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Foundations constructed by the deep mixing method have been used to successfully support embankments, structures, and excavations in Japan, Scandinavia, the U.S., and other countries. The current state of practice is that design is based on deterministic analyses of settlement and stability, even though deep mixed materials are highly variable. Conservative deterministic design procedures have evolved to limit failures. Disadvantages of this approach include (1) designs with an unknown degree of conservatism and (2) contract administration problems resulting from unrealistic specifications for deep mixed materials. This dissertation describes research conducted to develop reliability-based design procedures for foundations constructed using the deep mixing method. The emphasis of the research and the included examples are for embankment support applications, but the principles are applicable to foundations constructed for other purposes. Reliability analyses for foundations created by the deep mixing method are described and illustrated using an example embankment. The deterministic stability analyses for the example embankment were performed using two methods: limit equilibrium analyses and numerical stress-strain analyses. An important finding from the research is that both numerical analyses and reliability analyses are needed to properly design embankments supported on deep mixed columns. Numerical analyses are necessary to address failure modes, such as column bending and tilting, that are not addressed by limit equilibrium analyses, which only cover composite shearing. Reliability analyses are necessary to address the impacts of variability of the deep mixed materials and other system components. Reliability analyses also provide a rational basis for establishing statistical specifications for deep mixed materials. Such specifications will simplify administration of construction contracts and reduce claims while still providing assurance that the design intent is satisfied. It is recommended that reliability-based design and statistically-based specifications be implemented in practice now. / Ph. D.

In historical, large-magnitude earthquakes, lateral spreading has been a very damaging type of ground failure. When a subsurface soil deposit liquefies, intact blocks of surficial soil can move downslope, or toward a vertical free face, even when the ground surface is nearly level. A lateral spread is defined as the mostly horizontal movement of gently sloping ground (less than 5% surface slope) due to elevated pore pressures or liquefaction in undelying, saturated soils. Here, lateral spreading is defined specifically to exclude liquefaction failures of steeper embankments and retaining walls, which can also produce lateral surface deformations. Lateral spreads commonly occur at waterfront sites underlain by saturated, recent sediments and are particularly threatening to buried utilities and transportation networks. While the occurrence of soil liquefaction and lateral spreading can be predicted at a given site, methods are needed to estimate the magnitude of the resulting deformations. In this research effort, an empirical model was developed for predicting horizontal and vertical surface displacements due to liquefaction-induced lateral spreading. The resulting model is called "EPOLLS" for Empirical Prediction Of Liquefaction-induced Lateral Spreading. Multiple linear regression analyses were used to develop model equations from a compiled database of historical lateral spreads. The complete EPOLLS model is comprised of four components: (1) Regional-EPOLLS for predicting horizontal displacements based on the seismic source and local severity of shaking, (2) Site-EPOLLS for improved predictions with the addition of data on the site topography, (3) Geotechnical-EPOLLS using additional data from soil borings at the site, and (4) Vertical-EPOLLS for predicting vertical displacements. The EPOLLS model is useful in phased liquefaction risk studies: starting with regional risk assessments and minimal site information, more precise predictions of displacements can be made with the addition of detailed site-specific data. In each component of the EPOLLS model, equations are given for predicting the average and standard deviation of displacements. Maximum displacements can be estimated using probabilities and the gamma distribution for horizontal displacements or the normal distribution for vertical displacements. / Ph. D.

This study evaluates the seismically induced displacements of a slope using the Finite Element Method (FEM) in comparison to the results of twelve empirical predictive approaches. First, the existing methods to analyze the stability of slopes subjected to seismic loads are presented and their capabilities to predict the onset of failure and post-failure behavior are discussed. These methods include the pseudostatic method, the Newmark method, and stress-deformation numerical methods. Whereas the pseudostatic method defines a seismic coefficient for the analysis and provides a safety factor, the Newmark method incorporates a yield coefficient and the actual acceleration time history to estimate permanent displacements. Numerical methods incorporate advanced constitutive models to simulate the coupled stress-strain soil behavior, making the process computationally more costly. In this study, a model slope previously studied at laboratory scale is selected and scaled up to prototype dimensions. Then, the slope is subjected to 88 different input motions, and the seismic displacements obtained from the numerical and empirical approaches are compared statistically. From correlation analyses between seven ground motion parameters and the numerical results, new empirical predictive equations are developed for slope displacements. The results show that overall the FEM displacements are generally in agreement with the numerically developed methods by Fotopoulou and Pitilakis (2015) labelled "Method 2" and "Method 3", and the Newmark-type Makdisi and Seed (1978) and Bray and Travasarou (2007) methods for rigid slopes. Finally, functional forms for seismic slope displacement are proposed as a function of peak ground acceleration (PGA), Arias intensity (Ia), and yield acceleration ratio (Ay/PGA). These functions are expected to be valid for granular slopes such as earth dams, embankments, or landfills built on a rigid base and with low fundamental periods (Ts<0.2). / Master of Science / A landslide is a displacement on a sloped ground that can be triggered by earthquake shaking. Several authors have investigated the failure mechanisms that lead to landslide initiation and subsequent mass displacement and proposed methodologies to assess the stability of slopes subjected to seismic loads. The development of these methodologies has to rely on field data that in most of the cases are difficult to obtain because identifying the location of future earthquakes involves too many uncertainties to justify investments in field instrumentation (Kutter, 1995). Nevertheless, the use of scale models and numerical techniques have helped in the investigation of these geotechnical hazards and has led to development of equations that predict seismic displacements as function of different ground motion parameters. In this study, the capabilities and limitations of the most recognized approaches to assess seismic slope stability are reviewed and explained. In addition, a previous shaking-table model is used for reference and scaled up to realistic proportions to calculate its seismic displacement using different methods, including a Finite Element model in the commercial software Plaxis2D. These displacements are compared statistically and used to develop new predictive equations. This study is relevant to understand the capabilities of newer numerical approaches in comparison to classical empirical methods.

Thesis regarding the application of the Kinematic Element Method to slope stability analysis in geotechnical engineering. / In this thesis, the effectiveness of the Kinematic Element Method (KEM), developed by Dr. Gussmann at the University of Stuttgart, was evaluated by comparing the solutions with the Limit Equilibrium Method (LEM), specifically the Morgenstern-Price method. The KEM was evaluated using a variety of problems, ranging from homogeneous slopes to retaining walls. The KEM was shown to predict similar potential failure mechanisms and values for the factor of safety (FS) as the Morgenstern-Price method. The FS were generally within the ±6% which is the range of variance for rigorous limit equilibrium methods. A simplified version of KEM (KEMv) was developed based on limit equilibrium formulations. In KEMv, an alternate iterative scheme to determine the FS is proposed, in which boundaries between elements are vertical. The KEMv provided similar values for the factor of safety and interelement forces as Gussmann’s KEM for vertical interelement boundaries given similar element locations. The KEM was assumed by Gussmann to be an upper bound solution. However, given the similarities in the solutions between KEM and KEMv, it may be a limit equilibrium method. The interelement forces from the KEM and KEMv were found to be sensitive to the location of the elements. Elements in the upper part of the slope often had small normal forces relative to shear forces, possibly being negative as well. Sensitivity analysis regarding the number of elements showed that a 5-element solution predicts the appropriate failure mechanism and provides a reasonably accurate FS. In a parametric study, slope geometry and soil properties were varied and comparisons were made between KEM and the Morgenstern-Price method. The KEMv displayed similar trends in factor of safety as the Morgenstern-Price method but predicted slightly larger values. The change in KEM critical slip surfaces with soil properties was consistent with trends predicted by Janbu’s dimensionless parameter. / Thesis / Master of Applied Science (MASc) / The stability of slopes is a challenging subject in geotechnical engineering. Geotechnical engineers are often interested in the factor of safety (FS), which is a quantitative measure of the stability of a slope. In this thesis, the effectiveness of the Kinematic Element Method (KEM) is evaluated by comparing its solutions to the Limit Equilibrium Method (LEM). The KEM was shown to predict similar potential failure mechanisms and values for the factor of safety. A simplified version of the KEM (KEMv) was developed based on LEM formulations. In KEMv, an alternate iterative scheme to determine the FS is proposed, in which the boundaries between elements are vertical. The KEMv provided similar values for the factor of safety and element forces as Gussmann’s KEM for vertical interelement boundaries. In a parametric study, KEM displayed similar trends in the change in FS and critical slip surface as the LEM.

Failure of slopes adjacent to the UK transport infrastructure causes delays and these are expensive assets to repair and maintain. Understanding the processes that lead to failure will assist asset managers both now and in the future in the context of a changing climate. The EPSRC-funded multidisciplinary FUTURENET project investigated the effect of climate change on the resilience of the UK transport network and this thesis is a part of that project considering the weather patterns leading to slope failures along transport infrastructure slopes within the UK. To that end a series of slope failure case studies were investigated to understand the processes leading to failure. These were compiled using nationally held datasets as well as news reports. This research used data from the FUTURENET partners that hold national data sets and asset management information. This shows the wide reaching remit of a multidisciplinary collaborative project such as FUTURENET, but also highlights the limitations of datasets collected and used for very specific purposes and not necessarily suited to wider research. From these case studies a suite of slope failure weather thresholds were developed. These thresholds consider the antecedent period, water content within the slope through the soil moisture deficit and triggering rainfall through comparison to the long term average rainfall. Consideration was given to possible future weather using weather event sequences (WESQs), possible weather patterns for 2050 derived from the UKCP09 climate projection data. By considering these possible weather patterns with the slope failure thresholds a picture of a possible future was evaluated.

Σκοπός αυτής της Διπλωματικής εργασίας είναι η αποτύπωση της κατάστασης της κατολισθαίνουσας ζώνης στην επαρχιακή οδό Παλαιοχωρίου - Χρυσοχωρίου, στα δύο σημεία που παρατηρήθηκαν αστοχίες. Στην περιοχή αυτή πραγματοποιήθηκε αποτύπωση και χαρτογράφηση της κατολισθαίνουσας ζώνης, παρουσιάζονται τα αποτελέσματα της τεχνικογεωλογικής - γεωτεχνικής έρευνας που παρατηρήθηκαν στις δύο θέσεις αστοχίας, μετά από την μεγάλη κατολίσθηση που εκδηλώθηκε το Φεβρουάριο του 2010 από έντονες βροχοπτώσεις, καθώς και τον σχεδιασμό των μέτρων προστασίας της επαρχιακής οδού Παλαιοχωρίου -Χρυσοχωρίου. / The purpose of this essay is to capture the situation of landslide zone on provincial road Palaiochorioy - Chrysochorioy, at two failures were observed.In this area was done survey and maps of landslide zone which presents the results of geotechnical - geotechnical investigation, observed in both locations of failure, after major landslide that occurred in February 2010 after heavy rains, and the design of measures to protect the provincial road Palaiochorio-Chrysochorioy.

Seismic slope stability is often evaluated via permanent displacement analyses, which quantify the cumulative, downslope displacement of a sliding mass subjected to earthquake loading. Seismic sliding block displacements provide a useful index as to the seismic performance of a slope. Seismic sliding block displacements can be computed for a suite of acceleration-time histories selected to fit a design event. This thesis explores the effect of ground motion selection on computed seismic sliding block displacements through two approaches. First, rigid sliding block displacements were computed for ground motion suites developed to fit uniform hazard spectra (UHS), conditional mean spectra (CMS), and conditional probability distributions for peak ground velocity (PGV) and Arias Intensity (Ia). Evaluation of the suites in terms of their PGV and Ia distributions provided useful insight into the relative displacements computed for the suites. The PGV and Ia distributions of the suite selected to fit the UHS exceed the theoretical distributions of these ground motion parameters. In fact, the scaled Ia values of motions in the UHS suite are greater than the largest Ia values in the Next Generation Attenuation (NGA) ground motion database. As such, the displacements computed for the UHS suite exceed the displacements computed for any other suite. If only two ground motion parameters are to be considered in ground motion selection we recommend those parameters be PGA and PGV. However, it is important to consider PGA, PGV, and Ia when developing ground motion suites for permanent displacement analyses. Next, the use of simulated ground motions for permanent displacement analyses was addressed by comparing displacements computed for simulated ground motions to displacements computed for the corresponding recorded ground motion. Simulated ground motions generated via four seismological models were considered: the deterministic Composite Source Model (CSM), the stochastic model EXSIM, the deterministic-stochastic hybrid model by Graves and Pitarka (GP), and the deterministic-stochastic hybrid model developed at San Deigo State University (SDSU). The displacements computed for the SDSU simulations were the most similar to those computed using the recorded motions, with the average displacement of the SDSU simulations exceeding that of the corresponding recorded ground motion by about 6%. Additionally, the displacements from the SDSU simulations provided the smallest variability about the displacements computed for the recorded motions. / text

Let (L,h) → (X,ω) be a compact toric polarized Kahler manifold of complex dimension n. For each k ε N, the fibre-wise Hermitian metric hk on Lk induces a natural inner product on the vector space C∞(X,Lk) of smooth global sections of Lk by integration with respect to the volume form ωn /n! . The orthogonal projection Pk : C∞(X,Lk) → H0(X,Lk) onto the space H0(X,Lk) of global holomorphic sections of Lk is represented by an integral kernel Bk which is called the Bergman kernel (with parameter k ε N). The restriction ρk : X → R of the norm of Bk to the diagonal in X × X is called the density function of Bk. On a dense subset of X, we describe a method for computing the coefficients of the asymptotic expansion of ρk as k → ∞ in this toric setting. We also provide a direct proof of a result which illuminates the off-diagonal decay behaviour of toric Bergman kernels. We fix a parameter l ε N and consider the projection Pl,k from C∞(X,Lk) onto those global holomorphic sections of Lk that vanish to order at least lk along some toric submanifold of X. There exists an associated toric partial Bergman kernel Bl,k giving rise to a toric partial density function ρl,k : X → R. For such toric partial density functions, we determine new asymptotic expansions over certain subsets of X as k → ∞. Euler-Maclaurin sums and Laplace’s method are utilized as important tools for this. We discuss the case of a polarization of CPn in detail and also investigate the non-compact Bargmann-Fock model with imposed vanishing at the origin. We then discuss the relationship between the slope inequality and the asymptotics of Bergman kernels with vanishing and study how a version of Song and Zelditch’s toric localization of sums result generalizes to arbitrary polarized Kahler manifolds. Finally, we construct families of induced metrics on blow-ups of polarized Kahler manifolds. We relate those metrics to partial density functions and study their properties for a specific blow-up of Cn and CPn in more detail.

[pt] Movimentos de terra em encostas frequentemente causam grandes prejuízos econômicos, ambientais, sociais e, com freqüência, perda de vidas humanas. O mecanismo que desencadeia o processo de movimentação geralmente ocorre em períodos de chuvas intensas, principalmente nas encostas com pouca cobertura vegetal ou naquelas que sofreram mudanças recentes na topografia, geralmente pela execução de cortes. Neste trabalho foram realizadas análises de estabilidade da um trecho da encosta da BR-376, que liga as cidades de Curitiba a Joinville no km 55+800 do oleoduto OSPAR da Transpetro. Em 1995, cortes executados para duplicação da rodovia provocaram instabilidade em certa área da encosta. Em janeiro de 1997, durante um período de fortes chuvas, um novo escorregamento da porção inferior do talude provocou a ruptura do muro existente e uma série de escorregamentos sucessivos, que chegaram a atingir a faixa dos oleodutos. Diante desse cenário, utilizou-se primeiramente o programa de elementos finitos PLAXIS para as análises de estabilidade e posteriormente, a fim de comparação, o programa Slope/W e Sigma/W. Para as análises no PLAXIS foi utilizado o hardening soil model para o solo, com os parâmetros sendo determinados através de ensaios triaxiais com amostras obtidas de dois blocos de solo coletados das encosta. Os efeitos da movimentação da encosta no oleoduto OSPAR foram analisados por programa 3D de elementos finitos, dando-se ênfase às tensões e deformações para se a fim de verificar a integridade do duto. / [en] In densely populated urban areas, landslides generally cause large economic, social and environmental damages as well as, quite frequently, the loss of human lives. The main triggering factor for soil slope failures is the occurrence of heavy rainfalls and the most affected slopes are those with little vegetal covering or that had suffered recent changes in topography, generally due to the execution of cuts and excavations. In this work, stability analyses of a soil slope located at km 55+800 of the Transpetro’s OSPAR oil pipeline were carried out In 1995, the works for the duplication of the BR-376 highway, connecting the cities of Curitiba and Joinville, caused some instability in certain area of the soil slope. Later, in January 1997, during a period of heavy rainfall, a new landslide near the slope toe provoked the failure of the existing retaining wall and triggered a series of successive slides that reached the protected area were the oil pipeline was buried. In order to better understand the mechanics involved in this process, numerical analyses were carried out using the computational programs Slope/W, Sigma/W and Plaxis v.8. The soil behavior was simulated considering the hard soil model, whose constitutive parameters were estimated from triaxial tests. The influence of soil movements on the OSPAR oil pipeline were investigated through a 3D finite element analysis, with emphasis on stress and strain distributions in order to check the pile line structural integrity.