MIGUEL RODRIGUES, SERGIO OLIVEIRA, JOSE NUNO LIMA & JORGE PROENCA


where, at that point, it changes from convex to concave (inflection point), moving then towards stabilization. The referred swelling curve inflection point is also named the half-swelling point. Alternatively, the swelling effect can be represented by a polynomial function. The use of a polynomial or sigmoid-type function depends on the one that better adjusts itself to the observed data.


The independent term, k, is included in the model so it can take into account the initial observation (the first campaign of the analysed period).


With this formulation, an HSCT model curve adjusted to the observation values is obtained (see Figure 7) by applying the Least Squares Method (LSM). It is important to emphasize that before applying the LSM the SW creep component can be removed from the observed values, and corrected observed values are obtained for HSCT separation of effects analyses. To acquire reliable results for the HSCT-FEM outputs it is convenient to have observations in quantity, preferably obtained with assured quality and well distributed over time, where observed values are present for each season of the year, and at water levels representative of all the reservoir filling levels.


5.3. Applied HSCT-FEM model


This paper presents the measured displacement histories with the use of the plumbline, triangulation and GNSS methods.


Considering the methodology presented in the previous sub-chapter, after testing multiple regression model variations the HSCT-FEM model, which presented the best global adjustment involving all observed dam points, had the following characteristics: (i) for the HP elastic


effect estimation one exponential function with a cf value of 25 was considered (although, it is important to note that for the analysis of the plumblines an additional exponential with a


cf value of 20 was considered because at the analyzed locations, with the water level rise from empty reservoir to maximum capacity, there is not a monotonic increase in the measured displacements and, therefore, one exponential function alone cannot adjust itself correctly to the observable data because of its monotonic nature. Such a result is easily observable in the top left graphs of Figure 7 and Figure 8; additionally, considering the location of the plumbline points near the embankments, and the usual difficulty for the separation of effects models to adequately estimate the behaviour on those locations, the FEM results were used to draw the HP influence line); (ii) the temperature effect is estimated from the observed daily average air temperature considering an 18 day delay to simulate the heat wave propagation throughout the concrete; (iii) the HP creep effect is simulated by the creep coefficients application to the elastic response for the monthly water level history discretization in constant intervals, and considering


a concrete material with a Bazant and Panula creep law in which E0 = 25GPa, ϕ1 = 2.64, β = 0.042, m= 0.441 and n = 0.168, matching a concrete moderately damaged by swelling (there is evidence of swelling reaction occurrence from gel exudations at the upper inspection gallery); (iv) the self-weight creep effect is estimated using the same creep coefficient application to the elastic displacements determined by the FEM for the SW action; (v) the time effect related to


158 DAM ENGINEERING Vol XXXI Issue 3


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