The primary objective of this research is to develop and verify a methodology for modeling three dimensional discrete crack growth in concrete and reinforced concrete structures. Two main sources of damage, considered in this work, include the mechanical loading and the chemical interaction. The behavior of concrete is brittle in tension and becomes ductile behavior under compressive loading. At the same time, the chemical interaction triggers a progressive degradation of strength parameters. The main focus in this research is on numerical analysis of localized damage that is associated with formation of macrocracks. The specific form of chemical interaction examined here involves the alkali-silica reaction (ASR). The approach used in this work for describing the propagation of macrocraks is based on the volume averaging technique. This scheme represents a simplified form of strong discontinuity approach (SDA). It incorporates the notion of a ‘characteristic length’, which is defined as the ratio of area of the crack surface to the considered referential volume. It is demonstrated, based on an extensive numerical study, that this approach gives mesh-independent results which are consistent with the experimental evidence. The accuracy of the solutions is virtually the same as that based on SDA and/or the Extended Finite Element Method (XFEM), while the computational effort is significantly smaller. In order to describe the behavior of the fractured zone, a traction velocity discontinuity relation is formulated that is representative of different modes of damage propagation, including crack opening in tensile regime as well as shear band formation under compression. For tracing the discontinuity within domain, crack smoothening algorithm is employed to overcome any numerical instabilities that may occur close to ultimate load of the structure. The general methodology, as outlined above, has been enhanced by incorporating the chemoplasticity framework to describe the damage propagation in concrete affected by chemical interaction, i.e. continuing ASR. The latter is associated with progressive expansion of the silica gel that is coupled with degradation of strength properties. An implicit scheme has been developed, incorporating the return mapping algorithm, for the integration of the governing constitutive relations. The framework has been implemented in Abaqus software to examine the crack propagation pattern in structural elements subjected to continuing ASR. Another major topic addressed in this thesis is the ‘size effect’ phenomenon. The existing experimental studies, conducted primarily on various concrete structures, clearly show that the ultimate strength is strongly affected by the size of the structure. This phenomenon stems primarily from the effect of localized damage that accompanies the structural failure. The quantitative response depends on the geometry of the structure, type of loading and the material properties. The size effect has been investigated here for a number of notched and un-notched concrete beams, of different geometries, subjected to three-point bending. Both mechanical loading and the chemical interaction have been considered. The next topic considered in this study deals with analysis of localized fracture in 3D reinforced concrete structures. Here, a mesoscale approach is employed whereby the material is perceived as a composite medium comprising two constituents, i.e. concrete matrix and steel reinforcement. The response at the macroscale is obtained via a homogenization procedure that incorporates again the volume averaging. The latter incorporates a set of static and kinematic constraints that are representative of the response prior to the onset of fracture. After the formation of macrocracks, a traction-separation law within the fractured zone is modified by incorporating the Timoshenko beam theory in order to assess the stiffness characteristics in the presence of reinforcement. A number of numerical examples are given that examine the crack pattern formation and the associated fracture mechanism in concrete beams at different intensity of reinforcement. The final chapter of this thesis provides an illustrative example of the application of the proposed methodology to the analysis of a large scale structure. The focus here is on the assessment of structural damage in a hydraulic structure subjected to ASR continuing over of period of a few decades. The results, in term of the predicted extent of damage as well as the displacement history at some specific locations, are compared with in-situ monitoring. / Thesis / Doctor of Philosophy (PhD)