Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams

This paper presents frequency domain solution algorithms of the one-dimensional transient heat transfer equation that describes temperature variations in arch dam cross sections. Algorithms are developed to compute the temperature $T(x,t)$ , spatial distribution, and time evolution for the “direct” problem, where the temperature variations are specified at the upstream and downstream faces, and for the “inverse” problem, where temperatures have been measured at thermometers located inside instrumented dam sections. The resulting nonlinear temperature field is decomposed in an effective average temperature, $T_m\left(t\right)$ , and a linear temperature difference, $T_g(x,t)$ , from which the dam thermal displacement response can be deducted. The proposed frequency domain solution procedures are able to reproduce an arbitrary transient heat response by appending trailing temperatures at the end of thermal signals, thus transforming a periodic heat transfer problem in a transient one. The frequency domain solution procedures are used to develop the HTT (hydrostatic, temperature, time) statistical model to interpret concrete dam-recorded pendulum displacements. In the HTT model, the thermal loads are arbitrary and can contain temperature drift or unusual temperature conditions. The explicit use of $T_m\left(t\right)$ and $T_g(x,t)$ in the HTT dam displacement model allows extrapolation for temperature conditions that have never been experienced by the dam before (within the assumption of elastic behavior). The HTT model is applied to the 131-m-high Schlegeis arch dam, and the results are compared with the HST (hydrostatic, seasonal, time) displacement model that is widely used in practice.