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.

The properties of natural soil are inherently variable and influence design decisions in geotechnical engineering. Apart from the inherent variability of the soil, the variability may arise due to measurement of soil properties in the field or laboratory tests and model errors. These wide ranges of variability in soil are expressed in terms of mean, variance and autocorrelation function using probability/reliability based models. The most common term used in reliability based design is the reliability index, which is a probabilistic measure of assurance of performance of structure. The main objective of the reliability based design is to quantify probability of failure/reliability of a geotechnical system considering variability in the design parameters and associated safety. In foundation design, reliability based design is useful compared to deterministic factor of safety approach. Several design codes of practice recommend the use of limit state design concept based on probabilistic models, and suggest that, development of reliability based design methodologies for practical use are of immense value. The objective of the present study is to propose reliability based design methodologies for pile foundations under static and seismic loads. The work presented in this dissertation is subdivided into two parts, namely design of pile foundations under static vertical and lateral loading; and design of piles under seismic loading, embedded in non-liquefiable and liquefiable soil. The significance of consideration of variability in soil parameters in the design of pile foundation is highlighted. A brief review of literature is presented in Chapter 2 on current pile design methods under vertical, lateral and seismic loads. It also identifies the scope of the work. Chapter 3 discusses the methods of analysis which are subsequently used for the present study. Chapter 4 presents the reliability based design methodology for vertically and laterally loaded piles based on cone penetration test data for cohesive soil. CPT data from Konaseema area in India is used for analysis. Ultimate limit sate and serviceability limit state are considered for reliability based design using CPT data and load displacement curves. Chapter 5 presents the load resistance factor design (LRFD) of vertically and laterally loaded piles based on load test data. Reliability based code calibrated partial factors are determined considering bias in failure criteria, model bias and variability in load and resistance. Chapter 6 illustrates a comprehensive study on the effect of soil spatial variability on response of vertically and laterally loaded pile foundations in undrained clay. Two-dimensional finite difference program, FLAC2D (Itasca 2005) is used to model the soil and pile. The response of pile foundations due to the effect of variance and spatial correlation of undrained shear strength is studied using Monte Carlo simulation. The influence of spatial variability on the propagation and formation of failure near the pile foundation is also examined. Chapter 7 describes reliability based design methodology of piles in non-liquefiable soil. The seismic load on pile foundation is determined from code specified elastic design response spectrum using pseudo-static approach. Variability in seismic load and soil undrained shear strength are incorporated. The effects of soil relative densities, pile diameters, earthquake predominant frequencies and peak acceleration values on the two plausible failure mechanisms; bending and buckling are examined in Chapter 8. The two-dimensional finite difference analysis is used for dynamic analysis. A probabilistic approach is proposed to identify governing failure modes of piles in liquefiable soil in Chapter 9. The variability in the soil parameters namely SPT-N value, friction angle, shear modulus, bulk modulus, permeability and shear strain at 50% of modulus ratio is considered. Monte Carlo simulation is used to determine the probability of failure. A well documented case of the failed pile of Showa Bridge in 1964 Niigata earthquake is considered as case example. Based on the studies reported in this dissertation, it can be concluded that the reliability based design of pile foundations considering variability and spatial correlation of soil enables a rational choice of design loads. The variability in the seismic design load and soil shear strength can quantify the risk involved for pile design in a rational basis. The identification of depth of liquefiable soil layer is found to be most important to identify failure mechanisms of piles in liquefiable soil. Considerations of soil type, earthquake intensity, predominant frequency of earthquake, pile material, variability of soil are also significant.

Design of retaining structures depends upon the load which is transferred from backfill soil as well as external loads and also the resisting capacity of the structure. The traditional safety factor approach of the design of retaining structures does not address the variability of soils and loads. The properties of backfill soil are inherently variable and influence the design decisions considerably. A rational procedure for the design of retaining structures needs to explicitly consider variability, as they may cause significant changes in the performance and stability assessment. Reliability based design enables identification and separation of different variabilities in loading and resistance and recommends reliability indices to ensure the margin of safety based on probability theory. Detailed studies in this area are limited and the work presented in the dissertation on the Optimum design of retaining structures under static and seismic conditions: A reliability based approach is an attempt in this direction. This thesis contains ten chapters including Chapter 1 which provides a general introduction regarding the contents of the thesis and Chapter 2 presents a detailed review of literature regarding static and seismic design of retaining structures and highlights the importance of consideration of variability in the optimum design and leads to scope of the investigation. Targeted stability is formulated as optimization problem in the framework of target reliability based design optimization (TRBDO) and presented in Chapter 3. In Chapter 4, TRBDO approach for cantilever sheet pile walls and anchored cantilever sheet pile walls penetrating sandy and clayey soils is developed. Design penetration depth and section modulus for the various anchor pulls are obtained considering the failure criteria (rotational, sliding, and flexural failure modes) as well as variability in the back fill soil properties, soil-steel pile interface friction angle, depth of the water table, total depth of embedment, yield strength of steel, section modulus of sheet pile and anchor pull. The stability of reinforced concrete gravity, cantilever and L-shaped retaining walls in static conditions is examined in the context of reliability based design optimization and results are presented in Chapter 5 considering failure modes viz. overturning, sliding, eccentricity, bearing, shear and moment failures in the base slab and stem of wall. Optimum wall proportions are proposed for different coefficients of variation of friction angle of the backfill soil and cohesion of the foundation soil corresponding to different values of component as well as lower bounds of system reliability indices. Chapter 6 presents an approach to obtain seismic passive resistance behind gravity walls using composite curved rupture surface considering limit equilibrium method of analysis with the pseudo-dynamic approach. The study is extended to obtain the rotational and sliding displacements of gravity retaining walls under passive condition when subjected to sinusoidal nature of earthquake loading. Chapter 7 focuses on the reliability based design of gravity retaining wall when subjected to passive condition during earthquakes. Reliability analysis is performed for two modes of failure namely rotation of the wall about its heel and sliding of the wall on its base are considering variabilities associated with characteristics of earthquake ground motions, geometric proportions of wall, backfill soil and foundation soil properties. The studies reported in Chapter 8 and Chapter 9 present a method to evaluate reliability for external as well as internal stability of reinforced soil structures (RSS) using reliability based design optimization in the framework of pseudo static and pseudo dynamic methods respectively. The optimum length of reinforcement needed to maintain the stability against four modes of failure (sliding, overturning, eccentricity and bearing) by taking into account the variabilities associated with the properties of reinforced backfill, retained backfill, foundation soil, tensile strength and length of the geosynthetic reinforcement by targeting various component and system reliability indices is computed. Finally, Chapter 10 contains the important conclusions, along with scope for further work in the area. It is hoped that the methodology and conclusions presented in this study will be beneficial to the geotechnical engineering community in particular and society as a whole.