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四川巴中红层滑坡降雨阈值克里金插值法研究

张群, 肖智林, 马志刚, 金圣杰, 李俊峰, 许钟元, 曾普, 张小琼

张群,肖智林,马志刚,等. 四川巴中红层滑坡降雨阈值克里金插值法研究[J]. 中国地质灾害与防治学报,2024,35(4): 36-44. DOI: 10.16031/j.cnki.issn.1003-8035.202403008
引用本文: 张群,肖智林,马志刚,等. 四川巴中红层滑坡降雨阈值克里金插值法研究[J]. 中国地质灾害与防治学报,2024,35(4): 36-44. DOI: 10.16031/j.cnki.issn.1003-8035.202403008
ZHANG Qun,XIAO Zhilin,MA Zhigang,et al. Study on the rainfall threshold of red strata landslides in Bazhong, Sichuan using Kriging interpolation method[J]. The Chinese Journal of Geological Hazard and Control,2024,35(4): 36-44. DOI: 10.16031/j.cnki.issn.1003-8035.202403008
Citation: ZHANG Qun,XIAO Zhilin,MA Zhigang,et al. Study on the rainfall threshold of red strata landslides in Bazhong, Sichuan using Kriging interpolation method[J]. The Chinese Journal of Geological Hazard and Control,2024,35(4): 36-44. DOI: 10.16031/j.cnki.issn.1003-8035.202403008

四川巴中红层滑坡降雨阈值克里金插值法研究

基金项目: 雅安市市级科研项目(N5118012023000092)
详细信息
    作者简介:

    张 群(1988—),女,四川内江人,硕士,高级工程师,主要从事地质灾害防治研究工作。E-mail:782961232@qq.com

    通讯作者:

    肖智林(1970—),男,四川广安人,学士,高级工程师,主要从事地质灾害防治相关工作。E-mail:xfyxzl@163.com

  • 中图分类号: P642.22

Study on the rainfall threshold of red strata landslides in Bazhong, Sichuan using Kriging interpolation method

  • 摘要:

    降雨阈值是目前最常用的降雨型滑坡预警判据之一,然而目前经验性降雨阈值主要是针对滑坡的区域性预警,对于该区域内随空间变化的单个滑坡的降雨阈值还缺乏探讨。基于巴中2014—2021年降雨型滑坡历史数据以及小时降雨数据,采用克里金插值法,提取2014—2020年各滑坡灾害的四类致灾短期雨量(1 h、12 h、24 h、72 h)和相应的长期雨量(滑坡发生前7 d),由此分成4类阈值模型进行分析,确定每组模型长期和短期致灾雨量阈值分布情况,并用2021年滑坡灾害数据验证所得的降雨阈值。研究结果显示4类阈值模型的预测准确率分布在40%~65%,表明4类阈值都具有较好的应用前景。同时,预测准确率随短期降雨时长增加而提高,由72 h至7 d致灾雨量数据所计算的降雨阈值预测准确率最高,为62%;而1 h至7 d模型计算的降雨阈值预测准确率最低,为46%。基于模型的最高预测准确率,研究计算得到4类模型的最佳短期与长期致灾雨量的划分比例,从而定量划分了短期降雨致灾滑坡和长期降雨致灾滑坡。研究通过对致灾雨量空间分布的计算,可提取滑坡隐患点位上的降雨阈值,实现了区域一点一阈值的目标,丰富了现有降雨阈值计算模型。

    Abstract:

    The Rainfall thresholds are among the most commonly used criteria for predicting rainfall-induced landslides. However, existing empirical rainfall thresholds mainly focused on regional landslide warnings, lacking consideration for the spatial variability of rainfall thresholds for individual landslides within the region. This study uses historical rainfall-induced landslide data and hourly rainfall data from Bazhong City (2014 – 2021) to employ Kriging interpolation methods. It extracts four types of short-term rainfall (1 hour, 12 hours, 24 hours, 72 hours) and their corresponding long-term rainfall (7 days before the landslide occurrence). In these four threshold models, the distribution of long-term and short-term rainfall thresholds in each group is calculated and then validated using landslide disaster data from 2021. The research results indicate that the prediction accuracy of the four threshold models ranges from 40% to 65%, suggesting good potential for practical application. Additionally, the prediction accuracy improves with the increase in the duration of short-term rainfall. The prediction accuracy for rainfall thresholds calculated from the 72-hour-7-day model is highest, reaching 62%, while the 1-hour-7-day model achieves 46%. Based on the highest prediction accuracy of these models, the study calculates the optimal ratios for short-term and long-term disaster-causing rainfall for four types of models. This leads to a quantitative division between short-term rainfall-induced landslides and long-term rainfall-induced landslides. By calculating the spatial distribution of disaster-causing rainfall, the study extracts rainfall thresholds at potential landslide locations, achieving the goal of one threshold per site in the region and enhancing existing models for calculating rainfall thresholds.

  • 四川省作为典型的地质灾害多发易发区和生态环境脆弱区,是全国地质灾害最为严重的省份之一[12],其中滑坡是最常见的地质灾害之一,且大多数滑坡出现在暴雨多发区和强降雨地区[35]。众多学者研究认为降雨是导致滑坡发生的主要诱因之一,随着降雨入渗,滑带土的含水率增加,土体失稳发生滑坡甚至引发一系列链式灾害,尤其在土壤含水率由极低逐渐上升的过程中岩土体失稳特征表现更为显著[610]。气象预报可以较为准确地预测未来几天内滑坡发生区域的降雨量,因此常用来推测滑坡发生的可能性。目前,降雨阈值已成为最简便有效的滑坡预警判据之一,并在大量地区得到了应用[1114]

    降雨阈值是斜坡发生破坏的临界降雨值,其上部界限是坡体已发生了形变,下部界限是斜坡还未发生形变,但濒临破坏边缘[1517]。国内外的众多学者采用多种方法对降雨阈值进行了深入研究,主要包括物理预报方法和经验统计方法。物理预报法是以地貌、地质和水文特征等作为关键参数,通过数值模型或物理模型来分析滑坡发生的动力机制从而确定临界降雨值[18]。然而这些关键参数在大范围内一般较难精准获取,因此物理预报法常被用来分析小区域或单个滑坡的预警。经验统计方法则可用于大尺度区域的预警预报工作,它主要是以降雨为关键指标,通过统计分析滑坡发生时的降雨量,获得滑坡启动的临界降雨值。Baum等[19]提出目前常用的4种降雨阈值:① 降雨强度-历时阈值(I-D),② 累计降雨量-历时阈值(E-D),③ 累计降雨量-降雨强度阈值(E-I),④ 基于降雨诱发滑坡的总降雨量阈值。

    经验统计模型被广泛应用于全球各个国家和多种尺度[2022]。Hong等[23]通过搜集不同国家的历史滑坡和降雨数据,建立了全球降雨型滑坡临界雨量;Guzzetti等[2425]分析研究了欧洲中部和南部的滑坡降雨阈值,认为地形地貌以及气候模式对滑坡降雨阈值都有较大影响。Segoni等[26]研究认为选择正确的降雨参数来定义不同类型滑坡的阈值,对滑坡有更准确的预报。Rosi等[27]将I-D模型运用于斯洛文尼亚地区滑坡预警,并基于阈值分级方案建立了国家尺度的滑坡预警平台系统。

    近年来,国内外学者采用新技术新方法在很大程度上提高了经验性降雨阈值的准确率。如Leonarduzzi等[28]通过获取高精度降雨数据,并应用黑箱模型来研究瑞士地区滑坡降雨阈值;陈静静等[29]采用降雨数据统计插值手段计算湖南省滑坡阈值;黄发明等[30]采用逻辑回归方法优化降雨阈值建模;Steger等[31] 、Vessia等[32]采用地质统计方法耦合地质及地貌数据,建立了意大利地区滑坡的降雨阈值模型。

    目前大多数学者主要是在不考虑地质环境条件下,通过经验统计方法来获取滑坡区域性降雨阈值,这类方法对于区域内单个滑坡预测准确性较低。另外,滑坡可能由短期强降雨引起也可能与长期累计降雨相关,前人研究多是通过经验定性区分滑坡是短期降雨致灾还是长期降雨致灾[21, 33],其准确性有待考量。因此本次研究主要通过分析大量的降雨数据,采用克里金插值法计算每个滑坡的降雨阈值,并将预测阈值与滑坡事件发生的实际降雨量进行比较来评估该方法的有效性。同时通过试算不同短期-长期致灾雨量的比例,选择预测准确率最高的比例作为划分界限,将滑坡灾害分为短期和长期降雨触发事件。

    巴中市地处四川盆地北部边缘,总面积约1.2×104 km2,海拔从南部的200 m上升到北部的2600 m,见图1(a)。巴中市位于大巴山、秦岭和四川盆地的过渡地带,气候类型为典型的亚热带季风性湿润气候,主要特点为四季分明、气候温和、降水充足。根据气象资料表明巴中市多年平均降雨量为1020 mm左右,北部比南部更潮湿,见图1(b)。大部分地区年降水量超过900 mm,为滑坡的发生提供了有利的降雨条件。巴中地质构造以宽缓的隔挡式褶皱为主,地貌主要为单面山、似单面山和桌状山。该区域斜坡多顺岩层层面发育,倾向与岩层倾向基本一致,坡度普遍较缓,分布在10°~30°。斜坡表面多被开垦为耕地,呈现阶梯状坡型。主要发育地层岩性为三叠系—侏罗系砂泥岩互层,是典型的川东红层岩体。由于其特殊的互层结构、较低的岩体强度以及较差的遇水稳定特性,坡体自稳能力差。降雨后岩土介质饱和,裂缝增多增大,岩土体内部软化效应加剧,极易形成贯通软弱层面,诱发各类滑坡、崩塌灾害[3436]。因此,降雨对研究区内的滑坡孕灾成灾起着关键性作用,建立降雨阈值模型对该类型红层滑坡的防控具有重要意义[37]

    图  1  巴中市海拔(DEM)、年均降雨量和滑坡信息
    Figure  1.  The elevation, average annual precipitation and landslide information of Bazhong

    本次研究所使用的雨量数据来自四川省气象局。研究区共计233个气象站,提供了2014—2021年8年间的每小时降雨数据。气象站在研究区内分布较均匀,有利于本次研究,见图1(b)。本次研究历史滑坡数据来自四川省国土空间生态修复与地质灾害防治研究院,共提供了2014—2021年1119次滑坡事件,每个滑坡事件包括发生的日期、位置、规模、类型和诱发因素等信息。

    本次研究对象为降雨型滑坡,因此对滑坡数据进行筛选,剔除诱发因素与降雨无关的所有滑坡事件,剩余1011起降雨型滑坡,见图1(c)。根据图2得知6—9月的汛期时间累积了大量的降雨,其中93%的滑坡都在这段时间内引发,说明这部分滑坡的发生与降雨密切相关。之后再根据各滑坡发生时的雨量数据,将7 d内降雨量≤10 mm和缺乏足够降雨数据的滑坡予以剔除,最后剩余911次滑坡灾害事件参与后续计算。

    图  2  不同月份滑坡数量与降水量之间的关系
    Figure  2.  The relationship between the number of landslides and precipitation by month

    通过对四川省巴中市2014—2021年滑坡调查研究和统计分析,研究区降雨型滑坡具有以下特征。

    (1)滑坡规模小,多以中、小型为主,且90%以上为小型滑坡。

    (2)滑坡类型主要为土质滑坡,且坡体厚度集中在5 m以内。

    (3)滑坡集中发育在砂泥岩互层中,占90%以上。

    (4)滑坡主要集中分布在高程500~1000 m、坡度10°~30°的单斜构造顺向坡中,该类坡体具有较好的汇水条件,且长期受人类工程活动,在强降雨作用下极易发生灾害。

    降雨入渗土壤之后,土体孔隙水压力增加,土体抗剪强度降低,坡体下滑力增大,在连续数日的降雨入渗下,最终可能导致滑坡失稳破坏。因此,前期降雨成为定义滑坡阈值的关键参数。由于蒸散和排水过程,每次降雨事件只有部分降雨量对滑坡的发生起作用,本文引入有效降雨量Pe,计算公式为:

    Pe=i=0nkiPi (1)
    Pi=j=124Rij (2)

    式中:Pi——滑坡发生前第i天降雨量;

    Rij——滑坡发生前第i天第j小时降雨值,具体计 算公式参见式(3);

    n——滑坡发生前的天数;

    k——降雨衰减因子。

    根据前人对四川地区的研究[38],本次研究将k=0.84作为研究区的降雨衰减因子。

    滑坡灾害通常由两种降雨事件引起:长时间的低强度降雨和短时间的高强度降雨。西南地区降雨情况统计分析表明7 d是前期降雨对滑坡灾害影响的合理时间[3839]。因此,本次研究设计了一个长期降雨参数和多个短期降雨参数,将7 d有效降雨量(D7)作为长期降雨参数,短期降雨参数则包括滑坡发生前1 h降雨量(H1)、12 h降雨量(H12)、24 h降雨量(H24)和72 h有效降雨量(H72)。

    本研究通过距离加权均值的方法从雨量站提取了各滑坡发生前各个时刻的雨量数据见式(3)。

    R=p=1nwpRpp=1nwp (3)
    wp=1Dp+0.5 (4)

    式中:R——某一滑坡发生前某一天某小时降雨值;

    Rp——第p个雨量站在该时刻所记录的降雨量;

    Dp——滑坡与第p个雨量站之间的距离;

    wp——根据Dp计算的权重。

    根据2014—2020年的滑坡和降雨数据,建立了研究区的降雨阈值模型,再利用2021年的数据对模型的性能进行验证。主要阈值计算过程分为3个计算步骤(图3):

    图  3  阈值方法和验证过程的工作流程框架
    Figure  3.  Workflow and general framework for the threshold method and validation process

    (1)数据划分:根据降雨数据将所有滑坡分为短期降雨滑坡或长期降雨滑坡,并用4种类型表示:H1-D7、H12-D7、H24-D7、H72-D7。计算每个滑坡的短期降雨参数(H1、H12、H24和H72)和长期降雨参数(D7),以及每个短期参数与长期参数的比率(R1=H1/D7、R12=H12/D7、R24=H24/D7和R72=H72/D7),当滑坡的比率(R1、R12、R24和R72)大于特定系数时(RC1、RC12、RC24、RC72),认为是由短期降雨引起的滑坡,相反,则认为是由长期降雨引起的滑坡。定义这类特定系数为长短期比例系数,比例系数不是定值,而要通过循环试算最终求取最佳比例系数。

    (2)克里金插值:利用球面变差函数对研究区域内的短期降雨量和长期降雨量分别进行克里金插值,根据采样点的致灾雨量值估计未采样位置的雨量值。通过两张克里金插值图(图3),提取了2021年的滑坡数据点的短期降雨量值和长期降雨量值,并将这些雨量值作为2021年的滑坡阈值。

    (3)验证:通过克里金插值得到2021年滑坡的长期、短期降雨量阈值,将其与实际触发降雨量进行了比较。结果显示当阈值大于实际降雨量时,意味着该方法无法预测此次滑坡的发生;当阈值比实际值小很多时,可能会导致许多错误警告。因此,将预测的降雨量阈值略小于实际致灾雨量数据作为预测目标。在短期或长期条件下,当实际致灾雨量与计算阈值的比值在1~1.5倍时,则可视为一次成功的滑坡预测。在对比验证了巴中市2021年所有滑坡数据与计算值后给出相应的预测准确率(图3)。

    以上3个步骤仅为一次降雨阈值计算,由于需要确定最佳长短期比例系数,整个研究过程需进行数次重复循环试算,具体操作过程如下:

    ① 从4类阈值模型(H1-D7、H12-D7、H24-D7、H72-D7)中选取一个类,以选取H24-D7为例;

    ② 根据滑坡降雨数据关系见式(1)和式(2),计算研究区内每个滑坡的R24;

    ③ 定义RC24=0.01,根据每个滑坡的R24,按照步骤(1)将这些滑坡分为短期降雨引起的滑坡和长期降雨引起的滑坡;

    ④ 按照步骤(2)计算研究区内短期致灾降雨量和长期致灾降雨量分布图,并提取2021年的滑坡数据点的短期降雨量值和长期降雨量值;

    ⑤ 按照步骤(3)进行验证,获得整个研究区对2021年所有滑坡的预测准确率;

    ⑥ 重新定义RC24=0.02,并重复③—⑤步,计算预测准确率。以此类推计算RC24=0.01~0.99的所有准确率;

    ⑦ 对比所有准确率,选取准确率最高的RC24,定义为最佳比例系数;

    ⑧ 选取下一个阈值模型,重复②—⑦步,获取最佳比例系数。以此类推计算四类模型的最佳比例系数。

    短期与长期降雨参数比值的改变会导致短期和长期降雨模型中不同的滑坡数据分布,从而得出不同的预测准确率。图4显示四类阈值模型的滑坡预测准确率随长短期比例系数的变化规律。预测准确率在0.4~0.65,在某一比例系数下准确率可达到最大值,定义该比例系数为最佳比例系数。对比四类阈值模型,研究发现短期降雨参数时间越长,预测的准确率越高。其中,H72-D7方法的预测率最高,当比例系数位于0.64~0.68时,约62%的滑坡能被成功预测;H24-D7和H12-D7两种方法的最高预测率比较接近,当比例系数位于0.23~0.26和0.17~0.20时,分别获得58%和55%的最高预测率;H1-D7方法的预测性能相对较差,最佳比例系数为0.07,成功预测了46%的滑坡灾害(图4)。

    图  4  四类短期-长期降雨参数的比例系数及预测率
    Figure  4.  The relationship between prediction rates and the ratio coefficient of four short-term and long-term rainfall methods

    滑坡数据和阈值的分布因模型采用不同的短期致灾雨量而有所不同,图5显示在最佳长短期比例系数下四类模型的致灾雨量分布情况。短期降雨插值显示北部地区的阈值较高,表明由降雨因素导致的滑坡易发性较低见图5(c)(e)(g),而南部低阈值则意味着短期强降雨导致滑坡易发性更高,特别是在巴中区、恩阳区和平昌县的某些地区,当降雨量超过10 mm/h可能会引发滑坡,见图5(a)。当7天内的降雨量超过150 mm,长期降雨插值显示的阈值分布较为均匀,通江县西北部和南江县的阈值相对较高,巴州区、恩阳区以及平昌县的阈值相对较低见图5(b)(d)(f)。3 d降雨插值显示的阈值分布与其他短期降雨量插值不同,但与长期降雨量插值相似,说明大多数的滑坡是由3 d内累计降雨引发的,见图5(g)。此外,滑坡点的分布表明恩阳区以及南江县西部的滑坡更多是由3 d或长期降雨条件引发,而巴州区以及东部地区短期降雨条件诱发的滑坡数量与长期降雨条件诱发的滑坡数量比较接近。

    图  5  巴中市阈值预测准确率最高工况下的降雨阈值及滑坡隐患点分布图
    Figure  5.  Landslide data points and threshold distribution calculated by Kriging interpolation at the best ratio coefficient in Bazhong

    基于致灾降雨阈值分布图,可依据滑坡隐患点位置提取各类型的长期和短期降雨阈值(图5),从而达到对这些隐患点进行预测的目的。

    本次计算降雨阈值的克里金插值方法,目前被广泛应用于气候和地质统计学建模。这种方法主要是基于非均质分布假设条件和实际观测值对区域数据进行分异处理,进而获取点位上的降雨阈值。对于缺乏详细地貌、地质数据的地区,该方法进一步地考虑了地质信息在空间上的差异性分布。然而,该方法未直接将地质、地貌、岩性等数据应用于降雨阈值模型,对于地形地貌、地质结构分布非常复杂的地区,这种方法任具有较大局限性。因此,未来的研究可采用协同克里金插值法将地形地貌分布、岩性分布和地质灾害分布等信息整合到统计模型中,同时致力于建立多时段的滑坡灾害预警模式,提高滑坡灾害预测预警的准确性。

    本次研究基于历史滑坡数据及前期降雨量,通过克里金插值方法,分析建立研究区降雨阈值分布图,进而提取预测滑坡隐患点阈值。在实际应用中,还需考虑天气预报准确性这一重要因素。相对于未来3 d的气象预测,天气预报对短期的预测更为准确,例如对未来一小时的降水量的预测准确率最高。而本次研究的结果表明H72-D7阈值具有最高的预测率(图4),基于此,未来的研究应将地质统计学模型和天气预报相结合进行滑坡预测,致力于提高H1-D7到H24-D7时间段的预测率。

    一般情况下,北部地区滑坡较多的原因有两个:一是北部降水量较高,见图1(b);二是北部地区山地较多,见图1(a)。然而,在南部地区可以观测到更多的滑坡,见图1(c),这很可能是由于在南部平原地区有更多的人口和人类活动,从而将滑坡预警和监测工作主要集中在这些地区,并监测到更多的滑坡数据,见图1(c),和滑坡记录。这说明在数据收集与分布中人为因素对滑坡易发性预测发挥着重要作用。因此,在滑坡预测和监测中应充分考虑人为因素,获取更多的精确数据用于数据库插值研究。

    (1)克里金插值计算的降雨阈值在预测2021年滑坡发生时表现良好,4组方法的滑坡预测准确率分布在46%~62%。

    (2)滑坡预测准确率随短期降雨时长(1 h至72 h)增加而提高,由72 h至7 d致灾雨量数据所计算的降雨阈值准确率最高,而1 h至7 d阈值预测准确率最低。

    (3)通过4组短期-长期降雨阈值的最佳预测率,定量确定长短期分类比例系数,将滑坡分为降雨短期触发和长期触发。该系数可用于未来的滑坡分析,完善滑坡预警系统。

    (4)巴中恩阳区以及南江县西部的滑坡更多是由3 d或长期降雨条件引发,而巴州区以及东部地区短期降雨条件诱发的滑坡数量与长期降雨条件诱发的滑坡数量比较接近。

  • 图  1   巴中市海拔(DEM)、年均降雨量和滑坡信息

    Figure  1.   The elevation, average annual precipitation and landslide information of Bazhong

    图  2   不同月份滑坡数量与降水量之间的关系

    Figure  2.   The relationship between the number of landslides and precipitation by month

    图  3   阈值方法和验证过程的工作流程框架

    Figure  3.   Workflow and general framework for the threshold method and validation process

    图  4   四类短期-长期降雨参数的比例系数及预测率

    Figure  4.   The relationship between prediction rates and the ratio coefficient of four short-term and long-term rainfall methods

    图  5   巴中市阈值预测准确率最高工况下的降雨阈值及滑坡隐患点分布图

    Figure  5.   Landslide data points and threshold distribution calculated by Kriging interpolation at the best ratio coefficient in Bazhong

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出版历程
  • 收稿日期:  2024-03-04
  • 修回日期:  2024-06-25
  • 录用日期:  2024-06-25
  • 网络出版日期:  2024-06-27
  • 刊出日期:  2024-08-21

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