Academic literature on the topic 'Earthquake dynamics'

Med utviklingen som har funnet sted innenfor den norske oljebransjen de siste årene har både teknologien og utfordringene blitt mer komplekse. Subsea-operasjoner har blitt mer vanlig og gir utslag i at det på havbunnen i mange felt er sammenkoblede systemer av konstruksjoner. I relasjon til seismisk aktivitet reises da spørsmålet om disse systemene med brønner, rør og andre konstruksjoner kan tåle å bli utsatt for et jordskjelv av en viss størrelse. For å ta et steg i retningen av å besvare dette spørsmålet, dreier denne hovedoppgaven seg om studien av en beskyttelseskonstruksjon som utsettes for grunnakselerasjoner funnet ved probabilistisk evaluering av valgte jordskjelvdata tilgjengelig for den norske kontinentalsokkelen.Den valgte konstruksjonen er lokalisert i Åsgårdfeltet på Haltenbanken vest for midt-Norge. Det er en ganske liten og slank konstruksjon hvis funksjon er å beskytte oljeinstallasjoner fra eventuelle skader forårsaket fra trål og fallende objekter i forbindelse med fiskeriindustrien. I modelleringen av konstruksjonen vurderes den som et produkt av tre forskjellige systemer. Det første systemet er konstruksjonen alene, det andre systemet er jordsystemet og det tredje er fluidsystemet. Dermed ble tre modeller laget der de forskjellige systemegenskapene (fjærer/dempere, hydrodynamiske krefter) ble introdusert stegvis.For å undersøke konstruksjonens respons i forhold til påsatte grunnakselerasjoner, måtte representative tidsrekker for jordskjelv brukes. Disse tidsrekkene ble funnet ved hjelp av probabilistisk vurdering av en syntetisk jorskjelvkatalog. Denne jordskjelvkatalogen ble generert ved å bruke Gutenberg-Richter relasjonen, og de tilhørende parametrene og områdene de gjelder for ble funnet i en rapport angående seismisk inndeling av Norge \cite{zonation}. Jordskjelvparameteren som ble valgt var maksimum grunnakselerasjon (PGA) i både horisontal og vertikal retning estimert ved en relasjon funnet av Ambraseys, med flere \cite{ambhor}\cite{ambver}. Videre ble ordningsstatistikk brukt på de genererte PGA-verdiene ved å bruke Gumbels fordeling for maksima. De resulterende PGA-verdiene i horisontal og vertikal retning ble så brukt for å finne en passende tidsrekke for akselerasjon i en database over jordskjelv for Europa og Midtøsten \cite{esmd}. Deretter ble disse akselerasjonene påsatt de tre modellene og responsen ble evaluert ved ikkelineær direkte implisitt integrasjon. Videre ble en modal analysis av responene utført på den fullt neddykkede modellen for sammenlikningens skyld. Enda en tidsserie ble også påsatt den fullt neddykkede modellen som ble generert basert på det området med høyest seismisk aktivitet, funnet i rapporten nevnt ovenfor for å vurdere det verst tenkelige tilfellet.Resultatene av disse analysene viste at med introduksjon av jord-konstruksjon-interaksjon modellert ved fjærer og dempere, så økte forskyvningene sammenliknet med den fast innspente modellen (konstruksjonen alene). Videre så økte forskyvningene ytterligere ved å introdusere hydrodynamiske krefter. På grunn av små forskyvninger dominerte treghetskreftene responsen for den neddykkede modellen. Med tanke på konstruksjonens oppførsel så ble konstruksjonen nesten ikke affisert av de påsatte grunnakselerasjonene - som er et godt tegn. Imidlertid er det vanskelig å konkludere hvordan andre typer konstruksjoner som rør og platformer ville ha respondert hvis de ble utsatt for de samme grunnakselerasjonene ettersom disse har mye større dimensjoner og annerledes geometri.

Pas de résumé<br>This thesis consists in two separate parts: one on subcritical fracture experiments, and another one on earthquake statistics. The dynamics of these processes was mainly studied through their scale invariant dynamics, reflected in power law distri- butions of event sizes and times between events. The analyses focuses particularly on the variation of their exponent values and the origins of these variations. Subcritical fracture was studied by two experimental set-ups: creep experiments on paper, and constant-strain fracture of fibre bundles. Paper fracture has been studied in our group for more than 10 years now by visually observing the propaga- tion of the crack. We added acoustic emission monitoring to the experimental set-up in order to compare it to visualisation. The comparison between low frequency image analysis and the high frequency acoustic monitoring allowed to identify the impor- tance of the frequency of analysis for temporally correlated systems, and acoustic emission monitoring revealed the existence of aftershocks in the dynamics of paper fracture. The fibre bundle experiments concentrate on the temporal distribution of the frac- ture events, which follows an Omori law. We studied the influence of the temperature and stress on its exponent, and compared it with results from fibre bundle model analytical predictions and simulations. Our work on earthquakes was initially motivated by the results obtained on pa- per fracture experiments. Hence it starts by a study of aftershock sequences, their Gutenberg-Richter exponent, and the influence of the frequency of analysis on this exponent. By lowering the frequency of the time-magnitude signal we showed that at low frequencies the exponent of the Gutenberg-Richter law depends on the expo- nent of the Omori law. The last chapter of this thesis is concentrated on the early aftershocks. We in- spected the evolution of the properties of an aftershock sequence with time, and observed differences between aftershock occurring shortly after a mainshock, and late aftershocks. These results can be related to the recent proposition of existence of magnitude correlations in earthquakes

The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter subdomain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions.

Ce travail détaille une approche de calcul pour la résolution de problèmes dynamiques qui combinent des discrétisations en temps et dans le domaine de Laplace reposant sur une technique de sous-structuration. En particulier, la méthode développée cherche à remplir le besoin industriel de réaliser des calculs dynamiques tridimensionnels pour le risque sismique en prenant en compte des effets non-linéaires d'interaction sol-structure (ISS). Deux sous-domaines sont considérés dans ce problème. D'une part, le domaine de sol linéaire et non-borné qui est modélisé par une impédance de bord discrétisée dans le domaine de Laplace au moyen d'une méthode d'éléments de frontière ; et, de l'autre part, la superstructure qui fait référence pas seulement à la structure et sa fondation mais aussi, éventuellement, à une partie du sol présentant un comportement non-linéaire. Ce dernier sous-domaine est formulé dans le domaine temporel et discrétisé avec la méthode des éléments finis (FE). Dans ce cadre, les forces liées à l'ISS s'écrivent sous la forme d'une intégrale de convolution en temps dont le noyau est la transformée de Laplace inverse de la matrice d'impédance de sol. Pour pouvoir évaluer cette convolution dans le domaine temporel à partir d'une impédance de sol définie dans le domaine de Laplace, une approche basée sur des Quadratures de Convolution (QC) est présentée : la méthode hybride Laplace-Temps (L-T). La stabilité numérique de son couplage avec un schéma d'intégration de type Newmark est ensuite étudiée sur plusieurs modèles d'ISS en dynamique linéaire et non-linéaire. Finalement, la méthode L-T est testée sur un modèle numérique plus complexe, proche d'une application sismique de caractère industriel, et des résultats satisfaisants sont obtenus par rapport aux solutions de référence<br>The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter subdomain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions

A semi-analytical method of dynamic analysis, capable of predicting both the magnitude and pattern of earthquake induced deformations, is presented. The analysis is based on a modulus reduction approach which uses a reduced modulus to simulate the softening induced in soils during cyclic loading. The effects of the inertia forces developed during dynamic loading on the induced deformations are also included through an appropriate selection of the reduced modulus. The reduced modulus is utilized in a static stress-strain analysis to predict the magnitude and pattern of the deformations induced during earthquake loading. The appropriate modulus reduction is determined from laboratory tests on undisturbed soil samples. Three methods of computing a suitable post-cyclic modulus were investigated but only the cyclic strain approach, in which the modulus is determined from cyclic loading tests that duplicate the field stress conditions, yields reductions of sufficient magnitude to provide realistic estimates of earthquake induced deformations. The modulus reduction analysis was used to predict the deformations occurring during dynamic loading of a model tailings slope in a laboratory shaking table test and of the Upper San Fernando Dam during the earthquake of February, 1971. These studies showed that the modulus reduction analysis is capable of reproducing the dynamically induced deformations and that reductions in the modulus of up to 1000 times may be required. Unfortunately, limitations of the testing equipment and inadequacies in the available data required that the appropriate modulus reductions could not be determined entirely through laboratory and field investigations. Some assumptions were necessary in selecting the reduced modulus values used in the analyses. Although these case studies were, hence, unable to provide full verification of the proposed method, they do demonstrate the reliability and simplicity of the analysis as a method of assessing the performance of soil structures during earthquake loading.<br>Applied Science, Faculty of<br>Civil Engineering, Department of<br>Graduate