岩石变形破坏过程中的能量演化机制
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摘要
冲击地压、岩爆等岩体工程灾害本质上是能量非线性演化至灾变的过程,从能量角度研究岩石的变形破坏规律,可以突破应力应变分析的传统模式局限,对于岩体力学行为的深入认识带来一种新的视角和分析方法。本文针对岩石变形破坏过程中的能量演化机制,从能量转化作用、能量演化及分配规律、能量演化的非线性特性、能量演化的细观特征等四个方面研究了岩石在受载过程中的能量行为,主要取得以下进展：
(1)分析了岩石变形破坏过程中的能量转化作用。受载岩石能量转化大致分为能量输入、能量积聚、能量耗散、能量释放四个过程,输入的总能量部分转化为弹性能,部分转化为其他形式的能量耗散掉；分别建立了碎块数量与耗散能、碎块速率与弹性能的关系,发现能量耗散决定了岩石破碎块度,碎块形成后剩余的弹性能决定了岩石破碎剧烈程度；能量驱动岩石变形破坏主要有两种机制：能量耗散使岩石抵抗破坏的能力降低、能量积聚使驱动岩石破坏的能力增强。
(2)获得了岩石变形破坏过程中的能量演化及分配规律。提出了岩石储能极限、残余弹性能密度和最大耗散能密度概念。单轴压缩下弹性能随应力呈现慢-快-慢的增长模式,并于破坏时释放出来,储能极限约为0.21MJ/m3,耗散能起初增长较缓慢,临近破坏时大幅增加,增幅可达85%左右,整个加载过程中输入能量转化为弹性能的比例约从60%增加到82%,临近破坏阶段有小幅下降。研究了岩石能量演化及分配规律的加载速率效应、围压效应、岩性效应和水环境效应,并进一步得到不同开采条件下能量演化的差异,无煤柱开采的工作面前方煤岩体最大弹性能密度是放顶煤开采的1.5倍,是保护层开采的2.3倍,而峰后能量释放速率也由保护层开采、放顶煤开采、无煤柱开采依次增大。
(3)揭示了岩石能量演化的分叉和混沌特性。建立了岩石能量转化的自我抑制模型,得到并验证了岩石内部能量随应力变化的演化方程,所建模型适用于岩石变形破坏峰前阶段；能量演化具有分叉和混沌性质,当轴向应力达到约92%峰值应力时,系统进入倍周期分叉区,达到约97.5%峰值应力时,进入混沌状态；提出了能量迭代增长因子μ,其表征岩石受载过程中能量的迭代增长效应,根据能量迭代增长因子的非线性演化,可将岩石变形破坏过程分为4个阶段：0<μ≤1、1<μ≤3、3<μ≤3.5699、3.5699<μ≤4,分别表征了岩石中的能量衰减、能量积聚、能量耗散和能量释放主导阶段。
(4)探究了岩石能量演化的细观特征。沟通了岩石细观几何及强度特征——能量演化特征——细观破裂特征的内在联系：一方面,得到了岩石细观基元的平均强度、均质度和特征尺度以及裂纹分布特征对岩石能量演化特征的影响规律,并建立了细观特征与能量耗散的关系,表明基元均质度决定了能量耗散的模式,而临界能耗值和基元平均强度决定了能量耗散的量值；另一方面,探讨了岩石能量演化特征对其细观破裂模式的影响,建立了有效冲击能指数与破裂面分形维数的关系,表明存在分形维数阈值,当破裂面分形维数小于此阈值时,岩石有效冲击能指数与分形维数值呈正相关关系,反之,呈反相关关系,建立了有效冲击能指数与微破裂演化之间的关系,表明有效冲击能指数越大,岩石微破裂演化表现为“突变”的性质,有效冲击能指数越小,岩石微破裂演化表现为“渐变”的性质。
该论文有图138幅,表28个,参考文献245篇。
Rock mass engineering disaster such as coal bump and rock burst results fromnonlinear evolution and catastrophe of energy. Research on rock deformation andfailure from the point of energy evolution can break through the limit of stress-strainanalysis, and offer a new view and method to know deep the mechanical behavior ofrock mass. Aim at the energy evolution mechanism during rock deformation andfailure, four aspects i.e. energy transformation, energy evolution and allocation,nonlinear characteristic and mesoscopic characteristic of energy evolution werediscussed. The main progresses are as follows.
(1) Energy transformations during rock deformation and failure were analyzed.The energy transforming process can be divided as four steps i.e. energy input, energyaccumulation, energy dissipation and energy release roughly. A part of inputted energyis transformed into elastic energy, while another part is transformed into other energydissipated. The relationship between the number of rock fragments and dissipatedenergy as well as the one between the velocity of rock fragments and elastic energywere established respectively, and the results show that the dissipated energy decidesthe rock fragmentation, while the residual elastic energy after failure decides therupture intensity. There are two main mechanism of energy drives rock fracture i.e.energy dissipation reduces the failure resistance and energy accumulation enhancesthe driving force of rock failure.
(2) Energy evolution and allocation pattern during rock deformation and failurewere obtained. Firstly, the accumulation energy limit, the residual elastic energydensity and the maximum dissipated energy density are put forward. Secondly, theelastic energy shows a slow-fast-slow growth pattern with the accumulation energylimit of0.21MJ/m3under uniaxial compression, while the dissipated energy growsgently at first and has a sharp increase near failure with the amplification of85%; theratio of inputted energy transforming into elastic energy is about60%~82%at thewhole loading process, and it drops slightly near failure. Thirdly, the effects of loadingrate, confining pressure, lithology, and water environment on energy evolution andallocation pattern are investigated. Lastly, the difference of energy evolution amongthree typical mining ways is got, and the maximum elastic energy density in front coalmass of coal mining working face without pillars is1.5times as that in caving mining,while2.5times as that in protective layer mining. The energy release rate increases orderly along protective layer mining, caving mining and coal mining without pillars.
(3) Bifurcation and chaos characteristics of rock energy evolution were revealed.The self-repression model reflecting energy transformation was constructed, and theevolution equation of rock energy with stress was obtained and proved. The model issuitable for energy evolution before peak strength. Rock energy evolution has thecharacteristics of bifurcation and chaos, and rock system turns into period doublingbifurcation region when the axial stress reaches92%of peak strength, while it turnsinto chaos state when the axial stress reaches97.5%of peak strength. The energyiteration growth factor μ is put forward, and it can describe the iteration growth effectof rock energy. According to the nonlinear evolution of μ, the process of rockdeformation and failure can be divided four stages i.e.0<μ≤1,1<μ≤3,3<μ≤3.5699and3.5699<μ≤4, and they represent the phase of energy decrement, energyaccumulation, energy dissipation and energy release leading respectively.
(4) Mesoscopic characteristics of rock energy evolution were investigated. Theinternal relation among mesoscopic characteristics on geometry and strength, energyevolution characteristic and mesoscopic fracture characteristic is discovered. On theone hand, the effect of average strength, homogeneity, characteristic scale of rockelement and fissure distribution on rock energy evolution was studied, and therelationship between mesoscopic characteristic and dissipated energy was set up.These show that the homogeneity of rock element decides the pattern of energydissipation, while the average strength of rock element and the critical dissipatedenergy decide the value of energy dissipation. On the other hand, the effect of rockenergy characteristic on mesoscopic rupture pattern was discussed. The relationshipbetween effective impact energy index and fractal dimension of fracture surface wasset up, which shows a threshold of fractal dimension exists, and it is positivecorrelation between effective impact energy index and fractal dimension of fracturesurface when the fractal dimension is less than the threshold, while inverse correlationwhen the fractal dimension is more than it. The relationship between effective impactenergy index and micro-rupture evolution is set up too, which shows micro-ruptureevolution has property of catastrophe when the effective impact energy index is large,while it has property of gradualness when the effective impact energy index is small.
(1)分析了岩石变形破坏过程中的能量转化作用。受载岩石能量转化大致分为能量输入、能量积聚、能量耗散、能量释放四个过程,输入的总能量部分转化为弹性能,部分转化为其他形式的能量耗散掉；分别建立了碎块数量与耗散能、碎块速率与弹性能的关系,发现能量耗散决定了岩石破碎块度,碎块形成后剩余的弹性能决定了岩石破碎剧烈程度；能量驱动岩石变形破坏主要有两种机制：能量耗散使岩石抵抗破坏的能力降低、能量积聚使驱动岩石破坏的能力增强。
(2)获得了岩石变形破坏过程中的能量演化及分配规律。提出了岩石储能极限、残余弹性能密度和最大耗散能密度概念。单轴压缩下弹性能随应力呈现慢-快-慢的增长模式,并于破坏时释放出来,储能极限约为0.21MJ/m3,耗散能起初增长较缓慢,临近破坏时大幅增加,增幅可达85%左右,整个加载过程中输入能量转化为弹性能的比例约从60%增加到82%,临近破坏阶段有小幅下降。研究了岩石能量演化及分配规律的加载速率效应、围压效应、岩性效应和水环境效应,并进一步得到不同开采条件下能量演化的差异,无煤柱开采的工作面前方煤岩体最大弹性能密度是放顶煤开采的1.5倍,是保护层开采的2.3倍,而峰后能量释放速率也由保护层开采、放顶煤开采、无煤柱开采依次增大。
(3)揭示了岩石能量演化的分叉和混沌特性。建立了岩石能量转化的自我抑制模型,得到并验证了岩石内部能量随应力变化的演化方程,所建模型适用于岩石变形破坏峰前阶段；能量演化具有分叉和混沌性质,当轴向应力达到约92%峰值应力时,系统进入倍周期分叉区,达到约97.5%峰值应力时,进入混沌状态；提出了能量迭代增长因子μ,其表征岩石受载过程中能量的迭代增长效应,根据能量迭代增长因子的非线性演化,可将岩石变形破坏过程分为4个阶段：0<μ≤1、1<μ≤3、3<μ≤3.5699、3.5699<μ≤4,分别表征了岩石中的能量衰减、能量积聚、能量耗散和能量释放主导阶段。
(4)探究了岩石能量演化的细观特征。沟通了岩石细观几何及强度特征——能量演化特征——细观破裂特征的内在联系：一方面,得到了岩石细观基元的平均强度、均质度和特征尺度以及裂纹分布特征对岩石能量演化特征的影响规律,并建立了细观特征与能量耗散的关系,表明基元均质度决定了能量耗散的模式,而临界能耗值和基元平均强度决定了能量耗散的量值；另一方面,探讨了岩石能量演化特征对其细观破裂模式的影响,建立了有效冲击能指数与破裂面分形维数的关系,表明存在分形维数阈值,当破裂面分形维数小于此阈值时,岩石有效冲击能指数与分形维数值呈正相关关系,反之,呈反相关关系,建立了有效冲击能指数与微破裂演化之间的关系,表明有效冲击能指数越大,岩石微破裂演化表现为“突变”的性质,有效冲击能指数越小,岩石微破裂演化表现为“渐变”的性质。
该论文有图138幅,表28个,参考文献245篇。
Rock mass engineering disaster such as coal bump and rock burst results fromnonlinear evolution and catastrophe of energy. Research on rock deformation andfailure from the point of energy evolution can break through the limit of stress-strainanalysis, and offer a new view and method to know deep the mechanical behavior ofrock mass. Aim at the energy evolution mechanism during rock deformation andfailure, four aspects i.e. energy transformation, energy evolution and allocation,nonlinear characteristic and mesoscopic characteristic of energy evolution werediscussed. The main progresses are as follows.
(1) Energy transformations during rock deformation and failure were analyzed.The energy transforming process can be divided as four steps i.e. energy input, energyaccumulation, energy dissipation and energy release roughly. A part of inputted energyis transformed into elastic energy, while another part is transformed into other energydissipated. The relationship between the number of rock fragments and dissipatedenergy as well as the one between the velocity of rock fragments and elastic energywere established respectively, and the results show that the dissipated energy decidesthe rock fragmentation, while the residual elastic energy after failure decides therupture intensity. There are two main mechanism of energy drives rock fracture i.e.energy dissipation reduces the failure resistance and energy accumulation enhancesthe driving force of rock failure.
(2) Energy evolution and allocation pattern during rock deformation and failurewere obtained. Firstly, the accumulation energy limit, the residual elastic energydensity and the maximum dissipated energy density are put forward. Secondly, theelastic energy shows a slow-fast-slow growth pattern with the accumulation energylimit of0.21MJ/m3under uniaxial compression, while the dissipated energy growsgently at first and has a sharp increase near failure with the amplification of85%; theratio of inputted energy transforming into elastic energy is about60%~82%at thewhole loading process, and it drops slightly near failure. Thirdly, the effects of loadingrate, confining pressure, lithology, and water environment on energy evolution andallocation pattern are investigated. Lastly, the difference of energy evolution amongthree typical mining ways is got, and the maximum elastic energy density in front coalmass of coal mining working face without pillars is1.5times as that in caving mining,while2.5times as that in protective layer mining. The energy release rate increases orderly along protective layer mining, caving mining and coal mining without pillars.
(3) Bifurcation and chaos characteristics of rock energy evolution were revealed.The self-repression model reflecting energy transformation was constructed, and theevolution equation of rock energy with stress was obtained and proved. The model issuitable for energy evolution before peak strength. Rock energy evolution has thecharacteristics of bifurcation and chaos, and rock system turns into period doublingbifurcation region when the axial stress reaches92%of peak strength, while it turnsinto chaos state when the axial stress reaches97.5%of peak strength. The energyiteration growth factor μ is put forward, and it can describe the iteration growth effectof rock energy. According to the nonlinear evolution of μ, the process of rockdeformation and failure can be divided four stages i.e.0<μ≤1,1<μ≤3,3<μ≤3.5699and3.5699<μ≤4, and they represent the phase of energy decrement, energyaccumulation, energy dissipation and energy release leading respectively.
(4) Mesoscopic characteristics of rock energy evolution were investigated. Theinternal relation among mesoscopic characteristics on geometry and strength, energyevolution characteristic and mesoscopic fracture characteristic is discovered. On theone hand, the effect of average strength, homogeneity, characteristic scale of rockelement and fissure distribution on rock energy evolution was studied, and therelationship between mesoscopic characteristic and dissipated energy was set up.These show that the homogeneity of rock element decides the pattern of energydissipation, while the average strength of rock element and the critical dissipatedenergy decide the value of energy dissipation. On the other hand, the effect of rockenergy characteristic on mesoscopic rupture pattern was discussed. The relationshipbetween effective impact energy index and fractal dimension of fracture surface wasset up, which shows a threshold of fractal dimension exists, and it is positivecorrelation between effective impact energy index and fractal dimension of fracturesurface when the fractal dimension is less than the threshold, while inverse correlationwhen the fractal dimension is more than it. The relationship between effective impactenergy index and micro-rupture evolution is set up too, which shows micro-ruptureevolution has property of catastrophe when the effective impact energy index is large,while it has property of gradualness when the effective impact energy index is small.
引文
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