Research on Fractal Crack Propagation Mechanism of Hydraulic Tunnel Concrete Lining

Based on the fractal geometry theory, the bending form of crack expansion on concrete lining of hydraulic tunnel is described, according to the model of fractal fracture, stress intensity factor of concrete lining crack of hydraulic tunnel is established. Combined with the fracture mechanics theory, the relationship of stress intensity factor on l concrete lining crack is obtained under the hypothesis of crack linear expansion and crack irregular expansion, while the stress intensity factor of latter is less than the former, which is more close to the actual circumstance and more reasonable, whose fractal dimension is obviously larger than the former. The conclusion can provide reference for the engineering design.

Study of the Residual Strength of an RC Shear Wall with Fractal Crack Taking into Account Interlocking Interface Phenomena

In the present paper, the postcracking strength of an RC shear wall element which follows the construction practices applied in Greece during the 70s is examined by taking into account the complex geometry of the crack of the wall and the mixed friction-plastification mechanisms that develop in the vicinity of the crack. Due to the significance of the crack geometry, a multiresolution analysis based on fractal geometry is performed, taking into account the size of the aggregates of concrete. 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 interfaces of the crack, unilateral contact and friction conditions are assumed to hold. For every structure corresponding to each resolution of the interface, a classical Euclidean problem is solved. The obtained results lead to interesting conclusions concerning the influence of the simulation of the geometry of the fractal crack on the mechanical interlock between the two faces of the crack, a factor which seems to be very important to the postcracking strength of the lightly reinforced shear wall studied here.

FRACTAL CRACK PATTERNS IN LAPONITE FILMS AND THEIR SCALING BEHAVIOR

We study crack patterns in laponite films of different thickness. The patterns show a self-similarity under coarse-graining, the fractal dimension determined by box-counting has a value around 1.66, independent of film thickness. The cracks on layers of different thickness show a remarkable scaling bahavior. We have measured the cumulative area covered by the cracks versus minimum crack-width resolved. Curves representing crack area for different thickness collapse onto a single curve, when the crack widths are scaled by the film thickness.

GENERALIZATION OF BARENBLATT'S COHESIVE FRACTURE THEORY FOR FRACTAL CRACKS

In this paper, we generalize Barenblatt's cohesive fracture theory for fractal cracks. We discuss the difficulties of generalizing the concept of traction on a fractal surface. Borodich's modification of Griffith's theory for fractal cracks is reviewed. Irwin's driving force is generalized for fractal cracks and a fractal driving force (Gf) is defined. It is shown that to generalize Barenblatt's theory for fractal cracks it is necessary to introduce a new quantity, D-fractal cohesive pseudo-stress. This new quantity is cohesive force per unit of a fractal measure. Fractal modulus of cohesion is seen to be a function of both the material and the fractal dimension of the crack. Equivalence of fractal Barenblatt's and Griffith's theories is discussed. It is seen that the order of stress singularity at the tip of a fractal crack cannot be obtained using modified Barenblatt's theory because this theory is a local theory and assumes the order of stress singularity a priori.

On Fractal Cracks in Micropolar Elastic Solids

In this paper we review the fracture mechanics of smooth cracks in micropolar (Cosserat) elastic solids. Griffith’s fracture theory is generalized for cracks in micropolar solids and shown to have two possible forms. The effect of fractality of fracture surfaces on the powers of stress and couple-stress singularity is studied. We obtain the orders of stress and couple-stress singularities at the tip of a fractal crack in a micropolar solid using dimensional analysis and an asymptotic method that we call “method of crack-effect zone.” It is shown that orders of stress and couple-stress singularities are equal to the order of stress singularity at the tip of the same fractal crack in a classical solid.

EXAMPLES OF FRACTALS IN SOIL MECHANICS

Models will be presented for fractal structures appearing naturally in soils. On the one hand, we discuss the opening of brittle media via hydraulic fracturing at constant pressure using a square lattice beam model with disorder. We consider the case in which only beams under tension can break, and discuss under which conditions the resulting cracks may develop fractal patterns. The stress field of the fractal cracks is visualized by photoelastic fringes. Then we present a modelization for a fluid penetrating under a pressure gradient into a fractal crack which it is itself opening. To do this, we investigate invasion percolation fingers in a quenched medium in which the randomness has a gradient corresponding to the density of microcracks that arise in a self-organized way around a large crack.