Correlation of granite rock properties with longitudinal wave velocity in rock bolt

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Abstract

Physico-mechanical rock properties are typically investigated via laboratory tests using core samples. However, sample coring is time consuming and expensive. The longitudinal wave velocity in rock bolts embedded in a rock mass depends on the surrounding rock properties. Hence, the longitudinal wave velocity in rock bolts can be utilized to predict rock properties. This study presents the relationship between granite rock properties and longitudinal wave velocity (vL) in rock bolts to predict rock properties using the longitudinal wave velocity in a rock bolt. Chemical (saline solution) and mechanical (slake durability test) weathering processes are employed to diversify the properties of the rock specimens. Laboratory tests are conducted on rock specimens to measure the physico-mechanical rock properties, including the velocities (vp and vs) associated with constrained and shear moduli, density (ρ), Young's modulus (E), Poisson's ratio (μ), and porosity (η), compressive strength (fc), and slake durability index (SDI). The measured rock properties are used in the rock mass model, and variations in vL in the rock bolt with different properties are investigated via numerical simulations. Results show that vp, vs, ρ, E, and fc are correlated significantly with vL (R2 > 0.9), whereas η and SDI are moderately correlated with vL (R2 > 0.7). However, a meaningful correlation between μ and vL is not obtained. The root mean square and mean absolute percentage errors are estimated to validate the correlation equations, and errors are not considered. Results of the t-test show that the calculated t-value is higher than the critical t-value, and the p-value is smaller than the significance level of 0.05, indicating that the correlation coefficient is significant. This study shows that the velocity of longitudinal waves in a rock bolt can be a useful indicator for predicting in-situ rock properties.

Introduction

The physico-mechanical properties of rock mass are fundamental factors in the design and construction of mining, tunneling, and stabilizing slopes. The physico-mechanical properties of rocks are typically investigated using rock core samples via laboratory tests. Ultrasonic testing is one of the most widely used nondestructive testing methods to indirectly infer the physico-mechanical properties of a rock by measuring the elastic wave velocity. Therefore, ultrasonic transducers are used to generate and detect elastic waves at a certain frequency, and then the velocity of elastic waves in rock specimens is obtained. Based on the dependence of elastic waves on density and the elastic properties, the elastic wave velocity in rock has been correlated with porosity, density, elastic modulus, uniaxial compressive strength, and weathering degree.1, 2, 3, 4, 5, 6 However, it is difficult to accurately represent the in-situ condition of rock masses based on laboratory tests owing to the stress relief and vibrations generated by extraction and transportation, respectively. Hence, an appropriate method for predicting the physico-mechanical properties of in-situ rock using data measured from field tests is necessitated. Herein, the propagation velocity of longitudinal waves in a rock bolt is proposed as an alternative indicator for predicting in-situ rock properties.

Rock bolts are widely used to reinforce rock masses and improve rock stability in rock engineering or geotechnical engineering, such as mining, tunneling, and excavation. In general, the length of a rock bolt is significantly greater than its diameter. In this regard, longitudinal waves propagate in the rock bolt with both longitudinal and radial motions, and the relevant elastic modulus is the Young's modulus. This longitudinal wave is similarly known as a bar or rod wave. The propagation of longitudinal waves in terms of the Young's modulus is significantly affected by the surrounding materials of the medium. It is well known that the propagation characteristics of longitudinal waves in rock bolts depend on the surrounding rock properties.7, 8, 9 Hence, the prediction of rock properties based on longitudinal waves in rock bolts may be a feasible concept.

The objective of this study was to investigate the feasibility of using longitudinal waves in a rock bolt to predict the properties of surrounding rock masses, as well as to correlate the physico-mechanical properties of a granitic rock with the longitudinal wave velocity in a rock bolt. Laboratory tests were performed on granitic rock specimens acquired from eight different sites in Icheon, Korea, and their physico-mechanical properties were diversified through artificial weathering processes. The measured rock properties were employed in numerical simulations as properties of the rock mass surrounding a rock bolt and correlated with the velocity of the simulated longitudinal waves in the rock bolt. Correlation equations were proposed via regression analyses and validated by calculating the root mean square error (RMSE) and mean absolute percentage error (MAPE) between the estimated and measured values. A t-test was conducted to evaluate the statistical significance of the correlation coefficient. In the remainder of this paper, the theoretical background, materials and methods, results and discussion, and summary and conclusions are presented.

Section snippets

Longitudinal wave velocity in rod

For a longitudinal wave propagation in an elastic continuum whose length is much greater than its cross-sectional dimension (e.g., rods, bars, beams, columns, and pipes), the relevant material stiffness can be used to approximate the Young's modulus (E) instead of the constrained modulus (M). This approximation is excellent if the wavelength (λ) of the longitudinal waves is much greater than the cross-sectional dimension because the propagation of longitudinal waves tends to result in lateral

Rock specimen and sampling

The geology of Icheon in Korea comprises primarily igneous rocks and partially sedimentary rocks, as shown in Fig. 1. Jurassic igneous rocks are distributed throughout most parts of the Icheon and are dominated by biotite granites. Precambrian igneous rocks are widely distributed along the northwestern edge of Incheon and are characterized by biotite gneiss. Quaternary alluvium, which is composed of sedimentary rocks, encompasses certain regions of Icheon. Igneous rock samples without any

Physico-mechanical properties of rock specimens

In this study, rock samples were acquired from four boreholes at sites A–H. Hence, the number of specimens used in the laboratory experiments was 32. However, the properties of the specimens were diversified over 12 stages of the artificial weathering process, resulting in 384 specimens with different properties. The measured physico-mechanical properties of the rock specimens, including the velocities (vp and vs), density (ρ), Young's modulus (E), Poisson's ratio (μ), porosity (η), compressive

Summary and conclusions

This study was conducted to investigate the feasibility of using the vL in rock bolts to predict the physico-mechanical properties of in-situ granitic rocks without performing additional laboratory tests. Granite rocks were acquired from Icheon, Korea, and artificial weathering processes were conducted to obtain rock specimens with different properties. Physico-mechanical rock properties including the elastic wave velocities related to constrained and shear moduli (i.e., vp and vs,

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (NRF-2021R1C1C2005687).

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