3.1. Strength Law after Concrete Deterioration
The uniaxial compressive strength and modulus of elasticity of the concrete under the influence of different deterioration conditions are shown in
Table 3.
To determine whether the effect of stress level and the number of wet–dry cycles on the uniaxial compressive strength of concrete is significant, based on
Table 3, a two-factor ANOVA was performed using origin software, as shown in
Table 4. It was found that the
p-values of the stress level, the number of wet–dry cycles, and the interaction between the two factors were all less than 0.05. It can be concluded that both the stress level and number of wet–dry cycles had a significant effect on the uniaxial compressive strength of concrete.
Based on the data in
Table 3, the effects of the coupled condition on the deterioration of concrete are discussed in terms of the number of wet–dry cycles and stress levels, respectively, as shown in
Figure 5As shown in
Figure 5A, the effect of different stress levels on concrete uniaxial compressive strength deterioration also differed when the number of wet–dry cycles was the same. There were two thresholds of a and b for the effect of the stress level on the uniaxial strength deterioration of concrete in both the first and third wet–dry cycles, where the stress level was 0% for interval a and 35% for interval b, and the uniaxial compressive strength of the concrete was negatively correlated with the stress level. However, in the interval from a to b, the uniaxial compressive strength of concrete increased with the increase in stress level, and at the same time, the length of the interval in the range from a to b gradually decreased with the increase in the number of wet–dry cycles.
The analysis showed that, as the stress level increased, the pores inside the concrete first closed and then ruptured to develop cracks. When the stress level was in the interval of 0% to a, the pores started to close and the pore size kept shrinking. According to the literature [
23,
24], the height of capillary water absorption inside the concrete is inversely proportional to the capillary pore size. Therefore, as the stress level increases, the water invades deeper into the concrete, increasing the contact area between the particles and the water. Then, the bond between the particles is weakened, making the uniaxial compressive strength of concrete decreasing. In the stress level in the interval a to b, the pore closure, to a certain extent, made the pore diameter smaller than the capillary pore diameter, thus gradually blocking the water to the internal erosion. Therefore, in this interval, the uniaxial compressive strength of concrete was positively related to the stress level. When the stress level was at b to 35%, the pores inside the concrete gradually expanded and converged into cracks under the stress. This led to an increase in the contact area between the internal particles of the concrete and water, making its uniaxial compressive strength decrease with the increasing stress level. In addition, this analysis could be verified at different numbers of wet–dry cycles affecting the length of interval from a to b. After different times of wet–dry cycle deterioration, the uniaxial compressive strength of concrete decreased, resulting in a corresponding decrease in the initiating crack stress and a corresponding decrease in threshold b.
As shown in
Figure 5B, the overall concrete uniaxial compressive strength decreased with the increase in the number of wet–dry cycles. However, the decreasing trend of uniaxial compressive strength varied under different stress levels. At a stress level
λc of 0%, the uniaxial compressive strength of concrete decreased approximately linearly. Nevertheless, at a stress level
λc of 10%, the uniaxial compressive strength of the concrete decreased in a concave curve. This is because the bond between the particles inside the concrete was weakened by the external load when a continuous load with a stress level
λc of 10% was applied to the concrete. At this time s, the first few wet–dry cycles of concrete deterioration increased. However, with the increase in the number of wet–dry cycles, the bond between the internal particles of concrete was reduced. Thus, the concrete uniaxial compressive strength tended to stabilize. At stress levels
λc of 20% and 35%, the uniaxial compressive strength of concrete showed a convex non-linear decreasing trend. This was because for the stress level at this stage, the concrete internal cracks started to develop, while water intrusion at the cracks dissolved the cement between the particles. At the same time, with the increase in the number of wet–dry cycles, the repeated dissolution of water on the particles at the concrete fissured. This led to the development of more cracks, which in turn accelerated the rate of concrete strength decline.
3.2. Regression Analysis of Uniaxial Compressive Strength of Concrete
To analyze the variation of the uniaxial compressive strength of concrete under the action of different coupling conditions we used non-linear surface fitting of the uniaxial compressive strength of concrete, with the stress level and number of wet–dry cycles as independent variables in the software origin. After several fitting comparisons, the uniaxial compressive strength RationalTaylor nonlinear surface regression model was obtained, as shown in Equation (3).
where
z is the uniaxial compressive strength of concrete after deterioration,
x is the number of wet–dry cycles, and
y is the stress level.
As shown in
Figure 6, a visualization model was constructed to analyze the variation of the uniaxial compressive strength of concrete after the action of different coupling conditions. Overall, the relationship between the stress level and the uniaxial compressive strength of concrete tended to be gradually negative from the threshold fluctuations as the number of wet–dry cycles increased. Overall, with the increase in the number of wet–dry cycles, the relationship between the stress level and uniaxial compressive strength of concrete fluctuated from a threshold value then gradually tended to have a negative correlation.
3.3. Analysis of Concrete Damage Evolution
Numerous studies have shown that the damage variable
D of concrete under external loading should satisfy the Weibull distribution, whose expression is as follows:
where
ξ is the strain,
m is the shape parameter, and
a is the material parameter. According to the summary of Wu [
25], the larger the value of
m, the more elastic or brittle the material tends to be, and the smaller the value of
m, the more plastic the material tends to be.
Also according to the literature [
25], parameters
m and
a are related to the material properties as follows:
where
E is the initial modulus of elasticity of the concrete,
E0 is the cut-line modulus of the concrete past the peak load point after deterioration, and
ξmax is the strain corresponding to the maximum stress value of the concrete after deterioration.
To facilitate a comparison of the concrete damage curves under different deterioration conditions, define
ξ/ξ max = x and substitute into Equation (4), i.e.,
We then completed an analysis of the initial damage to the concrete after the action of different coupling conditions and the damage during uniaxial compression. For reasons of space, the damage curves for concrete subjected to seven wet–dry cycles and after a stress level of 35% deterioration were compared separately in this paper. The relevant parameters of the damaged specimens are shown in
Table 5.
As shown in
Figure 7a, the growth rate of the concrete damage variable D at the initial stage was proportional to the stress level, until the strain was less than the peak strain. For both, after the strain ratio was greater than 0.75, the damage variable D tended to level off. The degree of deterioration of concrete deepened with the increase in the stress level of the load applied after the action of multiple wet–dry cyclic processes.
As shown in
Figure 7b, at a stress level
λc of 35%, the damage curve of the first wet–dry cycle concrete was first below the third and then rose above the third wet–dry cycle. The analysis showed that in the concrete curing process, there are some silicate components without a hydration reaction. Therefore, in the process of the wet–dry cycle, the internal joint weakness of the concrete will be destroyed by water erosion. However, the strong joint cannot be eroded by water, and thus the hydration reaction was carried out to strengthen the particles’ association with each other. For the first and third wet–dry cycle damage curves, the early stage of the damage curve depended on the damage at the weak internal concrete joint [
26,
27], while the later stage depended on the hydration reaction at the strong internal concrete joint. As the number of wet–dry cycles increased, the damage variable D gradually increased from slow to rapid in the initial stage. This indicates that the concrete was more deeply affected by the deterioration. Summarizing the relevant literature [
28,
29] and as described in
Figure 7, under coupled action conditions, the number of wet–dry cycles determined the lower limit of concrete deterioration, while the upper limit of concrete deterioration depended on the stress level of the sustained load.