Predicting the Building Stone Cutting Rate Based on Rock Properties and Device Pullback Amperage in Quarries Using M5P Model Tree

Abstract

One of the key parameters that affect the selection of equipment and the cost estimation of dimension stone quarries is the rock cutting rate or production rate. In this study, the M5P tree algorithm is used to determine the relationship between the hard rock sawability and its factors especially the physical and mechanical characteristics of rock. To achieve the research goal, a variety of eleven types of hard dimension stone were selected and nine major physical and mechanical characteristics of rock including uniaxial compressive strength, Young’s modulus, Brazilian tensile strength, equivalent quarts content, grain size, Mohs hardness, point load test, density and P-wave velocity of these samples were evaluated. The cutting rate of diamond wire for all of the Workpiece was measured at different pullback amperage with a fully instrumented cutting platform in laboratory. All operational parameters of cutting process were entirely controlled. Thus, a database containing 99 datasets was provided and it has been used for analyses. The obtained results from the pruned and unpruned tree models showed a significant relationship between cutting rate and its factors. In the end, the results of M5P tree method were compared with statistical analyses (i.e., linear and nonlinear regression). The coefficient of determination be equal with 0.92, 0.86, 0.77 and 0.63 for unpruned tree, pruned tree, linear and nonlinear regression method respectively. This comparison showed that the both method of M5P tree technique have a better performance in predicting the cutting rate rather than the statistical regression methods.

Appendix: Description of P-Wave Velocity and Grain Size

1.1 P-Wave Velocity

The Samples with approximate dimensions of 70 mm were provided from the block samples in the laboratory (Fig. 10). In the measurements, the PUNDIT Lab + and two transducers (a transmitter and a receiver) having a frequency of 54 kHz were used, described by ISRM (1981). The sample ends were cut parallel to each other and perpendicular to the long axis and smoothened. The two-transducer units were fixed to the smooth faces of the sample by applying grease, which ensured a tight contact between the transducers and the sample faces. The time needed for a longitudinal impulse was recorded in microseconds. The distance between the emitter and receiver was measured and recorded. The velocity was calculated from the ratio of travel distance to travel time of the P-wave through the sample. At least five measurements were taken from each rock type and average values were calculated (Vasconcelos et al. 2007).

Fig. 10

P-wave velocity test

1.2 Grain Size

The mineralogical composition and mean grain size of the samples were determined from thin sections using polarizing microscope and TS view software (Fig. 11).

Fig. 11

Tine sections study for evaluation of samples grain size

Diameter equivalent or grain size (Gs) in each particle is obtained by Eq. (11) (Ghaysari et al. 2012). According to Eq. (12), the grain size for any sample is the average of grains size in tine sections.

$$D_{equi} = \sqrt {\frac{{4A_{i} }}{\pi }}$$

(11)

$$Gs = \frac{{\mathop \sum \nolimits_{i = 1}^{N} \mathop \sum \nolimits_{k = 1}^{n} D_{k} }}{N \times n}$$

(12)

where D_equi is diameter equivalent in term of mm, A_i represents area of grain (mm²), N is the number of tine sections, n represents the number of grain in any thin section and D is the same Dequi.