Elsevier

Computers & Geosciences

Volume 32, Issue 8, October 2006, Pages 1069-1078
Computers & Geosciences

An inverse analysis of unobserved trigger factor for slope stability evaluation

https://doi.org/10.1016/j.cageo.2006.02.004Get rights and content

Abstract

This paper presents an inverse analysis of unobserved trigger factors for slope failures and landslides, based on structural equation modeling (SEM). Quantitative prediction models generally elucidate the relationship between past slope failures and causal factors (e.g. lithology, soil, slope, aspect, etc.), but do not consider trigger factors (e.g. rail fall, earthquake, weathering, etc.), due to difficulties in pixel-by-pixel observation of trigger factors. To overcome these, an inverse analysis algorithm on trigger factors is proposed, according to the following steps:

  • Step 1: The relationship between past slope failures (i.e. the endogenous variables), causal factors and trigger factors (i.e. the exogenous variables) are delineated on the path diagram used in SEM.

  • Step 2: The regression weights in the path diagram are estimated to minimize errors between the observed and reemerged ‘variance–covariance matrix’ by the model.

  • Step 3: As an inverse estimation, through the measurement equation in SEM between causal and trigger factors, a trigger factor influence (TFI) map is proposed.

As an application, TFI maps are produced with respect to ‘slope failures’ and ‘landslides’, separately. As a final outcome, the differences in these TFI maps are delineated on a ‘difference’ (DIF) map. The DIF map and its interpretation are useful, not only for assessing danger areas affected by trigger factors, but also for ‘heuristic information’ in locating field measuring systems.

Introduction

The ‘when’, ‘where’ and ‘scale’ of slope failures and landslides are important aspects in preventing loss of life, as well as social and economic infrastructures against unpredictable risk. Due to the limitation of detailed field investigations, a research approach, applying the satellite remote sensing data and the various types of geographical information (causal factor), could identify areas susceptible to slope failure and landslides. However, at present, quantitative prediction models for the slope failures deal only with causal factors (Kasa et al., 1991; Carrara et al., 1995, Carrara et al., 1998; Chung et al., 1995; Obayashi et al., 1999) and do not consider trigger factors, such as the localized downpours, earthquake, weathering, etc., because of the difficulty of pixel-by-pixel observation of the trigger factors themselves.

As opposed to previous research, we consider it important that trigger factors should be treated as ‘unobserved factors’, in terms of time and space, and used in prediction. In estimating such trigger factors, the key questions are:

  • How can we incorporate trigger factors in prediction modeling?

  • Is it possible to estimate trigger factors quantitatively?

With the above background, we tackled the following problems:

  • To construct an inverse analysis algorithm for trigger factors, based on the structural equation modeling (SEM).

  • To produce the trigger factor influence (TFI) maps with respect to slope failure and landslides, as well as considering its application in slope failure and landslide hazard assessment.

The study area is located on Futtu in Chiba Prefecture (Japan). In the rainy season, between June and August in 1988, localized downpours, with continuous rainfall, caused slope failures and landslides in this area. The slope failure and landslide occurred on June 22 and August 14, 1988, respectively. Through field investigation and aerial photography, the occurrences were precisely plotted on a topographical map as the training data sets for constructing the quantitative prediction model. It should be noted that there were no major slope failures or landslides subsequent to 1988. The reason being that there were no exceptional ‘localized downpours with ‘continuous rainfall’ during the rainy season after 1988. In such exceptional weather conditions, the trigger factor should be estimated for landslide and slope failure hazard assessment.

The quantitative prediction model constructs the relationship between past occurrences and the following nine causal factors (Table 1): (1) vegetation, (2) surface geology, (3) soil, (4) vegetation index, (5) land cover, (6) slope, (7) aspect, (8) elevation, and (9) drainage. Each causal factor consists of 100×50 pixels (3.0×1.5 km, 30 m/pixel, corresponding to the ground resolution of the Landsat TM data). The latter four factors were produced from the digital elevation model (DEM). Experts in each research field constructed the soil, surface geology and vegetation maps. The land cover map was made through the maximum likelihood classification (MLC) for the Landsat TM data. The vegetation index map was also produced by calculating the normalized vegetation index (NVI) given byNVI=(B7-B5)/(B7+B5),where B5 and B7 are the digital numbers in each pixel, corresponding to TM-Band 5 and TM-Band 7, respectively.

Section snippets

Concept of an inverse analysis of trigger factor

Fig. 1 shows the inverse analysis concept of unobserved trigger factors, expanding the previous quantitative prediction model. Chung and Fabbri (1999) have adopted formulae for geologic hazard zonation as part of a ‘favorability function’ approach, and the various procedures have been applied to the landslide prediction. To upgrade these models, as well as optimizing prediction, practical analytical procedures have been presented as follows: (i) comparative strategy of the prediction models (

Formulation of estimating unobserved trigger factor

Note that the path components connecting unobserved variables to each other and observed variables to unobserved variables are generally termed structural equations and measurement equations, respectively. In this study, through the measurement equation, the influences of the trigger factor are inversely estimated in each pixel and delineated on a TFI map. In the path diagram shown in Fig. 3a, the measurement equation between trigger factors (as unobserved variables) and causal factors (as

Conclusions

In this paper, we have discussed the inverse analysis of unobserved trigger factors with respect to slope failures, as well as landslides, based on structural equation modeling (SEM). The results can be summarized as follows:

  • Due to difficulties in pixel-based observation of the trigger factor, we highlight the necessity for inverse estimation of unobserved trigger factors themselves. As an innovative approach, based on the measurement equation between causal factors (as observed variables) and

Acknowledgements

Funding was partly supported by the Grant-in-Aid for Scientific research program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan. We wish to thank Professor Ryosuke Kitamura of Kagoshima University, who provided useful comments on the inverse analysis results of the trigger factor, with respect to the hazardous slope composed of shirasu deposits in this study area.

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