# Effect of Mix Proportion Parameters on Behaviors of Basalt Fiber RPC Based on Box-Behnken Model
## 3 Results and Discussion
### Influence of Parameters on the Performance of BFRPC
#### 3.2.3 Compressive Strength  
The variance analysis results of the compressive strength model based on the BBD design are shown in Table 7, and the model equation is given by Equation (3). According to the \(p\) value of parameters listed in Table 7, it can be seen that the influence degree of different factors on compressive strength is: \(B>CD>AD>BD>BC\). Among them, the most significant factor is the \(w\)\(b\) ratio (\(B\)), followed by \(CD\) and \(AD\). As can be seen from the contour line in Figure 6 the \(w\)/\(b\) ratio is always inversely proportional to the compressive strength. In other words, the compressive strength decreases with the increase of the \(w\)/\(b\) ratio. Since the silica fume to cement ratio (\(D\)) has an interactive relationship with both \(A\), \(B\) and \(C\), it can be seen that silica fume, as a component of cementing material, has a great influence on the compressive strength of the specimen.  
As significant model terms, the influence of \(CD\) and \(AD\) on the compressive strength of the specimen is shown in Figure 7. It can be seen from Figure 7a,b, the influence of the sand/binder ratio (\(A\)) and basalt fiber content (C) on the compressive strength presented different trends in the case of a change in silica fume/cement ratio (\(D\)). When \(D=0.2\), the compressive strength increased with the increase of fiber content and decreased with the increase of the quartz sand content. When \(D=0.4\), the compressive strength decreased with the increase of fiber content and increased with the  
Figure 4: Contour plots of the \(s\)\(b\) ratio (\(A\)) and \(w\)/\(b\) ratio (\(B\)) on flexural strength. (**a**) \(C=0.225\), \(D=0.4\) and (**b**) \(C=0.3\), \(D=0.2\).  
Figure 5: Influence of basalt fiber content (\(C\)) and silica fume/cement ratio (\(D\)) on flexural strength. (**a**) Interaction of \(C\) and \(D\) and (**b**) contour plot of \(CD\) on flexural strength.  
increase of quartz sand content. Figure 7c,d shows that \(D\) = 0.3 is a critical value. Under this condition, the changes of \(A\) and \(C\) have only a small impact on the compressive strength. Silica fume and cement were components of cementitious materials, the ratio between them had an impact on the bonding performance of cementitious materials, aggregate and fiber, leading to the change of concrete density and thereby affecting the compressive strength of specimens. According to the comprehensive analysis of the above figures, the optimal compressive strength can be obtained when \(A\) = 0.9, \(D\) = 0.2 or \(A\) = 1.1, \(D\) = 0.4.  
Figure 6: Contour plots of the \(wb\) ratio (\(B\)) and basalt fiber content (\(C\)) on compressive strength. (a) \(A\) = 0.9, \(D\) = 0.2; (b) \(A\) = 1, \(D\) = 0.3 and (c) \(A\) = 1.1, \(D\) = 0.4.  
Figure 7: Influence of \(CD\) and \(AD\) on compressive strength. (a) Interaction of \(C\) and \(D\), \(D\) = 0.2, \(D\) = 0.4; (b) interaction of \(A\) and \(D\), \(D\) = 0.2, \(D\) = 0.4; (c) interaction of \(C\) and \(D\), \(D\) = 0.3 and (d) interaction of \(A\) and \(D\), \(D\) = 0.3.  
Refer to the above analysis, the contour diagram of compressive strength under the influence of \(BC\) is shown in Figure 7. Under the optimal conditions of \(A=0.9\) and \(D=0.2\), it can be seen from Figure 7a that the maximum compressive strength can be obtained when the fiber content \(C=0.3\), indicating that the addition of fiber plays a positive role in promoting the compressive strength of the specimen. When the silica fume to cement ratio reaches the critical value of 0.3 (Figure 7b), the water/binder ratio becomes the only effect of compressive strength, which shows an inverse proportional relationship. In the case of another optimal value (\(A=1.1\), \(D=0.4\), Figure 7c), the increase of fiber content causes a certain degree of loss in compressive strength, but it is not significant and remains at a high strength level.