the upper part and liquid water transfer in the lower part of the soil. This study develops an analytical model for identifying the vaporization plane where the evaporation occurs, and the model consists of three partial differential equations that respectively govern the vapor flow, liquid water flow and heat transfer. These equations are solved simultaneously for the transient water content profile, evaporation rate, transient temperature profile and location of the vaporization plane. A series of experiments are used to validate the proposed analytical model, which indicates that this model can reasonably well predict the temporal water content profile and evaporation rate during the evaporation process. The result shows that the evaporation rate during falling rate stage is proportional to the inverse of the square root of elapsed time, and the proportionality is affected by the vapor diffusion coefficient, heat diffusion coefficient, and critical water content. The depth of vaporization plane is found to be independent of soil hydraulic properties, but only dependent on the heat diffusion coefficient of the soil. It is also revealed that heat diffusion coefficient has a pronounced influence on the evaporation process, which has not been observed in previous studies. A larger thermal diffusion coefficient leads to a faster advancing and a deeper vaporization plane, as well as a faster decreasing evaporation rate. The analytical model provides a useful tool for investigating the mechanism of the evaporation process. [ABSTRACT FROM AUTHOR]

Abstract A three-step computer program is developed for simulating the load-displacement response of a single pile in unsaturated expansive soil taking account of influence of water infiltration. In the first step, peak and residual pile-interface shear strength variation with suction are estimated. The relationship between interface shear strength and pile-soil relative displacement and pile base resistance and pile base settlement is achieved by modifying universal transfer curve model, in the second step. Lastly, traditional load transfer method was modified for analyzing the load-displacement response. The validity of program is verified using a laboratory model test and a field investigation case study. [ABSTRACT FROM AUTHOR]

Abstract In this study, exponential functions were incorporated in a one-dimensional model to represent the relationships of hydraulic and electro-osmotic conductivities with matric suction and the soil-water characteristic curve. Analytical solutions for pore water pressure, water content and drainage were derived, and laboratory tests were performed to verify the effectiveness of these solutions. Finally, a parametric study indicated that the soil-water characteristics of the soil had a remarkable impact on the drainage behaviour of electro-osmosis under unsaturated conditions and that the proposed analytical solutions could be used to design electro-osmotic drainage systems in unsaturated soils. [ABSTRACT FROM AUTHOR]

This paper discusses the 2D plane strain consolidation problem of unsaturated soil considering the time-dependent drainage boundaries. A set of time-growing exponential functions are firstly used to describe the changes of excess pore-pressures at the drainage boundaries of an unsaturated soil layer. Then, a generalized analytical solution for the 2D plane strain consolidation under these boundaries and constant initial excess pore-pressures is obtained using the finite Fourier transform and Laplace transform methods. Further, the comparisons are presented to verify the accuracy of the proposed solution. It is shown that the proposed solution is more general in the drainage boundary, and in a good agreement with the analytical solution available in the literature and the finite difference solution. Finally, a worked example is presented to investigate the consolidation characteristics under four changing drainage parameters of time-dependent drainage boundaries. The average degrees of consolidation for both air and water phases as well as that for the soil layer are presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract This study presents a new cavity expansion solution in unsaturated soils of finite radial extent. The solution is formulated for spherical and cylindrical cavities subjected to two boundary conditions under the drainage condition where the contribution of suction to the effective stress is constant. It is found that samples with a higher suction value are under more influence of the boundary size effect and this is more obvious with higher mean net stress and higher void ratio. Potential application of the solution in calibration chamber studies for in-situ tests in unsaturated samples is discussed. [ABSTRACT FROM AUTHOR]

This paper presents semi-analytical solutions to two-dimensional plane strain consolidation of unsaturated soils under different initial and boundary conditions. By applying the finite sine and Laplace transforms, the partial differential equations are converted to the ordinary differential equations. The semi-analytical solutions are obtained by using the finite sine inversion transform. Crump’s method is adopted to perform the inverse Laplace transform to obtain analytical solutions in time domain. The present solutions are more general and can be degenerated into conventional solutions to one-dimensional consolidation of unsaturated soils. Several examples are provided to investigate two-dimensional plane strain consolidation behavior of unsaturated soils. [ABSTRACT FROM AUTHOR]

The collapse susceptibility of intact soil should be determined before designing infrastructures in loess regions. It is significantly affected by many factors, including soil type (i.e. sandy, silty or clayey loess), moisture, porosity, stress and structure. So far, many relevant empirical equations and theoretical models were reported in the literature. Each empirical equation has a narrow application range and the theoretical models cannot be easily calibrated. In this study, a new and simple method was developed to predict the loading- and wetting-induced collapse of intact loess within the elasto-plastic framework. The compression curves of intact loess under saturated and unsaturated conditions were normalised using the void index and applied to analyse the loading- and wetting-induced collapse. This method can readily be used by engineers to predict the collapse potential in a wide range of loess types and conditions, with the input of only three state variables (i.e. initial void ratio, vertical stress and initial water content) and the void ratio at the liquid limit state. To verify this new method, it was applied to simulate about 200 laboratory wetting tests and one in-situ ponding test. The measured and predicted results are reasonably matched, demonstrating a good capability of the method. [ABSTRACT FROM AUTHOR]

Saturation conditions play a significant role in the mechanical behavior of granular material and the evolution of an interparticle contact system during the loading process. Using data derived from discrete element simulations of granular assemblies subject to triaxial compression loading with different suctions, we examine the properties of an interparticle contact network and force chain structure to provide a comprehensive picture of the evolution of a particle-scale contact system. The study focuses on the evolution of the topological statistic features (including degree and triangles) and the force chain structure characteristics influenced by suction conditions. To comprehensively evaluate the characteristics of the force chain system, combined statistical parameters are proposed for describing the linearization and intensity of the force chain structure, which account for multiple features of force chains. Accordingly, a novel expression combined with multiscale properties is proposed for strength prediction that convincingly explains data results in the studied suction range. This study illustrates the consistency of the evolving force chain structure features with mechanical behavior that provides new insights for understanding the particle-scale force chain structure evolution from which these properties dominate the macroscopic response. [ABSTRACT FROM AUTHOR]

Clay soils can exhibit excessive swelling due to changes in water content. The clay swelling threatens the long-term stability of structures and foundations, thus an accurate prediction of clay swelling properties is essential in many geotechnical projects. We present feed-forward and cascade-forward neural network models trained with the Levenberg–Marquardt and Bayesian optimization algorithms to determine the swelling potential of natural and artificial clayey soils. The compiled experimental dataset includes various types of soils covering a wide span of swelling potential, ranging from 0.01 to 168.6%. The activity, water content, dry unit weight, liquid limit, plastic limit, plasticity index, and clay content were considered as the input parameters of the models as they are commonly measured during the experimental testing of soil behaviour. The results show that the feed-forward neural network trained with the Levenberg–Marquardt algorithm is the most accurate model for the prediction task. The performance of the model is satisfactory, showing an acceptable agreement with experimental data. The developed model showed substantial improvements over previous empirical and semi-empirical correlations in determining the swelling potentials of both natural and artificial soils. • Developing a feed-forward neural network model to determine swelling potential of clayey soils • The effectiveness of the model was compared with empirical and semi-empirical correlations • The model determines swelling potential of clayey soils with sufficient degree accuracy [ABSTRACT FROM AUTHOR]

A diagnostic method to detect the inception of strain localization, which is based on the singularity of a total acoustic tensor, was developed for variably saturated soils. The effective stress approach was used to establish coupling between the multiphase fluid flow and deformation fields, while isotropic hardening/softening due to changes in suction and plastic volumetric strain were accounted for. To this end, several fundamental testing conditions were investigated, including Conventional Triaxial Compression (CTC) and Extension (CTE), Plane Strain Compression (PSC) and Extension (PSE) under drained, constant water content, and undrained loadings. It was found that, for the silty soil and stress histories considered, suction can completely prevent the onset of strain localization in undrained CTE tests and partially prevent the onset in constant water content and drained CTE tests. Furthermore, while suction can significantly affect the inception of strain localization in all PSC tests, it has almost no effect on the onset of strain localization in all PSE tests. Finally, suction affects more significantly the orientation and mode of shear bands at the inception of strain localization in extension tests than in compression tests. [ABSTRACT FROM AUTHOR]

Shallow strip foundations are ubiquitous in the field of geotechnical engineering. However, most of the analyses regarding the strip foundations were performed without considering the unsaturated state of the soil. The present article aims to evaluate the upper bound collapse load of the strip footing by duly considering the matric suction developed above the water table. The effect of the vadose zone is considered by employing the suction-stress-based effective stress approach. The suction stress is modelled by employing van-Genuchten's soil water characteristics curve and Gardner's one-parameter hydraulic conductivity function. The kinematic admissibility of the problem is ensured by considering a Hill-type mechanism. A new bearing capacity factor is introduced into the formulation which takes care of the unsaturated soil properties and the climate changes. The obtained results are in good agreement with the available solutions. [ABSTRACT FROM AUTHOR]

The present study has developed a constitutive model for both saturated and unsaturated soils. The model considers the effect of mechanical and hydraulic loading on the soil behavior in critical state framework. The mechanical part has separate mechanisms, deviatoric mechanism taking advantage of multi-yield surface plasticity, and isotropic mechanism with classical plasticity formulation. The water retention part is based on the bounding surface concept. Comparison of experimental data and model predictions for saturated and unsaturated states in frictional and cohesive soils, validates the model performance considering soil behavior under different drainage and loading conditions by using one set parameters. [ABSTRACT FROM AUTHOR]

The degree of saturation ( S ) of soil can be separated into two components: the degree of capillary saturation ( S ′ ) that is based on the capillary water and the degree of adsorptive saturation ( S ″ ) that is based on the adsorbed water. This paper discusses the role of the degree of capillary saturation ( S ′ ) in modelling the coupled hydro-mechanical behaviour of unsaturated soils and proposes a new constitutive model for unsaturated soils by using the degree of capillary saturation ( S ′ ) and the effective inter-particle stress ( σ ij ′ ). An enhanced hydraulic model is introduced to describe the hydraulic hysteresis and hydro-mechanical interaction in terms of the degree of capillary saturation ( S ′ ). In the proposed constitutive model, the shear strength, yield stress and deformation behaviour of unsaturated soils are governed directly by the above two constitutive variables, namely σ ij ′ and S ′ . To be in line with the existing finite element frameworks for unsaturated soils, the proposed model is eventually generalised to constitutive functions consisting of only primary variables such as the net stress ( σ ij ), suction ( s ) and degree of saturation ( S ). The typical performance of the model for simulating the characteristic trends of unsaturated soil behaviour is discussed in several different scenarios. The model is then validated against a variety of experimental data in the literature, and the results show that a reasonable agreement can be obtained using this new constitutive model. [ABSTRACT FROM AUTHOR]

To investigate the soil-water retention behavior of a clayey silt over a wide suction range, the suction is imposed on clayey silt specimens using the pressure plate method and vapor equilibrium technique with saturated salt solutions. The test results show that the soil-water retention curves (SWRCs) in terms of gravimetric water content versus suction relation over a wide suction range are independent of the initial dry density or void ratio when the suction is higher than a specific value, which can be determined by results of the mercury intrusion porosimetry test. When the SWRC is expressed in terms of degree of saturation versus suction relation over a wide suction range, the influence of dry density or void ratio is highlighted. This behavior can be explained by the features of the pore-size distribution. Residual suction and water content of specimens with different void ratios are almost the same and the air entry values of specimens show a linear relationship in the plane of water content versus suction with the logarithmic coordinate. Finally, the Fredlund and Xing SWRC equation is used to uniformly describe the SWRCs of specimens with different void ratios by taking above features of the SWRC into consideration, and the predicted results are compared well with measured values. [ABSTRACT FROM AUTHOR]

This paper presents semi-analytical solutions to Fredlund and Hasan’s one-dimensional consolidation for unsaturated soils under symmetric semi-permeable drainage boundary conditions. Two variables are introduced to transform two coupled governing equations of pore-air and pore-water pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. Then, the pore-air and pore-water pressures, and soil settlement are obtained in the Laplace domain. Crump’s method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in time domain. It is shown that the present solution is more applicable to various types of drainage boundary conditions, and in a good agreement with existing solutions from the literature. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with traditional drainage boundary (single or double), and single-sided and double-sided semi-permeable drainage boundaries. Finally, it illustrates the changes in pore-air and pore-water pressures and soil settlement with time at different values of symmetric semi-permeable drainage boundary conditions parameters. In addition, parametric studies are conducted by the variations of pore-air and pore-water pressures at different ratios of air-water permeability coefficient and the depth. [ABSTRACT FROM AUTHOR]

Material point method (MPM) offers an effective approach for analysing large-deformation problems, such as landslides that often involve unsaturated soil. Several MPM formulations for unsaturated soil have been reported in the literature, but they assumed that water retention ability and permeability function are independent of soil deformation. Furthermore, most studies used a single set of material points, so they cannot simulate some processes (e.g., the infiltration of free water into unsaturated soil). To address these problems, a two-point MPM formulation has been extended from saturated to unsaturated soils, considering the influence of porosity change on the water retention curve and permeability function. The information of solid and liquid phases is carried by two individual sets of material points, assuming zero air pressure. The elastoplastic mechanical behaviour is modelled by the Drucker-Prager model using Bishop's stress. The MPM simulations were compared with the results of physical model tests (for large-deformation problems) and finite element analysis (for small-deformation problems). It is evident that the proposed MPM formulation is able to capture various hydro-mechanical problems well. In particular, the computed failure processes of unsaturated soil slope under rainfall are consistent with results from physical model tests. [ABSTRACT FROM AUTHOR]

This paper presents an analytical method to predict the horizontal capacity of piles in unsaturated soils. The method extends the well-known Broms approach to account for the combined effect of the groundwater table and the apparent cohesion of the unsaturated soil above it. Similar to the original formulation of Broms, the present method calculates the maximum horizontal force and bending moment that can be sustained by the pile for two different head fixities (i.e. free-head and restrained-head) as a function of non-dimensional parameters that depend on the geometry and flexural resistance of the pile (i.e. yielding moment), the soil resistance and the type of failure mechanism (i.e. short, intermediate or long pile). Compared to Broms' solution, the method introduces additional non-dimensional parameters that relate the water retention behaviour of the soil to the geometry of the pile. The proposed formulation accurately predicts the lateral capacity of piles as experimentally measured in previous works. Results confirm that consideration of the partially saturated state of the soil above the groundwater table is essential for a reliable estimate of the horizontal capacity of piles. [ABSTRACT FROM AUTHOR]

An isogeometric analysis (IGA) is introduced to obtain a head-based solution to Richards equation for unsaturated flow in porous media. IGA uses Non-Uniform Rational B-Spline (NURBS) as shape functions, which provide a higher level of inter-element continuity in comparison with Lagrange shape functions. The semi-discrete nonlinear algebraic equations are solved using a combination of implicit backward-Euler time-integration and Newton-Raphson scheme. The time-step size is adaptively controlled based on the rate of changes in the pore pressure. The results from the proposed formulation are compared and verified against an analytical solution for one-dimensional transient unsaturated flow in a homogenous soil column. The proposed method is then applied to four more complex problems including two-dimensional unsaturated flow in a two-layered soil and a semi-circular furrow. The test cases in two-layered soil system involve sharp variations in the pressure gradient at the intersection of the two media, where the pore water pressure abruptly changes. It is shown that the proposed head-based IGA is able to properly simulate changes in pore pressure at the soils interface using fewer degrees of freedom and higher orders of approximation in comparison with the conventional finite element method. [ABSTRACT FROM AUTHOR]

In foundation vibration control, the multi-layer isolation barrier has a good vibration isolation effect due to its ability to block the propagation of elastic waves multiple times. In this paper, using the double-layer wave impeding block(WIB) as an example, the calculation model of a double-layer WIB as a vibration isolation barrier in the unsaturated soil foundation is established. The analytical solution of the transmission/reflection amplitude ratio when the S wave passes through the double-layer WIB in the unsaturated soil foundation is calculated by using the Helmholtz vector decomposition theorem. In addition, the influence of parameters such as the wave impedance ratio, saturation, shear modulus and density on the vibration isolation performance of the WIB are analyzed by numerical examples. The results show that the wave impedance ratio, shear modulus and density of the WIB material have a significant influence on the transmission/reflection amplitude ratio. Saturation has little effect on the transmission/reflection amplitude ratio of P 1 and S waves but has a great effect on the amplitude ratio of P 2 and P 3 waves. The best vibration isolation effect can be obtained by selecting the optimal wave impedance ratio and shear modulus of the double-layer WIB material. [ABSTRACT FROM AUTHOR]

The spatial variability is an inherent characteristic of soils. In addition to isotropic and transversely anisotropic soils, rotated anisotropic soils can also be observed in nature owing to deposition and weathering. Recent studies revealed that the spatially variable soil strength parameters can significantly affect rotated anisotropically deposited soil slope stability. However, the influence of spatial variability of saturated water permeability (k s) on this type of slope stability has been not fully understood, especially for the three-dimensional (3D) slope analysis. This paper aims to investigate unsaturated soil slope reliability with 3D k s rotated anisotropy random fields under rainfall infiltration. Due to the low efficiency of the covariance matric decomposition method (CMD) in simulating large-scale 3D rotated anisotropy random fields, a modified CMD method is proposed to save the computational cost. Moreover, comparisons between 2D and 3D random finite element analyses are also discussed. The results indicate the modified CMD method can markedly improve computational efficiency by more than 3.3 times compared with the CMD method. Only applying variations of pore water pressure (PWP) of a section or groundwater table (GWT) cannot sufficiently account for the uncertainty of slope stability. The cross-dip slope, where the dip direction of the slope is perpendicular to the dip direction of strata, has a larger reliability index (1.3−3.0 times) than the dip slope and reverse slope at the same soil bedding plane orientation. The most unfavorable soil bedding plane orientation for the cross-dip slope and the dip/reverse slope is 0° (horizontally deposited) and 30° (slightly larger than slope angle), respectively. It is attributed to the relatively low k s along these two orientations being more likely to form the aquiclude, affecting overall variations of PWP, leading to a larger standard deviation of the factor of safety and a lower reliability index. Furthermore, the reliability of cross-dip slope can only be studied in 3D, while the dip slope and reverse slope reliability can be studied with 2D analysis to decrease computational burden when the slope length does not exceed 50 m. [ABSTRACT FROM AUTHOR]

A weak form quadrature element formulation is proposed for coupled analysis of unsaturated soils. In the formulation, integration points are coincident with nodes where all variables are obtained so that numerical implementation is made easy. Accuracy can be improved by the increase of the approximation order. An elasto-plastic constitutive model is used for description of the mechanical behavior, and hydraulic hysteresis of the soil water characteristic curve is considered. Results are compared with available analytical solutions, experimental data and numerical solutions in the literature, and good agreement is reached. Rapid convergence is reached as compared with the conventional finite element method. The effect of the ground water level is discussed. [ABSTRACT FROM AUTHOR]

This paper deals with a new model for solving coupled hydromechanical problems, based on an existing unified model. Firstly, the unified model for granular media, describing solid and fluid states with the transition between them, is briefly presented and extended to the unsaturated domain using Bishop’s effective stress. Secondly, an adapted stress–strain relationship is derived from modified Van Genuchten–Mualem’s water retention curves. On this basis, a finite element formulation with Lagrangian integration points in a visco-elasto-plastic framework is proposed and implemented in a FEMLIP tool. Finally, the formulation is validated with reference to several benchmarks. The results and analysis show its reliability, and by means of FEMLIP, more complex and realistic problems are expected to be solved in the field of natural risks. [ABSTRACT FROM AUTHOR]

The bearing capacity of strip footings on unsaturated soils is studied using slip line theory. The suction profiles considered are non-uniform with depth and correspond to vertical flow of water by infiltration or evaporation. The slip line theory assumes a plastic equilibrium state of a Mohr–Coulomb soil in which suction influences are included using the effective stress concept. This paper shows the similar and independent effects of cohesion and the contribution of suction to the effective stress in the governing equations. It shows that the influence of a non-uniform suction profile on bearing capacity is significant, and the depth to the ground water table and the footing width have significant roles in how much suction influences the bearing capacity. By approximating the contribution of suction to the effective stress as a function that varies linearly with depth, the effect of suction on bearing capacity is represented in dimensionless form in separate charts for smooth and rough footings. Using the charts the bearing capacity can be determined for any combination of friction angle, footing width, surcharge, soil unit weight and linear profiles of cohesion and the contribution of suction to the effective stress. An example is given which highlights the significant influence suction can have. These charts also permit assessment of bearing capacity changes that may occur when changes to suction are expected, due to seasonal fluctuations of soil moisture, drought or flooding. [ABSTRACT FROM AUTHOR]

Some Authors highlight the hysteretic response to wetting of unsaturated soils, showing that the operative SWCC may significantly diverge from the one usually adopted in conventional approaches. Accounting for the typical range of values covered by the suction–degree of saturation relationship for loose granular pyroclastic soils, the paper examines the influence of potential wetting paths on slope stability conditions. [ABSTRACT FROM AUTHOR]

The distinct lattice spring model (DLSM) is extended to modelling soil desiccation cracking by introducing a two-phase bond model. The bond, which comprises a spring bond and water bond, is developed to consider the interaction of the pore pressure with deformation of the soil matrix. A parameter representing soil heterogeneity is introduced to consider the uneven drying during desiccation. The capability of the model is demonstrated through a number of numerical examples, which are in good agreement with the experimental observations. Three significant factors controlling desiccation cracking, which are soil particle size, heterogeneity and boundary conditions, are identified. [ABSTRACT FROM AUTHOR]

Expansive soil slopes are usually characterized with conspicuous fissures. Pre-stressed anchor cables are effective techniques in improving the slope stability. Explicit considerations of the fissures and the suction effect become crucial in producing more realistic solutions. Based on the kinematic limit analysis theorem, this paper performs a limit analysis of the stability for expansive soil slopes stabilized by anchor cables. The upper bound solution to the slope stability was optimized and compared with the published solutions, demonstrating the applicability of the proposed method. An illustrative slope reinforced with two different reinforcement patterns was investigated to show the role of soil suction and anchor reinforcement in the safety assessments of expansive soil slopes. The results indicate that the slope stability and anchor reinforcement relate closely to the fissures. A threshold value of the fissure height exists, beyond which the slope stability is significantly reduced. An optimum inclination angle (ξ opt) of anchors exists universally and is reduced as the anchor height, the internal friction angle and the surcharge load increase. [ABSTRACT FROM AUTHOR]