Influence of Mechanical Yielding on Predictions of Saturation: The Saturation Line

It is now well accepted that the mechanical and the water retention behaviour of a soil under unsaturated conditions are coupled and, that such coupling, should be incorporated into a constitutive model for a realistic representation of soil’s response. In existing models, the influence of the mechanical behaviour on the water retention is often represented by a shift of the main wetting retention curve to higher values of matric suction (the difference between pore air and pore water pressures) when the specific volume decreases. This means that any variation of total volumetric strains of compression (whether these are elastic or elasto-plastic) will result in a shift of the main wetting and drying curves to the right, when these curves are represented in the water retention plane. This shift of the main water retention curves, however, should not only influence the unsaturated stress states as often described in the literature, it should also have some impact on the saturated stress states and, more specifically, on the predictions of de-saturation (air-entry point) and saturation (air-exclusion point). From a modelling point of view, it is advantageous to represent this influence through the plastic component of volumetric strain of compression only because, in this way, a consistent representation of the mechanical behaviour for both unsaturated and saturated states can be naturally achieved. This and other advantages resulting from this singular approach are demonstrated in the paper in the context of the Glasgow Coupled Model (GCM)

The Mechanical Yield Stress in Unsaturated and Saturated Soils

This paper discusses how the variation of mechanical yield stress with matric suction is represented in consti-tutive models for unsaturated and saturated soils. Particular emphasis is placed on how the mechanical yield stress is modelled across transitions between saturated and unsaturated conditions, highlighting the role of water retention hysteresis and the influence of mechanical behaviour on the water retention response. When the constitutive model used represents the unsaturated condition of the soil solely through matric suction (ig-noring any influence of degree of saturation) the variation of mechanical yield stress with matric suction is unique and corresponds to the conventional loading-collapse LC yield curve of the Barcelona Basic Model and many other subsequent models. The incorporation of degree of saturation in modelling unsaturated soil behaviour and, more specifically, inclusion of the hysteretic variation of degree of saturation with suction, suggests that a more realistic representation of the evolution of mechanical yield stress with suction should distinguish between decreasing (wetting) and increasing (drying) variations of suction. These and other rele-vant implications of incorporating water retention hysteresis in a coupled constitutive model for unsaturated soils are discussed in the paper in the context of the Glasgow Coupled Model

Numerical Modelling of Water Breakthrough in Coarse Soils Initially at Very Low Degree of Saturation

Conventional constitutive models describing the water retention and hydraulic conductivity behaviour of soils under unsaturated conditions (e.g. the Van Genuchten-Mualem model) have some shortcomings when applied in numerical modelling of problems where the initial degree of saturation is very low. The reason is that they assume that the hydraulic conductivity only tends to zero as suction tends to infinity (this is physically unreasonable, because continuity of liquid water will be lost at a finite value of suction). This shortcoming becomes particularly evident when modelling the breakthrough of water from the finer layer to the coarser layer of a capillary barrier system (CBS), where the coarser layer is initially at very low degree of saturation. Numerical results obtained using CODE_BRIGHT suggest that a model having the hydraulic conductivity tending to zero at a finite value of suction is able to simulate the phenomenon of breakthrough better than the Mualem model. The results presented in the paper demonstrate the importance of describing realistically the hydraulic behaviour of coarse soils at low degrees of saturation

A hysteretic hydraulic constitutive model for unsaturated soils and application to capillary barrier systems.

Unsaturated soils exhibit water retention hysteresis, with different water retention behaviour during drying and wetting paths. Water retention hysteresis has often been modelled using expressions for the main drying and main wetting water retention curves that are unsatisfactory at low values of degree of saturation. In addition, the effect of retention hysteresis on the unsaturated hydraulic conductivity behaviour has typically not been explicitly considered. This paper presents a new hysteretic hydraulic constitutive model for the water retention and hydraulic conductivity behaviour of unsaturated soils, which is effective and easy to apply. The model includes: (i) main wetting and main drying water retention curves modelled with a modified version of the van Genuchten model, improved at low degree of saturation; (ii) hysteretic scanning water retention curves modelled using a bounding surface approach; (iii) the effect of hydraulic hysteresis on a soil hydraulic conductivity curve (SHCC) model improved at low degree of saturation and including the effect of liquid film conductivity. The new hysteretic hydraulic model is then validated against experimental data. After implementation in the finite element software Code_Bright, the new hydraulic constitutive model is applied in a numerical study of the impact of hydraulic hysteresis on the behaviour of capillary barrier systems (CBSs). Water retention hysteresis, which has typically been neglected in the modelling of the hydraulic behaviour of CBSs, is shown to have a significant impact on: (i) movement and redistribution of water within the finer layer of a CBS; (ii) the phenomenon of water breakthrough across the interface between the finer and coarser layers of a CBS and the subsequent restoration of the CBS after infiltration at the ground surface ceases; (iii) the prediction of evaporation from a CBS into the atmosphere

A hysteretic hydraulic constitutive model for unsaturated soils and application to capillary barrier systems

Unsaturated soils exhibit water retention hysteresis, with different water retention behaviour during drying and wetting paths. Water retention hysteresis has often been modelled using expressions for the main drying and main wetting water retention curves that are unsatisfactory at low values of degree of saturation. In addition, the effect of retention hysteresis on the unsaturated hydraulic conductivity behaviour has typically not been explicitly considered. This paper presents a new hysteretic hydraulic constitutive model for the water retention and hydraulic conductivity behaviour of unsaturated soils, which is effective and easy to apply. The model includes: (i) main wetting and main drying water retention curves modelled with a modified version of the van Genuchten model, improved at low degree of saturation; (ii) hysteretic scanning water retention curves modelled using a bounding surface approach; (iii) the effect of hydraulic hysteresis on a soil hydraulic conductivity curve (SHCC) model improved at low degree of saturation and including the effect of liquid film conductivity. The new hysteretic hydraulic model is then validated against experimental data. After implementation in the finite element software Code_Bright, the new hydraulic constitutive model is applied in a numerical study of the impact of hydraulic hysteresis on the behaviour of capillary barrier systems (CBSs). Water retention hysteresis, which has typically been neglected in the modelling of the hydraulic behaviour of CBSs, is shown to have a significant impact on: (i) movement and redistribution of water within the finer layer of a CBS; (ii) the phenomenon of water breakthrough across the interface between the finer and coarser layers of a CBS and the subsequent restoration of the CBS after infiltration at the ground surface ceases; (iii) the prediction of evaporation from a CBS into the atmosphere

Conceptual Hydraulic Conductivity Model for Unsaturated Soils at Low Degree of Saturation and Its Application to the Study of Capillary Barrier Systems

Accurate modeling and prediction of the variation of the hydraulic conductivity of unsaturated soils at a very low degree of saturation has important implications in various engineering problems. Physical processes underlying the hydraulic behavior of unsaturated soils (retention behavior and variation of hydraulic conductivity) are first explained, and then a consistent set of new definitions for key transition hydraulic states is proposed. This lays the foundation for the presentation of a new predictive hydraulic conductivity model, accurate for the full range of degree of saturation and applicable to relatively coarse-grained soils (i.e., gravels, sands, and silts). The hydraulic conductivity is divided into two components—a bulk water component and a liquid film component—each of which varies with the degree of saturation or suction. The model is then validated against experimental data. Finally, the new hydraulic conductivity model is applied to the numerical study of the hydraulic behavior of capillary barrier systems (CBSs). The new model is able to predict the behavior of CBSs better than conventional models, and the numerical modeling highlights the role of liquid film flow, which is often neglected

Spatial Variability of Soil Properties in Saudi Arabia: Estimation of Correlation Length

Spatial variability of soil properties plays an important role in geotechnical engineering, influencing the design and performance of geo-structures. This study investigates the characterisation of this spatial variability by examining in-situ soil data obtained from 74 Cone Penetration Tests (CPTs) conducted in a reasonably homogeneous granular fill of a large construction project in Saudi Arabia. The primary focus of this work is to assess, from the available in-situ CPT data, the spatial variability of this sand fills in terms of the vertical correlation length (θv). The autocorrelation function (ACF) method is used to estimate θv, and the geo-statistical patterns of all estimated θvs are analysed through the values of its mean (µ), standard deviation (σ), coefficient of variation (CoV), and fitted probability density function (pd f). An assessment of the accuracy in the estimated θvs is then carried out from the statistical analysis of 1,000 one-dimensional (1−D) random fields with spatial statistical information similar to the in-situ fill. The study shows that as much as 25% error can be expected for the specific depth (D = 10m) and sampling interval (dx = 0.01m) of the 74 CPTs considered

Mathematical modelling of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect

Many geotechnical applications are affected by the melting and formation of ice in soils. Current state of practice involves incorporating the presence of ice within hydrological models for unsaturated soils using the so-called generalised Clapeyron equation [1]. This represents a modification of the conventional Clapeyron equation by allowing for the pressure in ice and liquid to be different at an ice-liquid interface. Such an idea has come about due to the effects of surface tension, which become important within the pores of porous materials such as soil and rock. However, a common assumption when using the generalised Clapeyron equation is that the ice pressure remains constant [2], which leads to unrealistic behaviour in the presence of significant pore-water pressure changes. Here we develop a new mathematical modelling framework to explore the impact of pressure induced freezing point depression within soils exhibiting strong capillary pressure effect. We solve the coupled mass and energy conservation problem using method of lines (e.g., [3]) with pressure and enthalpy as the primary dependent variables. Strong non-linear coupling develops through the chemical potential equation accounting for coexistence of ice and water in the presence of surface tension [5]. We present a sensitivity analysis showing how freezing point depression evolves within a porous block subject to temperature surface boundary cooling and varied capillary pressures

A bounding surface mechanical model for unsaturated cemented soils under isotropic stresses

This paper presents a model that describes the gradual yielding of unsaturated cemented soils subjected to isotropic loading. The model relies on the definition of a “cementation bonding function” which accounts for the progressive breakage of inter-granular cementation caused by loading. The combination of this cementing bonding function with the unsaturated model of Gallipoli and Bruno (2017) leads to the formulation of a “cemented unified normal compression line” (CUNCL), which describes the virgin behaviour of both cemented and uncemented soils under saturated and unsaturated conditions. Gradual yielding is described by assuming that, as the soil state moves towards the CUNCL, the slope of the loading curve tends towards the slope of the CUNCL. The model describes the hysteretic variation of void ratio for both cemented and uncemented soils under saturated and unsaturated conditions by using only seven parameters, i.e. five parameters for the uncemented behaviour plus two extra parameters accounting for the effect of cementation. The model has been calibrated and validated against the experimental data of Arroyo et al. (2013) demonstrating a good performance to describe the uncemented and cemented behaviour of soils under saturated and unsaturated conditions