The concept of reinforcement was developed in late 20th century and since then till the recent past there are many works carried out on the effect of fibers in imparting strength and stiffness to the soil. Experimental investigations on fiber reinforced soils showed an increase in shear strength and reduction in post peak loss of strength due to the reinforcement. Analytical/mechanistic models are developed to predict the stress-strain response of fiber reinforced soil (under discrete framework, energy dissipation methods, force equilibrium methods etc). Numerical investigations are also carried out, and it was observed that the presence of random reinforcing material in soils make the stress concentration diffuse more and restrict the shear band formation. Soil properties vary from point to point at micro level and influence stress mobilization. Hence, there is a need to carry out probabilistic analysis to capture the effects of uncertainties and variability in soil and their influence on stress-strain evolution. In the present thesis an attempt has been made to propose a mechanistic model that predicts the stress-strain response of fiber reinforced soil and also considers the effect of anisotropy of fibers. A stochastic/probabilistic model is developed that predicts the stochastic stress-strain response of fiber reinforced soil. In addition, probabilistic analysis is carried out to observe the effect of number of fibers across the shear plane in imparting shear resistance to soil. The mechanistic model and stochastic models are validated with reference to the experimental results of consolidated undrained (CU) triaxial tests on coir fiber reinforced red soil for different fiber contents. The entire thesis is divided into six chapters. Chapter-wise description is given below. Chapter one presents a general introduction to the works carried out on fiber reinforced soils and also the investigations carried out on probabilistic methodologies that takes into account the soil variability. Thus, the chapter gives an outline of the models developed under mechanistic and probabilistic frameworks in the thesis. The objectives and organization of the thesis are also presented. Chapter two presents a detailed review of literature on the role of fibers in fiber reinforced soil. The details of experimental investigations carried out and models developed are explained briefly. Also, the literature pertaining to the role of variability in soil on its engineering behavior is presented. Based on the literature presented in this chapter, concluding remarks are made. Chapter three presents the details of a new mechanistic model developed based on modified Cam-clay model. This model considers the effect of fiber content and also the effect of anisotropy due to fibers. The predictions from the mechanistic model are compared with the experimental results. Under anisotropic condition, as angles of inclination of fiber vary from 0° to 90° with the bedding plane, it is observed that the strength increment in the reinforced soil is not as significant as that observed in isotropic case. Horizontal fibers turn out to be most effective since they are subjected to maximum extension thereby inducing tensile resistance which in turn contributes for strength increase in fiber reinforced soil. Chapter four presents a new approach to predict the stochastic stress-strain response of soil. Non-homogeneous Markov chain (multi-level homogeneous Markov chain) modeling is used in the prediction of stochastic response of soil. The statistical variations in the basic variables are taken into account by considering the response quantities (viz. stress at a given strain or settlement at a given load level) as random. A bi-level Homogeneous Markov chain predicts the stochastic stress-strain response efficiently. The predicted results are in good agreement with the experimental results. An illustration of this model is done to predict the stochastic load-settlement response of cohesionless soil. A simple tri-level homogeneous Markov chain model is proposed to predict settlements of soil at a given load for an isolated square footing subjected to axial compression. A parametric study on the effect of correlation coefficient on the prediction of settlements is performed. Chapter five presents the results of probabilistic analysis carried out to determine the effect of number of fibers across the shear plane in improving the shear strength of soil. It is observed that as the percentage of fibers in the specimen increases, the probability of failure of specimen under the same stress condition reduces and thus the reliability of the fiber reinforced soil system increases. In Chapter six, a summary of the important conclusions from the various studies reported in the dissertation are presented.

The present thesis proposes model for the analyses of stress-strain response of fiber reinforced soil and municipal solid waste (MSW). The concept of reinforcing soils by introducing tension resisting elements such as fibers is becoming widely accepted. Fiber inclusions are found to improve the post-peak behavior of the soil. Evaluation of the stress-strain response of the fiber-reinforced soil indicates that mobilization of the fiber tension generally requires a strain level higher than that corresponding to the peak strength of unreinforced soil. Further, geotechnical engineering properties of MSW such as compressibility, shear strength and stiffness are of prime importance in design and maintenance of landfills. It is also referred in literature that MSW tends to behave as fiber-reinforced soil due to the presence of various types of wastes in its matrix. However, it is not well understood how the stress-strain and strength characteristics vary with time as the biodegradation of waste continues in the landfill. Based on the experimental observations, in this thesis, an attempt is made for developing generalized constitutive models based on the critical state soil mechanics frame work for fiber reinforced soils and municipal solid waste. The proposed models consider the fiber effect in fiber reinforced soil and, time dependent mechanical and biodegradation effects in case of municipal solid waste, respectively. The proposed models are able to capture the stress-strain and pore water pressure response in both the cases. For better understanding, the present thesis is divided into following seven chapters. Chapter 1 is an introductory chapter, in which the need for use of the constitutive models is presented. Further, the organization of thesis is also presented. Chapter 2 presents a brief description of the available studies in the literature on fiber-reinforced soils and municipal solid waste. Various studies on fiber-reinforced soil included experimental results (both laboratory and field) and modeling methods. Experiments on fiber-reinforced soils were mainly carried out with triaxial compression tests, unconfined compression tests, direct shear tests, one dimensional consolidation tests, etc. Force equilibrium model, limit equilibrium model, statistical theory, regression based models are some of the models available in the literature for quantifying the strength of the fiber-reinforced soil. Further, various studies with regard to the engineering properties of municipal solid waste and their characteristic properties available in the literature are presented. They include different models proposed by various researchers for the prediction of stress-strain response, time dependent behavior and load settlement analysis of the municipal solid waste. Finally, based on the literature review, the scope and objectives of the thesis are presented at the end. Chapter 3 describes various types of soils, properties of soils and fibers used in the present study. A detailed description of the sample preparation and methods adopted in the experimental program are presented in this chapter. Chapter 4 presents the experimental results of triaxial compression tests and one dimensional consolidation test carried out on fiber-reinforced soils. Based on the experimental observations, a constitutive model for fiber-reinforced soil in the frame work of modified cam clay model is proposed. Further, the detailed derivation of proposed model and the discussion on evaluation of the input model parameters from triaxial and consolidation tests are presented. The predictions from the proposed models are validated with the experimental data. From the comparison of the results from the proposed model and experiments, it is evident that the proposed model is able to capture stress-strain behavior of fiber-reinforced soils. Chapter 5 presents the experimental studies on the behavior of municipal solid waste based on the triaxial compression and consolidation tests. Based on the experimental observations, a constitutive model for municipal solid waste in the frame work of modified cam clay model is proposed which considers the mechanisms such as mechanical creep and biodegradation. It also provides detailed description of the selection of the input parameters required for the proposed model. The experimental results in the form of stress-strain and pore water pressure response are compared with the prediction from the proposed model. In addition, the applicability of the proposed model is illustrated using detailed parametric studies of parameters of the model for various ranges. Chapter 6 presents a brief study of load settlement response on municipal solid waste using a case example. The constitutive model for municipal solid waste proposed in chapter 5 is used to study the time-settlement response of municipal solid waste and to compare the results with available published models considering different mechanisms. The major conclusions from the study are presented at the end. Chapter 7 presents a brief summary and conclusions from the various studies reported in the present thesis. vi