## 4 Degradation Analysis
### Energy Dissipation Feature  
When it comes to rubber concrete, due to the mixing of rubber particles, the internal pores of the concrete are different. The study [40,41] found that energy is more easily absorbed and released after cyclic loading, especially in places with different porosity, which result in the release of elastic deformation, leading to structural damage. Therefore, analyzing energy dissipation is particularly pivotal for studying damage characteristics of concrete materials. Cyclic loading produces potential energy, and the potential energy of the object is calculated by the selected initial displacement deformation, so the work performed by the material is force multiplied by micro-displacement (\(F\cdot d_{\mathrm{r}}\)). In this paper, the total absorption energy and dissipation energy of concrete is calculated according to the stress-strain curve. The total absorption energy \(W\) is the area under the loading curve, and the dissipation energy \(W_{d}\) is the area of hysteresis loop. The energy dissipation is used to describe the damage of concrete to a certain extent, so the damage variable is defined by the energy dissipation rate which is shown in Equation (5):  
\[D(i)=\frac{W_{d}(i)}{W(i)} \tag{5}\]  
where '\(W\)' is dissipated energy, '\(W_{d}\)' is total absorption energy. Due to the first cycle having no hysteresis loop, the dissipation energy is calculated according to Figure 8 (1 in the figure represents the first cycle) [42]. This article selects \(W\) and \(W_{d}\) of 1, 2, 10, 20, 30, 40, and 50 cycle times to compare the damage variables \(D\) of rubber concrete mixed with different particles. By using damage variable \(D\), at the same time, we can monitor the damage process of each rubber concrete material in the cycle stage to obtain the suitable rubber particle size in concrete that can be applied in road works. Table 3 indicates the change rule of \(W\) and \(W_{\mathrm{d}}\) of rubber concrete with cycle times, and Figure 9 shows the change in cycles corresponding to the damage variable. Figure 8: The relationship between the values in the first cycle. (‘\(W\)’ is dissipated energy, ‘\(W_{d}\)’ is total absorption energy). As shown in Figure 9 and Table 3, \(W\) and \(W_{\rm d}\) change slightly after the first cycle, which demonstrates that the energy absorbed and dissipated by concrete in each cycle is almost the same in constant amplitude cyclic loading. The \(D\) of ordinary concrete fluctuates within 4.1\(\sim\)10.1%, and with the increase in cycle times, \(D\) shows a raising trend within a limited range. The larger the particle size of the rubber is, the larger the \(D\) of RC is, and the more damage occurs in the inner part of the test block. When rubber particles are added to the concrete, the internal damage of the concrete can occur after the first cycle loading, and the \(D\) of the first cycle is large; as the number of cycles increases, the internal damage cannot increase sharply, the internal pores of the test block are compacted, and the \(D\) tends to be stable. The \(D\) value of rubber concrete with particle sizes of 0.85 mm, 1-3 mm, and 3-6 mm is 51.1%, 52 5%, and 55.5%, respectively, in the first cycle. After that, \(D\) tends to be stable at 8.4-10.1%, 8.6-12.2%, and 10-11.4%, respectively. Moreover, the interface between rubber particles and cement mortar increases, and the pores on the interface increase with the growth of rubber particle size. After cyclic loading, the internal damage of the rubber concrete with large particle size is more serious; as the number of cycles increases, the damage accumulates. However, the damage accumulates slowly due to the constant amplitude of cyclic loading, and the \(D\) increases slightly in the cycle process. Therefore, the damage of RC is minor and it can resist the damage caused by cyclic loading when the size of rubber particles is 0.85 mm.