The present thesis is an attempt to investigate the interference effects on the magnitudes of the ultimate failure loads for a group of closely spaced strip footings and strip plate anchors. On account of an increase in the number of different civil engineering structures, footings and anchors are often need to be placed very close to each other. In such a situation, the ultimate bearing capacity/pullout capacity of an interfering footing/anchor becomes significantly different from that of a single isolated footing/anchor. The effect of interference on the magnitude of failure load is usually expressed in terms of an efficiency factor (%y); where £,y is defined as the ratio of the magnitude of the failure load for a strip footing/anchor of a given width in the presence of other footings/anchors to that of the magnitude of the failure load for an isolated single strip footing/anchor having exactly the same width. No rigorous analysis seems to have been carried out so far in literature to investigate the interference effect for a group of footings and anchors. In the present study, it is intended to use rigorous numerical upper bound limit analysis in combination with finite elements and linear programming in order to determine the collapse loads for the problems of both isolated and a group of footings and anchors. Three noded triangular elements are used throughout the thesis for carrying out the analysis for different problems. The velocity discontinuities are employed along the interfaces of all the elements. The plastic strains within the elements are incorporated by using an associated flow rule. The Mohr Coulomb yield surface is linearised by means of an exterior regular polygon circumscribing the actual failure surface so that the finite element formulation leads to a linear programming problem. In solving the different problems taken in this thesis, computer programs were developed using 'MATLAB' with the usage of 'LINPROG' - a library subprogram for doing the necessary optimization. The bearing capacity factor Ny for an isolated single rigid strip footing placed on a cohesionless ground surface has been computed and its variation with respect to the footing-soil roughness angle (8) has been examined in detail. It is clearly noted that an increase in 8 leads to a continuous increase in Ny. The solution is also obtained for a perfectly rough footing without considering any velocity discontinuity surface along the footing-soil interface. With 5 = <|), the magnitude of NY becomes almost the same as that for a perfectly rough footing. The size of the plastic zone increases with an increase in the values of 8 and <j). The obtained values of Ny for 5=0 and § compare quite favorably with the solutions reported earlier in literature. The ultimate bearing capacity for a group of two and an infinite number of multiple interfering rough strip footings placed on a cohesionless medium has been computed; all the footings are assumed to be perfectly rigid. It is specified that the footings are loaded simultaneously to failure exactly at the same magnitude of the failure load. For different clear spacing (S) between the adjacent footings, the magnitude of the efficiency factor (£,y) is determined. In the case of two footings, the value of E,y at S/B = 0 becomes exactly equal to 2.0, and the maximum ^occurs at a critical spacing (Scr). For S/B < Sor/B, the ultimate bearing pressure for a footing becomes equal to that of an isolated footing having the width (2B+S), and the ground mass encompassed between the two footings deforms mainly in the downward direction. In contrast, for S/B > Scr/B, ground heave is noticed along both the sides of the footing. As compared to the available theories in literature, the analysis presented in this thesis provides generally lower values of ^y for S/B > Scr/B. ' In the case of a group of multiple strip footings, the value of £y is found to increase continuously with a decrease in S/B. The effect of the variation of spacing on §y is found to be very extensive for small values of S/B; the magnitude of ^y approaches infinity at S/B = 0. For all the values of S/B ground heave is invariably observed on both the sides of the footings. The magnitudes of ^Y for given values of S/B and <|) for the two footings case are found to be smaller than the multiple footings case. The vertical uplift capacity of an isolated strip anchor embedded horizontally at shallow depths in sand has been examined; the anchor plate is assumed to be perfectly rigid and rough. The collapse load is expressed in terms of a non-dimensional uplift factor FY, the value of which needs to be known before calculating the failure load for an interfering anchor. The magnitude of Fr is found to increase continuously with increase in both embedment ratio (k) and the friction angle (<|>) of sand. Even though the analysis considers the development of plastic strain within all elements, however, at collapse, the soil mass just above the anchor is found to move as a single rigid block bounded by planar rupture surfaces; the rupture surfaces emerging from the anchor edges are seen to make approximately an angle <|> with the vertical. The vertical uplift capacity of a group of two and an infinite number of multiple interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. At collapse, it is specified that all the anchors in the group are loaded to failure simultaneously exactly at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (£Y) is determined. On account of interference, the magnitude of 4y is found to reduce continuously with a decrease in the spacing between the anchors. For all values of X and §, the magnitude of ^y for the multiple anchors case is found to be always smaller than that for the two anchors case. In contrast to a group of footings under compression, the magnitude of ^v for a group of anchors is found to decrease invariably with an increase in $ for a given value of S/B. For S > 2c/tan<j) , the uplift resistance of anchors in the group becomes equal to that of an isolated anchor, and no interference is seen to exist; where d is the depth of anchor. By examining the nodal velocity patterns, it was noted that in the event of collapse, a wedge of soil mass just above the anchors and encompassed within linear rupture surfaces moves vertically upward almost as a single rigid unit with the velocity same as that of the anchor plate itself. On this basis, a closed form solution of the problem has been developed. The results from the closed form solution for the group of two anchors as well as for multiple anchors are found to provide an excellent comparison with the rigorous upper bound numerical solution especially for the value of § greater than or equal to about 35°. For all the problems taken in this study, it has been seen that an upper bound limit analysis in combination with finite elements and linear programming is a very useful numerical tool for determining the magnitudes of collapse loads.

Οι κατασκευές εδαφικής αντιστήριξης εξακολουθούν να βρίσκονται σε ευρύτατη χρήση, με διαρκώς αυξανόμενο ενδιαφέρον λόγω των απαιτήσεων των σύγχρονων έργων υποδομής αλλά και των αναγκών δόμησης σε πυκνό αστικό περιβάλλον. Το ενδιαφέρον εστιάζεται σε κατασκευαστικές λύσεις και μεθόδους σχεδιασμού που συνδυάζουν ασφάλεια και οικονομία. Η ανάλυση των συγκεκριμένων κατασκευών αντιμετωπίζει πλήθος δυσεπίλυτων προβλημάτων στο αντικείμενο της αλληλεπίδρασης εδάφους-κατασκευής που συχνά καθορίζουν τη συμπεριφορά του έργου. Η κατανόηση αυτών των μηχανισμών επιτρέπει το σχεδιασμό με μικρότερα περιθώρια αβεβαιότητας που οδηγούν σε οικονομικότερες και ορθολογικότερες λύσεις. Στην κατεύθυνση αυτή συμβάλει η παρούσα Διατριβή, με την ανάπτυξη αναλυτικών εργαλείων και θεωρητικών ευρημάτων που βοηθούν στην κατανόηση των μηχανισμών της αλληλεπίδρασης και στην εκτίμηση της συμπεριφοράς των τοίχων αντιστήριξης υπό συνδυασμένη βαρυτική και σεισμική φόρτιση. Έμφαση δίνεται στην παραγωγή απλών κλειστών λύσεων και μεθοδολογιών για τον υπολογισμό των εδαφικών ωθήσεων και τη στατική ανάλυση του συστήματος τοίχου εδάφους. Συγκεκριμένα, παράγονται λύσεις άνω και κάτω ορίου για ενδόσιμους τοίχους, οι οποίες, παρότι προσεγγιστικές, πλεονεκτούν έναντι των κλασικών εξισώσεων Coulomb και Mononobe-Okabe τις οποίες μπορούν να αντικαταστήσουν. Σε ειδικές περιπτώσεις, όπως η περίπτωση τοίχων προβόλων με πεπλατυσμένο πέλμα, οι προτεινόμενες λύσεις οδηγούν σε ακριβή αποτελέσματα που βασίζονται σε ένα γενικευμένο πεδίο τάσεων Rankine. Επίσης παρουσιάζονται επεκτάσεις τους οι οποίες επιτρέπουν τον υπολογισμό μη-υδροστατικών κατανομών ωθήσεων γαιών λαμβάνοντας υπόψη την κυματική διάδοση της σεισμικής διέγερσης στο επίχωμα, σύμφωνα με μια ορθότερη παραλλαγή της ιδέας των Steedman & Zeng και τις διαφορετικές κινηματικές συνθήκες που προέρχονται από την απόκριση του τοίχου με περιστροφή περί την κορυφή ή τη βάση σύμφωνα με την τεχνική της Dubrova. Για την περίπτωση ανένδοτων τοίχων παρουσιάζεται μεθοδολογία για τη δραστική απλοποίηση των διαθέσιμων ελαστοδυναμικών, κυματικών λύσεων, όπως αυτή των Veletsos & Younan, η οποία καταλήγει σε κλειστές μαθηματικές εκφράσεις για τον υπολογισμό των ωθήσεων. Τέλος, παρουσιάζονται νέα ευρήματα στην κατεύθυνση της μαθηματικής αντιμετώπισης του δυσεπίλυτου προβλήματος της οριακής ισορροπίας ριπιδίου τάσεων σε εδαφικό μέσο στο οποίο ενεργούν βαρυτικές και αδρανειακές δυνάμεις πεδίου. Η παρούσα εργασία συμβάλλει στην περαιτέρω διερεύνηση του προβλήματος το οποίο θεμελίωσαν θεωρητικά οι Levy, Boussinesq, von Karman και Caquot, μέσω της δραστικής (αλλά ακριβούς) απλοποίησης του σε μία μη-γραμμική συνήθη διαφορική εξίσωση, η οποία επιτρέπει την επίλυση με απλές αριθμητικές και ημιαναλυτικές τεχνικές. Πέρα από τα ακριβή αριθμητικά αποτελέσματα, η προτεινόμενη ανάλυση προσφέρει μια βαθύτερη εποπτεία στο πρόβλημα και ανοίγει το δρόμο για περαιτέρω διερεύνηση ή και επέκταση της μεθόδου πέρα από τα όρια της κλασικής οριακής ανάλυσης. Η αξιοπιστία των προτεινόμενων λύσεων ελέγχεται μέσω συγκρίσεων με καθιερωμένες λύσεις και πειραματικά δεδομένα από τη βιβλιογραφία, αλλά και πρόσφατα πειραματικά αποτελέσματα που παρήχθησαν από τον συγγραφέα και ερευνητές στη σεισμική τράπεζα του Πανεπιστημίου του Bristol του Ηνωμένου Βασιλείου. / Earth retaining structures are still in widespread use, with growing interest due to the demands of modern infrastructure and building needs in a dense urban environment. Building solutions and design methodologies that combine safety and economy are the objectives of modern research. Significant difficulties in the analysis of retaining structures arise from the soil-structure interaction nature of the problem that often prescribes its behavior. Understanding these mechanisms allows design under smaller uncertainties, leading to economical and rational solutions. The contribution of the present thesis consists of the development of analytical tools and theoretical findings, helpful in understanding the mechanisms of interaction and the behavior of walls under combined gravity and seismic loading. Emphasis is given to the derivation of simple closed-form solutions and methodologies for the calculation of earth pressures and the static analysis of wall-soil system. Specifically, approximate Lower and Upper Bound solutions are produced for the case of yielding walls, which are advantageous compared to the classical equations Coulomb and Mononobe-Okabe. In special cases, such as the L-shaped cantilever walls, these solutions lead to exact results, pertaining to a generalized Rankine stress field. Extensions of the above solutions are presented allowing the calculation of non-hydrostatic earth pressure distributions, due to the wave propagation of the seismic excitation in the backfill, according to a better variant of the Steedman & Zeng approach and different kinematic conditions of the wall rotating around the top or bottom, according to the technique of Dubrova. For the case of non-yielding walls, a new methodology for the drastic simplification of available wave solutions, such as the Veletsos & Younan, is presented which leads to closed-form expressions for the dynamic pressure calculation. Finally, new theoretical findings are presented for the mathematical treatment of the intractable problem of plastic limit equilibrium in soil medium subjected to gravitational and inertial forces field. This work contributes to the further investigation of the problem which is founded theoretically by Levy, Boussinesq, von Karman and Caquot, through the significant (but accurate) simplification to a single, non-linear ordinary differential equation, easier to handle by simple numerical and semi-analytical techniques. Apart from the exact numerical results, the proposed analysis provides a deeper physical insight, leading the way to further investigation or extension of the method beyond the classical limit analysis assumptions. The reliability of the proposed solutions is checked through comparisons with established solutions and experimental data from the literature and recent experimental results obtained by the author and researchers in the shake table laboratory of the University of Bristol, UK.

The reliability analysis of plates and shells with respect to plastic collapse or to inadaptation is formulated on the basis of limit and shakedown theorems. The loading, the material strength and the shell thickness are considered as random variables. Based on a direct definition of the limit state function, the nonlinear problems may be efficiently solved by using the First and Second Order Reliability Methods (FORM/SORM). The sensitivity analyses in FORM/SORM can be based on the sensitivities of the deterministic shakedown problem. The problem of reliability of structural systems is also handled by the application of a special barrier technique which permits to find all the design points corresponding to all the failure modes. The direct plasticity approach reduces considerably the necessary knowledge of uncertain input data, computing costs and the numerical error. / Die Zuverlässigkeitsanalyse von Platten und Schalen in Bezug auf plastischen Kollaps oder Nicht-Anpassung wird mit den Traglast- und Einspielsätzen formuliert. Die Lasten, die Werkstofffestigkeit und die Schalendicke werden als Zufallsvariablen betrachtet. Auf der Grundlage einer direkten Definition der Grenzzustandsfunktion kann die Berechnung der Versagenswahrscheinlichkeit effektiv mit den Zuverlässigkeitsmethoden erster und zweiter Ordnung (FROM/SORM) gelöst werden. Die Sensitivitätsanalysen in FORM/SORM lassen sich auf der Basis der Sensitivitäten des deterministischen Einspielproblems berechnen. Die Schwierigkeiten bei der Ermittlung der Zuverlässigkeit von strukturellen Systemen werden durch Anwendung einer speziellen Barrieremethode behoben, die es erlaubt, alle Auslegungspunkte zu allen Versagensmoden zu finden. Die Anwendung direkter Plastizitätsmethoden führt zu einer beträchtlichen Verringerung der notwendigen Kenntnis der unsicheren Eingangsdaten, des Berechnungsaufwandes und der numerischen Fehler.