Estimating the long-term strength and time-to-failure of brittle rocks from laboratory testing

The long-term strength and time-to-failure of brittle rocks has become increasingly important with the increased interest in the storage of used nuclear fuel in deep geological repositories. This paper critically reviews and analyzes the currently available time-to-failure data for various brittle rock types. The current best approach on estimating time-to-failure of rock samples at the lab scale under a constant stress is using semi-log data based on the driving stress ratio and the logarithm of time. In most studies, the applied driving stress ratio is calculated based on the average strength of the rock, however, sample strength can vary up to 15%. Therefore, it is proposed that the crack-initiation stress threshold for each sample be used to calculate sample specific ultimate strengths based on relationships determined in literature. It is proposed that if a sample fails during a long-term strength test within the first 1–10 s, the applied stress for that test can be assumed equivalent to the ultimate strength. Additionally, a modified exponential function with a horizontal asymptote at the crack-initiation threshold is explored as an alternative to the typical log-linear approach. The exponential approach is non-linear in semi-log space and does not require an arbitrary cut-off for time-to-failure at the static fatigue limit of the rock as is the case of the semi-log approach. Ultimately, it is shown that although the exponential function does usually provide a better overall fit to data at relatively short times (<1,000,000 s), there is little evidence to justify the asymptotic behaviour in the longer term. Common practice has been to present the driving stress ratio as a function of time-to-failure, however, in theory these axes should be reversed as the variable of interest to the reader is the time-to-failure based on in-situ stresses. The consequence of plot orientation and subsequent error calculation are explored. The goal of this paper is to provide users and researchers with a reliable methodology to predict time-to-failure of brittle rocks both at the lab and excavation scale as well as a basis for incorporating explicit time-to-failure calculations into a continuum numerical model.