ISSN 1003-8035 CN 11-2852/P
  • 中国科技核心期刊
  • CSCD收录期刊
  • Caj-cd规范获奖期刊
  • Scopus 收录期刊
  • DOAJ 收录期刊
  • GeoRef收录期刊
欢迎扫码关注“i环境微平台”

独库高速公路克扎依—巩乃斯段雪崩易发性评价

程秋连, 刘杰, 杨治纬, 张天意, 王斌

程秋连,刘杰,杨治纬,等. 独库高速公路克扎依—巩乃斯段雪崩易发性评价[J]. 中国地质灾害与防治学报,2024,35(1): 60-71. DOI: 10.16031/j.cnki.issn.1003-8035.202302009
引用本文: 程秋连,刘杰,杨治纬,等. 独库高速公路克扎依—巩乃斯段雪崩易发性评价[J]. 中国地质灾害与防治学报,2024,35(1): 60-71. DOI: 10.16031/j.cnki.issn.1003-8035.202302009
CHENG Qiulian,LIU Jie,YANG Zhiwei,et al. Avalanche susceptibility evaluation of the Kezhayi to Gongnaisi section of the Duku expressway[J]. The Chinese Journal of Geological Hazard and Control,2024,35(1): 60-71. DOI: 10.16031/j.cnki.issn.1003-8035.202302009
Citation: CHENG Qiulian,LIU Jie,YANG Zhiwei,et al. Avalanche susceptibility evaluation of the Kezhayi to Gongnaisi section of the Duku expressway[J]. The Chinese Journal of Geological Hazard and Control,2024,35(1): 60-71. DOI: 10.16031/j.cnki.issn.1003-8035.202302009

独库高速公路克扎依—巩乃斯段雪崩易发性评价

基金项目: 交通运输行业重点科技项目(2022-ZD6-090);新疆交通运输科技项目(2022-ZD-006);新疆交投集团2021年度“揭榜挂帅”科技项目(ZKXFWCG2022060004);新疆交通设计院科技研发项目(KY2022021501)
详细信息
    作者简介:

    程秋连(1998—),女,硕士研究生,主要从事公路冰雪灾害防治方面的工作。E-mail:cql878583@163.com

    通讯作者:

    刘 杰(1986—),男,博士,高级工程师,主要从事公路冰雪灾害防治方面的工作。E-mail:hfutliujie@163.com

  • 中图分类号: P642.21

Avalanche susceptibility evaluation of the Kezhayi to Gongnaisi section of the Duku expressway

  • 摘要:

    独库高速公路克扎依—巩乃斯段以高山地貌为主,地形切割剧烈,为雪崩发育提供了有利的地形条件,对该区域进行雪崩易发性评价是独库高速公路安全建设及运行的重要前提。通过遥感解译和现场调查等手段获取149个雪崩点的因子数据,通过对因子进行相关性检测,筛选出10个评价因子,构成雪崩评价因子体系。在此基础上,运用K均值聚类法和随机法提取出非雪崩点和原始雪崩点构成样本集,通过机器学习中的多层感知器、支持向量机算法对研究区域开展雪崩易发性评价。研究结果表明,随机法和K均值聚类法提取出的样本集分别带入算法中训练,R-SVM、R-MLP、K-SVM、K-MLP四种模型的Kappa系数均大于0.6,4组模型对验证数据集的预测结果与实际值存在高度的一致性。经多层感知器训练的AUC值由0.762提高至0.983,经支持向量机训练的AUC值由0.724提高至0.951。基于本研究预测性能最佳的K-MLP模型分区显示该研究区雪崩发育对拟建线路影响较小,但对于隧道洞口可能会造成威胁。本研究可为独库高速公路建设、运营以及雪崩灾害防治工作提供理论支撑和方法参考。

    Abstract:

    The Kezhayi to Gongnaisi section of the Duku expressway is predominantly characterized by alpine landforms, with steep terrain cutting that provides conducive conditions for avalanche development. The study on the evaluation of snow avalanche susceptibility in this area is a crucial prerequisite for the safety construction and operation of the Duku expressway. The 149 snow avalanche points were collected by employing remote sensing interpretation and field investigations. Through correlation analysis of these factors, 10 evaluation factors were selected, forming the avalanche evaluation factor system. Subsequently, the non-avalanche points and original avalanche points were extracted using the K-means clustering method and random method to create a sample set. Machine learning techniques, including multilayer perceptron (MLP) and support vector machine (SVM) algorithms, were utilized to assess avalanche susceptibility in the study area. The results show that the sample datasets extracted by the random and K-means clustering methods were used for training, the Kappa coefficient of the R-SVM, R-MLP, K-SVM, and K-MLP models were greater than 0.6. These four sets of models exhibited a high degree of consistency between the predicted results and actual values of the validation dataset. The AUC (area under curve) value trained by MLP increased from 0.762 to 0.983, while the AUC value trained by SVM increased from 0.724 to 0.951. Based on the K-MLP model partition with the highest evaluation accuracy, the snow avalanche development in the research area has a relatively minor impact on the proposed route but may pose a threat to tunnel entrances. This study provides theoretical support and methodological references for the construction, operation and mitigation of sonw avalanche disasters for the Duku expressway.

  • 膨胀土边坡的稳定性一直是岩土界广泛关注的问题。目前,边坡稳定性分析的常用方法主要包括了极限平衡法、极限分析法等,都建立在极限平衡理论基础之上,并不适用于膨胀土边坡的稳定性分析[1]。另一种常用的方法是有限元强度折减法,早在1975年该方法就被Zienkiewice等[2]用来求解边坡稳定问题,随着计算机硬件技术和有限元软件技术的飞速发展,运用有限元强度折减法分析边坡稳定已经成为新的趋势[3-10]。国内很多学者将强度折减法运用到膨胀土边坡稳定分析中,取得了一系列成果。

    周健等[11]利用强度折减法研究膨胀土边坡的稳定性,发现干湿循环会导致膨胀土抗剪强度衰减,且随着干湿循环次数的增加,边坡稳定性降低,安全系数减小。刘明维等[12]研究了强度折减法在膨胀土斜坡地基路堤稳定性分析中的应用,发现强度折减法所得结果与实际情况相符。张硕等[3]基于有限元强度折减法研究了雨季土体增重、强度降低和膨胀作用对膨胀土边坡稳定性的影响,发现强度降低是导致边坡失稳的主要原因,膨胀作用次之,土体增重较小。程灿宇等[13]利用MIDAS/GTS、FLAC和ANSYS三种软件采用强度折减法分别对不同工况进行了稳定性分析,发现弱膨胀土边坡无论采用M-C屈服准则,还是D-P屈服准则所得结果差异不大。谭波等[14]采用强度折减法对不同条件下的膨胀土边坡的安全系数进行了计算,发现次生裂隙面发育是导致膨胀土边坡失稳的主要原因之一。杨才等[15]根据强度折减有限元法对不同条件失稳边坡稳定性分析结果,提出以最大塑性应变以及最小塑性应变的量级指标来判定塑性区贯通时刻。

    然而,干湿循环、降雨入渗等因素会引起浅层膨胀土干密度降低、吸力衰减,从而使抗剪强度大幅度下降。目前,在采用强度折减法分析膨胀土边坡稳定性的同时系统考虑抗剪强度衰减影响的研究尚不多见。为此,本文采用试验与数值模拟相结合的方式,系统地考虑了抗剪强度衰减特性的膨胀土边坡稳定性分析。首先对广西宁明膨胀土开展了室内直剪试验,分析了含水量、干密度对膨胀土抗剪强度衰减的影响;再以此为依据,利用Midas有限元分析软件研究考虑抗剪强度衰减特性对膨胀土边坡稳定性安全系数的影响,获取了边坡安全系数随抗剪强度折减的动态变化规律,以期为工程实践提供参考。

    土样取自广西崇左-夏石镇某高速公路膨胀土边坡路段,其天然含水量、最优含水量和天然干密度分别为32.5%,24%和1.40 g/cm3,其他土性指标,比重(Gs),液限(WL),塑限(WP),塑性指数(IP),自由膨胀率(σf)见表1。自由膨胀率为42.8%,按照《膨胀土地区建筑技术规范》[16]的分类,该膨胀土为弱膨胀性膨胀土。

    表  1  宁明膨胀土基本土体参数
    Table  1.  Basic soil parameters of Ningming expansive soil
    参数Gs/(g.cm−3wL/%wP/%IPσf/%
    取值2.8059.1124.6834.4342.8
    下载: 导出CSV 
    | 显示表格

    首先,将现场取回的扰动土试样碾散过2 mm筛,过筛后放入105℃的烘箱中烘24h,使试样具有相同的初始结构,并将烘干土用收纳箱密封保存备用。接着,按目标含水量(控制干密度为1.6 g/cm3)和目标干密度(控制含水量18%)要求配制成湿土,并装入保鲜袋,经闷料24 h后测得土样的最终含水量与目标含水量之间误差不超过1%;最后,为保证环刀试样均匀一致,采用自制的模具(图1)进行制样,并利用液压千斤顶脱模推出,控制试样的直径为61.8 mm,高度为15 mm,目的是使试样在竖直方向上能够充分膨胀,每组平行土样密度差不超过±0.02 g/cm3,否则废弃重做。试样配制过程如图2,最终制成的每个环刀试样表面均平整无破损,且长度误差不超过0.2 mm,则为满足要求的试样。

    图  1  制样模具
    Figure  1.  Sample preparation mould
    图  2  配土过程示意图
    Figure  2.  Diagram of the soil preparation process

    以初始干密度为1.6 g/cm3,含水量分别为9%、12%、15%、18%、21%、24%和27%制取环刀试样7组,每组4个;并以初始含水量为18%,干密度分别为1.4、1.5、1.6和1.7 g/cm3制取环刀试样4组,每组4个,然后进行常规直剪试验(图3),试验施加的竖向压力分别为100 kPa、200 kPa、300 kPa、400 kPa,剪切速率为0.02 mm/min,初始剪切位移均保持在3.850 mm左右,剪切位移量程13.000 mm。

    图  3  四联直剪仪
    Figure  3.  Quadruple direct shear testing device

    为研究广西宁明膨胀土的抗剪强度随含水量变化的规律,对不同含水量的土样进行直剪试验,试验结果如表2所示。

    表  2  宁明膨胀土抗剪强度试验结果表
    Table  2.  Results of shear strength of Ningming expensive soils
    试验参数w/%φ/(°)c/kPa
    试验结果8.8027.3100.36
    11.724.5693.28
    14.621.8067.34
    17.519.8254.64
    20.817.9241.22
    23.315.2030.86
    26.112.389.90
    下载: 导出CSV 
    | 显示表格

    根据表2可绘制出宁明膨胀土黏聚力和内摩擦角与含水量的关系如图4图5所示,拟合后可得到黏聚力和内摩擦角与含水量的关系式:

    图  4  宁明膨胀土黏聚力随含水量变化规律
    Figure  4.  Variation of cohesive force of Ningming expansive soil with water content
    图  5  宁明膨胀土内摩擦角随含水量变化规律
    Figure  5.  Variation of internal friction angle of Ningming expansive soil with water content
    $$ c = { - 5.192}w + 147.9 $$ (1)
    $$ \varphi = - 0.827w + 34.36 $$ (2)

    由式(1)和(2)可知,cφw都存在近似线性的关系,这与文献[17-18]结果一致,含水量每增大5%,其黏聚力约减小26 kPa,内摩擦角减小4.2°左右;为更好的表示cw的衰减规律,参考吕海波等[19]的研究,可计算出c的衰减率为:

    $$ \eta = \frac{{\left| {{c_0} - {c_1}} \right|}}{{{c_0}}} \times 100\% $$ (3)

    式中:η——黏聚力衰减率;

    c0——初始黏聚力;

    c1——随含水量变化后的黏聚力。

    根据表3可知,随着宁明膨胀土含水量的逐渐增大黏聚力不断衰减,在最低目标含水量9%以3%递增至目标含水量27%的过程中,黏聚力的衰减率变化趋势为增大-减小-增大,说明膨胀土在低含水量和接近饱和含水量时,黏聚力对含水量的变化显得十分敏感。

    表  3  宁明膨胀土黏聚力衰减率计算结果表
    Table  3.  Results of cohesion decay rate of Ningming expansive soil
    试验参数w/%c/kPaη/%
    试验结果8.8100.36
    11.793.287.05
    14.667.3427.81
    17.554.6418.86
    20.841.2224.56
    23.330.8625.13
    26.19.967.92
    下载: 导出CSV 
    | 显示表格

    在试样ρd保持一致的情况下(1.6 g/cm3),可从图6图7中看出在相同垂直应力作用下,抗剪强度随着w的增大呈现减小的趋势。

    图  6  不同含水量试样抗剪强度随垂直压力的变化
    Figure  6.  Change of the shear strength with vertical pressure of samples with different water contents
    图  7  不同荷载下试样抗剪强度随含水量的变化
    Figure  7.  Change of the shear strength with water content of specimens undergoing different vertical loads

    上述试验结果表明,宁明膨胀土的抗剪强度随着含水量的改变发生显著变化;主要表现为在含水量增大时黏聚力和内摩擦角发生衰减,其中黏聚力的衰减较内摩擦角更为明显。

    根据表4数据可拟合出试样黏聚力和内摩擦角随干密度的变化规律,如图8图9所示。

    表  4  不同干密度下试样试验结果记录表
    Table  4.  Record table of test results under different dry densities
    试验参数ρd/(g·cm−3c/(kPa)φ/(°)
    试验结果1.797.2626.5
    1.654.6419.82
    1.540.3417.82
    1.437.5716.87
    下载: 导出CSV 
    | 显示表格
    图  8  宁明膨胀土黏聚力随干密度变化规律
    Figure  8.  Variation of cohesive force of Ningming expansive soil with dry density
    图  9  宁明膨胀土内摩擦角随干密度变化规律
    Figure  9.  Variation of internal friction angle of Ningming expansive soil with dry density

    图8图9可观察出宁明膨胀土的黏聚力和内摩擦角随干密度的变化曲线符合乘幂函数的拟合结果,其中:

    $$ c = 0.126{{\rm{e}}^{3.884{\rho _{\rm{d}}}}} $$ (4)
    $$ \varphi = 1.631{{\rm{e}}^{1.614{\rho _{\rm{d}}}}} $$ (5)

    分析式(4)可知试样c随着ρd的减小而减小,且随着ρd的减小,c的衰减速率由快到慢,并最终趋于稳定;而在接近最大干密度(1.78 g/cm3)时变化较为显著,在干密度由1.4 g/cm3增大至1.6 g/cm3时,c增加了17.07 kPa;在干密度由1.6 g/cm3增大至1.7 g/cm3时,c增加了42.62 kPa。而由式(5)能看出φ亦随着ρd的减小而减小,但其整体的变化幅度并不大,干密度1.4 g/cm3与1.7 g/cm3的试样φ相差约9.6°;图10中各级载荷下的抗剪强度都随着试样ρd的减小而降低,且其变化幅度在高垂直应力条件下更为显著。

    图  10  不同干密度下试样抗剪强度随垂直应力的变化
    Figure  10.  Variation of shear strength with vertical stress of specimens of different dry densities

    干密度对宁明膨胀土抗剪强度的影响主要体现在黏聚力上,试样干密度越小,单位体积土体的土颗粒越少,土粒间水膜越薄,其抗剪强度越小;此外,膨胀土干密度越小,其吸力越大,试样的抗剪强度越低;而干密度对于内摩擦角的整体影响并不显著,其变化在10°以内。

    根据广西崇左-夏石镇某高速公路膨胀土边坡为研究对象,并参考该公路的地质勘察报告,该边坡土质主要由填土(①1和①2)、黏土②、强风化泥岩③和中风化泥岩④组成。同时根据地质调查及钻探、探槽揭示,该边坡滑动带基本位于黏土层,且下部强风化泥岩等土体不透水,大气影响深度为7 m,刚好大致为填土厚度和黏土厚度之和,影响急剧层深度为2.5 m。相关土层天然状态下基本参数指标见表5

    表  5  土层相关参数
    Table  5.  Soil layer related parameters
    地层岩性厚度
    /m
    重度
    /(kN·m−3
    内摩擦角
    /(°)
    黏聚力
    /kPa
    其它
    填土①10.2~118.0524成分黏土
    填土①22.5~3.318.8307上层砾砂,
    下层碎石
    黏土②0.3~418.48.435.6中等膨胀土
    强风化泥岩③0.6~119.32545质量等级Ⅴ级
    中风化泥岩④未钻穿19.63565质量等级Ⅴ级
    下载: 导出CSV 
    | 显示表格

    结合上述实际工程地质勘察报告,将膨胀土边坡考虑为非匀质边坡,同时为提高模型求解时间,取黏土弹性模量12000 kPa,容重18.4 N/m3,泊松比0.3,边坡高20 m,坡比1∶1.5。为避免尺寸效应带来的误差和便于模型求解收敛,坡顶取15 m,坡底取25 m,网格按线性梯度(长度)划分,起始长度1.2 m,结束长度0.5 m。由于填土土层由于土体较松散,易膨胀开裂,在降雨作用下容易引发降雨入渗,易软化下部土体,因此实际工程中对该部分填土进行了挖除。填土挖除后,为充分合理考虑到大气影响层对膨胀土边坡中黏土的影响,同时又不会影响到下部不透水泥岩,取大气影响层为距离坡面4 m范围的土体,正好为黏土厚度,急剧层为距离坡面1.5 m范围的土体(图11)。

    图  11  模型示意图
    Figure  11.  Numerical simulation model

    根据室内直剪试验结果,同时考虑到膨胀土具有浅层性,将测得的7个含水量下(干密度均为1.6 g/cm3)的膨胀土抗剪强度参数指标cφ赋予给受大气影响的风化层土体,即距离坡面4 m范围内的黏土。强、中风化泥岩层土体参数指标取地质勘察报告的值,具体数值见表5。计算得到不同含水量w下膨胀土边坡整体位移和潜在滑移面,如图12图13所示。

    图  12  1.6 g/cm3干密度不同含水量条件下的边坡位移
    Figure  12.  Slope displacement with the 1.6 g /cm3 dry density under different moisture content conditions
    图  13  1.6 g/cm3干密度不同含水量条件下的边坡潜在滑移面
    Figure  13.  Potential slip surface of slope with the dry density of 1.6 g/cm3under different moisture content

    分析图12图13可知,随着含水量w的增大,边坡的整体位移整体呈增大趋势,非饱和膨胀土边坡的浅层破坏由受大气影响层膨胀土强度衰减导致。随着含水量的增加,土体的c不断减小,边坡位移不断增大,滑移面逐渐变浅;破坏形式为浅层滑塌式的破坏。边坡失稳的滑移面位置位于大气影响层和不透水泥岩的交界处,且与黏土的底部相切。

    基于相同干密度,不同含水量下膨胀土的剪切试验和地质勘察报告,利用有限元分析软件对边坡进行稳定性分析,可得到随着膨胀土含水量的变化对边坡稳定性安全系数的影响规律,如图14所示的曲线,表达式为:

    图  14  边坡安全系数随含水量的变化规律
    Figure  14.  The variation of slope safety factor with water content
    $$ y = - {\text{0}}{\text{.008}}{x^2} + {\text{0}}{\text{.1884}}x + {\text{2}}{\text{.025}} $$ (6)

    随着w的增大,膨胀土的强度参数指标不断衰减,含水量较高比低含水量情况下的衰减速度更大。同时,膨胀土边坡在天然状况下处于稳定状态,但当w增大至27%时,其Fs为0.850,稳定性转变为失稳状态,发生滑坡、坍塌等工程现象;在此基础上,若继续增大含水量,膨胀土边坡将可能由浅层失稳进入完全失稳状态,这与实际工程中,在长时间降雨后,曾出现的多次滑坡现象类似。

    根据试验结果,将测得的四个干密度下(含水量均为18%)的膨胀土抗剪强度参数指标cφ赋予给距离坡面4 m范围的黏土。强、中风化泥岩层土体抗剪强度参数指标取地质勘察报告值,具体数值见表5。计算得到不同ρd下膨胀土边坡整体位移和潜在滑移面,如图15图16所示。

    图  15  18%含水量不同干密度条件下的边坡位移
    Figure  15.  Slope displacement under different dry densities with the moisture content of 18%
    图  16  18%含水量不同干密度条件下的边坡潜在滑移面
    Figure  16.  Potential slip surface of slope under different dry densities with the 18% moisture content

    图15图16中可以看出试样的ρd越小,边坡位移越大,潜在滑移面变浅;这是因为土体的c随着ρd的减小而减小,使得其抗剪强度降低;此时,边坡的破坏形式由整体滑动变为浅层滑塌。基于相同含水量,不同干密度下膨胀土的剪切试验和地质勘察报告,利用有限元分析软件对边坡进行稳定性分析,可得到随着膨胀土干密度的变化对边坡稳定性安全系数的影响规律,如图17所示的曲线,其表达式为:

    图  17  边坡安全系数随干密度的变化规律
    Figure  17.  The variation of slope safety factor with dry density
    $$ y = {\text{8}}{\text{.375}}{x^2} - {\text{23}}{\text{.24}}x + {\text{18}}{\text{.41}} $$ (7)

    试样ρd越小,其抗剪强度越低;且在ρd越大时其Fs增大趋势越为显著;1.5 g/cm3干密度下的Fs为2.409,比1.4 g/cm3的高出0.124,而1.7 g/cm3干密度下的Fs与1.6 g/cm3条件下的差值为0.459。

    (1)含水量的增大、干密度的减小都会引起膨胀土的峰值抗剪强度、黏聚力以及内摩擦角发生不同程度的衰减,其中,黏聚力的衰减幅度相较于内摩擦角更大。

    (2)通过多次膨胀土强度折减的方法可以很好地模拟降雨过程中由抗剪强度衰减引起的边坡稳定性的动态变化:风化层土体强度接近未风化层土体强度时,边坡处于稳定状态,潜在滑动面穿过分层界面;随着含水量增大、干密度变小,风化层抗剪强度会不断衰减,引起潜在滑动面逐渐外移,边坡稳定性降低。

    (3)数值模拟结果表明:与干密度减小相比,含水量的增大对边坡稳定更为不利,含水量增加到27%以后,膨胀土边坡由稳定状态变为欠稳定状态,因此在分析膨胀土边坡稳定性时,应着重考虑含水量变化的影响。

  • 图  1   研究区域雪崩遥感解译与分布图

    Figure  1.   Remote sensing interpretation and distribution of snow avalanches in the study area

    图  2   K均值聚类算法流程图

    Figure  2.   Flowchart of the k-means clustering algorithm

    图  3   MLP结构示意图

    Figure  3.   Schematic diagram of the MLP structure

    图  4   雪崩易发性评价流程图

    Figure  4.   Flowchart of sonw avalanche susceptibility evaluation

    图  5   雪崩评价因子图

    Figure  5.   Snow avalanche evaluation factors map

    图  6   雪崩易发性指数图

    Figure  6.   Snow avalanche susceptibility index map

    图  7   评价因子重要性统计图

    Figure  7.   Importance statistics of evaluation factors

    图  8   ROC曲线

    Figure  8.   ROC curves

    图  9   基于K-MLP模型雪崩易发性分区图

    Figure  9.   Snow avalanche susceptibility partition map based on K-MLP model

    表  1   评价因子数据源

    Table  1   Data sources for evaluates factors

    分类 评价因子 数据源
    地形条件 高程、坡度、坡向、地表粗糙度、
    地表起伏度、高程变异系数
    地理空间数据云DEM
    气候条件 1月平均温度、最大风速、
    年平均降雨量
    研究区及周边各站点
    的气象数据
    积雪条件 年平均降雪量、
    最大积雪厚度
    研究区及周边各站点
    的气象数据
    下载: 导出CSV

    表  2   雪崩评价因子分级量化结果

    Table  2   Quantitative results of snow avalanche evaluation factor grading

    评价因子 二级属性 $ {S _{ij}} $ $ {N_{ij}} $ $ {X_{ij}} $ $ {C_{ij}} $ 评价因子 二级属性 $ {S _{ij}} $ $ {N_{ij}} $ $ {X_{ij}} $ $ {C_{ij}} $
    高程/m 1873~2295 43244 5 0.241 0.000 地面粗糙度 1~1.1 149984 37 0.514 0.228
    >2295~2619 82136 15 0.381 0.051 >1.1~1.2 83112 48 1.206 0.536
    >2619~2927 59328 30 1.056 0.297 >1.2~1.4 51767 38 1.533 0.681
    >2927~3262 51439 31 1.258 0.370 >1.4~1.7 19965 21 2.196 0.976
    >3262~3627 43467 23 1.105 0.315 >1.7~2.4 4640 5 2.250 1.000
    >3627~4459 31463 45 2.986 1.000 >2.4~7.2 709 0 0.000 0.000
    坡度/(°) 0~10 62301 5 0.167 0.000 地形起伏度
    /m
    0~194 49218 1 0.042 0.000
    >10~19 56267 18 0.668 0.253 >194~332 55415 11 0.414 0.213
    >19~28 59776 28 0.978 0.410 >332~457 68499 31 0.945 0.516
    >28~37 62891 40 1.328 0.587 >457~588 67127 48 1.493 0.829
    >37~47 49479 38 1.603 0.726 >588~754 53605 46 1.792 1.000
    >47~82 19463 20 2.145 1.000 >754~1263 17213 12 1.455 0.808
    坡向 67060 31 0.962 0.373 1月平均气温
    / °C
    −14~−11 39756 15 0.788 0.045
    东北 23094 7 0.633 0.000 >−11~−9 201195 71 0.737 0.000
    22559 15 1.388 0.855 >−9~−7 70126 63 1.876 1.000
    东南 38180 21 1.148 0.583 年平均降雨量
    /mm
    43~45 65586 27 0.859 0.319
    48476 21 0.904 0.307 >45~47 127682 31 0.507 0.000
    西南 43794 17 0.810 0.201 >47~49 117809 91 1.613 1.000
    西 31664 23 1.517 1.000 最大风速
    /(m·s−1
    9~12 32130 18 1.170 0.760
    西北 35250 14 0.829 0.222 >12~15 169196 63 0.777 0.000
    高程
    变异系数
    0~0.016 41667 4 0.200 0.000 >15~19 109751 68 1.294 1.000
    >0.016~0.028 72137 27 0.781 0.540 年平均降雪量
    /mm
    11~15 22538 7 0.648 0.000
    >0.028~0.040 80064 48 1.252 0.977 >15~18 219917 77 0.731 0.062
    >0.040~0.051 63506 38 1.249 0.974 >18~21 68622 65 1.978 1.000
    >0.051~0.065 45784 28 1.277 1.000 地表切割度
    /m
    0~88 74711 2 0.056 0.000
    >0.065~0.107 7919 4 1.055 0.794 >88~161 70384 18 0.534 0.210
    最大积雪深度
    /mm
    55~61 121679 51 0.875 0.628 >161~232 62245 23 0.771 0.315
    >61~68 153748 95 1.290 1.000 >232~309 55587 62 2.329 1.000
    >68~78 35650 3 0.176 0.000 >309~401 39623 36 1.897 0.810
    >401~682 8527 8 1.959 0.837
    下载: 导出CSV

    表  3   雪崩评价因子相关性矩阵

    Table  3   Correlation matrix of snow avalanche evaluation factors

    高程 坡度 坡向 高程
    变异系数
    地表
    切割度
    地面
    粗糙度
    地形
    起伏度
    1月平均
    气温
    年平均
    降雨量
    最大
    风速
    年平均
    降雪量
    最大
    积雪深度
    高程 1
    坡度 0.12 1
    坡向 0.03 0.01 1
    高程变异系数 0.17 0.28 0.03 1
    地表切割度 0.21 0.11 0.05 0.11 1
    地面粗糙度 0.34 0.26 0.01 0.25 0.28 1
    地形起伏度 0.44 0.6 0.05 0.92 0.93 0.47 1
    1月平均气温 0.03 0.11 0.02 0.15 0.13 0.06 0.12 1
    年平均降雨量 0.01 0.07 0 0.04 0.06 −0.01 0.04 0.16 1
    最大风速 0.51 0.01 −0.01 −0.02 −0.13 −0.11 −0.17 0.61 0.07 1
    年平均降雪量 0.28 0.22 0.02 0.19 0.24 0.14 0.25 0.23 0.23 0.08 1
    最大积雪深度 −0.54 −0.19 −0.02 −0.13 −0.22 −0.19 −0.27 0.14 0.18 0.64 0.18 1
    下载: 导出CSV

    表  4   K均值聚类法分析结果

    Table  4   Results of K-means clustering algorithm method

    聚类结果栅格数量/个雪崩个数/个相对雪崩比
    113484467.122
    28556150.122
    364712471.516
    43304170.442
    5114280440.804
    下载: 导出CSV

    表  5   基于K-MLP模型雪崩易发性分区结果统计

    Table  5   Statistical results of snow avalanche susceptibility partition based on K-MLP model

    易发性等级 栅格
    数量/个
    面积
    /km2
    雪崩
    数/个
    分区
    比例/%
    雪崩比 雪崩密度
    /(个·km−2
    低易发区 79284 71.35 9 25.59 0.06 0.12
    中易发区 86287 77.66 24 27.74 0.16 0.31
    高易发区 83594 75.23 51 26.87 0.34 0.68
    极高易发区 61912 55.72 64 19.90 0.44 1.17
    下载: 导出CSV
  • [1] 王世金,效存德. 全球冰冻圈灾害高风险区:影响与态势[J]. 科学通报,2019,64(9):890 − 900. [WANG Shijin,XIAO Cunde. Global cryospheric disaster at high risk areas:Impacts and trend[J]. Chinese Science Bulletin,2019,64(9):890 − 900. (in Chinese with English abstract)]

    WANG Shijin, XIAO Cunde. Global cryospheric disaster at high risk areas: Impacts and trend[J]. Chinese Science Bulletin, 2019, 649): 890900. (in Chinese with English abstract)

    [2]

    SCHWEIZER J,BRUCE JAMIESON J,SCHNEEBELI M. Snow avalanche formation[J]. Reviews of Geophysics,2003,41(4):1016.

    [3] 杨金明,张旭,毛炜峄,等. 中国天山雪崩灾害调查分析[J]. 自然灾害学报,2022,31(1):188 − 197. [YANG Jinming,ZHANG Xu,MAO Weiyi,et al. Investigation and analysis of snow avalanche disaster in Tianshan Mountains of China[J]. Journal of Natural Disasters,2022,31(1):188 − 197. (in Chinese with English abstract)]

    YANG Jinming, ZHANG Xu, MAO Weiyi, et al. Investigation and analysis of snow avalanche disaster in Tianshan Mountains of China[J]. Journal of Natural Disasters, 2022, 311): 188197. (in Chinese with English abstract)

    [4] 史志文,徐俊荣,陈忠升,等. 天山西部寒区山地生态系统近40年来气候变化特征——以中国科学院天山积雪雪崩研究站为例[J]. 山地学报,2009,27(1):41 − 48. [SHI Zhiwen,XU Junrong,CHEN Zhongsheng,et al. Analysis on climatic changes under global climatic change:A case study of Tianshan snow and avalanche research station[J]. Journal of Mountain Science,2009,27(1):41 − 48. (in Chinese with English abstract)] DOI: 10.3969/j.issn.1008-2786.2009.01.006

    SHI Zhiwen, XU Junrong, CHEN Zhongsheng, et al. Analysis on climatic changes under global climatic change: A case study of Tianshan snow and avalanche research station[J]. Journal of Mountain Science, 2009, 271): 4148. (in Chinese with English abstract) DOI: 10.3969/j.issn.1008-2786.2009.01.006

    [5] 郝建盛,李兰海. 雪崩灾害防治研究进展及展望[J]. 冰川冻土,2022,44(3):762 − 770. [HAO Jiansheng,LI Lanhai. Research progress and prospect of snow avalanche disaster prevention and control[J]. Journal of Glaciology and Geocryology,2022,44(3):762 − 770. (in Chinese with English abstract)]

    HAO Jiansheng, LI Lanhai. Research progress and prospect of snow avalanche disaster prevention and control[J]. Journal of Glaciology and Geocryology, 2022, 443): 762770. (in Chinese with English abstract)

    [6]

    JACKSON M. Snow and ice-related hazards,risks,and disasters. 2nd edition. edited by wilfried haeberli and colin whiteman[J]. Mountain Research and Development,2022,42(2):1 − 5.

    [7]

    FAVIER P,ECKERT N,FAUG T,et al. A framework to account for structural damage,functional efficiency and reparation costs within the optimal design of countermeasures:Application to snow avalanche risk mitigation[J]. Cold Regions Science and Technology,2022,199:103559. DOI: 10.1016/j.coldregions.2022.103559

    [8] 郝建盛,黄法融,冯挺,等. 亚洲高山区雪崩灾害时空分布特点及其诱发因素分析[J]. 山地学报,2021,39(2):304 − 312. [HAO Jiansheng,HUANG Farong,FENG Ting,et al. Analysis of spatio-temporal distribution characteristics of snow avalanche disaster and its triggering factors in the high mountain Asia[J]. Mountain Research,2021,39(2):304 − 312. (in Chinese with English abstract)]

    HAO Jiansheng, HUANG Farong, FENG Ting, et al. Analysis of spatio-temporal distribution characteristics of snow avalanche disaster and its triggering factors in the high mountain Asia[J]. Mountain Research, 2021, 392): 304312. (in Chinese with English abstract)

    [9] 段仕美,刘时银,朱钰,等. 梅里雪山1991年和2019年雪崩事件重建及影响因素分析[J]. 冰川冻土,2022,44(3):771 − 783. [DUAN Shimei,LIU Shiyin,ZHU Yu,et al. Reconstructing and analyzing avalanche events of 1991 and 2019 in Meili Snow Mountain[J]. Journal of Glaciology and Geocryology,2022,44(3):771 − 783. (in Chinese with English abstract)]

    DUAN Shimei, LIU Shiyin, ZHU Yu, et al. Reconstructing and analyzing avalanche events of 1991 and 2019 in Meili Snow Mountain[J]. Journal of Glaciology and Geocryology, 2022, 443): 771783. (in Chinese with English abstract)

    [10]

    TROSHKINA E,GLAZOVSKAYA T,KONDAKOVA N,et al. Zoning of snowiness and avalanching in the mountains of western Transcaucasia[J]. Annals of Glaciology,2001,32:311 − 313. DOI: 10.3189/172756401781819012

    [11] 武万里,缑晓辉,刘垚. 基于GIS的路面积雪灾害风险分析与区划研究[J]. 防灾科技学院学报,2021,23(1):87 − 93. [WU Wanli,GOU Xiaohui,LIU Yao. Snow cover risk analysis and zoning of expressway in Ningxia based on GIS[J]. Journal of Institute of Disaster Prevention,2021,23(1):87 − 93. (in Chinese with English abstract)]

    WU Wanli, GOU Xiaohui, LIU Yao. Snow cover risk analysis and zoning of expressway in Ningxia based on GIS[J]. Journal of Institute of Disaster Prevention, 2021, 231): 8793. (in Chinese with English abstract)

    [12] 李靖,邓桃,潘前,等. 基于GIS和层次分析法的雪崩灾害危险性评估及线路工程减灾对策研究——以帕隆藏布流域为例[J]. 四川建筑,2019,39(2):59 − 61. [LI Jing,DENG Tao,PAN Qian,et al. Risk assessment of avalanche disaster based on GIS and analytic hierarchy process and research on disaster reduction countermeasures of line engineering:A case study of palong Zangbo Basin[J]. Sichuan Architecture,2019,39(2):59 − 61. (in Chinese)]

    LI Jing, DENG Tao, PAN Qian, et al. Risk assessment of avalanche disaster based on GIS and analytic hierarchy process and research on disaster reduction countermeasures of line engineering: A case study of palong Zangbo Basin[J]. Sichuan Architecture, 2019, 392): 5961. (in Chinese)

    [13]

    RAHMATI O,GHORBANZADEH O,TEIMURIAN T,et al. Spatial modeling of snow avalanche using machine learning models and geo-environmental factors:comparison of effectiveness in two mountain regions[J]. Remote Sensing,2019,11(24):2995. DOI: 10.3390/rs11242995

    [14] 文洪,巫锡勇,赵思远,等. 基于机器学习法的青藏高原沙鲁里山系中段雪崩易发性评价研究[J]. 冰川冻土,2022,44(6):1694 − 1706. [WEN Hong,WU Xiyong,ZHAO Siyuan,et al. Snow avalanche susceptibility evaluation in the central Shaluli Mountains of Tibetan Plateau based on machine learning method[J]. Journal of Glaciology and Geocryology,2022,44(6):1694 − 1706. (in Chinese with English abstract)]

    WEN Hong, WU Xiyong, ZHAO Siyuan, et al. Snow avalanche susceptibility evaluation in the central Shaluli Mountains of Tibetan Plateau based on machine learning method[J]. Journal of Glaciology and Geocryology, 2022, 446): 16941706. (in Chinese with English abstract)

    [15] 边瑞. 基于集成机器学习模型的沙鲁里山系中段雪崩易发性评价研究[D]. 成都:西南交通大学,2021. [BIAN Rui. Avalanche susceptibility evaluation in the middle part of Shaluli Mountain system based on integrated machine learning model[D]. Chengdu:Southwest Jiaotong University,2021. (in Chinese with English abstract)]

    BIAN Rui. Avalanche susceptibility evaluation in the middle part of Shaluli Mountain system based on integrated machine learning model[D]. Chengdu: Southwest Jiaotong University, 2021. (in Chinese with English abstract)

    [16]

    AKAY H. Spatial modeling of snow avalanche susceptibility using hybrid and ensemble machine learning techniques[J]. CATENA,2021,206:105524. DOI: 10.1016/j.catena.2021.105524

    [17]

    BALLESTEROS-CÁNOVAS J A,TRAPPMANN D,MADRIGAL-GONZÁLEZ J,et al. Climate warming enhances snow avalanche risk in the Western Himalayas[J]. Proceedings of the National Academy of Sciences of the United States of America,2018,115(13):3410 − 3415.

    [18]

    FROMM R,SCHÖNBERGER C. Estimating the danger of snow avalanches with a machine learning approach using a comprehensive snow cover model[J]. Machine Learning With Applications,2022,10:100405. DOI: 10.1016/j.mlwa.2022.100405

    [19] 刘福臻,王灵,肖东升. 机器学习模型在滑坡易发性评价中的应用[J]. 中国地质灾害与防治学报,2021,32(6):98 − 106. [LIU Fuzhen,WANG Ling,XIAO Dongsheng. Application of machine learning model in landslide susceptibility evaluation[J]. The Chinese Journal of Geological Hazard and Control,2021,32(6):98 − 106. (in Chinese with English abstract)]

    LIU Fuzhen, WANG Ling, XIAO Dongsheng. Application of machine learning model in landslide susceptibility evaluation[J]. The Chinese Journal of Geological Hazard and Control, 2021, 326): 98106. (in Chinese with English abstract)

    [20]

    LEE S. Current and future status of GIS-based landslide susceptibility mapping:A literature review[J]. Journal of Remote Sensing,2019,35:179 − 193.

    [21] 李倩楠. 基于不同算法的DEM地面曲率提取的比较分析[J]. 首都师范大学学报(自然科学版),2016,37(5):82 − 85. [LI Qiannan. Based on the difference of the digital elevation model(DEM) algorithm analysis and comparison of the ground curvature extraction[J]. Journal of Capital Normal University (Natural Science Edition),2016,37(5):82 − 85. (in Chinese with English abstract)] DOI: 10.3969/j.issn.1004-9398.2016.05.015

    LI Qiannan. Based on the difference of the digital elevation model(DEM) algorithm analysis and comparison of the ground curvature extraction[J]. Journal of Capital Normal University (Natural Science Edition), 2016, 375): 8285. (in Chinese with English abstract) DOI: 10.3969/j.issn.1004-9398.2016.05.015

    [22] 李艳,朱军,胡亚,等. 不同插值方法模拟四川省逐月降水量的对比分析[J]. 水土保持研究,2017,24(1):151 − 154. [LI Yan,ZHU Jun,HU Ya,et al. Comparison analysis on different spatial interpolation methods to simulate monthly precipitation in Sichuan Province[J]. Research of Soil and Water Conservation,2017,24(1):151 − 154. (in Chinese with English abstract)]

    LI Yan, ZHU Jun, HU Ya, et al. Comparison analysis on different spatial interpolation methods to simulate monthly precipitation in Sichuan Province[J]. Research of Soil and Water Conservation, 2017, 241): 151154. (in Chinese with English abstract)

    [23] 王新宇,黄鹏程. 基于GIS的气象要素插值方法比较研究[J]. 测绘与空间地理信息,2020,43(5):167 − 170. [WANG Xinyu,HUANG Pengcheng. Comparative study on interpolation methods of meteorological elements based on GIS[J]. Geomatics & Spatial Information Technology,2020,43(5):167 − 170. (in Chinese)] DOI: 10.3969/j.issn.1672-5867.2020.05.047

    WANG Xinyu, HUANG Pengcheng. Comparative study on interpolation methods of meteorological elements based on GIS[J]. Geomatics & Spatial Information Technology, 2020, 435): 167170. (in Chinese) DOI: 10.3969/j.issn.1672-5867.2020.05.047

    [24]

    JARVIS C H,STUART N. A comparison among strategies for interpolating maximum and minimum daily air temperatures. part II:the interaction between number of guiding variables and the type of interpolation method[J]. Journal of Applied Meteorology,2001,40(6):1075 − 1084. DOI: 10.1175/1520-0450(2001)040<1075:ACASFI>2.0.CO;2

    [25] 李文彦,王喜乐. 频率比与信息量模型在黄土沟壑区滑坡易发性评价中的应用与比较[J]. 自然灾害学报,2020,29(4):213 − 220. [LI Wenyan,WANG Xile. Application and comparison of frequency ratio and information value model for evaluating landslide susceptibility of loess gully region[J]. Journal of Natural Disasters,2020,29(4):213 − 220. (in Chinese with English abstract)]

    LI Wenyan, WANG Xile. Application and comparison of frequency ratio and information value model for evaluating landslide susceptibility of loess gully region[J]. Journal of Natural Disasters, 2020, 294): 213220. (in Chinese with English abstract)

    [26] 杜国梁,杨志华,袁颖,等. 基于逻辑回归-信息量的川藏交通廊道滑坡易发性评价[J]. 水文地质工程地质,2021,48(5):102 − 111. [DU Guoliang,YANG Zhihua,YUAN Ying,et al. Landslide susceptibility mapping in the Sichuan-Tibet traffic corridor using logistic regression-information value method[J]. Hydrogeology & Engineering Geology,2021,48(5):102 − 111. (in Chinese with English abstract)]

    DU Guoliang, YANG Zhihua, YUAN Ying, et al. Landslide susceptibility mapping in the Sichuan-Tibet traffic corridor using logistic regression-information value method[J]. Hydrogeology & Engineering Geology, 2021, 485): 102111. (in Chinese with English abstract)

    [27] 王森,刘琛,邢帅杰. K-means聚类算法研究综述[J]. 华东交通大学学报,2022,39(5):119 − 126. [WANG Sen,LIU Chen,XING Shuaijie. Review on K-means clustering algorithm[J]. Journal of East China Jiaotong University,2022,39(5):119 − 126. (in Chinese with English abstract)]

    WANG Sen, LIU Chen, XING Shuaijie. Review on K-means clustering algorithm[J]. Journal of East China Jiaotong University, 2022, 395): 119126. (in Chinese with English abstract)

    [28] 牛瑞卿,彭令,叶润青,等. 基于粗糙集的支持向量机滑坡易发性评价[J]. 吉林大学学报(地球科学版),2012,42(2):430 − 439. [NIU Ruiqing,PENG Ling,YE Runqing,et al. Landslide susceptibility assessment based on rough sets and support vector machine[J]. Journal of Jilin University (Earth Science Edition),2012,42(2):430 − 439. (in Chinese with English abstract)]

    NIU Ruiqing, PENG Ling, YE Runqing, et al. Landslide susceptibility assessment based on rough sets and support vector machine[J]. Journal of Jilin University (Earth Science Edition), 2012, 422): 430439. (in Chinese with English abstract)

    [29] 张驰,郭媛,黎明. 人工神经网络模型发展及应用综述[J]. 计算机工程与应用,2021,57(11):57 − 69. [ZHANG Chi,GUO Yuan,LI Ming. Review of development and application of artificial neural network models[J]. Computer Engineering and Applications,2021,57(11):57 − 69. (in Chinese with English abstract)]

    ZHANG Chi, GUO Yuan, LI Ming. Review of development and application of artificial neural network models[J]. Computer Engineering and Applications, 2021, 5711): 5769. (in Chinese with English abstract)

    [30] 周萍,邓辉,张文江,等. 基于信息量模型和机器学习方法的滑坡易发性评价研究——以四川理县为例[J]. 地理科学,2022,42(9):1665 − 1675. [ZHOU Ping,DENG Hui,ZHANG Wenjiang,et al. Landslide susceptibility evaluation based on information value modeland machine learning method: A case study of Lixian County, Sichuan Province[J]. Scientia Geographica Sinica,2022,42(9):1665 − 1675. (in Chinese with English abstract)]

    ZHOU Ping, DENG Hui, ZHANG Wenjiang, et al. Landslide susceptibility evaluation based on information value modeland machine learning method: A case study of Lixian County, Sichuan Province[J]. Scientia Geographica Sinica, 2022, 429): 16651675. (in Chinese with English abstract)

    [31] 熊小辉,汪长林,白永健,等. 基于不同耦合模型的县域滑坡易发性评价对比分析——以四川普格县为例[J]. 中国地质灾害与防治学报,2022,33(4):114 − 124. [XIONG Xiaohui,WANG Changlin,BAI Yongjian,et al. Comparison of landslide susceptibility assessment based on multiple hybrid models at County level:A case study for Puge County,Sichuan Province[J]. The Chinese Journal of Geological Hazard and Control,2022,33(4):114 − 124. (in Chinese with English abstract)]

    XIONG Xiaohui, WANG Changlin, BAI Yongjian, et al. Comparison of landslide susceptibility assessment based on multiple hybrid models at County level: A case study for Puge County, Sichuan Province[J]. The Chinese Journal of Geological Hazard and Control, 2022, 334): 114124. (in Chinese with English abstract)

    [32]

    MAGGIONI M,GRUBER U. The influence of topographic parameters on avalanche release dimension and frequency[J]. Cold Regions Science and Technology,2003,37(3):407 − 419. DOI: 10.1016/S0165-232X(03)00080-6

    [33] 王世金,任贾文. 国内外雪崩灾害研究综述[J]. 地理科学进展,2012,31(11):1529 − 1536. [WANG Shijin,REN Jiawen. A review of the progresses of avalanche hazards research[J]. Progress in Geography,2012,31(11):1529 − 1536. (in Chinese with English abstract)]

    WANG Shijin, REN Jiawen. A review of the progresses of avalanche hazards research[J]. Progress in Geography, 2012, 3111): 15291536. (in Chinese with English abstract)

    [34] 张钟远,邓明国,徐世光,等. 镇康县滑坡易发性评价模型对比研究[J]. 岩石力学与工程学报,2022,41(1):157 − 171. [ZHANG Zhongyuan,DENG Mingguo,XU Shiguang,et al. Comparison of landslide susceptibility assessment models in Zhenkang County,Yunnan Province,China[J]. Chinese Journal of Rock Mechanics and Engineering,2022,41(1):157 − 171. (in Chinese with English abstract)]

    ZHANG Zhongyuan, DENG Mingguo, XU Shiguang, et al. Comparison of landslide susceptibility assessment models in Zhenkang County, Yunnan Province, China[J]. Chinese Journal of Rock Mechanics and Engineering, 2022, 411): 157171. (in Chinese with English abstract)

    [35] 孙长明,马润勇,尚合欣,等. 基于滑坡分类的西宁市滑坡易发性评价[J]. 水文地质工程地质,2020,47(3):173 − 181. [SUN Changming,MA Runyong,SHANG Hexin,et al. Landslide susceptibility assessment in Xining based on landslide classification[J]. Hydrogeology & Engineering Geology,2020,47(3):173 − 181. (in Chinese with English abstract)] DOI: 10.16030/j.cnki.issn.1000-3665.201906074

    SUN Changming, MA Runyong, SHANG Hexin, et al. Landslide susceptibility assessment in Xining based on landslide classification[J]. Hydrogeology & Engineering Geology, 2020, 473): 173181. (in Chinese with English abstract) DOI: 10.16030/j.cnki.issn.1000-3665.201906074

  • 期刊类型引用(5)

    1. 贺伟明,石胜伟,蔡强,梁炯. 基于上下限解的膨胀土边坡首次滑动区域分析. 水文地质工程地质. 2025(01): 104-112 . 百度学术
    2. 孙银磊,余川,廖磊,李志妃. 钢渣粉固化改良膨胀性黏土机理研究进展. 水文地质工程地质. 2025(01): 113-129 . 百度学术
    3. 张锐,周豫,兰天,郑健龙,刘昭京,李彬. 高速铁路土工格栅加筋膨胀土边坡作用机制. 铁道科学与工程学报. 2024(01): 1-12 . 百度学术
    4. 纪佑军,熊军,蒋国斌,王泽根. 考虑应变软化的鸡场镇降雨型滑坡数值分析. 水文地质工程地质. 2024(04): 178-188 . 百度学术
    5. 张再江. 基于改进极限平衡原理的膨胀土边坡稳定性计算分析. 水利科技与经济. 2024(07): 48-51 . 百度学术

    其他类型引用(7)

图(9)  /  表(5)
计量
  • 文章访问数:  659
  • HTML全文浏览量:  794
  • PDF下载量:  88
  • 被引次数: 12
出版历程
  • 收稿日期:  2023-02-08
  • 修回日期:  2023-05-30
  • 录用日期:  2023-08-22
  • 网络出版日期:  2023-08-28
  • 刊出日期:  2024-01-31

目录

/

返回文章
返回