# The Time Variation Law of Concrete Compressive Strength: A Review
## 3 Comprehensive Study on Multiple Factors
### Statistical Analysis of Field Test Data  
In reality, the environment of concrete is very complex and not a simple superposition of influencing factors. Moreover, in addition to the service environment, the variation in loading conditions will also influence the strength. The concrete structures are basically under long-term load. Thus, the field test data of existing buildings provide more advantages for studying the time variation law of concrete compressive strength in practical engineering. The probability distribution of concrete strength was analyzed according to the field test data, and the normal distribution was verified [54; 55; 56; 120]. In contrast, [PERSON] et al. [120] pointed out that the gamma distribution was more suitable compared to the normal distribution. In addition to the distribution analysis, many researchers studied the time variation model of concrete compressive strength [54; 55; 56]. There were mainly three models, described as follows. 1. [PERSON]'s model  
[PERSON] et al. [54] established a time variation model of the mean and standard deviation of the normalized compressive strength based on a large number of long-term exposure tests, and field test data of existing buildings. The compressive strength data of [PERSON]'s model was normalized by dividing the mean value of the 28-day strength, to eliminate the influences of construction processes, curing conditions, mix proportions and other factors. [PERSON]'s model was expressed as follows:  
\[ \begin{split}\mu_{1}(t)&=1.4529\exp\left[-0.0246( \ln t-1.7154)^{2}\right]\\ \sigma_{1}(t)&=0.0305t+1.2368\end{split}  \tag{10}\]  
where \(\mu\) and \(\sigma\) are the mean and standard deviation of normalized compressive strength, respectively. 2. [PERSON]'s model  
[PERSON] et al. [55] established the time variation models of normalized compressive strength based on the data obtained by the rebound hammer method, and core test method from existing buildings in Shanghai, China. The compressive strength of [PERSON]'s model was normalized by dividing the mean value of the cube compressive strength. [PERSON]'s model can be formulated as follows:  
\[ \begin{split}\mu_{\text{R}-1}&=-2.0\times 10^{-4}t^{2 }+8.6\times 10^{-3}t+0.84\\ \mu_{\text{C}-1}&=-3.0\times 10^{-4}t^{2}+1.3\times 1 0^{-2}t+0.8819\end{split}  \tag{11}\]  
where \(\mu_{\text{R}}\) and \(\mu_{\text{C}}\) are the dimensionless mean values of the strengths measured by the rebound and core drilling methods, respectively. 3. [PERSON]'s model  
[PERSON] [56] established a time variation model of normalized compressive strength based on the data obtained by the rebound hammer method and core test method from existing buildings in Shandong, China. The normalized compressive strength of [PERSON]'s model is the ratio of the field test data to the mean value of axial compressive strength. [PERSON]'s model can be presented as follows:  
\[ \begin{split}\mu_{\text{R}-2}&=-1.8\times 10^{-4}t^{2 }+0.01t+1.06\\ \mu_{\text{C}-2}&=-2.4\times 10^{-4}t^{2}+0.01t+1.30 \end{split}  \tag{12}\]4. Comparative analysis of time variation models  
From the above model, it is observed that data normalization is usually processed via division by the mean value of the 28 d strength, or of the cubic compressive strength, or of the axial compressive strength. In order to study the similarities and differences, the above models are drawn under the same coordinate system, as shown in Figure 2.  
It can be seen in Figure 2 that the three models all show a trend of increases first, and then decreases with time. In addition, obvious differences between the models are observed due to the differences in data sources and normalization methods. First of all, with the exception of [PERSON]'s model, which is an exponential function, all other models are quadratic functions. The maximum value of normalized compressive strength in the models occurs at different service ages, which is about 5 years in [PERSON]'s model, about 30 years in [PERSON]'s model and about 25 years in [PERSON]'s model.