基于改进突变理论的滑坡危险性评价

张蕊; 郭荣昌; 贺攀; 余岭燕

doi:10.16031/j.cnki.issn.1003-8035.202112034

基于改进突变理论的滑坡危险性评价

兰州交通大学自动化与电气工程学院，甘肃兰州　730070

基金项目: 甘肃省自然科学基金（21JR1RA254）；兰州交通大学青年科学基金项目（2018021）

详细信息

作者简介: 张　蕊（1994-），女，汉族，陕西西安人，硕士研究生，研究方向为地质灾害风险评估。E-mail：2991099579@qq.com

通讯作者: 郭荣昌（1986-），男，汉族，河南林州人，博士，副教授，研究方向为地质灾害风险评估。E-mail：grc_mail@126.com

中图分类号: P642.22

收稿日期: 2021-12-28

修回日期: 2022-04-07

刊出日期: 2023-02-25

Landslide hazard assessment based on improved catastrophe theory

School of Automation & Electrical Engineering of Lanzhou Jiaotong University, Lanzhou，Gansu　730070, China

More Information

Corresponding author: GUO Rongchang, grc_mail@126.com

Received Date: 28 December 2021

Revised Date: 07 April 2022

Publish Date: 25 February 2023

摘要

摘要:
滑坡危险性评价是滑坡风险评估的重要组成部分，对滑坡的预测和防治意义重大。传统滑坡危险性评价在计算指标间重要性时多采用AHP、专家评判法、模糊综合评判等方法，但存在主观性较强，计算较为复杂等问题。研究基于一种改进的突变理论模型对滑坡进行危险性评价，选取坡度、坡向、高程、平面曲率、剖面曲率、距河流距离、地层岩性、土地利用类型、距断层距离、植被覆盖率、24 h降雨以及人类工程活动等12 个因子作为滑坡危险性评价的影响因子，采用熵权法判定指标间的相对重要性，并建立滑坡危险性评价体系；然后对指标进行标准化、归一化，计算总突变结果；最后使用拟合函数对总突变结果进行转换，得到新的滑坡危险性评价准则，并以雅安市的20 条滑坡对评价准则进行实例验证。结果表明，突变理论得到的评价结果准确率为90%，评价结果更加直观准确。
- 滑坡 /
- 危险性评价 /
- 突变理论 /
- 熵权法
Abstract:
Landslide hazard assessment is an important part of landslide risk assessment, which is of great significance to landslide prediction and prevention. Analytic Hierarchy Process（AHP）, expert evaluation, fuzzy comprehensive evaluation and other methods were often used in traditional landslide hazard evaluation to calculate the importance of inter-index, which were subjective and complicated. This paper introduced an improved model of mutation theory, which overcame the limitation of traditional methods and achieved higher evaluation accuracy. Firstly, according to field investigation and previous studies, 12 factors including slope, slope direction, elevation, plane curvature, profile curvature, distance from river, stratigraphic lithology, land use type, distance from fault, vegetation coverage rate, 24 h rainfall and human engineering activities were selected as influencing factors of landslide risk assessment, and the relative importance of indicators was determined by entropy weight method, and the landslide risk assessment system was established. Then the index was standardized and normalized, and the total mutation result was calculated. Finally, the fitting function was used to transform the total catastrophe result, and a new criterion of landslide risk assessment was obtained. Taking 20 landslides in Ya’an city as an example, the results showed that the accuracy of the evaluation results obtained by the catastrophe theory was 90%, and the improved evaluation results were more intuitive and accurate
- landslide /
- risk assessment /
- catastrophe theory /
- entropy weight method

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图 1 常用突变模型

Figure 1.

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图 2 底层指标与总突变结果拟合曲线

Figure 2.

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表 1 一维状态变量的突变模型

Table 1. Mutation model of one-dimensional state variables

突变模型	控制变量维数	势函数	归一公式
折叠突变	1
尖点突变	2
尖点突变	2
燕尾突变	3

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表 2 研究区滑坡的各评价指标

Table 2. Evaluation indexes of landslide in the study area

滑坡点	24 h降雨 /mm	地层岩性	距断层距离 /km	土地利用类型	坡度 /（°）	高程 /m	坡向 / （°）	平面曲率	剖面曲率	距河流距离 /km	植被覆盖率
1	17	砂岩	3.1176	有林地	11.5042	1403	22.8906	−0.5440	0.5321	0.3168	0.3029
2	2	砾岩	7.0588	灌木林	11.9137	1002	99.0903	−0.5742	0.1138	0.1740	0.1429
3	16	砂岩	11.1765	旱地	9.6462	789	11.3099	0.0217	0.1496	0.1740	−0.1176
4	9	砂岩	3.8235	疏林地	11.2428	968	326.9761	−0.0350	0.0433	0.1020	−0.0078
5	18	砂岩	7.0588	旱地	27.0311	696	210.9638	0.1002	−0.1583	0.4400	0.2735
6	12	砾岩	0.4118	旱地	15.9518	809	122.7352	0.0380	0.2003	0.0900	0.3369
7	18	砂岩	5.0588	水田	24.1319	1827	170.3625	0.0489	−0.0072	0.2800	0.4900
8	6	砂岩	7.6471	高覆盖度草地	16.7599	815	255.5792	−0.0965	0.0915	0.0432	0.4749
9	8	泥岩	2.3529	旱地	20.9576	1574	81.8699	−0.0307	−0.1013	0.2720	0.3189
10	17	泥岩	6.4706	中覆盖度草地	20.8143	1103	243.9967	−0.1543	−0.0356	0.1260	0.2003
11	3	砂岩	4.7059	城镇用地	12.9588	649	58.3245	0.1499	−0.0642	0.0300	−0.0732
12	17	砂岩	2.6471	有林地	20.7455	1205	124.3151	0.0250	−0.1204	0.3000	0.3348
13	15	砂岩	9.0000	中覆盖度草地	23.0888	2094	85.5154	−0.0577	−0.2289	8.6000	0.1837
14	18	砂岩	4.1176	旱地	7.8539	611	25.0169	−0.0866	0.2141	0.0800	0.1813
15	13	冲洪积砾石及砂土	2.2353	旱地	18.4350	1086	180.0000	−0.1286	−0.1171	0.1640	0.0000
16	5	砂岩	8.5294	旱地	18.5686	726	60.2551	0.0832	−0.0702	0.1000	0.2671
17	22	冲洪积砾石及砂土	2.3529	旱地	7.1172	1096	334.2900	−0.1590	0.4979	0.1680	0.3975
18	32	砂岩	8.4706	旱地	29.2601	1769	59.6209	0.1344	−0.0270	6.5000	0.4317
19	34	冲洪积砾石及砂土	8.8235	旱地	14.7525	576	85.4622	0.1103	0.0115	0.0440	0.2170
20	34	砂岩	7.0588	中覆盖度草地	14.7242	889	267.2737	0.3683	−0.3448	0.3120	0.3745

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表 3 滑坡危险性评价体系

Table 3. Landslide risk assessment system

目标层	突变模型	准则层	突变模型	中间层	突变模型	指标层
滑坡危险性A	燕尾突变（非互补）	地形地貌B₁	尖点突变（非互补）	地貌C₁	燕尾突变（非互补）	剖面曲率D₁
						平面曲率D₂
						坡向D₃
				滑坡形态C₂	尖点突变（互补）	高程D₄
						坡度D₅
		地质条件B₂	燕尾突变（非互补）	岩性条件C₃	折叠突变	地层岩性D₆
				构造条件C₄	尖点突变（非互补）	距断层距离D₇
						距河流距离D₈
				植被条件C₅	折叠突变	植被覆盖率D₉
		诱发因素B₃	折叠突变	致灾因子C₆	燕尾突变（非互补）	24 h降雨D₁₀
						土地利用类型D₁₁
						人类工程活动D₁₂

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表 4 底层指标$ x $与总突变结果$ y $对应关系

Table 4. Corresponding relationship between underlying indicators $ x $ and total mutation results $ y $

x	0.00	0.05	0.10	0.15	0.20	0.25	0.30
y	0.0000	0.5866	0.7407	0.7900	0.8215	0.8451	0.8640
x	0.35	0.40	0.45	0.50	0.55	0.60	0.65
y	0.8799	0.8937	0.9058	0.9167	0.9266	0.9356	0.9440
x	0.70	0.75	0.80	0.85	0.90	0.95	1.00
y	0.9517	0.9590	0.9658	0.9723	0.9784	0.9842	0.9897

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表 5 标准化结果

Table 5. Standardization results

序号	剖面曲率	平面曲率	坡向	高程	坡度	地层岩性	距断层距离	距河流距离	植被覆盖率	降雨	土地利用类型	人类工程活动
1	0.9448	0.0845	0.0749	0.4956	0.1978	0.90	0.7696	0.9693	0.3532	0.4299	0.70	0.89
2	0.5112	0.0554	0.5236	0.2709	0.2137	0.60	0.4391	0.9844	0.5926	0.0050	0.60	0.34
3	0.5483	0.6302	0.0067	0.1516	0.1257	0.90	0.0937	0.9844	0.9824	0.4142	0.50	0.35
4	0.4381	0.5755	0.2170	0.2519	0.1876	0.90	0.7104	0.9920	0.8180	0.1928	0.80	0.30
5	0.2291	0.7059	0.8351	0.0995	0.8000	0.90	0.4391	0.9562	0.3973	0.4484	0.50	0.40
6	0.6009	0.6459	0.6628	0.1628	0.3703	0.60	0.9965	0.9933	0.3023	0.3021	0.50	0.33
7	0.3858	0.6563	0.9432	0.7331	0.6876	0.90	0.6068	0.9732	0.0733	0.4619	0.40	0.80
8	0.4880	0.5161	0.5974	0.1662	0.4016	0.90	0.3897	0.9983	0.0958	0.1115	1.10	0.32
9	0.2882	0.5796	0.4222	0.5914	0.5645	1.40	0.8337	0.9740	0.3293	0.1648	0.50	0.32
10	0.3563	0.4604	0.6591	0.3275	0.5589	1.40	0.4884	0.9895	0.5067	0.4299	1.20	0.32
11	0.3266	0.7538	0.2835	0.0732	0.2542	0.90	0.6364	0.9997	0.9159	0.0415	0.10	0.20
12	0.2684	0.6333	0.6721	0.3846	0.5562	0.90	0.8091	0.9711	0.3054	0.4299	0.70	0.30
13	0.1559	0.5536	0.4436	0.8827	0.6471	0.90	0.2763	0.0912	0.5315	0.3869	1.20	0.48
14	0.6152	0.5257	0.0874	0.0519	0.0562	0.90	0.6857	0.9944	0.5351	0.4485	0.50	0.31
15	0.2718	0.4852	1.0000	0.3180	0.4666	1.50	0.8436	0.9855	0.8064	0.3077	0.50	0.32
16	0.3204	0.6895	0.2949	0.1163	0.4718	0.90	0.3157	0.9923	0.4068	0.0893	0.50	0.30
17	0.9093	0.4558	0.1781	0.3236	0.0276	1.50	0.8337	0.9851	0.2117	0.5660	0.50	0.30
18	0.3652	0.7389	0.2911	0.7006	0.8865	0.90	0.3207	0.3138	0.1605	0.8430	0.50	0.46
19	0.4051	0.7156	0.4433	0.0323	0.3238	1.50	0.2911	0.9982	0.4817	0.9048	0.50	0.35
20	0.0357	0.9645	0.5351	0.2076	0.3227	0.90	0.4391	0.9698	0.2461	0.9050	1.20	0.40

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表 6 滑坡危险性评价准则

Table 6. Criteria for landslide hazard assessment

危险性级别	高危险	中危险	低危险
改进前	(0.9100, 1]	(0.8500, 0.9100]	(0, 0.8500]
改进后	(0.4798, 1]	(0.2916, 0.4798]	(0, 0.2916]

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表 7 滑坡危险性评价结果

Table 7. Landslide risk assessment results

序号	改进前	危险性	改进后	危险性	现场调查结果
1	0.8057	低危险	0.2019	低危险	低危险
2	0.6435	低危险	0.0526	低危险	低危险
3	0.6586	低危险	0.0596	低危险	低危险
4	0.8561	中危险	0.3068	中危险	中危险
5	0.8880	中危险	0.3998	中危险	中危险
6	0.8654	中危险	0.3313	中危险	高危险
7	0.8493	低危险	0.2900	低危险	低危险
8	0.8330	低危险	0.2531	低危险	低危险
9	0.8605	中危险	0.3181	中危险	中危险
10	0.9140	高危险	0.4961	高危险	高危险
11	0.7670	低危险	0.1465	低危险	低危险
12	0.9216	高危险	0.5281	高危险	高危险
13	0.9019	中危险	0.4486	中危险	中危险
14	0.7434	低危险	0.1204	低危险	低危险
15	0.9046	中危险	0.4589	中危险	中危险
16	0.8177	低危险	0.2230	低危险	低危险
17	0.8124	低危险	0.2134	低危险	中危险
18	0.8919	中危险	0.4130	中危险	中危险
19	0.8113	低危险	0.2114	低危险	低危险
20	0.8310	低危险	0.2492	低危险	低危险

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