<p>U EN1998-1 i EN1998-2 su propisane metode za određivanje seizmičkih<br />uticaja koje koriste linearno-elastične modele u modalnoj analizi sa<br />spektrima odgovora. Za regularne konstrukcije, se može primeniti i<br />ekvivalentna statička metoda u slučaju da ne postoji značajan<br />doprinos viših tonova na odgovor sistema. U EN1998-2 su propisane,<br />kao alternativa linearno-elastičnim metodama analize, nelinearna<br />statička analiza i nelinearna dinamička analiza. U ovom radu su<br />primenjene linearne i nelinearne statičke i dinamičke analize<br />armiranobetonskih grednih mostova sa različitim kombinacijama<br />dužina stubova u cilju procene seizmičkih performansi.</p> / <p>The EN 1998-1 and EN1998-2 prescribed methods for the determination of<br />seismic action using linear-elastic models for modal analysis with response<br />spectrum. For regular structures, can be applied to the equivalent static<br />method in the action that there is a significant contribution to higher modes<br />on the response of the system. The EN1998-2 are prescribed as an<br />alternative to linear-elastic methods of analysis, nonlinear static analysis and<br />nonlinear dynamic analysis. This study applied linear and nonlinear static<br />and dynamic analysis of reinforced concrete girder bridges with different<br />combinations of length piers in order to assess the seismic performance.</p>

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As Civil Engineering structures, e.g., tall buildings, long span bridges, deep water offshore platforms, nuclear power plants, etc., have become more costly, complex and serve more critical functions, the consequences of their failure are catastrophic. Therefore, the protection of these structures against damage induced by large environmental loads, e.g., earthquakes, strong wind gusts and waves, etc., is without doubt, a worldwide priority. However, structures cannot be designed to withstand all possible external loads and some extraordinary loading episodes do occur, leading to damage or even failure of the structure. Protection of a structure against hazards can be achieved by various means such as modifying structural rigidities, increasing structural damping, and by attaching external devices, known as control devices. Control devices can be deployed either to isolate the structure from external excitation or to absorb input seismic energy to the structure (absorber) so as to mitigate vibration in the primary structure. Seismic base isolation is one such mechanism which isolates a structure from harmful ground excitations. Seismic base isolation is a widely accepted and implemented structural control mechanism due to its robustness and ease in deployment. Following the Northridge earthquake (1994), and Kobe earthquake (1995), the interest of structural engineers in understanding near-source ground motions has enhanced. Documents published after these earthquakes emphasized the issue of large base displacements because of the use of none or little isolation damping (of viscous type only) prior to these events. More recent studies have investigated analytically and experimentally, the efficiency of various dissipative mechanisms to protect seismic isolated structures from recorded near-source long period, pulse-type, high velocity ground motions. Consequently, hybrid isolation systems, seismic base isolation supplemented with damping mechanisms, have become the focus of current research trend in structural vibration control. Hybrid base isolation system incorporating passive supplemental damping devices like, viscous fluid dampers, etc., performs satisfactorily in minimizing isolator displacement but at the same time increases superstructure acceleration response. Furthermore, the passive system can be tuned to a particular frequency range and its performance decreases for frequencies of excitation outside the tunning bandwidth. In such a scenario, active control devices in addition to base isolation mechanism provide better performance in reducing base displacement and superstructure acceleration for a broad range of excitation frequencies. Tremendous power requirement and the possibility of power failure during seismic hazards restrict the usage of active systems as a supplemental device. Semi-active devices provide the robustness of passive devices and adaptive nature of active devices. These characteristics make them better suited for structural control applications. The recent focus is on the development of magnetorheological (MR) dampers as semi-active device for structural vibration control applications. MR dampers provide hysteretic damping and can operate with battery power. The thrust of this thesis is on developing a hybrid base isolation mechanism using MR dampers as a supplemental damping device. The use of MR damper as a semi-active device involves two steps; development of a model to describe the MR damper hysteretic behaviour; development of a proper nonlinear control algorithm to monitor MR damper current / voltage supply. Existing parametric models of MR damper hysteretic behaviour, e.g., Bouc-Wen model, fail to consider the effect of amplitude and frequency of excitation on the device. Recently reported literature has demonstrated the necessity of incorporating amplitude and frequency dependence of MR damper models. The current/voltage supply as the input variable to the MR damper restricts the direct use of any control algorithms developed for active control of structures. The force predicted by the available control algorithms should be mapped to equivalent current/voltage and then to be fed into the damper. Available semi-active algorithms in the literature used ‘on-off’ or ‘bang-bang’ strategy for MR applications due to nonlinear current/voltage-force relation of MR damper. The ‘on-off’ nature of these algorithms neither provides smooth change in MR damper current/voltage input nor considers all possible current/ voltage values within its minimum to maximum range. Secondly, these algorithms fail to consider the effect of the MR damper applied and commanded current/voltage dynamics. The thrust of this dissertation is to develop semi-active control algorithms to monitor MR damper supply current/voltage. The study develops a Bouc-Wen based model to characterize the MR damper hysteretic phenomenon. Experimental results and modeling details have been documented. A fuzzy based intelligent control and two model-based nonlinear control algorithms based on optimal dynamic inversion and integral backstepping have been developed. Performance of the fuzzy logic based intelligent control has been explored using experimental investigation on a three storey base isolated building. Further the application of the proposed controllers on a benchmark building; a benchmark highway bridge and a stay cable vibration reduction have been discussed. Experimental study has revealed that the performance of optimal FLC is better than manually designed FLC in terms of reducing base displacement and storey accelerations. The performance of both the FLCs (simple FLC and genetic algorithm based optimal FLC) is better than ‘passive-off’ (zero ampere current supply) and ‘passive-on’ (one ampere current supply) condition of MR damper applications. The ‘passive-off’ results have shown higher base displacements with lower storey accelerations, whereas, the ‘passive-on’ results have reduced base displacement to the least but at the same time increased the storey acceleration too much. The FLC monitored MR damper show a compromise between the two passive conditions. Analytical results confirm these observations. Numerical simulations of the base isolated building with the two model based MR damper control algorithms developed have shown a better performance over FLC and widely used clipped optimal algorithms. The applications of the proposed semi-active control algorithms (FLC, dynamic inversion and integral backstepping) have shown better performance in comparison to that of control algorithms provided with the benchmark studies.

Rammed earth is a technique of forming in-situ structural wall elements using rigid formwork. Advantages of rammed earth walls include flexibility in plan form, scope for adjusting strength and wall thickness, variety of textural finishes, lower embodied carbon and energy, etc. There is a growing interest in the construction of rammed earth buildings in the recent past. Well focused comprehensive studies in understanding the structural performance of rammed earth structures are scanty. Clear-cut guidelines on selecting soil grading and soil characteristics, assessing strength of rammed earth walls, density strength relationships, limits on shrinkage, standardised testing procedures, behaviour of rammed earth walls under in-plane and out of plane loads, etc are the areas needing attention. The thesis attempts to address some of these aspects of cement stabilized rammed earth for structural walls. Brief history and developments in rammed earth construction with illustrations of rammed earth buildings are presented. A review of the literature on rammed earth has been provided under two categories: (a) Unstabilised or pure rammed earth and (b) stabilised rammed earth. Review of the existing codes of practice on rammed earth has also been included. Summary of the literature on rammed earth along with points requiring attention for further R&D are discussed. Objectives and scope of the thesis are listed. The thesis deals with an extensive experimentation on cement stabilised rammed earth (CSRE) specimens and walls. Four varieties of specimens (cylindrical, prisms, wallettes and full scale walls) were used in the experiments. A natural soil and its reconstituted variants were used in the experimental work. Details of the experimental programme, characteristics of raw materials used in the experimental investigations, methods of preparing different types of specimens and their testing procedures are discussed in detail. Influence of soil grading, cement content, moulding water content, density and delayed compaction on compaction characteristics and strength of cement stabilised soil mixes were examined. Five different soil gradings with clay content ranging between 9 and 31.6% and three cement contents (5%, 8% and 12%) were considered. Effect of delayed compaction (time lag) on compaction characteristics and compressive strength of cement stabilised soils was examined by monitoring the results up to 10 hours of time lag. Influence of moulding water content and density on compressive strength and water absorption of cement stabilised soils was examined considering for a range of densities and water contents. The results indicate that (a) there is a considerable difference between dry and wet compressive strength of CSRE prisms, and the strength decreases as the moisture content at the time of testing increases, (b) wet strength is less than that of dry strength and the ratio between wet to dry strength depends upon the clay fraction of soil mix and cement content, (c) saturated moisture content depends upon the cement content and the clay content of the soil mix, (d) optimum clay percentage yielding maximum compressive strength is about 16%, (e) compressive strength of compacted cement stabilised soil increases with increase in density irrespective of cement content and moulding moisture content, and the strength increases by 300% for 20% increase in density from 15.70 kN/m3, (f) compressive strength of rammed earth is one - third higher than that of rammed earth brick masonry and (g) density decreases with increase in time lag and there is 50% decrease in strength with 10 hour time lag. Stress-strain relationships and elastic properties of cement stabilised rammed earth are essential for the analysis of CSRE structural elements and understanding the structural behaviour of CSRE walls. Influence of soil composition, density, cement content and moisture on stress-strain relationships of CSRE was studied. Three different densities (15.7 – 19.62 kN/m3) and three cement percentages (5%, 8% and 12% by weight) were considered for CSRE. Stress-strain characteristics of CSRE and rammed earth brick masonry were compared. The results reveal that (a) in dry condition the post peak response shows considerable deformation (strain hardening type behaviour) beyond the peak stress and ultimate strain values at failure (dry state) are as high as 3.5%, which is unusual for brittle materials, (b) modulus for CSRE increases with increase in density as well as cement content and there is 1 to 3 times increase as the cement content changes from 5% to 12%. Similarly the modulus increases by 2.5 to 5 times as the dry density increases from 15.7 to 19.62 kN/m3 and (c) the modulus of CSRE and masonry in dry state are nearly equal, whereas in wet state masonry has 20% less modulus. Compressive strength and behavior of storey height CSRE walls subjected to concentric compression was studied. The results of the wall strength were compared with those of wallette and prism strengths. The wall strength decreases with increase in slenderness ratio. There is nearly 30% reduction in strength as the height to thickness ratio increases from 4.65 to 19.74. It was attempted to calculate the ultimate compressive strength of CSRE walls using the tangent modulus theory. At higher slenderness ratios, there is a close agreement between the experimental and predicted values. The storey height walls show lateral deflections as the load approaches failure. The walls did not show visible buckling and the shear failure patterns indicate material failure. The shear failures noticed in the storey height walls resemble the shear failures of short height wallette specimens. The thesis ends with a summary of the results with concluding remarks in the last chapter.

In the present thesis, studies on the response of soil nail walls subjected to static and seismic conditions using finite element based numerical simulations and the principle of reliability analysis have been performed. The basic methodology constitutes the study of various aspects of soil nail walls such as analyses of important external, internal and facing failure modes, development of axial forces, and displacement observations by considering various typical and prototype cases. For better understanding and presentation, subject matter of the thesis is organised in the following ten chapters. Chapter 1 of the thesis provides an introduction to the soil nailing technique and highlights some of its applications, advantages, and limitations. Chapter 2 provides a detailed review of existing literature on the soil nailing technique. Chapter 3 provides a detailed overview the various methodologies adopted in the thesis for the analyses and response study of the soil nail walls. Chapter 4 deals with the important aspects related to the plane strain finite element based numerical simulations of soil nail walls. In particular, addresses the implications of the use of advanced soil models and the consideration of bending stiffness of soil nails on the overall response of the soil nail walls. Chapter 5 presents finite element simulations based appraisal of the conventional design methodology of soil nail walls, and studies the response of typical soil nail walls under static and seismic conditions. Chapter 6 presents a reliability based study of the important failure modes of soil nail walls subjected to the variability in in-situ soil parameters, and highlights the importance of reliability analysis in context of soil nail walls. Chapter 7 proposes load and resistance factor design (LRFD) methodology in context of soil nail walls, and highlights the need in advancement of the existing conventional design methodology for soil nail walls. Chapter 8 illustrates the use of factorial design of experiment methodology in developing regression models for stability criteria analysis of soil nail walls. Chapter 9 proposes methods for assessing the adequacy of field pullout tests performed in accordance with the prevalent soil nailing guidelines. Further, a reliability based methodology is proposed for the evaluation and various applications of field pullout tests results have been illustrated. Chapter 10 summarises the various studies reported in the thesis and provides a few important conclusions. It is believed that the various studies reported in the thesis contribute to the enhancement of the existing knowledge on soil nailing technique, advancement in the analysis and design methods, and in general, are useful to the soil nailing practice.

Space structures are inevitable while covering large spans. Space structures are skeletal structures, which are lighter for the same stiffness when compared with RCC roofs. Till now, space structures, like any other metal structures have been designed assuming the joints as rigid, although there have been several publications about semi rigid joints. Of course, the publications mostly deal with 2D structures and there are very few reports on 3D structures. Space structures, by their nature fall into the latter category. The joints in a space structure are popularly called as "nodes". Generally, nodes, which ensure concentricity of member axes, are either solid or hollow. These are either cast or forged. There are other proprietary types, which do not come under the above classification, and have not been considered in this thesis. Hollow nodes are obviously more economical than solid nodes, but also more flexible. While it is prudent to prefer hollow nodes, it is equally necessary to assess their flexibility, because of its influence on the behaviour of the structure. The hollow spherical node is very popular because of its simplicity and adaptability to various forms of space frames. Double layer grids, which are the most popular forms for roofing applications, are being increasingly implemented. While the hollow spherical node is well suited for double layer grids, an evolutionary development has been what is called as the hollow octahedral node (this node is simply referred to as the 'Octa ' node in this thesis). Chapter 1 introduces space frames and double layer grids in particular, with the advantages of using double-layer grids. Jointing systems available around the world are briefed and the node connector used in the present study is introduced with a brief write-up on its advantages and disadvantages. This chapter also explores the available literature and, the scope and objectives of the thesis are mentioned. Chapter 2 introduces 3D finite element models of the hollow spherical and octahedral nodes. The stiffness matrixes of these nodes have been derived by conducting analyses on the computer for six sizes each of the Octa and spherical nodes. Using the stiffness matrix of the node, a new method of incorporating this into the regular analysis of a space truss has been developed. The new method proposed yields realistic values for the forces in the members and takes into account the elastic deflections in the node under the action of member forces. Implementation of the proposed method has been carried out by writing a custom program using state-of-the-art object oriented programming techniques. A sample problem has been analyzed using this program to demonstrate the effect of including joint flexibility. The effect of flexibility of nodes on the effective length of compression members in double-layer grids has been evaluated. The effect of compliance on the dynamic characteristics of a space frame has also been evaluated for the sample space frame with flexible joints. The analysis program has been modified to evaluate the natural frequencies of the system using rigid or flexible nodes. The study of the Octanode and spherical node under the action of uniaxial compression and tension dominates the contents of Chapter 3. The two types of nodes have been analyzed using commercially available finite element software considering material nonlinearity. The stress patterns from the analyses have been examined thoroughly. Two consistent methods for fixing the load at yield in both uniaxial compression and tension have been proposed using the load-displacement curve. Yield loads for all the nodes have been evaluated using both the methods and the results agree well between the two methods. Three material yield values have been selected for each of the node size for evaluating the yield values viz. 240,320 and 415 MPa. The members of a double layer grid are connected to the nodes by bolts and holes are drilled in the nodes for this purpose. The bolthole patterns differ between two popular types of double-layer grids. Both these bolthole patterns have been modeled separately in the above exercise and the results for these two have been shown to be approximately the same. The effect of varying diameters of the boltholes on the response of the nodes has been examined. Relationships between the yield load, diameter, thickness and material yield have been developed using the method of least squares. The differences in the behaviour of the nodes under uniaxial compression and tension have been discussed. Ramberg Osgood type of relationships have been worked out for all the load-displacement curves obtained from the analyses. The simulation of non-linear behaviour of nodes with cracks with plastic crack closing forces have been carried out with useful insights into the behaviour of the two types of nodes in uniaxial compression and tension. Chapter 4 is devoted largely for studying the two types of nodes under the influence of biaxial load combinations. The combinations studied are dual compression, dual tension and compression-tension. In all cases equal loads are applied along two orthogonal; directions in the horizontal plane. Stress patterns have been examined for each type of load combination and yield values for each case have been obtained using one of the methods proposed in chapter 3. These have been compared with the corresponding uniaxial values in both compression and tension. Some useful inferences have been possible by studying the behaviour of the nodes under the various biaxial load combinations. In each case, relationships between the biaxial yield load, uniaxial yield load, diameter of node, thickness of node and material yield of node have been obtained using the method of least squares. The nodes have been analyzed under some selected Multi-axial loading and combinations of load which cause yield based on the second method proposed in Chapter 3 have been obtained and tabulated. However, a proper and thorough study of the nodes under multi-axial loading proved to be beyond the scope of this thesis. Chapter 5 contains the contributions made towards developing new methods and algorithms for obtaining the several results of chapters 2, 3 and 4, using object oriented programming (OOP) techniques. The contributions have been in Object Pascal, the underlying language of Delphi, a popular RAD tool developed by Borland/Inprise of USA. Several new modules have been developed to reliably handle the large amounts of data generated by the hundreds of analyses detailed in chapters 2,3 and 4. The ease with which new methods were possible to be incorporated into existing software using OOP has been demonstrated, with source code examples. Comparisons with other types of tools available and die advantages of using OOP have also been demonstrated using the experience during the preparation of this thesis. A strong case for OOP as an indispensable tool for the researcher has been made. Chapter 6: Several important conclusions and suggestions for future work have been made. Appendix 1 contains a brief note on the Method of Least Squares. Appendix 2 contains a small write-up on Delphi and OOP. Concepts of OOP have been briefly described and comparisons between three popular OOP languages have been attempted. A brief description of the features in Delphi's Object Pascal has also been provided. Appendix 3 contains the listing of Unit Arrays, which is a general purpose unit developed to make handling of large arrays easy. Several matrix calculations have been implemented which make the unit extremely useful for programmers. Appendix 4 contains the full listing of program FormK, which has been developed for chapter 2 to derive the fall stiffness matrix of a space frame node. The program picks up results from several analyses, forms a few columns of the stiffness matrix and then fills up the rest using the cyclic symmetry present in the space frame node. This program is given in full, with the intention that other researchers may find it useful to use it as-is or use after making small alterations to suit their circumstances. OOP is known for fast, reliable and easy ways of implementing modifications to existing code. Appendix 5 provides the full listing of the Object Pascal program for extracting Eigenvalues of a space truss with rigid joints or flexible joints. The incorporation of flexibility of the joints proposed in chapter 2 has been implemented. Descriptions of the program's implementations have been provided in chapter 5. Bibliography contains the alphabetical list of references.

With the advancement in knowledge of inelastic response of structures, the design and construction practices of reinforced concrete buildings have been changing worldwide. Most of the codes are incorporating the near-fault factors and performance based designs in the seismic codes. However, further investigation is needed to identify the physical behaviour of multi-storey buildings to near-fault ground motions. At present, quantitative evaluation of response and its mitigation to near field ground motions is a popular topic in earthquake engineering field. The present study discusses the inelastic response of symmetric and asymmetric multi-storey buildings to near-fault ground motions. The possibility of design approach is based on ‘expendable top storey’ for the multi-storey RC- buildings to near field records. If such behaviour is feasible one can conceive of a structure whose top storey is permitted and designed to undergo large inelastic deformations while reducing damage in the lower storey. The concept was first proposed in an earlier research (RaghuPrasad, 1977). Such a concept juxtaposes the often-mentioned ‘soft first storey’ concept. Further in this report, the performance evaluation of multi-storey buildings near Chiplun fault in Mumbai, India is also discussed. The thesis is organized in the following chapters: Introduction in Chapter-1 contains detailed literature review on inelastic response of symmetric and asymmetric buildings, response of buildings to near-fault records, elastic and inelastic vibration absorber concepts and performance based designs. The literature reveals that considerable amount of research has been carried out on the elastic, inelastic response of structures and vibration absorber concepts to ordinary ground motions. Recently, the effect of near field ground motions on the response of multi-storey buildings is gaining much importance. Most of the research publications are available on response of symmetric buildings subjected to near field ground motions. But many problems are yet to be investigated. They are, identification of important ground motion parameters in near fault records, vibration absorber concepts and torsional response of structures subjected to pulse type ground motions. These problems are clearly mentioned in the recently published state-of-the-art review by Shuang and Li-Li (2007). In this report an attempt has been made to solve these problems. Effect of near-fault ground motions on symmetric multi-storey buildings in Chapter-2, describes simplified non-dimensionalized equations of motion to study the response behaviour of multi-storey buildings to near fault records. The non-dimensionalized equations of motion are expressed in terms of near fault ground motion parameters. The objective is to find a relation between ductility demand and near field ground motion parameters through neural network approach. For this a neural network modeling was done to predict the ductility demand in terms of peak ground acceleration, peak ground velocity, epicentral distance and pulse period of the near field ground motion. A thorough sensitive analysis is carried out, to ascertain which parameters are having maximum influence on ductility demand. In this chapter further, a comparative study is made on the inelastic seismic response of multi-storey buildings to pulse type and non pulse type ground motions. The study shows that, it is necessary to consider the effect of near fault ground motions separately and make provisions for the design in the codes of practice accordingly. Vibration absorber effect in multi-storey buildings in chapter-3, discusses the behaviour of top storey as a vibration absorber during near field ground motions. For this purpose, a five storey symmetric building model is considered as an example problem to demonstrate the effectiveness of the proposed concept. Response of the structure is obtained for the various combinations of absorber storey parameters such as mass ratio, frequency ratio and yield displacement ratio. Here mass ratio means mass of the absorber storey to that of the bottom storey and similarly for the frequency and yield displacement ratios. Observing the storey-wise variation of these responses, we can say that for a range of mass ratios, frequency ratios and yield displacement ratios, the inelastic response of top storey is large compared to the lower storeys. This range is termed as ‘effective range’. Further, in this range the top storey absorbs the vibration energy of the structure by keeping the lower storeys in elastic state i.e. acts as a vibration absorber. The top storey can also be termed as ‘expendable top storey’. Effect of near-fault ground motions on asymmetric multi-storey buildings in Chapter-4, discusses the inelastic response of asymmetric buildings to single horizontal component and two horizontal components of near fault ground motions viz., fault normal and fault parallel components. For numerical investigations eight building models are considered. Eccentricity has been created by keeping the stiffness and mass centre separately. The building models are subjected to strong motion records of Imperial Valley Array-5 (1979) and Northridge-Sylmar (1994). A detailed study on the effect of base shear strength, eccentricity and pulse period of near fault ground motions on the response is investigated. Performance of multi-Storey buildings in Chapter-5, reported a detailed procedure for the performance evaluation of structures. The procedure is applied to find the performance evaluation of multi-storeyed buildings located in near fault region. Chiplun fault in Mumbai, India has been chosen for the study because several features of that fault are clearly published (RaghuKanth and Iyengar, 2006). Results of performance evaluation of five and ten storeyed symmetric buildings with and without infill panels are studied. Ground motion records consistent with the hazard spectrum for the design are considered. The performance of the building near the Chiplun fault in Mumbai, India shows operational under UHS-500 (uniform hazard spectrum) event and it collapses when the building is exposed to UHS-2500 record. The thesis is concluded in Chapter-6 with an overall summary of the report and suggestions for further scope of the work.

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.

A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the method through applications to non-linear oscillators, we also use the Girsanov transformation of measures to correct the truncation errors in lower order discretizations. In order to achieve efficiency in the computation of response statistics via Monte Carlo simulation, we propose in Chapter 4 a weak variance reduction strategy such that the ensemble size is significantly reduced without seriously affecting the accuracy of the predicted expectations of any smooth function of the response vector. The basis of the variance reduction strategy is to appropriately augment the governing system equations and then weakly replace the associated stochastic forcing functions through variance-reduced functions. In the process, the additional computational cost due to system augmentation is generally far less besides the accrued advantages due to a drastically reduced ensemble size. The variance reduction scheme is illustrated through applications to several non-linear oscillators, including a 3-DOF system. Finally, in Chapter 5, we exploit the explicit forms of the LTL techniques for state and parameters estimations of non-linear oscillators of engineering interest using a novel derivative-free EKF and a 2-EKF. In the derivative-free EKF, we use one-term, Euler and Newmark replacements for linearizations of the non-linear drift terms. In the 2-EKF, we use bias terms to account for errors due to lower order linearization and unmodelled dynamics in the mathematical model. Numerical studies establish the relative advantages of EKF-DLL as well as 2-EKF over the conventional forms of EKF. The thesis is concluded in Chapter 6 with an overall summary of the contributions made and suggestions for future research.

Development of dynamic state estimation techniques and their applications in problems of identification in structural engineering have been taken up. The thrust of the study has been the identification of structural systems that exhibit nonlinear behavior, mainly in the form of constitutive and geometric nonlinearities. Methods encompassing both linearization based strategies and those involving nonlinear filtering have been explored. The applications of derivative-free locally transversal linearization (LTL) and multi-step transversal linearization (MTrL) schemes for developing newer forms of the extended Kalman filter (EKF) algorithm have been explored. Apart from the inherent advantages of these methods in avoiding gradient calculations, the study also demonstrates their superior numerical accuracy and considerably less sensitivity to the choice of step sizes. The range of numerical illustrations covers SDOF as well as MDOF oscillators with time-invariant parameters and those with discontinuous temporal variations. A new form of the sequential importance sampling (SIS) filter is developed which explores the scope of the existing SIS filters to cover nonlinear measurement equations and more general forms of noise involving multiplicative and (or) Gaussian/ non-Gaussian noises. The formulation of this method involves Ito-Taylor’s expansions of the nonlinear functions in the measurement equation and the development of the ideal ispdf while accounting for the non-Gaussian terms appearing in the governing equation. Numerical illustrations on parameter identification of a few nonlinear oscillators and a geometrically nonlinear Euler–Bernoulli beam reveal a remarkably improved performance of the proposed methods over one of the best known algorithms, i.e. the unscented particle filter. The study demonstrates the applicability of diverse range of mathematical tools including Magnus’ functional expansions, theory of SDE-s, Ito-Taylor’s expansions and simulation and characterization of the non-Gaussian random variables to the problem of nonlinear structural system identification.