Application of Bayesian approach in geotechnical engineering

En esta Tesis Doctoral se emplean y desarrollan Métodos Bayesianos para su aplicación en análisis geotécnicos habituales, con un énfasis particular en (i) la valoración y selección de modelos geotécnicos basados en correlaciones empíricas; en (ii) el desarrollo de predicciones acerca de los resultados esperados en modelos geotécnicos complejos. Se llevan a cabo diferentes aplicaciones a problemas geotécnicos, como es el caso de: (1) En el caso de rocas intactas, se presenta un método Bayesiano para la evaluación de modelos que permiten estimar el módulo de Young a partir de la resistencia a compresión simple (UCS). La metodología desarrollada suministra estimaciones de las incertidumbres de los parámetros y predicciones y es capaz de diferenciar entre las diferentes fuentes de error. Se desarrollan modelos "específicos de roca" para los tipos de roca más comunes y se muestra cómo se pueden "actualizar" esos modelos "iniciales" para incorporar, cuando se encuentra disponible, la nueva información específica del proyecto, reduciendo las incertidumbres del modelo y mejorando sus capacidades predictivas. (2) Para macizos rocosos, se presenta una metodología, fundamentada en un criterio de selección de modelos, que permite determinar el modelo más apropiado, entre un conjunto de candidatos, para estimar el módulo de deformación de un macizo rocoso a partir de un conjunto de datos observados. Una vez que se ha seleccionado el modelo más apropiado, se emplea un método Bayesiano para obtener distribuciones predictivas de los módulos de deformación de macizos rocosos y para actualizarlos con la nueva información específica del proyecto. Este método Bayesiano de actualización puede reducir significativamente la incertidumbre asociada a la predicción, y por lo tanto, afectar las estimaciones que se hagan de la probabilidad de fallo, lo cual es de un interés significativo para los diseños de mecánica de rocas basados en fiabilidad. (3) En las primeras etapas de los diseños de mecánica de rocas, la información acerca de los parámetros geomecánicos y geométricos, las tensiones in-situ o los parámetros de sostenimiento, es, a menudo, escasa o incompleta. Esto plantea dificultades para aplicar las correlaciones empíricas tradicionales que no pueden trabajar con información incompleta para realizar predicciones. Por lo tanto, se propone la utilización de una Red Bayesiana para trabajar con información incompleta y, en particular, se desarrolla un clasificador Naïve Bayes para predecir la probabilidad de ocurrencia de grandes deformaciones (squeezing) en un túnel a partir de cinco parámetros de entrada habitualmente disponibles, al menos parcialmente, en la etapa de diseño. This dissertation employs and develops Bayesian methods to be used in typical geotechnical analyses, with a particular emphasis on (i) the assessment and selection of geotechnical models based on empirical correlations; on (ii) the development of probabilistic predictions of outcomes expected for complex geotechnical models. Examples of application to geotechnical problems are developed, as follows: (1) For intact rocks, we present a Bayesian framework for model assessment to estimate the Young’s moduli based on their UCS. Our approach provides uncertainty estimates of parameters and predictions, and can differentiate among the sources of error. We develop ‘rock-specific’ models for common rock types, and illustrate that such ‘initial’ models can be ‘updated’ to incorporate new project-specific information as it becomes available, reducing model uncertainties and improving their predictive capabilities. (2) For rock masses, we present an approach, based on model selection criteria to select the most appropriate model, among a set of candidate models, to estimate the deformation modulus of a rock mass, given a set of observed data. Once the most appropriate model is selected, a Bayesian framework is employed to develop predictive distributions of the deformation moduli of rock masses, and to update them with new project-specific data. Such Bayesian updating approach can significantly reduce the associated predictive uncertainty, and therefore, affect our computed estimates of probability of failure, which is of significant interest to reliability-based rock engineering design. (3) In the preliminary design stage of rock engineering, the information about geomechanical and geometrical parameters, in situ stress or support parameters is often scarce or incomplete. This poses difficulties in applying traditional empirical correlations that cannot deal with incomplete data to make predictions. Therefore, we propose the use of Bayesian Networks to deal with incomplete data and, in particular, a Naïve Bayes classifier is developed to predict the probability of occurrence of tunnel squeezing based on five input parameters that are commonly available, at least partially, at design stages.

Simulação numérica de dutos enterrados, submetidos à perda de apoio e elevação localizada.

Os recentes desastres ocorridos no país, como o rompimento da adutora em Campo Grande e os desastres relacionados às enchentes urbanas, mostram a necessidade de desenvolvimento de pesquisas científicas que auxiliem na compreensão e no dimensionamento das estruturas projetadas para atender a demanda da população. Os métodos analíticos e experimentais mais utilizados possuem algumas limitações de ordem teórica ou prática. Por outro lado, os métodos numéricos, capazes de simular etapas construtivas e envolver materiais com diferentes modelos constitutivos numa mesma análise, buscam atender às necessidades práticas dos projetos de geotecnia e, ao mesmo tempo, complementam os modelos analíticos e experimentais. Nesse trabalho foram realizadas comparações entre resultados obtidos em ensaios experimentais e resultados extraídos do modelo computacional, buscando aumentar a compreensão sobre a interação solo-estrutura em relação à distribuição de tensões mobilizadas e aos deslocamentos e deformações provocados. A simulação numérica foi feita com a utilização do PLAXIS/3D, software de análise geotécnica baseado no método dos elementos finitos. Os ensaios foram confeccionados na Escola de Engenharia de São Carlos/USP por Costa (2005) e envolveram dutos enterrados submetidos à perda de apoio ou elevação localizada. O estudo experimental foi realizado através de modelos físicos compostos por um maciço de areia pura, contendo um tubo repousando sobre um alçapão no centro do vão. Os modelos físicos foram equipados com instrumental capaz de medir as deflexões e as deformações específicas ao longo do duto, além das tensões totais no maciço de solo circundante e na base do equipamento.

Coupled foundation-superstructure analysis and influence of building stiffness on foundation response

This paper proposes a simple method to include superstructure stiffness in foundation analyses. The method involves extracting a small "condensed structural matrix" from finite element models of the superstructure, which can then be incorporated into pile group or piled raft analyses using common approaches such as elastic continuum or load transfer methods. The matrix condensation method directly couples structural and geotechnical analyses, and eliminates the need for iterative analyses between structural and geotechnical engineers. Effectiveness of the approach is illustrated through analyses of several buildings designed with a typical floor plan but with varying heights. The parametric study illustrates that superstructure stiffness can have a significant influence on foundation settlement estimates, and the stiffening effects are dominated by the lower stories of the superstructure. The proposed method aims to bridge the gap between structural and geotechnical analyses. Also, being a computationally simple and accurate approach, it is applicable to parametric or optimization studies that would otherwise involve large amounts of analyses. © 2010 ASCE.

Influence de la taille et de la gradation des particules sur la résistance au cisaillement et le comportement dilatant des matériaux granulaires

Résumé : Cette étude examine l'impact de la taille et de la gradation de particules sur les corrélations théoriques et empiriques existantes les plus connues entre la résistance au cisaillement et le comportement dilatatant des matériaux granulaires en condition de déformation plane et en compression triaxiale drainée. À cette fin, 276 tests de cisaillements symétriques directs et 35 tests de compressions triaxiales drainées ont été menés sur des échantillons composés de billes de basalte (particules rondes), et de sables constitués de particules angulaires (sable de Péribonka et sable d'Eastmain) sur une échelle de 63 µm à 2000 µm afin d'évaluer leur résistance au cisaillement et leur comportement de dilatance sur une vaste échelle de pressions normales et de densités relatives initiales. Premièrement, la fiabilité et l'applicabilité des limites de mesure à l’aide de tests physiques de cisaillements symétriques directs dans l'interprétation de la résistance au cisaillement frictionnel en déformation plane des matériaux granulaires ont été discutées et confirmées par l'usage du code informatique DEM, SiGran. L'accent a été particulièrement mis sur la validation du modèle DEM au moyen de comparaison des résultats des simulations DEM avec leurs équivalents physiques à une échelle macro. Les résultats virtuels DSA sont abordés du point de vue de la coaxialité entre les principales tensions et les principales directions des paliers de pression ainsi que de la déviation de la direction d'extension nulle à partir de la direction horizontale. Les résultats numériques fournissent également des données quantitatives sur les différentes formes d'énergie consommées durant le cisaillement confirmées par d'autres résultats physiques et numériques publiés. Sur la base des postulats précédents, un examen minutieux des résultats des essais de cisaillements directs et de données issues de la littérature a été accompli afin d'évaluer la fiabilité des formules empiriques bien connues de Bolton et Collins et al. avec leurs constantes couramment employées en condition de déformation plane. L'étude montre qu'une application des relations empiriques de force-dilatation de cisaillement avec les constantes proposées par Bolton (1986) et Collins et al. (1992) aux sables ayant une distribution de taille de particules différente peut conduire à surestimer leurs valeurs en terme de force de cisaillement. Dans cette étude, les coefficients des équations de Bolton et Collins et al. ont donc été ajustée afin de prendre en compte les caractéristiques des particules, en particulier le diamètre médian, D50. De manière analogue, les effets microstructuraux imposés par la géométrie interne des particules (par exemple la taille, la forme et la gradation des particules) sur la relation tension-dilatation très connue, celle de Rowe (1962), et son ajustement empirique en condition triaxiale drainée ont été examinés dans cette étude. Une comparaison des prédictions des formules proposées avec les données de force de cisaillement issues de la littérature fournit de nombreuses preuves en faveur des contraintes mises en place au sein des relations existantes de force-dilatation de cisaillement en condition de déformation plane et triaxiale. Ces comparaisons prouvent également que la prise en compte de la taille des grains conduit à des résultats plus tangibles que lorsque la taille de la particule n'est pas considérée. Les formules de force-dilatation ajustées peuvent se révéler avantageuses pour évaluer indépendamment la cohérence des forces de cisaillement déterminées expérimentalement et pour introduire des lois d’écoulement plus précises dans les analyses géotechniques analytiques et numériques.

Parametric finite element analyses of geocellsupported embankments

This paper presents the results from parametric finite element analyses of geocell-supported embankments constructed on weak foundation soils. A composite model is used to numerically simulate the improvement in the strength and stiffness of the soil as a result of geocell confinement. The shear strength of the geocell-encased soil is obtained as a function of the additional confining pressure due to the geocell encasement considering it as a thin cylinder subjected to internal pressure. The stiffness of the geocell-encased soil is obtained from the stiffness of the unreinforced soil and the tensile modulus of the geocell material using an empirical equation. The validity of the model is verified by simulating the laboratory experiments on model geocell-supported embankments. Parametric finite element analyses of the geocell-supported embankments are carried out by varying the dimensions of the geocell layer, the tensile strength of the material used for fabricating the geocell layer, the properties of the infill soil, and the depth of the foundation layer. Some important guidelines for selecting the geocell reinforcement to support embankments on weak foundation soils are established through these numerical studies.

3D FE Analyses of Buried Pipeline with Elbows Subjected to Lateral Loading

This study investigates the interaction between soil and pipeline in sand subjected to lateral ground displacements with emphasis on the peak force exerted to a bended elbow-pipe. A series of three-dimensional (3D) finite-element (FE) analyses were performed in both opening and closing modes of the elbow section for different initial pipe bending angles. To model the mechanical behavior of sands, two soil models were adopted: Mohr-Coulomb and Nor-Sand soil model. Investigations also included the effects of pipe embedment depth and soil density. Results show that the opening mode exhibits higher ultimate forces and greater localized deformations than the closing mode. Nondimensional charts that account for pipeline location, bending angle, and soil density are developed. Soil-spring pipeline analyses of an elbow-pipe were performed using modified F-δ soil-spring models based on the 3D FE results and were compared to the findings of conventional spring model analyses using the standard two-dimensional soil-spring model. Results show that the pipe strain does not change in the closing mode case. However, in the opening mode case, the pipe strain computed by the modified analysis is larger than that by the conventional analysis and the difference is more pronounced when the pipe stiffness is stiffer. © 2011 American Society of Civil Engineers.

Seismic analyses of shallow tunnels by dynamic centrifuge tests and finite elements

The increments of internal forces induced in a tunnel lining during earthquakes can be assessed with several procedures at different levels of complexity. However, the substantial lack of well-documented case histories still represents a difficulty in order to validate any of the methods proposed in literature. To bridge this gap, centrifuge model tests were carried out on a circular aluminium tunnel located at two different depths in dense and loose dry sand. Each model has been instrumented for measuring soil motion and internal loads in the lining and tested under several dynamic input signals. The tests performed represented an experimental benchmark to calibrate dynamic analyses with different approaches to account for soil-tunnel kinematic interaction. © 2009 IOS Press.

Quaternary geology of the German North Sea and Western Irish Sea Mud Belt: revised stratigraphies, geotechnical properties, sedimentology and anthropogenic impacts

The climatic development of the Mid to Late Quaternary (last 400,000 years) is characterised by fluctuation between glacial and interglacial periods leading to the present interglacial, the Holocene. In comparison to preceding periods it was believed the Holocene represented a time of relative climatic stability. However, recent work has shown that the Holocene can be divided into cooler periods such as the Little Ice Age alternating with time intervals where climatic conditions ameliorated i.e. Medieval Warm Period, Holocene Thermal Optimum and the present Modern Optimum. In addition, the Holocene is recognised as a period with increasing anthropogenic influence on the environment. Onshore records recording glacial/interglacial cycles as well as anthropogenic effects are limited. However, sites of sediment accumulation on the shallow continental shelf offer the potential to reconstruct these events. Such sites include tunnel valleys and low energy, depositional settings. In this study we interrogated the sediment stratigraphy at such sites in the North Sea and Irish Sea using traditional techniques, as well as novel applications of geotechnical data, to reconstruct the palaeoenvironmental record. Within the German North Sea sector a combination of core, seismic and in-situ Cone Penetration Testing (CPT) data was used to identify sedimentary units, place them within a morphological context, relate them to glacial or interglacial periods stratigraphically, and correlate them across the German North Sea. Subsequently, we were able to revise the Mid to Late Quaternary stratigraphy for the North Sea using this new and novel data. Similarly, Holocene environmental changes were investigated within the Irish Sea at a depositional site with active anthropogenic influence. The methods used included analyses on grain-size distribution, foraminifera, gamma spectrometry, AMS 14C and physical core logging. The investigation revealed a strong fluctuating climatic signal early in the areas history before anthropogenic influence affects the record through trawling.

Geotechnical and structural behavior of the railroad track in large-scale apparatus

This paper analyses the static and dynamic behavior of the railroad track model in laboratory. Measurements of stresses and strains on a large-scale railroad track apparatus were studied. The model includes: compacted soil, representing the final layers of platform, ballast layer, and ties (steel, wooden, and pre-stressed concrete). The soil and soil ballast interface were instrumented with pneumatic stress gauge. Settlement measurement device were positioned at the same levels as the load cells. Loads were applied by hydraulic actuators, statically and dynamically. After the prescribed number of load cycles, in pre-determined intervals, stresses and strains were measured. Observations indicate that stress and strain distributions, transmitted by wooden or steel ties, behave similarly. A more favorable behavior was observed with pre-stressed concrete mono block ties. Non-linear response was observed after a threshold numbers of cycles were surpassed, showing that the strain modulus increases with the numbers of cycles. © 2009 IOS Press.

Geotechnical properties of shelf sdiments from the Prydz Bay

This paper presents a geotechnical characterization of the glacigenic sediments in Prydz Bay, East Antarctica, based on the shipboard physical properties data obtained during Leg 119, combined with results of land-based analyses of 24 whole-round core samples. Main emphasis is placed on the land-based studies, which included oedometer consolidation tests, triaxial and simple shear tests for undrained shear strength, permeability tests in oedometer and triaxial cell, Atterberg limits, and grain-size analyses. The bulk of the tested sediments comprise overconsolidated diamictites of a relatively uniform lithology. The overconsolidation results from a combination of glacial loading and sediment overburden subsequently removed by extensive glacial erosion of the shelf. This leads to downhole profiles of physical properties that have been observed not to change as a function of the thickness of present overburden. A number of fluctuations in the parameters shows a relatively systematic trend and most likely results from changes in the proximity to the ice sheet grounding line in response to variations in the glacial regime. Very low permeabilities mainly result from high preconsolidation stresses (Pc'). Pc' values up to 10,000 kPa were estimated from the oedometer tests, and empirical estimates based on undrained shear strengths (up to 2500 kPa) indicate that the oedometer results are conservative. The diamictites generally classify as inactive, of low to medium plasticity, and they consolidate with little deformation, even when subjected to great stresses. This is the first report of geotechnical data from deep boreholes on the Antarctic continental shelf, but material of similar character can also be expected in other areas around the Antarctic.

Slope stability analyses based on sediment cores of the Ligurian Margin, Southern France

Submarine slope failures of various types and sizes are common along the tectonic and seismically active Ligurian margin, northwestern Mediterranean Sea, primarily because of seismicity up to ~M6, rapid sediment deposition in the Var fluvial system, and steepness of the continental slope (average 11°). We present geophysical, sedimentological and geotechnical results of two distinct slides in water depth >1,500 m: one located on the flank of the Upper Var Valley called Western Slide (WS), another located at the base of continental slope called Eastern Slide (ES). WS is a superficial slide characterized by a slope angle of ~4.6° and shallow scar (~30 m) whereas ES is a deep-seated slide with a lower slope angle (~3°) and deep scar (~100 m). Both areas mainly comprise clayey silt with intermediate plasticity, low water content (30-75 %) and underconsolidation to strong overconsolidation. Upslope undeformed sediments have low undrained shear strength (0-20 kPa) increasing gradually with depth, whereas an abrupt increase in strength up to 200 kPa occurs at a depth of ~3.6 m in the headwall of WS and ~1.0 m in the headwall of ES. These boundaries are interpreted as earlier failure planes that have been covered by hemipelagite or talus from upslope after landslide emplacement. Infinite slope stability analyses indicate both sites are stable under static conditions; however, slope failure may occur in undrained earthquake condition. Peak earthquake acceleration from 0.09 g on WS and 0.12 g on ES, i.e. M5-5.3 earthquakes on the spot, would be required to induce slope instability. Different failure styles include rapid sedimentation on steep canyon flanks with undercutting causing superficial slides in the west and an earthquake on the adjacent Marcel fault to trigger a deep-seated slide in the east.

Geotechnical properties of Lau Basin sediments

Distribution of pore space and degree of cementation appear to be the main factors controlling the permeability of sediments retrieved from the Lau Basin. The undisturbed microfabrics of two lithologies, nannofossil ooze and vitric sandy silt, commonly found at Holes 834A, 835A, 838A, and 839Aof Leg 135 were examined by scanning electron microscopy equipped with energy dispersive X-ray spectral analysis and image analysis systems. The results of these analyses were compared with laboratory determinations of porosity, grain-size distribution, and permeability on discrete samples from the same sediment depths. The permeability of the vitric sandy silt is 3-5 orders of magnitude higher than the nannofossil ooze samples. The porosity of nannofossil ooze ranges from 6% to 12% greater than the porosity of vitric sandy silt, which partially reflects the finer texture of nannofossil ooze. Although the correlation of higher porosity with lower permeability is not surprising, factors other than simply grain-size distribution must be invoked to explain the large differences in permeability found in these samples.