Experimental study on fracture law of key strata in coal mining process based on fiber Bragg grating detection

Abstract

To quantitatively investigate the interaction mechanism between the main key stratum and sub key stratum in the overlying strata of stope, a similar material physical model test was carried out to simulate the coal mining process in this study. A multi-point quasi-distributed fiber Bragg grating (FBG) sensing monitoring system was built by pre-embedding a distributed FBG sensor array in the model, realizing high-precision and distributed measurement of overlying strata movement inside the model. A similar material plane model with dimensions of 3 m × 1.19 m × 0.2 m was fabricated with a geometric similarity ratio of 1:100. Meanwhile, nine FBG sensors including three stainless steel-packaged (FBG01–FBG03) and six POE-packaged (FBG04–FBG09) sensors, together with one ceramic-packaged temperature sensor, were embedded in the model to study the corresponding relationship between the movement state of key strata and the test results of FBG sensors during model excavation. The experimental results show that the wavelength shift of FBG sensors is closely related to the movement state of overlying strata, and the interaction mechanism of fracture between the main and sub key strata is explained through the variation of wavelength shift.

1 Introduction

In the process of deep coal mining, the fracture behavior of key strata in overlying strata directly affects the stability of surrounding rock in stope, the characteristics of mine pressure behavior and the surface subsidence. Qian et al. (1996) defined the strata that control the movement of local or even all strata from the local to the surface in the overlying strata of mine stope as key strata. Based on the influence of strata on the control of overlying strata movement in stope, the key stratum theory classifies key strata into main key stratum and sub key stratum. The main key stratum controls the overall strata movement, while the sub key stratum governs the local deformation of overlying strata. The stress transfer effect caused by their coordinated fracture is the core inducement of dynamic disasters. The proposal of the key stratum theory provides a theoretical basis for accurately predicting the movement of mining-induced overlying strata and effectively controlling strata deformation and fracture, which has great engineering guiding significance for ensuring safe mine mining and preventing dynamic disasters. Many domestic scholars have conducted a large number of theoretical and model experimental studies on the fracture behavior and interaction mechanism of key strata based on the key stratum theory (Lin et al., 2008; Jia et al., 2006; Huang, 2005), which has greatly developed the theory. In recent years, scholars at home and abroad have revealed the temporal characteristics of key stratum fracture through theoretical modeling and physical model tests. The “beam-arch” structure formed after the fracture of the main key stratum will trigger the redistribution of strata stress, and then induce the progressive instability of sub key strata (Xu et al., 2009; Wang et al., 2024; Pan et al., 2022). However, due to the relatively lagging development of monitoring methods and instruments for stress-strain, displacement and deformation, such as the insufficient spatial resolution, weak anti-interference ability and low sensor survival rate of traditional monitoring technologies (e.g., resistance strain gauges, acoustic emission), there is still a lack of quantitative characterization of the evolution of dynamic strain field inside the key strata of overlying strata and their interaction mechanism, resulting in the inability to accurately test and characterize the stress-strain inside the model (Zhu et al., 2020; 2017; Shi et al., 2019; Gao et al., 2026; Lin et al., 2026; Friedel et al., 2026; Li et al., 2026).

With the continuous development of optical fiber sensing technology since the 1970s, its application in energy, oil and natural gas, environmental monitoring and other fields has become increasingly widespread. Fiber Bragg grating (FBG) has become an important sensing and monitoring tool due to its advantages of high sensitivity, anti-electromagnetic interference and quasi-distributed measurement. Many scholars have implanted FBG sensors into composite materials such as concrete to monitor parameters such as stress, strain and displacement inside structures. This technology has also made remarkable progress in geotechnical engineering monitoring and provided a new technical approach for the deformation monitoring of mine roadway roof. Chai (2003) and Chai and Chang (2004) first introduced optical fiber sensing technology into similar physical simulation tests, realizing real-time monitoring of the occurrence and development process of rock mass failure and capturing the dynamic evolution process of rock mass fracture. Dong et al. (2009) proposed a monitoring method based on the coupling of FBG and elastic rod. By pasting FBG on the surface of cylindrical elastic rod, the experimental monitoring of internal displacement changes of structural model under overload conditions was realized. Li et al. (2010) and Feng et al. (2010) extended the application of this technology to water inrush disaster monitoring, and verified the effective capture ability of optical fiber sensing technology for the coupling response characteristics of multi-physical fields through experiments. With the development of distributed fiber optic sensing (DFOS) technology, scholars have further realized the full-section monitoring of rock mass deformation field. Liang et al. (2025) constructed a 3D strain field reconstruction model of mining-induced overlying strata based on Brillouin optical time domain analysis (BOTDA) technology. Pashaie et al. (2024) revealed the evolution of strain localization during key stratum fracture by combining FBG and digital image correlation (DIC) technology. Yan et al. (2016) focused on improving the performance of monitoring sensors, developed an optical fiber-rock coupling enhancement technology, and improved the strain measurement accuracy to the 1με level.

In the field of mining engineering, it is still difficult to quantitatively analyze the coordinated fracture mechanism of main and sub key strata during mine mining, mainly because the lag of monitoring methods restricts the accurate identification of the precursor of key stratum instability (Wang et al., 2021; Wang and Zhang, 2025). As mentioned in relevant studies, traditional point sensors are difficult to capture the spatiotemporal heterogeneity of strain gradient during fracture, making most of the existing experiments focus on the fracture characteristics of a single key stratum (Wang and Bao, 2026), and also leading to the lack of quantitative characterization of the evolution of dynamic strain field inside strata (Sun et al., 2017; Ma et al., 2025). The rapid development of optical fiber sensing technology provides a new way to break through this dilemma. Relying on the advantages of high sensitivity, anti-electromagnetic interference and quasi-distributed measurement, optical fiber sensing technology shows significant potential in multi-physical field response capture, 3D strain field reconstruction and high-precision monitoring, which just makes up for the deficiencies of traditional methods in spatial coverage and data quality. Based on this, this paper applies optical fiber sensing technology to similar material physical model tests to monitor and study the fracture behavior of main and sub key strata during the mining process. By pre-setting a distributed FBG sensor array in the model, a multi-point quasi-distributed FBG sensing monitoring system is built to capture the evolution characteristics of strain field inside key strata in real time during mining, and to study the variation of stress and strain inside key strata and overlying strata with the advance of working face. The research results are expected to provide theoretical support for the control of overlying strata movement and the prevention and control of dynamic disasters in deep mining, and promote the engineering application of optical fiber sensing technology in intelligent mine monitoring.

2 Fracture of key strata

2.1 Disturbance induced by sub key stratum fracture in rock mass

According to the existing theory of mine pressure and strata control, the fracture of the main roof (i.e., sub key stratum) will produce a disturbance effect in the rock mass, and a disturbance pressure is formed on the main roof due to mining. The medium with a certain thickness above and below the main roof is regarded as an elastic medium, and it is approximately considered to satisfy the Winkler elastic foundation assumption, as expressed by Equation 1.where p is the disturbance pressure on the main roof caused by mining, y is the vertical displacement of the main roof, k is the Winkler foundation coefficient, which is related to the thickness and mechanical properties of the soft strata clamped above and below. Based on the theory, the mechanical models of the main roof before and after fracture during mining activities can be established, as shown in Figure 1. M₀, Q₀ and N are the sectional internal forces and bending moment corresponding to the position of the coal wall of the working face (x = 0). When the overhang distance of the main roof is L, the distance from the support resistance F to the coal wall is z, and the acting forces of the overlying fractured strata on the overhang section of the main roof are N′, Q′ and q, where q is the distributed load on the overhang section.

FIGURE 1

The equilibrium differential equation of the main roof is established for the mechanical models before and after the fracture distance of the main roof. The mechanical solutions of the vertical displacement of the main roof and the disturbance pressure bearing with the advance of the working face are given by Equations 2, 3, respectively:where φ is the internal friction angle of rock, and the other parameters are constants related to the Winkler foundation coefficient; Y is maximum vertical displacement coefficient of key stratum; α and β are attenuation and oscillation coefficients related to Winkler foundation property. It can be seen from the formulas that the vertical displacement y and the disturbance pressure p of the main roof are cosine functions decaying according to the negative exponential law e^−ax.

According to the FBG sensing principle (Liang et al., 2003), the central wavelength shift of the grating has a linear relationship with the axial strain on the grating, that is:where Δλ_B is the central wavelength shift, ε_g is the axial strain of the FBG sensor, K_ε is the strain calibration coefficient of FBG.

The strain transfer between the FBG sensor and the measured matrix material during the measurement process will directly affect the axial strain of the FBG sensor. Tests show that strain transfer is affected by the bonding material and packaging method between the FBG sensor and the measured matrix material. The relationship between the axial strain of the FBG sensor and the axial strain of the measured matrix material is expressed as:where ε_g is the axial strain of the FBG sensor, ε_m is the strain of the measured matrix material, and α(k,l) is the average strain transfer coefficient of the bonding length of the FBG sensor. The actual strain transfer coefficient α(k,l) is acquired from the above prefabricated specimen calibration experiment, which eliminates the error induced by interface debonding between FBG and similar matrix.

For the FBG sensor vertically embedded in the key stratum of the model test, the variation of vertical stress has a linear relationship with the wavelength shift. The matrix material is a similar material with an elastic modulus of E_m. Derived from Equations 3–5, the calculation formula of the wavelength shift of FBG sensor with the advance of working face is obtained:

The strain transfer coefficient α(k,l) and strain calibration coefficient K_ε in Equation 4–6 are not empirical constants, which are obtained from independent pre-calibration for sensors with different packaging forms, so as to distinguish the difference of strain transfer induced by diverse packaging and embedding modes of FBG sensors.

2.2 Influence of fracture distance of main and sub key strata on periodic weighting step

Existing studies (Qian et al., 2010; Chen et al., 2004; Miao and Qian, 2003; Ju et al., 2011) have shown that when the overlying strata of the stope have two or more key strata, the fracture distance between the upper key strata may have an impact on the periodic weighting step of the working face. To analyze the influence of multi-key stratum fracture on stope pressure in a concise and intuitive way, a stope pressure model with two layers of key strata is established, as shown in Figure 2. Among them, the thickness of the sub key stratum is h₁, and the thickness of the overlying soft strata load layer is ∑h₁; the thickness of the main key stratum is h₂, and the total thickness of the load layer from its upper part to the surface is ∑h₂. Based on the stope pressure model, the fracture steps of the main and sub key strata are analyzed, and the influence of the fracture of main and sub key strata on stope pressure is clarified.

FIGURE 2

The key stratum fracture is simulated and evolved according to the stope pressure model, and the mechanical model of key stratum fracture is established based on the material mechanics theory to calculate the ultimate span of the stope key stratum during beam-type fracture. The first weighting is a mechanical model of a fixed beam at both ends under uniform load, and the periodic weighting is a mechanical model of a cantilever beam under uniform load, as shown in Figure 3. Accordingly, the first weighting step L_ci and periodic weighting step L_zi of the key stratum can be expressed as:where R_Ti is the ultimate tensile strength of the main and sub key strata, q_i is the load of the overlying load layer of the key stratum (Equation 8), i = 1 represents the sub key stratum, and i = 2 represents the main key stratum.

FIGURE 3

According to the above theoretical analysis, the relative size relationship between the first weighting step L_ci and periodic weighting step L_zi of the key stratum will directly affect the strength characteristics of stope weighting. When L_c1 = L_c2 (or L_z1 = L_z2), the stope weighting strength is a simple superposition of the two. When L_c1>L_c2 (or L_z1>L_z2), that is, the main key stratum fractures before the sub key stratum, the weighting step of the working face is controlled by the main key stratum, and the weighting step L = L_c2 (or L_z2). When L_c1<L_c2 (or L_z1<L_z2), the fracture of the main key stratum will cause non-uniform changes in stope weighting, and periodic weighting intensity will display a repeating alternation of weak and strong cycles. The periodic weighting steps are L₁ = L_z1, L₂ = L_z2-L_z1, L₃ = L_z1, L₄ = L_z2-L_z1, L₅ = L_z1, and so on.

3 Similar physical model test

3.1 Similar model

In this model test, a large mining height fully mechanized working face of a mine in Northern Shaanxi was selected as the geological prototype, and the strata structure and thickness parameters are shown in Table 1. A plane model frame with dimensions of 3 m × 1.19 m × 0.2 m was adopted in the experiment, with a simulated coal seam thickness of 4 cm, corresponding to an actual mining height of 4 m. According to the similarity theory, a geometric similarity ratio of 100 and a bulk density similarity ratio of 1.6 were selected, and river sand, gypsum, white powder and coal powder were used as similar materials.

According to similarity theory, geometric similarity ratio C_l = 100, bulk density similarity ratio C_γ = 1.6; accordingly, elastic modulus and compressive/tensile strength similarity ratio C_E = C_σ = C_l⋅ C_γ = 160. Time similarity ratio C_t = = 10. The mixture proportion of river sand, gypsum, talcum powder and coal powder is designed iteratively via preform specimen mechanical tests to make the model’s density, elastic modulus and rock strength strictly conform to above similarity constants and mechanical similarity criteria.

During the model construction, the mix ratio of similar materials was determined according to the structure of overlying strata and rock mechanical property parameters of the simulated stratum. All materials were mixed with water according to the mix ratio and laid layer by layer in the model frame, and 8∼20 mesh mica powder was sprinkled between layers to simulate the strata interface.

Based on above step-by-step calculation targeting the geological condition of the prototype working face in Northern Shaanxi, two typical hard sandstone layers were screened out: the lower sandstone layer controls partial overlying strata deformation and is confirmed as sub-key stratum, while the upper thick sandstone dominates the overall movement of full overlying strata up to ground surface and is identified as main key stratum. The above calculated results provide quantitative theoretical basis for key stratum partitioning and layered FBG sensor layout in this physical model.

A total of 9 FBG sensors were embedded in the model test, including stainless steel-packaged FBG01∼FBG03 sensors and POE-packaged FBG04∼FBG09 sensors. Considering that strata fracture and bulking may lead to premature sensor failure, referring to relevant empirical practices, the lower FBG sensors were properly kept at a certain distance from the coal seam (Chai et al., 2013). The layout of the grating sensors is as follows: FBG01, FBG04 and FBG07 were embedded at the upper part of the sub key stratum 250 mm from the coal seam floor; FBG02, FBG05 and FBG08 were embedded at the intermediate load layer 50 cm above the coal seam roof; FBG03, FBG06 and FBG09 were embedded at the main key stratum 700 mm from the coal seam floor. The layout scheme of nine FBG sensors is determined based on the key strata control theory. All sensors are arranged hierarchically at three typical critical layers where stress concentration and rock fracture concentrate: upper sub-key stratum, intermediate overlying load layer and main key stratum, with three sensors configured for each layer. The soft interlayers between key strata have minor stress variation and rarely generate strain localization and cracking, so no redundant FBG is embedded to avoid ineffective monitoring. In addition to nine FBG embedded points, two total station measuring lines (A and B) with 50 dense measuring points (25 points per line, 100 mm spacing) are laid out along sub-key and main key strata to realize full-range macroscopic displacement monitoring of overlying strata. The combination of layered quasi-distributed FBG internal strain monitoring and dense total station surface displacement monitoring forms a complementary monitoring system for overlying rock deformation.

For the comparison of monitoring results, a dial indicator was set up at the embedding position of the FBG sensor. To compensate for the temperature effect on the FBG sensor, an FBGT FBG temperature sensor was embedded in the area outside the model mining boundary without stress influence to compensate for the wavelength shift caused by temperature. Prior to model embedding, all FBG sensors with stainless steel and POE two kinds of packaging were calibrated via indoor uniaxial compression test under constant temperature environment. The strain calibration coefficient K_ε and average strain transfer coefficient α(k,l) of each single sensor were tested and recorded respectively. During data processing, the individually calibrated coefficients were substituted into Equation 6 to calculate the actual stratum strain of each measuring point instead of unified constant parameters. Meanwhile, the ceramic packaged temperature compensation sensor embedded in stress-free zone eliminates the wavelength drift caused by environmental temperature change, and all measured wavelength data in this paper are processed by temperature compensation. Independent pre-calibration for each sensor guarantees the accuracy and comparability of monitoring data from different measuring points.

All nine FBG sensors were individually calibrated at constant ambient temperature before embedding. The strain sensitivity coefficient K_ε and strain transfer coefficient α(k,l) of each sensor (FBG01∼FBG09) were separately recorded. The adopted FBG demodulator owns basic wavelength test precision of ±1 pm. All raw wavelength data were processed with unified temperature compensation via the stress-free ceramic temperature sensor, eliminating thermal drift error. The measurement uncertainty induced by packaging difference, embedding gap and instrument error is within ±5 pm for all sensors. Calibration tables of parameters for all sensors are summarized in supplementary attachment.

During sensor embedding, epoxy resin glue was selected as the bonding adhesive between FBG and surrounding similar rock material, which owns high elastic compatibility consistent with the prototype similar material. Before layered paving of model strata, preset tiny grooves with the designed depth were chiselled at predetermined measuring positions to fix sensors, and the adhesive was evenly coated around the sensor surface to eliminate local air gap and interface separation. Strict positioning calibration relying on steel ruler and horizontal level was carried out to guarantee the embedded depth and vertical coordinate of each FBG matching pre-designed layout scheme. After sensor fixation, fine-grained similar mortar was backfilled layer by layer for wrapping protection to avoid extrusion damage from upper laid strata. Prior to formal model test, three standard small calibration specimens made of the same mixed similar material were prefabricated with embedded FBG sensors to conduct uniaxial loading tests for strain transfer efficiency verification. Test results show no obvious interface slip or debonding between sensor and matrix material, and the measured strain transfer coefficient remains stable, which confirms that collected FBG wavelength shift data can effectively reflect the authentic internal strain variation of overlying strata inside the physical model.

In addition, two total station survey lines A and B were arranged in the main key stratum and sub key stratum respectively, with 25 measuring points set on each survey line at an interval of 100 mm, numbered A1–A25 and B1–B25 respectively, to monitor the movement state of key strata, as shown in Figure 4a.

FIGURE 4

Three independent monitoring technologies including embedded FBG, surface dial indicators and full-range total station measurement are adopted for mutual cross validation. FBG captures internal strain evolution inside key strata, dial indicators record local concentrated subsidence at sensor positions, and total stations realize continuous overall subsidence monitoring of main and sub key strata, forming multi-index mutual verification of stratum deformation and fracture.

3.2 Experimental process and main phenomena

30 cm protective coal pillars were reserved on both the left and right sides of the model, the open-off cut width was 4 cm, and the working face advanced from left to right. The central wavelength of FBG and the reading of dial indicator were collected every 2 cm of advance. After the completion of model mining, the caving form of overlying strata is shown in Figure 4b. The working face advanced a total of 119 times with an advance distance of 240 cm. Except for the first weighting during the mining process, 16 times of periodic weighting occurred, with the weighting step concentrated in 8∼12 cm and an average weighting step of 11.15 cm. Except for the first fracture of the main key stratum, 8 times of periodic fracture occurred, with the fracture distance concentrated in 20∼22 cm and an average fracture distance of 18 cm. After the completion of mining, the “three zones” characteristics of the overlying strata in the stope are obviously distributed. Affected by the large mining height, some sub key strata enter the caving zone with a height of about 250 mm. The fractured zone covers the remaining sub key strata, load layer and main key stratum with a height of about 550 mm; the bending subsidence zone is located in the strata above the main key stratum with a height of about 350 mm. Among the 16 observed periodic weightings, an obvious alternating phenomenon of large and small periodic weightings was presented. The 5th, 7th, 8th, 10th, 12th, 14th, 16th and 18th times were large periodic weightings, and the others were small periodic weightings. The weighting situation of the working face is shown in Table 2.

4 Experimental results

4.1 Movement of main and sub key strata

With the advance of the working face, the subsidence variation curves of total station survey lines A and B arranged at the key strata positions are shown in Figure 5, with the abscissa representing the advance distance of the working face and the ordinate representing the subsidence. When the working face advanced to 60 cm, partial caving of the sub key stratum occurred to form the first weighting, and the uncaved sub key stratum showed obvious bending subsidence; when advancing to 68 cm, the sub key stratum completely caved to form the first periodic weighting, and the maximum subsidence of the sub key stratum reached 3.0 cm. After that, with the continuous advance of the working face, the sub key stratum formed periodic fracture. When the working face advanced to 102 cm, the first fracture of the main key stratum occurred with a maximum subsidence of 0.3 cm. After that, the subsidence of the main key stratum increased continuously with the advance of the working face, reaching the maximum value of 2.7 cm when the working face advanced to 208 cm, and the advance process is shown in Figure 5.

FIGURE 5

4.2 Comparison of wavelength shift and dial indicator monitoring results

The curves of the wavelength shift of FBG02 and FBG03 and the subsidence of the dial indicator at the corresponding positions before reaching the peak are obtained from the experiment, as shown in Figure 6. The wavelength shift of FBG02 increased slowly in the range of 0∼66 cm of working face advance, corresponding to the slow increase of dial indicator subsidence; when the working face advanced to 68 cm, the wavelength shift suddenly increased to 21.46 p.m., with little change in the dial indicator; with the continuous advance of the working face, the wavelength shift increased slowly, and the dial indicator subsidence increased slowly; when the working face advanced to 84 cm, the wavelength shift suddenly increased to 105.53 p.m., and the corresponding dial indicator suddenly increased from 0.164 cm to 2.742 mm; when the working face advanced to 94 cm, the wavelength shift suddenly increased from 109.52 p.m. to nearly the peak of 130.5 p.m., and the corresponding dial indicator subsidence also suddenly increased to 4.682 mm.

FIGURE 6

The wavelength shift of FBG03 increased slowly in the range of 0∼82 cm of working face advance, corresponding to the slow increase of dial indicator subsidence; when the working face advanced to 84 cm, the wavelength shift suddenly increased from 8.4 p.m. to 26.74 p.m., with little change in the corresponding dial indicator; after that, the wavelength shift increased slowly, and when the working face advanced to 102 cm, the wavelength shift suddenly increased to 123.39 p.m., and the dial indicator subsidence suddenly increased to 2.492 mm; when the working face advanced to 116 cm, the wavelength shift suddenly increased to nearly the peak of 309.32 p.m., and the corresponding dial indicator subsidence also suddenly increased to 4.985 mm.

Linear regression was carried out on the wavelength shift of FBG02, FBG03 and the subsidence of the dial indicator, and the linear regression curves were obtained as shown in Figure 7. The wavelength shift of FBG has a correlation with the strata subsidence before reaching the peak, with correlation coefficients of 0.9508 and 0.9429 respectively, indicating that FBG sensors can accurately reflect the movement and deformation of strata. Synchronous abrupt changes of FBG wavelength shift, dial indicator subsidence and total station subsidence data appear consistently when periodic weighting and key stratum fracture occur, which further cross-verifies the reliability of the measured monitoring results from different testing methods.

FIGURE 7

Apart from FBG02 and FBG03 with explicit linear fitting, the remaining seven FBG sensors also present obvious positive correlation between wavelength shift and surrounding rock subsidence. Consistent abrupt wavelength jumps synchronize with periodic weighting moments for all measuring points, which further validates the reliability of the full-set monitoring data rather than limited two-point fitting results.

4.3 Wavelength shift and overlying strata movement state

The curve of the wavelength shift of FBG01 (the wavelength shift of all sensors in this paper has been temperature-compensated) with the advance distance of the working face is shown in Figure 8, and the sensor is embedded at 50 cm from the open-off cut of the working face. The abscissa in the figure represents the advance distance of the working face, and the ordinate represents the FBG wavelength shift. The comparison of FBG03 wavelength shift with the movement of main and sub key strata is presented in Figure 9.

FIGURE 8

FIGURE 9

In the range of 0∼58 cm of working face advance (OA section), the immediate roof caved in a large area, as shown in Figure 10a. According to rock mechanics, the tensile stress on the sub key stratum increased at this time. In the range of 60∼66 cm of working face advance (AB section), the growth rate of wavelength shift slowed down. The sub key stratum where FBG01 is located formed a relatively stable cantilever beam structure due to periodic weighting, as shown in Figure 10b. Then the immediate roof did not cave immediately with the advance of the working face, so the immediate roof always provided a supporting reaction force to the sub key stratum, making the tensile stress of the sub key stratum increase slowly, thus leading to the slowdown of the growth rate of sensor wavelength shift, as shown in Figure 10c. Until the working face advanced from 66 cm to 68 cm (BC section), the wavelength shift of FBG01 rose sharply to the peak of 167.03 p.m. The immediate roof under the strata where FBG01 is located suddenly caved completely, and the immediate roof no longer provided a supporting reaction force to the sub key stratum, thus making the tensile stress of the sensor increase suddenly. Then the main roof caved successively, and the first periodic weighting was formed on the working face, forming a layered stacked voussoir beam structure after fracture, as shown in Figure 10d. When the working face continued to advance in the range of 70∼82 cm (CD section), the bed separation between the layered voussoir beam structures gradually closed, and its tensile stress was relieved. However, due to the existence of the voussoir beam structure, the wavelength shift of FBG01 still maintained a high level. When the working face advanced to 84 cm (DE section), the wavelength shift of FBG01 dropped sharply to a negative value of −14.92 pm, corresponding to the experimental phenomenon of the second periodic weighting of the working face. The voussoir beam structure lost stability and caved, rotated reversely to the working face and was recompacted by the overlying strata, and the tensile stress of the sensor decreased immediately, as shown in Figure 10e. With the continuous advance of the working face (EF section), the wavelength shift of FBG01 gradually increased from a negative value and was close to zero, indicating that the rock mass where FBG01 is located was gradually recompacted and restored to the in-situ stress state, as shown in Figure 10f.

FIGURE 10

The experimental phenomena show that the wavelength shift of FBG sensors embedded in strata is closely related to the movement state of overlying strata. Before periodic weighting, the wavelength shift of sensors embedded in the sub key stratum will suddenly jump to around the peak. During periodic weighting, due to the formation of the voussoir beam structure in the sub key stratum, the wavelength shift will fluctuate at a high level until the next periodic weighting, the voussoir beam structure loses stability, and the wavelength shift drops sharply again. The sensor can still effectively reflect the tensile and compressive stress state of the located stratum after experiencing strata caving.

4.4 Influence of sub key stratum fracture on main key stratum

The curves of the wavelength shift of FBG04, FBG05 and FBG06 with the advance distance of the working face are shown in Figure 11.

FIGURE 11

With the advance of the working face, the wavelength shift of FBG04 embedded in the sub key stratum changed. When the working face advanced to 138 cm, the wavelength shift suddenly increased from 165.57 p.m. to the peak of 1,504.24 p.m. At this time, the 6th periodic weighting occurred on the working face, and the rock block where FBG04 is located caved to form a layered voussoir beam structure. With the continuous advance of the working face, the wavelength shift decreased slowly. Due to the existence of the layered voussoir beam structure, the tensile stress of the sensor decreased slowly, and its wavelength shift maintained a high level. When the working face advanced to 156 cm, the 8th periodic weighting occurred, and the voussoir beam structure rotated reversely, lost stability and caved. Due to the recompaction of the layered voussoir beam structure, the strata were then recompacted, resulting in a sharp decrease in the tensile stress of the sensor, and the corresponding FBG wavelength shift dropped sharply from 936.47 p.m. to −209.45 pm. The variation of wavelength shift of FBG04 embedded in the same stratum is completely consistent with that of FBG01, indicating that the monitoring data and variation of FBG sensors embedded in the same stratum have similarity and comparability.

It was found in the test that the wavelength shift of FBG03 and FBG06 embedded in the main key stratum both formed a “step” jump phenomenon for 2∼3 times. According to the previous analysis, the wavelength shift of the sensor at this stratum jumps to near the peak when the strata fracture. Therefore, except for the last step jump caused by key stratum fracture, the first 1∼2 sudden jumps of sensor wavelength shift are all caused by the sudden increase of tensile stress on the sensor. The jump of wavelength shift all occurred at the corresponding position of periodic weighting of the sub key stratum.

According to Equation 3, the periodic fracture of the overlying sub key stratum in the stope will cause disturbance inside the rock mass, and the disturbance effect on the main key stratum makes its tensile stress increase suddenly, that is, forming a “step” jump. Then, the main and sub key strata form a temporarily stable structure, and the tensile stress of the main key stratum remains unchanged (or changes slightly) with the advance of the working face, that is, the platform stage of the “step”. This process will be repeated until the next periodic weighting. However, the tensile stress on the main key stratum will not increase infinitely. After experiencing several disturbances of sub key stratum fracture, with the continuous advance of the working face, when the main key stratum reaches the ultimate overhang distance (due to the disturbance effect formed by the caving of the underlying strata, cracks may be generated in the main key stratum, thus making the ultimate overhang distance of the main key stratum smaller than the theoretical value), the strata will cave, forming the last “step” jump of wavelength shift. At this time, the periodic weighting formed by the simultaneous fracture of the main and sub key strata has a more intense weighting strength than the ordinary periodic weighting, that is, a large periodic weighting is formed.

Although the number of embedded FBG measuring points is limited, the targeted layered arrangement on core load-bearing key strata ensures that the abrupt wavelength mutation of each sensor can accurately reflect strain localization, crack initiation and periodic fracture of the corresponding stratum. Combined with dense total station full-section subsidence data, the initiation position and propagation of mining-induced cracks in main and sub key strata can be effectively captured, satisfying the test requirement of revealing the coordinated fracture interaction of double key strata in this research.

To quantitatively verify the causal relationship between sub-key stratum periodic rupture and step jump of main key stratum strain, the corresponding relationship among working face advancing distance, sub-key periodic weighting occurrence, step abrupt change of main-key embedded FBG wavelength and field visible fracture phenomenon is summarized in Table 3. The synchronous chronological matching of these multi-source monitoring data provides direct experimental evidence for the stepwise disturbance transmission mechanism. Each step jump of main-key FBG always occurs synchronously after the sub-key stratum weighting, which proves the fracture of sub-key stratum is the direct inducement of main key stratum’s stepwise stress mutation.

5 Discussion

Based on a physical model test using similar materials, this study employed a multi-point quasi-distributed fiber Bragg grating sensing system to monitor and analyze the failure process of the main and sub-key strata overlying the working face, as well as their interaction. The results show that the wavelength shift recorded by the FBG sensors corresponds well to the movement state of the overlying strata. It can effectively capture strain accumulation before key stratum failure, abrupt stress changes during failure, and unloading and adjustment after failure. This observation is consistent with the understanding of coordinated deformation between the main and sub-key strata in Qian Minggao’s key stratum theory. Compared with conventional measurement methods and dial gauges, the FBG sensors maintained stable operation after bending, fracturing, and local collapse of the rock strata. They also enabled simultaneous acquisition of strain information at multiple stratigraphic levels, demonstrating high monitoring survivability and spatial resolution.

To further clarify the influence of sub-key stratum failure on the stress evolution of the main key stratum, the wavelength shifts of FBG04, FBG05, and FBG06 were converted into equivalent strain after temperature compensation, and their evolution with working face advance is shown in Figure 12. The results indicate that the strain responses of the main and sub-key strata exhibit distinct staged characteristics and a stepwise transfer pattern. In Stage I, the strain recorded by FBG04 increased first and rose rapidly at approximately 132–138 cm, whereas the responses of FBG05 and FBG06 remained relatively weak, suggesting that the mining-induced disturbance was initially concentrated near the sub-key stratum and had not yet been transferred to the main key stratum. In Stage II, FBG04 unloaded rapidly after reaching a high-strain state and then entered a compressive strain state, while the strain of FBG05 increased sharply to a high level and that of FBG06 continued to increase. These responses indicate that the disturbance induced by sub-key stratum failure was progressively transferred upward through interlayer contact, rotation of the voussoir beam structure, and subsequent recompaction, causing the high-strain response zone to migrate upward and become amplified in a stepwise manner. In Stage III, FBG06 maintained a high strain level over the range of 168–184 cm, followed by a rapid decrease at approximately 186 cm and a transition to strong compressive strain, indicating that the main key stratum reached its critical suspended state after the cumulative effect of repeated disturbances, subsequently underwent instability and failure, and then entered a stage of stress release and redistribution.

FIGURE 12

These results indicate that failure of the main key stratum does not occur as an isolated event, but is the outcome of progressive evolution under repeated periodic failure disturbances of the sub-key stratum. Failure of the sub-key stratum not only causes local stress release, but also imposes continuous disturbance and cumulative damage on the main key stratum through movement of the voussoir beam structure, changes in interlayer contact conditions, and bending deformation of the overlying strata. This may promote the premature development of microcracks within the main key stratum and reduce its actual failure interval relative to the theoretical value. Therefore, in ground pressure monitoring of the working face, attention should be paid not only to the critical suspended span of the main key stratum itself, but also to the progressive disturbance effect of periodic sub-key stratum failure on the main key stratum.

The study still has several limitations. First, although the engineering mining process was simulated according to similarity theory in terms of the main physical and mechanical parameters, including geometric dimensions, bulk density, strength, and elastic modulus, several complex factors in natural rock masses cannot be fully reproduced in a laboratory similar-material model. These factors include natural joints and fractures, differences in bedding structures, fracture surface roughness, heterogeneity, anisotropy, long-term creep deformation, and groundwater-induced weakening. Therefore, the results of the physical model test are mainly intended to qualitatively reveal the relative deformation trend, fracture sequence, and disturbance transfer mechanism during the fracture of the main and sub-key strata. They cannot be directly used for quantitative prediction of field deformation magnitudes or stress values.

Second, the two-dimensional plane model adopted in this study is a simplified representation of the actual mining engineering environment. During working face mining, overburden fracture is jointly controlled by working face length, lateral surrounding rock confinement, end-boundary effects, out-of-plane fracture propagation, and three-dimensional spatial stress redistribution. In contrast, the two-dimensional model mainly reflects overburden deformation and key stratum fracture characteristics along the central section of the working face strike. It cannot fully represent the entire stress evolution process under mining conditions. Therefore, when applying the model test results to engineering practice, further correction and validation should be conducted by considering the specific working face dimensions, boundary conditions, and field monitoring results.

In terms of monitoring methods, the pre-embedded FBG sensors can sensitively capture abrupt strain changes inside the key strata, and the results can be mutually verified by dial indicator and total station measurements. However, due to the limitations of model size and sensor layout space, the number of FBG monitoring points is relatively limited. This restricts the ability to identify local crack initiation positions and micro-scale crack propagation processes. In addition, FBG sensors in the laboratory environment are relatively stable and protected, whereas sensors installed in the field are exposed to more complex conditions, such as temperature variation, groundwater influence, high in-situ stress, extrusion by fractured rock masses, and dynamic disturbance. As a result, their survival rate, coupling condition, and strain transfer efficiency may be less favorable than those under model test conditions, and should be specifically optimized according to the actual engineering conditions.

Future research may combine three-dimensional similar-material modeling with distributed optical fiber sensing and other techniques to jointly observe the spatial strain field, fracture evolution, and energy release characteristics during the fracture of the main and sub-key strata, thereby further revealing the coordinated fracture mechanism of key strata. For engineering applications, future work should focus on field borehole FBG monitoring to verify the proposed disturbance mechanism and reduce scale-effect errors.

6 Conclusion

References

• 1

  ChaiJ. (2003). Basic Study on Crack and Deflection of Rock by Optical Fiber Sensing Technology (Ph.D. Thesis). Xi'an: Xi'an University of Science and Technology.

  • Google Scholar
  • View reference in article

• 2

  ChaiJ.ChangX. T. (2004). Compatibility study of optical fiber sensor in similar material model testing. J. Exp. Mech. (04), 453–458.

  • Google Scholar
  • View reference in article

• 3

  ChaiJ.WangZ. S.YuanQ.LiY.HaoL.SuP. Z. (2013). Detection and analysis of similar physical model deformation using fiber bragg grating sensors. J. Xi'an Univ. Sci. Technol.33 (06), 633–639. 10.13800/j.cnki.xakjdxxb.2013.06.017

  • CrossRef
  • Google Scholar
  • View reference in article

• 4

  ChenR. H.PuH.MiaoX. X.QianM. G. (2004). The effect of the inferior key strata breaking on weighting of longwall face. J. China Coal Soc. (03), 257–259.

  • Google Scholar
  • View reference in article

• 5

  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 (01), 41–46. 10.15961/j.jsuese.2009.01.035

  • CrossRef
  • Google Scholar
  • View reference in article

• 6

  FengX. D.LiS. C.LiS. C.WangJ.LiL. P.YuanC.et al (2010). The development of fiber optic Bragg grating sensors and their applications to the mine water-inrush model test. J. China Coal Soc.35 (02), 283–287. 10.13225/j.cnki.jccs.2010.02.026

  • CrossRef
  • Google Scholar
  • View reference in article

• 7

  FriedelM.DongY.KonietzkyH.MorgensternA.WilsnackT. (2026). A novel approach to measure direct tensile strength on short-length cylindrical samples. GeoEnergy Commun.2, 8. 10.1007/s44421-026-00019-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 8

  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. 10.1007/s44421-025-00014-1

  • CrossRef
  • Google Scholar
  • View reference in article

• 9

  HuangQ. X. (2005). Study on loading distribution law on key roof and its structure upon mining face under thick sandy layer. J. China Univ. Min. Technol. (03), 289–293.

  • Google Scholar
  • View reference in article

• 10

  JiaJ. Q.WangH. T.TangJ. X.LiX. H.LiK. X.HuG. Z. (2006). Determination of key strata and interval of roofing breaking of hard and soft composite roofs. J. Chin. J. Rock Mech. Eng. (05), 974–978.

  • Google Scholar
  • View reference in article

• 11

  JuJ. F.XuJ. L.WangQ. X. (2011). Cantilever structure moving type of key strata and its influence on ground pressure in large mining height workface. J. China Coal Soc.36 (12), 2115–2120. 10.13225/j.cnki.jccs.2011.12.028

  • CrossRef
  • Google Scholar
  • View reference in article

• 12

  LiS. C.LiL. P.LiS. C.ZhuH. H.YinJ. H.HuC. Q.et al (2010). Development and application of similar physical model test system for water inrush of underground engineering. J. Min. Saf. Eng.27 (03), 299–304.

  • Google Scholar
  • View reference in article

• 13

  LiY.LinJ.TuJ.PengS.LiuY.WuY.et al (2026). Experimental study on the loss of pore water in geological CO₂ storage reservoirs and analysis of storage characteristics. GeoEnergy Commun.2, 10. 10.1007/s44421-026-00022-9

  • CrossRef
  • Google Scholar
  • View reference in article

• 14

  LiangL.JiangD. S.ZhouX. F.NanQ. M. (2003). Application of fiber Bragg grating sensing technology in experimental mechanics. J. Nanchang Univ. (Eng. Technol.) (02), 14–18.

  • Google Scholar
  • View reference in article

• 15

  LiangB.XingJ. C.SunW. J.FangS. J. (2025). Mechanisms and three-dimensional spatial characteristics of fissures induced under the influence of fracture of mining overburden rocks. J. Coal Sci. Technol.53 (01), 107–121. 10.12438/cst.2024-0764

  • CrossRef
  • Google Scholar
  • View reference in article

• 16

  LinH. F.LiS. G.ChengL. H.ZhangW. (2008). Key layer distinguishing method of overlying strata based on the thin slab theory. J. China Coal Soc. (10), 1081–1085. 10.13225/j.cnki.jccs.2008.10.005

  • CrossRef
  • Google Scholar
  • View reference in article

• 17

  LinS.ChangX.LiuS. (2026). Integrating hydrogen production and subsurface storage: toward a sustainable hydrogen economy: a critical review. GeoEnergy Commun.2, 6. 10.1007/s44421-026-00017-6

  • CrossRef
  • Google Scholar
  • View reference in article

• 18

  MaY. K.LiuH. J.ZhaoA. H.MaD. Y.WangG. Y.ZhangX.et al (2025). Strain field response to cross-interface propagation in DIC-based roof-guiding hydraulic fracture networks. J. Chin. J. Rock Mech. Eng.44 (08), 2007–2018. 10.3724/1000-6915.jrme.2024.0630

  • CrossRef
  • Google Scholar
  • View reference in article

• 19

  MiaoX. X.QianM. G. (2003). Broken feature of key strata and its influence on rock pressure in super-length fully-mechanized coal face. J. Chin. J. Rock Mech. Eng. (01), 45–47.

  • Google Scholar
  • View reference in article

• 20

  PanC.XiaB. W.ZuoY. J.YuB.OuC. N. (2022). Mechanism and control technology of strong ground pressure behaviour induced by high-position hard roofs in extra-thick coal seam mining. Int. J. Min. Sci. Technol.32 (3), 499–511. 10.1016/j.jrmge.2022.11.004

  • CrossRef
  • Google Scholar
  • View reference in article

• 21

  PashaieR.ShokriehM. M.VahediM.MirzaeiA. H.AkbariS. (2024). A comparative study of residual stress measurement of laminated composites using FBG sensor, DIC technique, and strain gauge. J. Opt. Quantum Electron.56 (11), 1–19. 10.1007/s11082-024-07676-x

  • CrossRef
  • Google Scholar
  • View reference in article

• 22

  QianM. G.MiaoX. X.XuJ. L. (1996). Theoretical study on key stratum in ground control. J. China Coal Soc. (03), 2–7. 10.13225/j.cnki.jccs.1996.03.001

  • CrossRef
  • Google Scholar
  • View reference in article

• 23

  QianM. G.ShiP. W.XuJ. L. (2010). Mine Pressure and Strata Control, 76–84. Xuzhou: China University of Mining and Technology Press, 93–99.

  • Google Scholar
  • View reference in article

• 24

  ShiL. H.WuS. X.LiuC.AnY. F.WangJ. L.ZhangH. W.et al (2019). Development and application of simulation test system for confined water conduction in fault zone. J. Coal Sci. Technol.47 (07), 136–141. 10.13199/j.cnki.cst.2019.07.016

  • CrossRef
  • Google Scholar
  • View reference in article

• 25

  SunB. Y.ZhangP. S.FuM. R.XuS. (2017). Fiber optic test and results of failure law of floor strata in coal mining site. J. Hefei Univ. Technol. (Nat. Sci.)40 (05), 701–707. 10.3969/j.issn.1003-5060.2017.05.025

  • CrossRef
  • Google Scholar
  • View reference in article

• 26

  WangY.BaoY. (2026). Distributed acoustic sensing-based real-time monitoring of far-field cracks in reinforced concrete bridge decks. J. Autom. Constr.183, 106821. 10.1016/j.autcon.2026.106821

  • CrossRef
  • Google Scholar
  • View reference in article

• 27

  WangS.ZhangX. (2025). Application and optimization of ground fracturing technology for key strata of extra thick coal seam roof. J. Shaanxi Coal44 (01), 128–132+164. 10.20120/j.cnki.issn.1671-749x.2025.0125

  • CrossRef
  • Google Scholar
  • View reference in article

• 28

  WangJ.ZhuW. B.XieJ. L. (2021). Research on subsidence law of overlying strata in full mining of extra-thick coal seam. J. Ind. Mine Autom.47 (10), 21–26. 10.13272/j.issn.1671-251x.17848

  • CrossRef
  • Google Scholar
  • View reference in article

• 29

  WangC. G.BaiJ. B.WangT. C.WuW. D. (2024). Energy evolution characteristics and hydraulic fracturing roof cutting technology for hard roof working face during initial mining: a case study. J. Appl. Sci.14 (16), 7405. 10.3390/app14167405

  • CrossRef
  • Google Scholar
  • View reference in article

• 30

  XuJ. L.WangX. Z.LiuW. T.WangZ. G. (2009). Effects of primary key stratum location on height of water flowing fracture zone. J. Chin. J. Rock Mech. Eng.28 (02), 380–385.

  • Google Scholar
  • View reference in article

• 31

  YanG.ZhuangW.LiuF.ZhuL. Q. (2016). Preload package and characteristics of a sensitizing effect sensor based Fiber Bragg Grating (FBG). J. Jilin Univ. (Eng. Technol. Ed.)46 (05), 1739–1745. 10.13229/j.cnki.jdxbgxb201605052

  • CrossRef
  • Google Scholar
  • View reference in article

• 32

  ZhuH. H.ShiB.ZhangC. C. (2017). FBG-based monitoring of geohazards: current status and trends. J. Sensors17 (03), 452. 10.3390/s17030452

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 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 (01), 178–188. 10.13544/j.cnki.jeg.2018-254

  • CrossRef
  • Google Scholar
  • View reference in article