 Some particular cases, particular solutions, or they are just not for payments. They are for breeze, or dams, or other type of constructions. Although there are four payments, but they are not as useful as we would like to have. So this is some summarized scheme of the mechanics which are taken in the concrete in the center. So we divided the problem in the four parts. You can see chemo, thermo, egro, and mechanical parts. And you can see the interrelations here also. In particular, our goal for this part will be the derivation of functions which are offering the optimal joint cutting time and also the joint spacing time, depending on all of these parameters. So let's talk about the methodology. So how we move is, first, we did a literature review. Then we discussed the thermal and moisture problems separately because there will be the base you will see soon. And then we defined a fine element tool which we should use in order to make the calculations for thermal problem and for moisture problem. And then we go through coupling, then validation, and calibration of the model, then readouts, and then we move all these things, all these custom models to the mechanical analysis. So here you can see some examples of, here you can see plain concrete pavement. You can see what environmental factors affecting. There might be radiation, radiation, convection by there. There might be wind. There might be evaporation from surface. Or there is a thermal conduction with the base or sub-base. So the first we should speak about the effect of the temperature and moisture alleged in that concrete pavement includes the early stream development and long-term durability that is to have an optimized model to avoid these undesirable cracks. And the concrete temperature, which is developing during the first three days, after placement has a bit vital impact on long-term pavement performance, that is also for the cracking reason. As a hydration of cement is an extraordinary process. There is heat liberated due to this process. And this generation should be examined. And depending on this optimized chemical compound of the cement to avoid very high temperatures or taking down the environmental factors of the place where the concrete pavement is placed to make the optimal design of the chemical composition of the cement. And the magnitude of the thermal stresses will depend on the magnitude of the temperature change in contrast to charge shifts. You can see here, there are two cases. Imagine this is a concrete slab. And here is the base or sub-base. In the first case, you can see downward cooling, curling, where the temperature in top is higher than in the bottom of the slab. This will happen most in the daytime. And this is upper case, when there is a gradation. And the surface is normally much colder than the bottom part. And with this equation, well, this is for one day. You can calculate how the stresses appear in some part of this pavement, which depends on the temperature change. This is the thermal expansion coefficient, the Young models raising the temperature. So the level of temperatures in the daily concrete may be described by Fourier law as a partial differential equation. You can see that, well, you don't have to be familiar with this equation. Just I separate the different parts. This is the transfer of thermal energy to the bottom. Or this is the thermal energy direction, which I told that it is depending on the heat addition and temperature position. And this is the changing energy story. This is your symbol. And as a part of the contradiction, there are some other conditions and initial conditions. That is, initial temperature distribution. This is when the concrete is getting missed, the initial temperature of the mix. This is the heat change with the vermin or with the ground. Soil expansion, et cetera. Thank you, H, for always talking about the chemical direction. Yes. This is actually the energy released due to the hydration, due to the chemical processes. So as you can see, there are many factors affecting the thermal behavior of the concrete. So this is the behavior of the concrete and concrete after placement is quite complex. And it is affected with the temperature of the concrete, place concrete or even temperature, solar radiation intensity, it might be depending on the clouds also and the boundary conditions of the pavement. So another part is the humidity problem. When the production of concrete is done, there is more water added than needed for rehabilitation in the organability of concrete. So this water is getting accumulated in the surface and then it gets evaporated, which is fast evaporation might bring to undesirable impacts also. So for this, some trick, this is to slow down the evaporation and diffusion of the water. And there it is. So here the mechanics of how the water, how the cement is getting hydrated and the type of water. So you can see the first, there is degree of hydration is zero. You can see we have unhydrated cement and water. Then by the time, you can see whenever all the cement is hydrated, there are water in two types of water, the chemically bound and non-bound water. This non-bound water are these two, which might be difficult. And this is the concrete is losing this humidity during the time, during all the life, because this is a very slow process. And the range of this will occur as a result of the drying of the water from pores. Therefore, it decided for us to decide accurately and accurately estimate the moisture loss. So the factors affecting the moisture loss may be different, it may be the ambient conditions and if they are just directly exposed to the environment without any cooling materials, top surfaces will lose water faster than the bottom surfaces, because the diffusion of the water includes a slow process and it is not managing to bring all the water. So the first layers will lose the water and they will eat my brick to crack. I think you can see if this is the initial length or this is not restraint, if there is a shrinkage, it is losing water, but it will shrink. If this is unrestrained from this side, it will shrink and come to this size. But imagine if it is recent in the rough side, here the acid terraces will appear, which will be higher than 10, 6 tanks and then the concrete will crack. So this is just an example of how the humidity will be to crack it. And this is the last part of my model, water brick, and this is just a view of the pilot element model, this is the mesh, and this is some result analysis. You can see there are like six slabs and they are cut, cuts made, cutting, yield transversal, transversal, and longitudinal cuts are made here, and we'll go with detail one by one. And what we choose as a tool for our analysis, we have looked for different softwares from academic to commercial, and we concluded it's because of the complexity of our model that we show a lot of parameters, and the concrete itself in early age will change all the mechanical parameters and thermal parameters and humidity parameters. During the first 28 days, we choose the analysis to be our tool for making the model. It is easy to model, well, it has three interfaces, but it has two parts. One is called APL and another is workbench, so workbench is more user-friendly, but it's not as flexible as APL, so we did it in APL. There are a lot of literature available for learning, but it is able to distinguish static, dynamic and thermal problems, and you can do any kind of mechanical or fluid analysis transfer, fluid dynamic analysis, like we said, it is there for software. Also, it has a post-processing tools, which is easy to analyze the results in the software itself. This is an example of thermal analysis, so what we do is just define the parameters, the material properties, model geometry, then we put the initial temperature as a passing temperature and boundary condition, depending on the boundary factors, boundary condition factors, then we get solution, and for each step, we solve a mechanical problem. In the similar way, we do with the reality and the determinant, then humidity, then mechanical, because what is happening is in thermal analysis, we don't create the values of humidity in the concrete, but in humidity, what we do in humidity, humidity analysis, then we need thermal analysis results from the first analysis. It is three-step analysis. So this is examples of my model, one of my models I have analyzed. We can see the kind of stuff, the splices, from proper and planters. This is the division of the concrete elements. This is the element and this is the subject. Here we can see a division, for example, in this case, six elements, and there are six elements and seven nodes for each element. First is thermal analysis. Here we can see two cases. Here, from the depth, I have divided and numbered with E1 to E6, the elements, and from N1 to N7, the number of the nodes. And here we can see the average temperatures in each element, from the surface to bottom. Here, this is an example of indoor pavement, where there is no effect of the sun, there is no any environmental effect of temperature. So this might be the case of the pavement in the room of Zeodarsen in Av, as I showed you the crack example. And this is for outdoor pavements. It might be concrete pavements, where there is a radiation and temperature change.