Design framework for rehabilitation grout materials during metro operation period: A combination of improved central composite design modeling and multi-objective particle swarm optimization

Grouting is one of the most effective measures for the rehabilitation of metro tunnels during the operation period. However, a paradox involving fast stiffening, high fluidity and reasonable setting time for grout materials might be encountered. For this achievement, a design framework for the operation metro grout materials based on improved central composite design (CCD) and multi-objective particle swarm optimization algorithm (MOPSO). Sulphoaluminate cement (SAC) is regarded as basis materials, mix proportion parameters are considered as decision variables, early strength, fluidity, and initial setting time are taken as objectives. Stepwise regression method is adopted to modify the classical method for indicators modeling. With the fitness functions by stepwise regression method, MOPSO is performed for multi-objective optimization. Finally, an optimal solution is determined by Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The results are as follows: (1) Stepwise regression method improved quadratic models could reduce complexity and increase significance. (2) The determination coefficients of prediction models for early strength, fluidity, and initial setting time are 0.918, 0.948, and 0.907, respectively. (3) Pareto set is obtained with the maximization of the objective. (4) The effect of weight distribution on the objectives is analyzed. The proposed design framework can be useful and practical for multiple decision making where engineers face grout design.