Scale effects or statistical misinterpretation: a critical assessment of uniaxial compressive strength data

Summary

Abstract

Despite significant improvements made on measurement techniques, testing capabilities, computer performance, and data acquisition systems, many rock engineering challenges still fall under the designation of “data-limited problems”. This means that, often, the number of tests is limited, compromising statistical representativeness. In contrast to other engineering disciplines, where the exact material can be selected based on the desired mechanical properties, in rock and rock mass engineering, it is the design that adapts to the material. This is why the mechanical characterisation of rocks and rock masses represents a key step for any successful design in the field of rock engineering. In addition to displaying large variability associated with its natural genesis, the mechanical behaviour of rock mass is scale- or size-dependent. Therefore, many researchers have studied the variation of rock properties with specimen size. As uniaxial compressive strength is one of the main design parameters in rock engineering, its scale effect in rock materials has been extensively studied, with several empirical correlations and size-effect laws suggested to date. However, many of these correlations appear not to be statistically sound. Specifically, a systematic reduction in the number of specimens tested with increasing physical specimen size has been detected in several datasets. This is typically due to a larger physical size making it more difficult to obtain suitable material, prepare specimens, and run the tests, leading to increased cost and duration compared to standard size specimens. This leads to varying levels of confidence depending on the physical specimen size, causing the high levels of uncertainty to permit a range of interpretations in addition to the proposed correlations. These shortcomings are analysed from a statistical viewpoint, and a critical assessment of the so-called scale effect is made for various uniaxial compressive strength datasets.