Deformation and Damage Characteristics of Deep Rock Specimens Based on 3D-DIC and FBG

Chang Liu; Duoxi Yao; Pingsong Zhang; Yuanchao Ou; Jiajian Lin; Yutong Tian; Xiaoding Xu

doi:10.2113/2022/4329713

Abstract

Specimen-scale testing of loaded rock parameters is an important research component of rock mechanics testing. In this paper, a method combining 3D-DIC and FBG (fiber Bragg grating) technology is proposed and applied to the study of deformation and damage characteristics of deep limestone and sandstone specimens under uniaxial loading conditions in the Panxie mine area of Huainan coalfield. The selection of optical fiber, the bonding method, and the process of rock specimen fabrication are introduced in detail. Two different fiber Bragg grating sensor arrays were constructed by using both multi-inclination type and orthogonal type deployment of fiber grating to dynamically monitor the strain response of rock specimens throughout the whole process. The results show that both 3D-DIC displacement monitoring and fiber Bragg grating strain captured the rock deformation and failure process well with identical outcomes. Under a continuous load of 0.3 kN/s, the local cracks of the rock specimen and the damage to the rock specimen resulted in different degrees of sudden changes in the fiber strain value. According to the differences in the degrees of brittleness and texture densities of the rock specimens, the local cracks evolution to transfixion of the limestone registered a certain time accumulation and produced more local cracks, while the sandstone at the same stage produced fewer local cracks within a shorter duration. The effective combination of regional noncontact testing and high-precision point contact can dynamically and accurately capture the rock deformation and damage characteristics at the specimen scale. In addition, the combined monitoring method of 3D-DIC and fiber grating can provide assistance in the prediction of rock crack expansion and potential fracture surfaces.

1. Introduction

As the dominant energy source in China, coal plays an important role in primary energy generation [1]. After decades of mining, the mining depth of the Panxie Mine in Huainan coalfield is gradually increasing. Insufficient understanding of rock mechanical properties and fracture expansion, which is a disaster-causing mechanism of deep surrounding rocks, seriously restricts the safe and efficient production of coal. Obtaining the parametric evolution of rock specimens under load is important for understanding the mechanical properties of rocks and structural health testing of geotechnical bodies. With the development of rock mechanics tests, more and more test methods are applied to rock testing. Yang et al. [2] used self-potential to dynamically characterize the deformation and failure process of coal samples under uniaxial loading. Ou et al. [3] used electrical parameters to characterize the process of rock deformation and failure. Gao and Wang [4] used acoustic emission to quantitatively describe the evolution process of rock damage. Li et al. [5] used a combination of ultrasonic and acoustic emission (AE) methods to measure the deformation of salt rocks under uniaxial loading conditions and divided the fracture evolution of salt rocks into four stages based on the change in covariance. Yin and Xu [6] used electrical impedance spectroscopy (EIS) to obtain the resistivity of sandstone under different loading conditions, on the basis of how the damage variables of sandstone were defined. Wang et al. [7] applied an equal amplitude cyclic load to sandstone specimen and simultaneously performed acoustic emission (AE) and resistivity parameter acquisition to establish a rock damage evolution model by combining the two parameters. In microscopic testing, Liu and Xu [8] used Hopkins rod to provide impact load to marble and analyzed the fracture morphology using a scanning electron microscope (SEM). Li et al. [9] conducted both uniaxial and triaxial compression tests as well as real-time CT scan tests on anthracite specimens, and the results confirmed that ash value, fracture volume, and CT porosity can be used as quantitative damage variables to evaluate the damage evolution of coal rocks.

Digital image correlation (DIC) is a noncontact optical digital technique for material deformation measurement [10], which was first proposed by Yamaguchi in the 1980s [11]. The 2D-DIC technique, however, cannot measure off-surface displacement, and the camera optical axis needs to be perpendicular to the object’s surface, which limits its application. With the development of digital image algorithms, three-dimensional-DIC (3D-DIC) was proposed in the late 20th century and developed rapidly. 3D-DIC can be used for surface displacement testing and to obtain interhole displacement and strain information for three-dimensional bodies. It is gradually being applied to rock mechanics testing [12]. Sharafisafa and Shen [13] used the digital image correlation (DIC) technique to determine the type, sprouting, expansion path, and merging types of new cracks in defective disc specimens. Peng et al. [14] conducted uniaxial compression tests on rock specimens containing prefabricated cracks and used 3D-DIC techniques to obtain strain field evolution maps of the damage process of the specimens. Li et al. [15] tested the deformation, damage, and fracture characteristics of granite specimens based on the three-dimensional digital image correlation (3D-DIC) technique. Shi et al. [16] conducted a study of concrete deformation and damage using the same technology.

In recent years, optical fiber sensing technology has developed rapidly. As a means for contact and high-precision testing, optical fiber sensing technology is now frequently used in rock mechanics testing. Sun et al. [17] used a multichannel fiber Bragg grating sensor array to monitor the strain change of sandstone specimens. Fan et al. [18] applied fiber grating to shale surface strain testing, and the results showed that the fiber grating test results were better than the cross-strain flower. Zhang et al. [19] used distributed optical fiber sensing technology to study the deformation and crack extension of rock specimens under uniaxial compression conditions and achieved an axial and circumferential strain changes on the specimen surface. Lin et al. [20] adopted a new distributed optical fiber installation method on the surface of rock samples, and the uniaxial loading tests on aluminum alloy, sandstone, and granite samples confirmed the ability of the method to measure the full-field strain distribution of rock specimens. Liu et al. [21] wrapped distributed optical fiber around the surface of a rock sample and categorized the damage process into four stages according to the strain test results. A test on rock uniaxial compression by Isah and Mohamad [22] using bare fiber and encapsulated fiber, respectively, showed that bare fiber was more sensitive than encapsulated fiber. However, encapsulated fiber was found to be more conducive to the test of coordinated deformation of materials. The high accuracy of fiber Bragg grating determines its suitability for testing small deformations in rock, and the reasonable packaging can make it more widely used. Compared with distributed optical fiber, fiber Bragg grating has the advantage in acquisition frequency. This can help achieve medium and high-frequency acquisition, which is advantageous to capture the change of coal rock rupture moment.

In rock mechanics testing, deformation is an important parameter, which plays a key role in understanding the deformation and failure mechanism of rock specimens. Traditional deformation testing methods, such as the plate displacement method [23], strain gauge method [24], and extensometer method [25], cannot test the regional deformation of rock specimens. 3D-DIC technology on the other hand can be applied in testing the regional deformation of rock specimens. At the same time, when combined with the light Bragg grating array, the difficulty in observing small cracks if only 3D-DIC is used is resolved, whilst the multiparameter, dynamic, and accurate monitoring of the specimen is realized. To summarize the existing literature, there are few studies on the characterization of damage evolution parameters of rock specimens based on both DIC and fiber grating. In this paper, two methods, 3D-DIC and fiber Bragg grating, were used to jointly characterize the damage evolution of rock specimens by regional displacement clouds and grid point strains under uniaxial loading conditions.

2. Overview of the Study Area

The study area is located in the Panxie mining area of the Huainan coalfield in eastern China. The Huainan coalfield is located at the junction of the Jianghuai Hills and the Yellow Huaihai Plain, with the characteristics of both plains and hills. The Huaihe River and its tributaries from the west (north) and east (south) run through the mining area along low-lying valley plains. To the north of the Huaihe River is part of the Yellow Huaihai Plain, with an altitude mostly between 21 and 26 m. The landscape is characterized by large flats and small unevenness. South of the river is the northern edge of the Jianghuai Hills, with an elevation of 25–241 m. The landform is between hills and posts. The main mining area in the Panxie minefield is the group A coal seam with a burial depth greater than 1000 m. Figure 1 shows the location, core, and borehole histogram of the study area. Core samples were extracted from the coring borehole. The water damage problems faced by coal seam mining mainly come from sandstone water on the overburden and limestone water of the coal floor. The rock mechanics properties and disaster-causing mechanism of sandstone and limestone of the overburden and the coal floor of group A of the study area are however not clear.

3. Principle of Testing Technology

3.1. 3D-DIC

3D-DIC technology is based on the principle of binocular stereo vision and image scatter matching technology (as shown in Figure 2), in which a region of interest (ROI) is captured by two cameras from different angles, and the 3D position of the ROI is reconstructed and tracked over time using stereo triangulation [26]. To achieve this, the reference coordinate system is first transformed into the camera coordinate system by means of external camera parameters as shown in Equation ().

\begin{matrix} (1) & [\begin{matrix} X_{2} \\ Y_{2} \\ Z_{2} \end{matrix}] = [\begin{matrix} R_{11} & R_{12} & R_{13} \\ R_{21} & R_{22} & R_{23} \\ R_{31} & R_{32} & R_{33} \end{matrix}] [\begin{matrix} X_{1} \\ Y_{1} \\ Z_{1} \end{matrix}] + [\begin{matrix} T_{x} \\ T_{y} \\ T_{z} \end{matrix}], \end{matrix}

where

R_{i j} (i, j = 1, 2, 3)

is the rotation matrix tensor, and

T_{x}

⁠,

T_{y}

⁠, and

T_{z}

are translation vectors. The camera coordinate system is thereafter transformed into graphic physical coordinate system using Equation ().

\begin{matrix} (2) & x_{3} = \frac{X_{2}}{Z_{2}}, y_{3} = \frac{Y_{2}}{Z_{2}} . \end{matrix}

Then the graphic physical coordinate system is transformed into pixel coordinate system as shown in Equation ().

\begin{matrix} (3) & [\begin{matrix} x_{4} \\ y_{4} \\ 1 \end{matrix}] = [\begin{matrix} f_{x} & s & c_{x} \\ 0 & f_{y} & c_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{3} \\ y_{3} \\ 1 \end{matrix}], \end{matrix}

where

f_{x}

and

f_{y}

are the focal lengths,

c_{x}

and

c_{y}

are the pixel coordinates of the principal point of the imaging plane, and

s

is the tilt factor. This time is taken

s = 0

which can be derived from Equations ()–().

\begin{matrix} (4) & x_{4} = f_{x} \frac{R_{11} X_{1} + R_{12} Y_{1} + R_{13} Z_{1} + T_{x}}{R_{31} X_{1} + R_{32} Y_{1} + R_{33} Z_{1} + T_{z}} + c_{x}, \\ (5) & y_{4} = f_{x} \frac{R_{21} X_{1} + R_{22} Y_{1} + R_{23} Z_{1} + T_{y}}{R_{31} X_{1} + R_{32} Y_{1} + R_{33} Z_{1} + T_{z}} + c_{y} . \end{matrix}

During the imaging process, due to the accuracy of the lens, some distortions in the image are produced, and the actual image coordinates deviate from the image pixel coordinate system. Equation Equation () can be replaced by the postdistortion coordinates [10].

\begin{matrix} (6) & [\begin{matrix} x_{5} \\ y_{5} \end{matrix}] = [1 + k_{1} r^{2} + k^{2} r^{4} + k_{3} r^{6}] [\begin{matrix} x_{3} \\ y_{3} \end{matrix}] + [\begin{matrix} 2 p_{1} x_{3} y_{3} + p_{2} (r^{2} + 2 x_{3}^{2}) \\ p_{1} (r^{2} + 2 y_{3}^{2}) + 2 p_{2} x_{3} y_{3} \end{matrix}] . \end{matrix}

In Equation (6), $r^{2} = x_{3}^{2} + y_{3}^{2}$ ⁠, $k_{i} (i = 1, 2, 3)$ ⁠, is the lens radial distortion coefficient, $p_{1}$ and $p_{2}$ are the lens tangential distortion coefficients.

3.2. Fiber Bragg Grating

Fiber Bragg grating is generally considered to be the most effective testing technique for strain, temperature, and vibration to capture the deformation of coal rock specimens and detect the location of regional cracks. When a beam of broadband light propagates to the grid area along with the optical fiber, it will reflect a light wave of a specific wavelength (as shown in Figure 3). The wavelength of the light wave (called Bragg wavelength) follows Equation (). The variation of reflection wavelength of fiber Bragg grating with strain and temperature can be expressed by Equation () [27, 28].

\begin{matrix} (7) & λ_{B} = 2 n ʌ, \\ (8) & \frac{∆ λ_{B}}{λ_{0}} = (1 - P_{ε}) ε + (α_{ʌ} + α_{n}) ∆ T . \end{matrix}

In Equations () and (),

λ_{B}

is the Bragg wavelength,

n

is the effective refractive index,

ʌ

is the length of each small grating interval,

∆ λ_{B}

is the change of Bragg wavelength,

λ_{0}

is the initial Bragg wavelength,

P_{ε}

is the strain optical sensitivity coefficient,

ε

is the strain,

α_{ʌ}

is the coefficient of thermal expansion,

α_{n}

is the temperature optical sensitivity coefficient, and

∆ T

is the change of external temperature. Under indoor loading, the change of temperature is generally very small. At this time, the influence of temperature on the grating can be ignored. Based on this, the coupling relationship between the variation of reflection wavelength and strain under axial stress is expressed using Equation ().

\begin{matrix} (9) & \frac{∆ λ_{B}}{λ_{0}} = (1 - P_{ε}) ε, \\ (10) & P_{ε} = \frac{1}{2} n^{2} [P_{12} - (P_{11} + P_{12}) μ] . \end{matrix}

In Equation (10), $μ$ is Poisson’s ratio, and $P_{11} and P_{12}$ are the photoelastic coefficient. In general, the $P_{ε}$ variation is small, and the Bragg grating center wavelength variation is only related to the strain; so, it can be used for deformation testing of rock specimens.

4. Experimental Setup

4.1. Testing Equipment

Rock uniaxial loading test was conducted using the MTS 816 instrument, which is widely recognized both at home and abroad [29]. The composition of the test system (as shown in Figure 4) includes loading device, 3D-DIC cameras, fiber grating, multichannel fiber grating demodulator, patch cable, lighting device, and tripod and computer. The camera resolution of the 3D-DIC test system is $5 million \times 2$ ⁠, with a 3D strain test accuracy of ≤20 με, laser ranging from 0 to 10 m, and laser ranging accuracy of ±1 mm. The fiber grating demodulator contains 16 optical channels, which can achieve intermediate frequency demodulation from 1 Hz to 100 Hz. The acquisition wavelength range is 40/60/80 nm, the wavelength resolution is 1 pm, the dynamic range is 50 dB, and the optical interface type is FC/APC. In this test, a uniaxial loading method of 0.3 kN/s was adopted. Before the test, the rock sample was preloaded with a small force value, and then the instrument panel of MTS 816 was cleared. During the loading process, the 3D-DIC camera and fiber grating demodulator were collected in real-time synchronously. The loading is stopped until the rock specimen is completely destroyed.

4.2. Rock Specimen Making and Sensor Arrangement

In this experiment, fiber Bragg gratings are arranged in two ways, that is, multi-inclination type and orthogonal type. The multi-inclination type is to glue multiple fiber Bragg gratings on the surface of the rock specimen, which has different angles with the horizontal direction, as shown in Figure 5(a). The orthogonal type is an orthogonal Bragg grating with multiple fibers glued to the surface of the rock specimen in the axial and circumferential directions, with the angle between the two intersecting fibers being 90°, as shown in Figure 5(b). The length of the grating area in both axial and circumferential directions is 10 mm, and the midpoints of the two grating areas in the axial direction are 60 mm apart, whilst those of the two adjacent grating areas in the circumferential direction are 52 mm apart. After the fiber is completely bonded to the specimen, the scattered spots of the specimen are made. The displacement or deformation of the surface of the rock sample is obtained by calculating the displacement of the scattered spot through the computer after the scattered spot is made on the surface of the rock sample and photographed several times with the cameras.

4.3. Test Process

The test process followed the standards recommended by the International Society of Rock Mechanics and Rock Engineering (ISRM) [30]. A standard rock sample with dimensions of $50 mm \times 100 mm$ (diameter × height), and machining errors of ±0.5 mm and ±0.02 mm for the side and end surfaces, respectively, was used. After the rock sample was placed and the camera position was adjusted, the 3D-DIC and fiber grating background values were collected. The rock specimen was preloaded with the MTS indenter in contact with the upper surface of the rock sample, resulting in a sudden change in the data, followed by a steady increase in the load. During the test, the data acquisition interval was 2 s for 3D-DIC and 0.5 s for fiber grating.

5. Results

5.1. Multi-Inclination Type Test Results

The test limestone specimen was taken from the coal floor. Four two-point fiber optic gratings were glued to the surface of the rock specimen in a multi-inclination type, with the four fibers intersecting at one point at angles of 0°, 30°, 60°, and 90° in the horizontal direction, respectively. The locations of the eight fiber grating monitoring points on the surface of the rock sample are shown in Figure 6. The limestone specimen was analyzed compositionally and by scanning electron microscope (SEM). The main constituent elements of the rock sample were O (48.79%), Ca (34.38%), and C (14.59%). After observing a fresh section of the sample under low magnification, the main mineral found was calcite containing a small amount of quartz. Figure 7 shows two local scanning electron micrographs of the limestone specimen with developed internal pores, of which the bright white mineral in Figure 7(a) is pyrite.

5.1.1. 3D-DIC Results

The image acquisition of the loaded limestone specimen was performed using the 3D-DIC technique, and the displacement clouds in different directions in the observation area were obtained as shown in Figure 8. The color code of the displacement values and the numerical abundance are shown on the right side of each cloud image. This loading lasted 754 s, and the rock reached its peak strength in 752 s. Figure 8(a) shows the $x$ -direction displacement cloud diagram of the entire observation area of the limestone, when $T = 482 s$ ⁠, the specimen is in the uniform deformation stage, and there is no increase of local displacement. When $T = 612 s$ ⁠, it can be seen from the $x$ -direction cloud diagram that the upper and lower parts of the specimen observation area show larger changes, and the surface deformation no longer shows a regular change, which is a sign of the appearance of rock microfractures. From the results, the rock specimen entered the stage of local microfracture evolution and transfixion. When $T = 722 s$ ⁠, the $x$ -directional displacement field aggregated at the lower part and both sides of the specimen observation area resulting in the sprouting and accumulation of local microcracks which led to obvious local deformation in these areas. When $T = 752 s$ ⁠, the $x$ -directional displacement field aggregated at both sides of the specimen observation area, and the displacement value further increased, which is a sign of crack transfixion from here, and the specimen was in the process of exceeding the bearing limit. When $T = 754 s$ ⁠, the peak strength was reached with the fracturing of the specimen along both sides of the displacement concentration area, whilst a macroscopic rupture surface is formed, and the specimen destroyed. Figure 8(b) shows the displacement cloud in the $y$ -direction of the whole limestone observation area; when $T = 482 s$ ⁠, the specimen exhibited a more uniform deformation under the load, and a displacement concentration area started to appear at the lower right corner of the specimen. When $T = 752 s$ ⁠, the peak intensity was reached, and the displacement field in the $y$ -direction was highly concentrated on both sides of the specimen observation area, indicating the imminent destruction of the rock specimen. When $T = 754 s$ ⁠, the specimen ruptured along the observation area where the displacement was concentrated, and the macroscopic rupture surface of the specimen was completely formed. Figure 8(c) shows the displacement cloud image in the $z$ -direction throughout the observation area of the limestone. The displacement cloud of the $z$ -direction reflects the radial deformation of the specimen surface. When $T = 482 s$ ⁠, the surface deformation of the specimen was uniform, and the deformation of each part in the observation area was approximately equal. When $T = 612 s$ ⁠, the $z$ -direction displacement field was aggregated at the left edge of the observation area of the specimen, and local microfractures sprouted. When $T = 722 s$ ⁠, the specimen under the action of local rupture occurred in the radial direction. When $T = 752 s$ ⁠, the peak intensity was reached, and the displacement in the $z$ -direction was highly concentrated in the upper left part of the specimen, forming a local deformation zone, which indicates the imminent damage in this area. When $T = 754 s$ ⁠, the specimen fractured along the local deformation zone, and the macroscopic rupture surface was formed.

5.1.2. FBG Results

Figure 9 shows the fiber Bragg grating strain curves for the whole loading process of the limestone specimen. The raw fiber Bragg grating data were acquired at the wavelength (resolution: 1 pm) and converted into strain for presentation. To ensure the integrity of the fiber grating data acquisition, the fiber grating data acquisition started before preloading, and the data presentation started from continuous loading. Figures 9(a) and 9(b) show the strain records of two fiber Bragg grating points with an angle of 0° between the fiber and the horizontal direction. The overall process can be divided into three stages. The first stage is the original pore compression stage (0–611 s) whereby the specimen is compressed along the axial direction and expanded along the radial direction. The result indicated strain values of both fiber grating points 1 and 2 increasing steadily. The second stage is the cracks evolution and transfixion stage (612–754 s), which is the period of local cracks generation and development of the specimen, resulting in cracks on the surface of the specimen. For example, when $T = 612 s$ ⁠, the strain value of fiber grating point 1 increased abruptly from 381 με to 3729 με, and the strain value of fiber grating point 2 increased abruptly from 287 με to 2936 με. These changes were caused by the surface cracks at the fiber grating point of the specimen. After that, the fracture was further compacted by the load, and the specimen continued to compress in the axial direction and expanded in the radial direction. When $T = 740 s$ ⁠, the strain value of fiber grating point 2 increased from 3387 με to 5482 με, which means that there are new local cracks at fiber grating point 2, which made the strain value increase again. At this point, the specimen was completely destroyed. The third stage is the residual stage (after 755 s) when the specimen lost its load-bearing capacity and retains part of the residual load-bearing capacity, and the strain values of fiber grating monitoring points 1 and 2 gradually stabilize.

Figures 9(c) and 9(d) show the strain recordings of two fiber grating points with a horizontal fiber angle of 30°. The overall process can also be divided into the original pore compression stage, the cracks evolution and transfixion stage, and the residual stage. The elastic deformation time period was 0–611 s. During the original pore stage, the specimen was gradually compacted, and the strain value of the fiber grating monitoring points gradually increased. The fiber grating point 4 did not show a good monitoring effect at this stage, and the reason for analysis was that the fiber and specimen were not fully coupled under the action of epoxy resin adhesive, which needed to be improved in the subsequent test. In the subsequent loading, the specimen expanded along the radial direction under the load, which made the fiber grating point 4 return to normal. The cracks evolution and transfixion time period were from 612 s to 754 s. When $T = 612 s$ ⁠, the strain value of fiber grating point 3 increased abruptly from 43 με to 258 με, whilst that of point 4 increased abruptly from -26 με to 5579 με, with local cracks generated in the specimen. After a period of cracks compaction, the strain value of fiber grating point 3 increased from 300 με to 443 με when $T = 720 s$ and then to 598 με after 6 s, respectively. This represents the period of concentrated cracks generation at this location. Fiber grating point 4 reached 5254 με at the peak load. When $T = 755 s$ ⁠, the specimen started to enter the residual phase, and the strain values of fiber grating monitoring points 3 and 4 gradually decreased and stabilized.

Figures 9(e) and 9(f) show the strain recordings of two fiber grating points at an angle of 60° between the fiber and the horizontal direction. Unlike the first two inclination angles, the strain values of fiber grating monitoring points 5 and 6 exhibited a slow decrease during the original pore compression stage. This situation indicates that the effect of axial compression of the specimen on the fiber grating is greater than that of radial expansion when the fiber is horizontally clamped at an angle of 60°. During the cracks evolution and transfixion stage, the strain value of fiber grating point 5 increased from -370 με to -242 με when $T = 612 s$ ⁠, which was a result of local cracks generation in the specimen. After 120 s of loading, the strain value of fiber grating point 5 decreased from -318 με to -554 με when $T = 732 s$ ⁠, which was again a result of local cracks generation in the specimen. The strain value of fiber grating point 6 fluctuated similarly to that of fiber grating point 5, except that the strain value increased slightly when $T = 720 s$ ⁠. When $T = 754 s$ ⁠, the specimen was damaged and entered the residual stage, and the strain values of fiber grating monitoring points 5 and 6 fluctuated and decreased. The strain value fluctuations of points 5 and 6 decreased and gradually stabilized.

Figures 9(g) and 9(h) show the strain recordings of two fiber grating points at an angle of 90° between the fiber and the horizontal direction. The fiber at this inclination is almost unaffected by the radial expansion of the specimen. The fiber grating point 7 experienced the original pore compaction lasting 611 s. The strain value affected by the local rupture of the specimen increased from -683 με to -217.92 με when $T = 612 s$ ⁠. After experiencing the continuous action of the load, the specimen load reached a minimum of -826 με (the load carrying limit) when $T = 753 s$ ⁠. The observed strain value fluctuation was small because the deformation stage of fiber grating point 8 was similar to that of fiber grating point 7 but with no obvious rupture. When $T = 754 s$ ⁠, the specimen was damaged and entered the residual stage at the same time, whilst the strain value fluctuation of fiber grating monitoring points 7 and 8 decreased and gradually stabilized.

Through the whole monitoring of the limestone specimens with four inclination angles of fiber grating, the real-time dynamic information of deformation and damage of the specimen was obtained with a good characterization effect at the same time. The parametric responses at key time points were consistent with the 3D-DIC monitoring results with the two being mutually similar.

5.2. Orthogonal Type Test Results

The sandstone specimen used in the test was taken from the overburden of the coal seam. Two three-point fiber optic gratings and one two-point fiber optic grating were glued to the surface of the rock specimen, with one intersection point between the axial fiber and each of the two circular gratings. The locations of the eight fiber grating monitoring points on the surface of the rock specimen are shown in Figure 10. The composition and SEM analysis of the sandstone specimen was performed, and the main constituent elements of the rock samples were found to be O (48.40%), Ca (12.05%), Si (16.30%), and C (14.96%). When fresh sections of the samples were observed under low magnification, the main minerals identified were quartz, calcite, and clay. The quartz grain size was mostly in the range of 50 μm to 200 μm. Figure 11 shows two local SEM images of the sandstone specimen. The layered minerals in Figure 11(a) are clays, and Figure 11(b) shows a primary microfracture on the surface of the specimen.

5.2.1. 3D-DIC Results

The image acquisition of the sandstone specimen under loading was performed using the 3D-DIC technique, and the displacement clouds in different directions in the observation area were obtained as shown in Figure 12. The color code of displacement values and the numerical abundance are shown on the right side of each cloud image. The results showed that sandstone specimens are hard and dense, and the rupture is accompanied by a rock burst. The specimen was loaded for 614 s and reached its peak strength in 612 s. Figure 12(a) shows the $x$ -direction displacement cloud in the whole observation area of the sandstone. When $T = 360 s$ ⁠, the specimen was in the uniform deformation stage with no increment in local displacement. When $T = 480 s$ ⁠, the displacement in the $x$ -direction collected in the lower-left corner and upper-middle part of the specimen. Local cracks began to appear, and the displacement of the other parts increased uniformly. When $T = 600 s$ ⁠, the displacement in the $x$ -direction continued to accumulate locally in the specimen. Since the specimen was dense and had no joints, there was no large area change in the displacement cloud image. When $T = 612 s$ ⁠, the peak intensity was reached, and the displacement in the $x$ -direction was concentrated on the left side and the middle and upper part of the observation area of the specimen, which was different from the surrounding stable change area. The specimen was completely destroyed, and the rock mass in the middle and upper part of the observation area collapsed and formed a macroscopic rupture surface on each side. Figures 12(b) and 12(c) show the displacement clouds in the $y$ and $z$ directions throughout the observed area of the sandstone, which represents the deformation in the load direction and radial direction, respectively, and are steadily changing until the specimen is damaged, and the specimen fracture is penetrated. For intact and hard specimens, the surface was relatively intact before complete rupture occurred with the 3D-DIC technique is somewhat limited. However, the fracture derivation of the specimen could still be judged from the local displacement anomaly area. For the study of such rock specimens, the deformation and failure processes need to be deeply analyzed in combination with fiber Bragg grating.

5.2.2. FBG Results

Figure 13 shows the fiber Bragg grating strain curves for the whole loading process of the sandstone specimen. The raw fiber Bragg grating data were acquired at the wavelength (resolution: 1 pm) and converted into strain for presentation. To ensure the integrity of the fiber grating data acquisition, the fiber grating data acquisition starts before preloading, and the data presentation starts from continuous loading. Fiber grating points 1 and 2 are located on the axially arranged fiber, which is almost unaffected by the radial expansion of the specimen. As shown in Figures 13(a) and 13b), the strain values of both fiber grating points 1 and 2 under load decreased slowly during the initial pore compression phase of the specimen (0–479 s). When $T = 480 s$ ⁠, the strain value of fiber grating point 1 changed abruptly from -470 με to 486 με, which was due to local cracks generation at this location. The strain at fiber grating point 1 peaked at $T = 613 s$ ⁠. When $T = 614 s$ ⁠, the strain at fiber grating point 1 increased abruptly from -184 με to 445 με, and the specimen was completely destroyed. The strain at fiber grating point 2 was slightly different from fiber grating point 1 in that the strain at fiber grating point 2 did not change abruptly before the specimen was damaged. They showed a slow change in strain value, which was interpreted as good integrity of the specimen before rupture. This is consistent with the observation of 3D-DIC.

The fiber grating points 3–5 are located on the circular fiber in the upper part of the specimen with an equal spacing distribution. As shown in Figures 13(c)–13(e), the strain values of the three fiber grating points were mainly influenced by the radial expansion of the specimen during the initial pore compression phase (0–479 s), and all of them increased slowly. When $T = 480 s$ ⁠, the strain values of both fiber grating points 3 and 4 changed abruptly, which may be a result of local cracks generation. After that, the cracks were closed with the continuous action of the load. Fiber grating point 3 was affected by these cracks and did not respond until the specimen was presumably damaged, and the monitoring data disappeared. The strain value of fiber grating point 4 continued to increase slowly after the cracks closure, and the strain value increased abruptly to 3256 με when $T = 614 s$ ⁠, resulting in the complete destruction of the specimen. At the same time, the fiber was damaged at the light fiber point 4, and the strain data disappeared. The strain value of fiber grating point 5 continued to increase slowly before there was any damage to the specimen, whilst the structure was relatively intact. The strain value of fiber grating point 5 reached the maximum value of 2027 με when $T = 613 s$ ⁠, while the rupture surface of the specimen was completely formed. Combined with the site conditions, the explosion of the sandstone specimen led to the collapse of the rock mass structure, and such huge deformation was very likely to cause damage to the fiber.

Fiber grating points 6–8 were located on the ring fiber in the lower part of the specimen with an equal spacing distribution. As shown in Figures 13(f)–13(h), the strain values of fiber grating points 6–8 were in a slowly increasing state before the specimen was completely damaged, indicating that the lower part of the specimen maintained good integrity before the rock burst. This is consistent with the 3D-DIC observations. The strain values at fiber grating points 6–8 increased abruptly when $T = 614 s$ ⁠, which was a result of the large radial deformation caused by the specimen rupture. The fiber at all three fiber grating points suffered devastating damage, and the monitoring data disappeared. The strain response characteristics of the deformation and damage of the specimen were well captured by monitoring the strain of the sandstone specimen throughout the whole process. The fiber grating monitoring results are more consistent with the 3D-DIC monitoring results.

6. Discussion

The article investigates the deformation damage response characteristics of limestone and sandstone in the Panxie mine. The test results of the displacement field and the fiber grating point strain value of the specimen observation area were mainly analyzed by 3D-DIC. Some problems are discussed.

(1)
During the first stage for brittle rocks (such as dense sandstone), uniform strain changes occur under load, and the strain energy accumulated to a certain degree, which made the rock specimens cracks easily. It is often a relatively short period time from fracture generation to transfixion when the conventional low-frequency acquisition is difficult to capture the information on fracture evolution. At this point, medium or high-frequency acquisition is considered a more appropriate choice. For less brittle rocks, such as internal pore development limestone, the cracks evolution process often requires a certain amount of time to accumulate. There are no requirements for the acquisition frequency of such rocks, and the optional acquisition frequency is relatively broad. The optimal acquisition frequency should be selected for different types of rocks and different test purposes
(2)
The fiber Bragg grating is a contact test method, and the type of fiber selected and the bonding method of the fiber have a great influence on the experimental results [31, 32]. The grating fiber selected in the article is a coated fiber only, which can achieve the maximum efficiency of rock strain transfer with certain strength. The adhesion method of the optical fiber and the rock was first fixed initially with quick-drying glue, and then epoxy resin glue was applied evenly between the optical fiber and the specimen to fully bond the specimen with the rock sample. The experiment was carried out as soon as possible after the glue had completely solidified. During the loading process of the specimen, there was a certain vibration situation since the structural integrity is destroyed, which may lead to the dislodgement of the optical fiber. When testing, glue with strong adhesion should be chosen. When choosing a fiber grating and 3D-DIC coupling test, the fiber should be glued first, and then the scattered spot made. This can minimize the interference of the fiber to the 3D-DIC monitoring results
(3)
The monitoring method mentioned in this paper is applicable to rock samples with certain strengths. Because the rock specimens with low strength are easy to crack, the optical fiber may be easily damaged. When loading the rock specimen which is easy to crack, the arrangement of multi-inclination optical fiber is preferred. This ensures the survival of the sensor as much as possible and facilitates the acquisition of effective monitoring data

7. Conclusions

In this paper, by summarizing the existing literature, conducting rock mechanics multiparameter test experiments, and analyzing the experimental phenomena, the following main conclusions were drawn.

(1)
Compared with the existing rock specimen testing system, this paper proposes a combined testing method of 3D-DIC and FBG for rock specimens. The advantages of both methods complement each other to achieve dynamic and accurate monitoring of loading rock specimens
(2)
The paper proposes a new fiber grating arrangement on the surface of rock specimens, which is a multi-inclination type. This method can test the strain changes at different locations and angles of the rock specimen. By capturing the strain data of the fiber grating throughout the loading process, the loading process of the rock specimen can be divided into the original pore compression stage, the microfracture evolution and transfixion stage, and the residual stage according to the parametric response characteristics
(3)
In the article, a comparative study of multiparametric tests was conducted on limestone and sandstone. Under uniaxial loading, the parameter response characteristics of specimens with different lithology are different. However, before the failure of the rock specimens, obvious parameter changes appeared at the potential fracture surface. This method therefor helps to predict the crack extension and potential fracture surface of the rock specimens

Data Availability

The data used for calculation in this paper can be obtained from the corresponding author upon request.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

We gratefully acknowledge the financial support by the National Natural Science Foundation of China (Grant No. 41877268 and Grant No. 42074148) and the Graduate Innovation Fund Project of the Anhui University of Science and Technology (Grant No. 2020CX2003). We are also grateful to School of Electrical Engineering and Automation, Anhui University for providing the laboratory.

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