引用本文: 张敏哲, 王贻明, 王志凯, 王剑, 杨世兴. 基于响应面法的膨胀性充填体强度演化规律及配比优化[J]. 工程科学学报, 2024, 46(5): 800-811.
ZHANG Minzhe, WANG Yiming, WANG Zhikai, WANG Jian, YANG Shixing. Research on the strength evolution law and ratio optimization of expansive backfill based on response surface methodology[J]. Chinese Journal of Engineering, 2024, 46(5): 800-811.
 Citation: ZHANG Minzhe, WANG Yiming, WANG Zhikai, WANG Jian, YANG Shixing. Research on the strength evolution law and ratio optimization of expansive backfill based on response surface methodology[J]. Chinese Journal of Engineering, 2024, 46(5): 800-811.

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

• 摘要: 针对某铁矿采场充填接顶率低和接顶效果差的问题，通过添加复合膨胀剂可实现采场主动接顶. 采用响应面法，借助Design-Expert软件中的Box−Behnken design (BBD)方法，开展了膨胀性充填体强度配比试验，研究了料浆质量分数、胶固粉质量分数和复合膨胀剂质量分数对膨胀性充填体抗压强度的影响规律. 结果表明，单一因素及各因素间交互作用对膨胀性充填体抗压强度均有显著影响，其中胶固粉质量分数影响最大，复合膨胀剂质量分数次之，料浆质量分数最小；料浆质量分数与胶固粉质量分数的交互作用对充填体的早、中期抗压强度影响最为显著，胶固粉质量分数与复合膨胀剂质量分数的交互作用对充填体的后期抗压强度影响最为显著. 通过目标规划法确定了膨胀性充填体最优配比：料浆质量分数为69%，胶固粉质量分数为10%，复合膨胀剂质量分数为3×10–4. 利用X射线衍射 (XRD)和扫描电镜 (SEM)分析发现，复合膨胀剂可使充填体的内部结构疏松而引起膨胀，提高充填接顶率.

Abstract: 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.

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