Rock fracture with statistical determination of fictitious crack growth

Abstract A simple method for determining the material constants of rock (e.g., fracture toughness KIC and tensile strength ft) using normal distribution with respect to average grain size gav is proposed as an alternative to the commonly used of curve fitting using rock test data. Supposing different characteristic crack a ∞ ∗ and considering different fictitious crack growth length Δafic at peak load Pmax for different relative size W/gav, the normal distribution histograms of KIC and ft with the smallest discrete coefficient are statistically obtained. The Δafic of rock specimens with different size are quantitatively studied, and the corresponding design relations of Δafic for rock specimens with different W/gav are statistically derived. The full fracture curves of rock with different W/gav are constructed using the designed relation. The simple closed-form solutions for different notched rock specimens (e.g., three-point bending and compact tension) are proposed. The experimental Pmax using normal distribution methodology with 95% reliability and simple closed-form solutions with upper and lower limits are reliably predicted. KIC, ft, and Pmax of real rock structures with W/gav = 1000 are reliably obtained using the simple closed-form solutions.