Recent developments in safety assessment of concrete gravity dams

Most of the dams in India were built in the sixties, when only simple methods could be used to properly design them. Forty years later, despite the progress made in our capability to conduct sophisticated finite element studies, current analyses procedures for safety assessment remain essentially the same as those used earlier for design. The main objective of this article is to highlight the work done in the area of fracture mechanics for safety assessment of gravity dams. It is shown that the conventional strength of materials-based design leads to large factors of safety when compared to the more recent and rational concepts of fracture mechanics

Correlation between fracture and damage for quasi-brittle bi-material interface cracks

Fracture at a bi-material interface is essentially mixed-mode, even when the geometry is symmetric with respect to the crack and loading is of pure Mode I, due to the differences in the elastic properties across an interface which disrupts the symmetry. The linear elastic solutions of the crack tip stress and displacement fields show an oscillatory type of singularity. This poses numerical difficulties while modeling discrete interface cracks. Alternatively, the discrete cracks may be modeled using a distributed band of micro-cracks or damage such that energy equivalence is maintained between the two systems. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in quasi-brittle bi-material interface beams. The study is aimed at large size structures made of quasi-brittle materials failing at concrete–concrete interfaces. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. It is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained

Damage indices for failure of concrete beams under fatigue

In this study, an analytical method is proposed to correlate local damage variables such as relative crack depth and crack tip opening displacement with a newly defined global damage index for a concrete beam under fatigue loading. This global damage index may be used to assess the response of a degraded concrete beam under service loading. The damage is assumed to appear in the form of a major crack that propagates under constant amplitude fatigue loading. The progressive cracking phenomenon is modeled within a finite element framework using a crack beam element, which takes into account the compliance variation due to discrete cracking within the member. The flexural stiffness degradation of the member is computed based on an Eigen analysis of the global stiffness matrix.It is seen that the degree of flexural stiffness degradation due to discrete cracking is the same for geometrically similar specimens when the relative crack depth is used as a local damage parameter. Further, in order to improve the accuracy of the response prediction using the above global damage index, another global damage parameter is defined based on the nature of applied loading

Energy-based equivalence between damage and fracture in concrete under fatigue

Damage in concrete members, occur in a distributed manner due to the formation and coalescence of micro-cracks, and this can easily be described through a local damage approach. During subsequent loading cycles, this distributed zone of micro-cracks get transformed into a major crack, introducing a discrete discontinuity in the member. At this stage, concepts of fracture mechanics could be used to describe the behavior of the structural member. In this work, an approach is developed to correlate fracture and damage mechanics through energy equivalence concepts and to predict the damage scenario in concrete under fatigue loading. The objective is to smoothly move from fracture mechanics theory to damage mechanics theory or vice versa in order to characterize damage. The analytical methods developed here have been exemplified with some already available data in the literature. The strength and stiffness reduction due to progressive cracking or increase in damage distribution, has been characterized using the available indices such as the strength reduction and stiffness reduction factors. It is seen through numerical examples, that the strength and stiffness drop indices using fracture and damage mechanics theory agree well with each other. Hence, it is concluded, that through the energy approach a discrete crack may be modeled as an equivalent damage zone, wherein both correspond to the same energy loss. Finally, it is shown that by knowing the critical damage zone dimension, the critical fracture property such as the fracture energy can be obtained

Fracture Properties of Concrete-Concrete Interfaces Using Digital Image Correlation

The mode I and mode II fracture toughness and the critical strain energy release rate for different concrete-concrete jointed interfaces are experimentally determined using the Digital Image Correlation technique. Concrete beams having different compressive strength materials on either side of a centrally placed vertical interface are prepared and tested under three-point bending in a closed loop servo-controlled testing machine under crack mouth opening displacement control. Digital images are captured before loading (undeformed state) and at different instances of loading. These images are analyzed using correlation techniques to compute the surface displacements, strain components, crack opening and sliding displacements, load-point displacement, crack length and crack tip location. It is seen that the CMOD and vertical load-point displacement computed using DIC analysis matches well with those measured experimentally

Micromechanical Damage Model for Plain Concrete Considering Propagation of Matrix Microcracks

Based on the tenets of continuum micromechanics, a damage model is developed in the present work to investigate the effect of microcracking on the constitutive relations of cement based materials such as concrete. The model considers concrete as a two phase particulate composite consisting of coarse aggregates and mortar matrix. The microcracks are assumed to be present in the matrix material. Making use of Eshelby's solution for equivalent inclusion, the stress and strain fields are evaluated at the mesoscale. A two step homogenization scheme is adopted to obtain the effective response of the composite. The crack density parameter is used as a damage variable in the formulation. Strain energy release rate, obtained from the micromechanical analysis, is used as the criterion for describing the propagation of microcracks. The effect of various mesoscopic parameters, such as aggregate content, elastic properties of the phases, microcrack density and fracture resistance of the matrix, on the overall behavior of concrete is demonstrated through a parametric study