Statistical Methods for Dam Behaviour Analysis

Concrete dams can be affected by long-term processes such as alkali aggregate reaction, concrete ageing and irreversible rock mass deformation, from which they can suffer ser- ious damage. Therefore, an early detection of deficiencies by the use of a proper mon- itoring system in combination with a dam behaviour analysis model is essential. A dam behaviour analysis model links measured behaviour indicators, e.g. displacements, with the environmental conditions, i.e. mainly the water level and the temperature distribution in the dam body. This is usually done empirically by statistical methods. The effects of the environmental conditions are represented by model equations. A common approach to represent the effects of the water level are polynomials and there are several approaches proposed in the literature to represent the effects of temperature. Nevertheless, the differ- ent temperature variables are likely to be correlated. Thus, multicollinearity and unstable models result. The goal of this thesis is to evaluate existing statistical approaches used in the field of dam behaviour analysis and to improve them if necessary. The thesis is divided in the following main parts: (i) heat transfer analysis, (ii) evaluation of existing models and (iii) the presentation of new approaches and its (iv) application. In concrete dams, heat conduction can be regarded as a one-dimensional problem between the upstream and the downstream boundary. The analysis is done by the use of the fre- quency domain solution of the heat conduction equation. Usually the thermometers are embedded in the concrete body. Therefore, inverse heat conduction analysis has to be performed. Since this is an ill-conditioned problem, stabilising procedures are needed. Besides the evaluation of existing approaches, a new approach, based on the limitation of the amplification of high frequencies, is proposed. It is successfully applied to several case studies. In a next step, well known statistical approaches are assessed. The evaluation of the behaviour analysis procedures shows that the observation-prediction comparison, which is commonly applied, can lead to results that are not robust. Hence, wrong conclusions about the structural behaviour might be drawn. Thus, it is recommended to use adjusted behaviour indicators. The latter are obtained by subtracting the reversible effects from the measured behaviour indicator. It is shown that this approach is very robust and the results are independent of the chosen calibration period. Moreover, the evaluation of the approaches to consider temperature effects shows that their performance mainly depends on the data and less on the models itself. All models are able to detect artificial behaviour changes previously applied to the data. It is shown that the magnitude of the behaviour changes found by a model correlates with its residual standard error. Finally, new approaches are presented. Beam models are introduced to create physic- ally based shape functions that can be used to create hybrid models. For gravity dams, a cantilever beam model with an elastic abutment and for arch dams an arch-cantilever model is set up. The models have been applied to several dams. Due to the fact that only few uncorrelated variables result, multicollinearity does not occur. Therefore, beam models are very robust. Furthermore, the beam model for gravity dams is used to perform multi-objective calibration with the Markov Chain Monte Carlo method in a Bayesian framework. The advantage of multi-objective calibration is that the measured displace- ments are simultaneously matched with the model output on several levels. This leads to simple models that allow for drawing comprehensible conclusions based on engineering judgement. Moreover, due to the simultaneous analyses of the displacement at different levels, a potential abnormal behaviour can be detected and correctly located. Because the adjusted behaviour indicators are very robust with respect to different calib- ration periods, it is recommended to use all available measurement data for model calibra- tion. Consequently, extrapolations that may result in unstable predictions can be avoided. This change in the concept of behaviour analysis can be seen as a paradigm shift from a statistical prediction to a statistical inference problem