Abstract
Mining-induced deformation and failure of overlying strata may trigger roof collapse, surface subsidence, and abnormal gas emissions. To address this, this study proposes a distributed optical fiber monitoring method for large-scale rock mass deformation, leveraging the high sensitivity and distributed sensing advantages of Brillouin optical time-domain analysis (BOTDA) technology. A physical similar model experiment (geometric similarity ratio 1:100) was conducted to investigate overlying strata deformation characterization, with the introduction of the Average Frequency Shift Variation (AFSV) as a core indicator. The findings indicate: (1) AFSV ≥ 20 MHz serves as a reliable threshold for identifying significant rock mass deformation and failure, correlating with mine pressure behavior; (2) The optical fiber frequency shift curve exhibits a step-like pattern, enabling accurate characterization of the overburden three-zone structure (caving zone, fractured zone, bending subsidence zone) with a sampling interval of 10 mm; (3) Cross-validation with Fiber Bragg Grating (FBG) sensors and total stations shows that the AFSV-based characterization results have a linear fitting coefficient R2 ≥ 0.99 with FBG wavelength drift data. This high level of agreement demonstrates the accuracy and reliability of the proposed method. This study demonstrates that AFSV can effectively reflect mine pressure behavior patterns, providing a quantitative and reliable dynamic monitoring basis for overlying strata zoning, roof stability evaluation, and gas extraction optimization in mining engineering.
1 Introduction
The deformation of overlying strata in mining areas under the action of mining-induced pressure is a complex engineering problem (Qian et al., 2018). Over the years, a series of classical theories have been developed to effectively address issues related to the surrounding rock stability of working faces and the mechanics of rock strata in complex environments (Zhang and Wang, 2014). The deformation of overlying strata in mining areas under the action of mining-induced pressure is a complex engineering problem (Qian et al., 2018). Over the years, a series of classical theories have been developed to effectively address issues related to the surrounding rock stability of working faces and the mechanics of rock strata in complex environments (Peng, 2015; Zhang and Wang, 2014). However, the deformation of overlying strata in mining areas is a complex deformation and failure process driven by mine pressure, which is closely related to the distribution, mineral composition, geological structure, stress field, and defect evolution of rock strata (Shi et al., 2023; Shi et al., 2025). In addition, the mechanical response of surrounding rock and reinforced rock masses is also affected by fracture development, grouting reinforcement, and multi-scale defect coupling mechanisms (Wu et al., 2024; Wu et al. 2025a; Wu et al. 2025b; Shi et al., 2022). This makes it difficult to test and characterize the deformation state of rock strata (Lin et al., 2010). Engineering practice has put forward higher requirements for testing overburden deformation and describing its state; thus, the coal industry is in urgent need of testing technologies and characterization methods that can adapt to the large-scale deformation characteristics of overlying strata in mining areas (Meng et al., 2024; Kang et al., 2025; Hooper et al., 2025; Ji, 2026; Feng and Pandey, 2026; Gao et al., 2026; Barla and Insana, 2026).
With the integration of optical fiber sensing, communication, and computer technologies, intelligent optical fiber sensing has gradually matured (Zhu et al., 2020). Distributed optical fiber sensing technology enables long-distance distributed and real-time monitoring of the interior of rock and soil masses, and it exhibits low electromagnetic interference, high electromagnetic insulation, intrinsic safety, and networkability. It has been widely applied in geotechnical engineering for monitoring the stability and deformation of slopes, dams, and underground caverns (Chapeleau et al., 2013; Villalba and Casas, 2013). During monitoring, optical fiber sensors can be attached to the surface of existing structures or embedded in structures during casting to perform real-time measurements and monitor the initiation and propagation of structural damage (Dong et al., 2009). When a structure deforms or cracks due to mechanical and temperature changes, the embedded optical fiber is deformed accordingly, leading to changes in the intensity, phase, wavelength, or polarization of light transmitted through the fiber (Zhu et al., 2022). Optical fiber sensors determine the stress, deformation, or cracking of the structure by acquiring information about these light changes, enabling self-monitoring and self-diagnosis of structural stress, deformation, and cracking (Chai, 2003).
Zhang et al. (2024) analyzed the application of Brilouin optical time-domain analysis (BOTDA)-based distributed optical fiber sensing technology in geotechnical engineering and studied the optical fiber layout and monitoring methods for slope and foundation models. Chai et al. (2004) proposed a distributed optical fiber sensing system based on optical time-domain reflectometry, embedding distributed optical fiber sensors in model rock strata to monitor rock mass deformation. To address the difficulty in testing the internal deformation state and describing the movement process of rock strata in mining area model experiments, Chai et al. (2013), Chai et al. (2016) used BOTDA distributed optical fiber sensing technology to detect and characterize the rock stratum deformation and collapse processes. Li et al. (2017) determined that under the geological and mining conditions of Xinzhouyao Mine, significant pressure relief effects were achieved when pressure relief borehole was drilled more than 110 m ahead of the working face, by periodically testing the internal strain of the coal mass around the borehole pressure relief area using sensing cables.
In this paper, distributed optical fiber sensing technology is arranged in the physical similar model experiments to characterize the mine pressure behavior of surrounding rock induced by mining. It investigates the corresponding characterization relationships between AFSV and the fracturing deformation and pressure behavior of overlying strata, as well as the corresponding relationships between the initial and periodic pressure behavior, direct roof fracturing, fissure development, height of overburden zones, range of mining influence during working face excavation, and optical fiber frequency shift values. A characterization method of AFSV for the fracturing deformation and pressure behavior features of overlying strata is established, providing a basis for the intelligent monitoring application of optical fiber sensing technology in engineering fields.
2 Basic principles
2.1 Brillouin optical time-domain analysis (BOTDA)
2.1.1 System principles of BOTDA distributed optical fiber sensing technology
When the frequency difference between two lasers propagating in opposite directions in an optical fiber equals the Brillouin frequency shift, the weak pump signal is amplified by the strong pump signal, known as the Brillouin stimulated amplification effect, where energy transfer occurs between the two light beams. This phenomenon is called the stimulated Brillouin scattering principle (Liu et al., 2021) (Figure 1).
FIGURE 1
Based on this phenomenon, two light sources are used as the pump pulse light and the probe continuous light, respectively. The detection signal can be either the Brillouin gain signal or the Brillouin loss signal. When the temperature or strain at a certain part of the optical fiber changes, the corresponding Brillouin amplitude changes and/or the frequency shifts. By tuning the frequency difference between the two pump lights to equal the new Brillouin frequency shift, the Brillouin scattering signal at that point can be received. Detecting the power of the continuous light coupled out from one end of the optical fiber allows determining the frequency difference at which the energy transfer between segments of the optical fiber reaches its maximum, thereby determining the temperature and strain information and achieving distributed sensing (Chai et al., 2021a). This method is known as BOTDA, and its sensing principle and system architecture are shown in Figure 2.
FIGURE 2
2.1.2 BOTDA testing principles
The refractive index of an optical fiber is related to its temperature and the stress it is subjected to, causing the Brillouin frequency shift to vary with changes in these parameters. Experiments have found a linear relationship between Brillouin power and temperature and strain (Shang et al., 2017). Based on experimental results, the following Equation 1 is proposed:where, is the Brillouin frequency shift variation, is the relative variation in Brillouin power, δε and δT are the strain and temperature variations, respectively, Cvε and CvT are the Brillouin frequency shift strain coefficient and temperature coefficient, respectively, CPε and CPT are the Brillouin power strain coefficient and temperature coefficient, respectively. When the incident light wavelength is 1550 nm, the values of the above four constants are: Cvε = 0.0493/με, CvT = 1.20 MHz/°C, CPε = −7.8 × 10−4%/με, and CPT = 0.27%/°C. Thus, by detecting the Brillouin signal’s frequency shift and normalized signal power variation, the temperature and strain information along the optical fiber can be obtained, enabling distributed sensing.
The Brillouin frequency shift has a strict linear correlation with strain, and the frequency shift data used in this study is temperature-compensated, ensuring that the measured frequency shift only reflects the strain/deformation of the overlying rock mass. This study verifies that frequency shift can directly characterize rock mass strain in the mining overburden monitoring scenario, and thus frequency shift is used as the core characterization parameter for the research.
2.2 AFSV
2.2.1 Concept of AFSV
Combining the deformation characteristics of overlying strata during mining with the high-precision and distributed monitoring features of distributed optical fiber sensing, the deformation of overlying strata under mining conditions tends to be large-scale. The overlying stratum structure simultaneously exhibits complex characteristics such as strain, fissuring, and fracturing, and evolves continuously in space with the advancement of the working face. Owing to these characteristics, distributed optical fiber sensing can achieve high density strain sensing within the large deformation area of overlying strata. Therefore, the detection parameters of distributed optical fiber sensing can reflect the deformation structure along the optical fiber in overlying strata. Meanwhile, the magnitude of optical fiber frequency shift has a one-to-one correspondence with the degree of overburden deformation and can numerically reflect the intensity of deformation.
The overlying stratum structure is divided into the caving zone, fractured zone, and bending subsidence zone (Li et al., 2022). The stress distribution model of the optical fiber during rock stratum deformation is shown in Figure 3, where tensile stress is defined as positive and compressive stress as negative (Chai et al., 2021b). The relationship between the deformation degree of the three overburden zones under mining conditions and the frequency shift value at the corresponding spatial positions along the optical fiber is analyzed.
FIGURE 3
Assuming the optical fiber sensor consists of n sampling points, and BFSj is the frequency shift value at a certain moment and a certain sampling point within a certain range of the optical fiber sensor, the frequency shift value at the previous moment at the same sampling point is BFSj-1.
To clarify the frequency shift calculation logic and ensure the consistency of the static BOTDA sensing system, BFSj-1 is explicitly defined as the initial baseline frequency of each sampling point. This baseline is measured after the completion of model construction and optical fiber embedding, followed by a 24-h static standing period to eliminate initial stress concentration and stabilize the overlying rock mass. During the standing period, the NBX-6055A BOTDA system collects frequency data every 6 h for baseline stability verification, and the results show that the frequency variation of each sampling point is ≤ ±1 MHz (within the instrument noise threshold of ≤ ±2 MHz). The initial frequency data recorded at the end of the standing period (i.e., the state where the working face has not been excavated, excavation distance = 0 mm) is determined as BFSj-1, and all subsequent frequency shift calculations (ΔBFS = BFSj - BFSj-1) adopt this unique initial baseline to ensure the consistency of the positive/negative sign convention for tensile/compressive stress.
A set of unified sign conventions for stress, strain, displacement and Brillouin frequency shift variation is explicitly defined and consistently applied throughout this study to avoid confusion, with all physical quantities following these rules in subsequent equations, figures and discussions: (1) Stress: Tensile stress acting on the rock mass and optical fiber is defined as positive (+), and compressive stress is defined as negative (−); (2) Strain: Axial strain is linearly correlated with stress, thus tensile strain is defined as positive (+) and compressive strain as negative (−); (3) Displacement: For vertical displacement (the core overburden deformation in this study), downward subsidence (in the gravity direction) is defined as positive (+) and upward rebound as negative (−); for horizontal displacement along the working face advancing direction, forward deformation (consistent with excavation direction) is defined as positive (+) and reverse deformation as negative (−); (4) Brillouin frequency shift variation: Brillouin frequency shift is linearly correlated with axial strain (
Section 2.1.2), thus an increase in BFS induced by tensile strain is defined as positive (+), and a decrease in Brillouin frequency shift induced by compressive strain is defined as negative (−). Tensile stress is the dominant stress state for overburden fracturing and caving, and the above conventions are designed to directly reflect the correlation between overburden structural evolution and optical fiber sensing signals.
For the caving zone, a sampling point on the optical fiber experiences rock layer caving followed by compaction in the goaf as the working face advances. During rock layer caving, the tensile stress on the optical fiber gradually increases, leading to an increase in the optical fiber frequency shift value:
From Equation 2, it can be seen that the frequency shift value shows a positive increase during rock layer caving, and its numerical value indicates the degree of rock layer caving.
During compaction of the caved rock mass, the compressive stress on the optical fiber gradually increases, leading to a decrease in the optical fiber frequency shift value:
From
Equation 3, it can be seen that the frequency shift value shows a negative increase during rock layer compaction, and its numerical value indicates the degree of rock layer compaction.
For the fractured zone, a sampling point on the optical fiber experiences rock layer fissure development followed by fissure compaction as the working face advances.
During rock layer fissure development, the tensile stress on the optical fiber gradually increases, leading to an increase in the optical fiber frequency shift value:
From Equation 4, it can be seen that the frequency shift value shows a positive increase during rock layer fissure development, and its numerical value indicates the degree of rock layer fissure development.
During compaction of fissures in the caved rock mass, the compressive stress on the optical fiber gradually increases, leading to a decrease in the optical fiber frequency shift value, as expressed in
Equation 5:
For the bending subsidence zone, the stress state of the rock layers in this area remains largely unchanged, and the stress value does not change with coal mining. The numerical value at a sampling point on the optical fiber remains constant, as expressed in Equation 6:
From the above equation, it can be seen that the deformation degree of the rock layers in the bending subsidence zone is relatively small.
In summary, the sign of the frequency shift variation value at a sampling point on the optical fiber at a certain moment indicates the stress state of the rock mass at that location, and its numerical value indicates the degree of deformation of the rock mass under that stress state. Therefore, the absolute value of the difference in frequency shift variation values at a sampling point on the optical fiber, |BFSj| - |BFSj-1|, can be used to represent the degree of deformation of the rock mass at that location within a certain time interval.
Similarly, the sum of the frequency shift variation values at all sampling points on the optical fiber within that time interval represents the overall degree of deformation of the overlying rock layers along the optical fiber. Therefore, the concept of AFSV is introduced to reflect the deformation degree of rock strata. Based on the optical fiber monitoring database with n sampling points per frequency shift data sample in a specific spatial segment, the AFSV is calculated as the arithmetic mean of the absolute values of the frequency shift variations at all sampling points along the entire optical fiber segment. This calculation yields a dimensionless value that quantifies the overall deformation degree of the rock mass structure within the target spatial segment and reflects the intensity of stratal movement (Yuan, 2017).
2.2.2 Mathematical expression of AFSV
Based on the concept and physical meaning of the AFSV, its mathematical expression is:where, Dx is the AFSV when the working face is excavated to a distance of x;n is the number of sampling points on a section of the optical fiber. When the rock mass undergoes small deformations, the Brillouin frequency shift variation is relatively small. When significant bed separation or even fracture and collapse occur in the rock layers, the Brillouin frequency shift variation is relatively large.
The AFSV Dx represents the sum of the absolute values of all frequency shift values along a section of the sensing optical fiber divided by the number of sampling points. According to experimental results, during the model excavation process, when significant fracture deformation occurs in the overlying rock layers, the calculated value of Dx will suddenly increase, and the curve of the AFSV will exhibit sharp peaks as the working face advances. Based on physical model experiments, it has been found that when the overlying rock layers undergo significant fracture deformation, the calculated value of Dx is usually greater than 20 MHz, making this value an indicator of overlying rock layer fracture. Therefore, when the AFSV Dx is greater than 20 MHz, it indicates significant fracture and collapse in the overlying rock layers and the occurrence of mine pressure. The sharp peak in Dx indicates significant fracture and collapse in the rock mass monitored by the optical fiber, with the occurrence of mine pressure in the mining area. The AFSV Dx critical threshold of 20 MHz is calibrated for the low-ductility (brittle) overlying rock mass of the study area, and rock ductility is a key factor affecting the Dx value, which can be calibrated for different ductility rock masses in practical engineering applications.
Assuming m optical fiber sections are used to characterize the overall deformation degree and pressure behavior of overlying strata under coal mining conditions, the Dx can be expressed as shown in Equation 8:where, represents the AFSV in different rock layer ranges within the same monitoring section, indicating the deformation intensity in the rock layer range where the optical fiber is located; Vi is the ith sensing optical fiber.
3 Optical fiber frequency shift testing model experiment
3.1 Experimental design
A similar model was established based on the overlying stratum structure of a working face in a Baoji coal mine, considering the geological structure and physical-mechanical properties of the rocks in the mining area. The experiment was conducted on a two-dimensional stress model frame with dimensions of 3000 (Length) × 200 (Width) × 2000 (Height) mm, with a geometric similarity ratio of 1:100. The stiffness (elastic modulus) and strength similarity ratios of the model were derived as 1:105 based on the rock mass mechanics similarity criterion and the bulk density similarity ratio (1:1.05) of the prototype rock strata and model similar materials, and the mix ratio of similar materials was optimized via mechanical tests to match the derived mechanical parameter similarity ratios.
The model height was 1290 mm, including an overlying stratum thickness of 1180 mm, a coal seam thickness of 50 mm, and a floor thickness of 60 mm. The working face was excavated from left to right, with 300 mm-wide boundary coal pillars reserved on both sides of the model. The excavation step was 30 mm, with a total of 80 steps, covering an excavation distance of 2400 mm.
The simulated coal seam material in the model was removed step by step in accordance with the set excavation step distance. After each excavation, the model was kept stable, and the next excavation was conducted only after the overlying rock deformation tended to be gentle, so as to simulate the time effect of working face advance and overlying rock deformation in actual mining. During the excavation process, the caving morphology of the overlying rock (e.g., the development height of the caving zone and fractured zone) and the law of ground pressure behavior (the time and position of first weighting and periodic weighting) were observed in real time, and the rock deformation characteristics at different excavation distances were recorded.
3.2 Distributed optical fiber testing system
An NBX-6055A optical fiber stress analyzer was selected as the optical fiber testing instrument. The layout of the distributed optical fibers is shown in Figure 4, with three vertical sensing optical fibers (V1, V2, V3) buried at distances of 600 mm, 1200 mm, and 1800 mm from the open-off cut, respectively. Three horizontal sensing optical fibers (L1, L2, L3) were buried at heights of 350 mm, 550 mm, and 750 mm above the coal seam, respectively. Three total station survey lines were arranged in the model experiment, corresponding to the burial positions of the three horizontal optical fibers in the model.
FIGURE 4
To verify the accuracy of the distributed optical fiber testing results, two dial gauges (DG01, DG02) and two FBG sensors (FBG01, FBG02) were installed at the position corresponding to V2. The FBG sensors were embedded in the model at distances of 250 mm and 450 mm from the coal seam, respectively, with a horizontal offset of less than 10 mm from optical fiber V2. The dial gauges were arranged on the model surface at the position corresponding to V2, at the same height as the FBG sensors.
Two FBG sensors and two dial gauges are selected for cross-validation with the distributed optical fiber results, which is sufficient to verify the trend consistency and local quantitative accuracy of the optical fiber sensing. The sensors are strategically arranged at key deformation zones (250 mm and 450 mm from the coal seam) to maximize validation efficiency. Increasing the number of point sensors would not improve the validation effect but would cause structural damage to the similar model and sensor interference. Combined with the three total station survey lines for horizontal deformation validation, a multi-source cross-validation system is formed to ensure the reliability of the distributed optical fiber sensing results.
3.3 Model experiment process
After the installation of the distributed optical fiber and the completion of the entire model construction, the model was statically placed for 24 h to achieve stress stabilization. During this standing period, a free optical fiber segment (with the same length as the sensing optical fiber) was used for temperature compensation to eliminate the influence of environmental temperature changes on the optical fiber frequency. Meanwhile, the NBX-6055A BOTDA system was used to collect frequency data of the sensing optical fiber every 6 h to monitor baseline stability. The initial frequency data collected at the end of the 24-h standing period was recorded as the baseline frequency BFSj-1 for all sampling points, which served as the unique reference for all subsequent frequency shift calculations during the experiment.
With the advancement of the working face, the overlying strata gradually deformed and collapsed downward. Based on the initial and periodic fracturing of the main roof, a total of 1 initial pressure behavior (at a working face excavation distance of 540 mm) and 19 periodic pressure behaviors were observed during the experiment. Figure 5 shows the overburden collapse characteristics at working face excavation distances of 750 mm, 1020 mm, 1290 mm, and 1470 mm.
FIGURE 5
At 750 mm of working face excavation (Figure 5a), the overlying rock layers exhibited periodic fractures, with a collapsed rock layer height of 660 mm, including a caving zone height of 175 mm and a fractured zone height of 440 mm. The upper boundary of the collapsed area had a width of 270 mm, and the maximum bed separation development width was 10 mm. The relationship between the overlying rock collapse range and the positions of the buried sensing optical fibers was as follows: optical fibers L1 and L2 were within the collapse range, with collapse widths of 4500 mm and 360 mm, respectively, at the L1 and L2 levels; optical fiber V1 was within the collapse range, while V2 and V3 were not.
At 1020 mm of working face excavation (Figure 5b), the collapsed rock layer height was 970 mm, including a caving zone height of 175 mm and a fractured zone height of 775 mm. The upper boundary of the collapsed area had a width of 330 mm, and the maximum bed separation development width was 25 mm. The collapse height exceeded the height of optical fiber L3, and all three horizontal optical fibers were partially within the collapse-affected range, with collapse widths of 700 mm, 560 mm, and 530 mm at the L1, L2, and L3 levels, respectively; optical fiber V1 was in the center of the collapse range, while V2 and V3 were not.
At 1290 mm of working face excavation (Figure 5c), the overlying rock collapse extended to the top of the model, with a collapsed rock layer height of 1180 mm, including a caving zone height of 175 mm and a fractured zone height of 905 mm. The upper boundary of the collapsed area had a width of 630 mm, and multiple bed separations developed in the bending subsidence zone, with a maximum bed separation development width of 5 mm. All three horizontal optical fibers were partially within the collapse-affected range, with collapse widths of 990 mm, 930 mm, and 850 mm at the L1, L2, and L3 levels, respectively; optical fiber V1 was in the center-back of the collapse range, V2 had just entered the collapse range, and V3 was not within the collapse range.
At 1470 mm of working face excavation (Figure 5d), the collapsed rock layer height was 1180 mm, including a caving zone height of 175 mm and a fractured zone height of 915 mm. The upper boundary of the collapsed area had a width of 800 mm, with relatively developed bed separation fissures near the left side of the model, and a maximum bed separation development width of 5 mm. There were fewer obvious bed separations near the right side of the model. All three horizontal optical fibers were partially within the collapse-affected range, with collapse widths of 1180 mm, 1160 mm, and 115 mm at the L1, L2, and L3 levels, respectively. Optical fibers V1 and V2 were within the collapse range, while V3 was not.
3.3.1 Optical fiber testing results
The frequency shift test results for the three vertical optical fibers in the model experiment are shown in Figure 6. The frequency shift curve of optical fiber V1, as shown in Figure 6a, exhibits a typical three-stage characteristic: from 0 to 540 mm of working face excavation, the optical fiber frequency shift curve remains almost unchanged, showing a negative step change in the 0–180 mm model height range near 540 mm; from 660 mm to 1100 mm of working face excavation, the frequency shift curve exhibits a typical step pattern, with the height of the first step converging at 190 mm of model height, and the height of the second step continuously increasing with the advancement of the working face. The heights of the first and second steps are consistent with the measured heights of the caving zone and fractured zone in the model experiment; from 1200 mm to 1470 mm or beyond 1470 mm of working face excavation, the frequency shift curve shows a negative step change. Similar phenomena are also observed in the frequency shift curves of optical fibers V2 and V3, as shown in Figures 6b,c.
FIGURE 6
The step-like development of the frequency shift curves indicates that rock strata at different heights and excavation distances bear different tensile stresses and exhibit distinct zonal characteristics, with tensile stress remaining stable within a certain height range. According to the analysis of overburden movement laws, after the direct roof collapses, mining-induced fissures develop upward gradually, and the main roof begins to fracture and move. The rock mass along the optical fiber is subjected to tensile stress gradually, and the magnitude of tensile stress is related to the downward rotation and fracturing subsidence degree of the rock strata. It can be seen that the variation of the vertical optical fiber frequency shift curves in the model experiment is a direct reflection of the rock stratum load changes under the action of mine pressure. The frequency shift distribution characterizes the bottom-to-top zonal collapse of rock strata and the internal stress state changes of rock strata under mining influence.
3.3.2 Accuracy verification of distributed optical fiber testing
To analyze the accuracy of the distributed optical fiber testing results, total stations, dial gauges, and FBG sensors were also arranged in the model experiment. The displacement measured by the total station along a survey line was compared with the frequency shift of the corresponding horizontal optical fiber, the displacement measured by the dial gauge at a point was compared with the frequency shift at a corresponding point on the vertical optical fiber, and the strain measured by the FBG sensor at a point was compared with the frequency shift at a corresponding point on the vertical optical fiber, to verify the accuracy of the distributed optical fiber testing results.
3.3.2.1 Dial gauge testing verification
Based on the correspondence between the positions of the dial gauges and the optical fibers in the model experiment, the frequency shift changes at a point on the optical fiber corresponding to the position of the dial gauge were compared with the changes in the dial gauge readings during the advancement of the working face. The results are shown in Figure 7, where the horizontal axis represents the working face advancement distance, the left vertical axis represents the frequency shift at a point on the optical fiber, and the right vertical axis represents the changes in the dial gauge readings.
FIGURE 7
As shown in Figure 7a, before the working face advances 550 mm, the position where dial gauge 01 is set up is outside the rock layer collapse range, and the changes in the dial gauge readings (rock layer subsidence) and the frequency shift changes at the corresponding point on the optical fiber remain constant, indicating that the rock layer at this location is not affected by mining; as the working face continues to advance, the collapse range of the overlying rock layers continues to expand, and the rock layer at the location of the dial gauge collapses, resulting in a sharp increase in rock layer subsidence and a sudden increase in the frequency shift at the corresponding point on the sensing optical fiber, showing synchronicity; thereafter, the rock layer subsidence remains largely unchanged, while the tensile stress on the sensing optical fiber at the location above the collapsed rock layer is suddenly released, resulting in a sharp decrease in the optical fiber point frequency shift, which gradually experiences compressive stress as the rock layer is re-compacted. This sharp decrease in the optical fiber’s point frequency shift is closely related to the larger gauge length of the fiber relative to the dial gauge. The dial gauge is a point-type sensor with a negligible gauge length, only measuring the deformation at a single fixed point. However, the distributed optical fiber has a continuous linear gauge length, and the tensile stress on the fiber segment (larger gauge length) above the collapsed rock layer is released integrally when the rock collapses, causing a more abrupt drop in the fiber’s point frequency shift at the corresponding position. Meanwhile, the tensile stress can be transmitted along the fiber’s axial direction within its gauge length, which further amplifies this sharp decrease. It should be noted that the core trend of the fiber’s frequency shift variation is consistent with the dial gauge’s reading, which verifies the validity of the optical fiber sensing results.
The same pattern is also observed in Figure 7b, although the changes are smaller since dial gauge 02 is set up at a higher position and is less affected by mining. The above comparison results indicate that the rock layer subsidence at a point on the rock layer during the advancement of the working face is basically consistent with the frequency shift changes at the corresponding point on the optical fiber, and the distributed optical fiber sensing testing reflects the collapse state of the rock layers.
3.3.2.2 FBG testing comparison
Based on the correspondence between the positions of the FBG sensors and the optical fibers in the model experiment, the frequency shift changes of the optical fiber corresponding to the FBG sensors were compared with the changes in the FBG sensor wavelengths during the advancement of the working face. The results are shown in Figure 8, where the horizontal axis represents the working face advancement distance, the left vertical axis represents the frequency shift at a point on the optical fiber, and the right vertical axis represents the FBG wavelength drift.
FIGURE 8
The changes in the optical fiber point frequency shift and the FBG wavelength drift have basically the same trend, but the degree of frequency shift changes caused by coal excavation is greater than the degree of wavelength drift changes measured by the FBG sensors, with the change ranges exceeding and lagging behind the FBG sensor test change range by 50 mm. This is because the optical fiber is a linear continuum along its length, and the lower part of the optical fiber is subjected to tensile stress due to rock layer collapse, and the tensile stress is transmitted upwards along the optical fiber, causing the upper part of the optical fiber to experience tensile stress in advance, resulting in an increase in the optical fiber point frequency shift, with a larger change range than the FBG sensor, which measures changes at a fixed point. However, except for the slightly larger influence range of the optical fiber, the overall trend of the test results is basically the same, indicating that the optical fiber test results are basically consistent with the FBG test results, proving that the distributed optical fiber sensing test results have high testing accuracy.
3.3.2.3 Total station testing comparison
The rock layer displacements measured by the total station during the advancement of the working face were compared with the frequency shift changes of the corresponding horizontal optical fibers. The results are shown in Figure 9, where the horizontal axis represents the working face advancement distance, the upper vertical axis represents the frequency shift at a point on the optical fiber, and the lower vertical axis represents the rock layer displacements measured by the total station.
FIGURE 9
The rock layer fracture line is the boundary between the collapsed rock layers and the uncollapsed rock layers. Outside the fracture line, the rock layers deform under the action of overlying loads but remain largely intact, with relatively small vertical displacements; inside the fracture line, the rock layers collapse to a greater extent, with the largest vertical displacements, and the rock layers adjacent to the fracture line form a hinged structure with the uncollapsed rock layers, with relatively small vertical displacements. As shown in Figure 9a, at a model length of 380 mm, the optical fiber frequency shift reaches its left peak, and the corresponding rock layer displacement is less than 0.1 mm; as the working face advances, the right peaks of the frequency shift curve appear at 657, 976, 1161, 1345, 1592, 1859, and 2095 mm, with the corresponding rock layer vertical displacements all less than 1 mm, still relatively small. Additionally, the rock layer displacement curve measured by the total station changes more steeply on the left side of the model and more gradually on the right side, which also corresponds well with the frequency shift curve measured by the optical fiber. Therefore, comparing the test results of the total station survey line 1 and the optical fiber Fh11, the peak values of the frequency shift curve correspond to the smaller values of rock layer vertical displacement, which is consistent with the development characteristics of the rock layer collapse morphology. This indicates that the distributed optical fiber testing results are consistent with the total station testing results, and the distributed optical fiber testing reflects the rock layer collapse morphology.
3.3.3 Calculation of AFSV
The calculation results of the AFSV for the three vertical optical fibers in the model experiment are shown in Figure 10. As can be seen, the AFSV exhibits a spiky distribution over a certain range of excavation distances, remaining largely stable over the other excavation distances.
FIGURE 10
According to the basic principles of AFSV, when Dx ≥20 MHz, significant fracturing and collapse occur in the rock mass at the optical fiber burial position, which can be regarded as the occurrence of mine pressure behavior in the mining area, where the main roof fractures and exerts a load on the working face.
It can be seen that for the Dx calculated from the tests conducted by optical fiber V1, there are 6 points that satisfy the above condition, at working face advancements of 510, 630, 690, 780, 840, and 930 mm. Before the working face advances to 510 mm and after 930 mm, the Dx curve remains largely stable, with an average value not exceeding 10 MHz, indicating that mine pressure manifests at the working face during these 6 working face advancements. Similarly, analyzing the Dx curves calculated from the tests conducted by optical fibers V2 and V3, significant deformation and fracture occur in the rock mass at the locations of optical fiber V2 at working face advancements of 1050, 1140, 1230, 1350, 1470, 1620, and 1710 mm, and at the locations of optical fiber V3 at working face advancements of 1620, 1710, 1920, 2010, 2130, 2250, and 2370 mm.
The characterization ranges of the AFSV along the working face direction for optical fibers V1-V3 are shown in Table 1. As can be seen, when the spacing between optical fibers is 600 mm, it can basically characterize the degree of deformation of the overlying rock layers within the working face mining range, but the degree of deformation of the overlying rock layers within the working face advancement range of 930–1050 mm cannot be characterized, and this should be achieved by reducing the spacing between the arranged optical fibers. At this time, the average characterization ranges along the working face direction for optical fibers V1-V3 are 420 mm, 660 mm, and 750 mm, respectively, with an average characterization range of 610 mm along the working face direction.
TABLE 1
| Optical fiber | V1 | V2 | V3 |
|---|---|---|---|
| Distance from open-off cut (mm) | 600 | 1200 | 1800 |
| Characterization range of working face advancement (mm) | 510–930 | 1050–1710 | 1620–2370 |
| Characterization range along working face (mm) | 420 | 660 | 750 |
Characterization ranges of the AFSV along the working face direction for optical fibers V1-V3.
3.3.4 Characterization of mine pressure behavior patterns using AFSV
Combined with Equation 7, the mine pressure behavior patterns calculated by are shown in Figure 11, which can be divided into 1 initial pressure behavior and 17 periodic pressure behaviors. The initial pressure behavior occurs at an excavation distance of 510 mm, with an average periodic pressure behavior step of 90 mm.
FIGURE 11
Analysis of the Dx peak values shows that the peak values of the optical fiber test during mine pressure behavior can be divided into three levels:
Low intensity: The first, second, fifth, sixth, and eighth periodic pressure behaviors, with an average of about 10 MHz (relatively small rock stratum fracturing degree).
Medium intensity: The seventh, ninth, 13th, 15th, and 16th periodic pressure behaviors, with an average of about 15 MHz (moderate rock stratum fracturing).
High intensity: The third, fourth, 10th, 11th, 12th, 14th, and 17th periodic pressure behaviors, with an average of about 20 MHz (the most severe rock stratum fracturing).
This indicates that the mine pressure behavior at the working face during excavation exhibits a pattern of alternating large and small periodic pressure behaviors affecting the overlying strata. The basic forms of mine pressure behavior in the mining area overlying strata are obtained based on the AFSV Dx.
4 Conclusion
The concept of AFSV is introduced to reflect the deformation degree of rock strata. Based on the optical fiber monitoring database with n sampling points per frequency shift data sample in a specific spatial segment, the AFSV is calculated as the arithmetic mean of the absolute values of the frequency shift variations at all sampling points along the entire optical fiber segment. This calculation yields a dimensionless value that quantifies the overall deformation degree of the rock mass structure within the target spatial segment and reflects the intensity of stratal movement.
The mathematical expression of AFSV is proposed, which can be used to characterize the overburden deformation in different sections monitored by optical fibers. The influencing factors and application scope of AFSV are analyzed: AFSV is affected by the number of optical fiber sampling points, sampling interval, and optical fiber sensor spacing. Increasing the number of sampling points, reducing the sampling interval, and decreasing the sensor spacing can improve the precision of optical fiber-based overburden deformation characterization.
A correlation between AFSV and mine pressure behavior is proposed. Peak values in the AFSV curve during working face excavation indicate the occurrence of mine pressure behavior. The average AFSV characterization range of V1–V3 along the working face direction is 610 mm. Experimental analysis shows that when AFSV≥20 MHz, large-scale deformation and failure occur in the rock strata of the study area (matched with specific rock stiffness and strength parameters), which can be used as a key indicator of mine pressure behavior for this type of rock mass. For rock strata with different stiffness and strength characteristics, the AFSV critical value can be further calibrated and modified through targeted physical similar model experiments or field tests.
The validity of using AFSV to characterize working face mine pressure behavior is verified by cross-comparison with multi-source experimental monitoring data including Fiber Bragg Grating (FBG) sensors and total stations. The AFSV method can effectively reflect the mine pressure behavior patterns of overlying strata in the physical similar model experiment, which demonstrates its good reliability and application potential for the dynamic monitoring of mine pressure in practical engineering.
A clear corresponding relationship between optical fiber frequency shift and overburden structural evolution characteristics is established. As the working face advances, the optical fiber frequency shift curve presents a step-like pattern, reflecting the distinct zonal deformation of the rock mass and realizing the effective characterization of the overburden three-zone structure (caving zone, fractured zone, and bending subsidence zone). The accuracy of the optical fiber-based characterization is verified by cross-comparison with FBG sensors, where the strain converted from optical fiber frequency shift shows a high linear correlation with FBG wavelength drift data with a linear fitting coefficient R2≥0.99, further demonstrating the reliability of the proposed method.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
MW: Writing – original draft, Writing – review and editing. LZ: Writing – original draft, Writing – review and editing. QY: Writing – original draft, Writing – review and editing. GS: Writing – original draft, Writing – review and editing. PW: Writing – original draft, Writing – review and editing. GS: Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the China National Coal Group Key Science and Technology Project (20221CY001), the National Natural Science Foundation of China (51804052), and the Open Fund of the State Key Laboratory of Coal Mine Disaster Dynamics and Control (2011DA105287-MS202210).
Conflict of interest
Authors MW and LZ were employed by Shanghai Datun Energy Resources Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1
BarlaM.InsanaA. (2026). Energy tunnels for a sustainable future. GeoEnergy Commun.2 (4), 4. 10.1007/s44421-026-00016-7
2
ChaiJ. (2003). Basic Study on Crack and Deflection of Rock by Optical Fiber Sensing Technology. Xi’an: Xi’an University of Science and Technology.
3
ChaiJ.WeiS. M.ChangX. T.LiY. (2004). Distributed optical fiber sensor for monitoring rock deformation. Chin. J. Rock Mech. Eng.23 (23), 4068–4071.
4
ChaiJ.ZhaoW. H.LiY.CuiC.WangD. C. (2013). FBG monitoring test on settlement deformation of overlaying strata in similar models. J. China Coal Soc.38 (1), 55–60. 10.13225/j.cnki.jccs.2013.01.009
5
ChaiJ.YuanQ.LiY.ZhangD. D.LiuQ. (2016). Experimental study on overlying strata deformation based on distributed optical fiber sensing. Chin. J. Rock Mech. Eng.35 (S2), 3589–3596. 10.13722/j.cnki.jrme.2016.0892
6
ChaiJ.YangY. Y.OuyangY. B.ZhangD. D.DuW. G. (2021a). Comparison of optical measurement methods for deformation and failure simulation test of overburden in working face. J. China Coal Soc.46 (1), 154–163. 10.13225/j.cnki.jccs.2020.0141
7
ChaiJ.LiuY. L.YuanQ.ZhangD. D.DuW. G. (2021b). Theory-technology and application of optical fiber sensing on deformation and failure of mine surrounding rock. Coal Sci. Technol.49 (1), 208–217. 10.13199/j.cnki.cst.2021.01.016
8
ChapeleauX.SedranT.CottineauL.-M.CailliauJ.TailladeF.GueguenI.et al (2013). Study of ballastless track structure monitoring by distributed optical fiber sensors on a real-scale mockup in laboratory. Eng. Struct.56, 1751–1757. 10.1016/j.engstruct.2013.07.005
9
DongJ. H.XieH. P.ZhangL.ZhuH. H.YinJ. H.HuC. Q.et al (2009). Application of optical fiber grating sensor in gravity dam structure model test. J. Sichuan Univ. Eng. Sci. Ed.41 (1), 41–46. 10.15961/j.jsuese.2009.01.035
10
FengR.PandeyR. (2026). Multiscale evaluation of nanopore architecture and fractal geometry in shale reservoirs. GeoEnergy Commun.2 (2), 2. 10.1007/s44421-025-00012-3
11
GaoF.YangL.LuZ.WuR.LiuW.XiC. (2026). Real-time forecasting of brittle rock failure: a robust acoustic emission approach validated on a large experimental dataset. GeoEnergy Commun.2 (1), 1. 10.1007/s44421-025-00014-1
12
HooperM. P.XieA. Y.LiB. Q. (2025). Random forest forecasting of time to failure for granite hydraulic fracturing using acoustic emission signals. GeoEnergy Commun.1 (7), 7. 10.1007/s44421-025-00005-2
13
JiY. (2026). The century-long development of rock mechanics research: revisited for contemporary subsurface applications. GeoEnergy Commun.2 (3), 3. 10.1007/s44421-026-00015-8
14
KangH.WangB.GaoF.ZhangY.FanZ.LiS.et al (2025). Current status and prospects of coal mining science and technology in China. GeoEnergy Commun.1 (3), 3. 10.1007/s44421-025-00002-5
15
LiY. P.ZhangH. W.HanJ.ZhuF.GuoC. (2017). J. China Coal Soc.42 (11), 2834–2841. 10.13225/j.cnki.jccs.2017.0518
16
LiX.JiaoY. Y.ZouJ. P.ZhangX. F.WangC. (2022). Study on overlying strata movement and ground subsidence in deep coal mining. Saf. Environ. Eng.29 (2), 32–38. 10.13578/j.cnki.issn.1671-1556.20210578
17
LinH. F.LiS. G.ChengL. H.WangH. S. (2010). Similar material simulation experiment of evolution pattern of mining-induced fissure in overburden strata. J. Xi’an Univ. Sci. Technol.30 (5), 507–512. 10.13800/j.cnki.xakjdxxb.2010.05.004
18
LiuJ. Y.WangT.ZhangQ.ZhaoJ. R.ZhangM. J. (2021). Research progress on temperature-strain dual-parameter sensing in BOTDA system. Laser and Optoelectron. Prog.58 (13), 306–321.
19
MengX. J.LiY.ZhangG. C.GuoL. F.LiW. Q. (2024). Evolutionary laws of overburden structural movement under ultra-thick loose layers and uneven-thickness bedrock during mining. J. Min. Strata Control Eng.6 (6), 115–129. 10.13532/j.jmsce.cn10-1638/td.2024-1185
20
PengS. S. (2015). Topical areas of research needs in ground control: a state of the art review on coal mine ground control. J. China Univ. Min. and Technol.44 (1), 1–8. 10.13247/j.cnki.jcumt.000269
21
QianM. G.XuJ. L.WangJ. C. (2018). Further on the sustainable mining of coal. J. China Coal Soc.43 (1), 1–13. 10.13225/j.cnki.jccs.2017.4400
22
ShangQ. F.HuY. T.LiuW. (2017). Research on Brillouin frequency shift extraction method of BOTDA sensing system. Semicond. Optoelectron.38 (5), 633–638. 10.16818/j.issn1001-5868.2017.05.002
23
ShiH.SongL.ZhangH. Q.ChenW. L.LinH. S.LiD. Q.et al (2022). Experimental and numerical studies on progressive debonding of grouted rock bolts. Int. J. Min. Sci. Technol.32 (1), 63–74. 10.1016/j.ijmst.2021.10.002
24
ShiH.ChenW. L.ZhangH. Q.SongL.LiM.WangM. J.et al (2023). Dynamic strength characteristics of fractured rock mass. Eng. Fract. Mech.292, 109678. 10.1016/j.engfracmech.2023.109678
25
ShiH.ChenW. L.WuJ. Y.RongC. X.WangZ. S.SongL.et al (2025). Unified rock strength theory incorporating holistic consideration of macro-meso-micro defect coupling effects. Eng. Fract. Mech.328, 111534. 10.1016/j.engfracmech.2025.111534
26
VillalbaS.CasasJ. R. (2013). Application of optical fiber distributed sensing to health monitoring of concrete structures. Mech. Syst. Signal Process.39, 441–451. 10.1016/j.ymssp.2012.01.027
27
WuJ. Y.WongH. S.ZhangH.YinQ.JingH. W.MaD. (2024). Improvement of cemented rockfill by premixing low-alkalinity activator and fly ash for recycling gangue and partially replacing cement. Cem. Concr. Compos.145, 105345. 10.1016/j.cemconcomp.2023.105345
28
WuJ. Y.YangS.WilliamsonM.WongH. S.BhudiaT.PuH.et al (2025a). Microscopic mechanism of cellulose nanofibers modified cemented gangue backfill materials. Adv. Compos. Hybrid Mater.8 (2), 177. 10.1007/s42114-025-01270-9
29
WuJ. Y.ZhangW. Y.WangY. M.JuF.PuH.RiabokonE.et al (2025b). Effect of composite alkali activator proportion on macroscopic and microscopic properties of gangue cemented rockfill: experiments and molecular dynamic modelling. Int. J. Minerals, Metallurgy Mater.32 (8), 1813–1825. 10.1007/s12613-025-3140-8
30
YuanQ. (2017). Distributed Optical Fiber Detection and Characterization Simulation Test Study on mining-induced Overburden Deformation. Xi’an: Xi’an University of Science and Technology.
31
ZhangJ.WangJ. P. (2014). Similar simulation and practical research on the mining overburden roof strata “three-zones” height. J. Min. and Saf. Eng.31 (2), 249–254. 10.13545/j.issn1673-3363.2014.02.014
32
ZhangX. P.ZhangY. X.WangL.YuK. L.LiuB.YinG. L.et al (2024). Current status and future of research and applications of distributed fiber optic sensing technology. Acta Opt. Sin.44 (1), 11–73.
33
ZhuH. H.ShiB.ZhangC. C. (2020). Current progress and trends in opto-electronic sensor-based monitoring in geo-engineering—A summary of 6th OSMG-2017. J. Eng. Geol.28 (1), 178–188. 10.13544/j.cnki.jeg.2018-254
34
ZhuL.GuW. Z.ChaiJ.MaZ.QiuF. Q. (2022). Evolution of mining-induced overburden deformation using distributed optical fiber. J. Min. Strata Control Eng.4 (1), 43–50. 10.13532/j.jmsce.cn10-1638/td.20211014.002
Summary
Keywords
average frequency shift variation (AFSV), distributed optical fiber sensing, overburden deformation, similarity model, strata behavior
Citation
Weng M, Zhu L, Yuan Q, Song G, Wang P and Su G (2026) Distributed optical fiber characterization of mining-induced overburden deformation characteristics: a simulation experimental study. Front. Earth Sci. 14:1811357. doi: 10.3389/feart.2026.1811357
Received
14 February 2026
Revised
28 April 2026
Accepted
30 April 2026
Published
04 June 2026
Volume
14 - 2026
Edited by
Hao Shi, Anhui University of Science and Technology, China
Reviewed by
Krzysztof Skrzypkowski, AGH University of Krakow, Poland
Umar Zada, Polytechnic Institute of New York University, United States
Updates
Copyright
© 2026 Weng, Zhu, Yuan, Song, Wang and Su.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Qiang Yuan, qiangyuan@cqu.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.