Statistical modelling of thermal displacements for concrete dams: Influence of water temperature profile and dam thickness profile

Several factors are acting on concrete dams and affect dam displacements: hydrostatic load, thermal effect and irreversible phenomena (creep, swelling ...). The different influences need to be quantified for the analysis of monitoring measurements. In most statistical models for the dam behavior analysis, the thermal effect which is often the main contributor to the total displacement is introduced only by means of the dam temperatures. Recently Tatin et al. (2015) have introduced a global gradient across the dam of the temperature bringing an additional bending effect. However, the thermal gradient may be very different, even with opposite sign, from the top to the bottom depending on seasons. In this paper, a statistical model accounting for the water temperature profile is proposed. In this original statistical model, the dam is discretized along its height in n layers on which both mean and gradient of the dam temperature are computed for the evaluation of the thermal effect. It implies 2.n new explicative variables for the statistical model yielding a reduced dispersion of the residuals. However, statistical compensation occurs from one layer to the next leading to unrealistic influence functions along the height of the dam. In order to reduce this effect, the statistical problem is constrained by imposing a polynomial approximation of influence functions. The parameters of the polynomial may be estimated either beforehand by means of the dam numerical model or directly by the statistical process. The number of additional degrees of freedom of the statistical process is thus reduced but can still describe the effects of both profiles of the water temperature and the dam thickness on dam displacements. For the model construction and validation, an arch dam is modelled by means of the finite element method and serves as a virtual case study. Although results show only a slight reduced residual dispersion, physical meaning of the model to the intermediate quantities is increased.