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Magnitude–frequency relations in debris flow

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Environmental Geology

Abstract

Debris flow occurs frequently in mountainous regions in China. Because of the difficulties involved in predicting and catching live debris flows, an assessment of the potential for debris flow is crucial in hazard mitigation. Magnitude–frequency (MF) relations are of special significance in such assessments. In previous studies, MF relations have been inferred by analyzing environmental factors and historical records and using empirical relations. This paper is concerned with the derivation of MF relations at regional and valley scales, using a large database of statistics. At the regional scale, it is represented by the distribution of the valley area, because the area is often taken to indicate the potential magnitude of debris flow. Statistics from over 5,000 debris flow valleys in various provinces in China show that a power law holds for the distribution, i.e., p(A) ∼ A −n, where p(A) is the percentage of valleys with area A and n varies with region and thus describes regional differences. At the valley scale, a case study focusing on Jiangjia Gully (JJG) was conducted, and the MF relations derived from it were expressed by the distributions of discharge and runoff (i.e., the total volume) of living debris flows observed over the last 40 years. The distributions can be expressed as exponential functions where the exponents vary with the events. These MF relations provide not only a potential quantitative reference for practical purposes but also hint at the intrinsic properties of the debris flow.

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References

  • Alexander GN (1972) Effect of catchment area on flood magnitude. J Hydrol 16(3):225–240

    Article  Google Scholar 

  • AO HX, Liu J, Kuang MS, Zhang H, Bao HB (2006) Calculation of characteristics factors of debris flow under different frequency (in Chinese). Res Soil Water Conserv 13(4):93–95

    Google Scholar 

  • Bak P, Tang C, Wiesenfeld K (1988) Self-organized criticality. Phys Rev A38(1):364–374

    Google Scholar 

  • Beaty CB (1974) Debris flow, alluvial fans, and a revitalized catastrophism. Z Geomorphol 21(Suppl):39–51

    Google Scholar 

  • Chen H, Lee CF (2000) Numerical simulation of debris flows. Can Geotech J 37:146–160

    Article  Google Scholar 

  • Chen J, He YP, Wei FQ (2005) Debris flow erosion and deposition in Jiangjia Gully, Yunnan, China. Environ Geol 48:771–777

    Article  Google Scholar 

  • Cong WQ, Pan M, Li TF (2006) The prediction of debr is flows depending on hydrology and meteorology (in Chinese). J Mountain Sci 24(4):437–441

    Google Scholar 

  • Costa JE (1984) Physical geomorphology of debris flows. In: Costa JE, Fleischer PJ (eds) Developments and applications of geomorphology. Springer, Berlin, pp 268–317

  • Coussot P, Meunier M (1996) Recognition, classification and mechanical description of debris flows. Earth Sci Rev 40:209–227

    Article  Google Scholar 

  • Cui P, Chen XP, Wang YY, Hu KH, Li Y (2005) Jiangjia Ravine debris flows in the southwestern China. In: Jakob M, Hungr O (eds) Debris-flow hazards and related phenomena. Springer, Heidelberg, pp 565–594

  • D’Ambrosio D, Iovine G, Spataro W, Miyamoto H (2007) A macroscopic collisional model for debris-flows simulation. Environ Modell Softw 22:1417–1436

    Article  Google Scholar 

  • Davies TR (1986) Large debris flows: a macroviscous phenomenon. Acta Mech 63:161–178

    Article  Google Scholar 

  • Davies TR (1990) Debris-flow surges—experimental simulation. NZ J Hydrol 29:18–46

    Google Scholar 

  • Davies TR (1997) Using hydroscience and hydrotechnical engineering to reduce debris flow hazards. In: Chen C-L (ed) Debris-flow hazards mitigation: mechanics, prediction, and assessment: proceedings of the first international conference. American Society of Civil Engineers, San Francisco, CA, pp 787–810

  • Davies TR, Phillips CJ, Pearce AJ, Zhang XB (1991) New aspects of debris flow behavior. In: Proceedings of the US–Japan Workshop on Snow Avalanches, Landslides, Debris Flows Prediction and Control, 30 Sept–5 Oct, Tsukuba, Japan, pp 443–451

  • Fell R (1994) Landslide risk assessment and acceptable risk. Can Geotech J 31:261–272

    Article  Google Scholar 

  • Glade T (2005) Linking debris-flow hazard assessments with geomorphology. Geomorphology 66(14):189–213

    Article  Google Scholar 

  • Hergarten S (2002) Self-organized criticality in earth systems. Springer, Heidelberg, pp 272

    Google Scholar 

  • Hungr O (1997) Some methods of landslide hazard intensity mapping. In: Cruden D, Fell R (eds) International workshop on landslide risk assessment. Balkema, Amsterdam, pp 215–226

    Google Scholar 

  • Hungr O, Morgan GC, Kellerhals R (1984) Quantitative analysis of debris torrent hazards for design of remedial measures. Can Geotech J 21:663–677

    Article  Google Scholar 

  • Hürlimann M, Copons R, Altimir J (2006) Detailed debris flow hazard assessment in Andorra: a multidisciplinary approach. Geomorphology 78:359–372

    Article  Google Scholar 

  • Hutter K, Svendsen B, Rickenmann D (1996) Debris flow modeling: a review. Continuum Mech Thermodyn 8:1–35

    Article  Google Scholar 

  • Imran J, Parker G, Loeat J, Lee H (2001) 1D numerical model of muddy subaqueous and subaerial debris flows. J Hydraulic Eng 127(11):959–968

    Article  Google Scholar 

  • Innes JL (1985) Lichcnometric dating of debris-flow deposits on alpine colluvial fans in Southwest Norway. Earth Surf Process Landf 10:519–524

    Article  Google Scholar 

  • Iso N, Yamakawa K, Yonezawa H, Matsubara T (1980) Accumulation rates of alluvial cones, constructed by debris-flow deposits, in the drainage valley of the Takahara River, Gifu Prefecture, Central Japan. Geogr Rev 53:699–720

    Google Scholar 

  • Iverson RM (1997) The physics of debris flows. Rev Geophys 35(3):245–296

    Article  Google Scholar 

  • Iverson RM, Lahusen RG (1993) Friction in debris flows—inferences from large-scale flume experiments. In: Hydraulic engineering (Proc 1993 ASCE Conf). San Francisco, CA, pp 1604–1609

  • Jakob M (2005) Debris-flow hazard analysis. In: Jakob M, Hungr O (eds) Debris-flow hazards and related phenomena. Springer, Berlin, pp 411–443

    Chapter  Google Scholar 

  • Jarvis CS (1936) Flood in the united states. Geol Surv Water-Supply Pap (US) 771:1–479

    Google Scholar 

  • Johnson AM (1984) Debris flow. In: Brunsden D, Prior DB (eds) Slope instability. Wiley, New York, pp 257–361

    Google Scholar 

  • Kang ZC (1991) Calculation of peak discharges of debris flows (in Chinese). Chin J Water Soil Conserv 2:15–18

    Google Scholar 

  • Kang ZC, Cui P, Wei FQ, He SF (2006) Observation data of debris flows in Jiangjia Gully, Yunnan. Beijing Science Press, Beijing

    Google Scholar 

  • Li J, Yuan J, Luo D (1983) The main features of the mudflow in Jiangjia Ravine. Z Geomorphol 27:325–341

    Google Scholar 

  • Li Y, Hu KH, Cui P, Chen XQ, Yue ZQ (2002) Morphology of valley of debris flow. J Mountain Sci 20(1):1–11

    Google Scholar 

  • Li Y, Hu KH, Yue ZQ, Tham TG (2004) Termination and deposition of debris-flow surge. In: Lacerda W, Ehrlich M, Fontoura SAB, Sayao ASF (eds) Landslides: evaluation and stabilization. Taylor and Francis, London, pp 1451–1456

  • Li Y, Hu KH, Chen XQ, He SF (2005) Fractality of grain composition of debris flow. Acta Geogr Sin 15(3):353–359

    Google Scholar 

  • Li Y, Kang ZC, Yue ZQ, Tham LG, Lee CF, Law KT (2003) Surge waves of debris flow in Jiangjia Gully, Kunming, China. In: Picarelli L (ed) Proceedings of conference on fast slope movements prediction and prevention for risk mitigation, vol. 1. Patron Ed., Bologna, pp 303–307

  • Lin PS, Lin JY, Hung JC, Yang MD (2002) Assessing debris-flow hazard in a watershed in Taiwan. Eng Geol 66:295–313

    Article  Google Scholar 

  • Liu JJ, Li Y, Cheng ZL, Dang C (2007) Decaying of discharge of intermittent debris flow (in Chinese). J Graduate School Chin Acad Sci (in press)

  • Liu XL (1996) Assessment on the severity of debris flows in mountainous creeks of southwest China. In: Proceedings of the international symposium of INTERPRAEVENT 1996. Yagungspublikation, Garmisch-Partenkirchen, Germany, vol. 4, pp 145–154

  • Liu XL, Mo DW (2003) Risk assessment of debris flow (in Chinese). Sichuan Science Technology Press/Xin Jiang Science Sanitation Press, Chengdu/Urumchi

  • Liu XL, Tang C (1995) Hazard assessement of debris flow (in Chinese). Science Press, Beijing

    Google Scholar 

  • Liu XL, Zhang D (2004) Comparison of two empirical models for gully-specific debris flow hazard assessment in Xiaojiang Valley of Southwestern China. Nat Hazards 31:157–175

    Article  Google Scholar 

  • Major JJ (1997) Depositional processes in large-scale debris-flow experiments. J Geol 105:345–366

    Google Scholar 

  • Ohmori H, Hirano M (1988) Magnitude, frequency and geomorphologic significance of rocky mudflows, land creep and the collapse of steep slopes. Z Geomorphol 67(Suppl):55–65

    Google Scholar 

  • Parsons JD, Whipple KX, Simoni A (2001) Experimental study of the grain-flow. Fluid-mud transition in debris flows. J Geol 109:427–447

    Article  Google Scholar 

  • Pasuto A, Soldati M (2004) An integrated approach for hazard assessment and mitigation of debris flows in the Italian Dolomites. Geomorphology 61:59–70

    Article  Google Scholar 

  • PWRI (1988) Technical standard for measures against debris flow (draft; Technical Memorandum of PWRI, No. 2632). Ministry of Construction, Tokyo, Japan

  • Rapp A, Nyberg R (1981) Alpine debris flown in Northern Scandinavia. Geogr Ann 63A:183–196

    Article  Google Scholar 

  • Rickenmann D (1999) Empirical relationships for debris flows. Nat Hazards 19:47–77

    Article  Google Scholar 

  • Rigon R, Rinaldo A, Rodriguez-Iturbe I (1994) On landscape self-organization. J Geophys Res 99(6):11971–11993

    Article  Google Scholar 

  • Rodriguz-Iturbe I, Rinaldo RR (1997) Fractal river basins: chance and self-organization. Cambridge University Press, New York

    Google Scholar 

  • Sharp RP, Nobles LH (1953) Mudflow of 1941 at Wrightwood, Southern California. Bull Geol Soc Am 64:547–560

    Article  Google Scholar 

  • Stiny PJ (1997) Debris flows: an attempted monograph with particular reference to the conditions in the Tyrolean Alps (translation from the original 1910 German text by Jakob M, Skermer N). EBA Engineering Consultants Ltd., Vancouver, BC, Canada, pp 168

  • Takahashi T (1981) Debris flow. Ann Rev Fluid Mech 13:57–77

    Article  Google Scholar 

  • Takahashi T (2000) Initiation and flow of various types of debris flow. In: Wieczorek GF, Naeser ND (eds) Debris-flow hazards mitigation: mechanics, prediction, and assessment: proceedings of the second international conference. Balkema, Rotterdam, pp 15–25

  • Tan BY (1986) Quantified comprehensive evaluation for the scope and intensity of mud-rock flow gully activity (in Chinese). Bull Soil Water Conserv 6(1):51–57

    Google Scholar 

  • Tan WP, Wang CH, Yao LK (1994) Forecasting of rainstorm-induced landslides and debris flows, a case study in Panxi region (in Chinese). Sichuan Science and Technology Press, Chengdu, pp 187–192

    Google Scholar 

  • Turcotte DL (1997) Fractal and chaos in geology and geophysics. Cambridge University Press, Cambridge

    Google Scholar 

  • Van Steijn H (1996) Debris-flow magnitude–frequency relationships for mountainous regions of Central and Northwest Europe. Geomorphology 15:259–273

    Google Scholar 

  • Willgoose G, Bras RL, Rodriguez-Iturbe I (1991) A coupled channel network growth and hillslope evolution model 1. Theory Water Resour Res 27(7):1671–1684

    Article  Google Scholar 

  • Zhao SQ (1986) Physical geography of China. Wiley, New York

    Google Scholar 

  • Zhou BF, Li DJ, Luo DF (1991) A guide to debris flow prevention (in Chinese). Science Press, Beijing

Download references

Acknowledgments

Special thanks go out to the staff, especially Mr. Hong, the administrative director of the Dongchuan Station of Debris Flow Observation and Research, CAS, for their generosity in providing observation data. The authors would also like to thank the anonymous reviewers for their instructive comments. This research is supported by the China National Science Fund (Grant No. 40671025 and 40771010), the Innovation Project of CAS (IMHE, 1100001062), the Ministry of Communications (200631879284), and the Youth Foundation of IMHE, 2006 (1100001071).

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Authors and Affiliations

  1. Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences, Chengdu, 610041, Sichuan, People’s Republic of China

    J. J. Liu, Y. Li, P. C. Su & Z. L. Cheng

  2. Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, 610041, People’s Republic of China

    J. J. Liu, Y. Li, P. C. Su & Z. L. Cheng

  3. Graduate School of Chinese Academy of Sciences, Beijing, 100039, People’s Republic of China

    J. J. Liu & P. C. Su

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  1. J. J. Liu
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Correspondence to J. J. Liu.

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Liu, J.J., Li, Y., Su, P.C. et al. Magnitude–frequency relations in debris flow. Environ Geol 55, 1345–1354 (2008). https://doi.org/10.1007/s00254-007-1083-1

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