Response Of Unsaturated Soils Research Articles

Coupled Influence of Compaction and Moisture on Unsaturated Soil Response in Triaxial Tests

Coupled Influence of Compaction and Moisture on Unsaturated Soil Response in Triaxial Tests

A PINN-based modelling approach for hydromechanical behaviour of unsaturated expansive soils

Hydromechanical behaviour of unsaturated expansive soils is complex, and current constitutive models failed to accurately reproduce it. Different from conventional modelling, this study proposes a novel physics-informed neural networks (PINN)-based model utilising long short-term memory as the baseline algorithm and incorporating a physical constraint (water retention) to modify the loss function. Firstly, a series of laboratory tests on Zaoyang expansive clay, including wetting and drying cycle tests and triaxial tests, was compiled into a dataset and subsequently fed into the PINN-based model. Subsequently, a specific equation representing the soil water retention curve (SWRC) for expansive clay was derived by accounting for the influence of the void ratio, which was integrated into the PINN-based model as a physical law. The ultimate predictions from the PINN-based model are compared with experimental data of unsaturated expansive clay with excellent agreement. This study demonstrates the capability of the proposed PINN in modelling the hydromechanical response of unsaturated soils and provides an innovative approach to establish constitutive models in the unsaturated soil mechanics field.

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

AbstractWe develop an analytical solution to the problem of one‐dimensional consolidation of unsaturated soil subjected to cyclic loads with arbitrary waveforms. The solution predicts the excess pore water and pore air pressures and the accompanying vertical compression in a poroelastic, unsaturated soil material. Cyclic loading occurs in a variety of engineering applications and often generates higher excess pore fluid pressures and larger vertical compression than does a time‐invariant load. In the present study, the loading function is allowed to take on any arbitrary waveform represented by a Fourier trigonometric series. Analytical solution to the boundary‐value problem in one dimension is given in closed form describing the frequency‐independent and frequency‐dependent components of the poroelastic response. We verify the analytical solution through representative examples involving cyclic loads with square and triangular patterns. Apart from the shape of the forcing function, we also investigate the effects of initial water saturation, soil texture, and excitation frequency on the system response.

Development of a dynamic hollow cylinder apparatus for investigating the cyclic response of unsaturated soils subjected to stress anisotropy

The construction of most geo-structures like earthfill dams, roads, highways, embankments, and airport runways deals with the compaction of unsaturated soils under anisotropic cyclic/dynamic loadings. Many of these partially saturated geo-structures also experience three-dimensional dynamic loadings during service life. This paper presents a new hollow cylinder apparatus developed for the investigation of the cyclic response of unsaturated soils subjected to stress anisotropy. The device is unique as it enables, for the first time, studying the combined effects of stress anisotropy (effects of both parameters α and b) and the degree of saturation on the dynamic properties of unsaturated soils, the aspects that cannot be thoroughly captured using existing soil laboratory testing equipment. It allows independent control of the magnitudes and rotations of the principal stresses and measuring strains as well as control/measurement of pore water and pore air pressures in the unsaturated soil samples. The paper describes the main challenges and the adopted solutions for the development of the hollow cylinder apparatus, including the complexities associated with the non-uniformity of water content in the sample height and the measurement of the sample volume change. The relations for determining the effective stresses and strains in the unsaturated soil samples are also derived. The results of several dynamic tests on unsaturated sand over a wide range of shear strains are presented to demonstrate the capabilities of the apparatus.

Soil Moisture Active Passive (SMAP) Satellite Data and Unsaturated Soil Response

The importance of degree of soil saturation in geotechnical problems resulted in inclusion of unsaturated soil mechanics in various applications for several decades. However, in spite of recent progress in remotely sensed soil moisture measurement, geotechnical community has not yet taken advantage of these advances in analysis of unsaturated soils. NASA launched its Soil Moisture Active Passive (SMAP) satellite in 2015 with the aim of providing surface and root zone soil moisture content over the global land surface at 3-day average intervals. SMAP, as a widely validated and near-real-time database, offers a rich soil moisture database at a global scale that can be used in studies considering unsaturated soil behaviour. A study of the relationship between soil water content and seismic ground response is presented in this paper using SMAP, which includes the tracking of the variations in Earth's surface soil moisture caused by earthquakes.

A Unified Two Independent Stress Variable Approach to Moisture-Change-Induced Unsaturated Soil Volume Change

In 1968, Matyas and Radhakrishna introduced the concept of the state surface, demonstrating that unsaturated soil volume change is dependent on two independent stress state variables, net total stress and suction. For decades the basic theory of unsaturated soils has been known, and a holistic view of the elastoplastic response of unsaturated soils, based on a modified state surface approach (MSSA), makes it clear that a method accounting for independent roles of net total stress and suction is required to quantify volume change of unsaturated soils. Still, reliance on pre-unsaturated-soil-mechanics-era methods persists, particularly within the geotechnical practice community. Unsaturated soil theory forms the basis for compelling arguments for discarding long-held efforts to classify unsaturated soils as exclusively expansive or exclusively collapsible with respect to volume change response. A more fundamental and unified approach to thinking about volume change of unsaturated soils supports the use of a consistent Stress Path Method to practice-based volume change analyses. Implications of geotechnical engineers’ continued reliance on expansive and collapsible soil classifications, often based on index-based correlations and non-stress-path appropriate laboratory testing, are explored. Recommendations for laboratory testing and modeling for moisture-change induced unsaturated soil volume change are made.

A microstructure-based procedure to simulate the effect of wetting-drying cycles on the soil water retention curve

Analysing unsaturated soil response often requires the soil-water-retention-curve (SWRC). The SWRC depends upon the soil microstructure, which evolves with hydromechanical loading such as in-situ exposure to wetting-drying cycles. If in-situ response is of interest and studied in the laboratory, it is essential specimens have a structure representative of in-situ conditions. Simulating wetting-drying cycles in the laboratory is possible albeit time-consuming and a faster alternative procedure would be preferred, which is the focus of this paper. Mixtures of two soils were prepared in the laboratory by either: exposure to three simulated wetting-drying cycles, or one of two compaction approaches. The microstructure and drying-path SWRC of the specimens prepared with each method were measured. Most of the compacted specimens achieved similar pore size distributions to the cycled samples though the outcomes in terms of achieving a target SWRC, which was the objective of the study, are mixed. The SWRCs of most compacted samples had similar gravimetric water contents yet significantly higher saturation degree at every suction measured. This is explained by the compacted samples containing less macro pores than cycled samples. The compaction procedure, designed to produce specimens having a SWRC similar to that of cycled materials, seems promising but needs modification.

Two-phase fully-coupled smoothed particle hydrodynamics (SPH) model for unsaturated soils and its application to rainfall-induced slope collapse

In this paper, a new fully-coupled Smoothed Particle Hydrodynamics (SPH) formulation for unsaturated soils is developed to study the influence of rainfall infiltration on slope stability. The single-layer two-phase formulation is investigated in SPH for the first time to simulate the response of unsaturated soils. The use of a single set of particles improves the computational efficiency and facilitates the implementation of infiltration boundary conditions. The Drucker–Prager strain-softening model, with the use of Bishop's effective stress, is adopted as the soil’s constitutive model. New extensions of a first-order consistent wall boundary treatment are proposed for the coupled hydro-mechanical problem to enforce non-slip/free-slip conditions for the soil phase and water phase. A novel stress diffusion algorithm for general application is introduced to smooth out the numerical noise in the stress field under large deformation. The accuracy of the formulated SPH model is examined with available analytical solutions and experimental data. The proposed numerical scheme is finally applied to the simulation of rainfall-induced slope collapse of an unsaturated slope with two different bedrock geometries. Results demonstrate that the geometry of the bedrock is shown to play an important role in the failure initiation and propagation of the collapse. It is found that the proposed model allows the investigation of both triggering and post-failure mechanism, providing a smooth stress field even at large deformations.

Dynamic responses of graded nonhomogeneous unsaturated soils under a strip load

Abstract Based on the three-phase porous media mixed theory, the dynamic governing equations of unsaturated soils is established and the dynamic response of graded nonhomogeneous unsaturated soils subjected to a strip load is studied. Combined with the reverberation-ray matrix method (RRMM) and the boundary condition, the calculation formula of the displacement, stress and pore pressure of graded nonhomogeneous unsaturated soils is derived. Assuming that the continuous variation of physical and mechanical properties of unsaturated soils along the thickness-coordinate by exponential law distribution, the numerical solution of the displacement, stress, and pore pressure then obtained by using numerical inverse Fourier transformation, and the influence of soil heterogeneity and saturation on the dynamic response of unsaturated soils is discussed. The results show that the displacement decreased with increasing gradient factor, and the stress first increased then decreased with the gradient factor increased, and the pore pressure first decreased then increased with increasing gradient factor. The displacement and pore pressure under different gradient factors all increase with increasing saturation.

Review of expansive and collapsible soil volume change models within a unified elastoplastic framework

Numerous laboratory tests on unsaturated soils revealed complex volume-change response to reduction of soil suction, resulting in early development of state surface approaches that incorporate soil expansion or collapse due to wetting under load. Nonetheless, expansive and collapsible soils are often viewed separately in research and practice, resulting in development of numerous constitutive models specific to the direction of volume change resulting from suction decrease. In addition, several elastoplastic models, developed primarily for collapse or expansion, are modified by add-on, such as multiple yield curves/surfaces, to accommodate a broader range of soil response. Current tendency to think of unsaturated soils as either expansive or collapsible (or, sometimes, stable), has likely contributed to lack of development of a unified approach to unsaturated soil volume change. In this paper, common research and practice approaches to volume change of unsaturated soils are reviewed within a simple macro-level elastoplastic framework, the Modified State Surface Approach (MSSA). The MSSA emerges as a unifying approach that accommodates complex volume change response of unsaturated soil, whether the soil exhibits collapse, expansion, or both. Suggestions are made for minor adjustments to existing constitutive models from this review, typically resulting in simplification and/or benefit to some of the most-used constitutive models for unsaturated soil volume change. In the review of practice-based approaches, the surrogate path method (SPM), an oedometer/suction-based approach, is demonstrated to be consistent with the MSSA framework, broadly applicable for use with expansive and collapsible soils, and yielding results consistent with measured field stress-path soil response.

Determination of strain-dependent soil water retention characteristics from gradation curve

The importance of soil water retention characteristics in modelling the hydro-mechanical response of unsaturated soils has been well recognised by many investigators in recent years. Determination of strain-dependent soil water retention curve (SWRC) is likely to be extraordinarily difficult. The first two authors have recently shown that SWRC can be computed from the gradation curve and the calculation result is consistent with the experimental results obtained from pressure plate tests. In this paper, based on a hypothesis related to change in the pore size distribution (POSD) due to volumetric strain of soil skeleton, a method to compute strain-dependent SWRC is presented. It is found that at initial degrees of saturation higher than 0.8, the influence of volumetric strain may be marginal whilst at initial degrees of saturation lower than 0.8, its influence is likely to be substantial. In all cases, the gradation curve of the soil affects the SWRC.

Experimental study and constitutive modeling of volume change behavior in unsaturated soils

Unsaturated soils often show complex coupled hydro-mechanical behavior. We present a simple way to explore the 1D compression mechanical behavior of unsaturated soils under a constant degree of saturation by controlling the sample void ratio and suction. The experimental results presented here verify that the proposed method can control the degree of saturation during compression. The experimental data show that the hardening factor exhibits a linear relationship with the logarithmic degree of saturation. We apply a volume change equation using the hardening factor and effective stress as basic variables to simulate the hydro-mechanical behavior of unsaturated soils. We conducted numerical simulations to assess the model performance. Comparisons between the experimental data and simulations indicate that the model can well reproduce the mechanical and hydraulic response of unsaturated soils.

A Review on the Resilient Response of Unsaturated Subgrade Soils

Considering the great contribution of subgrade modulus to the overall performance of roads or railways, it is crucial to provide the best prediction of resilient modulus for their foundations. Incorporating the seasonal variation of moisture content, the resilient modulus variation of unsaturated soils will be accurately predicted. This paper aims to introduce and discuss the knowledge about resilient response of unsaturated soils and emphasize the effects of humidity. A literature review on resilient response of unsaturated soils is presented based on the previous studies. The affecting factors (i.e., wetting and drying, moisture content, and matric suction) were discussed. The prediction model development of the resilient response of unsaturated soils was presented. The limitations and advantages of the model were analyzed and compared. It reveals that the current models were limited regarding stress conditions, moisture content, matric suction, and soil types, and further studies are still needed to achieve a better understanding of resilient response of unsaturated soils.

Modelling Unsaturated Soil Response Beyond Residual Suction State via Vapor-Pressure Controlled Triaxial Testing

Most of the previous research has been focused on developing and validating constitutive models to predict response of unsaturated soils in low-medium suction range. However, there is a scarcity of efforts in developing soil models to simulate its mechanical response in high suction range, particularly above the residual suction. This article presents a new constitutive model introducing net stress and suction as two independent variables. Furthermore, non-associative flow rule incorporating modified stress-dilatancy relationship to take unsaturated state into account is introduced to improve the model results in low-medium to high suction range. The essential soil model parameters are calibrated using suction-controlled triaxial test results for predictions of compacted silty sand response at high values of total suction above residual suction. Preliminary simulations show that proposed model can reasonably simulate the post-peak strain softening response obtained from suction-controlled CTC tests above residual suction value with reasonable accuracy. Although, the proposed model captures initial compression followed by dilation volumetric response with reasonable accuracy, it needs some improvements to be able to capture volumetric response accurately over entire suction range.

A volumetric yield surface for compacted soils based on constant water content testing

Unsaturated soils exhibit various complex behaviours compared to saturated soils, such as collapse upon wetting. Therefore, understanding the response of unsaturated soils under general field conditions is essential for the design and construction of safe and economical geotechnical engineering structures. This research is based on the Monash-Peradeniya-Kodikara (MPK) framework proposed by Kodikara [1] for unsaturated compacted soils, which provides a direct link to the traditional compaction loaded curves and constant water content loading experiments. Kodikara [1] named the loaded compaction surface the loading wetting state boundary surface (LWSBS) and validated the model for a combination of loading and wetting stress paths. However, the experimental validation of the yield surface after drying stress paths was not addressed in the original paper. This paper reports the results of drying stress path tests carried out within the specific volume (v),specific moisture ratio (vw) and mean net stress (p) space of the MPK model, and observations suggest that the yield surface is unique after drying stress paths. Mathematical equations for the volumetric behaviour of unsaturated soils are derived using the constant degree of saturation hyperlines derived from constant water content testing, as this enables direct coupling with the soil water retention curve. Finally, the volumetric equations are validated based on the available experimental data.

Response of unsaturated soils to heating of geothermal energy pile

Geothermal energy piles (GEPs) are an environmentally friendly heat exchange technology that dualizes the role of structural foundation pile for load support and in meeting the building heating/cooling need. Energy loops made from high-density polyethylene which allow heat carrier fluid circulation, are fitted into the pile foundation elements to extract or inject and store heat energy in the soil surrounding the pile. This paper reports the results of a numerical study investigating the response of an energy pile embedded in unsaturated soils (sand, silt and clay) to natural thermal recovery, after heat injection process. It was found that the increase in soil saturation, duration of heating operation i.e. intermittent (8 or 16 h heating) or continuous mode, magnitude of the heat injection rates influences the temperature changes in the soil surrounding the pile, consequently impacting on the system performance. Similarly, it was observed that temperature at all location approached initial state in a duration equal to about twice that of the heating time. In addition, it was found that imposing excessive heat flux on the pile results in the drying up of the surrounding soil leading to lower thermal conductivity thus decreasing the overall GEP system performance.

Numerical framework for considering the dependency of SWCCs on volume changes and their hysteretic responses in modelling elasto-plastic response of unsaturated soils

This paper provides the mathematical framework for the continuum numerical modelling of dynamic and static problems of geomaterials when unsaturated in iso-thermal environments with chemically passive phases and immiscible flows. As the Soil Water Characteristic Curve (SWCC) plays a vital role in the response of unsaturated soils, the main attention in the presented framework is to include the full hysteretic response of the SWCC and its dependency on volume change; features which have been often ignored in the analyses of unsaturated soils.As incorporation of these features into the analysis of unsaturated soils brings additional complexities into the theoretical framework and the procedure of numerical implementation, the primary motivation of this study is to highlight these complexities and their associated numerical problems; and to propose a robust numerical framework by which simulations of unsaturated geomaterials at large scale can be facilitated.First, the procedure of modelling the elasto-plastic response of partially saturated soil, where the dependency of the SWCC on volume changes is considered in the analysis, is investigated; and the corresponding finite element solution to solve boundary value problems is provided. Numerical examples are presented for validation and to demonstrate the effect of the SWCC dependency on volume changes.Then, using the provided finite element approach, we illustrate the numerical problems which can arise from including the SWCC hysteretic behaviour when solving boundary value problems involving unsaturated soils. Then, a model to rectify these problems is provided. The introduced method yields an incremental nonlinear function which links the rate of saturation degree to the rate of porosity and the rate of suction. An integration scheme with automatic error control for updating the saturation degree during the analyses is introduced. Numerical examples are provided for validation and to demonstrate the capability of the proposed scheme in modelling hysteretic response of the SWCC.

A stress integration scheme for elasto-plastic response of unsaturated soils subjected to large deformations

This paper proposes an algorithm for performing explicit integration of constitutive models for unsaturated soils in problems where consideration of stress rate objectivity becomes necessary due to large deformations. As many constitutive models for unsaturated soils incorporate suction forces, as well as stresses and strains, into the material description, an accurate integration procedure is more complicated than similar schemes proposed for saturated soils. The difficulties of integration are also coupled with the need to incorporate objectivity (frame independency) within the integration procedure. Application of the proposed method is limited to constitutive models that assume additive decomposition of the strains. A fully coupled finite deformation numerical model is considered with displacement, pore water pressure and suction as the nodal variables. Details of the implementation of the stress integration algorithm at each stage of an analysis are given. The algorithm is then applied to solve some large-scale geotechnical problems. Numerical examples are also provided to assess the performance of the algorithm under different loading conditions.

Capillary forces between equally sized moving glass beads: an experimental study

The mechanical response of near-surface unsaturated soils in large-strain environments such as earthquakes, landslides or debris flows is highly dependent on capillary forces. While the evolution of capillary forces under static loading has been studied in detail, the dynamic response of unsaturated soils associated with the viscous deformation and rupture of interparticle liquid menisci at large strains is not as well characterized. Particle-scale pullout tests were conducted to achieve better understanding of how separation rates and distances contribute to capillary force evolution and meniscus rupture between two equally sized glass spheres. Capillary forces evolve nonmonotonically in a manner that first increases and then decreases with increasing separation distances and is dependent on the initial meniscus geometry and wettability of the particles. The rate of capillary force reduction and particle separation distance at liquid bridge rupture are functions of the meniscus volume and rate of particle separation. The two-particle experimental results suggest that the dynamic response of bulk (multi-particle) unsaturated soil systems would depend on processes of drainage and imbibition and provide insight into the evolution of stiffness and the ductility of unsaturated soils undergoing large-strain deformations.

A new approach to interpret the mechanical behaviour of unsaturated soil using effective stress and degree of saturation

Unsaturated soil shows complex mechanical behaviours compared to saturated soil. A number of constitutive models for unsaturated soil have been proposed. However, these models suffer limitations. In this paper, a new constitutive model has been proposed in terms of effective stress and degree of saturation based on the modelling assumption about the relationship between hardening effect and degree of saturation. The proposed volume change equation gives a new explanation for the volume change of unsaturated soil. Then, an alternative approach to simulate coupled hydraulic hysteresis and the influence of the volume change on soil–water characteristic curves is suggested. Finally, this paper presents comparisons between the model simulations and experimental data. It is shown that the proposed model represents great ability to reproduce the mechanical and hydraulic response of unsaturated soil.