基于最大熵-无限边坡模型的降雨诱发浅层黄土滑坡稳定性评价方法研究

刘凡; 邓亚虹; 慕焕东; 钱法桥

doi:10.16030/j.cnki.issn.1000-3665.202207050

基于最大熵-无限边坡模型的降雨诱发浅层黄土滑坡稳定性评价方法研究

doi: 10.16030/j.cnki.issn.1000-3665.202207050

刘凡^{1, 2, 3,},
邓亚虹^{1, 2, ,},
慕焕东⁴,
钱法桥^{1, 2, 3}

1.
长安大学地质工程与测绘学院，陕西西安　710054
2.
自然资源部矿山地质灾害成灾机理与防控重点实验室，陕西西安　710054
3.
陕西省地质调查院，陕西西安　710068
4.
西安理工大学岩土工程研究所，陕西西安　710048

基金项目: 陕西省公益性地质调查项目（202101）；国家自然科学基金项目（41772275）；陕西省教育厅科学研究计划专项项目（20JK0801）；陕西省自然科学基础研究计划一般项目（2022JQ-289）；

详细信息

作者简介:
刘凡（1997-），男，博士研究生，主要从事地质灾害防治研究工作。E-mail：2020126091@chd.edu.cn

通讯作者:
邓亚虹（1978-），男，教授，博士研究生导师，主要从事工程地质与地质灾害防治研究工作。E-mail： dgdyh@chd.edu.cn

中图分类号: P642.22
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出版历程
- 收稿日期: 2022-07-29
- 录用日期: 2022-10-21
- 修回日期: 2022-10-13
- 网络出版日期: 2023-08-29
- 刊出日期: 2023-09-19

A study of the stability evaluation method of rainfall-induced shallow loess landslides based on the Maxent-Sinmap slope model

LIU Fan^{1, 2, 3
,},
DENG Yahong^{1, 2
, ,},
MU Huandong⁴,
QIAN Faqiao^{1, 2, 3}

1.
College of Geology Engineering and Geomatics, Chang’an University, Xi’an, Shaanxi　710054, China
2.
Key Laboratory of Mine Geological Hazards Mechanism and Control, MNR，Xi’an, Shaanxi　710054, China
3.
Shaanxi Institute of Geological Survey, Xi’an, Shaanxi　710068, China
4.
Institute of Geotechnical Engineering, Xi’an University of Technology, Xi’an, Shaanxi　710048, China

摘要

摘要: 无限边坡（Sinmap）模型在评价降雨作用下浅层黄土滑坡稳定性时精度较低。针对这一问题，基于最大熵（Maxent）模型对Sinmap模型评价进行改进，构建了最大熵-无限边坡（Maxent-Sinmap）模型，评价降雨作用下区域性浅层降雨型黄土滑坡稳定性。以黄土滑坡高发区的陕西省志丹县为例，利用野外及室内相关工作获取地形、岩土体力学参数及地质灾害等相关数据，通过Maxent模型获取主要环境变量，再根据主要环境变量进行分区，通过Sinmap模型对降雨作用下不同分区的浅层黄土滑坡稳定性进行评价。研究结果表明：基于Maxent模型得到志丹县内滑坡主要受坡度、降雨量、地貌、道路缓冲区及归一化植被覆盖指数等5个指标影响，对历史灾点的贡献率分别为27.1%、20.3%、18.8%、18.7%、6.2%。相较于传统Sinmap模型，该模型不稳定区域灾点密度在小雨、中雨、大雨、暴雨和大暴雨情况下分别提高了17.26%、16.54%、17.39%、14.20%、12.96%。Maxent-Sinmap模型计算结果相较于Sinmap模型计算结果具有更大的稳定区域，且稳定区的扩大区无历史灾点分布。表明该模型具有更高精度及更可靠的结果，可以更好的为区域性浅层降雨型滑坡评价提供科学依据。
- Maxent-Sinmap /
- 降雨作用 /
- 区域性 /
- 浅层黄土滑坡 /
- 稳定性评价
Abstract: To address the problem of low evaluation accuracy of the Sinmap model in evaluating the stability of shallow loess landslides under the action of rainfall, a method based on the Maxent-Sinmap model is constructed to evaluate the stability of regional shallow rainfall loess landslides under the action of rainfall by improving the evaluation of the Sinmap model based on the maximum entropy model.Taking Zhidan County, Shaanxi Province, a high-incidence area of loess landslides, as an example, the relevant data of topography, geotechnical parameters and geological disasters were obtained by field and indoor work. The main environmental variables were obtained by Maxent model, and then the main environmental variables were partitioned. The Sinmap model was used to evaluate the stability of shallow loess landslides in different partitions under rainfall. The results show that based on the Maxent model, the landslide in Zhidan County is mainly affected by five indicators, such as slope, rainfall, landform, road buffer zone and normalized vegetation coverage index. The contribution rates to historical disaster points are 27.1 %, 20.3 %, 18.8 %, 18.7 % and 6.2 %, respectively. Compared with the traditional Sinmap model, the density of disaster points in the unstable area of the model increased by 17.26 %, 16.54 %, 17.39 %, 14.20 % and 12.96 % respectively under the conditions of light rainfall, moderate rainfall, heavy rainfall, rainstorm and downpour. The results of the Maxent-Sinmap model have a larger stable area than those of the Sinmap model, and there is no historical disaster distribution in the expanded area of the stable area. The model has higher accuracy and more reliable results, which can provide a better scientific basis for the evaluation of regional shallow rainfall landslides.
- Maxent-Sinmap /
- rainfall /
- regional /
- shallow loess landslide /
- stability evaluation

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图 1 志丹县历史滑坡分布图

Figure 1. Distribution of historical landslides in Zhidan County

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图 2 志丹县地质灾害易发性评价图

Figure 2. Evaluation map of geological disaster susceptibility in Zhidan County

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图 3 模型验证ROC曲线图

Figure 3. Model validation ROC curve

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图 4 影响因子贡献率图

Figure 4. Impact factor contribution

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图 5 主要影响因子响应曲线

Figure 5. Response of the main influence factors

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图 6 志丹县校准区图

Figure 6. Zoning map of calibration area in Zhidan County

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图 7 分区情况下不同降雨下面积变化

Figure 7. Area variation under different rainfall in the zoning situation

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图 8 分区计算模型地表稳定性指数图

Figure 8. Surface stability index map of the partition calculation model

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图 9 未分区情况下不同降雨下面积变化

Figure 9. Change in area under different rainfall without zoning

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图 11 研究区滑坡稳定性评价结果验证

Figure 11. Verification of landslide stability evaluation results in the study area

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图 10 未分区计算模型地表稳定性指数图

Figure 10. Surface stability index of the non-partitioned calculation model

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图 12 不同降雨条件下稳定区扩大区示意图

Figure 12. Schematic diagrams of the expansion area of the stable area under different rainfall conditions

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表 1 稳定性分级

Table 1. Stability classification

稳定性级别	稳定性指数	稳定性
1	SI≥1.5	极稳定区
2	1.5≥SI>1.25	稳定区
3	1.25≥SI>1.0	基本稳定区
4	1.0≥SI>0.5	潜在不稳定区
5	0.5≥SI>0	不稳定区
6	SI=0	极不稳定区

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表 2 不同降雨量下的T/R参数值

Table 2. T/R parameter values under different rainfall

降雨级别	降雨量值/（mm·d⁻¹）	T/R下限	T/R上限
小雨	0.1～9.9	1000	3000
中雨	10～24.9	573	1270
大雨	25～49.9	344	1032
暴雨	50～99.9	172	516
大暴雨	100～200	86	258

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表 3 研究区分区岩土体物理力学参数

Table 3. Physical and mechanical parameters of rock and soil mass in the study area

区域	湿度/%	黏聚力		内摩擦角/（°）		土体密度 /（kg·m⁻³）
区域	湿度/%	上限	下限	上限	下限	土体密度 /（kg·m⁻³）
低降雨黄土丘陵区	15	0.2	0.4	25	40	1750
低降雨土石山区	15	0.28	0.54	31	55	1870
高降雨黄土丘陵区	18	0.2	0.4	30	50	1520
高降雨土石山区	18	0.28	0.54	31	55	1870

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表 4 研究区总区域岩土体物理力学参数

Table 4. Physical and mechanical parameters of rock and soil mass in the study area

区域	湿度/%	黏聚力		内摩擦角/（°）		土体密度 /（kg·m⁻³）
区域	湿度/%	上限	下限	上限	下限	土体密度 /（kg·m⁻³）
研究区	16	0.2	0.54	25	55	1728

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表 5 研究区分区计算结果汇总

Table 5. Summary of zonal calculation results in the study area

稳定性等级	R=8.6 mm		R=15 mm		R=25 mm		R=50 mm		R=100 mm
稳定性等级	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处
极稳定	2266.3	59	2108.9	45	1917.2	39	1655.7	29	1435.5	21
稳定	478.9	46	496.9	43	507.8	27	487.6	20	413.1	13
基本稳定	471.7	36	515.1	46	551.6	53	567.5	44	581.6	26
潜在不稳定	409.2	58	488.7	64	614.2	75	819.7	89	984.3	101
不稳定	56.7	11	71.1	12	88.7	16	142.9	26	243.7	44
极不稳定	5.3	1	6.7	1	7.4	1	12.1	3	23.2	6

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表 6 研究区未分区计算结果汇总

Table 6. Summary of calculation results without partitions in the study area

稳定性等级	R=8.6mm		R=15mm		R=25mm		R=50mm		R=100mm
稳定性等级	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处	面积/km²	滑坡数/处
极稳定	2128.4	55	1970.3	42	1782.3	35	1545.8	27	1354.6	20
稳定	508.1	46	516.7	44	517	30	476.7	20	392.5	14
基本稳定	527.8	39	568.9	47	591.6	54	579.7	45	564.3	26
潜在不稳定	554.6	70	660.4	76	822.1	89	1099.0	113	1361.4	141
不稳定	5.8	1	8.4	2	11.7	3	23.4	6	51.7	10
极不稳定	0	0	0	0	0	0	0.1	0	0.2	0

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参考文献(37)

[1]	刘东生,安芷生,文启忠,等. 中国黄土的地质环境[J]. 科学通报,1978,23(1):1 − 9. [LIU Dongsheng,AN Zhisheng,WEN Qizhong,et al. Geological environment of loess in China[J]. Chinese Science Bulletin,1978,23(1):1 − 9. (in Chinese) doi: 10.1360/csb1978-23-1-1 LIU Dongsheng, AN Zhisheng, WEN Qizhong, et al. Geological environment of loess in China[J]. Chinese Science Bulletin, 1978, 23（1）: 1-9. （in Chinese） doi: 10.1360/csb1978-23-1-1
[2]	索安宁,李金朝,王天明,等. 黄土高原流域土地利用变化的水土流失效应[J]. 水利学报,2008,39(7):767 − 772. [SUO Anning,LI Jinchao,WANG Tianming,et al. Effects of land use changes on river basin soil and water loss in loess plateau[J]. Journal of Hydraulic Engineering,2008,39(7):767 − 772. (in Chinese with English abstract) doi: 10.13243/j.cnki.slxb.2008.07.019 SUO Anning, LI Jinchao, WANG Tianming, et al. Effects of land use changes on river basin soil and water loss in loess plateau[J]. Journal of Hydraulic Engineering, 2008, 39（7）: 767-772. （in Chinese with English abstract） doi: 10.13243/j.cnki.slxb.2008.07.019
[3]	QIU Haijun, CUI Peng,REGMI A D,et al. Slope height and slope gradient controls on the loess slide size within different slip surfaces[J]. Physical Geography,2017,38(4):303 − 317. doi: 10.1080/02723646.2017.1284581
[4]	彭建兵,林鸿州,王启耀,等. 黄土地质灾害研究中的关键问题与创新思路[J]. 工程地质学报,2014,22(4):684 − 691. [PENG Jianbing,LIN Hungchou,WANG Qiyao,et al. The critical issues and creative concepts in mitigation research of loess geological hazards[J]. Journal of Engineering Geology,2014,22(4):684 − 691. (in Chinese with English abstract) doi: 10.13544/j.cnki.jeg.2014.04.014 PENG Jianbing, LIN Hungchou, WANG Qiyao, et al. The critical issues and creative concepts in mitigation research of loess geological hazards[J]. Journal of Engineering Geology, 2014, 22（4）: 684-691. （in Chinese with English abstract） doi: 10.13544/j.cnki.jeg.2014.04.014
[5]	陈林万,张晓超,裴向军,等. 降雨诱发直线型黄土填方边坡失稳模型试验[J]. 水文地质工程地质,2021,48(6):151 − 160. [CHEN Linwan,ZHANG Xiaochao,PEI Xiangjun,et al. Model test of the linear loess fill slope instability induced by rainfall[J]. Hydrogeology & Engineering Geology,2021,48(6):151 − 160. (in Chinese with English abstract) CHEN Linwan, ZHANG Xiaochao, PEI Xiangjun, et al. Model test of the linear loess fill slope instability induced by rainfall[J]. Hydrogeology & Engineering Geology, 2021, 48（6）: 151-160. （in Chinese with English abstract）
[6]	刘朋飞. 黄土高原地区环境变迁与地质灾害关系研究——以延安地区滑坡为例[D]. 西安: 长安大学, 2010 LIU Pengfei. Study on the environmental change and geological disasters of the loess plateau region: Take the landslide of Yan’an as an example[D]. Xi’an: Changan University, 2010. （in Chinese with English abstract）
[7]	卢永兴,陈剑,霍志涛,等. 降雨与开挖作用下黄土滑坡失稳过程分析—以关中地区长武县杨厂村老庙滑坡为例[J]. 地质科技通报,2022,41(6):95 − 104. [LU Yongxing,CHEN Jian,HUO Zhitao,et al. Analysis of instability process of the loess landslides under rainfall and excavation actions:A case study of Laomiao landslide at Yangchang Village in Changwu County, Guanzhong area[J]. Bulletin of Geological Science and Technology,2022,41(6):95 − 104. (in Chinese with English abstract) [LU Yongxing, CHEN Jian, HUO Zhitao, et al. Analysis of instability process of the loess landslides under rainfall and excavation actions: a case study of Laomiao landslide at Yangchang Village in Changwu County, Guanzhong area[J]. Bulletin of Geological Science and Technology, 2022, 41(6): 95-104.(in Chinese with English abstract)
[8]	杨志华,吴瑞安,郭长宝,等. 川西巴塘断裂带地质灾害效应与典型滑坡发育特征[J]. 中国地质,2022,49(2):355 − 368. [YANG Zhihua,WU Ruian,GUO Changbao,et al. Geo-hazard effects and typical landslide characteristics of the Batang fault zone in the western Sichuan[J]. Geology in China,2022,49(2):355 − 368. (in Chinese with English abstract) [YANG Zhihua, WU Ruian, GUO Changbao, et al. Geo-hazard effects and typical landslide characteristics of the Batang fault zone in the western Sichuan[J]. Geology in China, 2022, 49(2): 355-368.(in Chinese with English abstract)
[9]	VAN WESTEN C J,VAN ASCH T W J,SOETERS R. Landslide hazard and risk zonation—why is it still so difficult?[J]. Bulletin of Engineering Geology and the Environment,2006,65(2):167 − 184. doi: 10.1007/s10064-005-0023-0
[10]	田春山,刘希林,汪佳. 基于CF和Logistic回归模型的广东省地质灾害易发性评价[J]. 水文地质工程地质,2016,43(6):154 − 161. [TIAN Chunshan,LIU Xilin,WANG Jia. Geohazard susceptibility assessment based on CF model and logistic regression models in Guangdong[J]. Hydrogeology & Engineering Geology,2016,43(6):154 − 161. (in Chinese with English abstract) TIAN Chunshan, LIU Xilin, WANG Jia. Geohazard susceptibility assessment based on CF model and Logistic Regression models in Guangdong[J]. Hydrogeology & Engineering Geology, 2016, 43（6）: 154-161. （in Chinese with English abstract）
[11]	AYALEW L,YAMAGISHI H. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains,Central Japan[J]. Geomorphology,2005,65(1/2):15 − 31.
[12]	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) 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）
[13]	LEE S,RYU J H,WON J S,et al. Determination and application of the weights for landslide susceptibility mapping using an artificial neural network[J]. Engineering Geology,2004,71(3/4):289 − 302.
[14]	PRADHAN B. A comparative study on the predictive ability of the decision tree,support vector machine and neuro-fuzzy models in landslide susceptibility mapping using GIS[J]. Computers & Geosciences,2013,51:350 − 365.
[15]	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, 42（2）: 430-439. （in Chinese with English abstract）
[16]	SAITO H,NAKAYAMA D,MATSUYAMA H. Comparison of landslide susceptibility based on a decision-tree model and actual landslide occurrence:The Akaishi Mountains,Japan[J]. Geomorphology,2009,109(3/4):108 − 121.
[17]	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, 48（5）: 102-111. （in Chinese with English abstract）
[18]	兰恒星,周成虎,伍法权,等. GIS支持下的降雨型滑坡危险性空间分析预测[J]. 科学通报,2003,48(5):507 − 512. [LAN Hengxing,ZHOU Chenghu,WU Faquan,et al. Spatial analysis and prediction of rainfall landslide risk based on GIS[J]. Chinese Science Bulletin,2003,48(5):507 − 512. (in Chinese) doi: 10.3321/j.issn:0023-074X.2003.05.021 LAN Hengxing, ZHOU Chenghu, WU Faquan, et al. Spatial analysis and prediction of rainfall landslide risk based on GIS[J]. Chinese Science Bulletin, 2003, 48（5）: 507-512. （in Chinese） doi: 10.3321/j.issn:0023-074X.2003.05.021
[19]	武利. 基于SINMAP模型的区域滑坡危险性定量评估及模型验证[J]. 地理与地理信息科学,2012,28(2):35 − 39. [WU Li. A SINMAP-based quantitative assessment and model verification of regional landslide hazard[J]. Geography and Geo-Information Science,2012,28(2):35 − 39. (in Chinese with English abstract) WU Li. A SINMAP-based quantitative assessment and model verification of regional landslide hazard[J]. Geography and Geo-Information Science, 2012, 28（2）: 35-39. （in Chinese with English abstract）
[20]	李艳杰,唐亚明,邓亚虹,等. 降雨型浅层黄土滑坡危险性评价与区划—以山西柳林县为例[J]. 中国地质灾害与防治学报,2022,33(2):105 − 114. [LI Yanjie,TANG Yaming,DENG Yahong,et al. Hazard assessment of shallow loess landslides induced by rainfall:A case study of Liulin County of Shanxi ProvinceFull text replacement[J]. The Chinese Journal of Geological Hazard and Control,2022,33(2):105 − 114. (in Chinese with English abstract) LI Yanjie, TANG Yaming, DENG Yahong, et al. Hazard assessment of shallow loess landslides induced by rainfall: a case study of Liulin County of Shanxi ProvinceFull text replacement[J]. The Chinese Journal of Geological Hazard and Control, 2022, 33（2）: 105-114. （in Chinese with English abstract）
[21]	HE Jianyin, QIU Haijun, QU Feihang,et al. Prediction of spatiotemporal stability and rainfall threshold of shallow landslides using the TRIGRS and Scoops3D models[J]. CATENA,2021,197:104999. doi: 10.1016/j.catena.2020.104999
[22]	吕佼佼,范文,吕远强. 考虑土层深度分布的浅层滑坡危险性评价—以陕西秦巴山区为例[J]. 灾害学,2018,33(2):218 − 223. [LYU Jiaojiao,FAN Wen,LYU Yuanqiang. Hazard assessment of shallow landslide considering soil depth distribution—A case study of qinba mountains in Shaanxi Province[J]. Journal of Catastrophology,2018,33(2):218 − 223. (in Chinese with English abstract) doi: 10.3969/j.issn.1000-811X.2018.02.038 LYU Jiaojiao, FAN Wen, LYU Yuanqiang. Hazard assessment of shallow landslide considering soil depth distribution—a case study of qinba mountains in Shaanxi Province[J]. Journal of Catastrophology, 2018, 33（2）: 218-223. （in Chinese with English abstract） doi: 10.3969/j.issn.1000-811X.2018.02.038
[23]	姚杰,李秀珍,徐瑞池. 降雨条件下拟建川藏铁路典型段潜在滑坡三维稳定性动态识别研究[J]. 防灾减灾工程学报,2021,41(3):422 − 431. [YAO Jie,LI Xiuzhen,XU Ruichi. Dynamic identification of three-dimensional stability of potential landslides in a typical section of the proposed Sichuan-Tibet railway under rainfall conditions[J]. Journal of Disaster Prevention and Mitigation Engineering,2021,41(3):422 − 431. (in Chinese with English abstract) YAO Jie, LI Xiuzhen, XU Ruichi. Dynamic identification of three-dimensional stability of potential landslides in a typical section of the proposed Sichuan-Tibet railway under rainfall conditions[J]. Journal of Disaster Prevention and Mitigation Engineering, 2021, 41（3）: 422-431. （in Chinese with English abstract）
[24]	WEIDNER L,DEPREKEL K,OOMMEN T,et al. Investigating large landslides along a river valley using combined physical,statistical,and hydrologic modeling[J]. Engineering Geology,2019,259:105169. doi: 10.1016/j.enggeo.2019.105169
[25]	PACK R T, TARBOTON D G, GOODWIN C N. The SINMAP approach to terrain stability mapping. Proceedings of the 8^th congress of the International Association of Engineering Geology. Netherlands: A Balkema Publisher, 1998. 1157-1165.
[26]	武利,张万昌,张东,等. 基于遥感与地理信息系统的分布式斜坡稳定性定量评估模型[J]. 地理科学,2004,24(4):458 − 464. [WU Li,ZHANG Wanchang,ZHANG Dong,et al. Remote sensing & GIS-based distributed hillslope stability:quantitative evaluation model[J]. Scientia Geographica Sinica,2004,24(4):458 − 464. (in Chinese with English abstract) doi: 10.3969/j.issn.1000-0690.2004.04.012 WU Li, ZHANG Wanchang, ZHANG Dong, et al. Remote sensing & GIS-based distributed hillslope stability: quantitative evaluation model[J]. Scientia Geographica Sinica, 2004, 24（4）: 458-464. （in Chinese with English abstract） doi: 10.3969/j.issn.1000-0690.2004.04.012
[27]	康超,谌文武,张帆宇. 基于DEM的分布式斜坡稳定性模型在黄土沟壑区浅层滑坡中的应用[J]. 中南大学学报(自然科学版),2010,41(5):1987 − 1992. [KANG Chao,CHEN Wenwu,ZHANG Fanyu. Application of distributed hillslope stability model based on DEM to stability of shallow landslide of the loess gully area[J]. Journal of Central South University (Science and Technology),2010,41(5):1987 − 1992. (in Chinese with English abstract) KANG Chao, CHEN Wenwu, ZHANG Fanyu. Application of distributed hillslope stability model based on DEM to stability of shallow landslide of the loess gully area[J]. Journal of Central South University （Science and Technology）, 2010, 41（5）: 1987-1992. （in Chinese with English abstract）
[28]	麦鉴锋,冼宇阳,刘桂林. 气候变化情景下广东省降雨诱发型滑坡灾害潜在分布及预测[J]. 地球信息科学学报,2021,23(11):2042 − 2054. [MAI Jianfeng,XIAN Yuyang,LIU Guilin. Predicting potential rainfall-triggered landslides sites in Guangdong Province(China)using MaxEnt model under climate changes scenarios[J]. Journal of Geo-Information Science,2021,23(11):2042 − 2054. (in Chinese with English abstract) doi: 10.12082/dqxxkx.2021.210182 MAI Jianfeng, XIAN Yuyang, LIU Guilin. Predicting potential rainfall-triggered landslides sites in Guangdong Province（China）using MaxEnt model under climate changes scenarios[J]. Journal of Geo-Information Science, 2021, 23（11）: 2042-2054. （in Chinese with English abstract） doi: 10.12082/dqxxkx.2021.210182
[29]	CHEN W,POURGHASEMI H R,KORNEJADY A,et al. Landslide spatial modeling:introducing new ensembles of ANN,MaxEnt,and SVM machine learning techniques[J]. Geoderma,2017,305:314 − 327. doi: 10.1016/j.geoderma.2017.06.020
[30]	万洋,郭捷,马凤山,等. 基于最大熵模型的中尼交通廊道滑坡易发性分析[J]. 中国地质灾害与防治学报,2022,33(2):88 − 95. [WAN Yang,GUO Jie,MA Fengshan,et al. Landslide susceptibility assessment based on MaxEnt model of along Sino-Nepal traffic corridor[J]. The Chinese Journal of Geological Hazard and Control,2022,33(2):88 − 95. (in Chinese with English abstract) doi: 10.16031/j.cnki.issn.1003-8035.2022.02-11 WAN Yang, GUO Jie, MA Fengshan, et al. Landslide susceptibility assessment based on MaxEnt model of along Sino-Nepal traffic corridor[J]. The Chinese Journal of Geological Hazard and Control, 2022, 33（2）: 88-95. （in Chinese with English abstract） doi: 10.16031/j.cnki.issn.1003-8035.2022.02-11
[31]	PHILLIPS S J, ANDERSON R P, SCHAPIRE R E. Maximum entropy modeling of species geographic distributions[J]. Ecological Modelling, 2006, 190（3/4）: 231 − 259.
[32]	YANG Jilin,DONG Jinwei,XIAO Xiangming,et al. Divergent shifts in peak photosynthesis timing of temperate and alpine grasslands in China[J]. Remote Sensing of Environment,2019,233:111395. doi: 10.1016/j.rse.2019.111395
[33]	杨文璐,邱海军,裴艳茜,等. 典型黄土丘陵区浅层黄土滑坡稳定性评价—以延安市志丹县为例[J]. 第四纪研究,2019(2):408 − 419. [YANG Wenlu,QIU Haijun,PEI Yanqian,et al. Evalution of shallow loess landslide stability in typical loess hilly region:a case study of Zhidan County in Yan'an area of Shaanxi Province[J]. Quaternary Sciences,2019(2):408 − 419. (in Chinese with English abstract) doi: 10.11928/j.issn.1001-7410.2019.02.13 YANG Wenlu, QIU Haijun, PEI Yanqian, et al. Evalution of shallow loess landslide stability in typical loess hilly region: a case study of Zhidan County in Yan'an area of Shaanxi Province[J]. Quaternary Sciences, 2019（2）: 408-419. （in Chinese with English abstract） doi: 10.11928/j.issn.1001-7410.2019.02.13
[34]	国家质量监督检验检疫总局, 中国国家标准化管理委员会. 降水量等级: GB/T 28592—2012[S]. 北京: 中国标准出版社, 2012 General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China, Standardization Administration of the People’s Republic of China. Grade of precipitation: GB/T 28592—2012[S]. Beijing: Standards Press of China, 2012. （in Chinese）
[35]	王丽英,王红梅,郭盈盈,等. 基于不同建模数据的陕西省志丹县滑坡易发性分区[J]. 人民长江,2021,52(12):99 − 106. [WANG Liying,WANG Hongmei,GUO Yingying,et al. Landslide susceptibility mapping based on differentiated modeling data in Zhidan County,Shaanxi Province[J]. Yangtze River,2021,52(12):99 − 106. (in Chinese with English abstract) WANG Liying, WANG Hongmei, GUO Yingying, et al. Landslide susceptibility mapping based on differentiated modeling data in Zhidan County, Shaanxi Province[J]. Yangtze River, 2021, 52（12）: 99-106. （in Chinese with English abstract）
[36]	谢定义, 邢义川. 黄土土力学[M]. 北京: 高等教育出版社, 2016 XIE Dingyi, XING Yichuan. Soil mechanics for loess soils[M]. Beijing: Higher Education Press, 2016. （in Chinese）
[37]	郭靖,骆亚生,郭鸿,等. 不同地区黄土的结构性试验研究[J]. 水土保持通报,2010,30(1):89 − 92. [GUO Jing,LUO Yasheng,GUO Hong,et al. Experimental study on structural characteristics of loess in different regions[J]. Bulletin of Soil and Water Conservation,2010,30(1):89 − 92. (in Chinese with English abstract) GUO Jing, LUO Yasheng, GUO Hong, et al. Experimental study on structural characteristics of loess in different regions[J]. Bulletin of Soil and Water Conservation, 2010, 30（1）: 89-92. （in Chinese with English abstract）