## 2 Grouting Diffusion Test for Tunnel Second Lining Cracks
### Slurry Initial Viscosity Test  
To investigate the impact of the water-cement ratio on diffusion, we conducted a series of experiments with fixed crack width, grouting pressure, and crack plane inclination. As detailed in Table 2, water-cement ratios of 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 were examined across five test sets.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Ultrafine Cement** & **Ultrafine Fly Ash** & **Expansive Agent** & **Early Strength** \\ \hline Particle Size/Grade/Type & \(\leq\)8 μm, D50 \(\leq\)18 μm, D90 & I & HSDZ-60 & MNF-9 \\ \hline Mass Ratio & 75\% & 20\% & 3\% & 2\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material mix ratio.  
Figure 1: Grouting materials and slurry diffusion pattern: (**a**) Four kinds of additive materials; (**b**) mixing device; (**c**) slurry morphology diagram.  
The water-cement ratio is an important influence on the rheological properties of cement-based grouting materials. If the water-cement ratio is too small, the material flow performance will be poor; if the water-cement ratio is too large, the material flow is relatively good, but the grouting material's caking rate, strength, and permeability will be affected to some extent. By adjusting the water-cement ratio to achieve control of the fluidity of the grouting material, when the water content in the slurry reaches the critical water content \(W_{0}\), the slurry has good fluidity and can produce a good lubrication effect. According to the range of the grouting material ratio, analyzing the rheological properties of different water-cement ratios, the test design of the water-cement ratio changes from 0.5 to 1.0 every 0.1 for a change in the difference, and the slurry viscosity test temperature is 20 degrees Celsius. The rheological curves of slurry with different water-cement ratios are shown in Figure 2.  
From Figure 2a, it can be seen that the shear stress is positively related to the shear rate, and the minimum value of the initial shear stress \(\tau_{0}\) is 0.12 Pa, which indicates that the type of ultrafine cement slurry is Bingham fluid; from Figure 2b, the viscosity is inversely related to the shear rate.  
The viscosity value is one of the factors that affects the spreading of the slurry, and the water-cement ratio affects the initial viscosity of the slurry, and the crack grouting materials commonly used the water-cement ratio of 0.5-1.0, the rheological curves were tested by the rheometer, the Bingham model was used for fitting analysis, and the initial viscosity values of slurries with different water-cement ratios were tested and obtained, as shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Crack Width** & **Water–Cement Ratio W/C** & **Initial Grouting Pressure P\({}_{0}\)** & **Fracture Plane Dip** & **Grouting Port** \\
0.4 mm & 0.5–1.0 & 0.05 MPa & 90\({}^{\circ}\) & 5 mL/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Grouting parameters.  
Figure 2: Rheological curve of slurry with different water cement ratio. (**a**) The variation curve of shear stress with shear rate; (**b**) the change curve of viscosity with shear rate.  
An analysis of the rheological curve shown in Figure 2b reveals that the initial viscosity of the slurry decreased progressively from 33.6 (mPa\(\cdot\)s) to 1.80 (mPa\(\cdot\)s) as the water-cement ratio was increased from 0.5 to 1.0. This variation in the water-cement ratio led to notable changes in the viscosity parameters of the cement grouting material.