Research progress in the geochemistry characteristics of scandium in Chinese coals
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摘要:
钪(Sc)具有较高熔点、较小密度，是最好的阻挡金属，广泛应用于照明、合金、陶瓷、催化剂等工业领域。在特定地质条件下，部分煤富集钪，可成为战略金属资源予以利用，因此，钪地球化学是煤地质学研究领域的热点问题之一。为阐明我国煤中钪的地球化学特征，在全面收集我国煤中钪测试数据的基础上，并结合安徽淮南煤、重庆南桐煤、四川宝鼎煤和云南勐托煤等实例，系统总结了我国煤中钪的含量水平、时空分布、赋存状态和富集成因，并初步评价了我国的煤系钪资源。结果表明：我国大多煤中钪含量正常，钪的平均含量为4.02 mg/kg，仅略高于世界硬煤。贵州、重庆、安徽、广西、内蒙古、山西、云南等局地煤中钪含量较高，最高达139 mg/kg。煤层顶、底板围岩及夹矸岩石较煤富集钪。我国富钪煤大多为二叠纪烟煤，晚侏罗–早白垩世煤中钪含量普遍较低。一般而言，高灰煤和腐泥煤因具较高的矿物质含量，常富集钪。钪为亲石元素，在煤中主要与矿物质结合，多赋存于高岭石等硅酸盐矿物和磷钇矿等自生矿物中，部分与有机质结合，与腐植质有关。我国煤中钪的主要富集成因类型包括：①基性源岩贡献型，钪为相容元素，基性岩中钪含量高于中酸性岩，因此，物源区基性源岩风化可导致部分煤中钪富集；②海陆过渡沉积环境贡献型，海水入侵导致泥炭沼泽的pH值增大，从而利于钪的迁移，此外，在泥炭沼泽的还原环境中，大量腐植酸生成，钪易与有机质结合而富集；③地下水淋滤贡献型，地下水淋滤围岩的含钪矿物导致煤层中钪局部富集；④热液贡献型，热液与围岩发生交代反应使钪迁移，改变煤的矿物质组成导致煤富集钪；⑤岩浆及变质贡献型，岩浆侵入导致煤阶提升，从而减少有机质结合态的钪，同时，伴随灰分的升高，煤中矿物结合态的钪相应增加；⑥同沉积火山灰贡献型，煤系基性凝灰岩层(蚀变黏土岩夹矸，Tonsteins)可为煤提供钪。
Abstract:Scandium (Sc), which has a high melting point and a low density, is widely used in lighting, alloys, ceramics, catalysts, and other industrial fields. Under a specific geological condition, Sc could be enriched in certain coal. As one of strategic metals hosted in coals, the geochemistry of Sc is a hot topic in coal geology. In order to clarify the geochemical characteristics of Sc in Chinese coals, based on a comprehensive collection of the data of Sc concentrations in Chinese coals and four cases of the Huainan coals of Anhui, the Nantong coals of Chongqing, the Baoding coals of Sichuan, and the Mengtuo coals of Yunnan, the content, temporal and spatial distribution, modes of occurrence, and enrichment mechanism of Sc in Chinese coals were discussed, and the Sc resources hosted in coal measures was assessed as well. Results indicated that the scandium in Chinese coals was at normal level with an average of 4.02 mg/kg, which was slightly higher than that of world hard coal. The concentrations of scandium in certain coals from Guizhou, Chongqing, Anhui, Guangxi, Inner Mongolia, Shanxi, and Yunnan were elevated, and with the maximum Sc concentration of 139 mg/kg. Regarding a coalbed, Sc was preferably enriched in country rocks, e.g., the roof, floor, and parting rocks, relative to coal benches. Most Sc-rich Chinese coals were bituminous and with a coal-forming period of Permian, while the Late Jurassic - Early Cretaceous coals were of a low Sc content. Overall, due to a high mineral matter content in the high-ash and sapropelic coals, its Sc concentrations increased. As a lithophilic element, Sc in coals was dominantly hosted in minerals, especially silicate minerals, e.g., kaolinite, and some authigenic minerals, e.g., xenotime. Sc was also partially bounded to organic matter, especially the humic matter in low rank coals. The genetic types of Sc enrichment in Chinese coals included: ① Mafic source rock type. As a compatible element, Sc was of a higher concentration in mafic rocks than that of intermediate and felsic ones. Correspondingly, the weathering of mafic source rock could lead to a Sc enrichment in certain coal; ② Paralic facies type. Due to the marine transgression, the increasing pH value of peat bogs with a large amount of humic acid facilitated the migration of Sc and its combination with organic matter; ③ Groundwater leaching type. The leaching of Sc-bearing minerals by groundwater resulted into a local Sc enrichment in coal benches of a coalbed; ④ Hydrothermal solution type. Hydrothermal solutions leached and/or transported Sc into a coal via a mineral precipitation; ⑤ Magmatic and metamorphic type. Igneous intrusion led to a rise of coal rank, resulting in a reduce of organic matter bound Sc. Meanwhile, Sc hosted by minerals in coals might be enriched due to the increased ash yields; ⑥ Volcanic ash type. Mafic tuff layers or tonsteins occurred in coal measures could provide the coalbeds with Sc.
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0. 引 言
我国煤矿开采过程中，受地质条件、开采接续及设计不合理等因素的影响，留设了大量不规则煤柱（孤岛煤柱、断层煤柱和边角煤柱等）[1-3]，该类煤柱在采掘初期其内部煤体发生变形、破坏，随时间增长产生明显的蠕变损伤，并且在开采扰动等的作用下，煤体历经数次增压、卸压应力作用，导致煤体在不同蠕变损伤程度下受到周期性循环载荷的作用。由于煤体蠕变损伤程度不同，并且在循环载荷作用下的破坏规律与静载下有着显著的差异，因此，将煤体的蠕变损伤程度考虑在内，开展循环载荷作用下煤体劣化演化机理的研究，这对于解决煤柱回采或在煤柱内掘进巷道而导致的煤柱劣化突变失稳冲击灾害的问题有重要的指导意义。
长期以来，蠕变损伤问题广泛存在于各类煤岩工程中，也一直是国内外研究的热点[4-5]，大量学者通过室内外研究试验获得了较为丰富的优秀成果。熊良宵等[6]针对硬岩的非线性流变力学特性，基于多类型流变体模型提出了一种包含多种变形构件的非线性弹黏塑性流变模型；徐鹏等[7]研究了三轴循环加卸载下煤岩的蠕变行为，建立了一种新的针对煤岩的弹塑性加载和弹性卸载蠕变损伤模型；张天军等[8]借助声发射技术研究了不同含水率条件下煤岩的蠕变特性，得出高含水率条件下煤岩的蠕变损伤呈指数增加的结论；尹光志等[9]采用卸围压的方式研究了含瓦斯脆性煤岩的蠕变特性，基于CHABOCHE黏塑性本构模型提出了一种描述含瓦斯煤的卸压短期蠕变损伤模型；DANESH等[10]研究了蠕变损伤对煤岩渗透性的影响，结果表明蠕变影响下煤岩渗透性改变25%以上。周期性循环载荷作用下的煤岩体劣化变形机制因与现场多次扰动后的实际工程更相吻合，因而得到了大量学者的关注[11-14]，也取得了一系列的科研成果。LIU等[15-16]研究了循环荷载下不同围压和不同加载频率对砂岩力学性能和损伤变量的影响；杨逾等[17]分析了不同应力幅值下砂岩的力学响应特性；ZHAO等[18]探讨了多类型组合应力下岩盐的损伤演化规律，并从能量耗散的角度定义了损伤变量；VANEGHI等[19]分析了循环加卸载条件下砂岩和花岗岩的强度变化，并从微观角度对比了2种类型岩石的结构和延性差异；段敏克等[20]研究了真三轴循环加卸载条件下煤样的断裂过程及能量演化特征，建立了真三轴加卸载煤样损伤变量方程。
上述研究分别针对煤岩体在蠕变或者循环载荷这一特征进行了大量试验，研究了蠕变和循环加卸载下煤岩体的能量聚释、强度及变形特征，对煤岩体劣化破坏理论和工程研究有一定的指向作用，但这些研究几乎都是在蠕变损伤或循环加卸载损伤等单一影响因素下进行的试验。然而，在深部煤矿开采等大型工程中，煤岩体会在初步扰动后因工程的复杂性首先受到不同应力水平和时间的蠕变作用，随后会在开采过程中再次经受周围采动应力的循环扰动作用，这实际上是对前期蠕变后煤岩体的再次加卸载作用，这就要求研究学者需要考虑长时蠕变作用损伤与循环加卸载作用损伤的叠加作用对煤岩体突变劣化性能的影响，但目前考虑二者叠加影响的相关文献鲜有报道。
因此，笔者在考虑煤岩体初始蠕变损伤效应的前提下，开展不同初始蠕变损伤对煤岩强度及变形性质的影响试验，研究初始蠕变损伤与循环载荷叠加作用下煤岩劣化特性的演化规律，分析循环载荷下不同应力区间煤岩的强度特征及累积损伤特性，探究了循环载荷次数对煤岩蠕变损伤效应的组合作用机制，进一步揭示蠕变损伤效应下煤岩变形破坏过程中能量转化机理，研究成果将对减少遗煤长时蠕变诱冲灾害，提高采空区遗煤回采效率，推动矿区生态文明建设具有重要的工程意义。
1. 蠕变−循环载荷−卸围压试验方案
试验所用煤样取自阳城煤矿3煤具有弱冲击倾向性的煤层，并将现场采集的煤块加工成直径50 mm、高度100 mm的圆柱体试件，依据GB/T 25217.2—2010《煤层冲击倾向性分类及指数的测定方法》，测得煤样冲击倾向性结果见表1。由于煤属于高孔隙率、高裂隙度介质，其内部的孔隙、裂隙和基质对煤的力学性质产生很大影响，因此，为降低煤样的离散性，加工后的试件采用CT图像重构技术分析了试件基质−孔隙−裂隙的统计学分布特征，进一步选择孔裂隙参数近似的试件进行试验，煤样孔裂隙网络模型三维重构流程如图1所示。
表 1 煤样冲击倾向性测定结果Table 1. Determination results of impact tendency of coal samples单轴抗压
强度/MPa冲击能量
指数弹性能量
指数动态破坏
时间/ms综合判定
结果10.68 2.26 17.2 2428 弱 ![]()
图 1 孔裂隙网络模型三维重构流程示意Figure 1. 3D reconstruction process of coal samples fracture-pore network试验设备选用RLJW-2000型流变试验机，借助MISTRAS系列PCI系统完成声发射数据的监测和采集工作。
首先，利用流变试验机对试件进行单轴压缩试验，获取原煤基本力学参数；其次，开展不同时长单轴蠕变试验（无围压），待加载应力达到60%单轴抗压强度时保持恒定加载，恒定加载时间分别为0、8、16、24 h；最后，分别进行三轴压缩试验和循环载荷加卸载试验。在循环加卸载试验中，将循环加卸载区间分成等幅3级（图2），并采用逐级递增的方式施加轴向载荷。受控于选用的现场煤样在单轴加载较短时长内会进入加速蠕变破坏阶段，导致煤样发生破坏，影响后续循环加卸载试验开展，为此恒定加载时间参考“三八制”生产进行选取。具体试验步骤：
1）为了避免煤样破裂或过度应变[21]，首先将围压按照0.05 MPa/s速率加载至单轴抗压强度σ的60%，试验期间保持恒定。
2）将第1级循环下限应力设置为同等围压条件下三轴抗压强度σ′的20%，上限应力设置为同等围压条件下三轴抗压强度σ′的40%，循环次数设定为N1次，当此级达到预设次数后，上下限分别增加同等围压条件下三轴抗压强度σ′的20%，进行第2级的N2次循环，然后再进行第3级的N3次循环。
3）循环加卸载采用0.1 kN/s应力控制方式，当最后一级循环载荷加载至预定次数后对围压进行卸载，围压卸载期间轴向循环载荷正常进行，直至试样破坏，以此较好地模拟在采动卸荷循环时工程失稳的发生，加载全过程应力路径示意如图2所示。
2. 常规加载煤岩蠕变特性
煤的离散性相较于其他岩石的离散性较高，因此在开展循环加卸载试验前对部分加工好的煤样进行常规单轴与三轴压缩试验，以此分析煤样的力学性能，单轴与三轴压缩试验煤样编号分别为Y1-3和T1-3。
2.1 三轴压缩损伤特征
图3为典型试样在单轴压缩试验下的应力−应变曲线，煤样在完全破坏之前，受内部裂隙的影响经历了数次局部损伤，可观察到图中所示每条应力−应变峰前曲线波动非常明显，呈锯齿状爬升（图内红色线圈所示）。
煤样平均单轴抗压强度为10.17 MPa，试验将围压恒定为平均单轴抗压强度的60%。由图4观察可得，三轴压缩试验的峰前应力−应变曲线未出现单轴压缩条件下曲线呈锯齿状爬升现象，峰值强度得到了大幅的提高。煤样在围压的抑制作用下，应力出现阶梯状陡降现象（图内红色线圈所示），与单轴压缩试验条件下损伤较为相似。
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图 4 常规三轴压缩试验应力−应变曲线Figure 4. Stress-strain curves of conventional triaxial compression test2.2 煤岩蠕变特性分析
将所选煤样分别进行不同时长蠕变预损伤准备，部分蠕变预损伤时程曲线如图5所示。试验可观察到蠕变预损伤仅表现出瞬态蠕变和稳态蠕变特征[22]，均未出现加速蠕变阶段。在瞬态蠕变阶段，声发射振铃计数较为活跃；进入稳态蠕变阶段，声发射振铃计数曲线零星散落，很少出现短时聚集突升现象，仅在轴向应变有微小增幅的情况下出现振铃计数突升。与文献[23-26]内煤样破裂阶段出现的万分量级振铃计数突升相比，本次的蠕变预损伤声发射振铃计数最大值均未超过800，属于低能量释放下的蠕变行为，表明煤样未出现明显大裂隙损伤，符合进行下一步试验的标准。
煤样进入稳态蠕变阶段后，稳态蠕变阶段的变形量随蠕变时间发生变化，如图5d所示，对比不同蠕变时间下稳态蠕变的变形量可以看出，稳态蠕变的变形量随蠕变时间的延长呈线性增加。由于煤样内部缺陷较其他岩样相比复杂，在恒载的不断延长下，微裂纹更容易沿内部缺陷扩展，导致稳态蠕变下变形量稳定增长，这也必然将对下一步周期载荷下煤样变形破坏产生叠效应加。
3. 煤岩蠕变损伤与周期循环载荷组合劣化特征
3.1 损伤煤岩周期应力−应变演化特征
受开采扰动次数的增加，煤岩体的承载性能在一定程度上降低，为更加全面地考虑真实煤岩循环受力状态，需要在低应力水平内将N1适当扩大，而在高应力水平内将N3适当缩小。假设周期循环加卸载煤样处于弹性变形，则每一级循环载荷作用下煤样积聚弹性能可采用应力−应变曲线包络面积表示，因此，将N1、N2、N3的循环次数按比例分别设定为20、10、5次。
3.1.1 应力应变特征
图6为蠕变损伤煤样在周期载荷作用下各试样应力−应变曲线，括号中为卸压破坏次数。蠕变预损伤煤样在经历周期循环载荷时，不同程度预损伤煤样其强度有明显的不同，且随着蠕变时长的增加，三轴压缩循环峰值应力与循环载荷总次数均呈现减小的趋势。
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图 6 不同蠕变时长试样应力−应变曲线Figure 6. Stress-strain curves of coal samples under different creep time从图6可以看出，煤样在0.2σ′～0.4σ′区间内变形量基本保持不变，应变速率较小，具有较相似的特征；在0.4σ′～0.6σ′区间内，蠕变时长增加到16 h时，环向变形开始增加，滞回曲线分布逐渐稀疏，应力滞回面积逐渐增大。对于蠕变时长达到24 h的煤样，超过8次循环后的变形量急剧增加，表明适当的循环载荷可以促进材料损伤的闭合，并提高其蠕变稳定性，当循环次数超过一定限度时，会导致新的损伤发展，并改变材料的损伤特性。表2为不同蠕变时长下各应力区间内循环次数及破坏情况的统计情况，未经蠕变与蠕变8 h的试样可进行完整的分级加卸载，并且可进行卸围压特性试验研究。在蠕变16 h时，煤样刚进入0.6σ′～0.8σ′区间便开始出现特大变形，仅维持4次加卸载循环便发生疲劳破坏；当蠕变达到24 h后，即便在0.2σ′～0.4σ′区间内，试样承受循环加卸载次数小于20次，并且可看到循环峰值应力始终在不断减小。蠕变造成的多梯度损伤对煤样的劣化作用较为明显，蠕变造成的长时损伤越大，试样的承载能力下降越多。
表 2 煤样不同蠕变时长下各应力区间内循环次数与破坏情况Table 2. Cycle times and failure of coal samples in different stress range under different creep time蠕变时长/h 循环次数 是否卸围压破坏 0.2σ′～0.4σ′ 0.4σ′～0.6σ′ 0.6σ′～0.8σ′ 0 20 10 5 是 8 20 10 5 是 16 20 10 4（破坏） 24 20（破坏） 3.1.2 卸压应力应变特性
煤岩冲击灾害实质是周围应力的卸载[27]，将不同蠕变时间各试样的部分应力水平曲线进行放大，在图7a—图7b中，红色圆圈所示为周期载荷次数达到5次后第1次围压卸载点，随着围压限制的减小，试样环向变形逐渐扩大，变形速率迅速增加；在轴向变形过程中，试样的应力−应变曲线与前几次的曲线几乎重合，变形量甚微，当围压卸除后试样仍未失稳。围压再次加载至6 MPa，进行图中绿色圆圈所示的第2次围压卸载，在围压加载期间，轴向变形出现回弹现象，与第1次卸载围压不同，环向应力−应变曲线与前5次恒围压时的应力−应变曲线近似平行，环向变形量很小，而轴向应力−应变曲线开始出现明显的偏移现象。表明试样的“损伤记忆”不仅表现在轴向变形方面，环向变形同样有这种现象，并且从本试验的现象来看，试样失稳破坏的前兆信息与轴向方向的变形有很大关系。
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图 7 不同蠕变时间下不同应力水平试样循环应力−应变曲线Figure 7. Cyclic stress-strain curves in different stress range under different creep time在图7c—图7d中，破坏时的应力达到30.91 MPa，围压开始卸载后（红色圆圈所示），环向变形与未进行蠕变的试样有较相似的特征，试样整体仍表现出一定的脆性特征，破坏后的塑性变形在同一应力下迅速扩展；当蠕变为16 h时，进行到第二水平应力阶段后，试样的滞回曲线开始呈现“疏—密—疏”的变化趋势，如图7e—图7f所示；在蠕变24 h后，除前6个循环变形量较小外，总环向变形仅为0.029×10−2，其他循环次数下变形量较高，在随后的3个循环下就达到了0.381×10−2。随着蠕变造成的损伤增加，煤样在破坏前的几个循环次数内变形增量随之迅速增加，蠕变造成的损伤程度越高，损伤变形增量越明显。
蠕变时间越久，对试件的长时损伤越明显，在循环加卸载阶段的压密压紧效果越差，试件的强度劣化速度呈倍数增加。结合试样变形特征可知，随着蠕变时长造成的损伤增加，试样在失稳后的破裂程度剧烈，磨损产生的煤屑显著增多，塑性逐渐增强，破裂模式显现出脆性破坏向塑性破坏过渡的趋势。
3.2 蠕变损伤与周期循环载荷组合劣化特征
变形模量作为衡量岩石压缩变形能力的重要指标，能较真实的反映岩石的变形特性[28-30]。不同蠕变时长煤样试样各级等幅循环荷载下加载变形模量、卸载变形模量随循环次数变化如图8所示。经不同蠕变时长作用后，煤样的加卸载变形模量变化趋势随着蠕变时长的增加，逐渐由平稳转向波动，整体变化趋势有较好的一致性。
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图 8 煤样加、卸载变形模量与循环次数关系Figure 8. Relation curves between loading and unloading deformation modulus and cycle number of coal samples当对试样进行蠕变预处理时，选取某个蠕变时长阈值去判定蠕变起到强化作用还是劣化作用。
1）当蠕变时长小于此阈值时，蠕变应力的施加处于弹性阶段内，岩样内部微裂隙逐步闭合，裂隙面咬合作用加强；当蠕变应力卸载后，微裂隙数量减少，抵抗变形的能力有所提高，因此会起到强化作用，如蠕变8 h试样。
2）当蠕变时长大于此阈值时，蠕变应力的长时施加会使得岩样提前进入裂隙稳定扩展阶段，小尺度裂隙增生，裂隙密度增加，当蠕变停止后裂隙扩展也随之停止，因此低应力区间内劣化作用相对不明显，只有在0.6σ′～0.8σ′高应力区间内劣化作用才得到显著呈现，如蠕变16 h试样。
3）随着蠕变时长的继续增加，小尺度裂隙开始扩展贯通成大尺度裂隙，导致煤样内部承载结构沿裂隙出现滑移现象，因而煤样即使在低应力区间内进行加卸载循环也无法抵抗较大的变形，如蠕变24 h试样。
随着加卸载应力区间的增大，试样的加卸载变形模量均会在每个循环区间的初次循环出现数值突变，主要原因在于应力上限值的增加会使应变迅速增加，而同一应力区间内其他循环的加卸载变形模量则是一个平稳变化的趋势。每个应力区间内加载变形模量的变化趋势主要呈先增加而后缓慢降低，反映在循环应力曲线上则表现为“疏—密—疏”的变化趋势，而卸载变形模量则表现为先降低而后缓慢增加的变化趋势，但总体增加幅度较小。当加载至最后几个循环时，除卸围压破坏试样外，加卸载变形模量均出现剧烈波动现象，并随着蠕变时长的增加，这种现象愈加明显，主要是由于蠕变损伤造成煤样的稳定性越来越差，循环加卸载导致试样损伤速率增快，塑性变形迅速累积，因此加卸载变形模量的突然下降或上升，预示着煤样处于即将失稳破坏的“临界点”。
4. 周期载荷下煤岩蠕变预损伤能量演化机制
4.1 蠕变与循环载荷损伤演化模型
损伤力学认为，试件由完整到破坏的加载过程中，所有可测并且随加载过程单调变化的状态量都可对试件损伤演化进行度量，例如弹性模量、累计应变与耗散能等参量[31-33]。
1）蠕变损伤演化模型。在蠕变损伤方面，应变型损伤模型中普遍得到认可的是基于延性耗竭理论的蠕变损伤模型。可用式（1）计算蠕变损伤[34]：
$$ {D_{\text{c}}} = \int_0^{{t_{_0}}} {\frac{{\dot \varepsilon }}{{{\varepsilon _{\text{f}}}\left( \varepsilon \right)}}} {\mathrm{d}}{{t}} $$ (1) 式中：$ {D_{\text{c}}} $为蠕变损伤；$ \dot \varepsilon $为应变速率，s−1；$ {\varepsilon _{\text{f}}}\left( \varepsilon \right) $为与应变相关的断裂延性；$ {t_0} $为保载时间，h。
而应力型损伤模型中应用较为广泛的主要为基于Burgers模型的改进Kachanov损伤模型，Kachanov提出的蠕变损伤演变方程为
$$ {D_{\text{c}}} = {\left[ {\frac{\sigma }{{A\left( {1 - D} \right)}}} \right]^{{r}}} $$ (2) 式中：$ A $和$ {{r}} $为模型参数，和材料有关，即$ \sigma = {\sigma _0} $时，蠕变损伤变化规律为
$$ {D_{\text{c}}} = 1 - {\left( {1 - \frac{t}{{{t_{\text{c}}}}}} \right)^{\tfrac{{\text{1}}}{{{{1 + r}}}}}} $$ (3) 式中：$ {t_{\text{c}}} $为试样破坏的蠕变总时长，h。
2）循环载荷下煤岩损伤演化模型。在循环载荷损伤方面，如果将损伤发展认为是每个循环后造成的不可逆塑性变形的累积，则可得到岩石损伤演化方程[35-36]为
$$ {D_{\text{f}}} = 1 - {\left[ {1 - {{\left( {\frac{N}{{{N_{\text{f}}}}}} \right)}^{\tfrac{1}{{1 - {{\alpha }}}}}}} \right]^{\tfrac{1}{{1 + {{\beta }}}}}} $$ (4) 式中：$ N $为循环数；$ {N_{\text{f}}} $为试样破坏总循环数；α和β为与材料有关的常数。
但由于上述模型相关参数的确定相对复杂，因此基于热力学理论的能量法损伤演化成为近年来学者研究的热点。将总输入能分为弹性能和耗散能，随着加载的进行，弹性能储存在试样内部并使结构发生一定变形但并不造成破坏，而耗散能则主要对试样的不可逆变形做功[37]，即：
$$ U = {U_{\text{e}}} + {U_{\text{d}}} $$ (5) 式中：U为总输入能，J；Ue为弹性能，J；Ud为耗散能，J。
在能量法损伤演化模型中，同样可应用D=0和D=1的边界条件，因此，利用试样的荷载逐级增加应力−应变曲线可计算得到任一循环下各能量数值，即：
$$ {U_{{i}}} = \int_{{\varepsilon _{{{i - }}1}}}^{{\varepsilon _{{{{\mathrm{a}}i}}}}} {{\sigma _{{i}}}{\mathrm{d}}\varepsilon } $$ (6) $$ {U_{{{i{\mathrm{e}}}}}} = \int_{{\varepsilon _{{i}}}}^{{\varepsilon _{{{{\mathrm{a}}i}}}}} {{{\sigma '}_{{i}}}{\mathrm{d}}\varepsilon } $$ (7) $$ {U_{i{\text{d}}}} = \int_{{\varepsilon _{{{i}} - 1}}}^{{\varepsilon _{{\mathrm{a}}i}}} {{\sigma _i}{\mathrm{d}}\varepsilon } - \int_{{\varepsilon _{{i}}}}^{{\varepsilon _{{{{\mathrm{a}}i}}}}} {{{\sigma '}_{{i}}}{\mathrm{d}}\varepsilon } $$ (8) 则循环加卸载至某一循环时的损伤变量可表示为
$$ {D_{\text{f}}} = \sum\limits_{i = 1}^{{N_{\text{f}}}} {{{{U_{{{i{\mathrm{d}}}}}}} \mathord{\left/ {\vphantom {{{U_{{\text{id}}}}} {{U_{\text{d}}}}}} \right. } {{U_{\text{d}}}}}} $$ (9) 式中：$ {U_{{i}}} $为第$ i $个循环岩石输入能，J；$ {U_{{{i}}{\mathrm{e}}}} $为第$ i $个循环岩石释放的弹性能，J；$ {U_{{{i{\mathrm{d}}}}}} $为第$ i $个循环岩石耗散能，J/m3；$ {\varepsilon _{{{{\mathrm{a}}i}}}} $为第i个循环峰值点应变；$ {\varepsilon _{{i}}} $为初始加载点应变；$ {\varepsilon _{{{i - 1}}}} $为卸载结束点应变；$ {\sigma _{{i}}} $和$ {\sigma '_{{i}}} $分别为第i个循环加载和卸载峰值应力，两者值相等；$ {U_{\text{d}}} $为岩石总耗散能，J/m3。
4.2 蠕变与循环载荷叠加作用损伤演化特征
蠕变与循环载荷损伤破坏在现实工程实际中并非单独作用，在长时蠕变遗留煤柱回采等特定工况下，考虑二者的叠加作用是建立一个准确损伤演化模型的前提。煤岩在蠕变试验中产生了瞬时应变和蠕变应变，而在蠕变应力卸除后，瞬时应变与蠕变应变中均会有部分可逆应变回弹，这将与上述未进行卸载的蠕变应变型或应力型损伤模型产生一定误差，因此，在叠加含蠕变损伤的加卸载循环试验中应引入折减系数考虑此可逆应变对试验带来的影响，含蠕变损伤的加卸载循环试验叠加的损伤演化模型可表示为
$$ {D_{{\text{total}}}} = {\varphi _{\text{c}}}{D_{\text{c}}} + {D_{\text{f}}} $$ (10) 式中：$ {\varphi _{\text{c}}} $为考虑可逆应变折减系数；$ {D_{\text{c}}} $为蠕变损伤演化模型；$ {D_{\text{f}}} $为循环载荷损伤演化模型。
在0、8 h蠕变过程中，由于煤样所产生的蠕变损伤处于较低水平，在达到预定的循环次数后，煤样需在卸围压的条件下发生破坏，该情况下叠加计算蠕变损伤与循环损伤的耗散能时会产生一定影响。为消除外部卸荷条件的影响，该部分只对未卸荷时的煤样耗散能进行叠加计算。
表3列出了在蠕变16 h和24 h条件下，各煤样的蠕变和循环耗散能、损伤变量及可逆增大系数值。当蠕变时长为16 h时，煤样蠕变耗散能平均值为16.58 J/m3，蠕变损伤变量平均值为0.23，循环耗散能平均值为71.23 J/m3，循环损伤变量平均值为0.69；当蠕变时长为24 h时，煤样蠕变耗散能平均值为28.28 J/m3，蠕变损伤变量平均值为0.39，循环耗散能平均值为53.08 J/m3，循环损伤变量平均值为0.52。上述数据表明，煤样的蠕变损伤变量由16 h时的0.23增加到24 h时的0.39，而循环损伤变量则从16 h时的0.69降低到24 h时的0.52，即蠕变损伤的增加会在一定程度上导致循环损伤变量降低。
表 3 不同蠕变时长下煤样蠕变与循环加载耗散能、损伤变量及可逆增大系数值Table 3. Dissipative energy, damage variable and reversible increase coefficient of creep and cyclic loading of coal samples under different creep durations蠕变
时间/h试件
编号蠕变耗
散能/
（J·m−3）蠕变耗散能
平均值/
（J·m−3）蠕变损伤
变量Dc蠕变损伤
变量Dc
平均值循环耗
散能/
（J·m−3）循环耗散能
平均值/
（J·m−3）蠕变损伤
变量Dc蠕变损伤
变量Dc
平均值可逆应变
增大系数$ {\varphi _{\mathrm{c}}} $可逆应变
增大系数$ {\varphi _{\mathrm{c}}} $平均值16 M16-1 15.36 16.58 0.21 0.23 70.88 71.23 0.69 0.69 1.48 1.36 M16-2 18.29 0.25 69.86 0.68 1.28 M16-3 16.09 0.22 72.94 0.71 1.32 24 M24-1 29.99 28.28 0.41 0.39 52.39 53.08 0.51 0.52 1.20 1.25 M24-2 26.33 0.36 56.50 0.55 1.25 M24-3 28.53 0.39 50.34 0.49 1.31 采用能量的方法统一量化蠕变与循环损伤并忽略可逆应变影响，总损伤变量值经数值叠加计算后始终低于1，精确度不高。按照式（11）拟合计算，得到平均可逆应变增大系数1.31。因此，得到考虑蠕变损伤的加卸载循环试验损伤演化模型为
$$ 1.31{D_{\text{c}}} + {D_{\text{f}}} = 1 $$ (11) 确定蠕变损伤值后，可利用上述蠕变损 伤与循环损伤演化模型计算理论循环损伤，即预测循环耗散能。以20 h蠕变为例，根据图5中稳态蠕变变形量拟合方程，得到稳态蠕变变形量为0.189×10−3，相应的蠕变耗散能为23.74 J/m3，蠕变损伤变量为0.32。代入式（11）可得$ {D_{\text{f}}} $为0.58，则剩余的循环耗散能为59.58 J/m3，介于16～24 h，符合计算要求。
4.3 不同初始损伤煤岩分段能量损伤演化特征
根据式（6）—式（9），将试样各区间加卸载循环输入能、弹性能和耗散能分析整理，绘制成如图9所示各能量密度随循环次数变化的关系曲线。
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图 9 不同蠕变时长煤样能量密度与循环次数关系Figure 9. Relation curves between energy density and cycle number of coal samples under different creep time由图9a观察可得，当试样处于较低应力区间时，输入能主要以弹性能的方式储存在试样中，此区间内试样并未有较大程度的损伤，因此耗散能始终维持在一个相对稳定的数值；随着应力区间不断上升，输入能和弹性能有一定程度的增加，但耗散能仍保持在较稳定的数值，表明试样还有一定的储能空间，储能能力并未达到极限。因蠕变损伤的存在，即使在低应力区间弹性能呈线性增加，但当增至较高的应力区间后，试样储能能力有所减弱，耗散能开始增高，随后又保持较为稳定的状态，如图9b红色圆圈所示，表明试样内已经出现部分损伤，但仍不足以达到完全损伤阶段，可见试样耗散能大小与蠕变损伤密切相关。
与其他瞬时应力造成的即时损伤不同，长时蠕变损伤属于缓慢“侵蚀”型损伤，并且有一定
的时滞性，因此在进行加卸载循环破坏时表现出一定的差异性。在图9c—图9d中，当试样加载至高应力区间后，耗散能急剧攀升并超过储存的弹性能，弹性能有所降低，试样已经处于一个非稳定阶段，强度接近峰值，抗疲劳能力明显下降，塑性变形特征明显。同样，在蠕变24 h的试样中，进行完整的前8个循环后，耗散能也开始迅速增加，但增加速度明显低于蠕变16 h试样，塑性变形特征更加明显。
总结可知，当试件未进行蠕变损伤或蠕变损伤较小时，试样能量密度能保持在一个较为稳定状态，此时输入能主要以弹性能储存，能量释放量较小；当蠕变损伤较小的试样在高应力区间进行循环加卸载试验时，耗散能开始缓慢增加，弹性能处于弱化阶段，试样仍具有较强的冲击性。当蠕变时长进一步增大至16 h，随着循环加卸载的进行，耗散能密度在进入高应力区间后迅速超过弹性能密度，试样在破坏前能量释放较为迅速；当蠕变时长达到24 h后，试样的冲击性能减弱明显，耗散能呈阶梯状缓慢增加。
5. 结 论
1）煤岩体的蠕变预损伤仅表现出瞬态蠕变和稳态蠕变特征，稳态蠕变阶段的声发射振铃计数曲线较少出现短时聚集突升现象，声发射振铃计数较低，未出现较大裂隙损伤，稳态蠕变阶段的变形量随蠕变时间的延长呈线性增加。
2）煤样在循环载荷低应力区间内受蠕变预损伤效应影响较小，变形量基本保持不变，随着应力水平区间的上升，因蠕变时长造成的预损伤对煤样的劣化损伤发展影响较明显，蠕变造成的长时损伤越大，试样的承载能力下降越多，煤岩非线性劣化越明显，塑性流动现象越显著，破裂模式显现出脆性破坏向塑性破坏过渡的趋势。
3）煤岩体的环向变形普遍高于轴向变形，分析加卸载变形模量发现存在蠕变时长阈值，此阈值一般不超过16 h；循环加卸载后期，加卸载变形模量剧烈波动，不可逆形变稳定增加，预示煤样处于即将失稳破坏的“临界点”，可作为煤样破坏之前的前兆信息。
4）蠕变损伤时长对试样卸围压特性有强敏感性，未经蠕变损伤的煤样在卸围压时应力释放十分迅速，突变失稳现象明显，而蠕变损伤后的煤样因在蠕变阶段已有所劣化，储存的能量较少，因此应力释放有所缓和；煤样储能能力的大小在蠕变损伤时长方面同样存在阈值，较长的蠕变损伤时长可使试样存储的可释放弹性能减小，延缓了弹性能的释放，减小了发生冲击动力灾害破坏的范围。
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图 1 中国煤中钪的平面分布
Figure 1. Lateral distribution of scandium in different coalfields of China
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图 2 煤层剖面钪的含量变化
Figure 2. Vertical variation of scandium concentrations in bench samples of a coal seam profile
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图 3 中国不同成煤时代煤中钪的含量变化
Figure 3. Variation of scandium concentrations in Chinese coals of different coal-forming periods
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图 4 部分煤中钪与灰分的相关性
Figure 4. Correlation between scandium concentrations and ash yields in different coals
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图 5 重庆东林矿4煤层煤中钪与灰分的相关性
Figure 5. Correlation between scandium content and ash yield of the No. 4 coals from Donglin Mine in Chongqing
表 1 中国煤中钪的测试数据信息
Table 1 Information on the reported scandium data of Chinese coals
聚煤区 样本数 煤阶 Sc含量范围/(mg·kg−1) 成煤时代 测试方法 赋存状态 东北聚煤区 126 褐煤、烟煤 0.2～27.9 / 5.93 晚石炭–早二叠世(42) 较新数据以ICP-MS为主，2010年前部分采用INAA和ICP-OES 兼具有机和无机亲和性，以无机亲和性为主，赋存于黏土矿物等铝硅酸盐矿物中 早–中侏罗世(29) 晚侏罗–早白垩世(47) 古近纪–新近纪(8) 西北聚煤区 194 褐煤、烟煤 <0.2～21.1 / 2.92 早–中侏罗世(194) 华北聚煤区 1185 褐煤、烟煤、无烟煤 bdl～76.2 / 7.17 晚石炭–早二叠世(977) 晚二叠世(114) 早–中侏罗世(56) 古近纪–新近纪(8) 滇藏聚煤区 60 褐煤 0.86～14.2 / 5.45 古近纪–新近纪(60) 华南聚煤区 648 烟煤、无烟煤 bdl～139 / 7.61 晚石炭–早二叠世(15) 晚二叠世(546) 晚三叠世(46) 古近纪–新近纪(9) 注：bdl表示低于检测限；含量范围数据格式为（最小值～最大值）/均值。 
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表 2 安徽淮南、重庆南桐、四川宝鼎和云南勐托采样信息
Table 2 Samples collected from tthe Huainan, Nantong, Baoding, and Mengtuo basins in Anhui, Chongqing, Sichuan, and Yunnan, respectively
采样地点 煤层 成煤时代 样品编号 岩性 采样方法 安徽淮南 4-2 中二叠世 PE-4-2、PS-4-2、ZJ-4-2、XQ-4-2、GQ-4-2、XZZ-4-2、DJ-4-2 煤 钻孔取心 重庆南桐 4 晚二叠世 DL-4-0 顶板岩石 井下刻槽 DL-4-1～17 煤 6 晚二叠世 DL-6-1 顶板岩石 DL-6-2～10 煤 DL-6-11 底板岩石 四川攀枝花 18 晚三叠世 TP-18-1 顶板岩石 井下刻槽 TP-18-2、3、6～14、16 煤 TP-18-4、5、15、17 夹矸岩石 TP-18-18 底板岩石 24 晚三叠世 TP-24-1 顶板岩石 TP-24-2、3、7、9、13、19、20、23～26 煤 TP-24-4～6、8、10～12、14～18、21、22 夹矸岩石 TP-24-27 底板岩石 云南勐托 — 中新世 Mt-1、3～6、8～10 褐煤 井口煤堆 Mt-2、7、11 碳质泥岩
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表 5 四川太平矿18煤和重庆东林矿6煤剖面分层样品的灰分和钪含量
Table 5 Ash yields and scandium concentrations of bench samples from the No. 18 coals of Taiping Mine in Sichuan and the No. 6 coals of Donglin Mine in Chongqing
样品编号 Aad/% Sc含量/ (mg·kg−1) 样品编号 Aad/% Sc含量/ (mg·kg−1) TP-18-1 85.46 13.4 TP-18-16 48.07 11.9 TP-18-2 6.64 0.73 TP-18-17 74.50 17.4 TP-18-3 2.24 1.91 TP-18-18 91.55 20.2 TP-18-4 71.52 16.6 DL-6-1 78.51 23.9 TP-18-5 86.19 15.1 DL-6-2 49.33 16.1 TP-18-6 7.38 1.18 DL-6-3 13.81 10.3 TP-18-7 31.77 9.94 DL-6-4 7.78 5.07 TP-18-8 41.87 11.8 DL-6-5 8.59 5.41 TP-18-9 49.33 13.1 DL-6-6 13.31 7.57 TP-18-10 5.36 0.39 DL-6-7 8.62 3.29 TP-18-11 3.41 bdl DL-6-8 9.72 4.31 TP-18-12 6.28 0.90 DL-6-9 14.60 4.61 TP-18-13 12.24 2.96 DL-6-10 55.66 4.20 TP-18-14 10.99 2.40 DL-6-11 70.45 14.0 TP-18-15 65.21 7.86
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表 6 部分煤中钪与主量元素氧化物的相关系数
Table 6 Correlation coefficients between scandium and major element oxides in different coals
主量元素 相关系数 SiO2 TiO2 Al2O3 Fe2O3 MgO CaO MnO Na2O K2O P2O5 重庆东林矿6煤 0.267 0.553 0.048 0.863 0.691 0.943 0.859 0.781 0.642 0.881 四川太平矿18煤 0.748 0.267 0.693 −0.627 −0.754 −0.808 −0.775 −0.289 0.932 −0.512 四川太平矿24煤 0.662 −0.612 −0.203 −0.738 −0.304 −0.582 0.313 −0.855 0.837 −0.030 云南勐托褐煤 0.750 0.777 0.727 0.757 0.844 −0.736 −0.702 0.769 0.787 0.445
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表 7 四川太平矿24煤和云南勐托褐煤的w(Al2O3)/w(TiO2)及钪含量
Table 7 w(Al2O3)/w(TiO2) and scandium concentrations of the No. 24 coals of Taiping Mine, Sichuan and the Mengtuo lignite of Yunnan
煤矿(层) 样品编号 w(Al2O3) w(TiO2) w(Al2O3)/
w(TiO2)Sc含量/
(mg·kg−1)w(Al2O3)/w(TiO2)与Sc相关系数 四川太平矿24煤 TP-24-2 21.30 2.33 9.14 7.01
−0.545TP-24-3 25.33 1.46 17.4 9.65 TP-24-7 24.11 1.23 19.6 13.9 TP-24-9 24.84 1.22 20.4 13.9 TP-24-13 23.98 1.35 17.8 11.2 TP-24-19 28.78 1.72 16.7 7.99 TP-24-20 25.05 2.10 11.9 2.20 TP-24-23 24.43 1.30 18.8 7.30 TP-24-24 25.12 1.37 18.3 10.4 TP-24-25 24.41 1.43 17.1 11.0 TP-24-26 26.35 1.53 17.2 1.48 云南勐托
褐煤Mt-1 1.95 0.05 39.0 3.31 Mt-3 2.04 0.05 40.8 1.98 Mt-4 5.26 0.09 58.4 3.45 Mt-5 5.16 0.15 34.4 5.77 Mt-6 1.82 0.05 36.4 1.82 Mt-8 10.25 0.30 34.2 5.45 Mt-9 1.88 0.04 47.0 1.41 Mt-10 9.26 0.22 42.1 3.79
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表 8 安徽淮南4-2煤、重庆东林矿4煤和四川太平矿18煤层煤的w(Sr)/w(Ba)与钪含量
Table 8 w(Sr)/w(Ba) and scandium concentrations of the Nos. 4-2, 4, and 18 coals from Anhui, Chongqing, and Sichuan, respectively
煤层 样品编号 Sr含量/
(mg·kg−1)Ba含量/
(mg·kg−1)w(Sr)/
w(Ba)Sc含量/
(mg·kg−1)w(Sr)/
w(Ba)与Sc
的相关系数安徽淮南
4-2煤PE-4-2 244 146 1.67 8.18 0.079 PS-4-2 71.0 72.1 0.98 5.76 ZJ-4-2 116 70.4 1.65 15.6 XQ-4-2 86.4 340 0.25 6.87 GQ-4-2 278 165 1.68 5.04 XZZ-4-2 148 163 0.90 7.66 DJ-4-2 155 52.5 2.95 6.63 重庆东
林矿4煤DL-4-1 273 30.3 9.01 4.94 −0.428 DL-4-2 636 1539 0.41 6.38 DL-4-3 166 15.2 10.9 5.13 DL-4-4 484 23.3 20.8 4.27 DL-4-5 154 16.2 9.51 6.53 DL-4-6 149 14.2 10.5 7.24 DL-4-7 126 11.1 11.4 4.94 DL-4-8 157 14.4 10.9 5.19 DL-4-9 181 9.12 19.8 6.21 DL-4-10 168 7.68 21.9 5.94 DL-4-11 208 832 0.25 8.56 DL-4-12 168 6.99 24.0 5.53 DL-4-13 180 5.12 35.2 3.58 DL-4-14 148 10.0 14.8 5.00 DL-4-15 195 5.19 37.6 6.50 DL-4-16 179 8.72 20.5 5.97 DL-4-17 166 12.0 13.8 7.01 四川太平
矿18煤TP-18-2 52.8 613 0.85 0.73 −0.784 TP-18-3 70.5 196 0.36 1.91 TP-18-6 64.0 135 0.47 1.18 TP-18-7 111 343 0.32 9.94 TP-18-8 113 482 0.23 11.8 TP-18-9 127 552 0.23 13.1 TP-18-10 86.6 69.4 1.25 0.39 TP-18-11 79.2 76.3 1.04 bdl TP-18-12 74.3 97.6 0.76 0.90 TP-18-13 130 2088 0.63 2.96 TP-18-14 101 162 0.62 2.40 TP-18-16 102 432 0.24 11.9
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表 9 重庆东林矿6煤层煤中稀土元素的含量及与钪的相关系数
Table 9 Rare earth elements and its correlation coefficients with Sc in the No. 6 coals of Donglin Mine, Chongqing
稀土元素 含量/（mg·kg−1） 与钪相关系数 La (5.86～43.9)/ 21.6 0.33 Ce (12.1～103)/ 45.0 0.45 Pr (1.58～11.9)/ 5.15 0.48 Nd (12～50.5)/ 20.2 0.57 Sm (2.11～10.6)/ 4.22 0.64 Eu (0.34～1.98)/ 0.60 0.88 Gd (2.8～10.3)/ 4.60 0.62 Tb (0.39～1.3)/ 0.68 0.55 Dy (2.4～6.82)/ 4.13 0.44 Y (12.7～36.1)/ 21.3 0.2 Ho (0.47～1.39)/ 0.82 0.35 Er (1.35～4.04)/ 2.44 0.37 Tm (0.17～0.54)/ 0.33 0.41 Yb (1.2～3.63)/ 2.3 0.44 Lu (0.17～0.52)/ 0.33 0.50 注：数据格式为（最小值～最大值）/平均值。
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表 10 重庆东林矿6煤层顶底板岩石中微量元素的含量
Table 10 Concentrations of trace elements in roof and floor rocks of the No. 6 coals of Donglin Mine, Chongqing
微量元素 含量/(mg·kg−1) DL-6-1 DL-6-11 Li 118 317 Be 3.04 3.83 B 68.1 44.8 F 3408 1688 Sc 23.9 14.0 V 397 135 Cr 248 126 Co 58.3 12.9 Ni 102 89.7 Cu 214 58.8 Zn 154 72.8 Ga 34.9 77.6 Ge 2.38 8.12 As 24.3 6.95 Se 5.25 4.88 Rb 6.92 8.09 Sr 388 213 Zr 568 1535 Nb 81.2 271 Mo 2.83 2.93 Ag 3.57 9.44 Cd 1.48 3.26 In 0.180 0.289 Sn 5.31 16.2 Sb 0.49 1.32 Cs 1.44 2.05 Ba 38.6 36.4 Ba 38.6 36.4 Hf 12.3 26.9 Ta 4.56 18.6 W 2.49 3.81 Hg 0.532 0.182 Tl 0.093 0.045 Pb 14.4 21.3 Bi 0.22 0.58 Th 10.1 37.6 U 5.29 8.83
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