Analytical Solution for Determining Fracture Attenuation

This work is devoted to the analytical solution of the damping of the fracture of the hydraulic fracturing. A solution is obtained for changing the dimensionless conductivity of the crack due to a decrease in the conductivity of the proppant and its removal from the crack. The considered crack geometry corresponds to the Perkins-Kern analytical model, which allows us to take into account the change in the crack width depending on its length. To calculate the proppant conductivity, laboratory studies were used, the data of which were extrapolated in order to predict the destruction of proppant balls during the operation of a well with a fractured hydraulic fracturing.

A Numerical Study on Chloride Diffusion in Cracked Concrete

The cracks in concrete are a fast transport path for chlorides and influence the service life of concrete structures in chloride environments. This study aimed to reveal the effect of crack geometry on chloride diffusion in cracked concrete. The chloride diffusion process in cracked concrete was simulated with the finite difference method by solving Fick’s law. The results showed that the apparent chloride diffusivity was lower in more tortuous cracks, and the cracks with more narrow points also showed lower apparent chloride diffusivity. For tortuous cracks, a higher crack width meant relatively more straight cracks, and consequently, higher apparent chloride diffusivity, while a lower crack width resulted in more tortuous cracks and lower apparent chloride diffusivity. The crack depth showed a more significant influence on the chloride penetration depth in cracked concrete than crack geometry did. Compared with rectangular and V-shaped cracks, the chloride diffusion process in cracked concrete with a tortuous crack was slower at the early immersion age. At the same crack depth, the crack geometry showed a marginal influence on the chloride penetration depth in cracked concrete during long-term immersion.

Quantification of the Complex Crack Geometry Effect On Fracture Resistance Using Strain Based FE Damage Analysis

This paper examines the effect of complex crack geometry on the J-resistance curves obtained by strain-based ductile tearing simulation of complex cracked tension (CC(T)) specimens. The damage model is determined by analyzing the results of a smooth bar tensile test and a C(T) specimen toughness test on an SA508 Gr.1a low-alloy steel at 316 ?. The validity of the damage model and simulation method is checked by comparing the fracture test data for two CC(T) specimen tests. To investigate the effect of the complex crack geometry on the crack growth profiles and J-resistance curves, two geometric parameters (namely, the through-wall crack length and the surface crack depth) are systematically varied. It is found that the J-resistance curves for the CC(T) specimens with various through-wall crack lengths and surface crack depths are consistently lower than the corresponding 1T C(T) J-resistance curves. The effect of the through-wall crack length upon the J-resistance curve is found to be less significant than that of the surface crack depth. Moreover, the J-resistance curve decreases continuously with increasing surface crack depth.