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ABSTRACT Abstract. Statistical variability in rock strength can be evaluated by rapid, inexpensive ultrasonic pulse velocity measurements, an important consideration since rational probabilistic design in rock is often hampered by the cost of obtaining sufficient strength data. Experimental ultrasonic pulse velocity measurements on a set of 96 limestone specimens showed two distinct statistical populations. Both populations followed Weibull distributions, with flexural strength distributions paralleling pulse velocity distributions. Thus, experimental results suggest that strength variability may be predicted from a few rationally selected strength measurements and several ultrasonic tests. The correspondence between strength and velocity may then be used to develop an experimental transformation function, allowing the development of a statistical distribution function for strength based on the known statistics of velocity. Comparison of experimental groups with full sets of corresponding strength/ velocity data showed the technique offers a fairly accurate description of the statistics of strength.
INTRODUCTION
Variation in rock strength is accepted as a significant factor in design. However, in reality variation is often neglected, and the design process becomes deterministic because obtaining sufficient data is too costly. Alternative actions involve inexpensive index tests allowing accumulation of statistical parameters which, at best, remotely relate to the parameters of concern. This paper presents preliminary work on a methodology in which statistical variation in rock strength is deduced from non-destructive ultra- sonic testing.
CONCEPT
The research presented in this paper evaluates the hypothesis that ultrasonic testing can be used to define probability frequency distribution for strength by transforming statistical parameters for pulse velocity with an experimental function derived from minimal, but rationally selected, specimens for strength testing.
The hypothesis is grounded in Griffith's theory that strength is controlled by the occurrence and position of flaws. Small air gaps associated with flaws have been shown to influence the velocity of ultrasonic pulse transmission. Since flaws controlling strength may also control pulse transmission time, the correlation between the two may be adequate to predict variations in strength. The present work applies the statistics of classical fracture mechanics to high-frequency non- destructive evaluation, and reviews the strength of brittle materials from three perspectives. The first is a mechanistic model capable, at least, of describing the phenomena at a conceptual level. Griffith's "weakest link" theory [1,2] and subsequent modifications [3] based on energy balance concepts illustrate that strength is dependent on frequency, orientation, size, and shape of flaws. Unfortunately, the Griffith model is not used in design because flaw characterization is impractical. The second is a statistical model suitable for partial observations, whether they be of strength or of a non-destructive index such as ultrasonic pulse velocity. While studying the "weakest link" theory, Weibull [4] formulated and demonstrated a three-parameter cumulative distribution function of the form(mathematical equation) (available in full paper) which gives the non-failure probability for strength, s; su , m, and so are locations, slope, and scale parameters, respectively.
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