Numerical Implementation of a Critical State Model for Soft Rocks

This paper details the basic tasks for the numerical implementation of a simple elasto-plastic critical state model for bonded materials (i.e. soft rocks-hard soils) into the finite element program SNAC developed at the University of Newcastle in Australia. The first task described focusses on the derivation of the incremental constitutive relationships used to represent the mechanical response of a bonded/cemented material under saturated conditions. The second task presents how these stress-strain relations can be numerically integrated using an explicit substepping scheme with automatic error control. The third task concentrates on the verification of the substepping algorithm proposed. The model used to represent the saturated mechanical response of a bonded material combines the modified Cam clay with the constitutive relationships for cemented materials proposed in Gens & Nova (1993), but incorporates some flexibility on the degradation law adopted. The role of suction and other relevant aspects of unsaturated behaviour are also discussed at the end of the paper

Normal Compression Planar Surfaces for Specific Volume and Degree of Saturation

The glasgow coupled model (GCM) predicts unique unsaturated normal compression planar surfaces for specific volume and degree of saturation when the soil states are at the intersection of the mechanical (M) and wetting retention (WR) yield curves. More generally, the model predictions for any stress path where plastic volumetric strains (compression) and plastic increases of degree of saturation occur simultaneously correspond to stress states on these two planar surfaces. The existence and form of these planar surfaces has been only validated against isotropic compression data on unsaturated samples of compacted Speswhite kaolin, but their suitability to represent one-dimensional (1D) loading conditions remains unclear. This paper investigates this aspect by deriving equivalent expressions for 1D normal compression conditions and then comparing them against the experimental response of unsaturated samples of compacted Jossigny silt subjected to 1D compression paths at different constant values of matric suction

Formulation of a three-dimensional constitutive model for unsaturated soils incorporating mechanical-water retention couplings

Wheeler, Sharma and Buisson proposed an elasto-plastic constitutive model for unsaturated soils that couples the mechanical and water retention behaviours. The model was formulated for isotropic stress states and adopts the mean Bishop's stress and modified suction as stress state variables. This paper deals with the extension of this constitutive model to general three-dimensional stress conditions, proposing the generalized stress–strain relationships required for the numerical integration of the constitutive model. A characteristic of the original model is the consideration of a number of elasto-plastic mechanisms to describe the complex behaviour of unsaturated soils. This work presents the three-dimensional formulation of these coupled irreversible mechanisms in a generalized way including anisotropic loading. The paper also compares the results from the model with published experiments performed under different loading conditions. The response of the model is very satisfactory in terms of both mechanical and water retention behaviours

Investigating the Scales of Fluctuation of an Artificial Sand Island

Artificial sand islands were constructed in the Canadian Beaufort Sea for use as hydrocarbon exploration platforms in the 1970s and 1980s. For some of these islands, extensive Cone Penetration Test (CPT) data are available for characterising the hydraulically placed sand during and after the construction process. Tarsiut P-45 was the first island using the 'Molikpaq' concept, which consisted of a mobile arctic caisson system to provide the temporary structure for the exploitation. Two main sand fills were constructed: (a) a sandfill berm on which the caisson system was founded; and (b) the body of the island structure (island core). This paper presents an investigation of the variability of the sand in the berm in terms of the vertical and horizontal scales of fluctuation. This geo-statistical investigation is carried out using CPT data from the berm before and after the founding of the caisson system, and sets the basis for a preliminary discussion on the potential soil variability changes caused by the installation and infilling of the caisson structure when placed on the berm

On the estimation of scale of fluctuation in geostatistics

Describing how soil properties vary spatially is of particular importance in stochastic analyses of geotechnical problems, because spatial variability has a significant influence on local material and global geotechnical response. In particular, the scale of fluctuation θ is a key parameter in the correlation model used to represent the spatial variability of a site through a random field. It is, therefore, of fundamental importance to accurately estimate θ in order to best model the actual soil heterogeneity. In this paper, two methodologies are investigated to assess their abilities to estimate the vertical and horizontal scales of fluctuation of a particular site using <i>in situ</i> cone penetration test (CPT) data. The first method belongs to the family of more traditional approaches, which are based on best fitting a theoretical correlation model to available CPT data. The second method involves a new strategy which combines information from conditional random fields with the traditional approach. Both methods are applied to a case study involving the estimation of θ at three two-dimensional sections across a site and the results obtained show general agreement between the two methods, suggesting a similar level of accuracy between the new and traditional approaches. However, in order to further assess the relative accuracy of estimates provided by each method, a second numerical analysis is proposed. The results confirm the general consistency observed in the case study calculations, particularly in the vertical direction where a large amount of data are available. Interestingly, for the horizontal direction, where data are typically scarce, some additional improvement in terms of relative error is obtained with the new approach. © 2013 Taylor & Francis

A single-stress model for the prediction of yielding of unsaturated cemented soils under isotropic loads

This paper presents a bounding surface model predicting the combined effects of cementation and partial saturation on the mechanical behaviour of soils subjected to isotropic loading. The loss of cementation caused by loading, wetting or drying of a normally consolidated soil is described by a “cementation bonding function”. This states that, under virgin conditions, the ratio between cemented and uncemented void ratios monotonically decreases with increasing levels of scaled stress. The scaled stress is the variable governing the intrinsic behaviour of the soil under both saturated and unsaturated conditions. Combination of the cementation bounding function with a previously proposed model for unsaturated soil behaviour leads to the formulation of a “cemented unified normal compression line” (CUNCL). This describes the virgin behaviour of both cemented and uncemented soils under saturated and unsaturated conditions. Progressive yielding is modelled by assuming that the slope of the generic loading curve tends towards the slope of the CUNCL as the soil state moves from overconsolidated to virgin conditions. The model has been calibrated and validated against existing experimental data demonstrating a good ability to predict the void ratio of cemented soils during isotropic loading, unloading and wetting under both saturated and unsaturated conditions

Investigating the scales of fluctuation of an artificial sand island

Artificial sand islands were constructed in the Canadian Beaufort Sea for use as hydrocarbon exploration platforms in the 1970s and 1980s. For some of these islands, extensive Cone Penetration Test (CPT) data are available for characterising the hydraulically placed sand during and after the construction process. Tarsiut P-45 was the first island using the 'Molikpaq' concept, which consisted of a mobile arctic caisson system to provide the temporary structure for the exploitation. Two main sand fills were constructed: (a) a sandfill berm on which the caisson system was founded; and (b) the body of the island structure (island core). This paper presents an investigation of the variability of the sand in the berm in terms of the vertical and horizontal scales of fluctuation. This geo-statistical investigation is carried out using CPT data from the berm before and after the founding of the caisson system, and sets the basis for a preliminary discussion on the potential soil variability changes caused by the installation and infilling of the caisson structure when placed on the berm

Error behaviour in explicit integration algorithms with automatic substepping

This paper studies the behaviour of the error incurred when numerically integrating the elasto-plastic mechanical relationships of a constitutive model for soils using an explicit substepping formulation with automatic error control. The correct update of all the variables involved in the numerical integration of the incremental stress–strain relationships is central to the computational performance of the integration scheme, and, although often missed in the literature, all variables (including specific volume) should be explicitly considered in the algorithmic formulation. This is demonstrated in the paper by studying, in the context of the Cam clay formulations for saturated soils, the influence that the updating of the specific volume has on the accuracy of the numerical solution. The fact that the variation of the local error with the size of the integrated strain depends on the order of local accuracy of the numerical method is also used in the paper to propose a simple and powerful strategy to verify the correctness of the implemented mathematical formulation. Copyright © 2016 John Wiley & Sons, Ltd