Abstract
Fractal phenomena are a naturally occurring characteristic of landslides. In the process of landsliding, a series of traces of the rupture surface on the ground surface extends progressively, as various types of slope failure occur. After this enlarging of the surface of rupture is completed, mass movements increase the volume of material because the displaced material dilates. After landslide occurrence, geometrical features of the rupture surface appearing on the ground surface are one way of providing information to evaluate slope instability. Correspondingly, fractal dimensions of the landslide boundary trace can reach a maximum in view of its geometry, which indicates that the landslide is in a critically stable state. In the case of changes of external factors, slide masses are likely to reactivate. This chapter addresses fractal dimensions of the trace of a landslide outline and its application in evaluating slope instability. In the vicinity of Badong County Town on the south shore of the Three Gorges Reservoir, fractal dimensions of 11 landslides with respect to boundary trace were calculated using a box-counting method. Six landslides were chosen as a case study to distinguish the relationship between fractal dimensions of boundary trace and slope instability. Compared with previous work in calculating the factor of safety, a landslide has the potential to reactivate if the value of fractal dimensions is between 1.4 and 1.5. A landslide is stable overall but minor slope failures are likely to occur in small areas, if the value of fractal dimensions is 1.1–1.3. A value of fractal dimensions of 1.0 indicates that the landslide is in a stable state. In summary, landslides with larger fractal dimensions in view of the boundary trace were evaluated as not being in a stable state.
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References
Bak P, Tang C, Wiesenfeld K (1988) Self-organized criticality. Physical Review A 11:364–374
Cai YJ, Guo QL, Yu YZ (2002) The reservoir-induced slope failure mechanism and prediction. Chinese Journal of Hubei Geology & Mineral Resources 16:4–8
Cruden DM, Varnes DJ (1996) Landslide types and processes. In: Turner, AK, Schuster RL (Eds.), Landslides Investigation and Mitigation. Transportation Research Board Special Report 247, National Research Council. National Academy Press: Washington DC, pp 36–75
Cui ZQ1 (1996) The main geological problem in the city of Badong county and its urgent countermeasures. Proceedings of International Symposium on Geological Environment of the Three Gorges Reservoir Area and Second Sino—Japan Strata Environment Mechanics. China Coal Industry Publishing House: Beijing, pp 15–22
Deng QL, Zhu ZY, Cui ZQ, Wang XP (2000) Mass rock creep and landsliding on the Huangtupo slope in the reservoir area of the Three Gorges Project, Yangtze River, China. Engineering Geology 58:67–83
Duncan JM (1996) State of the art: limit equilibrium and finite element analysis of slopes. Journal of Geotechnical Engineering 122:577–596
Geological Survey Bureau of Yangtze Water Resource Commission (1994). Report on the geological survey for the resettlement of Badong County Town in the Three Gorges Reservoir, unpublished
Guzzetti F, Malamud BD, Turcotte DL, Reichenbach P (2002) Power-law correlations of landslide areas in central Italy. Earth Planetary Science Letters 195:169–183
Li YS, Zhong YQ (Eds.) (1993) Large-scale landslides and rockfalls in the reservoir of Three Gorges project of Yangtze River. Guangdong Travel and Tourism Press: Guangzhou, China, pp 55–176
Liu B, Zeng QF, Yin ZL, Hu YJ (2002) The stability analysis and treatment study of Badong-Tongjiaping landslide. Chinese Journal of Hubei Geology & Mineral Resources 16:33–38
Liu CZ (1996) On some basic problems in evaluation of slope stability. Chinese Journal of Geological Hazard and Control 3:55–59
Nash D (1987) A comparative review of limit equilibrium methods of stability analysis. In: Anderson MG, Richards KS (Eds.), Slope Stability for Geotechnical Engineering and Geomorphology. John Wiley & Sons: New York, pp 11–75
Rouai M, Jaaidi EB (2003) Scaling properties of landslides in the Rif mountains of Morocco. Engineering Geology 68:353–359
Tan CX, Wang RJ (1999) Analysis on landslide stability by using three-dimensional numerical simulation. Chinese Journal of Changchun University of Science and Technology 29:267–271
Tang HM, Ma SZ, Liu YR, Jia HB (2002) Stability and control measures of Zhaoshuling landslide, Badong County, Three Gorges Reservoir. Chinese Journal of Earth Science 27:621–625
Turcotte DL, Malamud BD (2004) Landslides, forest fires, and earthquakes: examples of self-organized critical behavior. Physica. A, Statistical Mechanics and its Applications 340: 580–589
Wu SR, Shi L, Tan CX, Hu DG, Mei YT, Xu RC (2002a) Fractal analyses of the Huanglashi and Huangtupo landslides in the Three Gorges, Yangtze River China. Chinese Journal of Earth Science 25:61–65
Wu YF, Shi L, Wu MY, Huang SH (2002b) Questions in stability factor on control of large scale landslides of the Three Gorges Reservoir region. Chinese Journal of Hubei Geology & Mineral Resources 16:87–91
Yin TZ, Wu FQ, Yin KL (1989) Static and dynamic regularity of landslides and space-time prognosis of slope instability. Chinese Journal of Earth Science 2:119–133
Zhong YQ (1995) Study of prediction method by synthetic information for Huanglashi landslide. Chinese Journal of Geological Hazard and Control 4:68–80
Zhou PG, Ou ZD (1997) Stability estimation of the different types of gentle slope in the reservoir area of Three Gorge Project. Chinese Journal of Geological Hazard and Control 2:24–32
Acknowledgments
This research was financially supported by funding from National Nature Science Foundation of China (No. 40472153 and No. 40772170). Partial support from the Ministry of Science and Technology (No. 2006BAC04B05 and No. 2004DIB3J080) is acknowledged with thanks. The second author thanks the partial funding from Huazhong University of Science and Technology.
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Wu, S., Wang, H., Han, J., Shi, J., Shi, L., Zhang, Y. (2009). The Application of Fractal Dimensions of Landslide Boundary Trace for Evaluation of Slope Instability. In: Wang, F., Li, T. (eds) Landslide Disaster Mitigation in Three Gorges Reservoir, China. Environmental Science and Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00132-1_21
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DOI: https://doi.org/10.1007/978-3-642-00132-1_21
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