# Study on the Bearing Characteristics of Composite Foundations with Permeable Concrete Piles
## 2 The Best Mix Ratio Design of Permeable Concrete Piles
### Determination of Optimal Mix Proportion  
Building upon the previous experimental results, this study employs the effectiveness coefficient method for comprehensive analysis to determine the optimal water-cement ratio that balances compressive strength and permeability in pile materials [19; 20]. The efficacy coefficient method is a comprehensive quantitative evaluation method for multi-objective decision-making. Its core idea is to quantify multiple evaluation indexes in the evaluation system to the same degree and determine their efficacy coefficient values. The indices are then weighted and summed to obtain a comprehensive indicator--the total efficacy coefficient. The method has the following characteristics: (1) Based on multi-objective programming principles, the method comprehensively assesses the performance of pile materials to select the optimal mix design. (2) By establishing a unified evaluation scale and scoring the actual measurements, the method considers differences among evaluation indicators while ensuring consistency and accuracy, effectively reducing evaluation errors and enhancing the scientific validity of the results.  
This study first calculates the efficacy coefficients of compressive strength and permeability coefficient, and then comprehensively calculates the efficacy coefficients of compressive strength and permeability coefficient of the permeability concrete test block and obtains the total efficacy coefficient. Finally, the combination with the most significant total efficacy coefficient is taken as the optimal combination by analyzing the total efficacy coefficient [21]. The calculation method of the efficacy coefficient of a single influencing factor is shown in Equation (2), and the calculation method of the total efficacy coefficient is shown in Equation (3) [22].  
\[d_{mn}=\frac{C_{mn}}{C_{\text{max}}} \tag{2}\]  
\[D_{a}=\sqrt[i]{d_{a1}\times d_{a2}\times\dots\times d_{at-1}\times d_{at}} \tag{3}\]  
where \(d_{mn}\) represents the individual effectiveness coefficient for the \(n\) indicator in the \(m\) experimental group, \(C_{max}\) denotes the maximum value of the \(n\) indicator corresponding to the experimental values, \(C_{mn}\) is the test value corresponding to the \(n\) index in the \(m\) group  
Figure 4: Influence of water-to-cement ratio on permeability coefficient.  
test, and \(D_{a}\) refers to the total effectiveness coefficient of \(t\) evaluation indicators in the \(a\) experimental group.  
Table 2 shows the calculation results of the efficacy coefficient of permeable concrete samples under different ratios. From the data analyzed in the table, we can see that the PC-7 combination has the best comprehensive performance; therefore, the PC-7 combination with the largest total efficacy coefficient is selected as the optimal mix ratio. The optimal mix design identified using the effectiveness coefficient method is detailed in Table 3.  
Numerical simulation was carried out based on the optimal mix ratio obtained in the experiment, and the bearing characteristics of permeable concrete pile composite foundations were further explored. The research of Jun [23] shows that the model test of permeable concrete piles has a high degree of consistency with numerical simulation. For example, the simulation results of related parameters, such as the pile axial force and friction resistance of permeable piles, are the same as the test results, and the model test results are reliable. At the same time, the study also concluded that compared with impermeable piles, permeable piles could significantly accelerate the dissipation of superposed water pressure after the piles. In the load test, the consolidation time can be shortened, the lateral friction resistance can be increased, the peak of superposed water pressure can be reduced, and the characteristic value of bearing capacity can be improved. Therefore, the load-bearing characteristics of the permeable concrete piles were analyzed next.