Seismic strength evaluation of reinforced concrete shear walls with cracks, using the notion of fractal geometry

Abstract

Shear walls play an important role to the seismic strength of modern seismic resistant structures. They are designed so that they have significant bending and shear strengths and ductility. However, existing structures have lightly reinforced shear walls. In most cases, especially under cycling loading, shear cracks appear reducing the shear capacity of the wall. Here, a typical shear wall of an existing structure is examined in which it is assumed that a crack has been formed. For the modeling of the geometry of the crack a new approach is applied, using the notion of fractal geometry. The aim of the paper is the estimation of the postcracking strength of the wall, taking into account the geometry of the cracks and the mixed friction-plastification mechanisms that develop in the vicinity of the crack. Due to the significance of the crack geometry a multi-resolution analysis is performed. The materials (steel and concrete) are assumed to have elastic-plastic behaviour. For concrete both cracking and crushing are taken into account in an accurate manner. On the interface unilateral contact and friction conditions are assumed to hold. For every structure resulting for each resolution of the interface, a classical Euclidean problem is solved. The obtained results lead to interesting conclusions concerning the post-cracking strength of lightly reinforced shear walls.