## 4 Analysis of Test Results
### Spatial Distribution Characteristics of Goaf Pressure  
#### 4.2.1 Critical Layer Deformation  
Tensile failure mechanisms within the strata sequence initiate fracture propagation in the critical horizon [31]. Upon reaching the ultimate tensile strength at localized points within this horizon, fracture networks develop orthogonally to the principal tensile stress direction. The integrated fiber optic sensors, coupled with the rock mass, facilitate strain monitoring during the deformation process, registering positive strain measurements during tensile loading. This failure process manifests through several key mechanisms: initially, mining-induced disturbances generate bending deformation in the overlying strata, creating tensile stress concentration zones in critical horizons. When local tensile stress exceeds the rock mass strength, micro-fractures begin to nucleate, typically originating at weak interlayer interfaces or near existing structural planes. The primary fractures extend perpendicular to the maximum principal tensile stress direction, while secondary fractures gradually develop into a network structure as mining disturbance continues. The orientation and dip angle of these fractures are jointly controlled by regional geostress fields and mining-induced stress fields. The distributed fiber optic sensing system, intimately coupled with the rock mass, enables the real-time capture of deformation information, which proves invaluable for evaluating fracture propagation rates, predicting critical failure points, and analyzing the extent of mining influence. The mechanical process involves both tensile and shear failure modes, with fracture propagation being influenced by rock mass strength, bedding characteristics, and tectonic stress conditions. The fractured zone above the mined-out area exhibits distinct zonal characteristics. Under tensile crack propagation, a marked strain gradient manifests at the fracture interface, driving the fiber optic readings toward peak values. However, within fractured and destabilized zones, the sensing elements experience minimal residual tensile stress, resulting in attenuated response curves. Concurrent DIC monitoring validates these observations, confirming the strain measurement accuracy of both monitoring systems within these regions. As illustrated in Figure 7, the fiber optic strain response exhibits stability within a defined interval as the longwall face progresses from the excavation origin. Prior to face advancement reaching 48 cm, the measured strain values from the distributed sensing array are maintained within the 4000 \(\mu\epsilon\) threshold. Upon face progression to 104 cm, the strain profile demonstrates a stepped increment pattern, with peak magnitudes attaining 10,000 \(\mu\epsilon\), indicating critical horizon rupture. At 168 cm face advance, the strain distribution manifests a characteristic bimodal configuration. The recorded strain magnitudes at the  
Figure 6: The distribution of “three zones” of overburden rock. primary and secondary rupture interfaces register 10,487 \(\upmu\epsilon\) and 12,056 \(\upmu\epsilon\), respectively, corresponding to the bilateral fracture development. Figures 8 and 9 illustrate the spatiotemporal deformation characteristics of the critical stratum documented through the synchronized fiber optic and total station monitoring systems during extraction operations. The data demonstrate a correlation between internal strain distributions measured via distributed optical sensing and vertical displacement profiles obtained from total station surveys. Adopting the constitutive assumption of a continuous, homogeneous, and isotropic elastic medium, and applying limit equilibrium principles, the yielded rock mass exhibits linear elastic behavior under localized plasticity. Field geological investigation identifies the critical horizon as siltstone lithology. Laboratory testing on analogous specimens determines the ultimate compressive strength and elastic modulus values at 295 KPa and 77 MPa, respectively.