Experimental verification of the intrinsic strainburst proneness of various rock types

A portion of excess strain energy is converted into kinetic energy after the peak load in Class II rock. That is the intrinsic potential energy for strainburst. Therefore, the intrinsic strainburst proneness of the rock can be quantitatively assessed by the excess energy released from the rock, which can also be expressed by an intrinsic ejection velocity. This study aims to validate the idea of using the intrinsic ejection velocity as an index for the strainburst proneness of rock. Servo-controlled uniaxial compression tests were first conducted on 13 types of rocks. The intrinsic ejection velocities of rock specimens were assessed on the stress–strain curves. It was showed that the ejection velocity was greater than zero in twelve of the thirteen rock types, indicating that the twelve rock types were intrinsically prone to strainburst. The intrinsic ejection velocity was less than 5 m/s in eleven rock types, while up to 7.2 m/s in one. True triaxial tests were then conducted to examine the intensity of the bursting in six of the burst-prone rock types. The mass of the ejected rock fragments and the bursting sounds were recorded and analyzed afterward. The results showed that the orders of both the mass of the ejected rock fragments and the intensity of the bursting sounds were consistent with the order of the intrinsic ejection velocities of the rocks. It seems that the intrinsic ejection velocity is an appropriate index for the strainburst proneness of rock.


Introduction
Rockburst in underground rock excavations has become increasingly prominent with the increase in the depth of underground mines, civil tunnels, and underground hydropower plants (Cook 1976;Li 2010;He et al. 2010;Kaiser and Cai 2012). Rockbursts can be classified as self-initiated type and remotely triggered type (Kaiser et al. 1996;Li et al. 2019;Li 2021). A self-initiated rockburst is directly associated with stress concentration, and it occurs when the tangential stress in the rock reaches the level of strength after excavation (Ortlepp and Stacey 1994;He et al. 2021). Therefore, such a rockburst is also called strainburst. Remotely triggered rockbursts are often mobilized by seismic waves of blasting or fault-slips in the rock mass. The ejected rock could be intact or pre-fractured before bursting. It is also classified as a strainburst if the rock is intact before bursting. This paper focuses on strainbursts.
Researchers have made great efforts to estimate the proneness of rock to strainburst. Proposed indices for strainburst proneness include the discriminant index of impact property (Goodman 1980), the strain energy storage index (Kidybiński 1981), the decreased modulus index (Sing 1989), the potential energy of elastic strain (Wang and Park 2001), the surplus energy index (Tang et al. 2002), and the peak-strength strain energy storage index (Gong et al. 2019). Some indices of brittleness were based on the postpeak behavior of rock, such as by Tarasov and Potvin (2013) and brittleness indices were used to characterize strainburst proneness (Wang and Park 2001;Cai 2016;Leveille et al. 2017;Zhou et al. 2018). These discriminant indices quantitatively describe the proneness of rockburst from different angles. However, some of them are difficult to be determined and some are not yet being well verified.
The prerequisite for a strainburst is that elastic energy is released after rock failure. Its presence indicates the rock is prone to strainburst. The amount of the released elastic energy determines the intensity of the burst. The more energy that is released, the more intense is the burst. Proneness and intensity represent different things. The former tells whether a burst would occur, while the latter expresses how violent the burst would be. However, the two parameters are indeed related. A rock that can release a larger amount of elastic energy is more prone to burst, and the burst will be more intense. Therefore, proneness and intensity are synonymous in describing the potential violence of strainburst studied in this paper.
In this study, the strainburst proneness of 13 types of rocks was assessed using the intrinsic burst energy density of the rocks determined on the basis of the stress-strain curves of the rocks. Six types of rocks were tested under single-freeface true triaxial compression to examine the intensity of rock bursting. The results showed that the order of the burst intensity of the rocks was consistent with the intrinsic burst energy density. The intrinsic burst energy density is therefore an appropriate index for the strainburst proneness of rock.

Intrinsic elastic energy for strainburst
Rock is divided into two classes according to the post-peak stress-strain behavior. The slope of the stress-strain curve of rock becomes negative immediately after the peak stress in Class I rock, but it remains positive until the stress drops below a certain level in Class II rock, as shown in Fig. 1 (Wawersik and Fairhurst 1970). For Class I rock, the axial strain increases with decreasing axial stress after the peak stress. This implies that the strain energy stored in the rock is completely dissipated, so for the rock to fracture further, external energy must be supplied. On the contrary, for Class II rock the energy required for rock fracture after the peak stress is less than the strain energy stored in the rock so a part of the elastic strain energy stored in the rock must be released after the peak stress (Tkalich et al. 2016;Tarasov and Stacey 2017). The kinetic energy sources of strainburst are different in the two classes of rocks. For Class I rock, the kinetic energy of the strainburst body is provided solely by the surrounding rock mass, while for Class II rock, the kinetic energy comes from both the strainburst body and the surrounding rock mass. Tarasov and Potvin (2013) studied the post-peak instability of Class I and Class II rock specimens in terms of so-called intrinsic brittleness and relative brittleness. The former is defined as the elastic energy stored within the loaded material, and the latter refers to the elastic energy released from the loading system. In this paper, the focus is on the elastic energy released from the rock specimen. That means that the target rock type is Class II. Figure 1b shows a schematic stress-strain curve of Class II rock under uniaxial compression. This compression has four stages in the pre-peak region: crack closure, elastic deformation, stable crack propagation, and unstable crack growth (Martin and Chandler 1994). For Class II rock, under servo-controlled loading conditions, the axial stress declines after it reaches the peak stress point P, and the axial strain reverts to point A, as shown in Fig. 1b. Point A is the turning point of the post-peak strain. Below point A, the axial strain increases when axial stress declines, and it returns to the strain of the peak stress P at point B. Thereafter, external energy must be input for further rock fracture. After passing through the peak stress P, a portion of the elastic strain energy accumulated in the pre-peak stage is dissipated by fracturing the rock. It is represented by the area bounded by OPABCO in Fig. 1b (W bf ). The rest of the elastic strain energy is released when the axial stress drops from the peak Fig. 1 Schematic stress-strain curves of a Class I rock and b Class II rock under uniaxial compression. W bk is the intrinsic burst energy density, representing the strain energy in the rock transformed to kinetic energy during strainburst. W bf is the strain energy dissipated by rock fracturing stress P to point B. It is represented by the red area (W bk) in Fig. 1b. Under servo-controlled loading conditions, the actuator of the testing machine retracts, and the released strain energy is returned to the testing machine. If the test is not servo-controlled, no matter under stress-control or straincontrol, this portion of strain energy would be transformed to kinetic energy to eject the rock, that is, a strainburst occurs. The elastic energy released in Class II rock depends mainly on the lithology of the rock, and it is a constant per unit volume of the rock. Therefore, in this paper, it is called the intrinsic burst energy density (IBED) of the rock. The intrinsic burst energy density (W bk ) is a parameter that expresses the strainburst proneness of the rock (Zhang and Li 2019).
When a strainburst occurs, a portion of the rock is ejected and displaced from its original position. The greater the intensity of the strainburst, the higher the rock ejection velocity. The intrinsic ejection velocity (v) of the rock, which is purely dependent on the intrinsic burst energy density W bk , is calculated as: where ρ is the density of the rock in kg/m 3 , v is the ejection velocity in m/s, and W bk is the intrinsic burst energy density in kJ/m 3 . Both W bk and v express the intensity of the possible strainburst, but the ejection velocity is more direct, and it is easier to understand.

Specimens and experiment procedure
Thirteen types of rocks were tested under uniaxial compression to determine their intrinsic strainburst proneness. The types and properties of the rocks are presented in Tables 1 and 2. Cylindrical specimens in dimensions of Ф50 mm × 100 mm were prepared according to the method suggested by the International Society for Rock Mechanics and Rock Engineering (Fairhurst and Hudson 1999). The specimens of each rock type were drilled from the same block to reduce possible bias from mineral heterogeneity. The rock blocks selected for testing are intact, and do not contain visible defects and fractures.
The uniaxial compression tests were conducted on the ZTR-276 hard rock triaxial apparatus (Fig. 2a), which has an axial load capacity of 2000 kN and the frame stiffness is 7 GN/m. The triaxial pressure cell equipped on the testing machine has a capacity of 100 MPa for the confining stress. Figure 2b shows a close-up of a specimen before uniaxial compression testing, where the two thin bars on the sides of 2W bk the specimen, fixed on the black rings, are the axial linear variable differential transformer (LVDT) sensors, and the central rim is the radial LVDT. The LVDT sensors have a measurement range of 5 mm and a precision of 0.1%. The EDC 220 V control panel on the ZTR-276 hard rock triaxial apparatus collects all sensor signals and sends feedback signals to the Moog G761 electro-hydraulic servo valve to form the servo control loop. The experience of the authors is that the response speed of the actuator of the testing machine to the feedback signals of the servo control system is more important than the stiffness of the testing machine in capturing the post-peak stress-strain behavior of the rock. The servo control system of the ZTR-276 apparatus and the stiffness of the machine ensure that the complete stress-strain curves of all rock types can be successfully obtained. The stiffness of the rock specimens is calculated according to Eq. (2). The stiffness varies from 0.34 to 1.6 GN/m with the stiffness of the Kuru granite specimens being the highest at 1.60 GN/m (Table 2).
where, K is the stiffness of the rock specimen in GN/m, A stands for the cross-sectional area of the rock specimen in m 2 , E the Young's modulus of rock specimen in GPa, l the height of rock specimen in m.
Uniaxial compression test was carried out in two steps. First, the rock specimens were axially loaded to a level of approximately 60% of the expected peak stress, that is, the UCS, at a rate of 0.5 MPa/s under axial stress control. Then the loading mode was switched to radial displacement control. The rate of the radial displacement at the switching moment was used to continue the test into the post-peak stage. The plan was that two specimens for each rock type were tested first. The testing was completed if the results of the two specimens were satisfactory in repeatability. Otherwise, more specimens would be tested. It was shown that the test results of the two specimens for all 10 rock types were good in repeatability so that only two specimens were tested for each rock type in the study. Figure 3 shows the stress-strain curves for Shandong granite and Shandong marble under uniaxial compression. The stress-strain curves for all other rock types are presented in Appendix. This figure shows that the two curves of each rock type exhibit good repeatability. The two rock types are quite different in their strengths, but their deformation is similar in the pre-peak stage. That is, they both exhibit initial compaction, elastic deformation, stable rock damage, and unstable rock fracturing. However, the behavior of the two rock types is significantly different in the post-peak stage. Specifically, the axial strain of the Shandong granite first reverses as the axial stress declines after the peak stress, as shown in Fig. 3a. This implies that the stored strain energy is partially released from the specimens and the rock belongs to Class II. The intrinsic burst energy density W bk of the Shandong granite is 14.4 kJ/m 3 . The corresponding intrinsic ejection velocity v, calculated using Eq. (1), is 3.3 m/s. For the Shandong marble, the axial strain continues to increase with the decline in axial stress after the peak stress, exhibiting typical Class I characteristics (Fig. 3b). The Class I behavior of the Shandong marble indicates that the loading system must continuously input energy for further rock fracturing. The intrinsic burst energy density of the Shandong marble is zero, so it is not intrinsically prone to strainburst. The intrinsic burst energy density W bk and corresponding intrinsic ejection velocity v of all rocks are presented in Table 3. Twelve of the thirteen tested rock types were intrinsically prone to strainburst since their intrinsic burst energy densities were greater than zero. The intrinsic ejection velocity of the rock types except Linghai granite was below 5 m/s. The intrinsic ejection velocity of Linghai granite was as high as 7.2 m/s. Back-calculations of rockbursts in deep mines, such as, in Canada, have shown that the average ejection velocity of rockburst bodies is usually lower than 6 m/s, even though Ortlepp and Stacey (1994) claimed that the ejection velocity of rock could be 10 m/s. In reality, ejection velocities higher than 10 m/s have been observed only for small rock pieces of a couple of kilograms in rockburst events. The  issue of rock ejection velocity has been discussed many times in international conferences, such as, on Deep Mining. It is commonly agreed that the ejection velocity is usually below 6 m/s in the current underground metal mines of approximately 2000 m in depth. Hu et al. (2019) once conducted laboratory tests to simulate strainburst in a granite specimen with a circular hole. They measured by a high-speed camera that the maximum ejection velocity of rock fragments was approximately 7.41 m/s. The intrinsic ejection velocities of the rocks tested in our study are consistent with the velocities obtained by the back-calculations on the sites and measured in the laboratories. Therefore, it is possible that the kinetic energy of a strainburst is mainly contributed by the burst rock itself. Based on the magnitude of the intrinsic ejection velocity, the strainburst proneness of the 12 rocks is in this order from high to low: Linghai granite (

Test background
Take a small rock prism at the contour of an underground opening as an example. Before excavation, the prism is pressed under the state of true triaxial stresses with σ 1 > σ 2 > σ 3 , where σ 1 , σ 2 , and σ 3 are the in situ major, intermediate, and minor principal stresses, respectively. After excavation, the loading condition of the prism is changed to such a state that it is stressed on five of its six faces with one face of free stress, as shown in Fig. 4. The radial stress (σ r ) on the tunnel surface is zero, but it is slightly greater than zero on the backside of the rock prism. The tangential stress (σ θ ) is gradually increased during excavation, and it becomes significantly greater than the major principal stress, that is, σ θ > σ 1 in Fig. 4b. When σ θ exceeds the strength, the rock fails and a portion of the elastic strain energy stored in the rock is suddenly released, resulting in a strainburst. The burst either occurs in a short or relatively long time after excavation depending on how quick the redistribution of the tangential stress field occurs. It has been observed that the delay time varies from hours to days (Jiang et al. 2010;Zhang et al. 2012). The loading condition and the failure process of the tunnel surface rock can be simulated in a single-freeface TTC test (Su et al. 2017a, b). Therefore, single-freeface TTC tests were carried out on six of the 12 rocks that showed strainburst proneness in the uniaxial compression tests. In the TTC tests, the burst intensity of the specimens was determined by two parameters-the mass of the ejected fragments and the loudness of the sound of the burst.

Specimens and test procedure
The six rock types chosen for single-free-face TTC testing were Jinzhou granite, Shandong granite, Beishan granite, Shenyang sandstone, Yunnan sandstone, and Chifeng basalt, as shown in Fig. 5. According to the intrinsic burst energy densities of the rocks determined in the previous section, the strainburst proneness of the rocks in descending order was: Jinzhou granite, Shandong granite, Chifeng basalt, Shenyang sandstone, Yunnan sandstone, and Beishan granite.
In the single-free-face TTC tests, the rock specimens were prismatic with dimensions of 100 mm × 100 mm × Fig. 4 Sketches of the stress state of a the rock element in the tunnel sidewall on the site and b the rock element for the single-free-face TTC test in the laboratory 200 mm, as shown in Fig. 5. All the prismatic specimens of a rock type in the TTC tests were prepared from the same rock as the cylindrical specimens. Similar to the uniaxial compression test, the rocks selected in the singlefree-face TTC tests also are intact and do not contain visible defects and fracture surfaces. At least two singlefree-face TTC tests were performed for each type of rock.
The single-free-face TTC tests in this study were conducted on the Guangxi University's true triaxial rockburst testing machine (Su et al. 2017b, which has a stiffness of 9 GN/m in the vertical direction and 5 GN/m in the horizontal direction. The axial load capacity of the machine is 5000 kN, and the lateral load capacity is 3500 kN. Loads can be applied to the specimen in three orthogonal directions. In the tests, the displacement in the σ 1 direction was measured by miniature LVDT. A decibel meter (type DT-8852) was placed 500 mm from the rock specimen to record the sound of the bursts when the specimens failed.
The stress state of the rock specimen in the single-freeface TTC tests is shown in Fig. 6a. The stress paths in the test are illustrated in Fig. 6b. First, σ 1 , σ 2 , and σ 3 were synchronously applied to 5 MPa. Then, σ 1 and σ 2 were simultaneously increased to 30 MPa, while σ 3 remained unchanged. Finally, σ 1 was increased until failure of the specimen while both σ 2 and σ 3 remained unchanged. The stresses were applied at a rate of 0.5 MPa/s in all three stages.

Stress-strain curves
In the single-free-face TTC tests, all six rock types underwent bursting. The major principal stress (σ 1 )-major principal strain (ε 1 ) curves of all rock specimens are presented in Fig. 7. The curves of the rocks look similar, but their peak stresses are different. The specimens failed violently (strainburst) when σ 1 reached the peak point, and then σ 1 dropped rapidly to zero.

Failure mode
The failed rock specimens and corresponding spalled and ejected rock fragments are presented in Fig. 8. In all specimens, the free surface of the specimen facing σ 3 burst down, and fractures perpendicular to the σ 1 -σ 3 plane were created in the specimen. The fractures close to the free surface of the specimen were sub-parallel with the free surface and were in extension, while the inside fractures were in shear.
It seems that the volume of the ejected rock had a relationship with the number of inside fractures in the specimen. The tendency is that the more rock that was ejected, the fewer the inside fractures were. For example, the Jinzhou granite and Shandong granite (Fig. 8a, b) had only a few inside fractures, and the ejected rock was quite large in  . 6 a The stress state of the rock specimen and b the loading paths in single-free-face TTC tests the specimens of the two rock types. On the contrary, the Beishan granite had many inside fractures, and the ejected rock was small (Fig. 8f). Fewer fractures are created in a specimen, less energy is consumed for rock fracture so that a higher percentage of the strain energy is released for rock ejection. Therefore, the Jinzhou and Shandong granite specimens released a greater percentage of elastic energy than the Beishan granite specimens. This concept is illustrated in Fig. 1b. The rock-fracturing energy, W bf , of the Jinzhou granite and Shandong granite was a small portion of the total potential strain energy in the specimens so much of the strain energy was transformed to kinetic energy, W bk , to eject rock. This resulted in a large ejection volume. On the contrary, the rock fracturing energy, W bf , of the Beishan granite was a large portion of the potential strain energy so that the portion of the strain energy remaining for rock ejection was small. This resulted in a small ejection volume.

Mass of ejected rock
In the laboratory tests, rock at the surface was fragmented and ejected from the specimen during a strainburst. The distance of the ejected rock is a measure of the kinetic energy and so the intensity of the strainburst. However, such a distance is difficult to determine because the ejected rock fragmented and the fragments landed all around the specimen. It has been observed that the mass of the ejected rock is proportional to the intensity of strainburst. The mass of the Fig. 7 The σ 1 -ε 1 curves of all rock specimens in the singlefree-face TTC tests. a Jinzhou granite, b Shandong granite, c Chifeng basalt, d Shenyang sandstone, e Yunnan sandstone, and f Beishan granite Fig. 8 Failure modes of the rock specimens and rock fragments after testing in the singlefree-face TTC tests. a Jinzhou granite, b Shandong granite, c Chifeng basalt, d Shenyang sandstone, e Yunnan sandstone, and f Beishan granite ejected rock fragments is used to approximately assess the intensity of the burst. The masses of the ejected rock fragments of each specimen were collected and weighed after the tests, which are presented in Fig. 9a. As seen in the diagram, the masses of the ejected rock fragments were similar for the two specimens of each rock type. This indicates good repeatability in the burst volume of a given rock type. The average masses of the ejected rock of the six rock types were 709.6 g for JZG, 439.4 g for SDG, 331.4 g for CFB, 243.2 g for SYS, 164.1 g for YNS, and 114.8 g for BSG, respectively, which are 13.4%, 8.4%, 5.7%, 4.7%, 3.7%, 2.2% of the mass of the specimens.The intrinsic ejection velocities of the six rock types, calculated from the stress-strain curves, are presented in Fig. 9b for comparison. It should be noted that the order of the six rock types of the mass of ejected rock in Fig. 9a is the same as the order of the intrinsic ejection velocity in Fig. 9b.

Burst sound loudness
It is believed that the loudness of the sound of rock failure is proportional to the burst intensity of the specimen. The greater the burst intensity, the louder the sound. Therefore, the loudness of the sounds during rock failure in laboratory tests can be used to express the intensity of the strainburst (Su et al. 2017a). The sounds of all specimens recorded at the time of rock failure are represented in Fig. 10. The threshold used for the sound records was 63.5 dB. This guaranteed that ambient noises would not affect the recordings. The highest pulse signals corresponded to the bursts at rock failure. The average loudness of the sound pulses for the six rock types were 111.9 dB for JZG, 96.5 dB for SDG, 90.9 dB for CFB, 87.0 dB for SYS, 83 dB for YNS, and 82.5 dB for BSG. Among the six rock types, the sound loudness was greatest for Jinzhou granite and least for Beishan granite. This means that the intensity of the strainburst was highest in the former and lowest in the latter. It is important to note that the sound loudness was increased somewhat by sound from the testing machine, and this was proportional to the ultimate stress on the specimens. It is more convincing to compare the sound loudness of rock types, the strengths of which are similar. Among the six rock types, the peak stresses of the rocks JZG, SDG, and CFB were similar in the range from 310 to 340 MPa. The descending order of sound loudness for those three rock types was JZG, SDG, and CFB, which was consistent with the order in the intrinsic strainburst ejection velocity as shown in Fig. 9b. Similarly, the peak stresses of SYS and BSG were similar around 250 MPa. The sound loudness of SYS was higher than that of BSG, and their intrinsic strainburst ejection velocities were in the same order. In summary, the loudness of the sound pulses during rock failure is a measure of the burst intensity, particularly when the rock strengths are at approximately the same levels. As a comparison of Fig. 10 with Fig. 9b shows, the order of sound loudness of the six rock types was consistent with the order in the intrinsic ejection velocity.

On the capture of the post-peak behavior of Class II rock
The stiffness of the ZTR-276 hard rock triaxial apparatus used for the tests in this study is 7 GN/m which is higher than the minimum stiffness 5 GN/m required by the ISRM suggested method (Fairhurst and Hudson 1999). The frame stiffness of 7 GN/m can guarantee that the complete stress-strain curves of the rocks could be obtained. The energy released from the machine frame is so small that its influence on the rock failure can be neglected. Class II rock would fail violently under load control, that is, when the load is applied monotonically in a constant loading rate. The failure mode is similar to strainburst on sites. To capture the post-peak behavior of Class II rock, the test has to be conducted under radial displacement control. The radial displacement or strain of the specimen increases monotonically in the post-peak stage, as shown in Fig. 3, so that it is used as the feedback signal in displacement control. Under displacement control, the piston of the actuator of the testing machine reverses to let the Class II rock specimen displace axially backward to release the excess strain energy. In this process, the actuator continuously adjusts its actions following the feedback signals. The response of the actuator of the testing machine must be fast enough to the feedback signal in order to capture the reversing axial strain. Otherwise, the excess strain energy would be converted to kinetic energy to eject the rock. Taking the unloading line PA in Fig. 11 as an example, the piston of the actuator could not reverse quickly enough if the response of the system is too slow, which would lead to that the specimen is unloaded to A' instead A.
The excess strain energy is not properly released in this case and the specimen could fail out of control. The feedback frequency of the EDC 220 V control panel on the ZTR-276 hard rock triaxial apparatus is 2.5 kHz. The response frequency of the Moog G761 electro-hydraulic servo valve in the control system is 500 Hz, which can guarantee the servo speed of the testing system is enough for the tests.

Application of the intrinsic burst proneness index
The intrinsic burst proneness index can be used to assess the possibility of strainburst in a Class II rock and the intensity of the burst. In general, the intensity of a rockburst event is associated to the strain energy released from both the burst rock and the surrounding rock mass (Li 2021). In the case of strainburst, particularly a shallow one, the source of the kinetic energy is mainly from the burst rock itself, that is the intrinsic energy W bk . One can design proper ground support schemes based on the intrinsic burst energy of a specific rock. For instance, strong dynamic support elements, such as yield and energy-absorbing rock bolts, should be used in the ground support system in a rock mass the intrinsic ejection velocity of which is higher than 5 m/s. In a rock mass with small intrinsic ejection velocity, such as less than 3 m/s, one can think to use light dynamic support element in the support system.
The surrounding rock mass does contribute a role in the intensity of rockburst, particularly when the burst volume or depth is considerable. The role of the surrounding rock mass will be investigated in the subsequent studies.

Conclusions
The intrinsic burst energy density and the corresponding intrinsic ejection velocity of 13 rock types were determined on the stress-strain curves of cylindrical rock specimens under uniaxial compression. The intrinsic burst energy density was larger than zero for 12 of the 13 rock types, meaning that the 12 rocks are prone to strainburst. The intrinsic ejection velocities of 11 of the burst-prone rock types were below 5 m/s, while one type had an intrinsic ejection velocity as high as 7.2 m/s. Six of the 12 burst prone rocks were selected to conduct single-free-face true triaxial compression tests. All the specimens of these rock types failed in the form of strainbursts. The test results showed that the orders of the ejected mass and the loudness of the sound of bursting were consistent with the order of the intrinsic ejection velocity. Therefore, intrinsic ejection velocity can be used as an index of the intrinsic proneness to strainburst. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.