Destabilization damage characteristics and infrared radiation response of coal-rock complexes

To investigate the characteristics of destabilization damage in coal-rock complexes. Mechanical property tests were conducted on coal, rock, and their complexes. An infrared thermal camera was employed to real-time monitor the infrared (IR) radiation response signals during the destabilization damage process. A numerical model of coal-rock destabilization damage was developed, and its validity was verified. Deformed stress fields and displacement contours were obtained during the destabilization damage process. Upon destabilization, numerous cracks form at the base of the “coal” section, extending towards the interface, resulting in the formation of a wave-like deformation region. The differentiation in infrared thermal images is more pronounced in the “coal” section compared to the “rock” section. A high-stress region is evident at the interface, resulting in an area of high stress differentials. However, the bottom of the “coal” section also exhibits a region with high stress differentials and a more pronounced tendency towards destabilization damage. Displacement contours revealed that numerous units at the bottom of the “coal” section had slipped and misaligned, leading to the accumulation of damage and an elevation in the local damage level. It is a crucial factor contributing to the notable phenomenon of IR thermal image differentiation.

sand (particle size ≤ 3.5 mm), and water in a mass ratio of 1:1:0.5, while the "coal" section consisted of coal dust (particle size ≤ 5 mm), silicate cement, and water with a mass ratio of 1:1:0.45.Under constant conditions of 20 ℃ temperature and a relative humidity not less than 95%, the curing process for the cast specimens extended over 28 days.Standard cylinders measuring Φ50 × 100 mm were drilled and chosen as representative samples for rock, coal, and their complexes.Figure 1 illustrates the prepared samples, and Table 1 provides details regarding sample grouping.The mechanical property test system, as depicted in Fig. 2, was a digitally controlled electrohydraulic servo RMT-150 tester that utilized travel control and operated at a loading rate of 0.5 mm/s.The specific   www.nature.com/scientificreports/parameters of the test system are presented in Table 2.All samples underwent uniaxial load-damage experiments using the mechanical property test system to derive their stress-strain curves and damage characteristics.The Fotric225s thermal imager monitored temperature trends in real time during the loading of samples.

Destabilization damage numerical model
The fundamental parameters of the numerical model were adjusted by integrating the damage modes observed in physical experiments with the simulation results of stress field evolution.Subsequently, the research focused on the evolution law of the stress field in the complexes during the destabilization damage process.Simultaneously, the study investigates the characteristics of destabilization and damage patterns in coal-rock complexes through a comparative analysis of IR radiation response characteristics and the evolution process of displacement contours calculated by the model.Scale physical modeling was conducted based on the physical experimental dimensions of Φ50 × 100 mm, and partitions were established to assign properties to different areas of the model.The entire model was partitioned into 242,000 C3D8R units (8-node hexahedral linear reduced integral units), as depicted in Fig. 3.The damage behavior of coal rock during the load-compression process comprises both brittle and ductile damage.For a more accurate simulation of the material damage process, the stress-strain behavior of the model material adheres to an elastic-plastic constitutive relation.Utilizing the D-P criterion, the modified and simplified stress-strain experimental data from coal-rock samples were incorporated as the hardening rule of the model to achieve the simulation of elastic-plastic damage in coal rock 41 .The load-induced damage in coal rock can be considered as the synergistic effect of principal stress and corresponding partial stress.This effect is more accurately represented by adopting the modified D-P criterion.The model employs the maximum relative displacement of the unit as the criterion for assessing the failure behavior of the unit.Subsequently, it simulates specimen cracking by subjecting a portion of the unit to continuous strain until failure occurs.Eq. ( 1) represents the functional expression of the linear D-P model.Here, t = q when K = 1 .The yield surface conforms to the Mises yield criterion with regard to a circular yield surface [42][43][44] .
(1) where F is the elastic-plastic damage yield function; t is another form of partial stress, p is the principal stress; d is another form of internal cohesion; q is the partial stress; K is the tensile strength-compressive strength ratio; β is the friction angle of yield surface on the p-t stress surface.
In contrast to the yield surface, the flow rule governing the plastic potential surface of the linear D-P model is non-associative, following Eq.( 3).The depiction of the linear D-P model is presented in Fig. 4 ( dε pl is the equivalent plastic strain.) 45.
where G is the plastic potential function; and is the expansion angle on the p-t stress surface.
For enhanced comparison and analysis of destabilization damage pattern characteristics in physical experiments of coal rock samples, the nominal stress-strain is converted into real stress-strain data in the model, and an isomorphic model based on the D-P criterion is constructed.Additional basic parameters of the model are detailed in Table 3.
Assuming that the plane strain is in the direction of the maximum principal stress σ 1 , the principal stresses σ 1 , σ 2 and σ 3 can be rewritten in accordance with the plastic plane principal stress p and the partial stress q .Eqs. ( 7), ( 8), (9) show the conversion relations.
(2)   4), ( 5), (10), the constitutive relation of coal-rock complexes undergoing stress-strain is thoroughly explained.Based on the segmentation of coal and rock partitions, the C3D8R unit properties grid is chosen.The elastic-plastic constitutive relationship of the unit is established using the parameters in Table 3, experimental stress-strain data, and Eqs. ( 4), ( 5), ( 6), ( 7), ( 8), ( 9), (10).The judgment of the unit's failure behavior relies on the maximum relative displacement.This approach facilitates the simulation and resolution of cracking behavior, leading to the development of a finite-element numerical model for destabilization damage in coal-rock complexes.The model is solved using the ABAQUS/Explicit solver.

Strength characteristics and destabilization damage patterns
The substantial variation in mechanical properties among different areas within the coal-rock complexes leads to the following phenomenon.During the loading process, the high-strength area, while being "loaded, " also acts as the carrier of the "load".In contrast, the low-strength area becomes the focal point of damage, serving as the primary region where strain energy accumulates.Figure 5 illustrates the stress-strain curves of coal, rock, and their complexes obtained in the mechanical property experiments.The maximum uniaxial compressive strength (UCS) exhibits a trend of R > CR > C. As illustrated in Fig. 5, under the condition of "strong rock and weak coal," the UCS of the complexes falls between that of coal and rock.It experiences an increase of 11-25.9%compared to coal and a decline of 44.3-54.3%compared to rock.During the experiment, the UCS of the "coal" section governs the damage in the coal-rock complexes.However, the overall UCS of the coal-rock complexes surpasses that of the "coal" section.This phenomenon can be explained from two perspectives.Firstly, the destruction of the "coal" section increases.Secondly, the "rock" section of the structure absorbs some loads and deforms.Additionally, Fig. 5a-c illustrates that when the axial stress decreases dramatically, the axial strain of the final specimen exhibits a magnitude relationship of CR > C > R.This suggests that the overall degree of destabilization damage in the complexes is more severe.For a thorough analysis of the destabilization damage pattern in coal, rock, and their complexes, the equivalent plastic strain pattern of the coal-rock destabilization damage model was calculated.The results of the destabilization damage pattern of samples are highly consistent with the equivalent plastic strain pattern of the model.As shown in Fig. 6 (unit: mm).
In Fig. 6a, when the elastic modulus ER of the coal-rock complexes is approximately three times as high as that of coal (i.e.E R ≈ 3E C ), the "coal" section undergoes plastic deformation, and the size and extent of plas- tic deformation decrease as the interface is approached.During the loading process, the high-strength "rock" primarily acts to transfer the load work, and the combination of "coal" and "rock" at the interface enhances the deformation resistance of "coal" in that vicinity.The reason for this lies in the discontinuity of stress transfer within the complex.The inherent strength of the "rock" component enables it to transfer stresses more efficiently.Additionally, coal and rock represent distinct areas of the same geometry, implying that the interface bonds the coal-rock complex with higher strength.A comparative analysis of the damage patterns of coal, rock, and their complexes in Fig. 6 is conducted through color classification of deformation degree classes.In the early stages, the coal/rock samples exhibit green bands in an "X" shape, with the lower section displaying an overall tendency of green.Subsequently, reddish-yellow bands form, signifying the generation of macro-cracks.As the cracks expand, the samples will exhibit large "X"-shaped cracks.In the early stage of complex destabilization, the "coal" exhibits wavy cyan stripes, green stripes, and "X"-shaped reddish-yellow stripes from the interface to the lower end.Subsequently, macro-cracks originate from the lower end, leading to their expansion.The damage pattern of the "rock" part mirrors that of the test specimen, appearing blue and nearly strain-free.This outcome correlates with consistent friction angle and expansion angle in the monomer region, aligning with the model of an elastic-plastic ontological relationship.The unique destabilization damage pattern results from differences in the physical properties of coal and rock within the complex.Ultimately, the complex develops numerous intersecting "X"-shaped cracks at the lower end of the coal, extending towards the interface, and forms a deformation region with wavy cyan-colored bands at the interface.In the monomer, a few "X"-shaped cracks are generated in the middle and lower parts, crossing each other near the top and bottom ends.Greenish stripes, representing the tendency of crack expansion, form slant lines with a single expansion pattern.The physical differences between coal and rock induce stress transfer discontinuity, resulting in distinct destabilizing destructive behaviors of the monomer and the complex.This discrepancy is the primary cause behind the formation of the concentrated destructive location and heightened destructive degree in the destabilizing destructive morphology of the complex specimen during testing.

IR thermal image differentiation characteristics
The distribution and migration of the thermal field on the surface of the samples during the destabilization of coal-rock bodies are recorded by the infrared camera.This analysis discerns the differentiation and evolution characteristics to predict the location of destabilization damage by real-time monitoring of the IR temperature field on the samples' surface.For the comparison and analysis of the infrared thermal image differentiation characteristics of coal, rock, and their complexes, the IR temperature field at three moments of axial loading stress σ a = 0.1UCS , σ a = 0.65UCS and σ a = UCS is selected, and the amplitude of temperature difference is set to − 0.5-1.5 ℃, and the 3D spatial distribution chart of temperature difference values is plotted at the same time, as shown in Fig. 7 (unit: ℃).
In Fig. 7, the complex at σ a = 0.1UCS exhibits more pronounced differentiation characteristics compared to the monomer.This is attributed to the differing strengths of coal and rock, leading to discontinuous stress transfer within the complex and an increased likelihood of shear damage formation.In Fig. 7a, the C-1 surface at σ a = 0.65UCS exhibits a scattered distribution of yellow-green high-temperature areas, almost uniformly distributed.This indicates many small shear damages on the surface of the sample.When σ a = UCS , the sample surface shows reddish-yellow high-temperature bands, and the infrared thermal image differentiation characteristics of the sample surface can be observed more clearly from Fig. 7b.At the upper end of the sample, a localized red high-temperature region appears.Simultaneously, a high-temperature region emerges at the location of the reddish-yellow stripe shown in Fig. 7a.The sample undergoes single-bevel shear damage along the hightemperature region, resulting in a macrocrack consistent with the destabilized damage pattern of the sample.In Fig. 7c at σ a = 0.65UCS , R-1 exhibits a denser yellow-green scattering region than C-1.This indicates that the surface temperature increase is more significant when R-1 shows a destabilization damage trend.At σ a = UCS , the surface of R-1 exhibits clear thermal differentiation on the infrared image, revealing a "Y"-shaped crossed reddish-yellow high-temperature bands.This pattern is consistent with the cracking pattern of the sample.Figure 7e, f reveal that the infrared thermal image differentiation and evolutionary features of CR-1 differ significantly from C-1 and R-1.At σ a = 0.65UCS , the yellowish-green particles in the "coal" section are significantly larger and denser than in the "rock" section.Yellowish-green spots are also present at the coal-rock interface, representing the high-temperature region.At σ a = UCS , the yellow-green stripes in CR-1 are monoclinic in the "coal" section, paralleling the interface, and remain scattered in the "rock" section.During the process of axial stress loading, micro-deformations occurred in the "rock" section, but no macroscopic cracks formed, and only the tendency to destabilization damage was observed.
According to the above analysis, the surface temperature field distributions of samples R-1 and C-1 are very similar, but the differentiation feature of R-1 is more pronounced.In CR-1, the "coal" exhibits more pronounced differentiation characteristics than the "rock".Leveraging this feature, infrared thermography can be employed to monitor the infrared radiation temperature field of the surrounding rock.This facilitates the effective prediction of instability damage, particularly the more significant local radiation temperature divergence characteristics of coal-rock complexes, which proves highly beneficial for predicting instability damage.Such insights are of reference value for the safe mining of coal-rock complexes in the coal mining industry.The infrared thermal image differentiation characteristics of CR-1 align with the test and simulation results.The "rock" section exhibits minimal infrared differentiation and small amounts of micro-deformation, which are beneficial for increasing the UCS of the overall complexes.The "coal" and interface sections preferentially show destabilization damage tendency, produce macro-cracks, and increase the degree of destabilization damage.This is the main part of destabilization damage of coal-rock complexes.

Stress field evolution
After analyzing the strength characteristics and destabilization damage patterns of coal, rock, and their complexes, it was observed that the strength of the complex is more akin to coal than rock.Additionally, the degree of destabilization damage is more pronounced, with macro cracks predominantly concentrated in the "coal" section.During the destabilization damage process, infrared thermal image differentiation of the "rock" section of the complex shows a large number of shear-type micro-deformations.To better study the destabilization damage and damage evolution in coal-rock complexes, the analysis is conducted considering the behavior of stress field evolution.The stress contours resulting from the post-processing of the numerical model solution for destabilization damage to the coal-rock are displayed in Figs.   the yield surface exceeds a predefined failure limit, leading to the formation of macroscopic cracks, and the stress field tends toward a disordered state.By comparing Figs. 8 and 9, the difference in mechanical properties results in higher peak stress levels in Fig. 9a-d than those in Fig. 8a-d.Additionally, the peak stress levels in Figs.9(e) are lower than those in Fig. 8e during destabilizing damage.This finding aligns with the results of mechanical property tests, corresponding to the rapid stress decay observed after destabilization damage in rock samples 43 .It further confirms the validity of the model's stress field evolution.
In addition to the previously mentioned commonality in stress field evolution, the complex destabilization damage process demonstrates its unique stress field evolution behavior.In Fig. 10b, it is evident that the stress in the "coal" section is considerably lower than that in the "rock" section, and a differential stress region is preferentially formed at the interface.Ongoing axial loading generates a high-stress area at the interface and a lowstress area at the bottom of the "coal" section, indicating a tendency for destabilization damage.In Fig. 10c, the distribution of stress field weakening makes the interface and the "coal" section bottom susceptible to high-stress differentials, leading to destabilization.In Fig. 10e, the complex undergoes irreversible deformation, resulting in numerous low-stress regions.A small amount of high-stress region still exists at the interface, forming a highstress difference with the surrounding region, indicating a tendency for destabilization damage at the interface.Due to differences in the mechanical properties of coal and rock, the simultaneous existence of two regions of stress difference will lead to the destabilization damage tendency of both the interface and the bottom of the "coal" section 32 .In the simulation results, when the "coal" section is destabilized, the stress field at the interface is redistributed, weakening the destabilization tendency.Consequently, the macro crack expands from the bottom of the "coal" section toward the interface.

Analysis of the evolution of destabilization damage
Through an examination of the stress field evolution behavior and IR radiation response signals during the destabilization damage process of coal, rock, and their complexes, the behavior of coal-rock matrix slip and dislocation damage facilitates the intensification of local molecular motion.This forms the fundamental basis for the phenomenon of infrared thermal image differentiation.Therefore, this study elucidates the distinctions in displacement vector and slip dislocation damage of coal, rock, and their complex through the displacement contour.Furthermore, it compares and analyzes the IR radiation response behavior to explore the destabilization damage evolution during the coal-rock complex.According to the IR radiation signal monitoring principle of the infrared camera, each pixel point in the measurement area corresponds to a two-dimensional temperature data matrix of the sample surface.The p-th frame temperature matrix is then represented as follows 46 .where: m is the matrix row number, n is the matrix column number, L m is the maximum number of matrix rows, and L n is the maximum number of matrix columns.
The IR radiation signal during the destabilization damage process of the coal-rock is generally weak and prone to interference from background noise.Therefore, the differential radiation temperature method was chosen to process the infrared video and initiate the analysis 47 , as illustrated in Fig. 7. Throughout the destabilization damage process of the complex, the matrix of the coal-rock will persistently experience shear-tension damage under the influence of external forces.Upon the accumulation of a certain level of damage, macroscopic cracks will develop, as depicted in Fig. 11.The occurrence of shear damage leads to slip dislocation between the coal-rock matrices, resulting in the phenomenon of temperature rise and intensifying molecular movement, as illustrated in Fig. 12.
Drawing upon the relationship between temperature field and the damage evolution behavior of the sample, this analysis explores the displacement cloud and IR radiation response characterization of the destabilization damage process.The aim is to provide theoretical support for the study and prediction of the damage evolution behavior of the coal-rock during destabilization.Considering that shear damage is the primary cause of the anomalous increase in the local temperature field 12 , the displacement maps on U1, U2, and U3 in mutually perpendicular directions are proposed for selection here.This choice is conducive to the comparative analysis of shear damage between the coal and rock substrates.The displacement contours resulting from the calculated model destabilization damage are presented in Figs. 13, 14, 15 (unit: mm).To compare displacement differences in various regions of coal, rock, and their complexes, incremental steps were selected, corresponding to instances where a significant number of model units failed, and macroscopic cracks emerged.The results are depicted in Figs. 13, 14, 15.Figures 13, 14, 15 reveal that cracks, formed by failed units, divide the model into distinct regions with significantly differing displacement contours.Analyzing misalignment, slippage, and shear damage that occurs at the cracks between regions is facilitated by comparing different color divisions.Upon comparing Figs. 13, 14, 15, it was observed that monoliths formed "X" cracks, whereas cracks in the complexes expanded from the coal bottom to the interface, forming extremely dense cracks.This observation aligns with the phenomenon that the IR thermal image of the "coal" section in the test exhibits obvious differentiation characteristics, and the damage degree has increased 38 .In monoliths, the tops and bottoms of the cracks are compressed in the direction of U3, resulting in the lateral displacements U1 and U2.In the complexes, lateral displacement is predominantly observed at the bottom of the "coal" section, and the displacement contours at the interface resemble those of the "rock" section.Combining the displacement contours with the analysis of stress field evolution in Fig. 10, two main reasons are identified for the phenomenon of concentrated lateral displacement.Firstly, the coal-rock matrix at the interface will undergo different degrees of deformation simultaneously, and this deformation will suppress the destabilization damage tendency of the coal matrix at the interface.Secondly, there is no low-stress zone at the interface; that is, the stress difference at the "coal" section bottom is higher than at the interface.Drawing on the above analysis, the anomalous hightemperature scattering-intensive phenomenon of the infrared radiation signal in the destabilization damage of the complex results from the local dislocation and slippage of the coal-rock, coupled with the frictional heat effect.This effect gives rise to the anomalous high-temperature banding depicted in Fig. 7e, f, primarily concentrated in the "coal" section and the interface.Ultimately, this leads to cracks at the bottom of the "coal" section extending towards the interface.

Conclusions
(1) The maximum UCS of the cast complex samples, consisting of similar materials in the tests, surpassed that of the coal samples but remained significantly lower than that of the rock samples.The axial strain during the final complete destruction exhibits a magnitude relationship as follows: CR (complex) > C (coal) > R (rock).The validity of the model was confirmed through a comparison of the plastic deformation contours and the instability damage patterns of the samples.The simulation reveals that a substantial number of cracks initiate and extend towards the interface at the bottom of the "coal" section, forming a wave-like deformation region at the interface.This is in contrast to the single extension pattern observed in the monoliths.
(2) Both rock and coal samples exhibited anomalous high-temperature stripes, leading to damage along these anomalies and the subsequent formation of macro cracks.The rock samples exhibited more pronounced differences in the IR thermal images, with a more noticeable increase in surface temperature.Under complex loading conditions, the anomalous temperature scatters are notably denser in the 'coal' section compared to the 'rock' section.If the "rock" section displays a few anomalous high-temperature scatters, the "coal" section and interface have already developed anomalous high-temperature bands, indicating a tendency towards destabilization damage and the formation of macro-cracks.
(3) The process of destabilizing monoliths exposes low-stress zones parallel to the yield surface that intersect, giving rise to a high-stress differential region leading to damage.In the course of complex destabilization

Figure 4 .
Figure 4. Linear D-P model: yield surface and flow direction in the p-t stress plane.

Figure 5 .
Figure 5. Stress-strain curves and load-damage characteristics.(a) Curves of group 1.(b) Curves of group 2. (c) Curves of group 3. (d) Comparison before and after samples are subject to load-damage.

Figure 6 .
Figure 6.Characteristics of destabilizing damage patterns of coal and rock monoliths and their complexes.(a) Complexes.(b) Rock.(c) Coal. https://doi.org/10.1038/s41598-024-65029-wwww.nature.com/scientificreports/ 8, 9, 10 (unit: MPa).The evolution of the stress field during the destabilization damage model follows a specific process.As depicted in Figs.8a, 9a, 10a, the stress field diminishes and forms bands from top to bottom under axial loading, with a high-stress region generated at the top.With increasing axial stress, the stress field tends to distribute uniformly until a local unit stress imbalance and stress difference formation occur, indicating a tendency toward destabilization, as shown in Figs.8b, 9b, 10b.Low-stress bands crossing along the yield surface are evident in Figs.8c, 9c, 10c.In Figs.8d, 9d, the low-stress band in the coal-rock monoliths initially appears at the top-middle position and then rapidly expands toward the bottom.As low-stress strips continue to form, the unit strain on

Table 1 .
Information of sample grouping.

Table 2 .
Experimental parameters of the test system.

Table 3 .
Basic physical parameters of the model.