3.2. Grout Diffusion Pattern
After grouting, the position of the sensors corresponding to the signal lamp light in the visualization platform is shown in
Figure 6a. A rough range of grout diffusion can be seen from the visualization system, as shown in
Figure 6b. To obtain a more accurate grout diffusion pattern, the three-dimensional coordinate data of the sensors were exported from the visualization platform and put into MATLAB (7.14 version, Branch office of MathWorks in China, Beijing, China, 2012). Through these data, the grout diffusion pattern was synthesized by the interpolation method embedded in MATLAB. There are two kinds of interpolation methods in MATLAB when the two known arrays are used as independent variables, namely, two-dimensional interpolation (Interp2) and two-dimensional scattered point interpolation (Griddata). The Interp2 method is characterized by the gradient distribution of independent variables in the range, which can form a regular matrix. The Griddata method is characterized by the scattered distribution of independent variables in the range, which is not a uniform distribution. In this experiment, the two independent variables are the gradient distribution and the regular matrix, which can be formed. Therefore, the Interp2 method is used. The obtained grout diffusion pattern is as shown in
Figure 7. It can be seen that the flow pattern of the grout in fractured porous rock mass has a parabolic shape from the grouting hole to the bottom. The lower the level is, the larger the diffusion range of the grout is. In the horizontal direction, the grout diffusion surface around the grouting hole was an asymmetrical circular surface.
In conclusion, when the height of the grouting pipe, initial velocity of the grout, outlet angle and pore connectivity are determined, the shape of the diffusion surface is certain. Considering that the grout will solidify in a certain period of time, if only through a pipeline grouting, the first injected grout will cement to a solid within a certain range of the outlet, blocking the slurry outlet and reducing grouting efficiency. Therefore, when the spatial shape of the grouting range is determined, the grouting parameters must be designed according to the control range of each grouting pipe.
To obtain quantitative data of the grouting diffusion radius, plastic nets were arranged on three different layers of grouting. After grouting, the diffusion range of the paste on different plastic layers was measured. Considering the convenience of the measurement and later calculation, the diffusion surface of the different layers was circularly processed.
Figure 8 shows the grout diffusion range monitoring diagrams for different levels of experiment 1, and
Table 4 shows the range of the grout diffusion for different levels during different experiments.
The grouting times for experiments 1–5 were 211 s, 178 s, 192 s, 153 s and 121 s, respectively. According to experimental data in
Table 1 and the test data listed in
Table 4, MATLAB is used to perform a regression analysis between the diffusion radius of the grout and various factors, such as the water-cement ratio, grouting pressure, grouting time, permeability coefficient, and level of grout. From the data analysis of this test, we can see that there is a power function relationship between the test results and the influencing factors. A linear regression is the basis for solving problems. It is necessary to transform the power function relationship into a linear relationship. Therefore, if we suppose its basic model is:
The above model is a nonlinear model, and the two sides of the above formula are logarithmically obtained:
Assuming
, the above model can be transformed into a linear regression model:
In the formula,
is a constant, and
are the partial regression coefficients of the dependent variable
on the independent variable
(
). The solution is similar to a unitary equation. According to the principle of the least squares method, the square sum of the residuals are determined, and then the solutions of
and
can be calculated. The resulting regression analysis formula are as follows:
In Formula (6), the regression fitting exponents for grout water-cement ratio (m), grouting pressure (p), grouting time (t), permeability coefficient (k) and level of grout (d) are 0.195, 0.24, 0.172, 0.017, and 0.22, respectively. The larger the coefficient was, the greater the influence of this factor on the diffusion radius of the grout was. Therefore, the factor with the most substantial effect on the diffusion radius of the grout was the grouting pressure in the fractured porous rock mass. That is, when the other factors were fixed, the larger the grouting pressure was, the larger the grout diffusion radius was. The next most important factors were the level of grout and the water-cement ratio, and the factor with the least impact on the diffusion radius of the grout was the permeability coefficient. Therefore, in the grouting of fractured porous rock mass, the grouting pressure has the greatest influence on the grouting diffusion radius, followed by the grouting horizon and water cement ratio, with the grouting permeability coefficient having the least influence on the grouting diffusion radius.
3.3. Grouting Effect Testing
After one day’s worth of grouting, a sampling of the grouting stone bodies was performed, as shown in
Figure 9a. It can be determined that in the range of the grout diffusion, the grout diffused evenly, filled densely, and cemented well with the fractured porous rock mass, which can form a skeleton and improve the strength of the rock mass. Without the range of grout diffusion, the fractured porous rock mass was also soaked by water, indicating that the water evolution of the cement slurry is strong.
After 28 days’ placement in the laboratory, the grouting stone bodies were cored to test the uniaxial compressive strength, as shown in
Figure 9b,c. Cores with a diameter of 50 mm and a height of 100 mm were used to obtain the main mechanical properties. The stress-strain curves of the cores of different experiments are presented in
Figure 10. The uniaxial compressive strength of a different experiment is listed in
Table 5. It can be seen that the stress-strain curves of the five experiments have the same trend, but the uniaxial compressive strength is significantly different.
According to experiment data in
Table 1 and the uniaxial compressive strength of cores listed in
Table 5, MATLAB was used to perform a regression analysis between the uniaxial compressive strength of specimens and various factors, such as the porosity, water-cement ratio, grouting pressure, grouting time, etc. The regression analysis formula is as follows:
In Formula (7), the regression fitting exponents for porosity (n), grout water-cement ratio (m), grouting pressure (p), and grouting time (t) are 0.851, −0.954, 0.196, and 0.705, respectively. The negative exponent indicates that the factor and the compressive strength have a negative correlation. Therefore, when grouting the porous fractured coal and rock mass, the grout water-cement ratio has the greatest influence on the strength of the grouted gravel, followed by the grouting permeability. The grouting pressure coefficient has the least influence on the grouting diffusion radius.