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

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)

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 in situ 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

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

Probabilistic examination of the change in eigenfrequencies of an offshore wind turbine under progressive scour incorporating soil spatial variability

The trend for development in the offshore wind sector is towards larger turbines in deeper water. This results in higher wind and wave loads on these dynamically sensitive structures. Monopiles are the preferred foundation solution for offshore wind structures and have a typical expected design life of 20 years. These foundations have strict serviceability tolerances (e.g. mudline rotation of less than 0.25° during operation). Accurate determination of the system frequency is critical in order to ensure satisfactory performance over the design life, yet determination of the system stiffness and in particular the operational soil stiffness remains a significant challenge. Offshore site investigations typically focus on the determination of the soil conditions using Cone Penetration Test (CPT) data. This test gives large volumes of high quality data on the soil conditions at the test location, which can be correlated to soil strength and stiffness parameters and used directly in pile capacity models. However, a combination of factors including; parameter transformation, natural variability, the relatively small volume of the overall sea bed tested and operational effects such as the potential for scour development during turbine operation lead to large uncertainties in the soil stiffness values used in design. In this paper, the effects of scour erosion around unprotected foundations on the design system frequencies of an offshore wind turbine is investigated numerically. To account for the uncertainty in soil-structure interaction stiffness for a given offshore site, a stochastic ground model is developed using the data resulting from CPTs as inputs. Results indicate that the greater the depth of scour, the less certain a frequency-based SHM technique would be in accurately assessing scour magnitude based solely on first natural frequency measurements. However, using Receiver Operating Characteristic (ROC) curve analysis, the chance of detecting the presence of scour from the output frequencies is improved significantly and even modest scour depths of 0.25 pile diameters can be detected

Numerical modelling of coupled behaviour in unsaturated soils

Unsaturated soils are present in a wide range of geotechnical applications such as slopes, highways or earth dams, in addition to many other geo-environmental applications such as underground disposal of radioactive waste or landfills. Despite a significant number of improvements in understanding unsaturated soil behaviour over the last five decades, there are still several aspects to be addressed and to be better understood, including in the areas of constitutive modelling, development of experimental procedures and improvement of numerical techniques. This work concentrates on two of these aspects: constitutive modelling of unsaturated soils accounting for the coupling between mechanical and water retention response; and associated numerical and computational aspects employed to solve engineering problems involving unsaturated soil mechanics. Wheeler et al. (2003) proposed a coupled elasto-plastic constitutive model for the mechanical and water retention behaviour of unsaturated soils and this model constitutes the basis of the work developed within this thesis. For isotropic stress states this coupled model employs as stress state variables mean Bishop’s stress p* and modified suction s*. In the model, plastic volumetric strains occur when the stress state reaches a LC yield curve and plastic changes of degree of saturation Sr occur when the stress state reaches a SD or SI yield curve. Coupled movements of the yield curves represent the influence of plastic changes of degree of saturation on mechanical behaviour and the influence of plastic volumetric strains on water retention behaviour. According to this constitutive model, during many types of loading or wetting under isotropic stress states the soil state will ultimately arrive at the corner between the LC and SD yield curves. Analysis of the model suggests that such states should fall on a unique planar normal compression surface in v:lnp*:lns* space and also on a second unique planar surface in Sr:lnp*:lns* space. The experimental results of Sivakumar (1993) from constant suction isotropic loading of compacted speswhite kaolin are presented in these spaces, and are shown to lie on planar surfaces, as predicted by the model. Presenting experimental normal compression results in this way gives an ideal method for determining the values of the key soil parameters k1, k2, λs and κs in the model. A simple extension of the Wheeler et al. (2003) model to the stress conditions of the triaxial test, by including the role of deviator stress q, has been proposed by Lloret et al. ii (2008b) and Raveendiraraj (2009). According to this extended model, critical states will commonly occur at the intersection of the LC yield surface and the SD yield surface, and such critical states should fall on a second pair of unique planar surfaces in the v:lnp*:lns* and Sr:lnp*:lns* spaces. The experimental critical state data of Sivakumar (1993) have been plotted in these spaces and the results obtained are presented and discussed. The new constitutive model has been extended to general 3D stress conditions and generalised stress-strain relationships required for numerical integration of the model are presented. Furthermore, 3D extended functions to identify the different elasto-plastic mechanisms of the model are proposed. A partial validation of this extended model is also presented using the experimental results of Sivakumar (1993). Two strain-driver algorithms for the integration of the generalised model are presented including first and second order error schemes. The complete formulation of these explicit algorithms is described and the computed results from both integration schemes is compared and discussed. Finally, the generalised fully coupled constitutive model has been implemented within the finite element program CODE_BRIGHT (Olivella et al., 1996) to solve boundary value problems involving unsaturated soil. The performance of the new implemented model is analysed and discussed by considering application to a boundary value problem involving wetting of a cylindrical soil specimen.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Anomalous diffusion and search behavior in Caenorhabditis elegans

[eng] In this thesis, our focus was on unraveling how Caenorhabditis elegans samples its environment in the absence of gradients and food resources. We analyzed data from a relocation experiment in which individual worms, including wild-type isolates and defective mutants, were displaced from a food patch to an empty arena in tightly controlled environmental conditions. We characterized the spreading patterns of the worms and analyzed their movement dynamics at various temporal scales, ranging from milliseconds to hours. Our findings revealed an intricate, time-dependent spreading process, likely driven by internal states and memory relaxation due to the absence of clear external stimuli. Notably, C. elegans exhibited superdiffusive spreading behavior, prompting us to investigate the mechanisms behind this phenomenon and its adaptive significance in search contexts. To this end, we devised a classification algorithm that enabled us to characterize C. elegans trajectories into its elementary motor behaviors: sharp turns and crawls. Leveraging these insights, we developed a mechanistic model of movement that reproduces C. elegans search trajectories in great detail, shedding light on the emergence of superdiffusion. Additionally, we evaluated the search performance of various C. elegans-inspired movement models across multiple spatial scales, assuming two distinct search conditions: symmetric (all targets distant) and asymmetric (near and far targets) scenarios. Through this exercise, we quantitatively assessed the contribution of both superdiffusion and turning dynamics to the search performance of C. elegans. Finally, in an effort to reinforce our theoretical results with a real case study, we conducted a series of experiments with C. elegans individuals foraging in patchy landscapes with bacteria. In these experiments, we employed both homogeneous (regular) and heterogeneous (aggregate) landscapes, mirroring the search conditions evaluated in the synthetic simulations. Our findings confirmed that turning dynamics and superdiffusion are key elements of search behavior in C. elegans, fundamentally shaping its search performance in all landscape configurations analyzed. Furthermore, our results suggest that these two mechanisms have the potential to influence the ecological fitness of the species in the natural environment. While our conclusions are primarily based on the specific experimental conditions analyzed, which involve a sharp transition from resource-plentiful to empty arenas, we believe that the findings we present offer valuable insights into both the understanding of C. elegans search behavior and the adaptive value of superdiffusion and turning dynamics in search processes.[cat] En aquesta tesi ens hem centrat a entendre com Caenorhabditis elegans explora un entorn sense menjar ni gradients ambientals. Hem analitzat el moviment d’aquest animal en un experiment de reubicació, en el qual vàrem traslladar individus de diverses soques tant salvatges com mutants, des d’una placa de petri amb menjar, a un espai sense menjar i amb condicions de temperatura i humitat molt controlades. Per desenvolupar la nostra recerca hem caracteritzat detalladament els patrons de dispersi´o de C. elegans, basant-nos en les trajectòries obtingudes i també en la dinàmica del seu moviment mesurat a diverses escales de temps, des dels milisegons fins a l’hora. Els nostres resultats indiquen que C. elegans dispersa segons un procés no estacionari, probablement modulat pels seus estats interns i no pas per estímuls externs com per exemple gradients ambientals. Cal destacar que els indi- vidus de C. elegans estudiats varen exhibir un patró de dispersió superdifusiu, fet que va motivar-nos a investigar en profunditat els mecanismes físics que expliquen l’emergència d’aquest fenomen i també quina és la seva rellevància adaptativa en contextos de cerca. Per fer-ho, vàrem desenvolupar un algoritme de classificació per caracteritzar les trajectòries de C. elegans en els seus comportaments motrius elementals. Basant-nos en els resultats obtinguts, vàrem desenvolupar un model mecanicista del moviment de C. elegans que ens ha permès entendre quins mecanismes físics generen superdiffusió Seguidament, ens vàrem centrar a caracteritzar la seva eficiència en condicions de cerca simètriques, on tots els recursos es troben lluny, i en condicions de cerca asimètrica, on es poden trobar recursos tant a prop com lluny. A través de simulacions virtuals, vàrem quantificar la contribució de la superdifusió de la dinàmica de girs en l’eficiència de cerca de C. elegans. Finalment i amb la intenció de reforçar les nostres conclusions teòriques vàrem fer una sèrie d’experiments de cerca on individus de C. elegans podien buscar, trobar i consumir menjar distribuït segons un paisatge homogeni (regular), utilitzat per estudiar la condició simètrica, o un paisatge heterogeni (agregat), utilitzat per estudiar la condició asimètrica. Els resultats obtinguts varen confirmar que tant la dinàmica de girs com la superdifusió són dos elements clau en el comportament de cerca de C. elegans, ja que determinen la seva eficiència de cerca. Més encara, els nostres resultats suggereixen que aquests dos mecanismes podrien arribar a influir l’èxit reproductiu de l’espècie a la naturalesa. Tot i que les conclusions obtingudes en aquesta tesi són relatives a condicions experimentals específiques, creiem que els resultats presentats i les seves interpretacions, ofereixen un coneixement valuós per entendre el comportament de cerca de C. elegans i el valor adaptatiu de la superdifusió en els processos de cerca