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云南兰坪县啦井村泥石流模拟预测及风险评价

赵蔓, 孙俊, 朱恺悦

赵蔓,孙俊,朱恺悦. 云南兰坪县啦井村泥石流模拟预测及风险评价[J]. 中国地质灾害与防治学报,2024,35(5): 110-119. DOI: 10.16031/j.cnki.issn.1003-8035.202405025
引用本文: 赵蔓,孙俊,朱恺悦. 云南兰坪县啦井村泥石流模拟预测及风险评价[J]. 中国地质灾害与防治学报,2024,35(5): 110-119. DOI: 10.16031/j.cnki.issn.1003-8035.202405025
ZHAO Man,SUN Jun,ZHU Kaiyue. Simulation prediction and risk evaluation of debris flow in gullyprone ditches of Lajing Village, Lanping County, Yunnan Province, China[J]. The Chinese Journal of Geological Hazard and Control,2024,35(5): 110-119. DOI: 10.16031/j.cnki.issn.1003-8035.202405025
Citation: ZHAO Man,SUN Jun,ZHU Kaiyue. Simulation prediction and risk evaluation of debris flow in gullyprone ditches of Lajing Village, Lanping County, Yunnan Province, China[J]. The Chinese Journal of Geological Hazard and Control,2024,35(5): 110-119. DOI: 10.16031/j.cnki.issn.1003-8035.202405025

云南兰坪县啦井村泥石流模拟预测及风险评价

详细信息
    作者简介:

    赵 蔓(1986—),女,贵州黔西人,资源勘查工程专业,大学本科,工程师,主要从事地质灾害防治、水文地质、工程地质、环境地质相关研究。E-mail:306748206@qq.com

    通讯作者:

    朱恺悦(2001—),女,安徽淮北人,土木工程专业,博士研究生,主要从事地质灾害防治、岩土工程研究。E-mail:Judy0518@sjtu.edu.cn

  • 中图分类号: P642.23

Simulation prediction and risk evaluation of debris flow in gullyprone ditches of Lajing Village, Lanping County, Yunnan Province, China

  • 摘要:

    兰坪县位于云南省西北部,地质环境不良,近年来该地区受降雨影响泥石流灾害频发,但是该地区缺乏较为精确的灾害风险评价。为对该地区泥石流灾害进行防范预警,文章应用FLO-2D软件对兰坪县啦井村1#典型泥石流河灾害进行动力过程反演分析,基于反演所得模拟参数对2#沟在20年、50年和100年三种降雨重现期工况进行预测分析和灾害风险评价。结果表明:啦井村2#沟道泥石流淤积深度和最大流速随降雨强度的增大呈增加趋势,极端降雨条件下沟道底部淤积深度将超过2.5 m,流通区最大流速将大于5 m/s,泥石流携带更多的松散物于堆积区堆积,易造成安全隐患;啦井村2#沟中高风险区主要分布在沟道中流速泥深较大、沟道周围民房较为集中位置以及泥石流堆积区域。研究结果可为该地区防灾减灾工程与泥石流早期预警等研究提供一定参考。

    Abstract:

    Lanping County, located in the northwestern part of Yunnan Province, is characterized by unfavorable geological conditions. In recent years, debris flow disasters have frequently occurred in this area due to the influence of rainfall, yet there is a lack of accurate disaster risk evaluations. To enhance early warning preparedness for debris flow disasters in the region, the FLO-2D model was employed to perform an inverse analysis of a historical debris flow event in Lajing Village, Lanping County. Based on the parameters obtained from this analysis, predictions of the dynamic characteristics and risk assessments were conducted for another debris flow-prone gully under three rainfall recurrence period conditions: 20, 50 and 100 years. The results indicate that in Gully No. 2 of Lajing Village, the siltation depth and maximum flow velocity of debris flow increase with the intensification of rainfall. Under extreme rainfall conditions, the siltation depth at the trench bottom is expected to exceed 2.5 m, and the maximum flow velocity in the transportation zone may exceed 5 m/s, leading to the accumulation of more loose materials in the deposition area and creating significant safety hazards. The high-risk zones in gully No. 2 are primarily located in areas with high flow velocity and mud depth, around densely populated residential areas near the gully, and within the debris flow accumulation zone. The findings of this study provide valuable references for disaster prevention and mitigation engineering, as well as for early warning systems in the region.

  • 受全球变暖和夏季气温升高影响,多年冻土斜坡活动层融化导致大量水分汇集在冻融交界面,抗剪强度快速下降,活动层沿多年冻土层滑动[1],诱发的浅层冻土滑坡广泛分布于加拿大北极地区[2-4]、美国阿拉斯加北部[5]和中国青藏高原[6]等不连续多年冻土地区,破坏生态环境、制约社会经济发展。因此,研究气温变化对浅层冻土滑坡的影响,对相应灾害的防治工作具有指导意义。

    通过现场调查和野外勘察等手段,现有研究证实了浅层冻土滑坡与气温变化具有密切关联。通过现场调查,Huscroft等[2]认为全球变暖导致森林大火、快速融雪和强降雨等极端事件的概率增加,造成加拿大育空地区浅层冻土滑坡频发。Lewkowicz等[3]的现场调查数据表明1969年以来埃尔斯米尔岛气温呈升高趋势,最大地表加热指数和解冻天数显著增长,浅层冻土滑坡发生频率从每年3~6次上升到每年14次。结合气象观测资料,Lamoureux等[4]得出2007年7月梅尔维尔岛的极端高温导致活动层快速融化,一周内发生浅层冻土滑坡25次。通过野外勘察,Patton等[5]提出气温升高导致冻土融化,持续高温和干旱破坏地表植被、提高坡面蒸发率,导致阿拉斯加浅层冻土滑坡频发。以上研究得出:长时间尺度下全球变暖增加了极端天气事件发生率;短时间尺度下夏季气温升高导致冻土融化、浅层冻土滑坡频发。但是浅层冻土滑坡失稳是一个复杂的水热力耦合过程,气温变化对多年冻土斜坡水热力演化的影响机制不明,本文尝试在这方面模拟讨论。

    本文通过地质灾害遥感解译总结分析了青海省浅层冻土滑坡发育分布规律和孕灾条件,针对青海省具有发生浅层冻土滑坡隐患的斜坡,基于有限元软件COMSOL Multiphysics建立多年冻土斜坡水热力耦合模型,考虑全球变暖因素模拟了2020—2024年气温变化条件下多年冻土斜坡水热力复杂演化的过程,从而揭示气温变化这一单一因素对浅层冻土滑坡失稳的影响。研究结果对认识浅层冻土滑坡失稳机制和该类地质灾害的防灾减灾提供了理论依据和科学指导。

    青海省内多年冻土区面积3.57×104 km2,占青海省总面积的50%,受气候变化和人类活动影响,当地多年冻土稳定性下降,浅层冻土滑坡灾害频发。基于多源遥感数据调查青海省多年冻土区浅层冻土滑坡灾害分布特征,共解译该类型灾害290处,祁连县、治多县和曲麻莱县为青海省浅层冻土滑坡发育的典型地区(图1),灾害发生时间集中在每年7—9月。通过遥感解译得到祁连县重点工作区浅层冻土滑坡分布如图2所示,该区域发育有54处浅层冻土滑坡,其中,遥感影像呈椭圆状的为滑动型浅层冻土滑坡,活动层呈整体向下滑动的趋势,运动距离较近;遥感影像呈长条状的为流动型浅层冻土滑坡,由于滑体含水率较高,表层土以泥流形式向下运移,运动距离较远。

    图  1  青海省不同类型冻土区浅层冻土滑坡分布
    Figure  1.  Distribution of active layer detachments in different types of permafrost regions in Qinghai Province

    基于实地调查和遥感目视解译结果统计了青海省浅层冻土滑坡灾害分布与多年冻土发育的关系如图1所示,根据年平均地温(MAGT)范围可将多年冻土稳定性分为5类[7],结果表明: 97.24%的浅层冻土滑坡分布在不稳定多年冻土区(−0.5 °C≤MAGT<0.5 °C)、过渡型多年冻土区(−1.5 °C≤MAGT<−0.5 °C)和亚稳定多年冻土区(−3.0 °C≤MAGT<−1.5 °C),仅2.76%的浅层冻土滑坡分布在稳定型多年冻土区(−5.0 °C≤MAGT<−3.0 °C)和极稳定多年冻土区(MAGT<−5.0°C),由此推断,浅层冻土滑坡分布与多年冻土发育密切相关。

    图  2  青海省祁连县重点工作区浅层冻土滑坡分布
    Figure  2.  Distribution of active layer detachments in key working area of Qilian County, Qinghai Province

    大量研究表明气候变化是诱发浅层冻土滑坡的主要外部因素[2-5]。近年来青海省最高线性增温趋势达0.09 °C/a,远超全球平均水平[6-8],气温变化呈正弦函数形式,活动层不断经历冻融循环,土体自3—4月开始融化,8—9月融深达到最大,10—11月开始冻结[9]。青海省降水量季节分配不均,其中5—10月的降水量占全年总降水量的90%以上,7—8月降水量最大[10]。可以得出,研究区活动层融化、降水量增大与浅层冻土滑坡集中发育时间基本吻合,气候变化导致地温梯度改变,破坏冻土发育的连续性和均匀程度[11],对多年冻土斜坡稳定性产生不利影响。

    为进一步揭示研究区地质环境条件对浅层冻土滑坡发育的影响,对灾害发育斜坡进行了现场调查。统计结果显示,原始斜坡的坡向集中在270°~360°和0°~45°,坡度集中在5°~20 °。已有学者指出[12],缓坡地带多年冻土埋藏位置更浅,地下冰含量更高,冻土受外部影响融化对斜坡稳定性产生严重威胁;坡表植被以高原草甸为主,覆盖率大多达到65%以上,灾害发育位置主要为斜坡坡体冲沟部位,分析认为,植被覆盖度高和汇水条件良好的斜坡表层水分充足,阴坡积雪覆盖率高,隔热作用显著,有利于多年冻土发育[13];斜坡表层主要发育第四系坡积物(Qdl),活动层土体多为细粒土和泥炭,相关研究表明[14-15],细粒冻土富含冰晶,冻融循环作用下强度不断损失,融化时有液化的可能,容易诱发浅层冻土滑坡。综上所述,地质环境条件是影响浅层冻土滑坡发育的内在因素,通过控制冻土发育对青海省多年冻土斜坡稳定性产生影响,大量力学性质不良的冻土融化是诱发浅层冻土滑坡的必要条件,浅层冻土滑坡往往发育在植被覆盖率高、活动层土颗粒较细和汇水条件良好的低缓阴坡上。

    为简化土体冻融循环中的水热力演化过程,本文做如下假设:地温变化受热传导和冰水相变控制;水分迁移由基质吸力驱动,孔隙冰对水分迁移具有阻滞作用;水热过程单向影响土体应力应变;土体的破坏行为符合摩尔-库伦屈服准则。

    冻土内水热作用互相影响,水分迁移改变土的热物理参数,土体温度变化影响水力学参数,水热耦合方程选取常用的Harlan模型[16]。变形场以平衡方程和连续性方程为基础,建立冻胀模型描述冻胀融沉对土体应力应变的影响[17]

    青海省祁连县重点调查区某天然斜坡位于汇水面阴面,位置见图2,整体坡度约12°,表层土体为粉质黏土,植被覆盖率约70%,存在发生浅层冻土滑坡的隐患,因此以该斜坡为研究对象模拟2020—2024年气温变化条件下多年冻土斜坡水热力演化过程。

    钻孔资料(图3)显示地表以下0~1.6 m为活动层,土质为粉质黏土;1.6~12.7 m为多年冻土层,土质为黏土,有大量肉眼可见冰晶;12.7 m以下为砂砾岩。根据现场调查和钻孔资料所得典型斜坡地质剖面如图4所示。

    图  3  钻孔地层信息(水)
    Figure  3.  Stratum information based on borehole
    图  4  典型斜坡地质剖面
    Figure  4.  Typical geological section of the slope

    建立二维有限元模型,采用自由三角形网格进行划分,将活动层网格细化,见图5(a),布置2条测线和8个测点获取水热力时空分布计算结果,见图5(b):斜坡中间剖面布置测线1-1′;斜坡表面布置测线2-2′;坡脚活动层不同深度布置测点A-E;与坡顶水平距离为50 m的地表布置测点F;坡顶地表布置测点G;测点F以下1.68 m处布置测点H。

    图  5  有限元计算模型
    Figure  5.  Finite element computational model

    根据相关研究给出的青海地区粉质黏土、黏土和砂砾岩的物理力学参数[18-19]以及钻孔取样进行土工试验的结果,数值模拟所需参数设置如表1所示,水和冰的相变潜热取334.5 kJ/kg,土体初始冻结温度取−0.5 °C,完全融化温度取0 °C,冻土的比热容和导热系数与土中未冻水含量的关系根据相关研究[20-21]进行设置,土骨架的比热容和导热系数分别取1.4×106 J/(m3·°C)和1.3 W/(m·°C)。

    表  1  地层物理力学参数
    Table  1.  Physical and mechanical parameters of formation
    参数活动层多年冻土层基岩层
    密度/(kg·m−3180020002500
    弹性模量/MPa40305000
    泊松比0.250.30.15
    渗透系数/(m·s−11.2×10−68×10−100
    黏聚力/kPa1235
    内摩擦角/(°)2220
    下载: 导出CSV 
    | 显示表格

    祁连当地年气温线性增长速率为0.037 °C/a[22],根据附面层理论[16]得出模型,见图5(a),上表面温度边界条件表达式:

    $$ T = 2 + \frac{{0.037t}}{{8\;760}} + 13\sin \left(\frac{{2\text{π} t}}{{8\;760}} + \frac{{17\text{π} }}{{12}}\right) $$ (1)

    式中:t——时间/h。

    左右两侧为绝热边界;下表面温度为3 °C,热通量为0.03 W/m2。水分场上表面为自由渗透边界;左右两侧和下表面均为零流量边界。变形场上表面为自由边界,左右两侧水平位移为0,下表面为固定边界。

    图6 (a)为2020年10月地温的钻孔实测值和数值模拟计算值对比图,可以看出数值模拟所得地温与现场钻孔测温结果基本一致。2020年活动层从3月25日开始融化,至8月26日融深达到最大,整个融化过程持续约5个月,符合刘广岳等[9]的水热监测结果。图6 (b)为融深最大时刻(8月26日)斜坡融化程度云图,可知最大融深位于地表以下1.61 m,与图2所示多年冻土上限位置吻合。综上所述,该模型几乎准确地反演了气温变化条件下斜坡地温分布、融深达到最大的时刻和多年冻土上限位置,体现了模型的有效性。

    图  6  模型有效性验证
    Figure  6.  Effectiveness verification of model

    图7 (a)和图7 (b)分别为2020—2024年测点E和G的总体积含水率(含水率和含冰率的总和)变化曲线,对比可知测点E总体积含水率以0.16%/a的速度升高;测点G总体积含水率以0.16%/a的速度下降;根据总体积含水率变化趋势可以将水分迁移分为4个阶段:1月1日—3月15日土体处于冻结状态,孔隙冰的阻隔作用导致水分迁移现象不明显;3月15日—7月20日孔隙冰逐渐融化,土体渗透性提高,水分迁移速率增大;7月20日—10月20日,活动层土体融化程度较高,总体积含水率变化趋势最明显,这一阶段的水分迁移量占全年总迁移量的50%;随着气温降至负温,10月20日—12月31日土体再次冻结,水分迁移速率减小。

    图  7  水分迁移规律
    Figure  7.  Water migration rules

    图7 (c)为2020—2024年8月2-2′测线上总体积含水率分布,可以得出坡顶总体积含水率逐年减小,坡脚总体积含水率逐年增大,经历4个冻融循环后坡脚土体总体积含水率比坡顶大7.4%,说明水分自坡顶向坡脚迁移;越靠近坡顶和坡脚,总体积含水率变化趋势越明显,由于水分自坡顶的补给和向坡脚的运移达到平衡,距坡顶55 m处土体总体积含水率不变。

    图8 (a)和图8 (b)分别为2月1日含冰率分布云图和8月26日融深最大时刻含水率分布云图。由图8 (a)可知2月活动层土体内的水分主要以孔隙冰的形式存在,体积含冰率约16%,多年冻土上限以下体积含冰率呈先减小后增大再减小的趋势,其中活动层以下0~0.5 m范围内土体体积含水率达到28%左右。图8 (b)为8月26日含水率分布云图,可以得出此时活动层土体融化,体积含冰率约26%,且在活动层基底以下高含冰层有一定融化,出现厚度约15 cm、体积含水率达到40%的富水层。

    图  8  斜坡含水率和含冰率分布规律
    Figure  8.  Water content and ice content distribution law of slope

    图9为2020—2024年8月26日1-1'测线地温随深度的分布,融深最大时0 °C地温所在深度可视作多年冻土上限位置,由此得出2020年多年冻土上限位于地表以下161 cm,2024年多年冻土上限位于地表以下171.4 cm,下移10.4 cm,平均退化速率约2.6 cm/a;多年冻土上限下移量逐年增大,下移量的增幅逐年减小,说明气温升高对多年冻土退化的影响程度随深度的增加逐渐减弱。

    图  9  2020—2024年8月26日1-1'测线地温随深度分布
    Figure  9.  Depth distribution of ground temperature of 1-1'section on August 26 from 2020—2024

    图10 (a)和图10 (b)分别为2020—2024年8月26日测点H处地温和体积含水率,可以得出:2020—2024年测点H地温呈升高趋势,升高速率逐年降低,平均升高速率为0.017 °C/a;2020—2022年该处土体仍处于冻结状态,由于土体温度升高导致体积含水率增大3%;2023年多年冻土上限将退化至测点H以下,土体完全融化导致含水率突增,较2022年增大11%;2024年含水率相比2023年未发生明显变化,说明气温升高对含水率的影响随着土体完全融化而消失。

    图  10  2020—2024年测点H地温和体积含水率
    Figure  10.  Ground temperature and volumetric water content of monitoring point H on 2020—2024

    图11 (a)和图11 (b)分别为2020—2024年坡脚不同深度5个测点的水平位移和竖直位移变化,可以得出:位移随深度的增加逐渐减小,冻胀融沉循环仅发生在活动层;以测点E为例,土体自10月20日起发生冻胀,1月15日冻胀量达到最大,水平冻胀位移为2.5 cm,竖直冻胀位移为8.0 cm;土体随着气温的回升开始融沉,6月26日融沉量最大,产生1.0 cm的水平融沉位移和6.0 cm的竖直融沉位移。图11 (c)为测点E冻胀融沉位移示意图,E-E1为冻胀变形路径,E1-E2为融沉回退路径,测点E处的土颗粒经历一次冻胀融沉后运动至E2处,产生1.5 cm的水平净位移和2.0 cm的垂直净位移,总位移2.5 cm,与Harris等[22]通过位移监测得出的1.6 cm/a的坡表变形量相近。

    图  11  冻胀融沉位移变化规律
    Figure  11.  Displacement variation of frost heaving and thaw settlement

    图12 (a)为2020—2024年测点E、F、G的塑性应变变化曲线,可以得出塑性应变在每年的冻胀融沉期间发展,4—10月坡表土体完全融化期间塑性应变不发生变化;塑性应变随时间不断增大,且坡脚E点塑性应变增大的速率最大,坡顶G点最小。图12(b)为2024年12月测线2-2’塑性应变曲线,可见塑性应变至坡顶至坡脚逐渐增大,对比图7 (c)可以得出塑性应变的分布与体积含水率的分布有关,5年间坡脚E点产生的塑性应变比坡顶G点大20.98%。

    图  12  塑性应变变化规律
    Figure  12.  Variation of plastic strain

    计算结果显示,随着土体融化程度增大,水分自坡顶至坡脚迁移的现象愈发显著,根据总体积含水率的变化趋势将水分迁移过程分为四个阶段,其中5—10月水分迁移现象尤为显著,此时青海省处于雨季,降雨量占全年的80%以上[11],雨水大量入渗导致融土迅速饱和,土体应力状态改变[23]、孔隙水压力增加,对斜坡稳定性产生威胁。

    已有研究表明土体孔隙冰含量上升导致基质吸力和胶结力增大[24],2月活动层土体含冰量达到18%,此时土体黏聚力较大,冻结期斜坡稳定良好;通过冰分离现象、大气水和融水下渗、冻结初期双向冻结[25],多年冻土上限以下出现0.5 m厚高含冰量层,且含冰量有继续增大的可能[26],8月26日融深达到最大,高含冰量层有一定的融化,产生约15 cm厚的富水层,细粒土排水能力较差,孔隙水压力难以消散[17],发生浅层冻土滑坡的概率增大。

    在当地气温以0.37 °C/a的速度升高的情况下,斜坡多年冻土处于升温退化状态,2020—2024年多年冻土上限将下移10.4 cm,活动层厚度不断增大,夏季上覆融化的土体提供更大的下滑力。随着最大融深的增大,活动层以下的高含冰层有进一步融化的可能,冻融交界面含水量大幅度升高,孔隙水压难以消散、抗剪强度大幅下降,水分聚集产生的润滑作用导致抗滑力下降[6],活动层沿多年冻土层下滑的风险大大上升。

    10月—次年4月活动层土体发生冻胀融沉,坡表土体产生2.5 cm/a的位移,由此产生的塑性应变不断增大,表明土颗粒间胶结作用随冻融循环次数的增加逐渐减弱,抗剪强度有损失至残余值的可能[23],塑性应变从坡顶至坡脚逐渐增大,5a间坡脚产生的塑性应变比坡顶大20.98%,土体力学性质劣化显著,且坡脚处容易产生水分聚集,形成薄弱带,进而诱发牵引式浅层冻土滑坡。

    基于地质灾害遥感解译总结了青海省浅层冻土滑坡分布特征和孕灾条件,采用数值模拟方法考虑当地气候变暖模拟了2020—2024年气温变化条件下多年冻土斜坡水热力演化,探讨了气温变化对浅层冻土滑坡失稳的影响,得出以下结论:

    (1) 气温变化影响冻结程度,改变土体渗透性,从而控制水分迁移。根据总含水率变化趋势可将水分迁移分为四个阶段,当活动层融化后水分自坡顶至坡脚的迁移现象最显著。

    (2) 气温变化影响活动层未冻水的含量,导致土体力学性质存在季节性差异,夏季活动层下的高含冰量层融化产生15 cm厚富水层,冻融交界面孔隙水压大幅上升,且气候变暖导致多年冻土上限以2.6 cm/a的速度下移,富水层厚度有继续增大的可能,诱发浅层冻土滑坡的风险增加。

    (3) 气温周期性变化导致土体水分固液相态不断转换,冰水体积变化导致活动层经历冻胀融沉循环,斜坡表面每年产生数厘米膨胀变形和顺坡位移,表明土体抗剪强度逐渐损失,坡脚土体力学性质劣化程度最明显。

  • 图  1   研究区概况

    Figure  1.   Overview of the study area

    图  2   啦井村1#沟泥石流模拟结果

    Figure  2.   Simulation results of debris flow in gully No. 1, Lajing Village

    图  3   不同降雨工况下啦井村2#沟泥石流淤积深度分布

    Figure  3.   Debris flow deposition depth distribution in gully No. 2, Lajin Village, under different rainfall conditions

    图  4   不同降雨工况下啦井村2#沟泥石流流速分布

    Figure  4.   Flow velocity distribution of debris flow in gully No. 2, Lajing Village, under different rainfall conditions

    图  5   风险评价结果

    Figure  5.   Risk evaluation results

    表  1   沟道现场调查数据

    Table  1   The site investigation data of each ditch

    参数流域面积/km2
    (1#/2#)
    沟长/ km
    (1#/2#)
    平均坡降/‰
    (1#/2#)
    取值0.96/0.992.11/2.08301/432
    下载: 导出CSV

    表  2   流变系数

    Table  2   Rheological coefficient

    参数 α1 β1 α2 β2
    取值 0.811 13.72 0.00462 11.24
    下载: 导出CSV

    表  3   FLO-2D手册建议的层流阻力系数值

    Table  3   Recommended laminar flow resistance coefficient values from the FLO-2D manual

    地面条件 K值范围
    级配土 90~400
    被侵蚀黏土 100~500
    稀疏植被 10004000
    矮草原 300010000
    下载: 导出CSV

    表  4   FLO-2D数值模型主要物理力学参数

    Table  4   Main physical and mechanical parameters of the FLO-2D numerical model

    参数 曼宁
    系数
    摩擦
    系数
    泥石流重度
    /(t·m−3
    黏滞系数
    (1#/2#)
    屈服应力kPa
    /(1#/2#)
    取值 0.07 2280 1.65 3644.13/
    1860.49
    4.53/2.62
    下载: 导出CSV

    表  5   泥石流强度影响划分表[26]

    Table  5   Classification table of debris flow intensity impacts

    泥石流强度 泥深/m 关系 泥深与最大流速乘积/(m2·s−1
    H≥2.5 OR VH≥2.5
    0.5≤H<2.5 AND 0.5≤VH<2.5
    0<H<0.5 AND VH<0.5
    下载: 导出CSV

    表  6   易损性计算公式

    Table  6   Vulnerability calculation formula

    易损性指标 社会易损性 建筑易损性 交通易损性 经济易损性
    表达式 $F = \displaystyle\sum_{{{i}} = 1}^n {{F_{i,j}}} $
    F为社会易损性;Fi,j为主级指标
    权重标准化的值乘以次级
    指标权重标准化的值
    $M = \displaystyle\sum_{{{i}} = 1}^n {{A_{i,j}}} $
    M为物质易损性值(建筑/交通);
    Ai,j为承灾体主级指标权重标准化
    的值乘以次级指标权重标准化的值
    $J = G/N$
    J为经济易损性,无量纲,G为区域内每个
    承灾体家庭年收入(万元);
    N为区域人均年收入(万元)
    下载: 导出CSV
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  • 收稿日期:  2024-05-19
  • 修回日期:  2024-08-10
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