Deformation and failure characteristics of sandstone under uniaxial compression using distributed fiber optic strain sensing

Lingfn Zhng, Duoxing Yng, Zhonghui Chen, Aichun Liu

a Institute of Crustal Dynamics, China Earthquake Administration, Beijing,100085, China

b College of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing,100083, China

Keywords:Distributed fiber optic strain sensing(DFOSS)Uniaxial compression Strain localization

ABSTRACT This paper investigates the deformation and fracture propagation of sandstone specimen under uniaxial compression using the distributed fiber optic strain sensing (DFOSS) technology. It shows that the DFOSS-based circumferential strains are in agreement with the data monitored with the traditional strain gage. The DFOSS successfully scans the full-field view of axial and circumferential strains on the specimen surface. The spatiotemporal strain measurement based on DFOSS manifests crack closure and elastoplastic deformation, detects initialization of microcrack nucleation, and identifies strain localization within the specimen. The DFOSS well observes the effects of rock heterogeneity on rock deformation. The advantage of DFOSS-based strain acquisition includes the high spatiotemporal resolution of signals and the ability of full-surface strain scanning. The introduction to the DFOSS technology yields a better understanding of the rock damage process under uniaxial compression.

1. Introduction

Recently, due to the increasing imbalance between the tight supply of conventional energy(e.g.coal,oil and natural gas)and the rapid growth of total energy demand, exploitation of unconventional oil and gas resources (e.g. tight sandstone gas, shale oil and gas, and coalbed methane) has become a hot topic over the world(Li et al.,2016).However,subjected to insufficient understanding of rock mechanics and associated fracture propagation within in situ reservoirs, utilization of unconventional energy sources has severally challenged the development of rock mechanics(Hoek and Brown, 2019). It is well known that the hydro-fracturing remains most effective for enhancing oil or gas recovery. However, the effectiveness of hydro-fracturing mainly depends on the mechanical properties of reservoir rocks (e.g. sandstone). In conjunction with the spatiotemporal strain monitoring method(e.g.distributed strain acquisition), rock mechanics test is of significance to understand the fracture morphology and mechanical characteristics of reservoir rocks. The post-seismic strain diffusion along actively seismic faults has been numerically simulated (Viti, 2019) and validated using ground surface deformation obtained by interferometric synthetic aperture radar (InSAR). The co-seismic strain waves can be detected by the traditional borehole strain gage with the earth-tide signals observed (Liu et al., 2009). However, the InSAR can only monitor the ground surface deformation, and the borehole strain sensor merely detects strain signals for specific observation point. Within the earth faults, how to vertically and horizontally monitor the dynamic length or depth strain profiles is of great importance for understanding the strain wave propagation and diffusion.

With the development of rock mechanics, deformation and failure characteristics of natural rocks have been extensively investigated by means of theoretical analyses,laboratory tests and numerical simulations. A constitutive model of intact rocks has been proposed(Unteregger et al.,2015;Masoumi et al.,2016),and the failure criteria have been established for assessing rock failure behaviors (He et al., 2018; Zhou et al., 2019). Piezoelectric sensors have been used for monitoring acoustic emissions during rock deformation, and traditional strain gages have been adopted to determine the strain signals (Li et al., 2017; Hampton et al., 2018,2019; Wong and Xiong, 2018; Zhang et al., 2019a). Meanwhile,the digital image correlation (DIC) method has been developed to record the strains (Walter, 2011; Lin and Labuz, 2013; Mehdikhani et al., 2016; Munoz et al., 2016; Yao and Xia, 2019). Characteristics of rock damage have been numerically investigated using the rock failure process analysis (RFPA) method (Tang et al., 2000). The discontinuous deformation analysis (DDA) method (Sato et al.,2001) has been applied to numerically analyzing the effects of existing natural cracks on crack propagation.The accumulation and expansion law of rock mass fissures has been simulated with the discrete element method (Camones et al., 2013). Recently, an updated grain-based model(nGBM)has been proposed to examine the brittle failure of crystalline rocks(Zhou et al.,2019).To the best of the authors’ knowledge, by scanning the full-field view of axial and circumferential strains on the specimen surface, the deformation and failure of rocks remain poorly characterized in the laboratory test. For this, the distributed strain monitoring is of potential priority.However, the feasibility of the distributed strain sensing needs to be further evaluated and validated by laboratory and field tests.

Fig.1. Schematic of the monitoring principle of BOTDR (after Brown et al.,1999; Bao et al., 2001). Note that the scattered light has a frequency shift equal to a Brillouin shift, and travels opposite to the incident light.

The sensing technology based on the distributed fiber optics can accurately detect signals of strain, pressure, temperature and vibration(Sun et al.,2017;Fan et al.,2019).The distributed fiber optic sensor(DFOS)is suitable for in situ high pressure and temperature conditions, and it is electromagnetic-interference free and multiscale automobile (Sun et al., 2016), especially wavelengthencoded (Zhang et al., 2019b). In recent years, there have been a variety of geological engineering applications, such as strain and temperature monitoring in concrete and steel bridges(Gliˇsi′c et al.,2007,2011;He et al.,2013),composite structures(Murayama et al.,2003), embankments and dams (Zhu et al., 2011), landslide and slope stability assessment (Iten et al., 2011), heat transport (Read et al., 2013), underground excavations (Naruse et al., 2007; Moffat et al., 2015), pumping tests (Lei et al., 2019), and fault deformation(Yang et al.,2019).Using the DFOSs,laboratory tests have been performed for measuring extensional and shear deformations(Madjdabadi et al., 2016), detecting thermal breakthrough (de La Bernardie et al., 2018), and tracking carbon dioxide plumes (Fan et al., 2019; Zhang et al.,2019b).

For rock mechanics tests, the spatiotemporal measurement of strain remains a fundamental and essential procedure for analyzing rock damage mechanisms(Shen et al.,2020).This work focuses on the deformation and fracture propagation of a sandstone specimen under uniaxial compression using the distributed fiber optic strain sensing(DFOSS)technology.For this,a novel spatiotemporal strain monitoring method based on DFOSS has been developed to monitor axial and circumferential strains along the surface of a cylindrical rock specimen under uniaxial loading.In this study,the fiber optic sensors, corresponding to 301 circumferential strain measuring points on the specimen surface,and two built-in linear variable differential transformers (LVDTs) and MTS strain gage are utilized to measure strain-stress relationships. The DFOSS-based circumferential strains agree well with the data monitored with the traditional strain gage.The spatiotemporal strain measurement based on the DFOSS manifests the elasto-plastic deformation, and detects the initialization of microcrack nucleation (e.g. strain localization phenomenon) within the specimen. The fiber optic sensors wrapped over the specimen identify two-dimensional location of fracture propagation along the specimen surface. The DFOSS successfully scans the full-field view of the axial and circumferential strains on the specimen surface. The advantage of DFOSS-based strain monitoring includes high spatiotemporal resolution of signals, ability of full-surface strain scanning, and feasibility of detecting the strain localization.

2. Monitoring principle of the distributed fiber optic strain sensing (DFOSS)

As shown in Fig. 1, the Brillouin optical time-domain reflectometer (BOTDR) is generally used to detect the distributed fiber optic strain signals (Horiguchi et al.,1989; Brown et al.,1999; Sun et al., 2017). The Brillouin scattered light is attributed to the nonlinear interaction of the incident light to phonons excited in light-travelling media, and such scattered light has a frequency shift equal to a Brillouin shift and travels opposite to the incident light (Bao et al., 2001). A formula of frequency shift and acoustic velocity is given by Horiguchi et al. (1989):

where νBis the Brillouin frequency shift (BFS), n is the refractive index, Vais the acoustic velocity, and λ is the wavelength of light.The acoustic velocity is written as (Horiguchi et al.,1989):

where E is the Young’s modulus,ρ is the fiber density,and μ is the Poisson’s ratio. The BFS, νB, is associated with the strain (ε) and temperature(T) in the optical fiber:

where ν0is the Brillouin frequency at the initial reading at a given(T, ε) condition.

For the Brillouin scattering,the frequency shift caused by strain(0.002%°C-1)is larger than that caused by temperature(Song et al.,2017). For that reason, compared to the BFS in terms of strain change,the effect of temperature on the BFS is negligible,given that temperature variations remain within ±5°C (Sun et al., 2016).When strain exhibits in the longitudinal direction of an optical fiber, the Brillouin backscattered light receives a frequency shift,which is proportional to the strain(Horiguchi et al.,1989).The BFS as a function of strain takes the following form:

where νB(T0,0) is the original BFS. The strain coefficient, (Δnε+ΔEε+ Δμε+ Δρε), depends on optical properties of a fiber. Based on the mathematical principle between the BSF and strain (Bao et al., 2001), strain signals can be measured at each point along the optical fiber.

3. Experimental setup

3.1. Testing equipment

The uniaxial compression test is conducted using the MTS rock mechanics test system. A distributed fiber optic strain acquisition system is used to detect the strain signals. As shown in Fig. 2, an experimental setup mainly includes the servo-controlled hydraulic testing machine MTS 815 for the uniaxial loading, DFOSS monitoring and stress-strain monitoring instruments (Zhang et al.,2019b). The fiber strain monitoring instrument AV6419, which possesses high test accuracy and continuous acquisition capacity,is utilized for measuring the distributed strain signals (Sun et al.,2017). The BOTDR single-ended transmission mode is preferred in the process of data acquisition.The axial load and displacement are recorded with MTS Model 661.98C/D-03 and LVDTs, respectively.The lateral strain is recorded by the long strain gage of MTS Model 632.12E/F-20 (Zhang et al., 2019a). The optical strain sensor scans the full-field view of axial and circumferential strains on the specimen surface under uniaxial compression test. The MTS strain gage is located at the cylinder wall at the depth of 5 cm from the bottom of the specimen. This gage is used to record the circumferential strains. The optical strain sensors are glued at the specimen wall by a water-resistant coating.

Fig. 2. Schematic of uniaxial compression technique based on the servo-controlled hydraulic testing machine MTS 815. The distributed fiber optic sensors and strain gage are bonded upon a sandstone specimen.

3.2. Sample preparation

Following the standard recommended by the International Society for Rock Mechanics and Rock Engineering (ISRM) (Sun et al.,2016; Zhang et al., 2019a), a heterogeneous sandstone core is cut into the cylinder specimen with diameter of 50 mm and length of 100 mm,as shown in Fig.3b.The machining errors of sides and end faces are ±0.5 mm and ±0.02 mm, respectively. Although the machine interference and artificial faults are unavoidable in the process of sample preparation, these external errors can be neglected.The reason is that these factors will not have a significant impact on the test results(Feng et al., 2015).

3.3. Layout of distributed fiber optic sensors (DFOSs)

The physical properties and layout of fiber optic sensors directly affect the experimental results.Optical fibers selected in the test are sheathless strain sensing fibers with a diameter of 0.9 mm. The diameter of bare core is 0.25 mm. The G.652(B) fiber with the Brillouin reflectivity is used as the fiber core.A thin coating is used around the surface of the core,which can be well coupled with the measured specimen through the binder, and has high strain transfer performance (Zhang et al., 2019b). The optical fiber is strain-sensitive and flexible,and easy to be glued on the specimen surface. The sensor is laid out by means of the helical wrapping method. The modified acrylate adhesive is preferred to stick the fiber optic sensors to the specimen surface,as shown in Fig.3b.The binder can coagulate in a short time,which is conducive to the fast attachment of optical fibers. After coagulation of the binder, the deformation and fracture of the specimen will not be affected during the test. In the helical wrapping, the vertical distance between single loop lines is 1 cm,and nine circles of optical fibers are wrapped. The total length of the optical fiber is 5.18 m, while the effective length of the fiber adhering to the specimen is 1.5 m. For avoiding the influence of light scattering at the end of the fiber on the strain test,it is necessary to wrap two circles horizontally at the end of the rock specimen.After data acquisition,the signals of the effective part of the optical fiber are intercepted for the analysis.

Fig. 3. (a) Schematic of distributed fiber optic strain sensor mounted on sandstone specimen; and (b) The prepared sandstone specimen. Note that additional two spiral circles are bonded at the end of the specimen, in order to avoid the influence of the light scattering at the end of the fiber on the strain signals.

3.4. Test process

In the uniaxial compression test, the fiber optic strain instrument AV6419, the circumferential strain gage and the LVDTs are installed. At the beginning of the loading, the BOTDR instrument(AV6419)continues to record the Brillouin scattered lights.The MTS strain gage and the optical strain sensors simultaneously record the strains.During the loading process,the specimen is pre-loaded,and the axial strain of the specimen rapidly increases to 400 με from 0 με. In the test, the axial displacement is used to control the continuous loading. The loading rate is kept at 10-4mm/s. The whole loading process lasts for 100 min,and the entire deformation and failure evolution of the specimen is observed. The circumferential strain gage and LVDTs are utilized for monitoring the circumferential and axial strains, respectively. At the beginning of loading, the strain along the cylindrical surface of the specimen is measured with the optical strain sensors. The monitoring stops until the end of loading. The strain measurement has been performed for 85 times, and the sampling space-resolution is set to 5 mm. Totally 301 measuring points are set uniformly along the cylindrical surface of the specimen.

Fig. 4 illustrates three primary stages of the uniaxial compression test with optical strain sensors spirally bonded.A single-mode optical fiber is spirally pasted with an epoxy adhesive coating(Zhang et al., 2019b) along the cylindrical specimen surface. The sensor not only monitors the strain, but also detects the initialization of microcrack nucleation (e.g. strain localization). After initial compression,the specimen undergoes remarkable dilatation,followed by the occurrence of microcracks (Fig. 4b). When a peak stress is reached, the primary fractures within the specimen are well developed due to the plastic deformation. Adjacent to the main fractures along the specimen surface, the optical fiber is extensionally broken(Fig.4c),indicating the microcrack nucleation or strain localization.

4. Results

4.1. Stress-strain relationship

Fig. 5 shows the stress-strain profile of the specimen under uniaxial compression, which includes initial compression stage,elastic deformation stage, plastic deformation stage, and final failure stage. When the circumferential and volumetric strains increase, a remarkable dilatation phenomenon occurs. Prior to the peak strength, the rock deformation is dominated by contraction,while the circumferential expansion governs the formation of microcracks. The uniaxial compressive strength is 40.53 MPa, the elastic modulus is 9.768 GPa, and the Poisson’s ratio is 0.24. The closure of original cracks is attributed to the existing crack density and geometry of the sandstone at the initial stage. It is observed from Fig. 5 that the crack volumetric strain slowly increases, indicating the closure of the original cracks, and it keeps stable gradually for a short period of time. The crack closure threshold is estimated by the constant crack volumetric strain.When the crack volumetric strain is decreased, the cracks in the specimen experience dilation process. The total volumetric strain, εV, is defined as

Volumetric strain, εV, mainly includes two parts. One is caused by the closure of primary cracks in the specimen or the opening and propagation of new cracks under loading. The other is due to the elastic deformation (Shen et al., 2020). The elastic volumetric strain, εeV, is determined based on the generalized Hook theorem(Martin,1993):

Fig. 4. Schematic of the uniaxial compression, strain sensor data processing, and fracture propagation: (a) Spirally bonded optical strain sensors uniformly along the cylindrical surface of the specimen; (b) Microcracks well developed; and (c) Failure stage of the specimen in the loading process. ε1 and ε3 denote the axial and circumferential strains,respectively.

Fig.5. Stress-strain relationship obtained from the uniaxial compression test on the specimen.Both axial and circumferential strains are monitored with the LVDTs and MTS gage,while the total volumetric strain and the crack volumetric strain are derived from Eqs. (5) and (7), respectively.

where σ1and σ3are the axial and circumferential stresses under triaxial compression,respectively.The crack volumetric strain,εcV,is written by Martin (1993):

Prior to the peak strength, the total volumetric strain increases and then gradually decreases. At the post-peak strength stage, the rock deformation is dominated by dilatation.The variation of crack volumetric strain synchronizes with the total volumetric strain.Once the crack initiation threshold is reached, crack volumetric strain decreases,implying the generation of cracks in the specimen.

4.2. Strain monitoring with optical strain sensors

Considering the limited sensor measurement capacity of strain(Li et al., 2017), the spinal bonding of fiber optic sensors on the specimen is utilized, as shown in Fig. 6. A relationship (Martin,1993; Rambow et al., 2010; Li, 2016; Zhang et al., 2019b) is formulated between the strain on the sensor, εf, and the circumferential strain, εc, when the specimen experiences the radial expansion:

where θ is the wrapping angle.In this study,μ=0.24 and θ=3.6°are adopted, resulting in following relation:

Under uniaxial compression, the fiber optic sensor mainly measures the circumferential strain. For minimizing the bending loss of the light signals, the minimum approved bending radius is set to 5 mm (Zhang et al., 2019b).

4.2.1. Validation of radial strains measured by fiber optic sensors

Fig. 6. Schematic of helical attachment of the fiber optic sensors to the specimen. A single-mode optical fiber is spirally glued at the cylindrical specimen.

Fig. 7 shows the pre-peak radial strain-time profile, which is measured by the fiber optic sensors, for the spiral adjacent to the strain gage (MTS gage). Here, the circumferential strain measured with the fiber optic sensors is the calculated average value of strains monitored along the fiber spiral length ranging from 1.17 m to 1.32 m, which is located near the strain gage. The circumferential strains measured by fiber optic sensors generally agree with the data monitored with the traditional strain gage. We note that the fiber optic sensors and the MTS gage are situated in different spiral lines on the specimen surface, and then the relative error is estimated.The deformation process is well captured by the fiber optic sensors, compared to the phenomenon detected with the MTS gage. The fiber optic sensor effectively monitors the effects of the rock heterogeneity on the strain distribution on the specimen surface. Due to the fiber breakage, when the peak strength is reached, the strain signals at the post-peak stage cannot be monitored by the fiber optic sensor.Such phenomenon well reflects the onset time of the main fracture or the strain localization in the specimen.

4.2.2. Strain analysis of the specimen

Fig.8a shows the variations of circumferential strains with time.The circumferential strain on the specimen surface increases in the whole loading process.After reaching the peak strength,the strain at each measuring point vanishes, which is caused by fiber breakage. According to the temporal variation of circumferential strain, the deformation and failure of the specimen are separated into following four stages. At the crack closure stage, the strain signals vary from-500 με to 500 με,during which the compression and dilatation are entangled as a concentrated belt distribution.The belt distribution diverges into two separated zones due to elastic deformation. The divergence is enhanced in the period of plastic deformation stage,where the deformation is dominated by dilatation.At the elastic and plastic deformation stages,the upperbelt zone represents the top of the specimen corresponding to the fiber length of 0.5-0.65 m. At the onset of the failure stage, the strain regularly oscillates in the down-belt zone, ranging between -1000 με and 3000 με. The initiation of the specimen failure can be observed from the strain-time profile. The abovementioned mechanical phenomena are related to rupture bifurcation across an anisotropic fracture surface (Ando et al., 2010),second slip (Rubin, 2011) along an early ruptured surface, and capacity expansion (Shen et al., 2020).

Fig. 8b depicts the temporal variations of the circumferential strains along the fiber optic sensors. As the loading time increases, the dilatation-dominated deformation is gradually enhanced. The strain-time profiles clearly and effectively interpret the stages of the crack closure, the elastic and plastic deformation, and the failure onset. The transition is from the elastic to plastic stage and up to the onset of the failure. At the top of the specimen, the circumferential strain changes slightly during the loading period, due to the end friction between the top of the specimen and the testing machine (Shen et al., 2020).Therefore, the top of the specimen keeps relatively complete.Before the failure occurrence at 5250 s, the top of the specimen exhibits the compression state, indicating the shrinkage at the top of the rock prior to failure. The strong circumferential expansion appears along the fiber length of 1-1.5 m during the loading period.

Fig. 9 shows the spatiotemporal tomography of the circumferential strain, which clearly characterizes the deformation and failure processes of the specimen under uniaxial compression:

(1) Stage I: The crack closure stage is mainly attributed to the gradual closure of original cracks under uniaxial loading.The circumferential strain generally keeps constant, and the spatiotemporal strain distribution appears homogeneous,as shown in Fig. 9a. The circumferential strain ranges from-240 με to 605 με.

Fig.7. Pre-peak radial strain-time profiles monitored with the fiber optic sensors and MTS strain gage in the middle of the specimen along the cylindrical axis.The inset shows the relative error analysis. It is noted that the fiber optic sensors and the MTS gage are situated in different spiral lines on the specimen surface.

Fig. 8. (a) Circumferential strain-time profile, which clearly interprets the stages of the crack closure, the elastic and plastic deformation, and onset of failure; and (b) Circumferential strain-space profile, which effectively indicates the transition from the elastic to plastic stage and up to the onset of failure. We note that after the optical fiber was damaged by fracturing, the main crack did not break throughout the top of the specimen.

(2) Stage II:After the specimen exhibits elastic deformation,the circumferential strain is remarkably enhanced, and the spatiotemporal strain distribution appears heterogeneous.As can be seen from Fig. 5, the peak of the total volumetric strain is reached, once the crack damage threshold is satisfied,while the crack volumetric strain keeps constant.It is shown from Fig. 9a that the strain variations in region 1 remain insignificant, due to the end friction effect (Shen et al., 2020). However, the strain variations in regions 2-4 are significant. Fig. 9b shows that the strain in region 3 is larger than that in regions 2 and 4 at the end of the elastic deformation stage, indicating the onset of the strain localization in the upper-middle part of the specimen prior to irreversible deformation. The deformation in region 3 is accelerated.

Fig. 9. (a) Spatiotemporal tomography of the circumferential strain prior to the peak strength. The upper inset represents the loading process. The right inset shows the lengthstrain profiles corresponding to the end of the crack closure stage(T1),the end of the elastic deformation stage(T2),and the onset of the failure stage(T3),respectively.The bottom inset depicts the strain-time profiles denoting the transition of the adjacent two zones (e.g. A1, A2 and A3). (b) Spatiotemporal tomography at the time of 4200 s and 5180 s. (c)Contour of strain with various spatiotemporal values prior to the peak strength. The deformation stage is clearly identified as the original crack closure, the elastic and plastic deformation as well as the onset of failure. The strain acceleration and localization is effectively detected with the fiber optic sensor. The scale bar denotes the value of the circumferential strain (×10-6).

(3) Stage III:Plastic deformation stage is irreversible,with cracks being followed by nucleation(Zhang et al.,2019a).As shown in Fig.9a and c,the circumferential deformation is enhanced by microcracking and porosity enhancement (Violay et al.,2015;Yang et al.,2018).The crack volumetric and bulk strains are decreased during the plastic deformation (Fig. 6). The circumferential strain of the specimen mainly varies from-1085 με to -2775 με except for region 1. The zone of the strain localization significantly shrinks,compared to that at the elastic stage. This phenomenon implies that when irreversible deformation occurs, the strain localization region gradually decreases, and the fracture or nucleation appears. The specimen deformation is mainly governed by fracturing and frictional sliding (Behr et al., 2018).

(4) Stage IV:Failure stage.It is observed from Fig.9a-c that the circumferential strain in regions 2-4 is sharply increased prior to failure. Meanwhile, the compression (e.g. shrinkage phenomenon)becomes elevated in region 1.The peaks of the circumferential strain correspond to the spatial points along the failure distributions. The spatiotemporal strain distribution exhibits strong heterogeneity,as can be seen in Fig.9c.In the failure process, the optical fiber is broken due to large circumferential deformation of the specimen.The time of the strain signal elimination and the location of the fiber brokenpoint can denote the onset and location of the fracture,respectively. The strain localization causes the macrocrack growth, and finally results in the rock failure (Bhandari and Inoue, 2005; Hao et al., 2010; Mao et al., 2015; Munoz et al., 2016).

5. Concluding remarks

In this study, the deformation and failure characteristics are investigated for sandstone cylindrical specimen under uniaxial compression, by means of DFOSS. A single-mode optical fiber is spirally pasted by an epoxy adhesive coating on the cylindrical specimen surface. The DFOSS scans the full-field view of axial and circumferential strains on the specimen surface. The DFOSS-based circumferential strains generally agree with the data recorded with the MTS built-in strain gage (MTS gage).

The spatiotemporal tomography of circumferential strains can effectively detect the crack closure, the elastic and plastic deformation,and the failure onset.Meanwhile,the strain localization is clearly identified. Due to the fiber breakage at the peak strength,strain signals at the post-peak stage cannot be recorded by the fiber optic sensor.Such phenomena may well reflect the onset time and spatial position of the main fracture or nucleation in the specimen.The applications described herein demonstrate the effectiveness of the DFOSS used in rock mechanics test. The DFOSS-based strain signals can potentially provide identification of hydro-fractured formations in shale gas, geothermal formations, seismically active faults and oil reservoirs.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interests associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The support from the Institute of Crustal Dynamics, China Earthquake Administration(Grant No.ZDJ2016-20 and ZDJ2019-15)is greatly acknowledged. We also thank the anonymous reviewers for their valuable comments and suggestions to improve this manuscript.