降雨型群发浅层土质滑坡运动距离经验预测模型研究

黄瑞健; 冯文凯; 李双权; 柳侃; 唐雪峰; 郭朝旭; 易小宇

doi:10.19509/j.cnki.dzkq.tb20240364

降雨型群发浅层土质滑坡运动距离经验预测模型研究

doi: 10.19509/j.cnki.dzkq.tb20240364

1.
成都理工大学地质灾害防治与地质环境保护全国重点实验室，成都 610059
2.
自然资源部丘陵山地地质灾害防治重点实验室，福州 350002

基金项目: 国家自然科学基金（U2005205）；自然资源部丘陵山地地质灾害防治重点实验室（福建省地质灾害重点实验室）开放基金（FJKLGH2024K005）；福建省自然资源厅、福建省地质矿产勘查开发局科研项目（闽地灾专项务（2023）28号）

详细信息

作者简介:
黄瑞健：E-mail：1550392749@qq.com

通讯作者:
E-mail：fengwenkai@cdut.cn

中图分类号: P642.22
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- 文章访问数: 4
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-06-28
- 录用日期: 2025-02-14
- 修回日期: 2025-01-06
- 网络出版日期: 2025-04-24

Study on the Empirical Prediction Model for the Runout Distance of Rainfall-Induced Group-occurring Shallow Soil Landslides

1.
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China
2.
Key Laboratory of Geohazard Prevention of Hill Mountains of Ministry of Nature Resources, Fuzhou 350002, China

More Information

Author Bio:
E-mail：1550392749@qq.com

Corresponding author: E-mail：fengwenkai@cdut.cn

摘要

摘要:
降雨诱发的群发浅层土质滑坡具有突发性强和危险性高等特点，构建运动距离预测模型对滑坡风险防控具有重要意义。本研究以福建省武平县“5.27”群发滑坡事件为研究对象，基于灾前灾后遥感影像、数字高程模型、无人机三维模型和野外调查，获取了131个滑坡特征数据。根据剪出口位置和地形特征，将滑坡分为坡脚剪出型、坡中剪出和切坡剪出型，通过相关性分析确定影响群发浅层土质滑坡运动距离的主要因素，采用逐步非线性回归分析方法建立了3类滑坡运动距离的最优预测模型。研究表明，滑源区高差是降雨型群发浅层土质滑坡运动距离的主要影响因素；建立的最优预测模型残差平方和较小，调整R²值大于0.9，显示出较高的可信度和精度。模型验证表明，预测值与实际值的相对误差较小，坡脚剪出型、坡中剪出型和切坡剪出型的最大相对误差分别为15.6%、13.5%和12.4%。研究建立了基于统计分析的降雨型群发浅层土质滑坡运动距离预测模型，为类似地区的滑坡灾害防治提供了科学依据。尽管模型在不同类型的滑坡中表现出较高的预测精度，但研究数据主要来源于特定区域，在其他地区的适用性仍需进一步验证。未来研究可以考虑增加样本量和影响因子，进一步完善模型。
- 群发浅层土质滑坡 /
- 运动距离 /
- 相关性分析 /
- 逐步非线性回归
Abstract: Objective
Rainfall-induced group-occurring shallow soil landslides have the characteristics of strong and sudden occurrence and high risk. It is of great significance to build a runout distance prediction model for landslide risk prevention and control.
Methods
This study takes the "5.27" group-occurring landslide event in Wuping County, Fujian Province as the research object, and obtains 131 landslide characteristic data based on pre-disaster and post-disaster remote sensing images, digital elevation model, drone 3D model and field investigation. According to the location of the slip-out point and topographic characteristics, the landslides are divided into the foot slip-out type, the middle slope slip-out type and the cut slope slip-out type. The main factors affecting the runout distance of group-occurring shallow soil landslides were determined by correlation analysis, and the optimal prediction model for the runout distance of three types of landslides was established using stepwise nonlinear regression analysis.
Results
Correlation analysis shows that the height of the sliding source area is the main influencing factor of the runout distance of rainfall-induced group-occurring shallow soil landslides. The established optimal predictive models exhibited a small residual sum of squares (RSS) and an adjusted R² value greater than 0.9, indicating high reliability and precision. Model validation showed that the relative errors between the predicted and actual values were small, with maximum relative errors of 15.6%, 13.5%, and 12.4% for foot slip-out, middle slope slip-out, and cut slope slip-out types, respectively.
Conclusion
This study established a predictive model for the runout distance of rainfall-induced group-occurring shallow soil landslides based on statistical analysis, providing a scientific basis for landslide disaster prevention in similar regions. Although the models demonstrated high predictive accuracy across different types of landslides, the data were primarily sourced from a specific area, and further validation is needed for their applicability in other regions. Future research could consider increasing the sample size and influencing factors to further refine the models.
- group-occurring shallow soil landslides /
- runout distance /
- correlation analysis /
- stepwise nonlinear regression

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图 1 研究区数据来源

a. 灾前遥感影像；b. 灾后遥感影像；c. DEM；d. 三维模型多视角图

Figure 1. Data sources in the study area

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图 2 坡脚剪出型模式概化图

H. 滑源区高差；α. 滑坡坡度；L. 滑坡运动距离；下同

Figure 2. Schematic diagram of the foot slip-out type

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图 3 坡中剪出型模式概化图

β. 滑坡运动区坡度；下同

Figure 3. Schematic diagram of the middle slope slip-out type

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图 4 切坡剪出型滑坡示意图

H₁. 滑坡临空高度，下同

Figure 4. Schematic diagram of the cut slope slip-out type

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图 5 L与H的相关关系

a. 整体分析；b. 坡脚剪出型滑坡；c. 坡中剪出型滑坡；d. 切坡剪出型滑坡

Figure 5. Correlation between L and H

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图 6 L与S的相关关系

a. 整体分析；b. 坡脚剪出型滑坡；c. 坡中剪出型滑坡；d. 切坡剪出型滑坡

Figure 6. Correlation between L and S

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图 7 L与tanα的相关关系

a. 整体分析；b. 坡脚剪出型滑坡；c. 坡中剪出型滑坡；d. 切坡剪出型滑坡

Figure 7. Correlation between L and tanα

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图 8 L与λ的相关关系

a整体分析；b. 坡脚剪出型滑坡；c. 坡中剪出型滑坡；d. 切坡剪出型滑坡

Figure 8. Correlation between L and λ

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图 9 L与tanβ的相关关系

Figure 9. Correlation between L and tanβ

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图 10 L与H₁的相关关系

Figure 10. Correlation between L and H₁

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图 11 滑坡运动距离预测模型计算值与实际值对比

Figure 11. Comparison of calculated value and actual value of landslide runout distance prediction model

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表 1 用于坡脚剪出型预测模型构建的滑坡训练数据

Table 1. Landslide training data for constructing the prediction model of the foot slip-out type

序号	L/m	H/m	α/(°)	λ	S/m²	序号	L/m	H/m	α/(°)	λ	S/m²
1	37.5	12.6	44	1.2	215	34	20.3	10.1	45	1.5	118
2	64.1	20.4	40	2.9	321	35	65.7	27.7	39	2.0	1028
3	24.6	8.0	41	0.5	154	36	19.8	8.4	44	1.0	147
4	69.5	26.6	38	1.1	1404	37	25.3	7.8	43	1.0	145
5	43.4	19.5	42	1.2	541	38	30.0	11.8	43	2.0	121
6	60.7	23.6	39	1.5	794	39	77.8	34.0	39	1.7	1810
7	78.7	26.2	38	2.4	837	40	37.5	12.6	44	1.2	360
8	33.1	13.5	36	1.0	448	41	53.2	22.0	39	1.3	1185
9	82.0	32.2	39	1.7	1236	42	52.7	21.9	40	0.9	1121
10	78.9	26.1	40	1.7	957	43	47.5	22.5	40	1.2	938
11	88.5	36.5	40	2.2	1140	44	40.4	19.2	41	2.0	430
12	60.4	25.9	41	2.5	567	45	57.8	24.9	39	1.7	745
13	73.5	29.1	41	1.9	774	46	40.7	19.8	39	2.1	452
14	69.0	27.5	39	1.0	1879	47	61.8	30.6	41	1.6	1262
15	53.7	22.1	40	0.9	1461	48	23.3	11.9	44	0.9	306
16	47.5	22.6	39	1.2	1176	49	39.7	14.7	41	0.9	492
17	47.9	22.4	41	2.4	580	50	12.1	5.1	40	0.9	58
18	22.7	11.1	51	1.3	135	51	15.8	8.0	51	1.0	124
19	16.0	6.5	40	1.4	64	52	22.6	9.9	52	0.9	115
20	27.1	11.3	38	0.7	390	53	74.6	19.9	36	1.2	735
21	13.6	7.8	48	1.0	108	54	33.1	13.5	40	1.5	247
22	36.7	18.0	39	1.1	915	55	10.3	5.2	51	0.4	74
23	28.1	10.5	41	1.2	186	56	33.5	9.5	37	1.0	219
24	30.7	12.0	38	1.1	340	57	35.8	13.8	42	1.7	330
25	44.1	21.0	40	1.5	673	58	103.3	32.1	35	2.2	1452
26	35.2	11.7	40	1.2	285	59	23.4	7.5	41	0.8	146
27	17.7	8.6	42	1.8	81	60	21.2	9.2	44	1.7	76
28	63.1	26.8	38	2.2	1014	61	29.1	12.7	45	1.0	158
29	25.2	12.4	46	0.9	300	62	34.3	17.8	44	1.7	319
30	33.4	13.3	39	1.1	441	63	27.9	12.6	41	1.1	323
31	52.9	24.0	38	1.7	750	64	10.9	5.5	47	0.6	80
32	12.7	7.0	53	1.7	44	65	21.6	7.0	45	0.9	104
33	17.3	7.2	40	1.2	95
λ. 滑坡长宽比；S. 滑坡面积；下同

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表 2 用于坡中剪出型预测模型构建的滑坡训练数据

Table 2. Landslide training data for constructing the prediction model of the middle slope slip-out type

序号	L/m	H/m	α/(°)	λ	S/m²	β/(°)	序号	L/m	H/m	α/(°)	λ	S/m²	β/(°)
1	56.5	15.7	39	1.5	371	28	19	63.1	17.1	38	1.1	432	42
2	51.1	14.3	42	1.5	302	31	20	30.7	8.1	43	0.7	159	43
3	46.0	15.7	43	1.6	237	31	21	32.7	10.1	43	1.2	166	43
4	105.6	29.8	38	2.9	757	31	22	33.5	12.7	44	1.8	207	43
5	100.0	24.2	37	1.3	1181	32	23	54.8	16.2	42	2.0	345	43
6	56.0	19.2	40	1.1	823	33	24	62.8	19.6	39	1.6	641	44
7	75.3	19.1	41	1.3	660	33	25	80.9	22.1	40	1.0	1042	45
8	80.0	20.2	40	1.2	743	34	26	29.0	10.9	41	1.2	192	45
9	89.6	25.8	39	1.5	1123	34	27	64.9	22.8	40	1.6	776	45
10	88.5	21.5	37	1.6	677	34	28	26.9	8.5	38	1.1	148	46
11	45.5	12.9	39	0.8	521	36	29	82.0	22.9	38	1.8	720	46
12	50.2	12.9	43	1.4	331	36	30	43.6	14.3	36	1.0	619	47
13	92.0	17.6	36	1.6	545	36	31	28.9	9.0	39	1.1	163	48
14	43.6	15.5	42	2.6	278	39	32	50.0	15.3	40	1.3	480	48
15	58.9	15.7	42	1.3	422	40	33	24.8	9.9	44	1.1	178	50
16	77.6	27.2	42	1.9	1018	40	34	67.8	23.7	41	1.5	825	51
17	31.1	10.4	41	1.4	150	41	35	30.3	11.0	42	1.3	209	58
18	55.6	14.0	40	1.4	385	40

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表 3 用于切坡剪出型预测模型构建的滑坡训练数据

Table 3. Landslide training data for constructing the prediction model of the cut slope slip-out type

序号	L/m	H/m	α/(°)	λ	S/m²	H₁/m	序号	L/m	H/m	α/(°)	λ	S/m²	H₁/m
1	50.5	14.6	41	1.1	483	3.0	9	28.7	11.5	39	0.8	479	5.2
2	21.2	7.3	49	1.7	47	3.0	10	21.0	5.8	42	0.7	78	6.1
3	25.8	9.5	41	0.8	196	3.6	11	24.5	9.3	40	0.9	80	6.8
4	48.0	18.3	38	1.4	538	3.6	12	60.1	18.8	37	1.3	464	8.0
5	25.4	9.7	49	1.5	111	4.0	13	38.2	16.2	40	1.9	272	9.4
6	20.8	6.5	44	1.0	258	4.5	14	42.0	11.3	38	1.3	232	9.6
7	49.3	15.8	40	1.7	190	4.5	15	82.7	24.8	39	2.0	798	9.8
8	18.3	7.9	43	1.3	88	4.6	16	57.6	14.0	39	1.7	228	18.2

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表 4 坡脚剪出型滑运动距离预测回归模型

Table 4. Regression model for predicting the foot slip-out type landslides runout distance

序号	类型	预测模型	RSS	调整R²	F值
1	L(H)	L=2.23H^1.03	3295	0.8928	1336
2	L(H, S)	L=2.15H^0.98S^0.03	3276	0.8917	881
3	L(H, α)	L=2.67H^0.91(tanα)^−1.19	2289	0.9243	1270
4	L(H, α, λ)	L=2.86H^0.87(tanα)^−1.21(λ)^0.07	2240	0.9247	958

下载: 导出CSV

表 5 坡中剪出型滑运动距离预测回归模型

Table 5. Regression model for predicting the middle slope slip-out type landslides runout distance

序号	类型	预测模型	RSS	调整R²	F值
1	L(H)	L=3.063H^1.04	3159	0.8162	679
2	L(H, S)	L=2.46H^0.81S^0.14	2993	0.8204	463
3	L(H, α)	L=3.09H^0.95(tanα)^−1.42	1958	0.8825	714
4	L(H, S, α)	L=2.93H^0.91S^0.03(tanα)^−1.39	1952	0.8791	520
5	L(H, α, β)	L=3.55H^0.89(tanα)^−1.29(tanβ)^−0.24	1571	0.9027	648
6	L(H, α, β, λ)	L=3.29H^0.93(tanα)^−1.24(tanβ)^−0.24R^−0.07	1533	0.9019	514

下载: 导出CSV

表 6 切坡剪出型滑坡运动距离预测回归模型

Table 6. Regression model for predicting the cut slope slip-out type landslides runout distance

序号	类型	预测模型	RSS	调整R²	F值
1	L(H)	L=2.35H^1.1	563	0.8817	349
2	L(H, S)	L=2.4H^1.05S^0.02	662	0.8502	183
3	L(H, α)	L=2.5H^1.06(tanα)^−0.27	553	0.8749	220
4	L(H, λ)	L=2.65H^1.04(λ)^0.12	543	0.877	224
5	L(H, H₁)	L=2.13H^1.01H₁^0.18	367	0.9168	333

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