Analytical Model for Predicting the UCS from P-Wave Velocity, Density, and Porosity on Saturated Limestone

Abstract

Rock mechanics and rock engineering projects require determining, among other parameters, the uniaxial compressive strength (UCS) of rock. For such a purpose, it is not uncommon to perform ultrasonic pulse laboratory tests. Many researchers have found experimental relationships between strength and P-wave velocity, but these relationships are based mainly on dry conditions and without considering any other physical or chemical characteristics of the studied rock. Specifically, for limestone, there are 11 correlations reported in the literature, eight of which are simple and the remaining three are multiple, and, among the latter, only two of them consider the saturation. In order to evaluate the combined effect of P-wave velocity, density, and porosity on the UCS of saturated limestone, simple and multiple regression analyses were carried out on the test results of 13 saturated limestone specimens to determine the parameters of both previously mentioned predictive models. The results showed that density is not correlated with strength.

Scale Effect and Correlation between Uniaxial Compressive Strength and Point Load Index for Limestone and Travertine

“…The results of d, H, n eff , ρ dry , ρ sat , and σ c have already been published by González et al [31] and Saldaña et al [32], while those for the point load index (I s ) and the N-type Schmidt hammer rebounds (R N ) are new. The results of the simple regression analysis for limestone and travertine are presented below, ending with an estimate of the scale effect of σ c for both types of rock, in which only the Weibull models are taken into account (Equations ( 26) and ( 27)).…”

“…The limestone belongs to a quarry near Antofagasta (Chile) and dates from the Lower Cretaceous era, between 66 and 100 Ma old. It is a fine limestone rock with a variable CaCO 3 content between 78% and 90% [31].…”

“…To carry out the test following the suggestions of ASTM [22] and ISRM [3], irregular fragments that meet the specific geometric conditions were selected: the height/width (D/W) ratio of the cross section was between 0.3 and 1. The calculation of the equivalent diameter (d e ) was carried out according to Equation (31), where D is the distance between the conical tips of the point-load testing machine (height of the cross section) and W the average of the maximum and minimum width of the loaded cross section.…”

“…For this correlation, I s was used instead of I s( 50) , because I s(50) depends on the scale effect through k 2 (Equation ( 27)), so it was preferred to carry out a correlation as free as possible from other statistical correlations. Likewise, σ c comes from specimens with a d of 31 mm, so it would be appropriate to experimentally correlate σ c(31) with I s( 31) , but the practical application of I s (31) does not reach the level of importance and simplicity of I s and I s (50) .…”

“…For this reason, González et al [31] and Saldaña et al [32] used P wave velocity values (v p ), measured in cylindrical specimens of 31 mm diameter, in experimental correlations determined for other diameters, thus estimating an erroneous σ c value. This led them to the generation of their own experimental predictive models.…”