An Experimental Approach to Evaluate the Role of Rock Failure Modes in Mechanical Characterization of Metabasalts

A detailed understanding on rock failure modes testifies the competence of support designs for engineering work. Studying such failure modes using physical models of rock specimens under laboratory conditions can be time efficient, informative and economically viable. In this study, the mechanical behavior of massive metabasalts were characterized with reference to rock failure modes through index tests such as point load and Brazilian tests. Rock failure modes under point load test are categorized as (1) single plane, (2) triple junction, (3) twisted and (4) single plane (inclined) failure modes. Twisted and triple junction failure modes are observed in the specimens with higher point load strength values (> 6 MPa). A total of five types of rock failure modes were observed in metabasalts under Brazilian testing conditions namely (1) central multiple, (2) central, (3) non-central, (4) central multiple + layer activation and (5) conjugate failure modes. Central multiple failure mode is found to be the most common failure mode in metabasalts due to their massive nature. Failure modes under Brazilian tests are observed within a range of 8 to 12 MPa. Among all other observed rock failure modes, single plane (inclined) and conjugate failure modes under point load and Brazilian tests respectively are introduced in this study. It is evident that rock failure modes controlling the strength of rocks should be considered as an important aspect for mechanical characterization of rock materials.

most important factors which influence the strength and deformation behaviour of intact rocks (Tsidzi 1990;Saroglou 2004;Khanlari et al. 2014). Additionally, the evaluation of rock failure modes of virtually isotropic rocks (e.g., metabasalt) can provide information regarding their mechanical behaviour within an external stress field along with their material strength and inherent fabric (Szwedzicki 2007;Vishnu et al. 2010Vishnu et al. , 2018. The crystalline rocks preserve a range of micro-flaws leading to crack initiation, propagation, coalescence and subsequent failure (Scholz 1968;Martin and Chandler 1994;Eberhardt et al. 1998;Li et al. 2003;Jaeger et al. 2007). The deformation of micro-flaws has significant effect on the strength and failure behaviour of rock masses (Yang et al. 2008; Janeiro and Einstein 2010; Lee and Jeon 2011;Bahaaddini et al. 2013;Zhou et al. 2014;Du et al. 2020). Therefore, a comprehensive study on such aspects is important to analyse the geometric arrangements of particles and micro-flaws (Akessan et al. 2004;Hudyma et al. 2004;Basu 2006;Szwedzicki 2007;Basu et al. 2009). Although there are no such theoretical models that can predict the failure modes, a number of physical models have been frequently used to obtain insightful information on the failure modes of crystalline rocks. Such physical models are also used for examining the behaviour of inherent micro-flaws under laboratory conditions (Jaeger and Cook 1979;Bieniawski 1984;Santarelli and Brown 1989;Hudyma et al. 2004;Klein et al. 2001). With this notion, Basu et al. (2013) documented the failure modes in the physical models of granite, sandstone and schist under uniaxial compression, Brazilian and point load conditions and evaluated their relation with the mechanical strength of rock materials. Additionally, several researchers (e.g., Tien and Kuo 2001;Debecker and Vervoort 2009;Tavallali and Vervoort 2010;Kim et al. 2016) have investigated the failure modes in anisotropic rocks under different loading conditions. Although numerous studies were performed relating mechanical properties and rock failure modes, yet such experimental studies involving the fine grained, brittle, massive volcanic rocks such as basalts or metabasalts, have not gained significant prominence.
Tensile stress zones frequently occur in the vicinity of rock masses and tensile failure has been recognized as the primary failure mode in several rock excavation projects such as in the construction of tunnels and mines (Xue et al. 2020). Therefore, rock failure modes along the tensional regime are routinely considered as the key factor to characterize the damaging properties of rocks (Li and Wong, 2013;Liu et al., 2019). Accordingly, we intend to understand the rock failure patterns in metabasalts under different index testing procedures such as point load and Brazilian testing conditions. It should be noted that, under both tensile and point load tests, the intact rock fails under compression induced tension (Russell and Muir Wood 2009;Masoumi et al. 2018). Importance of point load tests in estimating the UCS as well as in the geomechanical classification of rock masses have been widely discussed by several researchers in the past (Bieniawski 1975;Yin et al. 2017;Xue et al. 2020). In this study, a total of 21 specimens were tested under point load testing conditions and 16 specimens were tested under Brazilian testing conditions. Variation in strength index of the metabasalts were discussed subsequently in terms of rock failure modes. Additionally, the P-wave velocity was also used to check the dependence of micro-flaws on the variation of point load strength index in the investigated metabasalts.

Specimen Collection
Block specimens of metabasalts were collected from the exposures in and around Chitradurga, western Dharwar craton (WDC), south India (Fig. 1a). The metabasalts are dark greyish to blackish, massive to fine grained, altered and devoid of any mesoscopic foliation Mondal 2020, 2021). The collected blocks were used for core retrieval, and the obtained cores were later investigated for mechanical characterization.
The study area (see Fig. 1b) is a part of the Chitradurga Greenstone Belt (CSB), western Dharwar craton (WDC), south India. Dharwar craton consists of two blocks; the western (WDC) and the eastern blocks (EDC). Stabilization of the craton is dated back to 2.75-2.51 Ga, with the accretion of these two blocks along the Chitradurga Shear Zone (CSZ) (Naqvi and Rogers 1987;Chadwick et al. 2003;Jayananda et al. 2006). The Chitradurga schist belt (CSB) situated in the eastern part of WDC comprises the gneisses and the younger supracrustals. The latter consists of the metavolcanics/metabasalts (greenstone belt; greenschist to lower amphibolite facies metamorphism), metamorphosed greywacke-argillite (interbanded with ferruginous chert and banded iron formation), polymict conglomerate, and ferruginous chert Mondal 2020, 2021). Petrological and geochemical investigation confirms the presence of actinolite, albite, chlorite, epidote, quartz and calcite in the basaltic rocks of the study area (Chakrabarti et al. 2006).

Specimen Preparation
Core specimens were drilled from the collected blocks in the laboratory. Some of the core specimens were also collected from the older drilling sites. Subsequently, the drilled cores were saw-cut into point load and Brazilian test specimens. The specimen dimensions were maintained as per the specifications of the International Society for Rock Mechanics, ISRM (2007); length-diameter ratio for point load test and Brazilian test were fixed at 1 and 0.5 respectively. All the specimens were air-dried to constant mass before the tests were conducted.

Experimental Setups and Testing Procedures
A total of 37 intact core specimens with 21 specimens for point load test and 16 specimens for Brazilian test were prepared (Fig. 2a, see Tables 1 and 2). P-wave velocity (V P ) has been determined for each of the point load specimens using the Portable Ultrasonic Nondestructive Digital Indicating Tester (PUNDIT) (Fig. 2b) following the ISRM (2007) standards.
For the point load test, a load system of about 100 kN load capacity was used along with a deformation sensor (range = 50 mm; resolution = 0.01 mm) that remains attached with the testing frame. The specimen core is placed axially along the line of loading (line joining the two centres on the opposite faces of the specimen), in between the two conical platens (see Fig. 2c). The data acquisition system continuously measures the applied load along with the corresponding deformation, as a function of time.
The Brazilian testing frame remains fitted within the point load testing system. The specimen is placed diametrically inside the testing frame (Fig. 2d). As compression is applied, the specimen fails due to the induced tensile stress. The corresponding peak load is recorded through the data acquisition system. Photographs of the failed specimens obtained from both the testing procedures are shown in (Fig. 2e, point load test) and (Fig. 2f, Brazilian test). The entire testing procedures and determination of the point load strength index, Brazilian tensile strength have been conducted in compliance with ISRM (2007ISRM ( , 2014.

Results and Discussion
The calculation of point load strength index (I s(50) ) and Brazilian tensile strength (BTS) of each specimen is done in accordance with ISRM (2007). Mechanical characteristics of the metabasalts based on the point load, P-wave velocity (V P ) and Brazilian tests are provided in the Tables 1 and 2. The I s(50) values are plotted against V P in Fig. 3 in order to substantiate the role of inherent microstructure on the variation of mechanical strength of the rock. It should be noted that the velocity of ultrasonic waves in rocks is commonly used as an index in evaluating microstructure and associated properties of rocks (Basu and Aydin 2006). A positive linear correlation between these two properties with R 2 = 0.77 is noticeable (Fig. 3). In order to understand the role of rock failure modes in strength determination of metabasalts, the different failure modes under the point loading condition and indirect tension are subsequently analysed and discussed further. c Fig. 2 a Representative metabasalt specimens for analysis. b Pwave velocity determination. c and d show the set-up for Point load test (PLT) and Brazilian tensile strength test (BTS) respectively. e and f are the close-up views of failed specimens after PLT and BTS respectively Several rock failure modes are found in metabasalts under the point load test and can be classified as single plane failure mode (i.e., single extensional failure plane containing the line of loading), triple junction failure mode (i.e., failure along three extensional planes containing the line of loading), twisted failure mode (i.e., failure along a twisted or curved surface containing the points of loading) and single plane (inclined) (i.e., single extensional failure plane containing the line of loading, at an angle). It should be noted that the first three rock failure modes were also documented by Basu et al. (2013); however, the last one, single plane (inclined) is introduced in this study which is observed in a few metabasalt specimens. The schematic diagram of rock failure modes in metabasalts are shown in Fig. 4. The number of specimens that failed under different ranges of point load strength with their corresponding failure modes are shown in Fig. 5 and the photographs of the failed metabasalt specimens are shown in Fig. 6. As depicted in Fig. 5, single plane and single plane (inclined) failure modes transpired within point load strength of 6 MPa, however, at higher point load strength values i.e., more than 6 MPa, twisted and triple junction failure modes are apparent. It is also evident from this investigation that twisted failure mode shows a wide range of strength values.
As mentioned earlier, point load test involves loading rock specimens between two conical platens to obtain the strength of the rock. The rock specimens should fail by the development of one or more extensional planes containing the line of loading (ISRM 2007). Under the point load test, an induced tension is generated due to the applied compression perpendicular to the line of loading, resulting in rock failure along a single plane. This is regarded as the primary failure mode under point loading conditions. However, in some cases, for example, when a rock resists high amounts of stress, triple junction failure mode is materialized in order to release the high strain  (Fig. 5). Similarly, twisted and single plane (inclined) failure modes are also found in a few specimens. This could be attributed to fracture propagation along selective pathways depending upon the inherent microstructure of the specimen, assisting in rapid release of the stored strain energy. Broadly, it can be said that several rock failure modes might occur under point load test depending upon the presence of inherent micro-flaws, which also has a significant effect on the strength of the rock materials.

Failure Modes Under Brazilian Test
Several types of failure of disc specimens are possible under Brazilian testing conditions such as (1) central fracture (failure plane is roughly parallel to the loading direction and located in the central part), (2) layer activation (failure planes are parallel to the foliation plane), (3) non-central fracture (failure planes deviate from the central part and do not correspond to layer activation), (4) central multiple fractures (multiple failure planes parallel to the loading direction and located in the central part) and central or noncentral ? layer activation (central or non-central failure plane with layer activation). The first three failure modes were proposed based on the investigation of anisotropic rocks whereas the latter ones were included based on a detailed study of both isotropic and anisotropic rocks (Basu et al. 2013;and Tavallali and Vervoort 2010). Following the above discussed approach, the rock failure modes of metabasalts under indirect testing conditions were classified. In this investigation an additional failure mode i.e., conjugate failure mode (with multiple failure planes intersecting each other) is also identified in a specimen. So, in total five types of rock failure modes i.e., (1) central multiple, (2) central, (3) non-central, (4) central multiple ? layer activation and (5) conjugate are observed in metabasalts under the Brazilian testing conditions. The schematic diagrams of different failure modes observed in this investigation are shown in Fig. 7. The number of specimens which failed under different ranges of tensile strength with their corresponding failure modes are shown in Fig. 8 and the photographs of the failed metabasalt specimens are given in Fig. 9.
From Fig. 8, it is evident that central multiple is the most common failure mode in metabasalts. This could be materialized because of the massive nature of the metabasalts for which it released high stored strain energy during loading. However, central multiple ? layer activation is observed in some specimens due to the presence of inherent fractures which got reactivated during the process of loading. When there are multiple inherent microfractures present and if they propagate in such a way that fracture planes intersect each other, it may result in conjugate fracturing. Although this is not a common failure mode under the compression induced tensile conditions, this type of failure mode might be a possibility in case of massive rocks, where the inherent micro-flaws are essentially difficult to identify. Under the compression induced tensile stress regime, central failure mode is usually expected, which develops when the This is also evident from Fig. 8 that in between the mean zone of tensile strength of metabasalts (i.e., 8-12 MPa), all possible failure modes are transpired. This can be conceived that rock materials may fail in any failure mode depending upon the presence and distribution of the inherent micro-flaws. Therefore, investigation of failure modes will prove to be a useful index in the identification of micro-flaws or weakness planes in the rock materials. Mechanical characterization incorporating rock failure modes can provide a better understanding of the mechanical behaviour of isotropic rocks such as metabasalts and can be insightful for adopting engineering measures.

Conclusions
In a routine engineering environment, rock failure modes along the tensional stress regime are considered as the key factor to characterize the damaging properties of rocks. In accordance with this, strength characterization of metabasalts is demonstrated with reference to two different indirect tensile stress conditions like point load and Brazilian tests and the results are analysed with the obtained rock failure modes. The conclusions from this study are as follows: 1. Several rock failure modes might occur in metabasalts under point load and Brazilian tests which could be attributed to the presence and inhomogeneous distribution of the inherent microflaws. It is demonstrated that the variation in rock failure modes is significantly related to the strength of rock materials. 2. Single plane failure mode is the most prevalent one under the point load test. However, when the metabasalts resist high amounts of stress, triple junction and twisted failure modes are materialized in order to release the high strain energy. 3. Similarly, single plane (inclined) failure mode is also prominent in a few specimens which could be attributed to fracture propagation along selective b Fig. 6 Failed specimens after PLT with their respective failure modes annotated below each photograph. The dependence between the modes of failure and strength of rock specimens investigated under point load and Brazilian testing conditions is presented to incite further investigation on this issue. Further, a detailed micro-structural analysis can be conducted using modern techniques such as X-ray micro-CT. Visualizing the internal failure mechanism of microflaws that controls the strength and failure modes of rock materials as envisaged from this investigation can be regarded as the future scope of this work. Acknowledgements This study is a part of doctoral research of the first author, being funded by DST Inspire, Govt. of India (IF170912). The second author acknowledges the Department of Geology and Geophysics, Indian Institute of Technology Kharagpur, India for providing overall facilities to perform the tests. The third author acknowledges DST-SERB, (File No. ECR/2015/000079), RUSA 2.0 and Indian Statistical Institute for funding the research. The authors thank Prof. Arindam Basu (Department of Geology and Geophysics, Indian Institute of Technology Kharagpur, India) for allowing the instruments to carry out the experiments. Detailed reviews by the two anonymous reviewers helped to improve the paper considerably. Editorial handling by Prof. Paul Marinos and Prof.
Pinnaduwa H.S.W. Kulatilake is greatly appreciated. Geological Survey of India (GSI), Chitradurga is also acknowledged for their logistics support. The authors also thank the Department of Geological Sciences (Jadavpur University, India) and the Geological Studies Unit (Indian Statistical Institute, Kolkata, India) for providing adequate infrastructural facilities and environment for carrying out this research.