ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semicircular bend specimen is herein presented. The specimen is semicircular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied

SFA, TFA and a new thick frontier: graphical and analytical comparisons

This article compares OLS, the normal-half normal stochastic frontier approach (SFA) and the thick frontier approach (TFA) to an alternative thick frontier approach based on a mixture approach. Unlike the TFA approach, the new approach developed here uses all of the data, does not require grouping of the data into an arbitary number of size categories, does not require an arbitrarily chosen fraction (usually the lowest quartile) of lowest average cost firms upon which to base the frontier. The new thick frontier requires the estimation of only one more parameter than the SFA model, and is flexible enough to describe skewness in the data of almost any type. This article presents comparisons of the empirical relationships between these methods using a multiproduct cost function and data on US savings and loans in 1988. The new thick frontier method produces a much thinner 'thick' frontier characterizing a much greater fraction of the data than the old TFA approach.