## 2 Test Design and Test Method
### Test Process  
The synchronous grouting slurry necessitates three key properties: fluidity, stability, and strength [42]. However, existing research [34] indicates the substantial impact of factors like the water-binder ratio (w/b), binder-sand ratio (b/s), fly flash-cement ratio (f/c), soil-binder ratio (so/b), water-reducing admixture (SPs), and much particle size on these properties. Thus, based on 20 uniformity tests [43], the properties of the synchronous grouting slurry were evaluated under varying conditions of the w/b, b/s, f/c, so/b, SPs, and much particle size. Notably, cementitious material encompasses both fly flash and cement. The water-binder ratio signifies the proportion of water to binding material, while the binder-sand ratio represents the ratio of binding material to sand. The fly flash-cement ratio denotes the proportion of fly flash to cement, and the soil-binder ratio is the ratio of much to cementitious material. The content of the water-reducing agent is expressed as the ratio of water-reducing admixture to water. Prior to the tests, the ranges of these factors were established according to previous experience in grouting engineering, relevant specifications [44], existing research [32; 34], and are presented in Table 5: water-binder ratio from 0.6 to 1.0, binder-sand ratio from 0.5 to 0.7, fly flash-cement ratio from 1.0 to 3.0, soil-binder ratio from 0.2 to 1.0, water-reducing admixture content from 0% to 6%, and much particle size ranging from 0.5 mm to 0 mm. To guarantee test precision, avoid the effect of incomplete data on the results, and comprehensively capture the response surface, this paper delineates specific test points within these factor ranges, drawing upon existing studies [32; 42]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Chemical Constituent** & **SiO\({}_{2}\)** & **Al\({}_{2}\)O\({}_{3}\)** & **Fe\({}_{2}\)O\({}_{3}\)** & **CoO** & **MgO** & **SO\({}_{3}\)** & **Na\({}_{2}\)O** & **K\({}_{2}\)O** & **LOI** \\ \hline Content & 49.23\% & 30.17\% & 3.86\% & 5.41\% & 2.46\% & 3.00\% & 2.66\% & 1.28\% & 1.93\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Chemical composition of fly flash. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Chemical Constituent** & **CaO** & **SiO\({}_{2}\)** & **Al\({}_{2}\)O\({}_{3}\)** & **Fe\({}_{2}\)O\({}_{3}\)** & **MgO** & **SO\({}_{3}\)** & **LOI** \\ \hline Content & 65.81\% & 18.32\% & 1.72\% & 5.41\% & 3.48\% & 2.45\% & \textless{}4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Chemical composition of cement. The methods for determining the density, bleeding rate, consistency, fluidity, setting, time, and strength of the slurry are as follows:  
(1) Density: Pour the prepared slurry into a 250 mL graduated cylinder and allow it to settle, as shown in Figure 5a. Subsequently, measure the weight and volume of the slurry, thereby enabling the calculation of the slurry's density. (2) Bleeding rate: In accordance with relevant specifications [44], pour the prepared slurry into a 250 mL measuring cylinder and allow it to stand until all water precipitation from the slurry within the cylinder ceases [45], as depicted in Figure 5b. The bleeding rate is defined as the ratio of the final upper water film volume to the total slurry volume. (3) Consistency: In accordance with relevant specifications [46], the mortar consistency tester (SC-145) was utilized to determine the slurry consistency, as shown in Figure 5c. Prior to the test, the slide rod was lubricated with oil, and both the conical container and test cone were wiped clean using a damp cloth. The slurry was then poured into the conical container in a single motion, followed by even tamping with the rammer from the center towards the edge for 25 times. The container was shaken 5 to 6 times to ensure a smooth slurry surface and positioned on the base. With the test cone's tip adjusted to touch the slurry surface, the brake screw was released, and the starting time was noted.