Factor analysis for the statistical modeling of earthquake-induced landslides

Abstract

Earthquake-induced landslides are difficult to assess and predict owing to the inherent unpredictability of earthquakes. In most existing studies, the landslide potential is statistically assessed by collecting and analyzing the data of historical landslide events and earthquake observation records. Unlike rainfall-induced landslides, earthquake-induced landslides cannot be predicted in advance using real-time monitoring systems, and the development of the models for these landslides should instead depend on early earthquake warnings and estimations. Hence, in this study, factor analysis was performed and the frequency distribution method was employed to investigate the potential risk of the landslides caused by earthquakes. Factors such as the slope gradient, lithology (geology), aspect, and elevation were selected and classified as influential factors to facilitate the construction of a landslide database for the area of study.

Keywords

earthquake / factor analysis / slope landslides / statistical modeling

Research background and objective

The dynamic reliability and factor analysis for the project is still in search of domestic and international research in the exploration stage [¹]. Slope landslides are affected by various factors including earthquakes, rainfall, geology, topography, and gradient. Conventional methods for determining the probability of the slope disasters caused by earthquakes are generally limited to local engineering models, which require detailed geological surveys and reasonable geomechanical models, and the models are analyzed by using a collection of historical landslide cases and earthquake records [²–⁴]. These are done to systematically reduce the landslide risk by for instance upgrading substandard man-made slopes to modern safety standards [⁵]. Some numerical methods for analyzing the slope stability can also be considered [⁶–⁸].

Scientists have recently proposed methods based on physical modeling, suggesting that these may be more accurate because they use expressions based on universal physical laws. Furthermore, analysis of past landslides may provide useful data, which can be used in methods based on physical modeling [⁹–¹⁴]. In this study, factor analysis was performed and the frequency distribution method was employed to investigate the potential risk and factors of the slope landslides caused by earthquakes [¹⁵]. Factors such as the slope gradient, lithology (geology), aspect, and elevation were included in the analysis and classified as influential factors to facilitate the construction of a landslide database for the area of study.

Factors that affect the potential of slope landslides

The factors that induce slope landslides and debris flows can be categorized into two types: potential and inducing factors. Potential factors are the intrinsic characteristics of the slopes that contribute to the occurrence of landslides, and these include topographic and geological features, such as geology, aspect, slope, rock strength, joint orientation, and distance to faults. Inducing factors generally refer to the external damaging factors that can directly induce landslides, such as earthquakes, rainfall, weathering, typhoons, and construction. Generally, potential factors are determined by the type of the slope, whereas the inducing factors decide the timing of a hazardous event.

Lithology is one of the major controling factors of landslides. For instance, landslides tend to occur in loose rock strata and frequently in ancient and hard grounds, where the strata tend to be relatively fragmented [¹⁶–¹⁸]. In addition, the slope gradient is a primary determinant for the occurrence of landslides. It is commonly observed that a slope becomes increasingly unstable as its gradient increases, and landslides have, therefore, a high probability of occurrence in extremely steep slope regions. For example, the landslides induced by the Taiwan, China 921 Jiji earthquake in 1999 occurred mostly in areas with a slope gradient of over 55% (≈29°) and a significantly large number of landslides also occurred in areas with gradients over 100% (≈45°) [¹⁶].

In this study, we reviewed carefully selected 76 landslide-related articles that were published from 1985 to 2014, including the articles from 1996 to 2005 that were reviewed by Wen [¹⁸]. The potential landslide factors in each article were extracted, and then counted and summarized, as presented in Table 1. A total of 12 factors were considered.

Factor analysis and the frequency distribution method

Factor analysis is a method for simplifying variables, analyzing the categorization of variables, and constructing relationships between variables. In factor analysis, the sample size and model selection are key issues [³¹]; a large sample size will be preferable in factor analysis to increase its effectiveness [³²].

The objective of factor analysis is to examine the correlation between variables: 1) in Bartlett’s test of sphericity, if the results are statistically significant, there must be a level of homoscedasticity in the correlation coefficients of the variables, and the p value must be less than 0.05; 2) to determine whether the variables are highly correlated, we derived the measure of sampling adequacy (MSA) coefficients, and then averaged these to obtain the Kaiser-Meyer-Olkin (KMO) MSA. If the KMO MSA is larger than 0.6, the samples are suitable for factor analysis [³²]. The results of these tests for the factors affecting the potential risk of slope landslides (listed in Table 1) are presented in Table 2; the KMO MSA value of 0.600 is within the acceptable range.

To simplify the factor analysis, the number of factors included within the analysis should be minimized. The criteria for the number of principal components that were used to determine the components to be retained were: 1) principal components corresponding to the correlation matrix of the measured variables with eigenvalues larger than 1.0 are retained; 2) the Scree test is based on the same principles as those of the principal component analysis; therefore, Scree plots are used as information for determining the number of influential factors [³²]. Figure 1 illustrates the Scree plot for the 12 factors (Table 1) that affect the potential of slope landslides.

In comparison, the frequency distribution of the data are useful for identifying the characteristics of the data. Based on the Scree plot of the factor analysis shown in Fig. 1, it is inferred that four factors having corresponding eigenvalues larger than 1.0 can be selected as the influential factors. Thus, four of the most frequently selected factors for the potential of slope landslides are chosen. These are the slope gradient, lithology (geology), aspect, and elevation.

Conclusions

In this study, the potential risk and factors of slope landslides induced by earthquakes were analyzed. The 12 potential factors reported in 76 articles were summarized and simplified via factor analysis and the frequency distribution method. The Scree test was performed to determine the number of influential factors, namely, the slope gradient, lithology (geology), aspect, and elevation. The Scree test and frequency distribution method could be adopted to simplify the number of influential factors and obtain the Kaiser-Meyer-Olkin measure of sampling adequacy of the selected variables. The inherent unpredictability of earthquakes makes it difficult to predict the landslide disasters caused by them. In most of the existing studies, the landslide potential is statistically assessed by collecting and analyzing the data of the historical landslide events and earthquake observation records, and these are used for providing early earthquake warnings and risk assessments. Future research will apply the proposed methodology for modeling earthquake-induced landslide fragility curves.

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