 Good morning. My case study is about a bridge in the uniform of a two-ride used corrosion. The bridge was built in the center of Portugal in the seaside, it's only 500 meters away from the sea. This is a view, a picture taken on the bridge to the sea, so to have an idea about what was the bridge. The bridge was built in 1970. It's a small bridge, 16 meters long. The owner was a public institution, but not focused in bridges. Water services, but for different reasons they have some small bridges. It is important for the old case. During the many years the bridge has no maintenance and no inspections at all. So, some years ago, 2004, during an inspection, the situation was really, really bad. We had cracking, but especially, huge problems with corrosion as you can see here. After that, some tests were carried out in order to check the determination of concrete cover, to measure the combination of deep potential and good corrosion rate. The result was also not good. The probability of corrosion is very high in all the bridges. Some parts were taken in order to do some laboratory tests. The focus of the tests were the chloride content of concrete, carbonation, compressive strength, and also to do some microscope analysis. As you can see, the chloride penetration was already very, very important. So, taking into account the advanced state of degradation and very deep penetration of chloride, the bridge replacement was recommended. After that, some inspections took place. And the situation was worse, even worse naturally. So, in 2010, the owner decided to replace the bridge, but at the time, the question is, it will be safe to keep the bridge in service until the new one is ready to use. So, that was the question. And for a check of this problem, safety of the bridge, the critical of the new state was depending on the span section of the central length of the left beam. The left beam was behind the sea side, and the degradation was much worse in the bridge. According to the Portuguese National Code that was used for the design of the bridge, the bridge was unsafe. Using a target area of 3.8 and doing a probabilistic analysis based on the prior information and considering all these basic variables, the result was the same. The bridge is not safe because the index was lower than the target. So, the sustainability analysis was carried out. And the result was this, I mean, the most important variable was the residual section index. I mean, the area of reinforced fire that remains after the corrosion that happened. So, the idea was to collect more information about the residual areas of reinforcement. But their proposed measurements were carried out in the reinforced bars that was already exposed, but also some small windows were opened in order to check it. And the difference was this one, I mean, this is the model of the residual section index with the prior information. And after the new data, we have this one. And after this, with the new probabilistic variation, we get a relatively index higher than the target and the problem was solved. I mean, the bridge was maintained in service until the construction of the new one. And after that, the bridge was demolished. This is the new bridge. Now, in 60 seconds, just to remind the problem. The problem was the bridge with a high degradation level. Some lab tests that problem was a chloride in this corrosion. The bridge replacement was decided. And the question at the time was, is the bridge safe until replacement? Using code-based safety assessment bridge that's inside. And using probabilistic approach only with prior information, the result was the same. So it's this point that I'm finding, applying our approach. And the result at that time of the problem was doing sensitivity analysis in order to see what were the variables most important to circle safety. And then to collect information about what was really important, the residual section index and doing another analysis of new information and which was considered safe. So this is the solution. And the main problem, the main objective was to guarantee the safety of the bridge. The decision was to keep it in service. The decision is very clear. Yes or no? Yes or no? It's possible to keep it in service with traffic restraining constraints. But the consequences here have been the costs or the disadvantage not to have a bridge until it's built. This is the data I don't have yet. Yes, yes. And then there are technical questions for the reliability analysis that you, so this reinforcement pass, you tested their intention, right? Yes. And then you used extreme distribution or the extreme erosion pit? Yes. Just depends on the length or you did these considerations. I'm sorry, did considerations aren't... So you measured this cross-sectional variability. Yes. And the most important is to know the spot where we have the most... I measured in different situations. I mean, we exposed the very degraded bars and I measured with exposed but not... So high level of degradation. And I measured also the windows open to this purpose. In general, in the measurements, the bars was almost perfect. And in your after-work analysis, what did you assume? The higher levels? 50%. I mean, there are two levels, two levels. The bottom reinforcement bars, they are two levels. And I admit that the upper level is 100% okay. And the other is 50%. Because they already have to make a probabilistic statement. So in this after-work analysis, sex is actually a good idea to consider this corrosion loss as a random variable. Yes. Yeah. And give this random variable a rather high uncertainty because you're not sure about it. And that's then what you update with your measurements. It's here. The measurements was visual inspection and... The measurement was like this. So it's mainly visual inspection and... Yeah, it was a scruffy shot. I remember the graph. But I think all the extreme value distribution, the vital distribution, because it's about the minimum, right? Yes. The minimum cross-section assumption. And then, of course, you have variability in the tension, stress, this reinforcement part. Yes. So now, mechanically, it's very... Yes, but the critical section was the mid-spin section. So the analysis was about the safety or not, was about that section only. Okay? Yeah, but you have... I agree that you have no section where you have the maximum moment and the maximum stress, but you can have the maximum... So it's not so easy, right? No. So you can also have a very severe corrosion close to the mid-spin. Yes. Yes, of course. It's a thank you. Okay, but, yeah, probabilistic modeling, there's several interesting aspects, but let's take the decision scenario. Yes. So we... So what you have done so far now is not a decision. You are working with reliability and thresholds. Next step. So what are we after with the decision analysis? The most efficient way of... I think this is what you are after. The most efficient way of measuring and getting the structure safe. So that's why you did the sensitivity analysis. But it's only a reliability, but a value of information analysis is characterized by the type. That's exactly what you are after. It's the type, it's the precision. The type is the relevance, that's the sensitivity analysis. It's the precision, how precise your technology is, and it's the costs. And there may also be... So the highest sensitivity was clearly the residual cross-section area, which if you look to the sensitivity... Yeah, this one. So this is clearly the highest sensitivity. I think it's a good idea on reliability basis. But then it's just the precision and the type. Or note that this is about the type. The precision goes in here and also the costs. And it could be also that the reinforcing strength is... The theoretically could be that this is cheaper. Yeah? No. No, I mean, we know at the time the type of the steel used. But we don't have bars out of the circuit to test. So it's more complicated. And the measurement of the section was quite easy. So in your case you have these measurements of the section. And especially the reinforced bars. Yeah. And you want all these... The distance of the value of measuring this area. In order to... The value of all these processes, I mean the additional information... The additional information is about... ...the reach, the remaining service until the new one. Until the... So the value of the... The reliability based on the measure of the cross section. Yes. Experimental data is... What's the measurement of the cross section? Okay. Okay, in general we need to speed up. But let's try to get to the point where we have a clear decision analysis. Yeah, I think it's very good engineering. You are overview and you are having the focus on most important things. And maybe it's this problem. You are completely overview. You don't have to do a decision analysis. Yes, but I was trying to think at the time of... To take the decision in 2010. To take the decision to keep the bridge in service. To close it. Yes, that's the point. That's the decision on the system. The decision on the possible measurement actions is... Should I measure or not? So you set yourself into the point of 2010. Yes. And then you need the cost of these additional measurements. And the effect on the reduction on quality. And then... It can be done. Yes, surely. The back view. Yes, surely also in the back view. And it won't be better if there was an alternative measurement. Which is mostly for instance. Because Louise, you are completely overview of the situation. So you most probably have found the best way to do it already. You can compare the proof loading. Interesting. That you destroyed the bridge. It's actually interesting. Okay, this will be very interesting. Okay. Yeah. I think it's a very good case. The decision will be in 2010. And this is one way and maybe proof loading could be another way. Yes. Which we cannot overview. Okay. Okay, super. Thanks.