PSI - Issue 64

Federico Pinto et al. / Procedia Structural Integrity 64 (2024) 766–773 Author name / Structural Integrity Procedia 00 (2019) 000–000

770

5

campaign, no temperature measurements or thermal corrections were made, so the references made about that initial campaign are only qualitative in nature. Table 3 shows the values of the elastic modulus of concrete found to provide an optimal correlation between measured and computed results. The elastic modulus of the cylindrical wall is found to be approximately 80% of the initially estimated value obtained from wave propagation tests performed at points that were accessible in the 2012 campaign. Such result is consistent with the experience of testing pre-stressed concrete structures, where only limited or no micro cracking has occurred. On the other hand, concrete of the dome was found to be approximately 10% stiffer that initially assumed, which is attributed in part to the presence of a significant contribution of the steel reinforcement bars. According to the low level of daily variations observed in the displacements measured in the dome, the thermal diffusion coefficient of this structural element, which is proportional to the thermal conductivity and inversely proportional to the specific heat capacity, was reduced as indicated by Table 3.

Table 3. Adjusted values of the thermo-mechanical parameters used for the numerical model. Parameter Unit Base Slab Cylinder Shell

Ring Beam

Dome

kN/m 2

E

3.20  10 7

3.20  10 7

4.40  10 7

20.00  10 7 (*)

Joule/kg/°C Watt/m/°C

880

880

880

1400

c p

1.70

1.70

1.70

0.80

k

(*) Apparent elastic modulus by stiffening produced by the internal structure

Fig. 4 shows a comparison between the total recorded displacements and those calculated by means of the model at some points where measurements were taken. The displacements in this figure are shown with respect to the average measured value between days 12 and 15. This is convenient, as the beginning of the simulations does not necessarily coincide with the beginning of the readings for all transducers. It is seen that some differences arise until the model reaches a quasi-steady thermal regime. This figure also shows displacements due only to the applied pressure, where it is generally seen that for the first pressure step of 43.8 kPa the displacements due to thermal variations are negative, thus decreasing the total displacements, while for the second pressure step of 126.0 kPa thermal strains are positive, thus causing an increase in total displacements. As can be observed in these figures, measured displacements exhibit oscillations associated with the temperature changes. Such oscillations are relatively larger in relation to the moving average values for those points that undergo smaller displacements. In order to filter out the effect of the thermal oscillations from the measured displacements, the numerical model was also used to estimate displacements induced by temperature changes and then deduct them from the measured displacements. Fig. 5 shows the displacements caused by the change of pressure alone. The results also allow direct evidence of the residual displacements after the tests. The solid lines represent the displacements calculated by the model, while the dashed lines are obtained as the difference between the total measured displacements and those obtained by means of the model for the thermal variations. Good general agreement is found between measured and computed displacements at maximum pressure. The average values (circles) obtained for each constant pressure stage show differences in less than 30% in most cases. Residual values at the end of the tests also comply with estimated allowable limits in areas where displacements are largest. The averages of the displacements for maximum pressure and for the 3 days after the complete depressurization are shown in Table 4 in order to quantify the level of correspondence reached. The percentage differences indicated in bold for the displacements of maximum pressure are those that exceed 30% in absolute value, while for residual displacements are those that exceed 20% in absolute value. These percentage limits have been defined as "Admissibility Criteria" to evaluate the results of the leak-rate test in technical specifications prepared for this purpose following widely used general criteria to evaluate the load test results of reinforced and pre-stressed concrete structures. The displacements associated with the maximum pressure that differ in more than 30% of those estimated by calculation correspond to the same points that had noticeable differences in the total displacements, that is to say: MD11, MD21, MD43, MD44 and MD45. It is important to note that between these points only in MD11 was measured a displacement value greater than the calculated, for which the model shows the lowest displacement value of all analyzed points. The points whose residual displacements exceed 20% in absolute value are all on the line L3