Adaptive control of dynamic mobile robots withnonholonomic constraintsFarzad Pourboghrat *,Mattias P.KarlssonDepartment of Electrical and Computer Engineering,Southern Illinois University,Carbondale,IL 62901-6603,USAReceived 16November 1999;accepted 22August 2000AbstractThis paper presents adaptive control rules,at the dynamics level,for the nonholonomic mobile robots with unknown dynamic parameters.Adaptive controls are derived for mobile robots,using backstepping technique,for tracking of a reference trajectory and stabilization to a fixed posture.For the tracking problem,the controller guarantees the asymptotic convergence of the tracking error to zero.For stabili-zation,the problem is converted to an equivalent tracking problem,using a time varying error feedback,before the tracking control is applied.The designed controller ensures the asymptotic zeroing of the sta-bilization error.The proposed control laws include a velocity/acceleration limiter that prevents the robot Õs wheels from slipping.Ó2002Elsevier Science Ltd.All rights reserved.Keywords:Mobile robot;Nonholonomic constraint;Dynamics level motion control;Stabilization and tracking;Adaptive control;Backstepping technique;Asymptotic stability1.IntroductionMotion control of mobile robots has found considerable attention over the past few years.Most of these reports have focused on the steering or trajectory generation problem at the ki-nematics level i.e.,considering the system velocities as control inputs and ignoring the mechanical system dynamics [1–3].Very few reports have been published on control design in the presence of uncertainties in the dynamic model [4].Some preliminary results on control of nonholonomic systems with uncertainties are given in Refs.[4–6].Two of the most important control problems concerning mobile robots are tracking of a refer-ence trajectory and stabilization to a fixed posture.The tracking problem has received solutions *Corresponding author.Tel.:+1-618-453-7026.E-mail address:pour@ (F.Pourboghrat).0045-7906/02/$-see front matter Ó2002Elsevier Science Ltd.All rights reserved.PII:S0045-7906(00)00053-7242 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253including classical nonlinear control techniques[1,2,7].The basic idea is to have a reference car that generates a trajectory for the mobile robot to follow.In Refs.[1,2],nonlinear velocity control inputs were defined that made the tracking error go to zero as long as the reference car was moving.In Ref.[7],they used input–output linearization to make a mobile platform follow a desired trajec-tory.The problem of stabilization about afixed posture has been shown to be rather complicated. This is due to violating the BrockettÕs condition[8],which states that for nonholonomic systems a single equilibrium solution cannot be asymptotically stabilized using continuous static state feedback[9,10].The BrockettÕs condition essentially states that for nonholonomic systems an equilibrium solution can be asymptotically stabilized only by either a time varying,a discontin-uous,or a dynamic state feedback.In addressing the above problem,in Ref.[10]a smooth feedback control was presented for the kinematics control problem resulting in a globally marginally stable closed loop system.They also designed a smooth feedback control for a dynamical state-space model resulting in a Lagrange stable closed loop system,as defined in their paper.A two dimensional Lyapunov function was utilized in Ref.[3]to prescribe a set of desired trajectories to navigate a mobile robot to a specified configuration.The desired trajectory was then tracked using sliding mode control,resulting in discontinuous control signals.The mobile robot was shown to be exponentially stable for a class of quadratic Lyapunov functions.In Ref.[9],they formulated a reduced order state equation for a class of nonholonomic systems.Several other researchers have later used this reduced order state equation in their studies.In Ref.[4],the problem of controlling nonholonomic mechanical sys-tems with uncertainties,at the dynamics level,was ing the reduced state equation in Ref.[9],they proposed an adaptive controller for a number of important nonholonomic control problems,including stabilization of general systems to an equilibrium manifold and stabilization of differentiallyflat and Caplygin systems to an equilibrium point.In Ref.[2],they gave several examples on how the stabilization problem can be solved for a mobile robot at the kinematics level.Their solutions included time-varying control,piecewise continuous control,and time-varying piecewise continuous control.They also showed how a solution to the tracking problem could be extended to work even for the stabilization problem.Here,we present adaptive control schemes for the tracking problem and for the problem of stabilization to afixed posture when the dynamic model of the mobile robot contains unknown parameters.Our work is based on,and can be seen as an extension of,the work presented in Refs. [1,2].Using backstepping technique we derive adaptive control laws that work even when the model of the dynamical system contains uncertainties in the form of unknown constants.The assumption for the uncertainty in robotÕs parameters,particularly the mass,and hence the inertia, can be justified in real applications such as in automotive manufacturing industry and warehouses, where the robots are to move a variety of parts with different shapes and masses.In these cases,the robotÕs mass and inertia may vary up to10%or20%,justifying an adaptive control approach.2.Dynamic model of mobile robotHere,we consider a three-wheeled mobile robot moving on a horizontal plane(Fig.1).The mobile robot features two differentially driven rear wheels and a castor front wheel.The radius ofthe wheels is denoted r and the length of the rear wheel axis is 2l .Inputs to the system are two torques T 1and T 2,provided by two motors attached to the rear wheels.The dynamic model for the above wheeled-mobile robot is given by Refs.[10,11].€x ¼k m sin /þb 1u 1cos /€y ¼Àk cos /þb 1u 1sin /€/¼b 2u 28><>:ð1Þ_x sin /À_y cos /¼0ð2Þwhere b 1¼1=ðrm Þ,b 2¼l =ðrI Þ,and that m and I denote the mass and the moment of inertia of the mobile robot,respectively.Also,u 1¼T 1þT 2and u 2¼T 1ÀT 2are the control inputs,and k is the Lagrange multiplier,given by k ¼Àm _/_x cos /þ_y sin /ðÞ.Here,it is assumed that b 1and b 2are unknown constants with known signs.The assumption that the signs of b 1and b 2are known is practical since b 1and b 2represent combinations of the robot Õs mass,moment of inertia,wheel radius,and distance between the rear wheels.Eq.(2)is the nonholonomic constraint,coming from the assumption that the wheels do not slip.The triplet vector function q t ðÞ¼x t ðÞ;y t ðÞ;/t ðÞ½ T denotes the trajectory (position and orientation)of the robot with respect to a fixed workspace frame.That is,at any given time,q ¼½x ;y ;/ T describes the robot Õs configuration (posture)at that time.We assume that,at any time,the robot Õs posture,q ¼½x ;y ;/ T ,as well as its derivative,_q¼½_x ;_y ;_/ T ,are available for feedback.3.Tracking problem definitionThe tracking problem consists of making the trajectory q of the mobile robot follow a reference trajectory q r .The reference trajectory q r t ðÞ¼x r t ðÞ;y r t ðÞ;/r t ðÞ½ T is generated by a reference ve-hicle/robot whose equations are_xr ¼v r cos /r _y r¼v r sin /_/r ¼x r8<:ð3ÞThe subscript ‘‘r’’stands for reference,and v r and x r are the reference translational (linear)velocity and the reference rotational (angular)velocity,respectively.We assume that v r and x r ,as well as their derivatives are available and that they all are bounded.Assumption A 1.For the tracking problem it is assumed that the reference velocities v r and x r do not both go to zero simultaneously.That is,it is assumed that at any time either lim t !1v r t ðÞ90and/or lim t !1x r t ðÞ90.The tracking problem,under the Assumption A 1,is to find a feedback control law u 1u 2 ¼u q ;_q ;q r ;v r ;x r ;_v r ;_x r ðÞsuch that lim t !1~q t ðÞ¼0,where ~q t ðÞ¼q r t ðÞÀq t ðÞis defined as the trajectory tracking error.As in Ref.[1],we define the equivalent trajectory tracking error ase ¼T ~qð4Þwhere e ¼½e 1;e 2;e 3 T ,and T ¼cos /sin /0Àsin /cos /00010@1A .Note that since T matrix is nonsingular,e is nonzero as long as ~q¼0.Assuming that the angles /r and /are given in the range ½Àp ;p ,we have the equivalent trajectory tracking error e ¼0only if q ¼q r .The purpose of the tracking controller is to force the equivalent trajectory tracking error e to 0.In the sequel we refer to e as the trajectory tracking error.Using the nonholonomic constraint (2),the derivative of the trajectory tracking error given in Eq.(4)can be written as,[1],_e1¼e 2x Àv þv r cos e 3_e 2¼Àe 1x þv r sin e 3_e3¼x r Àx 8<:ð5Þwhere v and x are the translational and rotational velocities of the mobile robot,respectively,and are expressed asv ¼_xcos /þ_y sin /x ¼_/ð6Þ4.Tracking controller designHere,the goal is to design a controller to force the tracking error e ¼½e 1;e 2;e 3 T to ing backstepping technique,since the actual control variables u 1and u 2do not appear in Eq.(5),we consider variables v and x as virtual controls.Let v d and x d denote the desired virtual controls for the mobile robot.That is,with v d and x d the trajectory tracking error e converges tozero asymptotically.Also let us define ~vand ~x as virtual control errors.Then,v and x can be written asv ¼v d þ~vx ¼x d þ~x ð7Þ244 F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253Let us choose the virtual controls v d and x d ,asv d v r ;x r ;e 1;e 3ðÞ¼v r cos e 3þk 1v r ;x r ðÞe 1x d v r ;x r ;e 2;e 3ðÞ¼x r þk 2v r e 2þk 3v r ;x r ðÞsin e 3ð8Þwhere k 2is a positive constant and k 1ðÁÞand k 3ðÁÞare bounded continuous functions with bounded first derivatives,strictly positive on R ÂR -ð0;0Þ.Observe that our approach from here on is general for any v d and x d (with well defined first derivatives),i.e.any differentiable control law that makes the kinematics model of the mobile robot track a desired trajectory can be used instead of Eq.(8).Eq.(8)is similar to the control law proposed by Ref.[1],but with the advantage,as we are going to prove later,that it can be used to track any reference trajectory as long as As-sumption A 1holds.Now,consider the following adaptive control scheme:u 1¼^b 1ðÀc 1~v þe 1þ_v d Þu 2¼^b 2 Àc 2~x þ1k 2sin e 3þ_x d _^b 1¼Àc 1sign b 1ðÞ~v ðÀc 1~v þe 1þ_v d Þ_^b 2¼Àc 2sign b 2ðÞ~x Àc 2~x þ1k 2sin e 3þ_x d ð9Þwhere c 1,c 2,c 1,and c 2are positive constants and ^b 1is an estimate of b 1¼1=b 1and ^b 2is an estimate of b 2¼1=b 2.Result 1.If Assumption A 1holds ,then the adaptive control scheme (9)makes the origin e ¼0uniformly asymptotically stable.Proof .Consider the following Lyapunov function candidateV 1¼12e 21Àþe 22Áþ1k 21ðÀcos e 3Þð10Þwhere k 2is a positive constant.Clearly V 1is positive definite and V 1¼0only if e ¼0.Taking the time derivative of V 1,we obtain_V 1¼e 1ðÀv þv r cos e 3Þþe 2v r sin e 3þ1k 2sin e 3x r ðÀx Þð11ÞFurthermore,using Eqs.(7)and (8),we have_V 1¼Àk 1e 21Àk 3k 2sin 2e 3À~v e 1À~x 1k 2sin e 3ð12ÞIn view of Eqs.(1),(2)and (6),we find the time derivatives of ~vand ~x ,as _~v¼_v À_v d ¼€x cos /À_x sin /_/þ€y sin /þ_y cos /_/À_v d ¼b 1u 1À_v d _~x ¼_x À_x d ¼€/À_x d ¼b 2u 2À_x d ð13ÞF.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253245Consider the Lyapunov function candidateV2¼V1þ12ð~v2þ~x2Þþb1j j2c1~b21þb2j j2c2~b22ð14Þwhere~b1¼b1À^b1¼1=b1À^b1and~b2¼b2À^b2¼1=b2À^b2.Considering Eq.(9)we get:_V 2¼Àk1e21Àk3k2sin2e3Àc1~v2Àc2~x260ð15ÞSince V2is bounded from below and_V2is negative semi-definite,V2converges to afinite limit. Also,V2,as well as,e1,e2,e3,~v,~x,^b1,and^b2are all bounded.Furthermore,using Eqs.(5),(7)–(9)and(13),the second derivative of V2can be written as€V 2¼À2k1e1e2ðx rþk2v r e2þk3sin e3þ~xÞþ2k1e1ðk1e1þ~vÞÀ_k1e21þ2k3k2cos e3sin e3ðk2v r e2þk3sin e3þ~xÞÀ_k3k2sin2e3À2c1~vðb1^b1ðÀc1~vþe1þ_v dÞÀ_v dÞÀ2c2~x b2^b2Àc2~xþ1k2sin e3þ_x dÀ_x dð16Þwhich from the properties of k1,k2,and k3,the assumption that v r and x r and their derivatives are bounded,and from the above results,can be shown to be bounded,i.e.,_V2is uniformly contin-uous.Since V2ðtÞis differentiable and converges to some constant value and that€V2is bounded,by BarbalatÕs lemma,_V2tðÞ!0as t!1.This in turn implies that e1,e3,~v,and~x converge to zero [12,13].To show that e2also goes to zero,note that,using the above results,thefirst error equation can be written as_e1¼e2x rÀk1e1ð17ÞThe second derivative of e1is€e1¼_x r e2þx rðÀe1xþv r sin e3ÞÀk1e2x rðÀk1e1ÞÀ_k1e1ð18Þwhich can be shown to be bounded by once again using the properties of k1,the assumptions on v r and x r,and Eqs.(7)and(8).Since e1is differentiable and converges to zero and€e1is bounded,by BarbalatÕs lemma,_e1,and hence,e2x r tend to zero.Proceeding in the same manner,the third error equation can be written as_e3¼Àk2v r e2Àk3sin e3ð19Þand its second derivative can be shown to be bounded.Since e3is differentiable and converges to zero and€e3is bounded,again by BarbalatÕs lemma,_e3!0as t!1.Hence,k2v r e2and thus v r e2 tend to zero as t!1.Clearly,both v r e2and x r e2converge to zero.However,since v r and x r do not both tend to zero(by Assumption A1),e2must converge to zero.That is,e1,e2,e3,~v,and~x must all converge to zero.hIn Section3,we demonstrated that the system is stable if k2is a positive constant,and that k1ðÁÞand k3ðÁÞare bounded continuous functions with boundedfirst derivatives and are strictly positive on RÂR-ð0;0Þ.To get a better understanding on how the control gains affect the response of the system,we write the equations for the closed loop system when~v and~x are equal to zero as[1] 246 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253_e¼Àk 1e 1þx r þk 2v r e 2þk 3sin e 3ðÞe 2Àx r þk 2v r e 2þk 3sin e 3ðÞe 1þv r sin e 3Àk 2v r e 2Àk 3sin e 30@1A ð20ÞBy linearizing the differential equation (20)around e ¼0,we get_e¼Ae ð21Þwhere A ¼Àk 1x r 0Àx r 0v r 0Àk 2v r Àk 30@1A ð22ÞTo simplify the analysis,we assume that v r and x r are constants.The system Õs closed loop poles are now equal to the roots of the following characteristic polynomial equation:s ðþ2nx 0Þs 2Àþ2nx 0s þx 20Áð23Þwhere n and x 0are positive real numbers.The corresponding control gains arek 1¼2nx 0k 2¼x 20Àx 2r v 2r k 3¼2nx 0ð24ÞWith a fixed pole placement strategy (n and x 0are constant),the control gain k 2increaseswithout bound when v r tends to zero.One way to avoid this is by letting the closed loop polesdepend on the values of v r and x r .As in Ref.[2],we choose x 0¼x 2r þbv 2r ÀÁð1=2Þwith b >0.The control gains then becomek 1¼2n x 2r Àþbv 2rÁ1=2k 2¼b k 3¼2n x 2r Àþbv 2r Á1=2ð25Þand the resulting control is now defined for any values of v r and x r .In the above,it is shown that the proposed algorithm works for any desired velocities,ðv d ;x d Þ.However,in practice,if the tracking errors initially are large or if the reference trajectory does not have a continuous curvature (e.g.,if the reference trajectory is a straight line connected to a circle segment),either or both of the virtual reference velocities in Eq.(8)might become too large for a real robot to attain in practice.Hence,the translational/rotational acceleration might become too large causing the robot to slip [1].In order to prevent the mobile robot from slipping,in a real application,a simple velocity/acceleration limiter may be implemented [1],as shown in Fig.2.This limits the virtual reference velocities ðv d ;x d Þby constants ðv max ;x max Þand the virtual referenceaccelerations ða ;a Þby constants ða max ;a max Þ,where a ¼_vd and a ¼_x d are the virtual reference accelerations.In practice,these parameters must be determined experimentally as the largest values with which the mobile robot never slips.F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253247An important advantage of adding the limiter is that it lowers the control gains indirectly only when the tracking errors are large,i.e.,when too high a gain could cause the robot to slip,while for small tracking errors it does not affect the performance at all.Thus,by using the limiter one can have higher control gains for small tracking errors to allow for better tracking,while letting the limiter to‘‘scale down’’the gains,indirectly,for large tracking errors,to prevent the robot from slipping.5.Simulation results for tracking control problemHere,the results of computer simulation,using MATLAB/SIMULINK,are presented for a mobile robot with the proposed tracking control and with the velocity/acceleration limiter.The computer simulations for the above controller without the limiter,although not shown here,produce similar results,but with somewhat different transient characteristics.All simulations have the common parameters of c1¼c2¼100,c1¼c2¼10and b¼250.Also selected are,the damping factor n¼1,v max¼1:5m/s,x max¼3rad/s,a max¼5m/s2and a max¼25rad/s2.Moreover,the robotÕs dy-namic parameters are chosen as b1¼b2¼0:5,which are assumed to be unknown to the con-troller,but with known signs.Simulation results for the case where the reference trajectory is a straight line are shown in Figs. 3and4for t2½0;10 .The reference trajectory is given by x rðtÞ¼0:5t,y rðtÞ¼0:5t and/rðtÞ¼p=4, defining a straight line,starting from q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½0;0;p=4 T.The mobile robot, however,is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½1;0;0 T,where/¼0indicates that the robot is heading toward positive direction of x.As it can be seen from thesefigures,first the robot backs up and then heads toward the virtual reference robot moving on the straight line.Figs.5and6show the simulation results for tracking a circular trajectory.The reference trajectory is a point moving counter clockwise on a circle of radius1,starting at q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½1;0;p=2 T.The reference velocity is kept constant at v rðtÞ¼0:5m/s.The initial conditions for the mobile robot,however,is taken as qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;0;0 T.Again,as it is seen from thesefigures,the robot immediately heads toward the reference robot,which is moving on the circle.It then reaches it quickly and continues to track it.6.Stabilization problem definitionThe stabilization problem,given an arbitrary desired posture q d ,is to find a feedback control law,u 1u 2¼u q Àq d ;_q ;t ðÞ,such that lim t !1q t ðÞÀq d ðÞ¼0,for any arbitrary initial robot posture q ð0Þ.Without loss of generality,we may take q d ¼½0;0;0 T.6.1.Stabilization controller designRecall that there is no continuous static state feedback that can asymptotically stabilize a nonholonomic system about a fixed posture [8–10].The approach to the problem taken here is the dynamic extension of that in Ref.[2]where a kinematics model of the mobile robot is used.In-stead of designing a new controller for the stabilization problem the same controller as for the tracking problem is used.The idea is to let the reference vehicle move along a path that passes through the point ðx d ;y d Þwith heading angle /d .The stabilization to a fixed posture problem isnow equivalent to,and can be treated as,a tracking problem(convergence of the tracking errors to zero)with the additional requirement that the reference vehicle should itself be asymptotically stabilized about the desired posture.As in Ref.[2],we let the reference vehicle move along the x-axis,i.e.y rðtÞ¼0and/rðtÞ¼0,for all values on t.The design method is the same as derived for the tracking case.However,in this casev r¼_x r¼Àk4x rþgðe;tÞ;ð26Þwithgðe;tÞ¼k e k sin tð27Þwhere k4>0.Different time-varying functions gðe;tÞhave also been suggested in the literature,see Refs.[2,11]and the references therein.Since,from the Section5,the tracking errors e1,e2,and e3are bounded,the time-varying function gðe;tÞis bounded.Therefore v r and the state x r also remain bounded.By taking the time derivative of Eq.(26),it can be shown in the same way that_v r is bounded.Since v r and_v r are bounded,the assumptions made in Section3concerning the reference velocity are fulfilled.If v r is not equal to zero,then e must converge to zero.When e tends to zero,gðe;tÞalso tends to zero. Therefore,the robotÕs position x must track x r,which converges to zero and hence lead the mobile robot to the desired posture.6.2.Simulation results for stabilization control problemHere,the simulation results for the stabilization problem are shown in Figs.7and8.The control parameters and system parameters are the same as for the simulations shown for the tracking problem and k4¼1.The mobile robot is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;1;0 T.As it is seen from thefigures,the stabilization about thefinal posture at the origin is achieved quite satisfactorily.Note,in this case,that the robot actually turns around and backs up into the final posture.7.ConclusionsTwo important control problems concerning mobile robots with unknown dynamic parameters have been considered,namely,tracking of a reference trajectory and stabilization to afixed posture.An adaptive control law has been proposed for the tracking problem and has been ex-tended for the stabilization problem.A simple velocity/acceleration limiter was added to the controller,for practical applications,to avoid any slippage of the robotÕs wheels,and to improve the tracking performance.Several simulation results have been included to demonstrate the performance of the proposed adaptive control law.References[1]Kanayama Y,Kimura Y,Miyazaki F,Noguchi T.A stable tracking control method for an autonomous mobilerobot.vol.1.Proceedings of IEEE International Conference on Robotics and Automation,Cincinnati,Ohio,1990, p.384–9.[2]Canudas de Wit C,Khennouf H,Samson C,Sordalen OJ.Nonlinear control design for mobile robots.In:ZhengYF,editor.Recent trends in Mobile robots,World Scientific,1993.p.121–56.[3]Guldner J,Utkin VI.Stabilization of nonholonomic mobile robot using Lyapunov functions for navigation andsliding mode control.Control-Theory Adv Technol1994;10(4):635–47.[4]Colbaugh R,Barany E,Glass K.Adaptive Control of Nonholonomic Mechanical Systems.Proceedings of35thConference on Decision and Control,Kobe,Japan,1996.p.1428–34.[5]Fierro R,Lewis FL.Control of nonholonomic mobile robot:backstepping kinematics into dynamics.J Robot Sys1997;14(3)149-163.[6]Jiang ZP,Pomet bining backstepping and time-varying techniques for a new set of adaptive controllers.Proceedings of33rd IEEE Conf on Decision and Control,Lake Buena Vista,FL,1994.p.2207–12.[7]Sarkar N,Yun X,Kumar V.Control of mechanical systems with rolling constraints:application to dynamiccontrol of mobile robots.Int J Robot Res1994;13(1):55–69.[8]Brockett RW.Asymptotic stability and feedback stabilization.In:Brockett RW,Millman RS,Sussmann HJ,editors.Differential Geometric Control Theory,Boston,MA:Birkhauser;1983.p.181–91.[9]Bloch AM,Reyhanoglu MR,McClamroch NH.Control and stabilization of nonholonomic dynamic systems.IEEE Trans Automat Contr1992;37(11):1746–56.[10]Campion G,d’Andrea-Novel B,Bastin G.Controllability and state feedback stabilization of nonholonomicmechanical systems.Canudas de Wit C,editor.Advanced Robot Control,Berlin:Springer;1991.p.106–24. [11]Kolmanovsky I,McClamroch NH.Developments in nonholonomic control problems.IEEE Contr Sys Magaz1995;15(6):20–36.[12]Krstic M,Kanellakopoulos I,Kokotovic P.Nonlinear and Adaptive Control Design,New York:Wiley;1995.[13]Karlsson MP.Control of nonholonomic systems with applications to mobile robots.Master Thesis,SouthernIllinois University,Carbondale,IL62901,USA,1997.Farzad Pourboghrat received his Ph.D.degree in Electrical Engineering from the University of Iowa in1984. He is now with the Department of Electrical and Computer Engineering at Southern Illinois University at Carbondale(SIU-C)where he is an Associate Professor.His research interests are in adaptive and slidingcontrol with applications to DSP embedded systems,mechatronics,flexible structures andMEMS.Mattias Karlsson received the B.S.E.E.degree from the University of Bor a s,Sweden and the M.S.E.E.degree from Southern Illinois University,Carbondale,IL,in1995and1997,respectively.He has been employed at Orian Technology since1997.He is currently an on-site consultant at Caterpillar Inc.Õs Technical Center, Mossville,IL.His current interests include control algorithm development for mechanical and electrical systems and software development for embedded systems.F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253253。
㊀第４９卷第４期煤炭科学技术Ｖｏｌ ４９㊀Ｎｏ ４㊀㊀２０２１年４月ＣｏａｌＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ㊀Ａｐｒ．２０２１㊀移动扫码阅读邓志刚．动静载作用下煤岩多场耦合冲击危险性动态评价技术［Ｊ］．煤炭科学技术，２０２１，４９（４）：１２１－１３２ ｄｏｉ：１０ １３１９９／ｊ ｃｎｋｉ ｃｓｔ ２０２１ ０４ ０１５ＤＥＮＧＺｈｉｇａｎｇ．Ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｏｎｓｉｄｅｒｉｎｇｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄ［Ｊ］．ＣｏａｌＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，２０２１，４９（４）：１２１－１３２ ｄｏｉ：１０ １３１９９／ｊ ｃｎｋｉ ｃｓｔ ２０２１ ０４ ０１５动静载作用下煤岩多场耦合冲击危险性动态评价技术邓㊀志㊀刚１，２（１．煤炭科学技术研究院有限公司安全分院，北京㊀１０００１３；２．煤炭资源高效开采与洁净利用国家重点实验室，北京㊀１０００１３）摘㊀要：深部开采冲击地压灾害孕灾过程中既有静态基础量又有动态变化量，剧增的原岩应力与覆岩断裂㊁井下爆破等引起的动载扰动是诱发冲击地压灾害的源头，因此实现冲击危险性快速㊁高精度评价必须综合考虑动静载作用㊂笔者开展了典型煤岩霍普金森压杆试验及数值模拟，分析了动载对煤岩体破坏作用以及对应力场的影响，针对应力变化可以直接引起介质中震动波波速变化，且波速变化前的幅值与变化幅度均受应力场影响这一特性，掌握了震动场与应力场的耦合关系，建立了多场耦合冲击危险性动态评价技术：以原岩应力场表示煤岩孕灾过程的静态基础量，以采动应力场和震动场表示煤岩孕灾过程的动态变化量，以波速异常指数㊁波速梯度指数㊁应力异常指数㊁应力梯度指数为评价指标可实现煤岩冲击危险性动态评价㊂研究结果表明：动载作用下能量以震动波形式传递，造成应力场的重新分布，应力呈现分区传递特点，并且在能量达到某一阈值后引起煤岩损伤破坏，但无论动载直接作用在岩石上还是煤体上，岩石是能量传递路径，煤层是能量耗散㊁释放主体，破坏主要发生在煤体中㊂多场耦合冲击危险性评价技术在某工作面经现场应用，在工作面逐渐揭露断层过程中冲击危险性由强冲击危险性降低到中等冲击危险性，现场监测数据表明评价结果与现场实际相符㊂关键词：动静载荷；冲击危险性；震动场；多场耦合；动态评价中图分类号：ＴＤ３２４㊀㊀㊀文献标志码：Ａ㊀㊀㊀文章编号：０２５３－２３３６（２０２１）０４－０１２１－１２Ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｏｎｓｉｄｅｒｉｎｇｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄＤＥＮＧＺｈｉｇａｎｇ１，２（１．ＭｉｎｅＳａｆｅｔｙＴｅｃｈｎｏｌｏｇｙＢｒａｎｃｈ，ＣｈｉｎａＣｏａｌＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅ，Ｂｅｉｊｉｎｇ㊀１０００１３，Ｃｈｉｎａ；２．ＳｔａｔｅＫｅｙＬａｂｏｒａｔｏｒｙｏｆＣｏａｌＭｉｎｉｎｇａｎｄＣｌｅａｎＵｔｉｌｉｚａｔｉｏｎ，Ｂｅｉｊｉｎｇ㊀１０００１３，Ｃｈｉｎａ）收稿日期：２０２０－１２－０２；责任编辑：朱恩光基金项目：国家科技重大专项资助项目（２０１６ＺＸ０５０４５００３－００６－００２）；国家自然科学基金面上资助项目（５１６７４１４３）作者简介：邓志刚（１９８１ ），男，吉林长春人，研究员，博士，中国煤炭科工集团三级首席科学家㊂Ｔｅｌ：０１０－８４２６１５８１，Ｅ－ｍａｉｌ：ｄｅｎｇｚｈｉｇａｎｇ２００４＠１６３．ｃｏｍＡｂｓｔｒａｃｔ：Ｓｔａｔｉｃｂａｓｉｃｑｕａｎｔｉｔｙａｎｄｄｙｎａｍｉｃｖａｒｉａｔｉｏｎｑｕａｎｔｉｔｙｅｘｉｓｔｉｎｔｈｅｐｒｏｃｅｓｓｏｆｒｏｃｋｂｕｒｓｔｉｎｄｅｅｐｍｉｎｉｎｇ．Ｄｙｎａｍｉｃｌｏａｄｄｉｓｔｕｒｂａｎｃｅａｎｄｔｈｅｉｎｃｒｅａｓｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｒｅｔｈｅｓｏｕｒｃｅｏｆｒｏｃｋｂｕｒｓｔ．Ｔｈｅｒｅｆｏｒｅ，ｔｈｅｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄｍｕｓｔｂｅｃｏｎｓｉｄｅｒｅｄｃｏｍｐｒｅｈｅｎｓｉｖｅｌｙｉｎｔｈｅｆａｓｔａｎｄｈｉｇｈ－ｐｒｅｃｉｓｉｏｎｅｖａｌｕａｔｉｏｎｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄ．Ｈｏｐｋｉｎｓｏｎｐｒｅｓｓｕｒｅｂａｒｅｘｐｅｒｉｍｅｎｔｓａｎｄｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｗｅｒｅｃａｒｒｉｅｄｏｕｔｔｏａｎａｌｙｚｅｔｈｅｉｎｆｌｕｅｎｃｅｓｏｆｄｙｎａｍｉｃｌｏａｄｏｎｔｈｅｄａｍａｇｅａｎｄｓｔｒｅｓｓｆｉｅｌｄｏｆｔｈｅｃｏａｌｒｏｃｋ．Ｉｎｖｉｅｗｏｆｔｈｅｆａｃｔｔｈａｔｔｈｅｃｈａｎｇｅｏｆｓｔｒｅｓｓｃｏｕｌｄｄｉ⁃ｒｅｃｔｌｙｃａｕｓｅｔｈｅｃｈａｎｇｅｏｆｖｉｂｒａｔｉｏｎｗａｖｅｖｅｌｏｃｉｔｙａｎｄｔｈｅａｍｐｌｉｔｕｄｅｂｅｆｏｒｅａｎｄａｆｔｅｒｔｈｅｃｈａｎｇｅｏｆｗａｖｅｖｅｌｏｃｉｔｙｗｅｒｅａｆｆｅｃｔｅｄｂｙｔｈｅｓｔｒｅｓｓｆｉｅｌｄ，ｔｈｅｃｏｕｐｌｉｎｇｒｅｌａｔｉｏｎｓｈｉｐｂｅｔｗｅｅｎｖｉｂｒａｔｉｏｎｆｉｅｌｄａｎｄｓｔｒｅｓｓｆｉｅｌｄｗａｓｍａｓｔｅｒｅｄａｎｄｔｈｅｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄｗａｓｅｓｔａｂｌｉｓｈｅｄ．Ｉｎｔｈｅｐｒｏｃｅｓｓｏｆｃａｔａｓｔｒｏｐｈｅ，ｔｈｅｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄｒｅｐｒｅｓｅｎｔｓｔｈｅｓｔａｔｉｃｆｏｕｎｄａｔｉｏｎｑｕａｎｔｉｔｙ，ａｎｄｔｈｅｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄａｎｄｔｈｅｖｉｂｒａｔｉｏｎｆｉｅｌｄｒｅｐｒｅｓｅｎｔｔｈｅｄｙｎａｍｉｃｃｈａｎｇｅｑｕａｎｔｉｔｙ．Ｔｈｅｗａｖｅｖｅｌｏｃｉｔｙａｎｏｍａｌｙｉｎｄｅｘ，ｗａｖｅｖｅｌｏｃｉｔｙｇｒａｄｉｅｎｔｉｎ⁃ｄｅｘ，ｓｔｒｅｓｓａｎｏｍａｌｙｉｎｄｅｘａｎｄｓｔｒｅｓｓｇｒａｄｉｅｎｔｉｎｄｅｘａｒｅｕｓｅｄａｓｅｖａｌｕａｔｉｏｎｉｎｄｅｘｅｓｔｏｒｅａｌｉｚｅｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｏｆｒｏｃｋｂｕｒｓｔｈａｚａｒｄ．Ｔｈｅｒｅ⁃ｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｅｎｅｒｇｙｉｓｔｒａｎｓｍｉｔｔｅｄｉｎｔｈｅｆｏｒｍｏｆｖｉｂｒａｔｉｏｎｗａｖｅｕｎｄｅｒｄｙｎａｍｉｃｌｏａｄ，ｒｅｓｕｌｔｉｎｇｉｎｔｈｅｒｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｓｔｒｅｓｓｆｉｅｌｄ．Ｔｈｅｓｔｒｅｓｓｐｒｅｓｅｎｔｓｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｚｏｎａｌｔｒａｎｓｍｉｓｓｉｏｎ，ａｎｄｃａｕｓｅｓｔｈｅｄａｍａｇｅｏｆｃｏａｌａｎｄｒｏｃｋｗｈｅｎｔｈｅｅｎｅｒｇｙｒｅａｃｈｅｓａｃｅｒｔａｉｎｔｈｒｅｓｈｏｌｄ．Ｈｏｗｅｖｅｒ，ｎｏｍａｔｔｅｒｔｈｅｄｙｎａｍｉｃｌｏａｄｄｉｒｅｃｔｌｙａｃｔｓｏｎｔｈｅｒｏｃｋｏｒｔｈｅｃｏａｌ，ｔｈｅｒｏｃｋｉｓｔｈｅｅｎｅｒｇｙｔｒａｎｓｆｅｒｐａｔｈ，ｔｈｅｃｏａｌｓｅａｍｉｓｔｈｅｍａｉｎｂｏｄｙｏｆｅｎｅｒｇｙｄｉｓｓｉｐａｔｉｏｎａｎｄｒｅｌｅａｓｅ，ａｎｄｔｈｅｆａｉｌｕｒｅｍａｉｎｌｙｏｃｃｕｒｓｉｎｔｈｅｃｏａｌ．Ｔｈｅｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎｍｅｔｈｏｄｏｆｒｏｃｋｂｕｒｓｔ１２１２０２１年第４期煤炭科学技术第４９卷ｈａｚａｒｄｗａｓａｐｐｌｉｅｄｏｎａｃｅｒｔａｉｎｗｏｒｋｉｎｇｆａｃｅ．Ｔｈｅｒｏｃｋｂｕｒｓｔｈａｚａｒｄｗａｓｒｅｄｕｃｅｄｆｒｏｍｓｔｒｏｎｇｔｏｍｅｄｉｕｍｉｎｔｈｅｐｒｏｃｅｓｓｏｆｇｒａｄｕａｌｌｙｅｘｐｏｓｉｎｇｆａｕｌｔｓ．Ｔｈｅｆｉｅｌｄｍｏｎｉｔｏｒｉｎｇｄａｔａｓｈｏｗｅｄｔｈａｔｔｈｅｅｖａｌｕａｔｉｏｎｒｅｓｕｌｔｓｗｅｒｅｃｏｎｓｉｓｔｅｎｔｗｉｔｈｔｈｅａｃｔｕａｌｓｉｔｕａｔｉｏｎ．Ｋｅｙｗｏｒｄｓ：ｄｙｎａｍｉｃａｎｄｓｔａｔｉｃｌｏａｄｓ；ｒｏｃｋｂｕｒｓｔｈａｚａｒｄ；ｖｉｂｒａｔｉｏｎｆｉｅｌｄ；ｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇ；ｄｙｎａｍｉｃｅｖａｌｕａｔｉｏｎ０㊀引㊀㊀言我国多数矿井进入深部开采阶段，冲击地压灾害频度㊁强度显著增加［１］，冲击地压防治工作任重道远㊂２０１８年８月１日，国家煤矿安全监察局印发的‘防治煤矿冲击地压细则“开始实施，规定： 开采具有冲击倾向性的煤层必须进行冲击危险性评价 ， 开采冲击地压煤层必须进行采区㊁采掘工作面冲击危险性评价 ， 当评估煤层有冲击倾向性时，应当进行冲击危险性评价 ，并且以冲击危险性评价结果作为冲击地压监测㊁卸压等工作开展的依据㊂目前冲击危险性评价方法较多㊂一类是以冲击地压主要诱因为切入点的冲击危险性静态评价技术，如窦林名等［２］提出的综合指数法，综合考虑了岩体结构㊁力学特性㊁地质因素等条件㊂姜福兴等［３］采用模糊数学的方法，用垂直应力与煤体单轴抗压强度的比值㊁弹性能量指数２个指标评价煤体的冲击危险性，且根据应力叠加原理建立了冲击危险性评价模型，后又在此基础上提出了冲击地压分类评价技术手段㊂张科学等［６］综合考虑开采深度㊁冲击倾向性㊁煤层顶底板性质㊁地质构造㊁开采技术提出了基于层次分析法的煤层冲击危险性模糊综合评价模型㊂张宏伟等［７］应用地质动力区划方法对煤矿冲击危险进行评价㊂邓志刚［１０］基于三维地应力场反演技术开展了相关研究，综合考虑构造应力㊁采动影响等因素，实现了对采区宏观区域的冲击危险评价㊂欧阳振华等［１１］考虑瓦斯作用，将煤层气属性㊁抽采效果分析作为一类地质因素㊁开采技术条件，提出一种含瓦斯煤冲击危险性改进型综合指数评价方法㊂但是由于冲击地压致灾机理不清，灾害孕育㊁发展㊁发生的过程中影响因素繁杂，以及复杂多变的采掘及地质条件，致使静态评价方法主要是宏观上为煤层开采前的防冲工作提供一定参考，缺少对于采掘过程中因局部区域地质及开采条件变化㊁卸压措施等因素引起的冲击危险性动态变化的量化能力，因此，另一类基于现场监测数据的冲击危险性动态评价技术是当前研究工作的重点，如刘少虹等［１２］基于地音与电磁波ＣＴ探测数据提出的冲击危险性层次化评价方法；李宏艳等［１４］基于微震监测数据建立的考虑响应能量和无响应时间的冲击危险性动态评价技术㊂姜福兴等［１５］应用矿压观测法观测冲击地压工作面支架压力㊁立柱压缩量，判断工作面顶板来压规律，结合巷道的变形及其围岩应力分布进行观测，评价及预测冲击危险性㊂何学秋等［１７］采用电磁辐射法评价冲击危险性，主要参数为电磁辐射强度和脉冲数㊂曹民远等［１９］采用数值模拟和理论计算的方法分析了采掘工作面应力扰动叠加的影响，提出了近直立煤层动态权重评价法的计算体系㊂但是冲击地压的孕灾过程中既有静态基础量，又有动态变化量，因此目前仅依靠单一理论或方法快速㊁高精度的进行冲击危险性评价难度较大㊂我国煤矿进入深部开采后，剧增的原岩应力场成为冲击地压灾害发生的必要条件㊂覆岩断裂㊁井下爆破等带来的强动载扰动易成为诱发冲击灾变的充分条件，但目前冲击危险性评价的研究工作中少有兼顾动静载综合作用的理论或方法㊂为此，笔者以震动场㊁采动应力场表示孕灾过程中动态变化量，以原岩应力场表示孕灾过程中静态基础量㊂提出了波速异常指数㊁波速梯度指数㊁应力异常指数㊁应力梯度指数４个冲击危险性评价指标，并在此基础上建立了多场耦合冲击危险性动态评价技术以实现井下高精度冲击危险性动态评价㊂１㊀煤岩动载破坏试验分析１．１㊀典型煤岩动载破坏霍普金森压杆试验分离式霍普金森压杆（ＳＨＰＢ）试验系统（图１）由压杆系统㊁测量系统和数据采集处理系统３个部分组成㊂图１㊀ＳＨＰＢ试验装置Ｆｉｇ．１㊀ＳＨＰＢｅｘｐｅｒｉｍｅｎｔａｌｄｅｖｉｃｅ当动载试块受到不同气压后获得不同初速度撞击入射杆，在杆内产生入射脉冲εｉ，试件在该应力作用下产生高速变形，同时产生反射脉冲εｒ和透射脉冲εｔ㊂如图２所示㊂选取强冲击倾向性煤样试件４２２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期个，中砂岩试件４个，尺寸均为ø５０ｍｍˑ１００ｍｍ㊂本次试验煤岩样取样点分别为某典型冲击地压矿井３－１煤回风大巷ＨＦ６导点处顶板和３１１１０２工作面煤层㊂煤岩物理力学参数见表１㊂分别采用气压０．２㊁０．４㊁０．６㊁０．８ＭＰａ发射子弹，撞击入射杆，记录其入射㊁反射和透射波曲线㊂图２㊀ＳＨＰＢ试验原理Ｆｉｇ．２㊀ＰｒｉｎｃｉｐｌｅｏｆＳＨＰＢｅｘｐｅｒｉｍｅｎｔａｌ㊀㊀煤样㊁岩样入射波㊁反射波和透射波曲线如图３㊁图４所示，仅出示驱动应力为０．２㊁０．４㊁０．８ＭＰａ时的结果㊂对比分析可知，随着撞击杆驱动应力增加，入射波波速幅值㊁入射波波速变化率均有所增加，反射波和透射波波峰和波谷增高，透射波持续时间缩短，这也和冲击地压发生的突然㊁猛烈性质一致㊂１．２㊀典型煤岩动载破坏数值模拟采取有限元方法对煤岩霍普金森压杆试验进行模拟，进一步分析动载作用下煤岩体损伤破坏机理㊂数值模型如图５所示㊂模拟试件分为煤样㊁岩样㊁煤－岩组合样，岩－煤组合样，其中煤－岩组合样是指震动波入射端在煤上，岩－煤组合样是指震动波入射端在岩石上㊂煤样㊁岩样尺寸为ø５０ｍｍˑ１００ｍｍ，煤岩组合样中煤㊁岩样尺寸均为ø５０ｍｍˑ５０ｍｍ㊂入射杆㊁透射杆材料参数按钢材设定［２０］，密度为７７９４ｋｇ／ｍ３，弹性模量为２１１ＧＰａ，泊松比为０．２８５㊂表１㊀煤岩物理力学参数Ｔａｂｌｅ１㊀Ｐｈｙｓｉｃａｌａｎｄｍｅｃｈａｎｉｃａｌｐａｒａｍｅｔｅｒｓｏｆｃｏａｌａｎｄｒｏｃｋ试样密度／（ｋｇ㊃ｍ－３）单轴抗压强度／ＭＰａ弹性模量／ＧＰａ泊松比抗拉强度／ＭＰａ内摩擦角／（ʎ）黏聚力／ＭＰａ煤样１３２５．４０３８．７６２３．４７４０．２８２２．４９３１８．５２１３．８９４岩样２１１１．９８４０．４３４７．３９５０．２２２２．８３９３５．６０１５．５２５图３㊀煤样不同气压下的波形Ｆｉｇ．３㊀Ｗａｖｅｆｏｒｍｓｏｆｃｏａｌｕｎｄｅｒｄｉｆｆｅｒｅｎｔａｉｒｐｒｅｓｓｕｒｅ图４㊀岩样不同气压下的波形Ｆｉｇ．４㊀Ｗａｖｅｆｏｒｍｓｏｆｒｏｃｋｕｎｄｅｒｄｉｆｆｅｒｅｎｔａｉｒｐｒｅｓｓｕｒｅ３２１２０２１年第４期煤炭科学技术第４９卷图５㊀霍普金森试验数值模型Ｆｉｇ．５㊀ＳＨＰＢｅｘｐｅｒｉｍｅｎｔｎｕｍｅｒｉｃａｌｍｏｄｅｌ煤岩物理力学参数见表２㊂加载在入射杆端部的震动波信号为ＳＨＰＢ试验中不同气压驱动子弹记录的入射杆应变波信号㊂不同震动波作用下煤岩体应力㊁损伤分布如图６ 图９所示，限于篇幅煤样㊁岩样仅出示驱动应力为０．２㊁０．４㊁０．８ＭＰａ时的结果，煤岩组合样仅出示驱动应力为０．２ＭＰａ和０．８ＭＰａ时的结果㊂分析可知，震动波作用引起煤岩应力重新分布，应力传递呈现分区传递特点，即存在应力传递优势面㊂在震动波波速峰值㊁波速变化率较低时，震动波对煤岩介质表２㊀数值模拟参数Ｔａｂｌｅ２㊀Ｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｐａｒａｍｅｔｅｒｓ试样弹性模量／ＧＰａ泊松比密度／（ｋｇ㊃ｍ－３）屈服强度／ＭＰａ单轴抗压强度／ＭＰａ内摩擦角／（ʎ）黏聚力／ＭＰａ煤样３．４７４０．３２１３２０１７．２５２４．６０１８．５２１３．８９０岩样７．６８３０．２３２５１９４４．９７５０．２７４３．１０１０．６５６图６㊀煤样应力与损伤分布情况Ｆｉｇ．６㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｃｏａｌｓｐｅｃｉｍｅｎ没有破坏作用，即震动波对煤岩介质的破坏与损伤存在阈值㊂煤岩体发生破坏的位置同时是单元受拉损伤㊁受压损伤极值位置，因此震动波作用下煤岩体破坏模式为拉压复合破坏㊂无论震动波直接作用在岩石上还是煤上，煤岩组合试件的破坏主要发生在煤体上，说明岩石是能量传播的路径，煤体是能量耗４２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期图７㊀岩样应力与损伤分布情况Ｆｉｇ．７㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｒｏｃｋｓｐｅｃｉｍｅｎ图８㊀煤－岩样应力与损伤分布情况Ｆｉｇ．８㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｃｏａｌ－ｒｏｃｋｓｐｅｃｉｍｅｎ５２１２０２１年第４期煤炭科学技术第４９卷图９㊀岩－煤样应力与损伤分布情况Ｆｉｇ．９㊀Ｓｔｒｅｓｓａｎｄｄａｍａｇｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆｒｏｃｋ－ｃｏａｌｓｐｅｃｉｍｅｎ散㊁释放的主体，这也符合冲击地压主要发生在煤层中的事实㊂１．３㊀震动场与煤岩冲击危险性的关联依据采煤工作面和掘进工作面煤岩体破坏失稳主要形式，结合ＳＨＰＢ试验和数值模拟研究结果，煤岩体震动场与冲击危险性的关系总结如下：①震动波是能量传递的载体，震动波所具有的能量超过一定阈值时可引起煤岩破坏，易诱发冲击地压灾害㊂②震动波传递引起应力分布变化，应力传递沿优势面进行㊂随着震动波能量增加，优势面周围易出现煤岩损伤破坏，引起煤岩冲击灾变㊂③当震源位于岩层时，能量传递速度较快，在煤岩界面发生衰减，煤体在震动波作用下发生破坏；当震源位于煤层时，煤体对震动波传递速度相对较慢，能量多耗散在煤层中，主要诱发煤体破坏，对岩层造成的破坏较小㊂２㊀煤岩动㊁静载冲击危险性评价指标考虑动静载作用煤岩冲击危险性评价指标包括应力场相关指标和震动场相关指标，其中静载作用主要表现为应力场的变化，动载作用主要引起震动场的变化㊂２．１㊀应力场冲击危险性评价指标基于煤矿冲击地压应力控制理论［２１］，煤岩体冲击破坏是应力作用的结果，一是取决于应力绝对值大小，二是应力梯度变化㊂因此，建立应力异常指数和应力梯度指数㊂应力异常指数表征一定区域内不同位置应力差异的指标，计算公式为γσ＝σｒ－σｍｉｎσｍａｘ－σｍｉｎˑ１０（１）式中：γσ为应力异常指数；σｒ为监测区域某点应力，ＭＰａ；σｍａｘ㊁σｍｉｎ分别为监测区域内实时应力最大值和最小值，ＭＰａ㊂应力梯度指数是表征一定区域内不同位置应力变化速度差异的指标，计算公式为ｇσ＝ｇσｒ－ｇσｍｉｎｇσｍａｘ－ｇσｍｉｎˑ１０（２）式中：ｇσ为应力梯度异常指数；ｇσｒ为监测区域内某一点的应力场梯度；ｇσｍａｘ㊁ｇσｍｉｎ分别为监测区域内应力最大㊁最小梯度㊂２．２㊀震动场冲击危险性评价指标综上，震动场波速绝对值㊁变化速率对煤岩破坏有显著影响㊂因此，提出表征震动波波速的波速异常指数和表征震动波波速变化速率的波速梯度指数，作为２个基于震动场的冲击危险性动态评价指数㊂波速异常指数表征一定区域内不同位置震动波波速的差异，计算公式为γθ＝θｒ－θｍｉｎθｍａｘ－θｍｉｎˑ１０（３）式中：γθ为波速异常指数；θｒ为监测区域某点震动波６２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期波速，ｍ／ｓ；θｍａｘ㊁θｍｉｎ分别为监测区域内震动波波速最大值和最小值，ｍ／ｓ㊂波速梯度指数ｇθ是通过震动场波速变化速率表征煤岩体发生冲击地压的危险程度，计算公式为ｇθ＝ｇθｒ－ｇθｍｉｎｇθｍａｘ－ｇθｍｉｎˑ１０（４）式中：ｇθ为波速梯度异常指数；ｇθｒ为监测区域内某一点的震动波波速梯度；ｇθｍａｘ㊁ｇθｍｉｎ为监测区域内震动波波速最大㊁最小梯度㊂３㊀煤岩多场耦合冲击危险性动态评价技术结合笔者以往研究［２２］和上述研究成果可知，一方面煤岩应力场改变可以直接引起介质中震动波波速变化，且波速变化前的幅值与变化幅度均与应力场大小相关；另一方面，震动场传递会造成煤岩应力场的重新分布㊂因此，考虑动㊁静载作用开展煤岩冲击危险性动态评价关键在于分析震动场－应力场的耦合作用㊂煤炭开采之前，煤岩体处于重力和构造应力组成的原岩应力场之中；开采过程中，煤岩体形成采动应力场；原岩应力场和采动应力场相互作用，煤岩体损伤变形，震动产生，以弹性波的形式向外传播形成震动场㊂冲击地压是原岩应力场㊁采动应力场和震动场综合作用的结果，煤岩体中多场耦合关系如图１０所示㊂图１０㊀煤岩体中多场耦合关系Ｆｉｇ．１０㊀Ｆｉｅｌｄｉｎｃｏａｌｒｏｃｋｍａｓｓａｎｄｉｔｓｃｏｕｐｌｉｎｇｒｅｌａｔｉｏｎｓｈｉｐ为了准确描述煤岩体中各种场的关系，从冲击危险性评价角度建立统一数学模型Ｒ（ｔｉ，ｓ；ｍｊ）＝０㊀㊀（ｉ，ｊ＝１，２，３， ）（５）式中：ｔｉ为场的变量，一般情况下有多个，既可以是标量也可以是矢量；ｓ为场的源或者汇，通常只有一个；ｍｊ为煤岩体的物理性质变量，如弹性模量㊁泊松比㊁剪切模量㊁波速等多个变量㊂基于该函数煤岩体中的３种场的冲击危险性评价具体表达式如下：１）原岩应力场为Ｙ（ｈ，ｃ，ｆ；ρ，μ）＝０（６）式中：ｈ为采深；ｃ为地应力；ｆ为体积力；ρ为煤岩体密度；μ为泊松比㊂２）震动场为Ｓ（ｘ，ｙ，ｚ，ｔ，Ｅ，ｆ；ρ，μ）＝０（７）式中：ｘ㊁ｙ㊁ｚ为震源的位置坐标；ｔ为发震时间；Ｅ为震源能量㊂３）采动应力场为Ｆ（ｕ，ｆ；ρ，μ）＝０（８）式中：ｕ为位移㊂３．１㊀原岩应力场与采动应力场（ＲＭ）耦合冲击危险性评价模型㊀㊀原岩应力场冲击危险性评价指标见表３㊂原岩应力场冲击危险性指数定义为Ｒ＝（Ｒ１＋Ｒ２＋Ｒ３＋Ｒ４）／４（９）其中，Ｒ１㊁Ｒ２㊁Ｒ３㊁Ｒ４为不同评价指标得分㊂原岩应力冲击危险性反映煤岩体自身发生冲击地压的固有属性，其数值大小反映了煤岩体采动后，发生自发型冲击地压的可能性和危险性㊂原岩应力场冲击危险性指数取值与冲击危险等级关系见表４㊂表３㊀原岩应力场冲击危险性评价指标Ｔａｂｌｅ３㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｅｖａｌｕａｔｉｏｎｉｎｄｅｘｓｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄ变量影响因素阈值分值Ｒ１开采深度ｈｈɤ４００ｍ１４００ｍ＜ｈɤ６００ｍ２６００ｍ＜ｈɤ８００ｍ３ｈ＞８００ｍ４Ｒ２向落差大于３ｍ的断层推进的工作面或巷道，工作面或掘进工作面至断层的距离ＬｄＬｄȡ１００ｍ１５０ｍɤＬｄ＜１００ｍ２２０ｍɤＬｄ＜５０ｍ３Ｌｄ＜２０ｍ４Ｒ３向背斜或向斜推进的工作面或巷道，工作面或掘进工作面与之距离ＬｚＬｚȡ５０ｍ１２０ｍɤＬｚ＜５０ｍ２１０ｍɤＬｚ＜２０ｍ３Ｌｚ＜１０ｍ４Ｒ４同一水平煤层冲击地压发生次数ｎｎ＝０１ｎ＝１２２ɤｎ＜３３ｎȡ３４㊀㊀采动应力冲击危险指标包括：应力异常指数和应力梯度指数㊂二者取值与冲击危险等级之间的关系见表５㊁表６㊂７２１２０２１年第４期煤炭科学技术第４９卷表４㊀原岩应力场冲击危险性等级划分标准Ｔａｂｌｅ４㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级Ｒɤ１１无１＜Ｒ＜２２弱２ɤＲ＜３３中等Ｒȡ３４强表５㊀应力异常指数冲击危险性等级划分标准Ｔａｂｌｅ５㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｓｔｒｅｓｓａｎｏｍａｌｙｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级γσɤ１１无１＜γσ＜３２弱３ɤγσ＜５３中等γσȡ５４强表６㊀应力梯度指数冲击危险性等级划分标准Ｔａｂｌｅ６㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｓｔｒｅｓｓｇｒａｄｉｅｎｔｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级ｇθɤ１１无１＜ｇθ＜３２弱３ɤｇθ＜５３中等ｇθȡ５４强㊀㊀基于原岩应力场与采动应力场耦合的冲击危险性评价模型为ＤＲＭ＝ａ１Ｒ＋ｂ１γσ＋ｃ１ｇσ（１０）㊀㊀其中：ＤＲＭ是原岩应力场与采动应力场耦合的冲击危险性评价指数；ａ１，ｂ１，ｃ１分别为原岩应力场和采动应力场耦合冲击危险性评价权重系数，不同矿井取值不同㊂原岩应力场与采动应力场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表７㊂表７㊀原岩应力场与采动应力场耦合冲击危险性等级划分标准Ｔａｂｌｅ７㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｎｄｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＲＭɤ１１无１＜ＤＲＭ＜３２弱３ɤＤＲＭ＜５３中等ＤＲＭȡ５４强３．２㊀原岩应力场与震动场（ＲＳ）耦合冲击危险性评价模型㊀㊀震动场冲击危险性指标包括：波速异常指数和波速梯度指数㊂二者取值与冲击危险等级之间的关系见表８㊁表９㊂原岩应力场与震动场耦合的冲击危险性评价模型为ＤＲＳ＝ａ２Ｒ＋ｂ２γθ＋ｃ２ｇθ（１１）㊀㊀其中：ＤＲＳ为原岩应力场和震动场耦合的冲击危险性评价指数；ａ２，ｂ２，ｃ２为原岩应力场和震动场耦合冲击危险性评价权重系数，不同矿井取值不同㊂原岩应力场与震动场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表１０㊂表８㊀波速异常指数冲击危险性等级划分标准Ｔａｂｌｅ８㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｗａｖｅｖｅｌｏｃｉｔｙａｎｏｍａｌｙｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级γθɤ１１无１＜γθ＜３２弱３ɤγθ＜５３中等γθȡ５４强表９㊀波速梯度指数冲击危险性等级划分标准Ｔａｂｌｅ９㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｗａｖｅｖｅｌｏｃｉｔｙｇｒａｄｉｅｎｔｉｎｄｅｘ阈值冲击危险性评价指数冲击危险等级ｇθɤ１１无１＜ｇθ＜３２弱３ɤｇθ＜５３中等ｇθȡ５４强表１０㊀原岩应力场与震动场耦合冲击危险性等级划分标准Ｔａｂｌｅ１０㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｉｎ－ｓｉｔｕｓｔｒｅｓｓｆｉｅｌｄａｎｄｖｉｂｒａｔｉｏｎｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＲＳɤ１１无１＜ＤＲＳ＜３２弱３ɤＤＲＳ＜５３中等ＤＲＳȡ５４强３．３㊀采动应力场与震动场（ＭＳ）耦合冲击危险性评价模型㊀㊀采动应力场与震动场耦合冲击危险性评价模型为ＤＭＳ＝ａ３γσ＋ｂ３ｇσ＋ｃ３γθ＋ｄ３ｇθ（１２）㊀㊀其中：ＤＭＳ为采动应力场与震动场耦合冲击危险性评价指数；ａ３，ｂ３，ｃ３，ｄ３分别为应力异常指数，应力梯度指数，波速异常指数，波速梯度指数的权重系数，不同矿井取值不同㊂采动应力场与震动场耦合的冲击危险性指数取值与冲击危险等级之间的关系见表１１㊂３．４㊀多场耦合（ＲＭＳ）冲击危险性动态评价模型冲击地压发生的本质是煤岩体具有的冲击能量８２１邓志刚等：动静载作用下煤岩多场耦合冲击危险性动态评价技术２０２１年第４期超过围岩吸收能量的极限㊂应力场可以表现煤岩体表１１㊀采动应力场与震动场耦合冲击危险性等级划分标准Ｔａｂｌｅ１１㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｃｏｕｐｌｉｎｇｏｆｍｉｎｉｎｇｓｔｒｅｓｓｆｉｅｌｄａｎｄｖｉｂｒａｔｉｏｎｆｉｅｌｄ阈值冲击危险性评价指数冲击危险等级ＤＭＳɤ１１无１＜ＤＭＳ＜３２弱３ɤＤＭＳ＜５３中等ＤＭＳȡ５４强未受扰动的地应力场和受采动影响而形成的采动应力场，是煤岩体承受应力的状态量㊂震动场主要表现煤岩体无法承受外部高应力差作用发生损伤破坏，在此过程中以震动形式释放出能量的时空域，可以表现煤岩体积蓄能量的过程㊂冲击地压的不仅发生在高应力区，也发生在煤岩体由低应力区向高应力区转化的过程中，采用煤岩体多场耦合的方法可以充分全面评价监测区域的冲击危险性㊂基于上述对ＲＭ耦合㊁ＲＳ耦合和ＭＳ耦合的冲击危险性评价模型，构建煤岩体多场耦合（ＲＭＳ）冲击危险性动态评价模型㊂冲击危险性指数算法如下Ｄ＝ＤＲＭ＋ＤＲＳ＋ＤＭＳ（１３）多场耦合冲击危险性评价指数Ｄ与冲击危险性等级的对应关系见表１２㊂表１２㊀多场耦合（ＲＭＳ）冲击危险性等级划分标准Ｔａｂｌｅ１２㊀Ｒｏｃｋｂｕｒｓｔｈａｚａｒｄｃｌａｓｓｉｆｉｃａｔｉｏｎｃｒｉｔｅｒｉａｂａｓｅｄｏｎｍｕｌｔｉ－ｆｉｅｌｄｃｏｕｐｌｉｎｇ阈值冲击危险性评价指数冲击危险等级Ｄɤ５１无５＜Ｄ＜１０２弱１０ɤＤ＜１５３中等Ｄȡ１５４强４㊀工程应用选取典型冲击地压矿井３１１２０２工作面为现场，开展相关应用㊂４．１㊀工作面概况３１１２０２工作面是该矿井１２盘区第２个回采工作面，是首个沿空回采工作面，位于１２盘区北部，为３１１２０１接续工作面，东部以１２盘区辅运大巷为界，西部至１２盘区西部边界，南部为实体煤，北部为正在回采的３１１２０１工作面，保护煤柱宽度６ｍ㊂该工作面采用走向长壁综合机械化一次采全高采煤法，采高５．２５ｍ，工作面倾斜长度２９９ｍ，走向长度３１４０ｍ，全部垮落法管理顶板，两回采巷道采用液压支架进行超前支护㊂工作面布置如图１１所示㊂图１１㊀３１１２０２工作面布置Ｆｉｇ．１１㊀ＬａｙｏｕｔｏｆＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ经鉴定，３－１煤及其顶底板均具有弱冲击倾向性，３－１煤层冲击危险等级为中等冲击危险㊂３１１２０２工作面所在地层构造形态总体为一向北西倾斜的单斜构造，倾向３００ʎ ３２０ʎ㊁倾角１ʎ ３ʎ，地层产状沿走向及倾向均有一定变化，沿走向发育有宽缓的波状起伏㊂３１１２０２工作面受ＤＦ１９㊁ＤＦ１８㊁Ｆ２２㊁Ｆ２４断层影响较大，其中ＤＦ１９断层影响最为显著，该断层走向长度约１２００ｍ，落差６．５ １０．０ｍ，预计影响３１１２０２工作面走向长度５６０ｍ，对生产过程中的冲击地压灾害影响最大㊂３１１２０２工作面主要断层情况见表１３，３１１２０２工作面煤层顶底板结构特征见表１４㊂表１３㊀３１１２０２工作面断层特征Ｔａｂｌｅ１３㊀ＦａｕｌｔｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ断层走向／（ʎ）倾向／（ʎ）倾角／（ʎ）性质落差／ｍＤＦ１８３１２４２７０正断层０ ５．０ＤＦ１９２９６２６４９正断层６．５ １０．０Ｆ２２２８５１５３０正断层１．１Ｆ２４３５７９０４６正断层０．３表１４㊀３１１２０２工作面煤层顶底板结构特征Ｔａｂｌｅ１４㊀ＳｔｒｕｃｔｕｒａｌｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｃｏａｌｓｅａｍｒｏｏｆａｎｄｆｌｏｏｒｉｎＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ顶底板岩性厚度／ｍ平均厚度／ｍ基本顶细粒砂岩９．２５ １９．７０１５．８４直接顶砂质泥岩２．２８ １２．８５８．５０直接底砂质泥岩４．６９ １２．９９７．６８基本底细粒砂岩５．２１ ２１．４５１４．８２４．２㊀多场耦合冲击危险性动态评价原岩应力场包括重力场和构造应力场，通过地应力测试及三维反演可得到㊂采动应力场通过应力在线监测系统监测得到㊂在３１１２０２回风巷生产帮安设应力在线监测系统，距离开切眼６０ｍ生产帮侧９２１２０２１年第４期煤炭科学技术第４９卷安设第１组应力测点，之后每隔４０ｍ安设一组，共布置１０组，主要监测工作面超前３００ｍ范围内回风巷一侧煤体采动应力分布情况；每组垂直于煤壁施工２个ø４４ｍｍ应力钻孔，孔深分别为１１ｍ和１６ｍ，钻孔间距１ｍ㊂当测点与工作面距离小于３０ｍ时开始回撤，随着工作面回采，测点依次前移，直至回采结束㊂测点布置方案如图１２所示㊂收集了３１１２０２工作面２０１９年５月至１１月的回风巷采动应力监测数据，并进行了分析和应用㊂图１２㊀应力在线监测测点布置Ｆｉｇ．１２㊀Ｌａｙｏｕｔｏｆｍｅａｓｕｒｉｎｇｐｏｉｎｔｓｆｏｒｏｎｌｉｎｅｓｔｒｅｓｓｍｏｎｉｔｏｒｉｎｇ工作面震动场数据由ＡＲＡＭＩＳＭ／Ｅ微震监测系统监测得到㊂３１１２０２工作面测站布置情况如图１３所示㊂井下布置４台微震拾震器（编号Ｓ９至Ｓ１２）和６个移动式监测探头（编号Ｔ１９至Ｔ２４），地面布置１台编号为Ａ２矿震测站组成联合监测网，对工作面进行全面监测㊂图１３㊀３１１２０２回采工作面微震监测系统测站布置Ｆｉｇ．１３㊀ＡｒｒａｎｇｅｍｅｎｔｏｆｔｈｅｓｔａｔｉｏｎｏｆｍｉｃｒｏｓｅｉｓｍｉｃｍｏｎｉｔｏｒｉｎｇｓｙｓｔｅｍｉｎＮｏ．３１１２０２ｍｉｎｉｎｇｆａｃｅ选取３１１２０２工作面回采至距离ＤＦ１９断层１０ｍ时，开始揭露ＤＦ１９断层时以及揭露ＤＦ１９断层２９５ｍ时，３个时间节点３１１２０２工作面超前１５０ｍ范围内的冲击危险性评价情况㊂回采至距离ＤＦ１９断层１０ｍ时，计算原岩应力场冲击危险性指数Ｒ，３－１煤层平均采深６２０ｍ，Ｒ１＝３；工作面距离断层１０ｍ，Ｒ２＝４；工作面前方无背斜或向斜，Ｒ３＝１；该区域未发生过冲击地压，Ｒ４＝１㊂根据式（９）计算得到Ｒ＝２．３㊂按照式（１）㊁式（２）计算得到γσ＝２．３，ｇσ＝３．３㊂３１１２０２工作面最大主应力与水平应力比约为１，取ａ１＝ｂ１＝ｃ１＝０．５，根据式（１０）计算得到ＤＲＭ＝４．０㊂同理计算出，揭露断层时ＤＲＭ＝５．０；揭露断层２９５ｍ时ＤＲＭ＝４．０㊂回采至距离ＤＦ１９断层１０ｍ时，Ｒ＝２．３；根据式（３）㊁（４）计算得到γθ＝３．４，ｇθ＝５．０；工作面最大主应力与水平应力比约为１，取ａ２＝ｂ２＝ｃ２＝０．５，根据式（１１）计算得到ＤＲＳ＝５．４㊂同理计算出，揭露断层时ＤＲＳ＝６．５；揭露断层２９５ｍ时ＤＲＳ＝４．５㊂回采至距离ＤＦ１９断层１０ｍ时，根据式（１）㊁式（２）计算得到γσ＝２．３，ｇσ＝３．３；根据式（３）㊁式（４）计算得到γθ＝３．４，ｇθ＝５．０㊂３１１２０２工作面最大主应力与水平应力比约为１，取ａ３＝ｂ３＝ｃ３＝ｄ３＝０．５，根据式（１２）计算得到ＤＭＳ＝７．０㊂同理计算出，揭露断层时ＤＭＳ＝９．２；揭露断层２９５ｍ时ＤＭＳ＝６．２㊂根据式（１３）计算得到，回采至距离ＤＦ１９断层１０ｍ时Ｄ＝１６．４，具有强冲击危险性；揭露断层时Ｄ＝２０．７，具有强冲击危险性；揭露断层２９５ｍ时Ｄ＝１４．７，具有中等冲击危险性㊂４．３㊀评价结果验证与对比依据３１１２０２工作面回采期间超前工作面３００ｍ范围内微震监测数据㊁钻孔应力监测数据平均值验证评价结果㊂在距离ＤＦ１９断层１０ｍ附近，当天微震释放总能量约为１９３００Ｊ，单次最大能量为７０００Ｊ，微震事件２６次；揭露断层时，当天微震释放总能量约为２２３００Ｊ，单次最大能量约为９０００Ｊ，微震事件１７次；揭露断层２９６ｍ附近，当天微震释放总能量约为７７００Ｊ，单次最大能量约为６０００Ｊ，微震事件６次㊂从微震事件能量㊁频次中可以看出冲击危险性降低㊂在距离断层１０ｍ附近㊁揭露断层附近以及揭露断层２９６ｍ附近选取３个煤层钻孔应力测点，３个测点应力监测数据如图１４所示㊂工作面推进过程中煤层应力数值增加，强冲击危险区域应力始终高于中等冲击危险区域㊂微震和煤层钻孔应力监测数据验证了冲击危险性动态评价结果的合理性㊂图１４㊀煤层钻孔应力监测数据平均值Ｆｉｇ．１４㊀Ａｖｅｒａｇｅｖａｌｕｅｓｏｆｓｔｒｅｓｓｍｏｎｉｔｏｒｉｎｇｄａｔａｓｉｎｃｏａｌｓｅａｍ０３１。
