Assessing the uniaxial compressive strength and tangent Young’s modulus of basalt rock using the Leeb rebound hardness test

H. Aldeeky ^a*, O. Al Hattamleh^a, S. Rababah^b

a. Civil Engineering Department, College of Engineering, The Hashemite University, (Zarqa, Jordan)

b. Civil Engineering Department, College of Engineering, Jordan University of Science &Technology, (Irbid, Jordan)

*: aldeeky@hu.edu.jo

1. INTRODUCTIONTOP

Restoration of historic buildings and monuments is a challenging task. In most cases, destructive tests are not allowed, therefore, non-destructive tests to evaluate mechanical behavior are required. Uniaxial compressive strength (UCS) and tangent Young’s modulus (E_t) are the main input parameters of the mechanical behavior of rock, especially in ascertaining rock shear strength, rock mass rating (RMR), classification, and earth structure design such as foundation and tunneling (1–6).

Conducting a UCS test in the laboratory according to ISRM (7) and ASTM D7012 (8) requires a specified core of premium quality with certain dimensions. Sometimes a core sample is not possible, especially in foliated, soft, weathered, and fractured rock, or it is not allowed in historic buildings. In addition, the UCS test is a destructive, expensive, and time-consuming method as reported by many researchers (9–14). For these reasons, the correlation between UCS and E_t with the non-destructive or simple tests that require no sample preparation is more desired (15–17). Different empirical models have been developed to estimate the UCS and E_t depending on simple or non-destructive tests. These tests include porosity, dry density, Brazilian tensile strength test, point load, pulse velocity, slake durability index, Schmidt hammer hardness, Shore scleroscope hardness, and Brinell hardness tests (18–24).

The Schmidt hammer procedure is a non-destructive and rapid test of hardness. Therefore, many researchers have developed numerous correlations between Schmidt hammer hardness, either linear or non-linear, and UCS and E_t for diverse types of rocks (25–35).

An Equotip hardness tester also was recommended for use in geological and rock mechanical applications (36, 37). Hack et al. (36) used Equotip hardness type D to evaluate wall strength discontinuity. For this purpose, they used cubic samples with a 20 cm edge side from different rock types (granite, limestone, and sandstone). They found that the influence of layer thickness on Equotip hardness is very small compared to Schmidt hammer hardness and that Equotip is better at reflecting wall discontinuity. Also, they concluded that rock strength and surface roughness affected the Equotip hardness value more than rock density and elastic modulus. Verwaal and Mulder (38) studied the possibility of estimating UCS from the Equotip L-value test and the effect of size and roughness on Equotip L-value. Based on limestone cores with different diameters and lengths, they concluded that Equotip L-value increases with the increase in both diameter and length. On the other hand, they found the surface roughness presents no major influence on Equotip L-value. Meulenkamp and Grima (39) used neural networks to correlate UCS with Equotip L-value, porosity, density, rock texture, and rock type for sandstone, limestone, dolomite, granite, and granodiorites.

Okawa et al. (40) found that both surface roughness and curvature have no influence on Equotip L-value. Kawasaki et al. (41) conducted an Equotip hardness test on core rock samples for many rock types (sandstone, greenschist, hornfels, granite, shale), recommending a linear relationship between Equotip L-values and USC. This recommended equation depends on rock type and Equotip L-values. Aoki and Matsukura (37) found a good correlation between Equotip L-values, porosity, and USC for different rock types (tuff, sandstone, granite, gabbro, limestone). Using hybrid dynamic hardness (HDH) to investigate the effect of the test procedure on the UCS prediction on carbonate rocks, Ylimaz (42) found that the test procedure based on single impacts is more suitable for UCS prediction. Also, based on cubic samples with edge dimensions of 5, 9, 11, 13, and 15 cm, he concluded that there is no size effect on mean rebound values. Lee et al. (43) utilized Leeb rebound hardness to study the relation between Leeb rebound hardness number (RHN) and UCS for 24 shale samples; they found that UCS varies exponentially with RHN.

Siri et al. (44) presented a nonlinear relation between type D Leeb Hardness values (LRH) and UCS for sandstone rocks. They recommended that there is no size effect if the sample volume is greater than 100 cm³. Corkum et al. (45) studied the correlation between LRH test values and UCS for various rock types. Based on 213 sedimentary, 40 metamorphic, and 58 igneous rocks, they found a nonlinear power function between LRH and USC. They concluded that there is no scale effect on LRH value if the specimen’s volume is at least 90 cm³ for block or irregular block specimens, or with about L/D > 0.4 for core specimens. Kovler et al. (46) used static Schmidt rebound test and dynamic LRH test to evaluate concrete compressive strength with different water-cement ratios. They found that the LRH could be applied in predicting concrete compressive strength within a 10 % margin of error for all water-cement ratios. On the other hand, they reported that the Schmidt rebound test can be considered a semi-destructive method since they found a significant strength reduction (on average by 10.5 MPa) after applying Schmidt hammer impact on specimens, while there was no damage in the concrete sample after applying LRH test. Yilmaz and Goktan (47) used two types of non-destructive hardness tests (L-type Schmidt hammer and the Equotip 3 hardness tester with D-probe) to evaluate UCS. They used 11 rock core samples with a diameter of 54 mm for basalt, limestone, andesite, tuff, travertine, and marble rocks. They proposed a power relation between Equotip hardness, Schmidt hammer, and USC. Also, they found a good prediction accuracy with R² = 0.87 between USC and Equotip hardness and an accuracy ratio = 0.60 compared to Schmidt hammer hardness.

To study the effect of core holder type on LRH, Yilmaz and Goktan (48) used two different holders, a V-shape holder and an arch-shape holder. They found that the difference between LRH magnitudes in both holders is small and varies from one rock to another. Celik and Cobanoglu (49) predicted the physical and mechanical properties of different rock type, igneous, sedimentary, and metamorphic rock, using three types of non-destructive hardness tests. Based on their results, they concluded that Leeb hardness is more accurate in predicting mechanical and physical rock properties compared with shore scleroscope and Schmidt hammer type L.

Based on his results using Equotip (type D) hardness test to evaluate the mechanical properties of volcanic tuff building stone in Turkey, Yüksek (50) found that there is a moderately good exponential correlation between LRH with UCS and dry unit weight; also, he found a fairly linear correlation with porosity and water absorption. Desarnaud et al. (51) studied the effect of sample size, moisture content, and surface roughness on the Equotip rebound hardness of sandstone rock samples. They recorded that Equotip rebound hardness is reduced by 26 % in the saturated cases compared with the dry cases and also that sample size has a significant effect on Equotip rebound hardness compared with surface roughness. Table 1 summarizes some of the previous correlations between UCS and LRH.

LRHT was adopted in this research because it is a portable device, non-destructive, and a simple test that has a high testing rate with each test taking about 2 seconds. In addition to being low cost and suitable for hard and soft materials, it measures in any direction and can be directly converted to Rockwell, Brinell, and Vickers hardness. Few researchers have attempted to find a relationship between UCS and E_t with LRHT.

The aim of this research was to acquire a correlation using the LRHT to predict the UCS and the E_t of basalt rocks in Harrat al-Sham in eastern Jordan. The developed model might be useful in the restoration of the historic city Umm al-Jimal and in the rehabilitation of other existing structures. To achieve this target, the UCS and E_t along with LRHT of basalt samples collected from the neighboring area of Umm al-Jimal were determined in the laboratory, then the power and linear relationship between UCS and E_t with LRHT test was established respectively.

2. BASALT IN JORDAN AND STUDY AREATOP

Basalt rock covers about 11 % of Jordan’s area (54, 55). As explained in Figure 1, basalt rock covers about 11400 km², in both Harrat al-Shamin in the northeast and Harrat Irbid in the northwestern part of Jordan (57, 58). As a building stone, basalt was used in many historic and ancient cities in Jordan such as Umm Qais located to the north of Jordan, Qasr al-Mashta and Umm al-Jimal (east of Al-Mafraq), Qasr al-Hallabat and Qastal (south of Jordan), and Qasr al-Azraq (59), as presented in Figure 2. During the Roman period, basalt stones were used as road pavement. Nowadays, basalt is used as aggregates, dimension stone, curbstone, paving stone, and in industrial applications due to it is wide availability in Jordan where basalt stone constitutes about 15 % of the country’s economic rocks (60–62).

Thirty basalt boulders with dimensions of approximately 30 × 30 × 50 cm were collected from the neighboring area of the historic Umm al-Jimal village located in the northeast of Jordan; the study area is located at latitude 32° 19′ 36″ N, and longitude 36° 22′ 11″ E (Figure 3).

3. LEEB REBOUND HARDNESS TEST (LRH)TOP

In 1975, Leeb and Brandestini developed LRH, a portable nondestructive device with dynamic impact energy, for the Proceq SA Company in Switzerland to test the hardness of metals (63). The Leeb rebound hardness was calculated based on the following Equation [1]:

Where LRH: Leeb rebound hardness, Vr: impact speed, Vi: rebound speed.

LRH type D is a non-destructive test with low impact energy of about 11 N mm, about 1/200 of the rebound Schmidt hammer test type N and 1/66 type L (64). Because it is low energy, this test is suitable for soft and thin layers. LRH can be repeated on the same spot without affecting the rock sample, compared with Schmidt hammer as recommended by Aoki and Matsukura (65). Table 2 summarizes a compression between Schmidt hammer type N and LRH type D.

4. MATERIALS AND METHODSTOP

Thirty basalt boulders with dimensions of approximately 30 × 30 × 50 cm were collected from the neighboring area of Umm al-Jimal in northeastern Jordan. Selected boulder samples had no joints or fractures. From each boulder, three NX cylindrical rock core specimens with a diameter of 64.0 mm and length of 130.0 mm were prepared according to ASTM D4543 (66) and ISRM (7). After coring, samples were cut to a 2:1 ratio of length to diameter. The specimens were polished using a suitable machine to ensure a smooth surface.

The ASTM A956 (67) testing procedure for LRH is standard for steel products only; therefore, the ASTM is not applicable for rock specimens. Since there is no international standard test procedure for LRH on rock materials regarding test procedure, data evaluation, or specimen preparation, a single impact method was adopted as recommended by Daniels et al. (68) and Corkum et al. (45). Using this method, an air-dry core specimen was fixed, and the device was pressed perpendicular to the specimen surface (Figure 4). Twelve impact values were conducted on each core specimen, then the average of the remaining 10 values was recorded as the LRH value after excluding the maximum and minimum value.

UCS and E_t tests were performed according to ISRM (7) and ASTM D 7012 (69) using a computerized MTS compression machine (Matest–Italy) with a maximum compression static load of 2000 kN. A stress rate of 0.5 MPa/s was applied to reach failure within 5–10 min. The reported UCS was equal to the failure load divided by the cross-sectional area of the cylindrical specimen. The tests were conducted on the three prepared cylindrical specimens of each boulder sample and the average was reported.

E_t is a key factor in evaluating rock deformation. E_t can be determined from the stress-strain curve analysis, where E_t is the slope of the tangent of the stress-strain curve at point represent 50 % of UCS as described by Bejarbaneh et al. (70) and Malkowskia et al. (71).

A Phillips X-ray florescence (XRF) Majex Pw-242 model, available from the Water, Environment, and Arid Regions Research Center at Al al-Bayt University in Jordan, was adopted to determine the major elements analyzed using fused glass discs. Of the basalt samples. A basalt sample was dried then crushed until it reached a size of 10 mm. The sample was then ground into powder using a ball mill with a tungsten carbide barrel at 400 RPM until the sample reached a size of about 0.075 mm. Two grams of the powder sample were mixed with 8 g of lithium tetraborate then fused in platinum crucibles over gas burners at 1000 ^oC for one hour, then the melted sample poured in a mold to create glass disks. The test results were analyzed using GEOS software calibration to international geological rock standards. The contents of the major oxides of Si, Ti, Al, Fe, Mg, Mn, Ca, Na, and K were analyzed. Loss on ignition was determined first by drying the powder sample at 110 ^oC for eight hours, then weighted before and after ignition at 1000 ^oC. The sample preparation and test were conducted according to ASTM E1621 (72).

An X-ray diffractometer (XRD) type XRD-7000 (CuKα1 radiation, λ = 1.54060Å), using 99 % silicon powder and 325 mesh (0.044 mm) for calibration was available through the geology department at Hashemite University. A randomly oriented powder mount was adopted in this test. The mounts are typically X-rayed between the angles of 5 and 65 degrees 2 theta using copper K alpha radiation at a scanning rate of 2 degrees per minute. First, the sample was crushed and powdered to reach a size 0.040 mm, then 1 g of the powder was used on the sample holder. The sample preparation and test were conducted according to “A Laboratory Manual for X-Ray Powder Diffraction” (73).

A thin slab of a basalt core sample about 30 mm × 20 mm × 10 mm was cut and polished using silicon carbide powder, then stack with glass slide of 26 mm × 42 mm using a special adherent, then an automated multiplate grinder machine was used to make the slides about 0.030 mm thinner in thickness, following the procedure laid out by Grundmann and Scholz (74). A Nikon optical microscope was used particularly to identify mineral constituents of the studied basaltic rocks and to determine their mineralogical properties and textures. Modal analysis with five hundred points as recommended by ASTM E562 (75) was used to determine the mineral percentage as % of volume. The point-counting method depends on using a grid mesh with equally spaced points on the thin section slides, the grid distance, which is the distance between successive points on a grid mesh, should not exceed both grain size and texture. For the same mineral particle, the volume percentage was found by dividing the number of points by the total number of points counted.

5. RESULTS AND DISCUSSIONSTOP

5.1. Petrography analysisTOP

X-ray Fluorescence Spectrometry (XRF) was used to determine the dominant and minor oxides in rock samples (Table 3). The XRF analysis shows that the majority of oxides are based on plotting the test results on the total alkali (Na₂O + K₂O) versus SiO₂ diagram (TAS) as shown in Figures 5a and 5b. The basalt rock in this study is classified as mafic alkaline basalt rock. The basalt samples are considered non-weathered basalt since L.O.I is less than 2.64 wt. % (76).

XRD test results showed that plagioclase, pyroxene, magnetite, and olivine, are the major minerals in the studied samples (Figure 6).

Based on the microphotographs of mineral components (Figure 7) and modal analysis, plagioclase is the most abundant mineral in the studied rock samples, forming approximately 50 % of the rock volume. Plagioclase was found to be subhedral to euhedral with a tabular shape, with length ranging between 0.5–3.0 mm. Pyroxene, the second most abundant mineral, formed about 20 % of the rock volume. Pyroxene, which is mainly an augite mineral composition, had anhedral to subhedral crystals with a size range between 0.3–1.0 mm [Figure 7 (c)]. Olivine composed about 13 % of the volume of the rock sample. Olivine crystals range in size between 0.05–0.3 mm. Olivine minerals subjected to hydration and the oxidation process produced brownish iddingsite mineral [Figure 7 (d)]. Magnetite formed about 8 % of the rock volume, the size ranging from 0.03 mm to 0.5 m [Figure 7 (a)]. Basalt vascularity (voids) about 6 % by volume, some voids are filled with calcite and chloride minerals [Figure 7 (b)]. A secondary mineral-like sericite (weathered plagioclase), iddingsite (weathered olivine), chloride (weathered pyroxene) composed about 3 % by volume. Based on the Modal analysis with 500 points, the rock samples can be classified as plagioclase–pyroxene–olivine basalt, according to (79).

5.2. Mechanical propertiesTOP

The results of UCS, E_t, and LRH tests conducted on 90 core rock specimens extracted from 30 rock boulders collected from the study area are shown in Figure 8. Statistical parameters values of maximum, minimum, mean, coefficient of variation, and standard deviation of the results are shown in Table 4. As seen in Table 4, the mean UCS for the basalt rock samples used in this study was 83.82 MPa, with a range between 51.75 and 115.70 MPa. In addition, the mean of the E_t, about 50.78 GPa, varies between 31.77 and 68.39 GPa. This variation of test results might be due to the effect of non-isotropy, mineralogical composition, porosity, and grain boundaries. The current basalt rock was classified as strong to very strong rock based on the UCS results according to ISO 14689-1 (80) classification. On the other hand, the studied basalt rock was designated as medium strength (CH) to high strength (BH) according to Deere and Miller’s (81) classification system.

Stress–strain curves for the first sample are shown in Figure 9. As illustrated in Figure 9, at initial loading there is a non-linear relationship between stress and strain because, at this stage, there is a closing of preexisting micro-cracks inside the specimen due to the stress history of the rock specimen including rock coring. As the loading increases, the stress–strain curve becomes linear, and the rock behavior is more elastic. After the elastic range, the stress–strain curve becomes nonlinear and large deformation occurs until the maximum stress is reached. The LRH shows an average value of 640.9 with a range between 315 and 980; these values indicate that the basalt rock in the study area has a high hardness. The high hardness can be explained by the fact that the basalt rock is composed of plagioclase, pyroxene, and olivine minerals that have a hardness on Mohs’ scale of 6, 6.6, and 6.5, respectively. The variation is due to micro-crack and small voids.

5.3. Regression analysisTOP

The prediction of UCS and E_t using simple regression from non-destructive simple tests are widely used by many researchers (82-84). In this research, simple regression equations such as linear, exponential, logarithm, and power were adapted to examine the relationship between UCS, E_t, and LRH test values of basalt rock. Both UCS and E_t increased with the increase LRH value (Figure 10 and 11).

Moreover, to evaluate the predicted simple regression equations (linear, power, logarithm, and polynomial) and to select the best equation to estimate both UCS and E_t based on LRH value, the evaluation was conducted based on statistical performance indices, coefficient of determination (R²), and root mean square error (RMSE), which has been adapted by many researchers (85, 86). A strong correlation model can be considered if R² equals 1.0 and RMSE are close to zero (29, 33). The equations of these indices are listed below as Equations [2] and [3], and the results for each regression model are presented in Table 5. The power equation is the best equation to predict UCS, while the linear is best to predict E_t.

Where ym: measured value, yp: predicted value, ya: an average of the measured value, n: total number of data.

To check the validity of these correlations, UCS and E_t calculated from the adapted correlations were presented with the measured values (Figures 12 and 13). It can be concluded that these correlations are highly reliable in estimating both the UCS and the E_t since the majority scattered around the quality line (y = x) lay within the range ±20 %.

On the other hand, to check the validity of the power correlation proposed in this study to predict USC value for different rock types, the predicted values compared with measured values collected from previous literature (Figure 14). It can be concluded that for very low to low strength (class E and D) the predicted values are overestimated by the proposed correlations; for medium-strength (class C), the predicted value lays within ± 20 % of the measured values; while for high and very high strength (class A and B) the predicted values are underestimated.

However, the proposed power correlation to predict UCS in this study was compared with other researchers’ correlations presented in Table 1. The majority of the previous relationship is power relations which agree with this study. However, the previous studies included different rock types with a wide range of strength varied between very weak to very strong rock, while in the current study the rock samples were collected from the same source with little variation in UCS (Figure 15).

6. CONCLUSIONSTOP

This research examined the correlation between LRH and the mechanical engineering properties for both UCS and E_t for basalt rock. In this investigation, LRH value, UCS and E_t were conducted on core specimens extracted from 30 different boulders collected from the neighboring area of Umm al-Jimal city. Linear regression was performed to correlate LRH value with both the UCS and the E_t of basalt rock. From the analysis conducted, the following conclusions can be drawn:

ACKNOWLEDGEMENTTOP

The authors would like to thank Mr. Tareq Albeshety from the geology department at Al Hashemite University for his help in conducting XRD and thin section. Our great thanks to Prof. Ahmad al-Malabeh from the geology department at Al Hashemite University for reviewing and revising the petrography analysis part; his help is really appreciated.

REFERENCESTOP