Keywords: concrete, crack model, strong discontinuity kinematics, delayed embedded discontinuities, aggregate interlock, crack width, crack path.

The behavior and the durability of concrete structures is strongly influenced by cracking and by the width of existing cracks. Basically, one can distinguish between smeared crack models, discrete crack models and crack models, based on the strong discontinuity approach. In this contribution, adopting a proposal of [1], a rotating smeared crack model is combined with a crack model based on the strong discontinuity approach and formulated within the framework of elements with embedded discontinuities. The smeared crack model uses the Rankine criterion for crack initiation and an exponential softening law for controlling the development of normal crack opening. If the crack opening attains a prescribed threshold value then a discontinuity in the displacement field is embedded in the respective element. From that point on the crack direction is kept fixed and there are two options available for the crack path: either the discontinuities are embedded locally in the individual elements or continuity of the crack path is enforced by means of a crack tracking algorithm [2]. The interface law, describing the behavior of an embedded discontinuity, accounts for both normal and tangential crack opening. To this end the constitutive relations proposed by [3] are employed and the normal and tangential components of the displacement jump are determined by formulating a return mapping algorithm for multi-surface plasticity.

Modelling the early stages of crack evolution with a smeared crack model allows the correction of an initial misprediction of the crack direction as the crack grows. Hence, using the crack model with delayed embedded discontinuities improves the prediction of the direction of an embedded discontinuity and therefore improves the approximation of the evolution of a macroscopic crack.

The advantages of the implemented crack model are demonstrated by the numerical simulation of tests on plain concrete specimens with load histories resulting in combined normal and tangential crack openings. The experimental and numerical results show good correspondence. The application of the crack model with delayed embedded discontinuities to the numerical simulation of an anchor pull out test result in good predictions of the ultimate load, the crack paths and the crack openings. The evolution of a macroscopic crack is predicted in a realistic manner. In numerical simulations of model tests on pre-damaged bridge cantilever slabs, strengthened by different concrete overlays, the crack widths, the load carrying behavior and the stresses at the interface between the original cantilever slab and the concrete overlay are predicted in a satisfactory manner. The comparisons of the computed and observed load carrying behavior of models of plate strips strengthened by different concrete overlays demonstrate the ability of the numerical model to predict the effects of different properties of the concrete overlay on the structural behavior and, in particular, on the stress distribution at the interface.

1

M. Jirásek, T. Zimmermann, "Embedded crack model: Part II: Combination with smeared cracks", International Journal for Numerical Methods in Engineering, 50(6), 1291-1305, 2001. doi:10.1002/1097-0207(20010228)50:6<1291::AID-NME12>3.0.CO;2-Q

2

C. Feist, G. Hofstetter, "An Embedded Strong Discontinuity Model for Cracking of Plain Concrete", Computer Methods in Applied Mechanics and Engineering, 195, 7115-7138, 2006. doi:10.1016/j.cma.2005.01.028

3

J. Walraven, H. Reinhardt, "Theory and experiments on the mechanical behavior of cracks in plain and reinforced concrete subjected to shear loading", Heron, 26, 5-68, 1981.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)