Quantitative Precursory Information of Weak Shocking Failures of Composite Soft Roof

Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China State Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China College of Architecture and Civil Engineering, Liaocheng University, Liaocheng 252000, China


Introduction
Underground rock formations in underground construction and mining engineering can be regarded as composite structures with different geological bodies as dynamic disasters such as bursts in rocks and coal roadways caused by excavation, and mining disturbances are indeed results of instability deformations of composite structures caused by interactions of geological bodies with different mechanical properties [1][2][3].In underground tunnels, a composite loadbearing system consisting of roof, coal seam, and floor is observed, and instability of any body may cause the failures of the entire system.Due to differences in strength, stiffness, and lithology of different geological bodies, the failure characteristics of the composite body are completely different from that of any single body.e structural effect dominates mechanical behaviors of the composite system.erefore, it is of great significance to understand the overall mechanical effect and failure precursory information of rock-coal composite structures in order to predict dynamic disasters in mining.
In recent years, researchers have studied the failure characteristics of combined models of different geological bodies by traditional mechanical tests.For instance, the postpeak stability of two-body systems consisting of roof and coal was investigated [4].Based on the microfractures in the evolution of earthquake in two-body models, precursory principles of deformation localization and elastic rebound were clarified [5,6].In terms of coal-rock composite structures, mechanical properties and dynamic failure characteristics of coal-rock body with different height ratios were studied experimentally [7][8][9], and a nonlinear model to describe overall failures was established [10].Some researchers claimed that failures of coal-rock body may be attributed to contribution of energy accumulated in rock to failures of coal unit during loading [11][12][13].
ese results indicated that dynamic instability of coal rocks is a disaster of instability of surrounding rock-coal systems.Hence, for roof-coal-floor systems, interactions of subsystems such as roof, coal seam, and floor should be taken into full consideration in order to investigate the overall effects of subsystems and composite system on the dynamic instability tendency from the aspects of storage and release of deformation energy in coal and rock mass.However, it is difficult for traditional methods to effectively obtain the instability characteristics and precursor information of the composite body.erefore, the precursor of coal sample destruction was further studied by comprehensive monitoring methods, including infrared radiation and acoustic emission.Other studies indicated that the thermal effect is proportional to strength of microfracture of coal samples, and the temperature effect of infrared radiation was maximized at loading � 70% of the coal sample strength [14][15][16].Also, preliminary observations on the infrared radiation information produced by deformation and breakdown of the coal were obtained according to this principle [17,18].e results revealed that the ultimate failure precursor of the burst tendency of coal sample body under was approximately at 0.90σ c and 0.81σ c under uniaxial loading and cyclic loading, respectively.Based on that, compression tests of sandstone-coal body and sandstone-coal-mudstone body were performed using a synchronous device consisting of infrared imaging system and emission monitoring system.e quantitative precursory locations of instability failure of composite structures were captured by thermal infrared and acoustic emission, and the results showed that the instability precursor of the three-body model was behind that of the twobody model [19,20].e studies mentioned above demonstrated that underground engineering disasters are reflections of overall instability of composite structure systems with different geological bodies during mining disturbance.Currently, researchers have carried out various theoretical and experimental studies on the instability failure and rock burst of coalrock systems in mining engineering, and both qualitative and quantitative criteria of instability failures of combination body have been proposed to facilitate prediction and prevention of dynamic instability disasters.However, these conclusions were obtained based on hard rock-soft coal systems, and it is not applicable to weakly cemented soft rock strata.Moreover, the precursory information of instability failures was mostly qualitative, and acquisition of quantitative information was extremely complicated.It has been demonstrated that instability fractures of weakly consolidated rock sample do not occur at the peak.Instead, it is commonly observed at a certain position during the postpeak softening stage, and such instability points are readily observed in weak rock burst [21][22][23][24].Also, release of elastic energy was observed in rock mass during the postpeak softening stage.
For this reason, instability failure characteristics of strong-weak geological system with different stiffness were discussed according to the combined surrounding rock system with strain softening rock strata and coal seams.Quantitative criteria of instability failure characteristics of such structures were proposed based on theoretical analysis and numerical simulation.Additionally, the relevant conclusions are applied in engineering practice to provide references for prevention and control of weak roof shocking disasters in mining engineering in western China.

Mechanism of Instability Failures of
Strong-Weak Geological System with Strain-Softening Behaviors  [25], the instability failure of the weak body was initiated at the postpeak stress decreasing stage, and strain-softening of rock mass is prerequisite for sudden catastrophic damages.
Figure 1 shows the strong-weak geological system, and both bodies exhibit strain-softening behaviors.
e stiffnesses of strong and weak body at the prestage are defined as K s and K w , respectively.Under axial force (F 1 ), displacements of the strong body and the weak body were η s and η w , respectively.
erefore, the overall displacement of the system can be expressed as Figure 2 shows the load-displacement curves of the two bodies during loading.
e load-displacement can be expressed as [26] F where F s and F w refer to the axial loads on strong body and weak body, respectively.η sc and η wc refer to the axial displacements of strong body and weak body, respectively, at peak loading, and they are related to their peak strengths.η sp and η wp refer to the displacements of strong body and weak body, respectively, at yielding point.m and n refer to fitting parameters.
In the quasistatic loading process, the system is in equilibrium and the following relation should be satisfied before catastrophic damages in weak body: Shock and Vibration (3)

Energy Evolution Mechanism in Loading Process.
Before peak loading of the weak body, the system is in elastic stage with no damages, if the relatively short yield stage is not taken into consideration.In this case, the two bodies are in a state of energy accumulation due to elastic deformations.At peak loading of the weak body, internal damages caused by propagation of microcracks were observed.At postpeak loading process, the energy consumed by damages of the weak body can be calculated by e elastic energy released by the weak body is where K wa and η wa refer to elastic modulus and displacement, respectively, at loading point a of the weak body.Due to the sti ness deterioration at the postpeak stage, K wa < K w .In this process, the strong body is still at the elastic stage and will be unloaded to point a along the initial elastic loading line.e elastic energy released can be calculated by e external work can be calculated by Based on energy conservation, Substituting equations ( 4)∼( 7) into (8), 1 2 As catastrophic damages occur in the weak body, its displacement η w is regarded as the state variable of the system so that the displacement and load of the strong body are functions of η w at the postpeak stage.Based on the variation principle, equation ( 9) can be rewritten as

Instability Failure Criterion of Strong-Weak Geological
System.Let J 0 F t (η t )(δη t /δη w ) (δW/δη w ) be the energy input rate.Its physical meaning is that the energy required to be applied externally for unit deformation of the weak body produces δη w .Hence, equation ( 10) is rewritten as where F w ′ (η w ) refers to the tangent sti ness of the weak body at the postpeak strain softening stage.
Obviously, J 0 is a variable at the strain-softening stage.If J 0 ⟶ 0, external energy is not required and increasing deformation of the weak body can be achieved by the elastic energy released by the strong body and the weak body. is indicates that the system is not stable and catastrophic fractures tend to be observed.In this case, Equation ( 12) is the sti ness instability criterion of the strong-weak geological system.
However, the sti ness criterion of rock instability proposed by Cook is where k m refers to the tester sti ness and j refers to the starting point of the rock instability fracture.f ′ (u j ) refers to the tangent slope of point j at the softening stage.Let Equation ( 12) can be rewritten as As shown in equations ( 12) and ( 15), the sti ness criterion of instability failure proposed in this study is consistent with that by Cook.However, the elastic energy released from the weak body during fracturing is considered in the proposed model.erefore, the equivalent sti ness K 0 of the interaction system includes not only the sti ness of the strong body but also the deteriorating sti ness of the weak body at the softening stage, which is equivalent to the loading sti ness of the tester in Cook's equation.As K 0 < K s and K 0 < K wa , the catastrophic point of the instability failure of the weak body in this model is beyond the one in the model proposed by Cook.e system can be in two states before and after a sudden dynamic instability: the instability Shock and Vibration equilibrium state at the precursory stage of instability and a new stability equilibrium state after loading.For soft rocks with signi cant strain-softening behaviors, the catastrophic point may occur repeatedly due to their complicated softening.As a result, soft rocks are in the process of alternating stable and unstable deformations, as shown in Figure 3.
With a given ΔF t (η s ), displacement increments in strong and weak body can be calculated by e total displacement increment of the system is As ΔF s (η s ) ΔF w (η w ) ΔF t (η w ), equations ( 16) and ( 17) lead to e deformation rates of strong body and weak body can be expressed as where η t is the loading rate of the interaction system and it can be regarded as a constant.F s ′ (η s ) is the tangent slope of loading curve of strong body and should be substituted by K 0 .erefore, equation ( 19) shall be rewritten as According to equation (15), if e instability failure is proportional to the consistency of these two parameters.erefore, sudden changes in deformation rates of the two bodies can be regarded as the precursory information for catastrophic failures of the system.

Precursor Information of Instability
Failure in Coal-Rock Body by Numerical Simulations In order to fully understand the sti ness e ect on failures of soft rock-coal body and demonstrate the feasibility of regarding deformation rate as precursory information of instability failure, the model was veri ed using numerical simulations based on relevant experiments.

Computational Model.
A standard cylinder with diameter of 50 mm and height of 100 mm was constructed.Let the height ratio of rock and coal be 1 (Figure 4); the simulation was performed under uniaxial compressions.e particles on the upper and lower surfaces of the model were  Shock and Vibration allowed to move vertically only.Loads were applied by displacement control method at a rate v of 2 × 10 −8 per step.e physical and mechanical parameters of rock and coal are listed in Table 1.
To fully understand the failure characteristics of strainsoftening materials, the M-C ideal elastoplastic model and strain-softening model were employed for numerical calculations, and the results were compared with each other.In the M-C ideal elastoplastic model, the cohesion and the friction angle remain constant after yielding of elements.In the strain-softening model, however, strength parameters degraded after yielding of elements.According to relevant experimental results, the strength parameters of rock and coal attenuated at postpeak stage, as shown in Figure 5.
In the constitutive model of coal-rock body, elastoplastic-elastoplastic (M-M), elastoplastic-strain softening (M-S), and strain softening-strain softening (S-S) constitutive relations are observed.To guarantee uniform distribution of unit meshes and reasonable comparability of di erent constitutive models, the coal and rock were placed in the same grid system and divided into grids uniformly.It is assumed that the body interface exhibits high bonding strength with parameters as follows: normal stiness and tangential sti ness k n k s 300 GPa/m, cohesion C c 100 MPa, and friction angle ϕ c 40 °.Owing to e ects of strain localization (concentration of deformations and failures in a localized region), stress-strain curves of ideal elastoplastic model also declined at the postpeak stage.To avoid that, the mesh size shall not be oversmall in order to achieve uniform unit deformation.e numerical calculation mesh is as follows: the system was divided into 10 elements along the radial direction and 20 elements along the axial direction.Each element is in size of 5 mm.
Figure 6 illustrates the stress-strain curves of coal-rock body in di erent constitutive models.As observed, the uniaxial compressive strength of the system was 13 MPa in the M-M model and 11.5 MPa in both M-S model and S-S model.In terms of the entire deformation process, the stressstrain relations in the three models coincide completely at the prepeak elastic stage, while their nonlinear deformation characteristics were signi cantly di erent.In the M-M model, the strain increased rapidly upon reaching the peak strength, while the stress remained constant, which is typical ideal elastic-plastic deformation.In M-S model and M-M model, signi cant stress degradations were observed at the postpeak stage owing to increasing deformation as strength attenuation at postpeak stage was taken into consideration.Additionally, the stress degradation was proportional to the medium softening.For instance, the stress degradation modulus of the S-S model was larger than that of the M-S model.
In numerical simulations, failures start from one single element.Hence, the computational scale depends on the element size, and the computational time step is determined by the quantity of elements.In regions with high and concentrated maximum imbalance forces, element failures are readily observed.Based on that, the failure process of the model can be described, and the precursor information can be captured.As shown in Figure 6, the maximum imbalance forces varied smoothly during deformation and failure of M-M and M-S models, indicating progressive failures of the element.In the S-S model, the maximum unbalanced forces varied violently at the postpeak stress drop stage and several sudden increasing/decreasing cycles were observed, indicating sharp element failure at this stage and the failure concentration in one speci c region (localized localization).In this study, the S-S model should be employed.

Computational Results.
e sti ness ratio is de ned to be α E r /E m , where E r and E m are elastic moduli of rock and coal, respectively.With other parameters being constant, the failure characteristics of coal-rock body as a function of the   sti ness ratio α can be revealed by varying E r .Two monitoring points were arranged at the middle element node near the contact surface on each body.Figure 7 shows the correlation of stress evolution of the two-body system and deformations measured at the monitoring points at di erent sti ness ratios.Owing to the e ects of contact surface and the sti ness di erence, deformation rates of coal and body are severely inconsistent and uctuated signi cantly at the postpeak strain-softening stage.In terms of the stress evolution, a signi cant stress degradation was observed at α 1, demonstrating unexpectedness and instability of coal-rock system failures.is can be attributed to the fact that coal reaches its peak strength, while the rock body is still in the elastic stage.Like the loading system in the tester, the elastic energy of the rock at postpeak stage of the coal body is suddenly released due to the insu cient rock rigidity, resulting in shocking to the coal body.As α increased, the prepeak sti ness of the model was enhanced, and the postpeak stress degradation modulus dropped (smooth stress curve), demonstrating signi cant strain-softening behaviors.If α > 1, the stress curve uctuates and the uctuation frequency is proportional to the sti ness ratio, demonstrating gradual and severe localizations during the failure process.
Figure 8 shows the ultimate failure modes of coal-rock body under di erent sti ness ratios.As strengths of coal and rock are highly consistent, a single shear band through the contact surface was observed at α 1.At α 7, two conjugated shear bands were generated by the intersection of interfaces.At α 20, no shear bands were observed in the coal body, illustrating overall plastic deformation.Additionally, the overall compressive plastic deformation of rock body was also observed in the vicinity of the contact area, and two shear bands with di erent thicknesses were generated starting from the middle part of the contact surface.

Results and Discussion
. As α increased, the deformation rates of rock and coal exhibited two patterns.
First, the deformation rate exhibits a sudden drop near the peak point.e sudden drop was before the peak point at α 1 and after the peak point at α > 1. en, the deformation rate uctuated sharply at the softening stage and remained stable at the residual stage.e sudden drop of deformation rate of rock at the prepeak stage indicates rebound of its elastic deformation to the coal body, namely, sudden release of elastic deformation energy from rock to coal.e sudden drop of deformation rate of coal indicates microfractures in the coal body, resulting in deformation instability.In fact, another sudden jump point of deformation rate was observed near the residual stage.According to the results, the failure of the coal-rock body is directly related to the deformation rates of coal and rock.e sudden drop points of coal and rock exhibit the feature of simultaneous uctuation in one direction, and their position may vary due to the sti ness e ect.Damage precursor information of coal-rock body can be captured based on the sudden drop of deformation rate.e rst point is the starting point of the main fracturing of two-body system and can be regarded as the precursor information of the model failure; the second point is the breakthrough point of the main fracturing of two-body system.e uctuations can be readily identi ed as they are highly frequent during the uctuation section.
e uctuation frequency of the second point was signicantly higher than that of the rst point.For rock failures, a direct re ection of system instability is the maximum deformation rate.
Second, the uctuation frequency of deformation rate in rock body decreased gradually as the sti ness increased.At α > 20, the two sudden jumps in rock were eliminated, meaning that the rock has no shock e ect on coal, and the coal-rock body exhibits stability failure.However, the rst point was still observed in the coal body, indicating that the failure occurs in the coal body rst under loading.As shown in Figure 7, the second point of coal body is independent of the sti ness ratio at α < 9.
is can be attributed to the fact that deformation localization in the model initiates from the coal body and the complexity of shear band caused by localization as a function of sti ness.However, the second point of the coal body was also eliminated at α 30, indicating overall plastic deformation of the two-body system, and no main fracture band was presented.
In summary, the failure characteristics of the coal-rock body system are directly related to the sti ness ratio of rock body and coal body.With sti nesses of rock body and coal body being highly consistent, stress degradation was observed during stress evolution, and instability failure was observed.With sti nesses of rock body and coal body being highly inconsistent, signi cant strain-softening behaviors were observed, and the model exhibited progressive stability failure.e composite model was exposed to overall plastic deformations.In weak cementation soft rock strata in western China, instability and sudden failures of surrounding rocks are readily observed due to consistent sti nesses of soft rocks and coal.Although not as intense as those of hard rocks, these failures have a signi cant e ect on the stability of soft rock roadway.In summary, although varying with the elastic modulus of coal and rock, the two points re ecting the failure information are readily

6
Shock and Vibration identi ed and tested.Hence, the instability sudden failures of surrounding rocks can be predicted by monitoring the deformation rates of composite roof consisting of coal seams and rock layers in practical engineering.

Engineering Application
Located on the slope belt of southern margin of the Yili Basin in Xinjiang, the Yili No. 1 mine eld has coal seams whose Step (×10 Step (×10 Step (×10 3 ) (f ) erefore, roadways are often arranged in relatively stable coal seams, resulting in a typical coal-rock composite roof structure.However, working face excavation is often accompanied by weak roof shocking and the following characteristics are observed: (1) roof shocking is usually observed in coal bodies with good integrity, compacted structure, reduced crack propagation, and brittleness.(2) e roadway with roof shocking tends to be dry, and water drenching directly along the bolt, tray, and roof is seldom observed.(3) e roof shocking tends to be observed in a few hours or a few days after the head-on cut, and the frequency of roof shocking is inversely proportional to the distance of head-on.(4) In presence of intense roof shocking, bolt and tray may be loose, but the bolt does not shock out (Figure 9).Although not comparable to impact pressure, the roof shocking has a signi cant e ect on the stability of surrounding rocks, thus the construction safety.
Four mining pressure observation stations were designed along the three coalbelt downhill roadways, and locations of roof measuring points are illustrated in Figure 10.
e displacement meters were installed in rock stratum and coal seam near the coal-rock interface.By the method discussed in Section 3, the information of instability failures of surrounding rocks can be captured by monitoring deformations of roof seams and rock strata.
Figure 11 shows the deformation rates of rock strata and coal seams monitored.
e roadway deformation can be divided into the roadway excavation stage, the deformation limit stage, and stable deformation stage as the workface excavation progresses.e e ects of excavation unloading on surrounding rocks are re ected as rapid release of elastic deformation energy and high initial deformation rate.In order to avoid large deformations of surrounding rocks, the anchor net supports were arranged right after excavation.As observed in Figure 11, the deformation rate of surrounding rocks is relatively high in the rst 10 days, and two sudden  jumps of deformations were observed in coal seam and rock stratum.Practically, roof shocking basically occurred at the observation point of sudden jumps, which is also the moment when the bolt support structure is readily exposed to damages.After redistribution of deformation and stress in the supporting system, coupled deformation of surrounding rock and supporting structure is realized, and the supporting system tends to be in equilibrium state.Owing to the rheological characteristics of soft rocks, the equilibrium is achieved gradually.According to monitoring data and the practical situation of surrounding rocks, it is reasonable to adopt the sudden jump of deformation rate of rock-coal structure as the precursory information of instability failures induced by weak roof shocking.

Conclusions
Aimed at weak roof shocking in weakly cemented soft rock stratum in mining engineering of western China, the mechanism of instability failures was investigated based on the overall bearing characteristics of the composite roof consisting of weak cemented soft rock and coal.e precursory information of weak shocking failures of rock-coal body was proposed based on theoretical analysis and numerical calculations.Industrial applications demonstrated good applicability and accuracy of the proposed approach.
e following conclusions can be drawn: (1) e failure of composite structure is initiated at the postpeak stage of weak geologic body, and the strain softening of rock mass is prerequisite for sudden catastrophic failures.Likewise, the weak body also releases elastic energy at the postpeak failure stage.
According to the energy evolution in failure process of strong-weak body, the elastic energy released by the weak body at the postpeak stage also contributes to the failure of the composite structure.erefore, the criterion for the instability failure of strong-weak system is consistent with the stiffness criterion proposed by Cook.However, the equivalent stiffness in the proposed model consists of both the stiffness of strong body and the deterioration stiffness of weak body at the softening stage.(2) e critical point of instability failures of strongweak structure is earlier than that in the stiffness criterion proposed by Cook.e critical points may appear repeatedly in weak cemented soft rocks at the postpeak stage, and the system is in the alternating process of steady state and unsteady state.(3) In the proposed model, synchronous jumps of deformation rates in coal body and rock body can be recognized as the precursory information of catastrophes.e first sudden jump point is the starting point of the main fracturing, which can be regarded as the precursor information; the second sudden jump point is the breakthrough point of the main fracturing.e amplitudes of sudden jumps are significantly affected by stiffness.With large stiffness ratio of coal and rock, the two sudden jump points are eliminated, indicating that the strong body has no shock effect on the weak body and the system is exposed to stability failures.(4) For coal mines in western China, the stiffness of weak cemented soft rock is highly consistent with that of coal body, and the composite roof is exposed to instability failures.is is referred as roof shocking, which is confirmed by field monitoring and practical cases.e results proposed can be applied to the study of rock burst and impact pressure in the softening rock system under different structures and loadings.According to the results of the theoretical model, numerical simulation, and field monitoring, it is feasible to use the jump of deformation rate as the precursor information of instability failures.However, further studies are still needed, especially laboratory tests.

Figure 4 :
Figure 4: Compression model of coal-rock body.

Figure 5 :
Figure 5: Attenuation of strength parameters of coal and rock at softening stage.

Figure 6 :
Figure 6: Stress-strain curves of coal-rock body in di erent constitutive models.