Chapter 3 3.1 Introduction
3.1 Introduction Chapter 3 Paper II
Abstract
The formation of cracks in the concrete cover of reinforced concrete is often related to mechanical loading. Although, the formation of cracks is inevitable due to the brittle nature of concrete, they are not accounted for in existing guidelines for service life design even though it is generally accepted that cracks in the concrete cover may promote the risk of reinforcement corrosion since the ingress rate of eg moisture and/or chlorides may increase.
To account for the influence of cracks and in the concrete cover in the service life de-sign of a reinforced concrete structure it is of vital importance to determine the corre-lation between the risk of the initiation of reinforcement corrosion and the extent of cracking associated to the load applied. Experimental studies of load-induced crack formation have been presented in the literature. However, operational tools, eg numer-ical models, capable of correlating the applied load and the associated crack-formation in the concrete cover and debonding at the concrete/steel interface are not available at present.
The aim of this paper is to present a numerical model for the formation of tensile load-induced cracking in concrete. The model simulates the formation of a bending crack through the concrete cover as well as the formation of debonding at the con-crete/steel interface. The numerical model is based on theories of fracture mechanics, viz. the fictitious crack model, and the numerical simulations are compared to exper-imental data. The experexper-imental data cover observations of flexural loading of conven-tional reinforcement embedded in plain concrete as well as steel fibre reinforced con-crete (0.5 and 1.0 vol.-%).
Comparisons of the numerical and experimental results show, that the proposed model is capable of simulating the formation of a bending crack and – at the same time – the slip and separation at the concrete/steel interface accurately. Based on those observa-tions it may be concluded that the numerical model is based on correct physical as-sumptions.
Keywords
Numerical simulations, Fracture mechanics, Load-induced cracking, Service Life De-sign, Fibre Reinforced Concrete
Chapter 3 3.1 Introduction Paper II
3.1 Introduction
Reinforced concrete is the most widely used man-made construction material in the World for structures in the civil infrastructure. The serviceability of such structures is strongly related to the integrity, which is controlled by the durability. The deteriora-tion of reinforced concrete structures is caused by a number of mechanisms such as freeze-thaw reactions, alkali-silica reactions and reinforcement corrosion, of which corrosion is the predominant deterioration mechanism [Rendell et al., 2002].
Corrosion of reinforcement occurs among others due to the ingress of de-passivating substances such as CO2 and/or Cl-. The ingress rate of those substances is strongly promoted by cracks in the concrete cover, which may be formed due to eg mechanical loading and/or shrinkage. Such cracks in the concrete cover act as pathways for the de-passivating substances [Wang et al., 1997; Edvardsen, 1999; Aldea et al., 1999].
The formation of cracks in concrete is effectively inevitable due to the quasi-brittle nature of concrete.
The identification of the predominant role of cracks in the concrete on the transport of de-passivating substances led to different formulations of the correlation between cracking and the risk of reinforcement corrosion. Such formulations are vitally im-portant for the proper design of durable reinforced concrete structures.
One of those formulations is based on the hypothesis that the risk of reinforcement corrosion is correlated to the crack mouth opening displacement (CMOD) at the con-crete surface eg [Schießl and Raupach, 1997; Mohammed et al., 2001]. The proposed models for that relationship show reasonable correlations for exposure times less than approx. three years. However, other experimental observations by eg Kennedy [Ken-nedy, 1956] and Francois and Arliguie [Francois and Arliguie, 1998] show no corre-lation at all between crack width and risk of reinforcement corrosion.
Bearing those observations in mind, it was proposed by Tammo [Tammo and The-landersson, 2009; Tammo et al., 2009] that the risk of reinforcement corrosion is con-trolled by the crack opening displacement (COD) at the level of the reinforcement.
The COD is not explicitly correlated with the CMOD eg due to the formation of con-crete cones around the reinforcement, varying cover thickness, rebar-concon-crete bond etc. A similar approach for the formulation of the risk of reinforcement corrosion due to cracking of the concrete cover was suggested by Pease et al. [Pease et al., 2006;
Pease et al., 2011] proposing that the cracking state along the concrete/steel interface is a more fundamental measure than the CMOD at the concrete surface to describe the susceptibility of reinforcement corrosion. Results presented in [Pease et al., 2011]
were supported by observations presented in [Win et al., 2004] showing that cracking and debonding along the reinforcement resulted in a lateral ingress of chloride ions increasing the risk of reinforcement corrosion significantly.
3.1 Introduction Chapter 3 Paper II
Photogrammetric observations of the concrete/steel interface presented in [Pease et al., 2006] showed that significant cracking and debonding was induced at the con-crete/steel interface for reinforced beams subjected to bending. Similar observations concerning reinforced concrete beams made from both plain concrete (PC) and Steel Fibre Reinforced Concrete (SFRC) were presented by Solgaard et al. [Solgaard et al., 2013].
A numerical model predicting the cracking state along the concrete/steel interface is thus required to allow for durability design of reinforced concrete structures and for obtaining better understanding of the parameters influencing the interfacial cracking state. Such a model should consider the formation of a bending crack through the con-crete cover towards the reinforcement and characterization of the cracking state at the concrete/steel interface caused by applied flexural load. The cracking state at the con-crete/steel interface consists of slip, the displacement discontinuity parallel to the re-bar surface and separation, the displacement discontinuity perpendicular to the rere-bar surface.
Previous work concerning formation of cracks at the concrete/steel interface in con-ventional reinforced concrete beams subjected to mechanical loading has mainly fo-cused on the slip behavior eg [Tammo et al., 2009] whereas the separation along the reinforcement has not been investigated to the same extent.
The present paper describes a numerical, finite element (FE) based model for the pre-diction of load-induced cracking of reinforced concrete specimens subjected to flex-ural load in a three point bending test (3 PBT). The numerical model describes the initiation and propagation of a main bending crack from the tensile surface of the con-crete towards the reinforcement and the slip and separation at the concon-crete/steel inter-face. The presented numerical model is based on the fictitious crack model described by Hillerborg et al. [Hillerborg et al., 1976] taking the fracture mechanical properties of the concrete matrix into account. The numerical model is compared to experimental results presented in [Solgaard et al., 2013]. The procedure adapted for the experi-ments described in [Solgaard et al., 2013] covering state of the art techniques such as photogrammetric measurements is briefly presented in this paper.
Chapter 3 3.2 Model Description