ABSTRACT EFFECT OF INITIAL SUPPORT OF EXCAVATION ON SEISMIC PERFORMANCE OF CUT AND COVER STRUCTURES Rezaei, Hamidreza M.Sc., Department of Civil Engineering Supervisor: Asst. Prof. Dr. Alp Caner MAY 2011, 66 pages The effect of the initial support and its embedment depth, on the seismic performance of cut and cover tunnels is investigated. Cut and cover construction is one of the fastest and cheapest methods for constructing rectangular shallow tunnels. Construction of cut and cover structure in soil usually starts with installation of the initial support of excavation system, which may consists of rigid type of initial supports such as tangent piles or secant piles. These systems usually remain in place after completion of the final structure. However, to simplify the design, it is a common practice to ignore the contribution of initial support. In this study the effect of initial support of excavation on the seismic performance of cut and cover tunnels is investigated by means of a detailed dynamic finite element analysis. Three different tunnel geometries, three soil types and three acceleration histories were considered Results of the study show that depending on the soil stiffness (soft, medium, or stiff soil), the dynamic response of the tunnel deformations are affected significantly by the initial support of excavation. The effect of the initial support diminishes as the quality of the soil improves. Therefore, dynamic analyses are recommended for the final design of this type of structures especially in soft soils.

Uncertainty involved in the safe and comfort design of the structures is a major concern of civil engineers. Traditionally, the uncertainty has been overcome by utilizing various and relatively large safety factors for loads and structural properties. As a result in conventional design of for example tall buildings, the designed structural elements have unnecessary dimensions that sometimes are more than double of the ones needed to resist normal loads. On the other hand the requirements for strength and safety and comfort can be conflicting. Consequently, an alternative approach for design of the structures may be of great interest in design of safe and comfort structures that also offers economical advantages. Recently, there has been growing interest among the researchers in the concept of structural control as an alternative or complementary approach to the existing approaches of structural design. A few buildings have been designed and built based on this concept. The concept is to utilize a device for applying a force (known as control force) to encounter the effects of disturbing forces like earthquake force. However, the concept still has not found its rightful place among the practical engineers and more research is needed on the subject. One of the main problems in structural control is to find a proper algorithm for determining the optimum control force that should be applied to the structure. The investigation reported in this thesis is concerned with the application of active control to civil engineering structures. From the literature on control theory. (Particularly literature on the control of civil engineering structures) problems faced in application of control theory were identified and classified into two categories: 1) problems common to control of all dynamical systems, and 2) problems which are specially important in control of civil engineering structures. It was concluded that while many control algorithms are suitable for control of dynamical systems, considering the special problems in controlling civil structures and considering the unique future of structural control, many otherwise useful control algorithms face practical problems in application to civil structures. Consequently a set of criteria were set for judging the suitability of the control algorithms for use in control of civil engineering structures. Various types of existing control algorithms were investigated and finally it was concluded that predictive optimal control algorithms possess good characteristics for purpose of control of civil engineering structures. Among predictive control algorithms, those that use ARMA stochastic models for predicting the ground acceleration are better fitted to the structural control environment because all the past measured excitation is used to estimate the trends of the excitation for making qualified guesses about its coming values. However, existing ARMA based predictive algorithms are devised specially for earthquake and require on-line measurement of the external disturbing load which is not possible for dynamic loads like wind or blast. So, the algorithms are not suitable for tall buildings that experience both earthquake and wind loads during their life. Consequently, it was decided to establish a new closed loop predictive optimal control based on ARMA models as the first phase of the study. In this phase it was initially established that ARMA models are capable of predicting response of a linear SDOF system to the earthquake excitation a few steps ahead. The results of the predictions encouraged a search for finding a new closed loop optimal predictive control algorithm for linear SDOF structures based on prediction of the response by ARMA models. The second part of phase I, was devoted to developing and testing the proposed algorithm The new developed algorithm is different from other ARMA based optimal controls since it uses ARMA models for prediction of the structure response while existing algorithms predict the input excitation. Modeling the structure response as an AR or ARMA stochastic process is an effective mean for prediction of the structure response while avoiding measurement of the input excitation. ARMA models used in the algorithm enables it to avoid or reduce the time delay effect by predicting the structure response a few steps ahead. Being a closed loop control, the algorithm is suitable for all structural control conditions and can be used in a single control mechanism for vibration control of tall buildings against wind, earthquake or other random dynamic loads. Consequently the standby time is less than that for existing ARMA based algorithms devised only for earthquakes. This makes the control mechanism more reliable. The proposed algorithm utilizes and combines two different mathematical models. First model is an ARMA model representing the environment and the structure as a single system subjected to the unknown random excitation and the second model is a linear SDOF system which represents the structure subjected to a known past history of the applied control force only. The principle of superposition is then used to combine the results of these two models to predict the total response of the structure as a function of the control force. By using the predicted responses, the minimization of the performance index with respect to the control force is carried out for finding the optimal control force. As phase II, the proposed predictive control algorithm was extended to structures that are more complicated than linear SDOF structures. Initially, the algorithm was extended to linear MDOF structures. Although, the development of the algorithm for MDOF structures was relatively straightforward, during testing of the algorithm, it was found that prediction of the response by ARMA models can not be done as was done for SDOF case. In the SDOF case each of the two components of the state vector (i.e. displacement and velocity) was treated separately as an ARMA stochastic process. However, applying the same approach to each component of the state vector of a MDOF structure did not yield satisfactory results in prediction of the response. Considering the whole state vector as a multi-variable ARMA stochastic vector process yielded the desired results in predicting the response a few steps ahead. In the second part of this phase, the algorithm was extended to non-linear MDOF structures. Since the algorithm had been developed based on the principle of superposition, it was not possible to directly extend the algorithm to non-linear systems. Instead, some generalized response was defined. Then credibility of the ARMA models in predicting the generalized response was verified. Based on this credibility, the algorithm was extended for non-linear MDOF structures. Also in phase II, the stability of a controlled MDOF structure was proved. Both internal and external stability of the system were described and verified. In phase III, some problems of special interest, i.e. soil-structure interaction and control time delay, were investigated and compensated for in the framework of the developed predictive optimal control. In first part of phase III soil-structure interaction was studied. The half-space solution of the SSI effect leads to a frequency dependent representation of the structure-footing system, which is not fit for control purpose. Consequently an equivalent frequency independent system was proposed and defined as a system whose frequency response is equal to the original structure -footing system in the mean squares sense. This equivalent frequency independent system then was used in the control algorithm. In the second part of this phase, an analytical approach was used to tackle the time delay phenomenon in the context of the predictive algorithm described in previous chapters. A generalized performance index was defined considering time delay. Minimization of the generalized performance index resulted into a modified version of the algorithm in which time delay is compensated explicitly. Unlike the time delay compensation technique used in the previous phases of this investigation, which restricts time delay to be an integer multiplier of the sampling period, the modified algorithm allows time delay to be any non-negative number. However, the two approaches produce the same results if time delay is an integer multiplier of the sampling period. For evaluating the proposed algorithm and comparing it with other algorithms, several numerical simulations were carried during the research by using MATLAB and its toolboxes. A few interesting results of these simulations are enumerated below: ARM A models are able to predict the response of both linear and non-linear structures to random inputs such as earthquakes. The proposed predictive optimal control based on ARMA models has produced better results in the context of reducing velocity, displacement, total energy and operational cost compared to classic optimal control. Proposed active control algorithm is very effective in increasing safety and comfort. Its performance is not affected much by errors in the estimation of system parameters (e.g. damping). The effect of soil-structure interaction on the response to control force is considerable. Ignoring SSI will cause a significant change in the magnitude of the frequency response and a shift in the frequencies of the maximum response (resonant frequencies). Compensating the time delay effect by the modified version of the proposed algorithm will improve the performance of the control system in achieving the control goal and reduction of the structural response.

Dynamic soil-structure interaction problems are characterized by an unbounded soil-domain and thus by radiation damping. This radiation damping arises due to wave propagation from the excited structure into the subsoil and may lead to a reduction of the structural response. A consistent description of this radiation damping has been carried out by means of different concepts. A widely used approach truncates the unbounded medium by a special kind of absorbing boundaries which are free of artificial reflection. The resulting finite domain can be treated as usually by finite elements. In this report, an alternative method to represent an unbounded medium in a dynamic analysis is presented. In principle, it is a conjunction of the boundary element method (BEM) in the frequency domain to reproduce the far-field and the finite element method (FEM) in the time domain to analyze the near-field. This alternative procedure avoids the introduction of any artificial boundaries. The procedure is based on a rational approximation of the dynamic stiffness of the unbounded domain in the frequency-domain. In this report, the dynamic stiffness of the unbounded domain is obtained from the BEM. The matrix-valued coefficients of the rational approximation function are determined by means of a least-square procedure. The time-domain representation is achieved by splitting the rational force-displacement relation into a series of linear functions in the frequency-domain corresponding with first order differential equations in the time-domain. This splitting process has been demonstrated as numerically effective and in addition, no Fourier transformation is necessary. In this thesis, dynamic soil-structure interaction problems with a relatively large number of degrees of freedom have been examined. These degrees of freedom arise from the discretization of the coupling interface, internal variables from the splitting procedure and from modeling the structure. The new method is especially suitable for systems with transient excitations as arising from rotating machines at startup and shutdown. The theoretical part of the thesis contains elements of system theory and discusses particularly stability problems arising from the rational approximation. The practical part presents a large amount of convergence studies and numerical results for layered soil and finally represents the propagation damping as a kind of damping ratio which is typically used in elementary structural dynamics. / In der Dynamik der Boden-Bauwerk-Interaktion wird der Boden in vielen Fällen durch ein unbegrenztes elastisches Medium beschrieben, wodurch das Phänomen der Abstrahldämpfung begründet wird. Diese Dämpfung entsteht durch Energietransfer von der erregten Struktur in den Boden durch Wellenausbreitung und reduziert somit die Strukturschwingungen. Um das infinite Bodengebiet dennoch durch finite Elemente beschreiben zu können, werden üblicherweise als Hilfsmaßnahme künstliche sogenannte absorbierende Ränder eingeführt. In dieser Arbeit wird eine alternative Methode zur Darstellung des unbegrenzten Mediums in der Dynamik vorgelegt. Im Prinzip handelt es sich um eine Kopplung der Rand-Element-Methode (REM) für den unendlichen Boden (das sogenannte Fernfeld) im Frequenzbereich und der Finite-Element-Methode (FEM) für das Nahfeld im Zeitbereich. Dieses alternative Verfahren vermeidet die Einführung künstlicher Ränder. Das Verfahren basiert auf einer rationalen Beschreibung der dynamischen Steifigkeit des Fernfeldes im Frequenzbereich. Diese Steifigkeit wird in der vorliegenden Arbeit durch die Rand-Element-Methode erzeugt. Die Matrix-wertigen Koeffizienten der rationalen Frequenzfunktion werden durch Minimierung des Fehlerquadrates berechnet. Die Transformation dieser Frequenzdarstellung in den Zeitbereich gelingt durch algebraische Überführung der rationalen Funktion in ein in der Frequenz lineares Hypersystem mit einer zugeordneten Zustandsgleichung erste Ordnung im Zeitbereich. Dieser Prozess hat sich als numerisch effektiv erwiesen und erfordert darüberhinaus keine Fourier-Transformation. Das entwickelte Vorgehen wird in dieser Arbeit an Problemen der dynamischen Boden-Bauwerk-Interaktion mit einer großen Anzahl von Freiheitsgraden erprobt. Diese Freiheitsgrade folgen aus der Diskretisierung in der Koppelfuge zwischen Boden und Struktur, der Diskretisierung der Struktur selbst und aus der Überführung in das Hypersystem mittels interner Variablen. Das neue Verfahren eignet sich insbesondere für Systeme mit transienter Erregung, wie sie beim An- und Auslaufen von Rotationsmaschinen ensteht. Der theoretische Teil der Arbeit wird geprägt durch Elemente der Systemtheorie und setzt sich zudem mit typischen Stabilitätsproblemen auseinander, die aus der rationalen Beschreibung entstehen. Der praktische Teil präsentiert Konvergenzstudien und numerische Ergebnisse für Boden-Bauwerk- Interaktionsprobleme mit geschichtetem Boden bei transienter Erregung mit Resonanzdurchlauf. Zudem gelingt eine Darstellung der Abstrahldämpfung in Form des Dämpfungsgrades D, wie er in der klassischen Strukturdynamik verwendet wird.

Στην παρούσα εργασία, πραγματοποιείται η μελέτη του φαινομένου της δυναμικής αλληλεπίδρασης εδάφους-κατασκευής όταν αυτή θεμελιώνεται επί εύκαμπτων, επιφανειακών θεμελιώσεων με ή χωρίς πασσάλους. Η μέχρι σήμερα μελέτη της αλληλεπίδρασης εδάφους-κατασκευής έχει περιορισθεί κυρίως σε επιφανειακά, άκαμπτα ή εύκαμπτα θεμέλια και επιφανειακές ή βαθιές, άκαμπτες θεμελιώσεις επί πασσάλων. Ο συνδυασμός εύκαμπτων θεμελιώσεων, επιφανειακών ή βαθιών, και πασσαλώσεων, κοινή πρακτική σε πλείστες κατασκευές, δεν έχει μελετηθεί λόγω της περιπλοκότητας του φαινομένου και των σχετικών αβεβαιοτήτων όσον αφορά στα δεδομένα του προβλήματος. Συνεπώς, η κρισιμότητα των διαφόρων παραμέτρων, και των πολλαπλών αλληλεπιδράσεων τους, στη σεισμική απόκριση των κατασκευών παραμένει εν πολλοίς άγνωστη. Στόχος της εργασίας είναι η ανάπτυξη ενός διακριτού προσομοιώματος για τον εδαφικό ημιχώρο, το οποίο θα δύναται να χρησιμοποιηθεί για την δυναμική ανάλυση εύκαμπτων θεμελίων με ή χωρίς πασσάλους. Σε αυτή την μελέτη χρησιμοποιείται αποκλειστικά η μέθοδος των πεπερασμένων στοιχείων (ΜΠΣ), για την διακριτοποίηση της κατασκευής, του εδάφους και του συστήματος θεμελίωσης. Ειδικότερα, με τη χρήση του πακέτου πεπερασμένων στοιχείων ACS SASSI, διακριτοποιείται ο εδαφικός ημιχώρος και υπολογίζεται το πεδίο μετακινήσεων της επιφάνειας του ημιχώρου για διάφορες συχνότητες που αντιστοιχούν σε συνήθεις σεισμικές διεγέρσεις. Με γνωστό το πεδίο μετακινήσεων, υπολογίζονται οι δυναμικές δυσκαμψίες του ημιχώρου συναρτήσει της συχνότητας και της απόστασης από το σημείο φόρτισης και δημιουργείται ένα νέο διακριτό προσομοίωμα που αντικαθιστά το έδαφος, με βάση το μητρώο δυναμικών δυσκαμψιών. Τέλος με κατάλληλη αδιαστατοποίηση, προκύπτουν κλειστές εκφράσεις για τα στοιχεία του μητρώου δυναμικών δυσκαμψιών, που παρέχουν το επιπλέον πλεονέκτημα ότι είναι ανεξάρτητες της συχνότητας διέγερσης και έτσι γίνεται εφικτή η απευθείας ανάλυση συστημάτων αλληλεπίδρασης εδάφους – κατασκευής στο πεδίο του χρόνου. Το προτεινόμενο προσομοίωμα του ελαστικού ημιχώρου επεκτείνεται στην περίπτωση του μεμονωμένου πασσάλου σε εδαφικό ημιχώρο. Το διακριτό προσομοίωμα που αναπτύχθηκε προηγουμένως είναι κατάλληλο για εισαγωγή σε πρόγραμμα πεπερασμένων στοιχείων γενικού σκοπού ( όπως π.χ. ANSYS, SAP2000, ABAQUS ) και μπορεί να χρησιμοποιηθεί για κάθε είδος επιφανειακής εύκαμπτης ή άκαμπτης θεμελίωσης ανεξαρτήτου γεωμετρίας, υποκαθιστώντας τον ελαστικά γραμμικό εδαφικό ημιχώρο. Με αυτό τον τρόπο γίνεται εφικτή η επίλυση οποιουδήποτε συστήματος αλληλεπίδρασης εδάφους – κατασκευής. Η ακρίβεια και αποτελεσματικότητα του προτεινόμενου προσομοιώματος για τον εδαφικό ημιχώρο, γίνεται φανερή από μια σειρά συγκρίσεων με αποτελέσματα παλαιοτέρων δημοσιεύσεων για άκαμπτα και εύκαμπτα θεμέλια και κατασκευών με ή χωρίς πασσάλους. / During the last decades the problem of dynamic soil-structure interaction (SSI), has received considerable attention due to the large number of installations and structures sensitive to dynamic excitations such as multistory buildings, bridges, nuclear reactors, platforms etc. In fact every structure that lies on a deformable soil medium, experiences the effects of dynamic SSI. Although the phenomenon is thoroughly studied for a variety of soil-structure systems the main research effort has been focused on the dynamic behavior of rigid foundations. The assumption of foundation rigidity is so popular because it simplifies the solution procedure. In contrast, the dynamic analysis of flexible foundations adds more parameters to the problem, by requiring the discretization of both the soil medium and the foundation itself. In this work, the main goal is the study of the dynamic response of flexible foundations (e.g. mat foundations, raft foundations) and the development of a new discrete model for the analysis of soil-foundation-structure systems, which incorporates the effects of foundation flexibility. The problem under consideration consists of determining the dynamic response of the surface of the soil medium idealized as a linear elastic, isotropic half space. To this end the Finite element Method (FEM) is utilized throughout this work. The FEM computer code ACS SASSI is used to simulate the half space. Using the dynamic response of half space surface due to a unit harmonic load, calculated at a dense network of surface nodal points, the impedances of the half space are computed. Using these values a simplified, frequency independent discrete impedance matrix is constructed. Results of the above analysis are presented for a range of frequencies and half-space material properties, in easy to use graphs. This model is expanded to incorporate the case of a single flexible pile embedded on a homogenous half space. The above discrete model can easily be imported to any standard general purpose FEM code (e.g., ANSYS, SAP2000), where the solution of the soil-structure system can be obtained for a variety of soil-structure systems. The main advantages of this model are 1) Accurate, easy and fast discretization of the soil medium 2) No limitation exist due to foundation type or geometry 3) Analyses can be performed both in frequency and time domain.

The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead toerroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into anumerical code in order to investigate the effect of soil nonlinearity on dynamic soil structureinteraction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh / Caughey damping formulation, which is often already available in existing. Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case : modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in the soil and the response of the soil-structure system. Through these parametric studies we show that depending on the soil properties, frequency content of the soil response could change significantly due to the soil nonlinearity. The peaks of the transfer function between free field and outcropping responsesshift to lower frequencies and amplification happens at this frequency range. Amplificationreduction for the high frequencies and even deamplication may happen for high level inputmotions. These changes influence the structural response.We show that depending on the combination of the fundamental frequency of the structureand the the natural frequency of the soil, the effect of soil-structure interaction could be significant or negligible. However, the effect of structure weight and rocking of the superstructurecould change the results. Finally, the basin of Nice is used as an example of wave propagation ona heterogeneous nonlinear media and dynamic soil-structure interaction. The basin response isstrongly dependent on the combination of soil nonlinearity, topographic effects and impedancecontrast between soil layers. For the selected structures and soil profiles of this work, the performed numerical simulations show that the shift of the fundamental frequency is not a goodindex to discriminate linear from nonlinear soil behavior

In this work, it is proposed a mechanical behavior analysis of the soil-structure interaction from the development of a computational code using a coupling static formulation of Boundary Element Method (BEM) and Finite Element Method (FEM) for the displacements and stress calculation in structures in contact to the half space. Thus, it is intended to model the structure using the bending plate finite element DKT (discrete Kirchhoff triangle) and applying the concepts of the Boundary Element Method (BEM) formulation to model the soil, considered as a half- infinite and/or infinite space and using Kelvin s fundamental solution. The coupling between the media is done using the sub-regions technique. From the computational code development some practical examples of engineering are implemented, such as: soil-structure interaction analysis in superficial and buried plate foundations and others engineering structures, study on the behavior of a half- infinite space from the application of a distributed and concentrated load, analysis of bodies submitted to bend and traction, among others applications. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Neste trabalho, propõe-se a análise do comportamento mecânico da interação solo -estrutura a partir do desenvolvimento de um código computacional utilizando-se uma formulação estática conjunta do Método dos Elementos de Contorno (MEC) e do Método dos Elementos Finitos (MEF) para o cálculo de deslocamentos e tensões em estruturas em contato com o meio semiinfinito. Assim sendo, pretende-se modelar a estrutura a partir de elementos finitos de placa DKT (discrete Kirchhoff triangle) e utilizar o conceito da formulação do Método dos Elementos de Contorno (MEC) para modelar o solo, considerando-o como um espaço semi- infinito e/ou infinito e utilizando a solução fundamental de Kelvin. O acoplamento entre os meios é feito aplicando-se a técnica de sub-regiões. A partir do desenvolvimento de um código computacional são processados alguns exemplos de engenharia tais como: análise da interação solo -estrutura em fundações de placa superficiais e enterradas e outras estruturas de engenharia, estudo do comportamento de um espaço semi- infinito a partir da aplicação de um carregamento distribuído e carga concentrada, análise de corpos submetidos à flexão e à tração, entre outras aplicações.

This study aims the development of a computational tool used to analyze two dimensional problems of soil-structure interaction, where soil is modeled by Boundary Element Method (BEM) and structures are treated by the Finite Element Method (FEM). Fundamental solutions of Kelvin 2D and Melan to BEM are implemented, where boundary elements with linear approximation are used. Structures modeled with FEM are discretized with two-dimensional frame finite elements. Coupling among media is done using the sub-region technique, where conditions of compatibility of displacements and equilibrium of tractions are applied to the interfaces between various sub-regions. Both soil and structures are considered as composed of homogeneous, isotropic, elastic and linear materials. However, sub-region technique allows the soil to be considered as stratified. Application for various acting loads, on structure or on soil, are considered slow, therefore the proposed analyses are statics. Examples are presented using the developed computational code. / Fundação de Amparo a Pesquisa do Estado de Alagoas / O presente trabalho tem como objetivo o desenvolvimento de uma ferramenta computacional para analisar problemas bidimensionais de interação solo-estrutura, onde o solo é modelado pelo Método dos Elementos de Contorno (MEC) e as estruturas são tratadas pelo Método dos Elementos Finitos (MEF). São implementadas as soluções fundamentais de Kelvin 2D e Melan para o MEC, onde elementos de contorno com aproximação linear são utilizados. As estruturas modeladas pelo MEF são discretizadas por elementos finitos de pórtico bidimensional. O acoplamento entre os meios é feito pela utilização da técnica de sub-regiões, onde condições de compatibilidade de deslocamentos e condições de equilíbrio de forças são aplicadas às interfaces entre as diversas sub-regiões. Tanto o solo quanto as estruturas são considerados como compostos por materiais homogêneos, isotrópicos, elásticos e lineares. Porém, a técnica de sub-regiões permite que o solo seja considerado como estratificado. A aplicação dos diversos carregamentos atuantes, na estrutura ou no solo, é considerada lenta, assim, as análises propostas são estáticas. São apresentados exemplos de aplicação do código computacional desenvolvido.

Le renforcement des sols en zone sismique par des colonnes ballastées et/ou des inclusions rigides représente une alternative prometteuse et de plus en plus répandue par rapport aux solutions lourdes de fondations sur pieux. On sait que les pieux subissent, du fait de leur rigidité, des moments très importants au niveau de la liaison chevêtre-pieu. Les inclusions rigides surmontées d'un matelas granulaire permettent de mieux dissiper les efforts inertiels transmis par la superstructure, mais peuvent nécessiter des armatures si ce matelas n'est pas suffisamment épais. On peut penser que la colonne à module mixte (CMM) offre une solution combinant l'effet « matelas » à travers sa partie supérieure en colonne ballastée plus flexible et l'effet stabilisateur de la colonne inférieure. Cette thèse présente dans une première partie l'étude expérimentale réalisée au Laboratoire 3S-R (Grenoble) sur des modèles réduits à l'échelle 1/10 afin d'analyser la réponse de ces systèmes sous différentes charges statiques et dynamiques. Le modèle physique se compose d'une semelle carrée reposant directement sur l'argile renforcée. Le chargement vertical et horizontal, statique et dynamique est appliqué par l'intermédiaire de la fondation. Une instrumentation a été placée au niveau de la semelle pour obtenir la réponse globale du système, ainsi que dans la partie rigide inférieure du modèle pour évaluer la répartition des efforts entre inclusion et partie flexible supérieure. Une attention toute particulière a été donnée à la simulation de l'effet inertiel d'un séisme. Les profils de moments, d'efforts tranchants et de déplacements en fonction de la profondeur déterminés à partir de 20 extensomètres répartis régulièrement sur toute la hauteur de la partie rigide ont permis d'étudier l'influence de la hauteur de la colonne ou du matelas. La comparaison entre les déplacements dynamiques de la semelle et les courbes P-y (pression latérale P fonction du déplacement latéral y de la tête de pieu), permet de quantifier la dissipation de l'énergie dans les différentes parties du système. Les résultats expérimentaux montrent que la partie supérieure souple absorbe l'essentiel de l'énergie inertielle sismique. Une modélisation numérique 3D confirme les tendances observées expérimentalement et souligne l'importance du rôle de la zone de transition entre partie souple et partie rigide. / Along with the increasing need of construction land, numerous soil reinforcement technologies are proposed in order to improve the soil mechanical properties on one hand and overall site response on the other hand. The presented study is carried out in the context of seismic soil reinforcement and its interaction with a shallow footing which undergoes inertial loading. The system is studied mainly through physical modelling when reduced scale models are constructed in order to simulate clay reinforcement, which is composed of a rigid lower part associated to a flexible upper part. The soft upper part offers shear and moment capacity and the rigid lower part gives bearing capacity. In order to design the reinforcement elements, the response of this combined system to different static and dynamic loads must be understood. This thesis presents results from a primarily experimental study performed in Laboratoire 3S-R (Grenoble). Two reduced (1/10) physical models consisting of a group of four rigid inclusions associated to an upper flexible part are studied in clay. Combined vertical and horizontal static and dynamic loading is applied with a shallow foundation model. A parametric study is done, varying the height of the flexible part of the models in order to define its effect on the settlements of the foundation and lateral performance of the rigid inclusion. A special emphasis was given to the study of the inertial effects of seismic type loading. For this purpose, one of the rigid inclusions was instrumented with 20 levels strain gauges measuring flexural strain, used to calculate the bending moment along the pile. This gives pile deflection (y) by double integration and soil reaction (P) by double derivation. P-y curves are thus obtained. The analysis of the dynamic deflection of the rigid inclusion compared to the movement of the foundation allowed an estimation of the energy dissipated. The results indicate that a large amount of the seismic energy is dissipated within the upper flexible part of the models. Even though the scaling laws are not strictly respected, the main objective of the physical modelling was to perform a qualitative study of the soil reinforcement, studying its behaviour under inertial loading and pointing out important mechanisms, which should be taken into account by the current practice.

Esta dissertação apresenta em primeira etapa o trabalho desenvolvido para averiguar a adequação dos modelos reológicos de Mohr-Coulomb e de Endurecimento de solo, para representar as deformações e distorções que ocorrem no sistema soloestrutura, quando do processo de escavação de valas escoradas. Além disto, em uma segunda etapa fazem-se estimativas de previsão de danos causados em edificações, em decorrência das escavações de uma vala escorada da linha 1 do Metropolitano de São Paulo (Metrô S.P.). A primeira e a segunda etapa foram feitas através de 810 simulações numéricas, em elementos finitos utilizando-se o software PLAXIS, associadas a retroanálise por processo direto do módulo de deformabilidade a 50% da tensão de ruptura dos solos utilizando-se para isto o processo direto. Apresenta-se também uma síntese da formação e dos tipos de solos que constituem a bacia sedimentar de São Paulo, onde se localiza a seção experimental nº1 objeto de estudo desta dissertação. Faz-se uma breve revisão bibliográfica a respeito das técnicas de retroanálise. Apresentam-se critérios para escolha de intervalos de parâmetros geotécnicos que representem o sistema solo-estrutura no processo de escavação. Foram feitas análises paramétricas para determinar os parâmetros geotécnicos que mais influenciam o sistema solo-estrutura. Comparam-se os modelos constitutivos de Mohr-Coulomb e de endurecimento na previsão das deformações. Por fim, faz-se a previsão do nível de danos causados pelas escavações da vala, a um edifício hipotético / This dissertation presents, in a first part, the work done to verify how appropriate are the Mohr-Coulomb and hardening soil constitutive models to represent the strains and the distortions associated with escavations of braced wall process. In the second part, estimates are made of the damages in constructions due to the braced excavations of line one of Sao Paulo Subway (Metrô S.P.). In the two phases, 810 numeric simulations were made, in finite elements using the software PLAXIS, associated the back analysis for direct process. It is presented a synthesis of the formation and the types of soils that constitute the basin of the sediments of the city of São Paulo, where is located the section experimental nº1, object of study of this dissertation. It is presented an short bibliographical revision regarding the back analysis techniques. Criteria for choice of intervals of parameters geotechnical that represent the system soil-structure in the excavation process are presented. Parametric analyses are made to determine which the parameters have larger influence in the behavior of the system soil-structure. The behavior of the soil-structure system is simulated using the Mohr-Coulomb and hardening soil constitutive models. The Mohr-Coulomb and hardening soil constitutive models are compared in the forecast of the deformations. Finally, it is made the forecast of the level of damages to a hypothetical building caused by the braced excavations

Neste trabalho foi desenvolvido um modelo para análise tridimensional não linear geométrica de edifícios considerando a influência de todas as partes componentes do sistema estrutural, incluindo a ligação núcleo-laje e o solo de fundação. Pilares e vigas são modelados com elementos finitos de barra com seção transversal de forma qualquer, enquanto as lajes são modeladas por elementos finitos de casca. Ambos consideram o comportamento não linear geométrico e adotam como graus de liberdade posições nodais e vetores generalizados ao invés de deslocamentos e rotações, sendo também considerado para o elemento de barra o grau de liberdade de empenamento da seção. Apresenta-se uma estratégia cinemática para o acoplamento de topo entre os elementos de casca e a seção dos elementos de barra, gerando assim um elemento de núcleo com diafragma. O acoplamento se dá através de uma matriz de incidência cinemática responsável por inserir na Hessiana e no vetor de forças internas do elemento de barra que discretiza o núcleo as contribuições de elementos de casca a ele conectadas. Admite-se para os materiais do edifício a lei constitutiva elástico-linear de Saint Venant-Kirchhoff e a não linearidade geométrica é considerada através de uma formulação Lagrangiana total com cinemática exata. A flexibilidade dos apoios é considerada através de uma matriz de rigidez do sistema solo-fundação. Esta matriz é calculada em outro programa de acoplamento entre o Método dos Elementos de Contorno e o Método dos Elementos Finitos por meio de uma estratégia numérica baseada, por sua vez, no Teorema de Betti-Maxwell. A estratégia consiste na determinação de coeficientes de flexibilidade de pontos sobre uma malha discreta do sistema solo-fundação, sendo o solo modelado via Método dos Elementos de Contorno com uso da solução fundamental de Mindlin e os elementos estruturais de fundação, que podem incluir placas, sapatas, blocos e estacas, são modeladas com elementos finitos convencionais de barra e de casca. O programa permite a análise de edifícios completos, considerando a influência do empenamento dos núcleos nos pavimentos e também os efeitos da interação solo-estrutura. Exemplos numéricos são apresentados para confirmar a eficiência e demonstrar o potencial de aplicação da formulação proposta. / In this thesis a numerical model for geometric nonlinear analysis of three-dimensional structures of tall buildings was developed, considering the influence of all structural components, including the core-slab connection and the foundation system. Columns and beams are modeled by a frame finite element which can have a cross section of any shape, while the slabs are modeled by shell finite elements. Both consider the nonlinear geometric behavior and adopt nodal positions and generalized vectors as degrees of freedom instead of displacements and rotations. For the frame finite element it is also considered the cross sectional warping as a degree of freedom. A numerical strategy is presented for the coupling between the shell elements and the frame\'s cross section, thus forming a structural-core element with diaphragm. The coupling is done through a kinematic array which is responsible for inserting the contributions of shell elements, connected to the core walls, into the Hessian matrix and also into the internal force vector of the frame element used to discretize the core. The linear-elastic constitutive relation of Saint Venant-Kirchhoff is adopted for the building materials and the geometric nonlinearity is considered via a Lagrangian formulation with exact kinematics. The foundation\'s flexibility is considered through a stiffness matrix for the soil-foundation system. This matrix is computed in another program based on the numerical coupling between the Boundary Element Method and the Finite Element Method, using a numerical strategy based on the Maxwell-Betti\'s Theorem. This strategy consists in determining the flexibility coefficient of points on a discrete mesh of the soil-foundation system. The soil is modeled by the Boundary Element Method using the fundamental solution of Mindlin. The structural foundation elements, including shallow foundation, footings, blocks and piles, are modeled using conventional frame and shell finite elements. The program is applied to the analysis of complete structural systems of tall buildings, considering the influence of the core warping on the mechanical behaviour of the slabs and also the soil-structure interaction effects. Numerical examples are presented to confirm the efficiency and to demonstrate the potential application of the proposed formulation.