Abstract
A long-term opening problem in geophysics and engineering is the generation mechanism of rock pulverization (e.g., fault gouge) within the shear zone when subjected to triaxial stress environment and dynamic loads. A novel triaxial Hopkinson bar is developed to apply quasi-static triaxial confinement and dynamic loads onto the testing rocks and to measure the energy release from the shearing zone. The results elucidate shear strain-rate threshold (i.e., over 125 s−1) for granite at the triaxial prestress of (10, 10, 10) MPa is required for fine fragments/gouge generation. The effects of shear and normal pre-stresses on dynamic shear strength and surface energy for rock pulverization are investigated, which will help explain fine fragments formed during the high-rate loading events. It is suggested that, except for the quasi-static cumulative slip attrition and multiple dynamic events, rock pulverization or fault gouge could be generated at relatively shallow depths (low geo-stress) in a single dynamic earthquake processes.
Highlights
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Triaxial static-dynamic coupled shear tests of rock were conducted using a novel triaxial Hopkinson bar (Tri-HB).
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The effects of strain rate and confinement on dynamic shear behaviors of rock.
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Abundant fault gouge can be formed at stress deformation conditions associated with a fast shear crack propagating (i.e., shear strain rate over 125 s−1).
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1 Introduction
Fault gouge with grain comminution and grain size reduction has been observed ubiquitously within the core zone of brittle faults (Lockner et al. 2011; Marone and Scholz 1989; Reches and Dewers 2005; Sammis et al. 1986; Wilson et al. 2005). It has the characteristics of extremely friable, incohesive, and is marked by severe fracturing down to the micron scale. The formation of fine fragments or fault gouge is commonly attributed to gradual damage and friction of sliding surfaces (Aubry et al. 2020; Brodsky et al. 2020; Kranz 1983; Nevitt et al. 2020; Sammis et al. 1986; Wilson et al. 2005) in quasi-static cumulative slip of mature faults, coseismic fault slip (Aubry et al. 2020), or pulverization of rock subjected to dynamic loading during earthquakes (Doan and Gary 2009; Dor et al. 2006; Reches and Dewers 2005; Rubino et al. 2022; Yuan et al. 2011). Seismic events like earthquakes not only occur as the ruptures along pre-existing faults in the earth’s crust, but also involve the dynamic shear rupture of initially intact rocks subjected to existing geo-stress. Although natural faults could be formed by multiple events over a long period of time after the first event and even quasi-static shear slip can generate fault gouge, the fine pulverized rock within fault zone may form initially from single dynamic rupture of intact rock. To fully understand the generation mechanism of fault zones that contains a hierarchical damage structure, it is necessary to investigate the rupture behaviour of rock under single dynamic shear load.
For rock dynamic pulverization, research exploring dynamic fracture of geomaterial such as rock and concrete through single or multiple earthquake cycles has focused predominantly on transient compressive or tensile loading under confinements (Zhu et al. 2011; Liu et al. 2019, 2020a; Liu and Zhao 2021; Smith and Griffith 2022; Xie et al. 2021; Li et al. 2022; Hu et al. 2023). It has been well reported that the dynamic compressive/tensile strength of rock exhibit rate-dependency, i.e., rock strength increases dramatically with loading rate over a critical value (Doan and Billi 2011; Yuan et al. 2011; Han et al. 2023a, b). Doan and Gary (2009) found out that the microstructures of intact centimetre-scale crystalline rocks are similar to those seen in natural pulverized rocks, which could be reproduced by split Hopkinson pressure bar (SHPB) experiments, and the required strain rate is higher than 150 s−1. Yuan et al. (2011) presented that a compressive strain rate of 250 s−1 or higher would lead to the pulverizing centimetre-scale rocks, and confirmed that confining pressure could suppress significantly the transition of rock failure mode to pulverization. Aben et al. (2016) show that pre-existing rock damage can reduce significantly the strain rate required for pulverization (e.g., a 50% reduction) in the dynamic successive compressive loadings. However, attention should be paid on rock pulverization and shear band evolution due to high-rate shear loading, especially under the multiaxial static-stress, which is similar to stress environment in natural earthquakes or engineering blasting. The world’s first piece of true triaxial Hopkinson bar was developed for geomaterials under true triaxial confinement and dynamic loads (Liu et al. 2019). Xie et al. (2021) developed a dynamic true triaxial electromagnetic Hopkinson bar testing system and successfully achieved six-directional synchronous dynamic loading for the first time. Questions remain open with regard to critical shear strain-rate threshold, the effect of shear loading rate and pre-stress states on the shear strength and the generation of fine fragments/fault gouge.
To accurately determine these properties, we developed a new procedure of dynamic direct shear of intact crystalline rock under triaxially static stress state using a novel triaxial Hopkinson bar (Tri-HB). The fine fragments/gouge with different particle diameters formed within the shear band, where the damage is usually localized along macroscopic principal shear plane, are observed by Synchrotron micro X-ray computed tomography (μ-CT). The post-shear surface wore by friction is further observed by scanning electron microscopy (SEM).
2 Materials and Methods
2.1 Specimen Preparation
The granite for this study was extracted from the seismically active zone of Longmen Mountain within Sichuan province, China. The Longmenshan Fault, running from southwest to northeast along the eastern side of the Longmen Mountains, acts as a geological demarcation between the elevated Plateau of Tibet and the flat Sichuan Basin. The compressional forces resulting from Mw 7.9 Wenchuan earthquake of 2008 caused significant shearing of the ground in two locations along the fault, leading to a thrusting of the ground upward by approximately 9 m in in certain areas. To investigate the shearing behaviours of destructive earthquakes, cubic specimens with the size of 50 × 50 × 50 mm are polished to a surface roughness of less than 0.02 mm and tested for physical and mechanical properties following the standard method. The granite material has Young’s modulus E 48.2 GPa, density ρ 2650 kg/m3, Poisson’s ratio µ 0.26, compressive strength σc 139 MPa, tensile strength σt 7.26 MPa and compressive wave speed 4532 m/s (Liu and Zhao 2021). Petrographic analysis by thin section shows that the granite consists of quartz (45%), orthoclase (20%), biotite (15%), muscovite (10%), microcline (7%) and magnetite (3%). The grain size varies quite significantly between different minerals, with the quartz grains are between 400 and 800 μm, while orthoclase has grain sizes between 300 μm and as large as 1 mm.
2.2 Testing Method and Measurement Techniques
2.2.1 Dynamic Direct Shear Configuration
Dynamic direction shear tests were performed on a novel triaxial Hopkinson bar system (Fig. 1a) (Liu et al. 2019), which not only allows to apply normal prestress and tangential dynamic loads, but also to accurately measure the stress waves emitting from the shearing zone. The rock specimen is initially subjected to a desired triaxial pre-stress of (\({\sigma }_{x}, {\sigma }_{y}, {\sigma }_{z}\)), then the dynamic loading is applied from the impact of the striker bar accelerated to end of the incident bar. The triaxial Hopkinson bar system and operation procedure are detailed in the reference (Liu and Zhao 2021; Liu et al. 2019, 2020a, b). To prevent collisions between adjacent bars, the steel discs are designed with chamfers at a 45° angle. During shear deformation and post-shear sliding of rock specimen, the steel discs with chamfers ensure that there is no contact with the bars, preventing mutual interference of stress waves between each bar. Strain gauge signals are collected from Wheatstone bridge circuits and amplified by a dynamic strain meter (SDY-2107A), with the sampling rate of 10 MHz. A 15 × 1.5 mm (diameter × thickness) pulse shaper, made of red copper discs, is employed to produce a well-repeatability ramped incident wave without high-frequency oscillations and dispersion. Teflon films smeared with Molybdenum disulfide are inserted into each interface between the bars and testing specimen to minimize the friction.
The stress evolution of testing specimen during the dynamic triaxial direct-shear is shown in Fig. 1b. During the dynamic direct shearing, when the striker bar impacts the incident bar, a compressive pulse is generated and then it propagates towards the specimen. Upon reaching the interface between the incident bar and the specimen, a portion of the stress pulse travels through the specimen and then transmits into the transmission bar as a compression pulse, while the remaining portion is reflected back into the incident bar as a tension pulse. Besides, the normal stress also varies due to the shearing dilatancy effect, and the induced stress waves propagate into the confined output bars.
Based on the one-dimensional wave theory, along the shear zone in the specimen (Fig. 1c), the particle displacement and velocity are denoted as u(x, t) and v(x, t), respectively, thus the shear strain γ and particle velocity v can be calculated as:
The kinematic compatibility condition follows:
Assumed that the dynamic force equilibrium across the specimen can be achieved during the impact, data interpretation for dynamic shear strain rate \(\dot{\gamma }\left(t\right)\), shear strain \(\gamma (t)\), shear stress \(\tau \left(t\right)\) normal stress \({\sigma }_{n}\left(t\right)\), and normal strain \({\varepsilon }_{n}\left(t\right)\) are obtained by:
The dimensions (length L of shear zone and cross-sectional area A0) of the specimen and properties (cross-sectional area Ab, wave speed Cb, Young’s modulus E and density ρ) of the bars are collected before a SHPB shear test. The subscripts b and s correspond to the bar and the specimen, respectively. From the test data, transient strains εI(t), εR(t), εT(t), εy1(t), εy2(t), εz1(t) and εz2(t) are extracted from strain gauge from the X impact direction and Y/Z confined bars. Surface energy Us of dynamic triaxial test is provided in the previous paper (Liu and Zhao 2021). For details on the pre and post processing of the data, as well as the assumptions and requirements for a reliable test, one can refer to the supporting information (Liu et al. 2019).
During the impact, typical stress waves captured on the bars along X and Y directions are shown in Fig. 2a. Note that compression positive is used here. Using the red copper disk (15 mm in diameter and 1.5 mm in thickness) as the pulse shaper in this study, non-dispersive ramp incident wave σIn., reflected wave σRe., transmission wave σTr., output stress waves σy1, σy2, σz1 and σz2 are well captured during the impact, and all these signals have a good synchronicity and same duration, and they carry the fracturing enery as well as friction energy. The stress waves σz1 and σz2 are generated due to the influence of the Poisson’s effect. However, the stress waves σy1 and σy2 arise from Poisson’s effect, shear dilatancy and post-shear friction. With synchronized incident σIn., reflected σRe., transmission σTr., output stress waves σy1, σy2, σz1 and σz2 can be used for the calculation of volumetric strain and dissipative energy during the dynamic triaxial shearing process. Figure 2b shows the stress balance check in X direction, where we can see that the dynamic force equilibrium across the specimen can be obtained before the peaks. Along the impact direction, it is pointed out that transmission wave σTr. is more reliable for the determination of dynamic shear stress in rock/rock joint (Yuan et al. 2023). Once the dynamic stress balance has been achieved, based on Eq. (3−5), the dynamic shear stress-strain curve can be obtained. In addition, the normal stress-strain curve is calculated by Eqs. (6) and (7). These stress-strain relationships are shown in Fig. 2c. The dynamic shear modulus Es, normal modulus En are calculated by the elastic slope of the stress-strain curves, respectively.
Typical experimental data at the impact velocity of 16 m/s and pre-stress conditions (10, 10, 10) MPa: a Stress waves in impact X/Y directions (In.: incident wave, Re.: reflected wave, Tr.: transmitted wave); b Stress balance check in X direction; c Stress and strain histories of granite in X, Y and Z directions
2.2.2 In-situ Synchrotron X-ray Phase-Contrast Microtomography
Internal shear bands of rock after the dynamic shear were scanned by synchrontron micro X-ray computed tomography (μ-CT) at Australian Synchrotron’s Imaging and Medical beamline (IMBL) (Liu et al. 2020a). Rock scanning was operated at a monochromatic beam of 80 keV, an exposure time of 0.5 s and a specimen-detector distance of 50 cm. The specimen rotated at 360-degree angle about its central axis in 0.1 degree steps to acquire a voxel size of 18.1 × 18.1 × 18.1 μm3 for the accurate measurement of the shear band. Post-processing and reconstruction of μ-CT images were performed in the Avizo (Thermo Fisher Scientific, USA) software, as also detailed in the reference (Liu et al. 2020). The particle size of fault gouge/pulverization can be influenced by factors such as the types of rocks involved, the amount of friction and stress along the fault, and the duration and intensity of faulting events. Typically, fault gouge/pulverization is characterized by fine-grained particles. These particles can range from clay-sized (less than 2 μm) to larger fragments, including sand-sized particles. It may contain a mixture of minerals from the rocks adjacent to the fault. In this study, the granite is predominantly composed of 45% quartz and approximately 20% orthoclase, with grain diameters of 800 μm and 300-1000 μm, respectively. For the purposes of this study, fragments with sizes less than 1000 μm are classified as gouge. Accordingly, the thickness of the gouge layer and the surface area of shear fracture surface are calculated by the image reconstruction and segmentation algorithm.
2.2.3 Scanning Electron Microscope
Scanning electron microscope (SEM) was adopted to comprehensively examine the microscopic asperities damage and friction mechanism of post shear surfaces. The high-performance SEM (FEI Quanta 3D FEGSEM) at an accelerating voltage of 15 kV and the magnifications from 100 × to 3500 × are used for this fractographic study.
3 Results and Discussion
3.1 Critical Shear Strain-Rate for Fault Gouge
The pulverization threshold of strain rate, defined for single or succussive dynamic loading, is an important parameter for rock failure under dynamic compression or tensile loading (Aben et al. 2016; Doan and Gary 2009; Yuan et al. 2011). Using the triaxial Hopkinson techniques, here, we present the critical shear strain-rate of rock rupture under triaxial confinements, which will help come out the generation condition of shear band as well as the transition from dynamically fractured and pulverized.
Figure 3 presents typical strain rate histories of granite experienced with the pre-stress (10, 10, 10) MPa and shear strain rates \(\dot{\gamma }\) varying from 82 s−1 to 202 s−1, corresponds to impact velocity changing from 12 to 21 m/s. The shear strain rate \(\dot{\gamma }\) is calculated by Eq. (3). At the low shear strain rates \(\dot{\gamma }\) of 82 and 95 s−1, microscopic damage of granite is being pregnant with a shear band, the stored elastic energy will release after the peak loading, and therefore the strain rate drops gradually. No fragments are observed at this stage. The upward inflection point in the strain rate history curve represents the onset of dynamic fracturing, where the dynamic fracture toughness of rock reach its critical fracture toughness (\(K_{{\text{S}}} \, = \,K_{{{\text{IS}}}}\)). It can be found that the pulverization threshold of shear strain rate is about 125 s−1, below which granite deforms elastically and the dynamic fracturing toughness is below the critical fracture toughness required for crack initiation (\(K_{{\text{S}}} \,{\kern 1pt} < \,K_{{{\text{IS}}}}\)). Once the dynamic fracturing criterion is satisfied, crack initiates and propagates within the shear band, with a few amount of gouge. With increasing impact velocity to a high strain rate of 202 s−1, the rock shear catastrophically at a large slip velocity, resulting in a distinct gouge zone within the core of shear band.
3.2 Effects of Shear Loading Rate and Triaxial Pre-stress
The loading rate and principal pre-stress components (σ1, σ2, σ3) on dynamic shear strength of crystalline rock, and the dynamic shear stress–strain curves of granite obtained from triaxial Hopkinson bar test are shown in Fig. 4a. The granite deforms elastically and then fails once reaching its shear strength, resulting in shear cracking across the specimen. At the same triaxial pre-stress state of (10, 10, 10) MPa, the shear strength of granite increases from 80 to 112 MPa with increasing shear strain rate \(\dot{\gamma }\) from 82 to 202 s−1, i.e., strain rate dependency. Failure modes of shear zone change from damaged band to gouge zone with pervasive fragmentation, as will be confirmed by the μCT images. Besides, it is evident in Fig. 4b that dynamic shear strength of granite exhibits confinement dependence. Dynamic strength decreases distinctly with increasing axial pre-stress σ1 from 10 to 30 MPa along the shear direction, while it increases with the increase of lateral pre-stresses σ2. Micro-cracks inside specimens are reactivated by pre-stress σ1, which also brings a pre-shear stress in the shear band. However, the shear dilatancy and post-shear friction are suppressed by the lateral confining pre-stresses σ2, and thus results in the enhancement of shear strength. It seems that the dynamic shear strength is unsensitive to σ3 as it is parallel to the shear plane. The generation of earthquake gouge is a coupled effect of strain rate and normal geo-stress. The earthquakes could be driven by the interaction of high plate tectonics force and dynamic events, accompanied by the rapid shear rupture of rock subjected to in-situ stress. During the earthquake, gouge generates when the shear strain rate is over the threshold at the certain stress states.
We then show the evidence of fault gouge generated at high shear rate under the dynamic triaxial shearing. Figure 5 presents gouge and shear surface of granite under triaxial pre-stress condition of (30, 20, 10) MPa and impact velocity of 21 m/s (\(\dot{\gamma }\) = 202 s−1). The post-impact shear band within localized zone and infilled gouge powder (rock flour) were observed in the middle part of the tested granite, as shown in Fig. 5a. The gouge, which is incohesive and consists of small particles with the white colour, is observed distinctly within the shear zone. This gouge is formed by rapid mineral grain crushing or breakage with regards to high-speed friction and rapid-elevated temperature along with large amount of energy transformation, and shows variation in sizes (Fig. 5b). The gouge powder contains minerals (quartz or feldspar) that may metamorphically altered into those such as talc, depending upon orientation and magnitude of the shearing force. The coarse-quartz gouge exhibits some strain hardening and required considerable shear strain before the onset of steady-state sliding behaviour. Usually, the coefficient of friction increases with a higher proportion of the quartz and a decrease in the particle sizes of quartz. The thin shear band within the rock confirms the observation that the thickness of localized zone is a few millimetres at extreme conditions (tensile stresses approach 5 GPa, volumetric strain rates exceed 105 s−1) and explains the observations of the texture of gouge from the San Andreas fault-zone and from rupture zones in South African mines (Scuderi et al. 2014).
Gouge and shear surface of granite specimen under triaxial pre-stress condition of (30, 20, 10) MPa and impact velocity of 21 m/s (\(\dot{\gamma }\) = 202 s−1): a Shear band in the middle part of tested granite, b Pulverized gouge, c Shear band observed by synchrotron μ-CT, d, e Shear rupture zones in microscopic f Surfaces without friction and g Surface with friction
3.3 Microstructures of Shear Band
The tested granite is further imaged by synchrotron micro X-ray computed tomography (μ-CT), with a resolution of 18 μm, and the observations are shown in Fig. 5c–e. Note that the normal pre-stress σn was applied along the Y direction, and the dynamic shear stress τ was along the X impact direction. It is visualized that a macroscopic fracture network generated in the shear rupture zone, i.e., the main shear band with a certain thickness crossing the whole specimen. In the shear localized zone, gouge with sub-micron grain size that controls the frictional resistance are observed. Higher shearing rate results in a finer and more pulverized matrix of the gouge, which indicates that larger shearing events at nature fault zones tend to decrease the particle size of the fault gouge (Chester et al. 2005; Ma et al. 2006). Besides, it is clear in Fig. 5d, e that, around the main shear band, several sets of inclined en-echelon fractures generated with similar orientations to the shear direction, indicating the stress rotation during the shearing. This orientations of foliated fracture generally depends on the principal pre-stress components (σ1, σ2, σ3) and the shear rates. The angle of foliations to the shear direction increases with the σ2, but seems to be independent to σ3, which will help to identify the stress states of the natural rock faults. In addition, we found that the thickness of the shear localized zone rises with the lateral confinement σ2 and loading rate \(\dot{\gamma }\), which means that the higher the confining pressure and shear rates, the more pulverised gouge or catacaustic damage in the formation of shear rupture due to the larger amount and rate of energy release.
From the SEM imaging, we found that surface shear presents a relatively flat roughness with distinctive steps (Fig. 5f), which attributes to rapid penetration across the grains, i.e., trans-granular microcracking (through the grain). Here, the red arrow indicates the penetration direction and the shear cracks penetrate the grains with a high cracking velocity limiting Rayleigh wave velocity, which results in some typical micro-cracking features, such as micro-branches and surface steps. Generally, higher impact velocity induces higher shear crack velocity, which contributes to a flatter shear surface with less roughness. Fig. 5f shows the fracture surface that experienced dynamic friction, and it appears to be smoother compared to that without friction. We found that the surface steps were further damaged pervasively into small debris due to the dynamic friction wear of contact asperities, along with local shear pulverisation and temperature elevation. Unlike the granular fault gouge having particle sizes of 105–149 µm (Reches and Letters, 1999), the small debris found in this research, with particle size of less than 10 µm, filled into the gaps of steps and thus reduced friction coefficient in shearing process. These findings can well explain the formation of fault gouges that studied by previous studies (Reches and Dewers 2005; Wilson et al. 2005). It can be concluded that fine-gouges within the central parts of natural fault-zones result from the coupled effects of trans-granular microcracks and dynamic friction, which prevails in the high-speed shearing of stressed rock during the earthquake.
In our study, the dissipative energy of rock is calculated by the signals from three pairs of the bars, geometric surface area of shear fracture surface is determined by the reconstruction of μ-CT images, as presented in Fig. 5c. It is observed that the shear band is nearly 1 mm on the fractured specimen (Fig. 5a) and μ-CT reconstruction (Fig. 5c–e). Independently, the surface areas of specimens tested under different triaxially static-dynamic coupled loadings were measured, and it is revealed that the surface area values is as high as 0.00275 m3 with the energy amount of 355 J, which corresponds to a surface energy Us of 0.129 MJ/m2 for a 1 mm thick gouge zone (for a specific surface energy of quartz of 1-1.8 Jm−2). This value agrees well with some studies on the gouge formation mechanism in Bosman Fault, Punchbowl fault, San Andreas Fault and South African gold mines (Reches and Dewers 2005; Reches and Letters 1999; Wilson et al. 2005; Yuan et al. 2011). Our experiment results lead us to conclude that fine-fragments or gouge can be formed by earthquake processes that are dependent of stress deformation conditions associated with a fast shear crack propagating (i.e., shear strain rate \(\dot{\gamma }\) over the critical threshold of 125 s−1). The enhanced surface area resulting from mechanical grain size reduction in the gouge strongly facilitates chemical processes within the fault zone, such as hydrothermal activities and grain growth. These processes can significantly alter the mechanical evolution of the fault.
4 Conclusions
This paper proposes a new dynamic direct shear setup to investigate the dynamic shear behaviour of rock under various shear rates and confining pre-stress using a novel triaxial Hopkinson bar. The dynamic fracture behaviours (e.g., dynamic shear strength and shear band morphology) of rocks were characterised macroscopically and microscopically to explain the generation mechanism of fine fragments/fault gouge. The following conclusions could be drawn from the experiments:
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1.
The dynamic direct shear setup using triaxial Hopkinson bar is capable of recreating different pre-stress states on rocks and followed by applying specified dynamic loads, which allows precise determination of dynamic shear stress-strain of rock under different confinement conditions, including triaxial pre-stress states. During the impact, the real-time evolution of the shear stress τ(t) and normal stress σn(t) can be successfully captured under the high rate loading, which provides the significant information of energy release during high rate shear fracturing of rock.
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2.
Dynamic shear strength of rock exhibits both confinement and strain rate dependences. Under the same pre-stress condition, dynamic shear strength of granite increases substantially with the increase of impact velocity from 12 to 21 m/s, corresponding to shear strain rates of approximately 80–200 s−1, respectively. At the given impact velocity or shear strain rate, dynamic shear strength decreases distinctly with increasing axial pre-stress σ1 from 10 to 30 MPa along the shear direction, while it increases with the increase of lateral pre-stresses σ2.
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3.
Abundant fault gouge can be formed by earthquake processes that are dependent of stress deformation conditions associated with a fast shear crack propagating (i.e., shear strain rate over the critical threshold of 125 s−1).
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We thank the Australian Research Council (LE150100058) for supporting this research.
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Liu, K., Hu, W. & Zhao, J. Dynamic Pulverization of Rock Under Triaxial Static-Stress and High-Rate Shearing. Rock Mech Rock Eng 57, 4669–4678 (2024). https://doi.org/10.1007/s00603-024-03799-5
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DOI: https://doi.org/10.1007/s00603-024-03799-5