俯冲带板内地震竖向加速度谱阻尼修正系数模型研究

陈心锋, 姜妍旭, 刘名吉

陈心锋,姜妍旭,刘名吉. 2022. 俯冲带板内地震竖向加速度谱阻尼修正系数模型研究. 地震学报,44(2):339−355. DOI: 10.11939/jass.20200198
引用本文: 陈心锋,姜妍旭,刘名吉. 2022. 俯冲带板内地震竖向加速度谱阻尼修正系数模型研究. 地震学报,44(2):339−355. DOI: 10.11939/jass.20200198
Chen X F,Jiang Y X,Liu M J. 2022. A damping modification factor model for vertical acceleration spectrum from slab earthquakes in subduction zone. Acta Seismologica Sinica44(2):339−355. DOI: 10.11939/jass.20200198
Citation: Chen X F,Jiang Y X,Liu M J. 2022. A damping modification factor model for vertical acceleration spectrum from slab earthquakes in subduction zone. Acta Seismologica Sinica44(2):339−355. DOI: 10.11939/jass.20200198

俯冲带板内地震竖向加速度谱阻尼修正系数模型研究

基金项目: 国家自然科学基金(51878396)资助
详细信息
    通讯作者:

    陈心锋,硕士研究生,主要从事岩土地震工程方面的研究,e-mail:chenxf1996@126.com

  • 中图分类号: P315.9

A damping modification factor model for vertical acceleration spectrum from slab earthquakes in subduction zone

  • 摘要: 基于日本K-NET和KiK-net台网的4 695条俯冲带板内地震记录,采用最小二乘法对阻尼修正系数(DMF)的几何均值进行关于阻尼比和谱周期的回归拟合,分场地类别建立了考虑阻尼比和谱周期的竖向加速度谱DMF模型。为探究震源、路径和场地效应对该模型残差分布的影响,采用随机效应模型将残差分离得到各类残差及相应的残差标准差,在此基础上进行DMF模型残差分析。研究结果表明,DMF可以采用阻尼比对数值的三次多项式、周期对数值的四次多项式来模拟。由于规范设计反应谱并非针对某一特定地震,规范提出的DMF模型并不包含震源和路径参数,但事件间和事件内残差关于矩震级、断层距离和断层深度的分布表明,在给定地震事件下,包含地震动参数的DMF模型将会改善模型的预测能力。
    Abstract: In this study, 4695 strong-motion records from subduction slab earthquakes in Japan obtained by the K-NET and KiK-net networks were used to develop a damping modification factor (DMF) model for the vertical acceleration spectrum. The DMF model considering the damping ratio and spectral period is established for four site classes, and the geometric mean values for DMF are used to perform regression fitting in respect to the damping ratio and spectral period by least squares method. To evaluate the influence of hypocenter, path, and site effects on the residual distribution of the model, the total model residuals and standard deviations were separated into between-event and within-event parts, and the within-event residuals were further divided into the between-site and within-site parts by using a random effects model. The results show that the effect of damping ratios on DMF can be modelled by the third-order polynomial of the logarithm of the damping ratios, a fourth-order polynomial of the logarithm of spectral periods can be used to model the effect of spectral periods for the DMF. The effects of source and path parameters were not modelled in this study because of DMF model is used to scale a design spectrum not associated with a given scenario earthquake. The distribution of the between- and within-event residual distributions with respect to moment magnitude, fault depth and source distance suggests that including these terms would improve prediction capability of the model when a DMF is designed for scaling a 5% acceleration spectrum associated with a scenario event for a give magnitude and source distance.
  • 北京时间2022年1月8日1时45分,青海省海北藏族自治州门源县发生了一次强烈地震。据中国地震台网中心(2022a)测定,该次地震的震级为MS6.9,震中位于(37.77°E,101.26°N),震源深度约为10 km。据美国地质调查局(USGS,2022)测定,此次地震震级为MW6.6,震中位于(37.828°N,101.290°)E,震源深度约为13 km,发震断层走向为N104°E,震源机制解节面 Ⅰ 倾角75°,滑动角13°,节面 Ⅱ 倾角88°,滑动角15°,显示为WNW向的高角度略带逆冲分量的左旋走滑错动事件。此次地震发生在祁连山中段的冷龙岭断裂西段与托莱山断裂的构造转换部位,是冷龙岭活动断裂带上继1986年门源MS6.4地震(徐纪人等,1986兰州地震研究所、青海省地震局联合考察队,1987)、2016年门源MS6.4地震(胡朝忠等,2016郭鹏等,2017姜文亮等,2017)之后发生的又一次破坏性地震。截至2022年8月底,共记录到MS≥3.0余震28次,其中MS5.0—5.9余震2次,MS4.0—4.9余震6次,MS3.0—3.9余震20次(中国地震台网中心,2022a),最大余震为2022年1月12日18时20分发生的MS5.2地震。

    此次门源地震发生后,我们第一时间前往震区进行应急科学考察,后又于2022年6月进行现场补充调查。综合野外调查发现,此次地震在地表形成了一条北侧的主破裂带及一条南西侧的次级破裂带,其中主破裂带长约22 km,次级破裂带长约9 km,两者以左旋左阶区相隔(袁道阳等,2023)。野外考察表明本次地震形成了类型丰富、形变特征典型的地表破裂现象,如水平位错、挤压鼓包、挤压脊、断层陡坎、张裂隙、拉分阶区等,为深入认识和理解此次地震事件的破裂性质和震害特征提供了重要参考。

    前人针对此次门源地震的地表破裂事件,已经根据应急考察资料归纳总结并发表了部分研究成果,例如:李智敏等(2022)结合地表调查和合成孔径雷达干涉测量(interferometric synthetic aperture radar,缩写为InSAR)的反演结果得出,此次地震的破裂带分布于冷龙岭断裂西段及托莱山断裂东段,总长度超过22 km,最大水平位错约2.41 m;潘家伟等(2022)根据实地调查获得的地震破裂带总长约27 km,南北两条破裂带之间的阶距约为3 km,最大水平位错约为3.7 m,并通过对其震级、破裂带规模和变形强度的综合分析认为,此次地震具有较浅的震源深度;袁道阳等(2023)根据野外调查和无人机航拍得出,此次地震形成的北侧破裂带的长度约为21 km,南侧破裂带的长度约为9 km,总长度为31 km,两条破裂带之间呈左阶斜列,最小阶距约为1.0 km,形成的最大位错约为(2.6±0.3) m;韩帅等(2022)则认为此次地震的最大位移约为(3±0.2) m,且在形成了南北累计长约22 km的主破裂带外,在北侧破裂带中东段的旁侧还发育了一条长约7.5 km、以右旋正断为主的次级破裂带;薛善余等(2022)认为本次破裂带总长约26 km,于地表破裂最明显的道沟—硫磺沟一带形成了最为显著的震害现象,指示了宏观震中的大致位置。这些研究大多侧重于沿破裂带分布及其位错特征等的调查结果论述,因时间紧加之冬季冰雪覆盖有些地段难以到达等原因,目前对破裂带的完整空间展布和两条破裂带间最小阶距的认识尚存一定差异。此外,前人对此次地震中不同类型地震破裂现象的归类总结及其形成机制等的讨论明显不足。鉴于此,本文拟在已有研究基础上,归纳总结此次地震破裂带不同类型的典型断错地貌特征及其成因机制,并对地震震害类型及相应破坏特征等进行分析探讨,为跨活动断裂及其邻区的工程建设和抗震设防提供参考。

    受青藏地块向北东方向的挤压扩展作用影响,青藏高原东北部的祁连山地区发育了一系列逆走滑活动断裂带和逆断裂褶皱带,如祁连山北缘断裂带、疏勒河断裂带、疏勒南山断裂带等,为地震活动的高发地区(张培震,1999邓起东等,2002)。本次门源MS6.9地震震中所处的祁连山中段更是发育有多条大型活动断裂带,如祁连—海原断裂带、肃南—祁连断裂和古浪断裂等,其中祁连—海原断裂带为横跨祁连山内部、以左旋走滑为主的大型地块边界断裂,自西向东由哈拉湖断裂、托莱山断裂、冷龙岭断裂、金强河断裂、毛毛山断裂、老虎山断裂、狭义海原断裂和六盘山断裂等组成(图1)(Gaudemer et al,1995Lasserre et al,2002袁道阳等,2004郑文俊等,2009Zheng et al,2013Liu et al,2022)。二十世纪以来,沿该大型边界断裂带发生了多次大地震,如1920年海原M8½地震、1927年古浪M8地震、1990年景泰MS6.2地震、1986年门源MS6.4地震和2016年门源MS6.4地震等(郭增建等,1976兰州地震研究所、青海省地震局联合考察队,1987侯珍清,才树骅,1990侯康明,1998胡朝忠等,2016郭鹏等,2017)。此次门源MS6.9地震则发生在祁连—海原断裂带中段的冷龙岭断裂上(李智敏等,2022潘家伟等,2022袁道阳等,2023)。

    图  1  祁连山中段活动构造分布及2022年门源MS6.9地震位置图
    断层数据修改自邓起东(2007)和徐锡伟等(2016),历史地震数据源自国家地震科学数据中心(2022),现代地震数据源自中国地震局震害防御司(1999)和中国地震台网中心(2022b),DEM数据源自美国地质调查局(USGS,2000
    Figure  1.  Active structures in central Qilian mountains and location of 2022 MS6.9 Menyuan earthquake
    Fault data are modified from Deng (2007) and Xu et al (2016),the historical earthquake data is from National Earthquake Data Center (2022),the modern earthquake data is from Earthquake Disaster Prevention Department of China Earthquake Administration (1999) and China Earthquake Networks Center (2022b). DEM data is from US Geological Survey (USGS,2000

    冷龙岭断裂东起天祝县双龙煤矿,过红腰岘、闸渠河、他里花沟、老虎沟、岗石尕等地,向西延伸至硫磺沟,总长约120 km,晚第四纪以来以左旋走滑为主兼具倾滑分量,全新世以来走滑速率为4—7 mm/a (何文贵等,2010郭鹏等,2017),其东段与古浪断裂(也称为天桥沟—黄羊川断裂)、金强河断裂相连,西段过冷龙岭后则分为活动性质不同的三条断裂:托莱山断裂、托莱山北缘断裂和肃南—祁连断裂。已有研究表明,东侧的古浪断裂和金强河断裂为全新世以来以左旋走滑为主的活动断裂带(Gaudemer et al,1995袁道阳等,1998郑文俊等,2004Zhang et al,2019Shao et al,2021),而西侧的三条断裂研究程度较低,除托莱山断裂晚第四纪活动性有部分研究(Yuan et al,2008李强等,2013)外,对肃南—祁连断裂活动性质的研究多集中在活动性较强的中段(郭敬信等,1990刘建生等,1994),而对于托莱山北缘断裂只有近年来关于祁连段阶地构造变形特征的研究(Hu et al,2021)。此次地震发生在冷龙岭断裂与托莱山断裂的构造转换处,是该区域深部构造活动及应力调整释放的结果,也是近年来发生在冷龙岭断裂附近震级最高、地表破裂最长的地震事件。

    实地调查发现,此次地震在地表形成了位于冷龙岭断裂带西段的北侧主破裂带(F1)和位于托莱山断裂东端的南西侧次级破裂带(F2),其间以左旋左阶区分隔开(图2)。其中,北侧主破裂带整体呈北西西向,东起于冷龙岭主峰附近,向西过硫磺沟南侧边坡,穿道沟后延伸至下大圈沟止,长度约为22 km。以硫磺沟公路为界,主破裂带大致可分为东段硫磺沟段F1-1 (其北侧还发育了一条与之斜交的次级分支破裂F1-3)和中段硫磺沟—下大圈沟段F1-2,整体呈较连续的线性分布,主破裂上的次级破裂则以小型左旋左阶拉张区和左旋右阶挤压区相连,地表表现为张性裂缝、拉分阶区、挤压鼓包、标志物左旋位错、断层陡坎等典型断错地貌特征,向主破裂带两端延伸位错现象逐渐减少,变为发散状的地裂缝。南西侧次级破裂带则为主破裂触发而形成的一条次级牵引破裂带(F2,南西段),呈近东西向展布,东起于道沟东侧的山体半坡处,向西延伸至大西沟西侧垭口,总长度约为9 km,其中:大西沟至狮子口以西一段见张性裂缝、挤压脊、挤压鼓包、纹沟及砂石路左旋位错、阶区右旋位错等地表破裂现象,长度约为5.3 km (F2-1,大西沟段);自狮子口向东至道沟处,则主要呈现为沿托莱山断裂发育的密集地裂缝带,长度约3.7 km (F2-2,狮子口段),宽度可达300400 m。假如严格按照以存在地表位错作为破裂带判定标志的规范,其与北侧主破裂带(F1)之间的最小阶距达3 km;但是若认为密集地震裂缝带也属于地表破裂带的另一种表现形式,则与主破裂带最小阶距仅约1 km,本文倾向于后者。此外,针对上述多种典型地表破裂现象进行了分类总结和成因机制分析,并归纳于下.

    图  2  2022年门源MS6.9地震破裂带展布图
    绿点代表后文介绍的几种破裂带典型几何结构,黄点代表水平位错地貌,白点代表垂直位错地貌,橙点代表挤压脊、鼓包,蓝点代表张性裂缝,青点代表典型震害,黑点代表远端地表效应。F1-1:主破裂带硫磺沟段;F1-2:主破裂带硫磺沟—下大圈沟段;F1-3:硫磺沟次级破裂带;F2-1:南西侧次级破裂带大西沟段; F2-2:南西侧次级破裂带狮子口段,下同
    Figure  2.  Distribution characteristics of the 2022 MS6.9 Menyuan earthquake rupture zone
    The green dots represent several typical geometric structures described later,the yellow dots represent the horizontal dislocations,the white dots represent the vertical dislocations,the orange dots represent the compressed ridges and bulges,the blue dots represent the tensional cracks,the cyan dots represent the typical earthquake damage,the black dots represent the remote surface effect。F1-1:Liuhuanggou section of the main rupture zone;F1-2:Liuhuanggou-Xiadaquangou section of the main rupture zone;F1-3:Liuhuanggou secondary rupture zone;F2-1:Daxigou section of the southwest secondary rupture zone;F2-3:Shizikou section of the southwest secondary rupture zone,the same below

    此次门源MS6.9地震形成了连续性好、规模壮观的地表破裂现象,构成了不同类型的几何细结构,主要包括雁列状破裂、左旋左阶区、左旋右阶区和树枝状、网状破裂等,这些结构具有极为丰富的破裂组合特征。已有研究表明,走滑型地震形成的次级破裂的成因机制大多符合里德尔(Riedel)剪切(R剪切)理论,近年来已在不同地震破裂事件研究中得到验证,如2010年玉树MS7.1地震(周春景等,2014)、2014年新疆于田MS7.3地震(Li et al,2016)、2021年玛多MS7.4地震(Ren et al,2021)等,而此次地震观测到的多种结构同样符合里德尔剪切破裂的特征。

    1) 雁列状破裂。本次门源地震在硫磺沟至道沟段F1-2可见与主破裂走向斜交的多条次级破裂呈雁列状分布(图3a),主破裂为宽10—30 cm的张裂隙,而其间的连接部位则形成小的挤压鼓包等。雁列状次级破裂总体走向约65°—80°,与主破裂整体走向290°之间呈30°—45°的夹角,总体表现为R剪切特征,为断层两盘之间发生羽状破裂的结果。

    图  3  破裂带典型区域无人机影像(左)与几何结构及成因机制素描图(右)
    R:里德尔剪切破裂;R′:共轭里德尔剪切破裂;T:张性破裂;Y:平行主位移方向的剪切破裂;P:次生压剪性破裂。(a) 雁列状破裂区;(b) 左旋左阶区,以左阶拉张为主,相邻左阶区间连接部位为挤压区;(c) 左旋右阶区,以右阶挤压为主;(d) 树枝状、网状分叉区,端部以分叉及网格状交错裂隙为主
    Figure  3.  UAV images (left panels),geometric structures and genetic mechanism sketches (right panels) of typical areas of the earthquake rupture zone
    R:Riedel shear fault;R′:Conjugate Riedel shear fault;T:Tensional fault;Y:Shear fault parallel to the principal displacement direction;P:Secondary compressed shear fault. (a) Echelon rupture;(b) Sinistral extensional step-overs dominated by stretching,where the connecting parts are compressed regions;(c) Sinistral compressed step-overs dominated by extruding;(d) The dendritic and netlike forked areas. The end member is dominated by bifurcation and meshed crisscrossed cracks

    2) 左旋左阶和左旋右阶区。在主破裂带内部的不同次级破裂之间,随局部力学性质的变化而发育连续的左旋左阶、左旋右阶等不连续阶区构造,一般阶距约20—100 m。随阶区性质的差异,左旋左阶区内发育斜交于主破裂带的张性裂隙(图3b),单条裂隙宽约10—40 cm (最大可达1 m),走向约50°—70°,与主破裂带呈T剪切特征排列,而阶区之间则以走向约310°—320°的挤压脊向前延伸,构成挤压脊与拉张裂隙相间排列的复杂几何图像。与此相反,在左旋右阶区内部发育近南北向的次级挤压脊(图3c),两侧伴有与之走向近垂直的次级牵引破裂,表现为与主破裂带近平行的Y剪切特征,而阶区之间则以北北西走向的挤压脊相连。

    3) 树枝状和网状破裂。与上述较规则的地表破裂不同,在一些构造复杂部位或断塞塘等地势低洼的场地,还形成了较为密集的树枝状或网状等破裂现象,如在靠近硫磺沟公路的山体半坡(图3d),可见细小的裂缝沿地震破裂带两侧发育,形成单条宽约2—10 cm的密集网状张性裂隙,向外无序分叉继而形成树枝状或格网状裂隙,向远端逐渐尖灭,破裂带宽度可达100 m。上述不同类型几何结构交替发育,形成多种组合的次级裂隙。

    本次地震地表破裂的左旋位错标志点非常丰富,野外考察可见动物脚印、冲沟河床、山间小路、冰面、围栏、公路路基和车辙等多种典型标志物被左旋错断的现象。在野外皮尺测量的基础上,结合精度优于1.5 cm的无人机低空正射影像对不同位错地貌进行多次测量及最终校对,排除视位移影响后,获取了沿这条破裂带较为精确的位错值(图4)。地震破裂带总体趋势为:中段F1-2的位错量最大,达(2.6±0.3) m (袁道阳等,2023),向两端延伸逐渐减小;南西侧次级破裂带F2的水平位错值最大约(1.0±0.1) m,向西很快终止,而向东过羊肠子沟形成密集的裂缝带。

    图  4  沿2022年门源MS6.9地震地表破裂带的水平位错空间分布特征(据袁道阳等,2023修改)
    Figure  4.  Distribution characteristics of horizontal dislocations along the surface rupture zone of the 2022 MS6.9 Menyuan earthquake (modified from Yuan et al,2023

    典型水平位错包括:① 围栏位错。在F1-2硫磺沟大拐弯至道沟间的高台地处,地震破裂造成近南北走向的五道围栏左旋位错,位错值分别为(2.41±0.05) m,(2.45±0.06) m (图5a),(2.60±0.3) m,(2.32±0.05) m,(2.25±0.03) m,其中最大位错值(2.60±0.3) m是在该地震破裂带上测得的最大位移量(袁道阳等,2023);② 路基及车辙位错。在这次地震中,形成了比较典型的砂土路和车辙左旋断错现象,因其边界线清晰而且延伸较长,结合无人机影像测量可以获得较准确的位错值,如在道沟内可见车辙印被清晰左旋错断(1.14±0.05) m (图5b);③ 动物印痕位错。由于震区位于祁连山内部高山牧区,冬季休牧期狼、熊等野生动物在雪后行走留下的印痕(经当地牧民鉴别确认)断错非常明显,如在中段F1-2道沟以西山坡上可见被明显错断的动物脚印,错位值为(1.20±0.10) m (图5c);④ 冰沟位错。本次地震还造成冬季高寒地区冰沟和河床左旋断错等特殊地貌标志,如道沟靠近下大圈沟段F1-2与主破裂带走向斜交的次级破裂上,可见冲沟冰面被斜向左旋断错(0.80±0.03) m (图5d)。

    图  5  多种类型地貌标志物的左旋位错
    黄色箭头为破裂带两盘水平相对运动方向;红色箭头为破裂带宏观展布方向(a) 围栏;(b) 车辙印;(c) 狼脚印;(d) 冲沟冰面
    Figure  5.  Left-lateral offsets of various types of geomorphic markers
    The yellow arrows represent the horizontal relative motion direction of both sides,and the red arrows represent the macroscopic direction spreading of the rupture zone。 (a) Fences;(b) Truck trace;(c) Wolf footprints;(d) Gully ice

    1) 逆冲型地震陡坎。本次地震地表破裂除了以左旋走滑运动为主之外,还兼具逆冲分量,因此沿地震地表破裂带广泛发育有单条或多条组合的具逆冲性质的地震断层陡坎,且由断层南盘逆冲于北盘之上。例如,在东段F1-1棵树沟对岸的一大冲沟河床在地震作用下形成近垂直的逆冲地震陡坎(图6a),高度约为(0.70±0.10) m;而在中段F1-2,此次地震新形成的逆冲陡坎高度多为0.2—0.5 m,另有部分地震陡坎叠加在早期断层陡坎(图6b)之上,新形成的陡坎高约(2.0±0.2) m,指示了该区断裂多期次的构造活动现象。

    图  6  2022年门源MS6.9地震破裂形成的各类垂直陡坎及其断错类型(左下角小图)
    (a) 近垂直逆冲陡坎;(b) 复合型逆冲陡坎;(c) 拉张型正断陡坎;(d) 近垂直正断陡坎
    Figure  6.  Various types of vertical scarps resulted from the 2022 MS6.9 Menyuan earthquake and their disloaction types (bottom-left insets)
    (a) Near-vertical thrust scarp;(b) Compound thrust scarp;(c) Tensional normal scarp;(d) Near-vertical normal scarp

    2) 正断型地震陡坎。本次地震中,局部地段于破裂带内部的次级构造转换部位形成具有拉张性质的正断陡坎。例如在F1-2上大圈沟—下大圈沟段,新形成的正断陡坎走向与主破裂带斜交,形成高差不一、边缘清晰陡直的线性边界(图6c),与逆冲地震陡坎不同,正断陡坎两侧地层在拉张作用下,形成了有垂直位错分量的张裂缝,宽约0.2—0.4 m。此外,于南西侧次级破裂带F2-1拉分阶区内则见部分正断陡坎两盘近垂直错断(图6d),高0.15—0.2 m,斜向汇入宏观破裂带。

    沿地震地表破裂带考察,各段多见广泛发育的挤压脊及地震鼓包等典型破裂现象,主要发育在左旋右阶区或沿地震断裂局部挤压环境下的走滑挤压作用一侧,其地表表现形式主要有挤压脊、帐篷式挤压鼓包等,一般高约0.5—2.5 m。例如在主破裂带中段F1-2,地震断裂的挤压逆冲分量使得地震破裂带多处拱起,形成长条状的挤压脊或帐篷式的挤压鼓包,其形成原因除与地震作用下的强烈垂直震动有关之外,也与高寒山区冬季地表冻结作用易于发生脆性破裂有关。在中段F1-2靠近道沟处,主破裂带逆冲分量使得高原冻土顺着主破裂带走向形成宽约4—5 m、长约数十m的地表隆起变形带(图7a);而在中段F1-2靠近上大圈沟处,则见地面冻土在强烈扰动下破裂翘起,形成帐篷式的对顶鼓包(图7b),高约1.8 m。与主破裂带相比,南西侧次级破裂带F2-1大西沟一带形成的挤压脊一般高约0.3—0.8 m,鼓包高约0.2—0.5 m,而狮子口以东破裂现象较为微弱,主要以密集发育的地裂缝为主,挤压脊及鼓包不明显。

    图  7  2022年门源MS6.9地震形成的挤压脊(a)和鼓包(b)
    黄色箭头为破裂带两盘水平相对运动方向,黑色箭头为受力方向
    Figure  7.  Compressed ridges (a) and bulges (b) caused by the 2022 MS6.9 Menyuan earthquake
    The yellow arrows represent the horizontal relative motion direction on both sides of the rupture zone,and the black arrows represent the directions of force

    本次地震破裂过程中还形成了不同成因、类型多样的张性裂缝。顺北侧主破裂带可见纯张性及张剪性裂缝,而于破裂带各次级段之间的左旋左阶区内可见与主破裂带走向斜交的张剪性及束状拉张裂隙,不同类型的张性裂缝在走向和宽度上往往有较大差异。例如:在主破裂带中段F1-2靠近道沟处,主破裂带两侧冻土在张应力作用下形成不规则拉张裂缝(图8a),最宽处约1 m,错动的冻土及上覆积雪层边界平整,与地面近乎垂直;在主破裂带中段F1-2上大圈沟—硫磺沟大拐弯中间错断的多组围栏处,则可见主破裂带在牵引作用下形成的数条张剪裂隙呈次级雁列状,与主破裂带总体走向斜交(图8b),走向约60°—70°,宽多为0.3—0.8 m,与南侧发育的贯通数条雁列状裂隙尾端的追踪式裂缝共同构成主破裂带的一部分;在主破裂带中段F1-2多组断错围栏以西处,可见主破裂带不同段间的拉分区内斜向发育多条近平行的张性或张剪性裂缝(图8c),走向约60°—65°,宽约0.1—0.6 m,部分伴有走滑分量。此外,与地震断层走向近平行的张裂隙不同,在拉分区内伸展受力区域与主破裂带的交会处,往往也会形成数条相互会聚的张性破裂,如在道沟—硫磺沟段的西侧(图8d),斜穿阶区中央的数条裂隙整体呈束状,由主破裂带向阶区内发散,走向由45°向75°逐渐过渡。

    图  8  2022年门源MS6.9地震破裂形成的各类裂缝和拉张阶区
    黄色箭头为破裂带两盘水平相对运动方向;红色箭头为破裂带的宏观展布方向。(a) 主破裂张裂缝;(b) 雁列状张剪裂缝及追踪式裂缝;(c) 拉分区张剪裂缝;(d) 南北两侧为挤压破裂,其间为左旋左阶阶区内束状拉张裂缝
    Figure  8.  Various types of cracks and extensional step-overs formed by the rupture of 2022 MS6.9 Menyuan earthquake
    The yellow arrows represent the horizontal relative motion direction of both sides of the rupture zone,and the red arrows mark the macroscopic distribution direction of the rupture zone。(a) Tensional cracks on the main rupture zone;(b) Echelon tensional shear cracks and tracing cracks;(c) Tensional shear cracks in the extensional step-overs;(d) Compressed ruptures on the north and south sides,between of which are bundles of tensional cracks in sinistral extensional step-overs

    根据中国地震局(2022)发布的门源MS6.9地震烈度图,此次地震极震区的最大烈度高达Ⅸ度。由于该地震发生在无人区,无人员伤亡,仅造成部分公路路基、大桥、铁路隧道破坏,兰新高铁因此而停运。而冷龙岭地区由于海拔较高、气候寒冷,地表主要被冻土、冰雪等覆盖,因此除沿冷龙岭断裂和托莱山断裂形成地表破裂带之外,未造成明显滑坡等灾害,仅见部分边坡有滚石或局部失稳垮塌现象。

    在地震地表破裂带穿过的硫磺沟公路处,可见公路西侧的山体边坡因地震作用发生垮塌(图9a),而路东侧顺地震断裂带延伸方向的硫磺沟河岸边坡发育数条宽约0.3—1 m不等的张性裂缝,并使公路形成明显的路基下陷。由于此处位于硫磺沟河岸二级阶地之上,公路路基由阶地砾石层及上方的细粉砂及冻结的土层组成,因此在地震的强震动作用下,硫磺沟河岸边坡失稳并顺河床发生滑塌作用(图9b)。

    图  9  2022年门源MS6.9地震造成的各类地质灾害及工程破坏现象
    红色箭头为破裂带展布,黑色箭头为桥面同震水平运动幅度
    Figure  9.  Various geological disasters and engineering damages caused by the 2022 MS6.9 Menyuan earthquake
    The red arrows represent the distribution of the rupture zone,and the black arrows represent the coseismic horizontal motion amplitude of the bridge deck

    本次地震地表破裂带穿过的多条公路均遭到了不同程度破坏。其中,北侧主破裂带造成的公路破损较为严重,如在硫磺沟处,破裂带穿过的硫磺沟公路路基受地震影响而发生左旋位错及挤压鼓起,而在道沟内的公路处,则见到路基受多方向应力作用发生脆性破裂而断为数段(图9c)。但在南西侧的次级破裂段F2,地震破裂带穿过的公路处往往仅见较窄的地裂缝而无明显位错现象,这反映了次级破裂带上较弱的地表变形效应。

    本次地震还造成了兰新高铁桥梁及隧道内部严重变形。经现场考察发现,桥墩上方的桥梁不同段落之间发生不同步错动及掀斜变形(图9d),致使桥面上的铁轨呈现扭曲变形。我们经实地调查分析,此处铁轨表现出的变形特征主要是在强烈地震动的作用下,位于破裂带北盘的桥梁路基及桥面各段不同步震动作用的结果,而铁轨的位错则是在多组桥墩不同振幅运动及掀斜过程中表现出的假象。鉴于地震作用对穿过断层的桥梁、隧道等重大工程造成的直接断错和基础设施的损毁,工程抗断及近断层强地面运动的抗震设防问题仍需进一步深入研究。

    在地震地表破裂带外围4 km范围内,零星可见此次地震强震动作用形成的次生冰面鼓包及地表裂缝。例如在G227国道旁边尚未投入使用的桥梁处,见到主破裂带顺先存断裂向西延伸的远端桥墩顶部发育多条次级裂隙(图10a,b),对桥梁安全造成隐患,而地表可见砂石路上新形成的较细的地表裂隙。这说明虽然主破裂带已在下大圈沟处逐渐尖灭,但是远端仍受地震强震动作用的影响。

    图  10  2022年门源MS6.9地震破裂带远端的地表效应
    (a) 地表裂隙;(b) 桥梁裂隙;(c) 冰面鼓包
    Figure  10.  Remote surface effects of the rupture zone of the 2022 MS6.9 Menyuan earthquake (a) Surface cracks;(b) Bridge cracks;(c) Ice bulges

    在次级破裂带F2向东延伸的道沟冰面上,见零散发育的冰面鼓包(图10c),垂直高度约为0.5—1 m,旁侧的砂石路上同样可见贯穿路面的地裂缝。考虑到此处已经远离主破裂带,鼓包主要受南侧牵引破裂带的影响,冰面鼓包则是在强烈地震动作用下形成的。

    2022年1月8日门源MS6.9地震发生于祁连山中段山区,位于冷龙岭断裂与托莱山断裂的构造转换部位,形成了类型丰富、形变特征典型的地表破裂现象。归纳起来,具有以下几类典型的地表破裂特征:

    1) 典型走滑破裂。此次地震形成了两条地表破裂带,变形样式以左旋走滑为主,总长约31 km,最大水平位移量为(2.6±0.3) m。其中,北侧主破裂带F1沿冷龙岭断裂西段分布,长约22 km,南西侧次级破裂带F2沿托莱山断裂东段展布,长约9 km. 若以具有地表位错的大西沟段F2-1为破裂带标志,南西侧次级破裂带与主破裂带的最小阶距约为3 km;若以发育弥散型裂缝带的狮子口段F2-2作为次级破裂带向东的终止端,则次级破裂带至主破裂带的最小阶距约为1 km。

    2) 地表破裂几何图像复杂。本次地震沿先存的冷龙岭断裂和托莱山断裂形成了典型的雁列状几何图像,但在不连续阶区部位形成了左旋左阶拉分区和左旋右阶挤压区,同时在构造转换部位形成了树枝状或网状的几何图像。

    3) 走滑和垂直位错类型多样。破裂带沿线错断了动物脚印、山间小路、公路路基、冲沟冰面、围栏、车辙印、冻融鼓包等多种地貌标志。受主破裂带内局部力学性质变化的影响,发育不同成因的张性裂缝、挤压脊、挤压鼓包以及挤压型、拉张型地震陡坎。

    4) 地质灾害和工程震害严重。此次地震除造成公路脆性变形、桥梁掀斜以及高铁铁轨扭曲变形等工程破坏外,还形成了山体滚石、河岸边坡失稳、地表崩塌等一系列震害现象。但在两条地表破裂带的远端仅见地表裂缝、冰面鼓包及桥梁裂缝零散发育,震害明显减轻。

    鉴于地震作用对穿过的公路路基、桥梁、铁路隧道等重要工程的严重破坏,未来的工程设计和建设中如何采取切实可行的措施加强跨地震断裂的工程抗断及近断层强地面运动设防技术研究,将是下一阶段的工作。

    感谢审稿专家对本文提出的诸多有益的意见和建议。

  • 图  1   地震数据分布图

    (a) 地震记录关于矩震级和断层距离的分布;(b) 地震事件关于矩震级和断层深度的分布

    Figure  1.   The distribution of earthquake dataset (a) The distribution of earthquake records with respect to moment magnitude and source distance;(b) The distribution of earthquakes with respect to moment magnitude and fault depth

    图  2   四类场地阻尼修正系数DMF的几何均值分布情况

    Figure  2.   The geometric mean values of DMF for four site classes

    (a) ζ=1%;(b) ζ=3%;(c) ζ=15% ;(d) ζ=30%

    图  3   四类场地间显著性检验统计值|Z|

    (a) Ⅰ类场地与Ⅱ类场地;(b) Ⅰ类场地与Ⅲ类场地;(c) Ⅰ类场地与Ⅳ类场地;(d) Ⅱ类场地与Ⅲ类场地;(e) Ⅱ类场地与Ⅳ类场地;(f) Ⅲ类场地与Ⅳ类场地

    Figure  3.   |Z| values for the statistical tests between each pair of four site classes

    (a) Site class Ⅰ vs site class Ⅱ;(b) Site class Ⅰ vs site class Ⅲ;(c) Site class Ⅰ vs site class Ⅳ; (d) Site class Ⅱ vs site class Ⅲ;(e) Site class Ⅱ vs site class Ⅳ;(f) Site class Ⅲ vs site class Ⅳ

    图  4   四类场地不同阻尼比的阻尼修正系数DMF模型拟合曲线与数据几何均值的对比

    (a) Ⅰ类场地;(b) Ⅱ类场地;(c) Ⅲ类场地;(d) Ⅳ类场地

    Figure  4.   DMF model comparisons with the geometrical mean of the vertical components for eight damping ratios of four site classes

    (a) Site class Ⅰ;(b) Site class Ⅱ;(c) Site class Ⅲ;(d) Site class Ⅳ

    图  5   阻尼修正系数DMF模型的残差标准差关于谱周期的分布图

    Figure  5.   The distribution of standard deviations of DMF models

    (a) ζ=1%;(b) ζ=3%;(c) ζ=10%;(d) ζ=30%

    图  6   阻尼比为25%时四类场地的场地内标准差(a)和场地间标准差(b)分布图

    Figure  6.   Distribution of within-site (a) and between-site (b) standard deviation for four site classes for a damping ratio of 25%

    图  7   T=2.5 s时阻尼修正系数DMF模型标准差关于对数坐标系下阻尼比的变化图

    (a) Ⅰ类场地;(b) Ⅱ类场地;(c) Ⅲ类场地;(d) Ⅳ类场地

    Figure  7.   Variations of standard deviation of DMF model with damping ratio at logarithmic scale by T=2.5 s

    (a) Site class Ⅰ;(b) Site class Ⅱ;(c) Site class Ⅲ;(d) Site class Ⅳ

    图  8   阻尼比为25%时阻尼修正系数DMF模型事件间残差分布图

    (a) T=0.1 s时残差关于断层深度的分布图;(b) T=0.1 s时残差关于矩震级的分布图;(c) T=3.0 s时残差关于断层深度的分布图;(d) T=3.0 s时残差关于矩震级的分布图

    Figure  8.   The distributions of between-event residuals of DMF model for a damping ratio of 25%

    (a) The distribution of residuals with respect to fault depth at T=0.1 s;(b) The distribution of residuals with respect to moment magnitude at T=0.1 s;(c) The distribution of residuals with respect to fault depth at T=3.0 s;(d) The distribution of residuals with respect to moment magnitude at T=3.0 s

    图  9   阻尼比为25%时DMF模型事件内残差分布图

    (a) T=0.1 s时残差关于断层距离的分布图;(b) T=0.1 s时残差关于矩震级的分布图;(c) T=3.0 s时残差关于断层距离的分布图;(d) T=3.0 s时残差关于矩震级的分布图

    Figure  9.   The distributions of within-event residuals of DMF model for a damping ratio of 25%

    (a) The distribution of residuals with respect to fault distance at T=0.1 s;(b) The distribution of residuals with respect to moment magnitude at T=0.1 s;(c) The distribution of residuals with respect to fault distance at T=3.0 s;(d) The distribution of residuals with respect to moment magnitude at T=3.0 s

    表  1   场地类别定义和各类场地记录数量

    Table  1   Site class definition and number of the records in each site class

    场地类别土质类型场地周期/s记录条数
    岩石Ts<0.22 022
    硬土0.2≤Ts<0.41 353
    中硬土0.4≤Ts<0.6442
    软土Ts≥0.6878
    下载: 导出CSV

    表  2   四类场地下阻尼修正系数模型的系数值

    Table  2   Coefficients of DMF model for four site classes

    T/sⅠ类场地Ⅱ类场地Ⅲ类场地Ⅳ类场地
    $ {c}_{1} $$ {c}_{2} $$ {c}_{3} $$ {c}_{1} $$ {c}_{2} $$ {c}_{3} $$ {c}_{1} $$ {c}_{2} $$ {c}_{3} $$ {c}_{1} $$ {c}_{2} $$ {c}_{3} $
    0.03 −0.020 0 −0.011 3 −0.015 0 −0.020 0 −0.005 4 −0.008 0 −0.008 3 −0.004 8 −0.008 0 −0.007 1 −0.004 7 −0.010 0
    0.04 −0.234 3 0.012 9 0.001 0 −0.152 1 0.016 7 −0.005 0 −0.138 9 0.018 3 −0.004 0 −0.120 8 0.013 3 −0.004 0
    0.05 −0.294 9 0.005 7 0.000 1 −0.235 9 0.012 9 0.001 4 −0.213 8 0.012 3 −0.001 1 −0.220 4 0.013 0 0.002 4
    0.06 −0.322 8 0.001 8 0.002 6 −0.283 5 0.006 7 0.003 1 −0.262 1 0.009 1 0.001 9 −0.273 8 0.008 2 0.005 0
    0.07 −0.340 8 −0.001 1 0.004 4 −0.314 7 0.002 1 0.004 4 −0.294 4 0.006 1 0.003 8 −0.308 7 0.004 7 0.006 6
    0.08 −0.352 8 −0.003 2 0.005 9 −0.335 7 −0.001 4 0.005 4 −0.317 1 0.003 4 0.005 1 −0.332 4 0.002 0 0.007 7
    0.09 −0.361 1 −0.004 9 0.007 1 −0.350 3 −0.004 0 0.006 2 −0.333 4 0.001 0 0.006 1 −0.349 1 −0.000 1 0.008 5
    0.10 −0.366 8 −0.006 3 0.008 1 −0.360 5 −0.006 1 0.007 0 −0.345 4 −0.001 0 0.006 8 −0.361 1 −0.001 8 0.009 1
    0.12 −0.373 5 −0.008 2 0.009 7 −0.372 8 −0.008 9 0.008 2 −0.361 2 −0.004 4 0.007 9 −0.376 3 −0.004 3 0.009 9
    0.14 −0.376 5 −0.009 4 0.011 0 −0.378 8 −0.010 6 0.009 3 −0.370 3 −0.007 0 0.008 7 −0.384 6 −0.006 1 0.010 5
    0.15 −0.377 1 −0.009 8 0.011 5 −0.380 3 −0.011 2 0.009 9 −0.373 4 −0.008 1 0.009 0 −0.387 3 −0.006 7 0.010 8
    0.16 −0.377 4 −0.010 1 0.012 1 −0.381 2 −0.011 6 0.010 4 −0.375 7 −0.009 0 0.009 3 −0.389 3 −0.007 3 0.011 0
    0.18 −0.377 1 −0.010 5 0.013 0 −0.381 6 −0.012 0 0.011 3 −0.378 8 −0.010 5 0.009 9 −0.391 8 −0.008 2 0.011 4
    0.20 −0.376 2 −0.010 7 0.013 9 −0.380 8 −0.012 1 0.012 2 −0.380 4 −0.011 6 0.010 5 −0.393 1 −0.008 8 0.011 8
    0.25 −0.372 3 −0.010 4 0.015 7 −0.376 3 −0.011 3 0.014 2 −0.381 1 −0.013 1 0.011 8 −0.393 4 −0.009 6 0.012 9
    0.30 −0.367 6 −0.009 5 0.017 2 −0.370 3 −0.009 7 0.016 0 −0.379 3 −0.013 5 0.013 1 −0.392 2 −0.009 7 0.013 9
    0.35 −0.362 7 −0.008 3 0.018 6 −0.364 2 −0.007 7 0.017 6 −0.376 6 −0.013 1 0.014 4 −0.390 6 −0.009 5 0.014 9
    0.40 −0.357 9 −0.006 9 0.019 8 −0.358 2 −0.005 5 0.019 2 −0.373 5 −0.012 2 0.015 6 −0.388 9 −0.008 9 0.016 0
    0.45 −0.353 2 −0.005 4 0.020 8 −0.352 5 −0.003 1 0.020 5 −0.370 1 −0.011 0 0.016 8 −0.387 3 −0.008 2 0.017 0
    0.50 −0.348 6 −0.003 8 0.021 8 −0.347 1 −0.000 8 0.021 8 −0.366 7 −0.009 5 0.018 0 −0.385 7 −0.007 3 0.018 0
    0.60 −0.339 8 −0.000 5 0.023 6 −0.337 0 0.003 9 0.024 1 −0.359 9 −0.006 2 0.020 2 −0.382 5 −0.005 4 0.020 0
    0.70 −0.331 3 0.002 9 0.025 0 −0.327 7 0.008 4 0.026 0 −0.353 1 −0.002 6 0.022 2 −0.379 3 −0.003 1 0.021 8
    0.80 −0.323 0 0.006 2 0.026 3 −0.319 0 0.012 8 0.027 7 −0.346 2 0.001 1 0.024 1 −0.375 9 −0.000 8 0.023 5
    0.90 −0.314 9 0.009 4 0.027 5 −0.310 6 0.016 9 0.029 2 −0.339 2 0.004 8 0.025 8 −0.372 2 0.001 6 0.025 1
    1.00 −0.306 8 0.012 6 0.028 5 −0.302 4 0.020 9 0.030 5 −0.332 2 0.008 5 0.027 3 −0.368 1 0.004 1 0.026 6
    1.25 −0.286 8 0.020 2 0.030 6 −0.282 5 0.030 0 0.033 1 −0.314 2 0.017 4 0.030 5 −0.356 2 0.010 4 0.029 8
    1.50 −0.266 7 0.027 4 0.032 1 −0.262 7 0.038 1 0.034 9 −0.295 4 0.025 6 0.033 1 −0.342 1 0.016 7 0.032 4
    2.00 −0.226 4 0.040 4 0.034 2 −0.222 5 0.052 1 0.037 2 −0.256 0 0.040 4 0.036 5 −0.307 9 0.029 0 0.036 2
    2.50 −0.185 6 0.052 2 0.035 3 −0.181 3 0.063 7 0.038 1 −0.214 6 0.053 0 0.038 4 −0.267 9 0.040 9 0.038 7
    3.00 −0.144 7 0.062 9 0.035 8 −0.139 1 0.073 8 0.038 1 −0.171 9 0.064 0 0.039 1 −0.223 6 0.052 3 0.040 3
    3.50 −0.103 8 0.072 8 0.035 9 −0.096 2 0.082 6 0.037 6 −0.128 3 0.073 7 0.039 1 −0.176 3 0.063 2 0.041 1
    4.00 −0.063 1 0.082 0 0.035 6 −0.052 9 0.090 4 0.036 6 −0.084 1 0.082 2 0.038 4 −0.126 9 0.073 8 0.041 3
    4.50 −0.022 6 0.090 6 0.035 1 −0.009 2 0.097 4 0.035 2 −0.039 6 0.089 8 0.037 3 −0.075 9 0.084 0 0.041 1
    5.00 0.017 7 0.098 7 0.034 4 0.034 6 0.103 8 0.033 6 0.005 0 0.096 7 0.035 8 −0.023 8 0.093 9 0.040 6
    下载: 导出CSV

    表  3   阻尼修正系数模型的总残差标准差${\sigma _T} $

    Table  3   Total standard deviations ${\sigma _T} $ of DMF model

    T/sσT
    ζ=1%ζ=2%ζ=3%ζ=4%ζ=6%ζ=7%ζ=8%ζ=9%ζ=10%ζ=15%ζ=20%ζ=25%ζ=30%
    0.030.056 00.014 70.011 60.005 70.000 00.005 40.010 40.015 20.019 80.024 30.046 00.066 50.086 4
    0.040.242 60.146 30.084 40.039 90.030 80.055 70.079 90.094 80.110 70.167 60.204 10.229 50.248 6
    0.050.238 60.148 70.087 90.042 50.033 00.060 10.082 90.102 70.120 20.184 10.225 50.255 40.277 7
    0.060.225 00.144 40.092 90.042 70.035 80.061 40.090 20.105 60.123 70.190 90.235 10.267 00.290 8
    0.070.215 50.139 60.090 00.041 50.034 60.059 80.088 00.103 00.120 70.187 60.232 00.263 60.287 1
    0.080.206 30.141 40.085 50.039 80.033 20.057 50.084 00.099 00.115 90.178 70.220 10.250 30.273 1
    0.090.200 40.136 40.082 70.038 50.030 80.056 20.082 30.096 20.112 70.174 60.215 70.245 10.266 9
    0.100.192 70.132 40.080 70.037 30.029 50.053 70.078 70.097 70.107 80.165 90.205 10.233 30.254 2
    0.120.188 50.122 90.077 80.034 50.030 50.055 60.076 60.094 80.105 70.160 90.197 30.223 80.243 6
    0.140.189 90.123 00.077 20.035 70.029 70.053 70.073 40.090 30.104 60.157 00.184 40.208 30.227 0
    0.150.188 80.122 10.076 80.033 10.029 40.053 40.069 30.090 80.105 90.159 40.194 30.208 60.227 8
    0.160.190 80.122 60.077 60.033 90.030 10.054 40.074 80.092 20.107 10.161 30.196 20.210 30.230 1
    0.180.191 80.123 90.074 00.035 20.029 00.052 60.072 00.088 50.102 90.155 70.190 80.207 50.228 1
    0.200.191 20.123 50.076 80.035 70.029 70.053 90.070 90.090 90.105 60.159 20.194 60.212 30.233 3
    0.250.191 70.124 30.077 00.035 50.029 50.053 30.069 80.085 90.104 50.150 00.184 40.211 70.235 5
    0.300.195 60.125 80.075 40.035 90.029 80.053 50.073 10.089 70.104 20.152 30.189 10.219 40.246 6
    0.350.191 20.129 80.077 50.034 00.029 50.053 40.070 00.090 90.106 40.163 80.195 20.227 40.256 7
    0.400.195 00.131 80.078 40.033 90.030 10.051 60.070 90.093 20.108 90.159 60.201 90.238 10.270 9
    0.450.198 70.128 20.077 90.035 80.029 80.054 40.072 80.089 90.108 60.163 80.208 50.247 50.283 4
    0.500.200 20.127 60.079 80.036 70.030 70.056 00.077 10.095 40.111 50.168 60.216 10.257 70.296 3
    0.600.199 60.128 40.077 50.037 70.030 10.054 90.076 10.097 80.111 40.177 90.231 70.278 70.321 8
    0.700.204 60.131 80.083 30.036 70.032 30.056 40.081 90.097 90.115 50.187 30.246 80.299 60.347 5
    0.800.208 80.133 90.084 60.037 00.033 20.058 00.084 90.100 90.119 30.196 40.260 30.316 30.367 4
    0.900.207 70.132 60.085 00.036 90.033 40.057 80.086 00.102 10.121 30.202 30.270 00.329 00.382 3
    1.000.211 50.134 70.086 10.039 80.031 80.058 90.083 20.104 90.125 00.210 30.281 60.343 50.398 6
    1.250.212 40.139 30.084 30.041 00.033 80.063 00.088 80.112 60.134 90.230 70.309 60.377 60.436 5
    1.500.216 50.143 50.087 80.041 00.036 10.067 90.096 30.122 60.147 10.252 20.340 20.413 00.475 9
    2.000.226 10.153 80.095 20.045 10.040 40.076 70.109 00.139 10.167 80.290 50.389 20.470 30.536 1
    2.500.231 10.160 70.100 60.048 00.043 90.083 50.119 70.153 30.185 10.321 30.426 20.510 20.576 5
    3.000.237 00.166 70.105 60.050 80.046 70.089 10.128 20.164 50.198 30.341 70.450 80.533 90.598 3
    3.500.245 70.175 60.112 10.054 30.050 20.096 00.137 50.176 20.212 80.363 00.473 30.556 30.619 1
    4.000.248 40.179 30.115 30.055 50.051 50.098 90.142 60.183 20.220 50.372 70.481 90.561 40.621 2
    4.500.258 30.187 30.120 40.058 40.054 00.103 50.149 10.191 10.229 90.385 10.495 00.573 20.630 5
    5.000.264 90.194 20.126 40.061 30.056 70.108 00.154 90.197 50.237 10.391 70.498 40.573 20.627 1
    下载: 导出CSV

    表  4   阻尼修正系数模型的事件内残差标准差σ

    Table  4   Within-event standard deviation σ of DMF model

    T/sσ
    ζ=1%ζ=2%ζ=3%ζ=4%ζ=6%ζ=7%ζ=8%ζ=9%ζ=10%ζ=15%ζ=20%ζ=25%ζ=30%
    0.030.017 80.013 80.009 70.005 10.000 00.004 90.009 40.013 70.017 60.021 30.037 90.051 10.061 9
    0.040.221 00.134 70.078 60.035 30.028 80.051 80.071 20.088 00.102 60.154 90.188 30.211 50.228 8
    0.050.222 30.140 00.083 10.037 90.031 00.056 30.077 60.096 10.112 20.171 20.209 10.236 10.256 0
    0.060.213 50.137 80.083 20.038 40.032 30.058 50.080 80.100 10.117 00.178 80.218 80.247 10.268 1
    0.070.206 40.134 00.081 10.037 40.031 20.057 00.078 60.097 30.113 70.174 80.214 50.242 40.263 1
    0.080.199 10.129 50.078 40.036 40.030 40.055 00.075 80.093 80.109 30.165 90.202 60.229 20.249 4
    0.090.195 30.126 80.076 60.035 50.029 90.054 40.074 80.092 40.107 60.163 70.200 80.227 10.246 8
    0.100.186 10.121 20.073 60.034 10.028 50.051 80.071 40.088 40.103 10.157 00.193 10.218 90.238 2
    0.120.183 30.119 80.072 40.033 50.028 20.051 30.070 70.087 40.101 80.154 20.188 50.213 60.232 3
    0.140.182 70.119 00.071 60.033 20.027 60.050 00.068 70.084 60.098 20.147 60.179 50.202 20.219 6
    0.150.181 40.117 50.070 30.032 20.027 00.049 10.067 50.083 20.097 00.146 60.178 90.202 10.220 1
    0.160.184 50.118 70.071 90.033 20.027 60.050 00.068 80.084 80.098 50.148 40.180 60.204 10.222 8
    0.180.185 30.120 00.072 30.033 10.027 30.049 40.067 50.082 70.096 10.144 70.177 10.201 10.220 6
    0.200.184 50.119 50.071 50.033 20.027 8−0.050 50.069 20.085 10.098 80.148 50.181 40.206 00.225 5
    0.250.184 00.118 80.071 40.032 90.027 30.049 30.067 80.083 40.096 90.144 50.176 50.201 10.221 7
    0.300.188 10.120 80.072 90.033 50.027 9−0.050 20.068 80.084 70.098 30.147 60.181 70.208 70.231 9
    0.350.185 60.119 70.072 10.033 30.027 70.050 10.068 70.085 00.099 20.151 90.188 50.217 70.242 9
    0.400.188 70.120 70.072 30.033 20.027 9−0.050 60.069 50.085 80.100 10.154 80.194 00.226 40.254 2
    0.450.192 20.123 60.073 60.033 70.028 30.051 40.070 80.087 30.101 80.156 90.197 70.231 80.261 7
    0.500.193 40.123 40.074 50.034 30.028 60.052 20.071 90.088 80.103 60.160 30.202 00.237 10.268 4
    0.600.191 40.122 70.074 20.034 30.029 00.052 80.072 90.090 40.105 90.165 70.211 60.250 00.283 3
    0.700.195 40.125 90.075 50.035 10.029 50.053 80.074 50.092 40.108 50.171 50.220 60.262 20.297 4
    0.800.199 80.128 10.076 80.035 50.030 10.054 70.075 60.093 80.110 20.176 30.228 30.271 80.308 7
    0.900.198 20.127 10.076 40.035 40.029 90.054 90.076 50.095 70.113 00.182 00.236 10.280 80.318 7
    1.000.199 60.127 00.075 80.035 00.029 70.054 80.076 80.096 20.113 90.185 80.242 10.287 90.326 1
    1.250.201 30.130 10.078 40.036 50.031 30.058 00.081 20.102 10.121 50.199 90.259 80.307 20.346 0
    1.500.201 90.131 70.080 00.037 20.032 40.060 10.084 60.106 50.126 40.208 10.271 40.321 30.361 7
    2.000.196 50.130 10.080 40.038 10.033 70.063 10.088 90.112 20.133 50.219 60.284 90.336 00.376 7
    2.500.195 70.132 50.082 40.039 20.035 00.065 40.092 50.117 20.139 90.232 20.299 50.351 30.390 6
    3.000.190 20.130 30.082 10.039 50.035 40.066 60.094 40.119 60.142 40.234 60.302 10.352 00.390 3
    3.500.194 90.135 90.086 00.041 20.036 90.069 50.098 40.124 70.148 30.243 00.309 70.358 20.395 1
    4.000.187 00.132 20.084 80.040 80.037 00.069 80.099 20.125 70.149 50.242 60.307 10.353 00.387 1
    4.500.185 70.132 60.085 00.041 10.037 00.069 50.098 50.124 50.147 90.239 30.301 50.345 30.378 0
    5.000.189 10.135 90.087 40.042 10.037 90.070 50.099 40.125 20.148 30.237 20.296 40.337 80.368 3
    下载: 导出CSV

    表  5   阻尼修正系数模型的事件间残差标准差τ

    Table  5   Between-event standard deviation τ of DMF model

    T/sτ
    ζ=1%ζ=2%ζ=3%ζ=4%ζ=6%ζ=7%ζ=8%ζ=9%ζ=10%ζ=15%ζ=20%ζ=25%ζ=30%
    0.030.053 10.004 90.006 30.002 50.000 00.002 20.004 40.006 70.009 10.011 70.026 10.042 60.060 3
    0.040.100 10.056 90.030 90.018 60.011 00.020 50.036 20.035 30.041 50.064 00.078 60.089 10.097 1
    0.050.086 70.050 10.028 40.019 40.011 30.020 90.029 10.036 40.043 00.067 70.084 40.097 40.107 6
    0.060.071 00.043 30.041 40.018 60.015 40.018 60.040 00.033 50.040 10.066 90.086 20.101 20.112 7
    0.070.062 10.039 30.039 00.017 80.014 80.018 00.039 70.033 90.040 60.068 00.088 30.103 50.114 9
    0.080.053 80.056 80.034 00.016 00.013 30.016 70.036 10.031 70.038 30.066 30.086 00.100 50.111 4
    0.090.044 70.050 50.031 20.014 90.007 40.014 30.034 30.027 00.033 70.060 60.078 90.092 20.101 7
    0.100.050 10.053 40.033 10.015 10.007 50.014 10.033 20.041 70.031 60.053 60.069 10.080 80.088 8
    0.120.044 00.027 60.028 50.008 10.011 60.021 30.029 40.036 70.028 20.046 10.058 30.066 90.073 3
    0.140.051 80.031 10.028 70.013 00.010 90.019 50.025 90.031 50.035 80.053 50.042 10.050 20.057 5
    0.150.052 30.033 30.031 00.007 90.011 70.021 10.015 70.036 40.042 60.062 50.075 90.051 70.058 7
    0.160.048 60.030 50.029 10.006 80.012 00.021 40.029 40.036 30.042 10.063 20.076 70.050 60.057 5
    0.180.049 50.030 70.028 50.011 90.010 00.018 20.025 30.031 50.036 80.057 40.071 00.051 00.057 7
    0.200.050 00.031 00.027 90.013 00.010 40.019 00.015 30.032 00.037 20.057 20.070 40.051 60.059 5
    0.250.053 60.036 40.028 70.013 50.011 20.020 10.016 70.020 70.039 00.040 40.053 60.066 10.079 4
    0.300.053 80.035 30.028 60.013 00.010 40.018 40.024 50.029 50.034 40.037 60.052 40.067 60.084 0
    0.350.045 90.050 10.028 50.006 80.010 10.018 30.013 40.032 40.038 40.061 40.050 70.065 60.083 0
    0.400.049 30.053 10.030 30.007 20.011 30.010 00.014 10.036 30.042 80.038 60.055 70.073 70.093 7
    0.450.050 50.034 20.025 40.012 20.009 40.017 80.017 00.021 60.037 80.047 10.066 30.086 90.108 7
    0.500.051 60.032 50.028 50.013 20.011 00.020 10.027 70.034 70.041 10.052 30.076 90.101 00.125 5
    0.600.056 40.037 70.031 90.015 40.008 00.015 20.021 70.037 20.034 70.064 80.094 30.123 30.152 8
    0.700.060 50.039 10.035 20.010 80.013 20.016 80.034 00.032 20.039 60.075 30.110 60.144 90.179 7
    0.800.060 80.038 90.035 50.010 70.014 10.019 20.038 60.037 00.045 70.086 30.125 10.161 90.199 3
    0.900.062 20.037 90.037 30.010 30.014 80.018 20.039 30.035 40.044 10.088 40.131 00.171 50.211 1
    1.000.069 70.044 80.040 70.019 00.011 30.021 60.031 90.041 80.051 70.098 60.143 80.187 30.229 1
    1.250.067 60.049 90.038 50.018 60.012 80.024 50.036 00.047 50.058 70.115 00.168 30.219 50.266 2
    1.500.078 10.057 10.044 70.017 10.016 00.031 50.046 00.060 70.075 30.142 60.205 20.259 50.309 3
    2.000.111 80.082 00.050 90.024 20.022 30.043 50.063 10.082 20.101 60.190 20.265 20.329 10.381 4
    2.500.123 00.091 00.057 70.027 80.026 50.051 90.076 00.098 90.121 20.222 10.303 30.370 00.423 9
    3.000.141 40.103 90.066 40.032 00.030 40.059 10.086 80.112 90.138 00.248 50.334 60.401 40.453 5
    3.500.149 60.111 20.071 80.035 30.034 10.066 20.096 00.124 50.152 60.269 60.357 90.425 60.476 6
    4.000.163 60.121 10.078 20.037 70.035 90.070 10.102 40.133 30.162 00.282 90.371 40.436 50.485 8
    4.500.179 50.132 30.085 30.041 40.039 30.076 70.111 90.145 00.176 00.301 70.392 60.457 50.504 5
    5.000.185 60.138 70.091 30.044 60.042 20.081 90.118 80.152 80.185 00.311 70.400 70.463 10.507 5
    下载: 导出CSV
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  • 收稿日期:  2020-12-02
  • 修回日期:  2021-05-25
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  • 发布日期:  2022-04-23

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