Geological hazard assessment based on the models of AHP, catastrophe theory and their combination: A case study in Pingshan County of Heibei Province
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摘要: 河北平山县受地形地貌、地质构造和生态环境等因素的影响，崩滑流等地质灾害频发。选取地形起伏度、坡度、坡向、河网密度、断裂带密度、地层岩性、NDVI、土地利用类型及地质灾害点密度9个评价因子，用AHP和突变理论分别求各评价因子权重，并按最小信息熵权法结合，建立AHP-突变理论组合模型并应用，对比基于三种方法的平山县地质灾害危险性评价结果。结果表明：组合模型的评价结果精度更高，符合该区地质灾害发育特征；组合模型法将主客观结合，综合考虑因子的影响，评价结果可靠。该研究为平山县及类似地区地质灾害危险性评价提供一种新的尝试和方法。Abstract: Pingshan County, Hebei was affected by topography, geological structure, ecological environment and other factors, geological disasters such as landslides occurred frequently. Nine evaluation factors including topographic relief, slope, aspect, river network density, fault zone density, stratigraphic lithology, NDVI, land use type and geological disaster point density were selected. The weights of each evaluation factor were calculated by AHP and catastrophe theory, and the combination model of AHP and catastrophe theory was established and applied according to the minimum information entropy weight method. The results of geological disaster risk assessment in Pingshan County based on three methods were compared. The results show that the evaluation results of the combined model have higher accuracy and are in line with the development characteristics of geological disasters in this area. Combined model method combines subjective and objective, considering the influence of factors, the evaluation results are reliable. This study provides a new attempt and method for geological disaster risk assessment in Pingshan County and similar areas.
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图 2 石家庄市崩滑流地质灾害隐患点分布
Figure 2. Distribution of potential and geological hazard points of collapse, landslide and debris flow in Shijiazhuang
图 6 基于AHP平山县地质灾害危险性分区
Figure 6. Geological hazard zoning in Pingshan County based on AHP
图 7 基于突变理论平山县地质灾害危险性分区
Figure 7. Geological hazard zoning in Pingshan County based on catastrophe theory
图 8 基于AHP-突变组合模型平山县地质灾害危险性分区
Figure 8. Geological hazard zoning in Pingshan County based on AHP - catastrophe combination model
表 1 各评价方法求得权重对比
Table 1. Weight comparison of each evaluation method
目标层 准则层 评价因子层 AHP权重w1 突变理论权重w2 AHP-突变组合模型权重w3 A平山县地质
灾害危害性评价B1 地形地貌 C1 地形起伏度 0.1761 0.0795 0.1359 C2 坡度 0.3731 0.0717 0.1880 C3 坡向 0.0815 0.0795 0.0925 C4 河网密度 0.0380 0.0818 0.0641 B2 地质构造 C5 断裂带密度 0.0405 0.1065 0.0755 C6 地层岩性 0.2026 0.2486 0.2579 B3 生态环境 C7 NDVI 0.0249 0.1182 0.0624 C8 土地利用类型 0.0567 0.1220 0.0956 C9 灾害点密度 0.0065 0.0921 0.0281 
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表 2 状态变量的突变模型
Table 2. Catastrophe model of state variable
突变模型 控制变量维数 势函数 归一化公式 折叠突变 1 $ \dfrac{1}{3}{x^3} + ax $ $ {x_a} = \sqrt a $ 尖点突变 2 $\dfrac{1}{4}{x^4} + \dfrac{1}{2}a{x^2} + bx$ $ {x_a} = \sqrt a $；$ {x_b} = \sqrt[3]{b} $ 燕尾突变 3 $\dfrac{1}{5}{x^5} + \dfrac{1}{3}a{x^3} + \dfrac{1}{2}b{x^2} + cx$ $ {x_a} = \sqrt a $；$ {x_b} = \sqrt[3]{b} $；$ {x_c} = \sqrt[4]{c} $ 蝴蝶突变 4 $\dfrac{1}{6}{x^6} + \dfrac{1}{4}a{x^4} + \dfrac{1}{3}b{x^3} + \dfrac{1}{2}c{x^2} + dx$ $ {x_a} = \sqrt a $；$ {x_b} = \sqrt[3]{b} $；$ {x_c} = \sqrt[4]{c} $；$ {x_d} = \sqrt[5]{d} $
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表 3 危险性分区统计与对比
Table 3. Risk zoning statistics and comparison
评价方法 危险性等级 面积占比/% AHP 低 25.14 中 33.37 高 27.16 极高 14.33 突变理论 低 13.96 中 26.36 高 28.16 极高 31.51 AHP-突变理论组合模型 低 18.39 中 32.61 高 27.49 极高 21.51
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