Multi-Objective Optimization Design of Foamed Cement Mix Proportion Based on Response Surface Methodology

Foam cement, as a building insulation material, encounters a major problem in practical application, which is the difficulty in achieving a balance between its strength and insulation performance. To achieve multi-objective optimization of foamed cement mix design, this study first determined the optimal ranges of nano-silica aerogel (NSA), foaming agent, and polypropylene (PP) fiber dosage through single-factor experiments. Then, response surface methodology (RSM) was employed to construct a quadratic polynomial regression model, systematically investigating the influence of different NSA contents, foaming agent contents, and PP fibers contents on the thermal conductivity and compressive strength of foamed cement. Finally, the optimal mix ratio was further predicted and experimentally validated. The results demonstrate that the regression model developed using RSM exhibits high accuracy and reliability. The correlation coefficients R2 of the regression models established by the response surface method are 0.9756 and 0.9684, respectively, indicating good prediction accuracy. The optimized mix ratio was determined as follows: NSA content, 9.548%; foaming agent content, 0.533%; and PP fiber content, 0.1%. Under this mix, the model predicted a thermal conductivity of 0.123 W/(m·K) and a 28-day compressive strength of 1.081 MPa. Experimental verification confirmed that the errors between predicted and measured values for all performance indicators were within 5%, demonstrating the high reliability of the predictive model. This study provides support for the practical application of foam cement as a thermal insulation material in construction projects and offers guidance for optimizing its mixture composition.