Estimation of uniaxial compressive and indirect tensile strengths of intact rock from Schmidt hammer rebound number

1 Introduction

In contexts involving rock engineering, rock failure is a significant issue. However, rock failure modes are complicated and challenging to measure or anticipate. Therefore, a thorough investigation of rock failure modes at the laboratory scale has the potential to be significant since it aids in determining if the support system is adequate given the nature of an engineering project.

The strength of rock must be studied to assess the stability of underground apertures, such as caverns, for hydraulic power plants and nuclear waste disposal installed underground. This is because the rock mass surrounding an underground opening is commonly humid due to the presence of groundwater. Stress corrosion should be included when determining the long-term strength of the rock in water or in a water vapor environment since water is known to be the most efficient agent for inducing stress corrosion of rock [1].

The classification of the rocks used, as well as their description and hardness measurement, are crucial in the construction industry. From this perspective, one of the most crucial factors in determining a rock's qualities is its hardness.

The key question here is “would the combination of inherent stresses and stresses induced by the construction and operation of building structural lead to failure?” in structural, civil, and mining activities that utilize rocks as either a foundation of structure or a construction material. To answer this issue, you must first understand how the stresses of rock specimens interact, as well as what the rock mass specs and quality are. You must also understand the most important mechanical and engineering features of intact rock and rock mass. Some UCS and Brazilian test (BT) evaluations necessitate the production and coring of a number of standard specimens as well as the use of costly laboratory equipment.

A number of recent studies have looked into the relationship between UCS and the mechanical and physical properties of rock tests, such as R and the point load test index “I _s” (50). The indirect BTS has become one of the most prominent tests in geotechnical engineering for estimating rock quality parameters for complete rock specimens.

When working with rock masses, obtaining core segments that are the right size for unconfined compressive and Brazilian tensile strength (BTS) testing can be problematic. As a result, engineers must rely on simple equipment like the Schmidt hammer to determine specimen strength for design purposes.

Dinçer et al. [2] examined the relationship between UCS, elastic modulus (E), and R by conducting laboratory tests on a variety of volcanic rocks (andesites, basalts, and tuffs) from the Bodrum Peninsula. There was a statistical analysis, correlation, and regression of the parameters based on the results of the tests.

Farah [3] studied the UCS and other physical parameters of aged Ocala limestone in depth to find a specific link. As a result, the correlation between UCS and the indirect BTS was better than the correlation between UCS and the corrected point load test index, I _S (50).

Saptono et al. [4] used the Schmidt hammer to determine the UCS of sedimentary rocks in the Warukin Formation at Tutupan open pit coal, South Kalimantan, Indonesia, by combining the Schmidt hammer rebound (R) with laboratory UCS test results, resulting in a high-reliability empirical equation.

Ramil et al. [5] conducted a series of laboratory tests on 20 limestone core specimens, including UCS, dry density, and Schmidt hammer. The results reveal a strong agreement between the results of experimental investigations and earlier and previous publications. The reliability of one of the most extensively used correlations in Malaysia (Miller's correlation) for UCS prediction utilizing a rebound hammer is studied, and a novel correlation with a high accuracy level for UCS prediction of limestone rocks is presented.

Jahangar and Ahmad [6] tested sandstone, clay, clay stones, calcites, and limestone samples gathered from four different Iraqi locations (Erbil, Sulaimaniya, Samawa, and Najaf). According to this research, a novel relationship was constructed to predict UCS using the point-corrected load index, I _S (50).

In their research, Basu et al. [7] compared the strengths of granite, schist, and sandstone by analyzing their failure modes under uniaxial compression, Brazilian, and plate loading test. As the UCS of granite and sandstone specimens rises, the primary failure mode shifts from axial splitting to shearing along a single plane to multiple fracturing. Low-UCS schist specimens break along foliations, while high-UCS schist specimens do not. Over the full range of BTS determinations, granite and sandstone failed primarily after central or central multiple-type fracturing, while schist failed primarily by layer activation combined with either central or non-central fractures.

Lin et al. [8] used the discrete element method to study the mechanical characteristics and the effects of different joint parameters on the strength and failure modes of a jointed rock mass with double circular holes subjected to uniaxial loading. The research confirmed that the mechanical behavior of the rock mass is compromised by the presence of joints.

The effects of height-to-width ratio and width-to-thickness ratio on the mechanical characteristics of granite, marble, and sandstone rectangular prism specimens and isolated pillars under uniaxial compressive stress were investigated by Du et al. [9]. It was discovered that thin or high rocks have a lower UCS, and that shape ratio has a significant impact on a rock's bearing ability. Additionally, it was determined that decreasing the height/width ratio and increasing the width/thickness ratio both have a positive impact on the strength of rocks.

So far, for Iraqi rocks, few studies have correlated Schmidt hammer rebound (R) with both unconfined compressive strength (UCS) and Brazilian tensile strength (BTS). In this study, the objective is to develop a relationship between the rebound number of Schmidt hammer surface hardness (rebound number) and both the BTS and the unconfined compressive strength (UCS) of different types of northern Iraqi rocks. This is due to the fact that testing the UCS of shale is laborious and expensive. Therefore, it is necessary to have an alternative way of measuring strength. It is thought that UCS can be estimated using the BTS and the Schmidt hammer surface hardness. There is no need for sample preparation, and the results are reliable if the variability introduced by the operator and the laboratory is kept to a minimum. In addition, it will be demonstrated that many of the same physical characteristics govern these tests as govern UCS. Using actual values for (UCS), (BT), and Schmidt hammer hardness, one can establish the necessary relationship.

2 Experimental work

This part discusses the location and geology of the study area from which the rock specimens were gotten, how they were prepared, and the number of specimens gotten. Moreover, a description of the tests performed, and the physical, destructive, and non-destructive tests are presented.

2.1 Geology of the study area

Three samples were taken from three different geological formations in the Kurdistan region of northern Iraq: the carbonate and shale rock formation in zone 1 (Zawita), the carbonate rock formation in zone 2 (Baadra), and the calcite rock formation in zone 3. (Domeez). The geological map of the study region and the areas from which rock samples were gathered are shown in Figure 1. The rock mass samples gathered from various places are shown in Figures 2 and 3.

Figure 1

Location and geological map of the study area.

Figure 2

Images for rock zone samples, Zawita, Baadra, and Domeez northern Iraq.

Figure 3

Rock samples taken from the three sites, Zawita Limestone, Baadra Claystone, and Domeez Sandstone.

2.2 Sample preparation

According to the type of test, block rock specimens were cored and sliced into cylindrical and disc samples with varying height-to-diameter ratios. The cylindrical standard samples that were developed according to (American Society for Testing and Materials (ASTM) D4543) [10] are required for the UCS test samples as shown in Figure 4. Brazilian test samples are disc samples manufactured in accordance with (ASTM D3967-95a) [11], as shown in Figure 5. The rock samples utilized in the studies are listed in Table 1. Full dry samples were utilized in this investigation, and before testing, the rock specimens were dried in the laboratory in an oven at (110°C) for 24 h according to the manufacturer's instructions (ASTM D2216-98) [12].

Figure 4

Unconfined compression test specimens.

Figure 5

Brazilian test specimens.

Table 1

Dimensions of specimens of rock

Rock type (claystone, limestone, and sandstone)
Test type	Average diameter (mm)		Average t, L (mm)		Average dry density (g/cm3)
	BT	UCS	BT	UCS
Claystone	54	53.5	24	100.4	2.259
Limestone	53.5	54	22.5	99.5	2.583
Sandstone	52.5	53.5	23.5	100.3	2.107

2.3 Schmidt hammer test

The Schmidt hammer is a simple, affordable device that determines the rebound hardness (R) of an unbroken rock specimen in the laboratory or a rock mass in situ. For rocks of at least moderate strength, the test is generally non-destructive; therefore, the same specimen can be used for several tests, Figure 6 [13].

Figure 6

Schmidt hammer test.

To establish the rebound number (R), the first test was done on all rock core specimens using an L-type Schmidt hammer with a Strike hammer stroke of 75.0 mm and an impact energy of 0.735 Nm (ASTM D5873-14) [14]. At various positions on each specimen's surface, twenty rebound number readings were recorded. About 50% of the highest measurements were used to compute the average R-value.

2.4 Unconfined compression test

The most crucial mechanical characteristic of rocks is strength, which is often assessed using the UCS test. Numerous samples are needed for UCS testing, which must be carefully collected and delivered to the lab to be prepared according to standards.

In this investigation, 20 UCS tests were carried out for each type of rock, with the testing being carried out on a (BESMAK) dual capacity compressive test machine shown in Figure 7. This machine has a maximum capacity of 3,000 kN and can apply compressive axial load at a constant strain rate to the specimen. The specimens were prepared, and the test was performed according to ASTM standard procedures (ASTM D 7012-e1) [15]. All specimens have the same L/D (length to diameter) ratio of 2.0, and they were loaded to failure at a consistent rate of 0.5 MPa/s. The applied load is deemed the failure load when a substantial displacement is seen due to a minor increase in the applied load (P _f).

Figure 7

BESMAK dual 3,000 kN capacity dual machine.

2.5 Brazilian test

The sample preparation and test procedure in this investigation followed the applicable ASTM standard practice (ASTM D 3967-95a) [11], with 20 tests done for each type of rock. All specimens had a t/D (thickness to diameter) ratio of 0.5. As indicated in Figures 8 and 9, the test was done using Brazilian test equipment that was put on two steel jaws and then loaded till failure. These two jaws ensure that the force is applied tangentially to the disc-shaped specimen, causing a tensile fracture along the specimen’s vertical width and diameter. The maximum value of the load is digitally shown via the load indicator. Eq. (1) was used to calculate the BTS [16]:

(1) BTS = 2 F π Dt ,

where BTS is Brazilian tensile strength (MPa), F is failure load (N), D is specimen diameter (mm), and t is specimen thickness (mm).

Figure 8

Brazilian test jaws.

Figure 9

Brazilian test apparatus.

3 Experimental results

A total of 120 laboratory tests of unconfined compressive and Brazilian tests were carried out on the specimens of the three rock types. Table 2 shows the experimental test results of the UCS and BTS values for all tested rock samples.

In broad, the fundamental failure mode of rocks is shear fracture under triaxial compression, which refers to a cluster of macrocracks oriented in the direction of loading. In addition, the extension fracture under uniaxial tension refers to a clean separation of specimen halves [17].

The failure load findings for the three types of rocks were plotted against the rebound number based on experimental results. The UCS values related to the BTS are shown in Figures 10–12. Using linear fit equations with R ² values between (0.910) and (0.912), the relationships indicate a strong association of 0.917.

Figure 10

Relationship between the UCS and R for Zawita limestone.

Figure 11

Relationship between the UCS and R for Baadra claystone.

Figure 12

Relationship between the UCS and R for Domeez sandstone.

Figures 13–15 demonstrate BTS values that are correlated with the BTS; utilizing linear fit equations with R ² values between 0.8 and 0.9, the relationships show good association (0.85).

Figure 13

Relationship between the BTS and R for Zawita limestone.

Figure 14

Relationship between the BTS and R for Baadra claystone.

Figure 15

Relationship between the BTS and R for Domeez sandstone.

The outcomes of the tests were subjected to statistical analysis. The Schmidt hammer rebound number (R), UCS, and BTS test findings are shown in Tables 3–5 with their average values, standard deviations, coefficients of variation, and 95% confidence intervals.

The equations created in this study may be helpful in the early stages of design, but they should only be used for the designated rock types. The strength and deformability of specific rock types can be strongly impacted by the geological history that rocks have undergone in a given geographic area (mainly sedimentary rocks like limestones and sandstones but also some metamorphic rocks, like marble).

The present results are in agreement with those of Karaman and Kesimal [18], who determined that the rebound index is the most accurate predictor of UCS based on the percentage error analysis because it best represents rock hardness as a whole.

4 Conclusions

In this study, the objective is to develop a relationship between the rebound number of Schmidt hammer surface hardness (rebound number) and both the Brazilian tensile strength (BTS) and the unconfined compressive strength (UCS) of different types of northern Iraqi rocks. The required relationship should be based on measured values of the UCS, BT and Schmidt hammer hardness. From 120 tests carried out on samples taken from three sites in northern Iraq, including UCS, indirect BTS, and rebound Schmidt hammer test, the following conclusions were obtained:

1. New correlations with high reliability were introduced correlated between both the UCS and BTS with R.

2. The reliability of the calculated correlation coefficients was tested by conducting correlation analyses. The correlation analysis revealed significant relationships between the variables in this investigation. A coefficient of determination (R ²) >0.90 indicates that the correlation between R and UCS is more reliable than its correlation with BTS.

3. The results achieved by only using the Schmidt hammer test for predicting the mechanical properties of rocks are less accurate than when a complete set of laboratory studies is undertaken; nevertheless, it is supposed that all these empirical equations will aid geotechnical engineers in making effective decisions at the initial stages of site investigation.

Nomenclature

BTS

Brazilian tensile strength, MPa

D

Diameter of the specimen, mm

F

Failure load, N

I _s

Point load strength index, MPa

I _s(50)

Corrected point load strength index, MPa

L

Length of the specimen, mm

R ²

Root square value

T

Thickness of Brazilian test specimen, mm

UCS

Unconfined compressive strength, MPa

R

Rebound number of Schmidt hammer