## 4 Analysis of Test Results
### Strength Performance Analysis
and lower compressive strength than Specim 12, whose force-deformation curve displays clear serrations suggesting intermittent load-bearing capacity. Specim 12 further shows a sawtooth shape, indicating internal structural instability resulting in fluctuating stresses but retaining some load-bearing capacity post-destruction. Examination of the specimens' deformation and damage reveals distinct characteristics: Specim 10 displays three varying-length cracks, Specim 11 features large transverse and longitudinal cracks intertwining vertically, while Specim 12 presents longitudinal cracks at the corners without significant surface cracks elsewhere. Table 3 is the strength of four groups of specimen test data; the analysis shows that the compressive strength of the inorganic cementitious filling materials and the proportion of B material, the amount of blowing agent, and the water/cement ratio are related to the highest compressive strength of the material obtained by the experiment, which was 1.01 MPa. The lowest was 0.38 MPa, and the visible composition of the material and the ratio correspond to a greater disparity between the compressive strength. In Figure 13, it is evident that a higher water/cement ratio correlates with lower compressive strength of the filling material. Similarly, increased blowing agent quantity results in decreased compressive strength, while a higher proportion of B material enhances compressive strength, though diminishing returns occur beyond a certain threshold. Therefore, when preparing inorganic cementitious filling materials, it is crucial to balance foaming times for economic efficiency, control the water/cement ratio for adequate strength, and optimize material ratios to ensure desired properties. Figure 12: Stress–strain curve of the fourth group. From the economic benefit point of view, the higher the foaming times of the filling material, the larger the volume of the abandoned roadway that can be filled by the unit quality of the cementitious material, and the lower the corresponding economic cost. From the point of view of the compressive strength of the material, the smaller the water/cement ratio, the greater the strength of the filling material. However, with the preparation of materials A and B, material consumption increases, the foaming times also reduce, and the corresponding economic costs rise steeply. Therefore, controlling the water/cement ratio and foaming times to determine a reasonable material ratio is the key factor in the preparation of inorganic cementitious filling materials. From the four groups of experimental results, program 10 has the largest number of foaming times at 4.02, but its compressive strength is low, only 0.41 MPa. Program 1 has the lowest foaming times at only 1.64 times, but the compressive strength is larger, at 0.88 MPa. Program 7's compressive strength is the largest, 1.01 MPa, but only foams 1.83 times. Program 9's compressive strength is the smallest, at only 0.38 MPa, but with foaming times of 3.54. Programs 3 and 12's strength and foaming times are more satisfactory, but with a water/cement ratio of 1:2 under the same conditions, the consumables are large, and the cost is high. The material properties obtained by these six schemes are more one-sided, failing to take into account the dual requirements of the economy and strength. According to the aforementioned analysis, through the empirical formula calculated by