Research on the strength evolution law and ratio optimization of expansive backfill based on response surface methodology

To address the challenges of low roof-contacted filling rates and poor roof-contacted filling effects in an iron mine stope in the Anhui province, a composite expansive agent is introduced into the last roof-contacted filling slurry. This approach allows for active roof-contacted filling and reduces filling costs simultaneously. This paper analyzes the physical and chemical properties of the test materials to assess the strength evolution law and determine the optimal ratio for expansive backfill. Herein, a response surface methodology (RSM) is employed for performing the strength ratio test of expansive backfill using Box−Behnken design (BBD) in Design-Expert software. Further, the influence rules of slurry mass fraction, cementitious powder mass fraction, and composite expansive agent mass fraction on the compressive strength of expansive backfill are studied. Subsequently, the paper establishes response surface regression models for analyzing the compressive strength of expansive backfill. The results show that the regression coefficients for 3 d, 7 d, and 28 d compressive strength regression equations are 0.9813, 0.9758, and 0.9857, respectively. These figures suggest that the regression models have a high degree of fitting. Further analysis of variance and comparison between measured and predicted values suggest the accuracy and reliability of these models. The results reveal that the compressive strength of expansive backfill is considerably affected not only by a single factor but also by the interaction between various factors. Among the single factors, cementitious powder mass fraction exerts the greatest influence, followed by composite expansive agent mass fraction, while slurry mass fraction has the least effect. The interaction between slurry mass fraction and cementitious powder mass fraction considerably affects the compressive strength during the early and middle stages. Meanwhile, the interaction between the cementitious powder mass fraction and composite expansive agent mass fraction substantially affects the later compressive strength. Based on these findings, this paper applies the goal programming method to optimize the ratio of expansive backfill, and the optimization models are established considering the compressive strength, expansion effect, and filling cost of backfill. The optimal ratio of expansive backfill is determined to be 69% slurry mass fraction, 10% cementitious powder mass fraction, and 3×10^–4 composite expansive agent mass fraction, meeting the requirements of compressive strength and roof-contacted filling. Finally, the microstructure of expansive backfill is analyzed using X-ray diffraction (XRD) and scanning electron microscopy (SEM). The results reveal that the composite expansive agent allows the filling slurry to expand and deform during the plastic stage, thereby improving the roof-contacted filling rate. Meanwhile, the composite expansive agent can loosen the internal structure and increase porosity, thereby reducing the compressive strength of backfill.