Evaluation Model of Dike Safety Based on Cusp Catastrophe Theory

Abstract:

Evaluation indexes (monitoring value) set in safety evaluation of dike, it was difficult in conforming the range of evaluation indexes, and could not reflect characteristic of outburst destroy. Catastrophe theory is a kind of mathematical method that problems of transition, discontinuity, and abrupt qualitative change based on analysissitus, problems about how a system of continuous quantitative change to evolving into jumping qualitative change can be analyzed. Firstly, the relation between deformation of dike with components of water pressure, temperature and time effect is analyzed, subdivision lemma of cusp catastrophe theory is cheesed, expression of potential formula on horizontal deformation is carried out based on influence of factor of time, water pressure and temperature. Moreover, normal form of catastrophe is advanced and critical rules of dike safety are put forward, evaluation model based on catastrophe theory is established. Finally, the model is validated with dike of Yellow River. Analysis shows that evaluating conclusion of the model is as the same as the practice, and it can not only reflect outburst destroy character of dike, but also evaluate safety degree in quantity, thus the model is good in adaptability and precision.

• Periodical: Applied Mechanics and Materials (Volumes 190-191)
• Pages: 1249-1253
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.190-191.1249
• Online since: July 2012
• Authors: Xi Zhong Shen, Xiao Ping Yang, Wei Dong Ma
• Keywords: Catastrophe Theory, Dike, Safety Evaluation, Yellow River

References

[1] C.X. Mao: Seepage calculation and control (China Water Power Press, Beijing 1988), In Chinese.

[2] Z.Y. Chen: Soil slope stability analysis - theory methods and programs (China Water Power Press, Beijing 2003), In Chinese.

[3] W.Y. Xu, W.B. Xing, K. Wang, et al: Hydro-science and Engineering Vol. 3 (2006), pp.39-44, In Chinese.

[4] T. Hu, Q.Y. Li, Y.X. Jie, et al: Journal of Yangtze River Scientific Research Institute Vol. 21 (2004), pp.36-40, In Chinese.

[5] J. Wang, S.Y. Li, L.Q. Bai: Yellow River Vol. 28 (2006), pp.14-16, In Chinese.

[6] J.B. Xie, J.J. Zhang, S. Liu, et al: Water Resources and Hydropower Engineering Vol. 38 (2007), pp.69-72, In Chinese.

[7] Y.L. Liu, C.Y. Zhou: Hydro-science and Engineering Vol. 1 (2011), pp.60-65, In Chinese.

[8] P. He, Z.Z. Zhao: Catastrophe theory and its application (Publishing House of Dalian University of Science and Technology, Dalian 1989), pp.20-35, In Chinese.

[9] Z.R. Wu: Safety monitoring theory and its application in hydraulics (Publishing House of Hehai university, Nanjing 1990), p.188~215, In Chinese.

[10] J.Z. Cui, X.Q. Zhang: Yellow River Vol. 24 (2002), pp.11-14, In Chinese.