Main Mechanism and Influencing Factors of Earthquakes Induced by Hydraulic Fracturing for Shale Gas Exploitation
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摘要: 随着水力压裂技术的发展与应用，各地区页岩气开采区的地震活动显著增强，且中等以上地震明显增多，严重影响工业和人类活动，为确保安全、绿色的页岩气开采，避免或减少破坏性地震活动，研究诱发地震机理和影响因素具有重要意义。为此总结美国、加拿大和我国典型页岩气开采区地震活动特征，并结合断层力学与莫尔-库仑破坏准则，较为系统地分析了目前对水力压裂技术诱发地震机制的主要认识，以及诱发地震的影响因素。研究结果表明，基于莫尔-库仑准则可以在宏观上解释注入式诱发地震活动，断层面摩擦系数、正应力、剪切应力和孔隙压力的变化都可能影响诱发地震活动的发生；在断层与诱发地震相对关系方面，地震活动有3种诱发机制，包括孔隙压力作用下的断层活化、孔隙弹性效应导致的断层活化、无震滑动引起的断层活化；诱发地震活动不仅与流体注入参数有关，还取决于区域断层孕震情况和应力状态等条件。目前由于影响水力压裂作用下断层剪切破裂起始及扩展的因素尚不完整，同时也缺乏有力的试验验证，有必要开展水力压裂试验工作，模拟页岩气开采过程中流体加载和应力边界等条件，进一步确定断层剪切破裂的驱动机制和关键影响因素。Abstract: With the development and application of hydraulic fracturing technology, the seismic activity in shale gas mining areas in various regions has obviously increased especially those above moderate level, seriously affecting industrial and human activities. In order to ensure safe and green shale gas exploitation and avoid or reduce destructive seismic activity, it is of great significance to study the mechanism and influencing factors of hydraulic fracturing induced earthquakes. By summarizing the seismic activity characteristics of typical shale gas mining areas in the United States, Canada and China, and combining fault mechanics and Coulomb-Mohr failure criteria, this paper systematically sorts out the main mechanisms and the influencing factors of hydraulic fracturing induced earthquakes. The conclusion and analysis show that injection-induced seismicity can be explained macroscopically based on Coulomb-Mohr criterion, and the changes of friction coefficient of a fault, normal stress,shear stress and pore pressure in reservoir area can affect the occurrence of induced seismicity. From the relative relationship between faults and induced earthquakes, there are three possible mechanisms: the first is the fault activation caused by pore pressure change, the second is the fault activation caused by pore elasticity effect, and the third is the fault activation caused by aseismic slip. Induced seismicity is not only related to fluid injection parameters, but also depends on conditions such as seismogenic background and stress state of regional faults. At present, due to the incomplete factors affecting the initiation and propagation of fault shear fracture under hydraulic fracturing, and the lack of strong experimental verification, it is necessary to carry out hydraulic fracturing experiments to simulate the conditions such as fluid loading and stress boundary during shale gas production, and further determine the driving mechanism and key influencing factors of fault shear fracture.
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引言
悬索桥结构主要由锚碇、索塔、缆索系统、加劲梁和附属结构组成，具有结构简单、轻便、易于标准化、构件易运输、方便悬吊拼装、施工限制较少等特点（铁道部大桥工程局桥梁科学研究所，1996；钱炜，2007），是特大桥梁的主要类型（李光军，2012）。地震是造成桥梁结构破坏的主要原因之一，桥梁是联系外界与地震灾区的重要纽带，桥梁一旦破坏，将中断通往灾区的通道，影响救灾工作进展，造成较大损失（刘润舟，2008）。因此，对悬索桥结构进行地震响应分析具有重要意义。国内外学者已开展了大跨度桥梁多点激励地震响应研究，如许基厚等（2019）对非对称单侧混合梁斜拉桥多点激励地震响应进行研究，分析了行波效应对塔顶、主梁、塔底等关键位置动力响应的影响，并研究了不同入射角对桥梁动力响应的影响，认为多点激励下主塔内力计算结果偏小，而主梁内力计算结果偏大，地震激励对非对称大跨度斜拉桥内力产生较大影响，内力变化可达20%；张凡等（2016）对不同波速下斜拉桥地震响应进行了分析，认为波速的影响显著；王再荣等（2016）分析行波效应下斜拉桥地震响应，得出辅助墩耗能降低、桥塔损伤增大的结论；刘旭政等（2018）考虑2种地震波和3种视波速的不同组合，以一座实际工程高桩大跨度连续刚构桥为例，研究行波效应对桥梁地震响应的影响，认为随着视波速的增大，行波效应对桥梁内力的影响程度减小；梅泽洪等（2017）研究了考虑局部场地效应桥梁结构在非一致激励下地震响应的特点，认为下部结构响应所受影响较小，而上部结构所受影响明显，考虑行波效应的非一致激励对桥梁地震响应有减弱效果；黎璟等（2019）以铁路工程实际桥梁为例，研究了非一致激励下大跨度铁路斜拉桥地震响应规律，认为在非一致激励下塔顶位移响应峰值与墩底弯矩响应峰值均随着相位差呈周期性变化，且变化周期与结构一阶自振周期基本一致。
本文选取某三跨两铰连续体系悬索桥，已有研究结果表明线性分析方法和非线性分析方法得到的该桥地震响应结果相近（Fleming等，1980；李丽等，2018a）。因此利用大型通用有限元软件ANSYS建立三维弹性有限元模型，分析一致激励与多点激励下悬索桥地震响应，研究其抗震性能。
1. 桥梁结构动力响应分析方法
桥梁结构动力响应分析方法主要包括一致激励动态时程分析方法及多点激励动态时程分析方法，目前多点激励动态时程分析方法的应用较多，该方法考虑地震行波效应和局部场地效应，对各独立基础或支撑结构输入不同的设计反应谱或加速度时程进行计算（张沧海，2011），主要包括相对运动法和大质量法（范立础等，2001；Leger等，1990）。相对运动法通过支撑点的加速度时程计算非支撑点的动力响应。大质量法是对结构模型进行动力等效的分析方法，在处理多点激励问题时需解除支撑点沿地震作用方向的约束，并赋予节点大质量，其值通常远大于结构体系的总质量（苏成等，2008）。本文采用相对运动法计算悬索桥在多点激励下的响应。
2. 桥梁结构概况
三跨连续悬索桥主跨124m，主梁设计为连续加劲梁，加劲梁采用正交异性板流线形扁平钢箱梁，梁高1.88m，宽（含风嘴）10.8m；纵向分配梁宽0.16m，厚0.28m；纵向斜腹杆，横向内侧竖杆，横向内、外侧斜腹杆截面宽度均为0.16m，厚度均为0.2m；纵向上、下弦杆截面宽度均为0.3m，厚度均为0.2m；纵向竖杆截面宽0.2m，厚0.18m；横向外侧竖杆截面宽0.2m，厚0.24m；横向上弦杆截面宽0.18m，厚0.24m；横向下弦杆截面宽0.18m，厚0.2m；抗风桁架截面宽0.12m，厚0.12m。主塔为H形，塔高36m，南、北桥塔未设置上、下横梁。塔柱截面宽2m，厚4m；柱间连接件截面宽4m，厚2m。桥面以上有3根主缆，南、北边跨吊索各12根，主跨共30根，索间距4m。主缆截面直径为0.079m，吊索截面直径为0.039m。桥梁结构各构件材料物理参数见表 1。
表 1 桥梁结构材料物理参数Table 1. The material physical parameters of bridge structure构件 材料 弹性模量/Pa 泊松比 密度/kg·m-3 主缆 钢丝绳 21.0×1010 0.167 7850 吊索 钢丝绳 21.0×1010 0.167 7850 加劲桁架、纵梁 C30混凝土 3.0×1010 0.300 2500 桥塔、桥面板 C20混凝土 2.8×1010 0.300 2500 3. 输入地震动
选取常用的Kobe地震波对悬索桥进行地震响应分析，顺桥向输入的加速度时程曲线如图 1，加速度峰值为0.345g，持时为24.79s。
图 1 输入Kobe波加速度时程曲线（顺桥向）Figure 1. The input Kobe wave of acceleration time history curve (Along the bridge)对于大跨度悬索桥，输入地震动时常将水平地震系数的1/2或2/3作为竖向地震系数，组合方式通常为顺桥向与竖向组合、横桥向与竖向组合（李国豪，2003），因此，进行一致激励下的地震响应分析时，本文将竖向地震系数取为水平地震系数的1/2，并选取顺桥向与竖向组合；进行多点激励下的地震响应分析时，将竖向地震系数取为水平地震系数的1/2，先对加速度时程曲线进行2次积分，第1次积分得到速度时程曲线，并将其进行基线校正，将校正后的速度时程曲线再次积分并进行基线校正，得到位移时程曲线，如图 2。
图 2 Kobe波位移时程曲线（顺桥向）Figure 2. The input Kobe wave of displacement time history curve (Along the bridge)多点激励位移输入位置为图 3中①-④桥梁支座位置，计算时考虑不同支座输入波形相位滞后现象，采用对不同支座延迟输入位移时程的方法考虑行波效应（刘春城等，2004；王蕾等，2006；严琨等，2017），根据大跨建筑结构多点输入地震响应计算结果（李丽等，2018b；景鹏旭等，2017）与抗震设计方法研究结果（江洋，2010），取视波速为1000m/s，根据支座间距计算各支座位移输入延迟时间，见表 2。
图 3 桥梁结构立面图及荷载激励点布置Figure 3. The elevation and load excitation point layout of the bridge表 2 输入位移时程延迟时间（s）Table 2. The delay time of input displacement time history (s)支座编号 ① ② ③ ④ 时间间隔 0.000 0.050 0.174 0.224 4. 有限元模型的建立
应用大型通用有限元软件ANSYS建立悬索桥三维有限元模型（图 4），应用link10单元模拟主缆及吊索，应用beam4单元模拟加劲桁架、纵向分配梁、抗风桁架、桥塔，应用shell63单元模拟桥面板。主缆及吊索初应变设为0.0043，先对结构进行重力分析，得到结构初始应力，然后对其进行模态分析，计算桥梁结构前2阶振型圆频率，应用APDL语言编制求解瑞利阻尼系数α和β：
ALPHAD, 2*DAMPRATIO*FREQ1*2*3.1415926
BETAD, 2*DAMPRATIO/(FREQ1*2*3.1415926)
5. 地震响应分析结果
计算得到主梁位移及南、北桥塔塔柱沿柱高方向的位移、轴力、剪力及弯矩包络图，如图 5-7。
图 5 主梁顺桥向最大位移包络图Figure 5. Envelope diagram of maximum displacement of main beam along bridge direction
图 6 南桥塔纵向位移、轴力、剪力及弯矩包络图Figure 6. The envelope of displacement, axial force, shearing force and bending moment of the occurrence bridge tower longitudinal
图 7 北桥塔纵向位移、轴力、剪力及弯矩包络图Figure 7. The envelope of displacement, axial force, shearing force and bending moment of the north bridge tower longitudinal由图 5可知，多点激励下主梁最大位移略高于一致激励下主梁最大位移，总体变化不大。由图 6、图 7可知，一致激励下南、北桥塔沿塔高的位移、轴力、剪力及弯矩计算结果相同，这符合有限元计算基本原理。多点激励下南、北桥塔计算结果不对称，说明地震波输入方式对计算结果具有一定影响，由于本研究中悬索桥跨度不大，所以一致激励和多点激励下计算结果差别不大。
6. 结语
本文对某对称悬索桥在一致激励及视波速1000m/s的多点激励下的地震响应进行分析，并对计算结果进行分析。计算结果表明地震波输入方式对模拟结果具有一定影响，计算结果存在一定差异，主梁在多点激励下的位移计算结果略高于一致激励下的计算结果，桥塔最大位移发生在塔中与塔顶之间，最大弯矩、轴力、剪力均发生在塔根处。
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图 1 可能引起地面沉降和断层活化的油气开发地下活动（Morton等，2006）
Figure 1. Oil and gas development subsurface events that may induce land subsidence and reactivate faults (from Morton et al., 2006)
图 2 美国中部与东部1973—2015年3级以上地震数目（Rubinstein等，2015）
Figure 2. Number of M≥3 earthquakes in the central and eastern United States from 1973 to 2015 (from Rubinstein et al., 2015)
图 3 Fox Creek西南地区100 km以内累计震级大于2.5级地震事件（Schultz等，2017）
Figure 3. Cumulative number of earthquakes greater than magnitude 2.5 within 100 km of the southwest of Fox Creek (from Schultz et al.,2017)
图 4 昭通、长宁地块地震活动统计（Meng等，2019）
Figure 4. Seismicity statistics in Zhaotong and Changning (from Meng et al., 2019)
图 5 诱发地震的3种主要机制（Ellsworth，2013；Eyre等，2019a）
Figure 5. Three main mechanisms of inducing earthquakes (from Ellsworth, 2013; Eyre et al., 2019a)
图 6 断层应力状态变化及典型的破坏机理（Li等，2019）
Figure 6. The typical damage mechanisms caused by change of fault stress state (from Li et al., 2019)
图 7 由于摩擦系数降低和内聚力降低而导致的断层弱化（Yeo等，2020）
Figure 7. Weakening of faults due to reduction of the coefficient of friction and reduced cohesion (from Yeo et al., 2020)
图 8 加拿大Fox Creek地区Duvernay组页岩气开发主要诱发地震（Schultz等，2018）
Figure 8. The main induced earthquakes by shale gas development in Duvernay play, Fox Creek area of Canada (from Schultz et al., 2018)
图 9 H储气库运营前后的孔隙压力随时间的变化及地震事件
Figure 9. Variation of pore pressure with time and seismic events before and after operation of H gas storage
图 10 油气开采及H储气库注采诱发应力变化预测结果（王成虎等，2020）
Figure 10. Predicted stress changes induced by oil and gas production and injection production in H gas storage (from Wang et al., 2020)
表 1 各地区最大水力压裂诱发地震事件（Atkinson等，2020）
Table 1. The largest seismic events for hydraulic fracturing by region (from Atkinson et al., 2020)
地区 最大震级/级 时间/(年-月-日) 中国，四川盆地（Lei等，2019） ML5.7 2018-12-16 加拿大，British Columbia，Fort St. John（Mahani等，2019） ML4.5 2018-11-29 美国，Texas（Fasola等，2019） M4.0 2018-05-01 加拿大，Alberta，Red Deer（Schultz等，2020） ML4.2 2019-03-04 加拿大，Alberta，Fox Creek（Eyre等，2019a，2019b） M4.1 2015-01-12 加拿大，British Columbia，Horn River（Farahbod等，2015） ML3.8 2011-05-19 美国，Ohio（Brudzinski等，2019） ML3.7 2017-06-03 美国，Oklahoma（Maxwell等，2009） ML3.6 2019-07-25 
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表 2 四川盆地页岩气开采诱发地震最大震级（Lei等，2017，2019；Meng等，2019）
Table 2. Statistics of maximum magnitude of earthquakes induced by shale gas exploitation in Sichuan Basin (from Lei et al., 2017，2019; Meng et al., 2019)
地点 纬度/（°N） 经度/（°E） MW 时间/(年-月-日) 震源深度Z/m N201～H24井场，兴文县 28.21 104.93 5.2 2018-12-16 3 090 N201～H18井场，珙县 28.20 104.70 4.8 2019-01-03 1 840 H7井场，珙县上罗镇 28.13 104.75 4.67 2017-01-28 1 800 威远县 29.52 104.83 3.4 2016 3 090
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