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Evaluation Model of Dike Safety Based on Cusp Catastrophe Theory
Applied Mechanics and Materials
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.
... From the above analysis we can find the limitation of absolute volume for transportation can not help of compr the situation improve ehensive transportation system due to comprehensive transportation demand [6][7] . Especially when the energy use level is higher, excessive restriction to absolute volume for transportation may make the situation worse. ...
The cusp catastrophic model based on catastrophe theory is presented to analyze the development pattern evolution of comprehensive transportation system (CTS for short). By establishing cusp catastastrophe model of development pattern we obtain that the construction of comprehensive transportation system should include two parts, the first part is the stock optimization and the second part is the increment construction. With the increment construction as the turning point, promoting the fast optimization of the stock should be the basic principles of the construction and development of CTS.
Stability prediction of rock slopes under seismic loads is important for landslide hazard assessment. For this work we designed and built a model of a slope with a middle locked segment. To investigate its dynamic response characteristics and instability criteria under the influence of an earthquake, comparative experiments on a large-scale shaking table were performed. The results show that the acceleration amplification factor within the model slope is clearly amplified by elevation and surface proximity. There are large differences in the acceleration response for a slope experiencing different types of input wave. The acceleration amplification factor first increases then decreases with the increase of input wave frequency, reaching a maximum value when the frequency is 20 Hz. A similar trend is observed with increasing input wave amplitude; the acceleration amplification factor of the slope generally increases then decreases as the amplitude increases. During the experiments, several cracks form and propagate in the locked segment between the prefabricated crack at the top and the weak interlayer at the bottom. These cracks develop continuously, coalescence into X-shapes, and finally form three sliding surfaces inside the slope. Under continuous vibration, the slope will slide along the three sliding surfaces. Based on cusp catastrophe theory and the experimental data, the relevant instability criteria are established. The critical acceleration amplitude of the dynamic instability of the slope is quantitatively determined to be 0.5 g.
Safety monitoring theory and its application in hydraulics (Publishing House of Hehai university
- Z R Wu
Soil slope stability analysis - theory methods and programs
- Z Y Chen