Safety concept for structures exposed to debris flow based on Grey numbers

Structures built have to be safe. This requirement is fulfilled by consideration of a safety concept for structures. Over time many such safety concepts have been developed. The present safety concepts are based on stochastic considerations (semi-probabilistic and probabilistic safety concept). The current development suggests, that all types of structures independent from there goal should follow the rules of such a probabilistic safety concepts. Additionally further safety concepts are developed parallel, which not only include some material inherent uncertainties, but also other uncertainties difficult to be included in stochastic investigations. Here only combined fuzzy-probabilistic safety concepts are mentioned. Especially for some natural processes, there is often not sufficient amount of data available to fulfil the requirements of stochastic techniques. In addition, the uncertainty reaches dimensions, which can not be dealt with standard stochastic procedures. In some regions techniques were modified to avoid the problem of insufficient data. For example in the Netherlands regional frequency analysis is used to extend the amount of data. But especially for natural hazards in Alpine regions this might not be appropriate and the high amount of uncertainty remains, for example for the estimation of debris flow volumes. Here newer mathematical techniques for the consideration of uncertainty might be applied. The author has used the Grey numbers techniques invented by Deng 1982 in China for flooding prediction. Since especially debris flow predictions is combined with high uncertainties, it might be appropriate to extend the safety concept for structures exposed to debris flow impacts considering Grey numbers. Therefore the goal of the research is the development of a combined Greymodel-stochastic safety concept for structures exposed to debris flow impacts considering high dimensions of uncertainty.

Indetermination and Uncertainty are immanent parts of our world. We are unable to fully exclude them. The most successful mathematical technique to handle uncertainty and indetermination is stochastics, e.g. probability and statistics. However, in many cases the basis for the application of this technique may not be fulfilled. Nevertheless, in most cases, engineers try to cover the uncertainty mainly by probabilistic or semi-probabilistic safety concepts. These concepts may fail under certain conditions, for example human failure is completely screened out. Also complex loading conditions, such as debris flow impacts, cannot be described by stochastic approaches. This FWF research project investigated the possible extension of the probabilistic safety concept for structures with Grey numbers. It focused only on structures exposed to debris flows. In general, in the concept of Grey numbers, originally developed by Deng, the numbers not only include value information, but also information about the uncertainty of this value. This uncertainty information is called Greyness. The concept of Greyness can be compared with the standard deviation of random numbers. The extension of probabilistic safety concepts with other mathematical techniques of uncertainty, such as fuzzy concepts has also been investigated. However, the application of Grey numbers in this field is new. Debris flow events and properties are extremely difficult to predict and therefore debris flow models consider significant uncertainties. Based on field measurement data from Switzerland and Austria, the quality of input variables for debris flow models was investigated and stochastic flaws, such as shifting populations, multimodality, censored data or outliers were identified. To overcome these flaws, Grey numbers were applied for these input variables. This Grey numbers were then included in Grey number functions, which substitute then probability functions in the probabilistic safety concept. An example is the Grey exponential function, which substitutes the exponential probability function. The research project showed, that Grey numbers can be used in safety concepts to describe uncertainty, Grey numbers can be incorporated into probabilistic safety concepts, in general, such merged Grey number probabilistic safety concepts show higher uncertainties (higher loads and lower return periods) for debris flow impacts, an extension of the Grey number functions is required to be able to substitute all possible probability functions, although some work was done during this project, further research is needed to interpret the results of combined Grey number probabilistic safety concept computations.