# Experimental Investigation of Mechanical Properties of Clay-Cement Slurry Containing Graphene Oxide
## 3 Results
### The Microstructural Characteristics of the Grout-Solid Interface
Therefore, this  
Figure 7: Comparison of microscopic reinforcement characteristics of GO composite interfaces: (a) GO-0; (b) GO-5 (50 \(\upmu\)m). study employed the fractal box dimension method to investigate the fractal characteristics of the fractured surface of oxidized graphene composite cement-based material and its control group. These materials were bound with fragmented gravel samples that underwent uniaxial compression failure. By applying fractal theory, the researchers explored the intricacies of the surface patterns and structures at a microscopic level. To facilitate the processing of scanning electron microscopy (SEM) images, the Matlab function \(T=\)_gravitythel_(\(I\)) was employed, and the Otsu method [45] was utilized to calculate the global threshold T based on the grayscale image I. The Otsu method selects a threshold that minimizes the intraclass variance in thresholded black and white pixels. As depicted in Figure 8, by determining the image threshold, SEM images can be converted into binary form. The processed image is shown in Figure 8c,d, where the white area appears relatively complete and regular, displaying consistent color. Conversely, the black area appears relatively scattered and discrete, exhibiting noticeable color differences. The calculation method of the fractal box dimension is as follows [46]: \(\mathbf{B}\in R^{n}\), \(\mathbf{B}\
eq\mathcal{O}\), \(\forall r>0\); (\(\mathbf{B}\)) is defined as the minimum value of the n-dimensional square required to cover the n-dimensional set \(\mathbf{B}\) and \(r\) is the side length of the square. If there is \(d\) when \(r\to 0\), the following is true:  
\[N_{r}(\mathbf{B})\propto 1/r^{d} \tag{13}\]  
\(d\) is regarded as the fractal box dimension of set \(\mathbf{B}\), where there exists a unique positive number \(a\), such that the following is true:  
\[\underset{r\to 0}{lim}\frac{N_{r}(B)}{1/r^{d}}=a \tag{14}\]  
Taking the absolute value of the logarithm on both sides of the above formula, the fractal box dimension \(d\) can be calculated:  
\[d=\left|\underset{r\to 0}{lim}\frac{\text{lg}a-\text{lg}N_{r}(B)}{\text{lg}r} \right|=\left|\underset{r\to 0}{lim}\frac{\text{lg}N_{r}(B)}{\text{lg}r}\right| \tag{15}\]  
According to the above method, taking the SEM image of the GO-0 sample as an example, the calculation process of the fractal box dimension on the fractured surface of the  
Figure 8: Relationship between gray value and pixel value of sample, diagrams of the microscopic morphology of the sample: (**a**) GO-0, gray value; (**b**) GO-5, gray value; (**c**) GO-0, microscopic morphology; (**d**) GO-5, microscopic morphology. fragmented gravel is explained. Black squares with different side lengths are used to cover the scanning electron microscope (SEM) image of the specimen's fracture surface, and the number \(N_{r}(B)\) of squares required to cover the black area is counted. As the side length r of the square increases, the number of squares required \(N_{r}(B)\) also decreases continuously until the number of boxes is small enough. Then, by drawing a scatter plot of (lgr\({}_{i}\), lgN\({}_{r_{i}}(B)\)) and performing linear fitting, the fractal box dimension of the fractured surface of the fragmented gravel after the uniaxial compression test can be obtained. Upon observing the fitted curve, it becomes apparent that the fractured surface's micromorphology after uniaxial compression of the specimen exhibits self-similarity. The fitting degree is very high (\(R^{2}=0.9997\)), which is consistent with the conclusion that the microscopic morphology of rock fracture surfaces has fractal characteristics obtained by [PERSON] and [PERSON] [44]. The fitting line of the fractal box dimension of GO-0 and GO-5 is shown in Figure 9.  
In this paper, five randomly selected fractured surfaces of oxidized graphene composite clay-cement slurry materials and their control group bound with fragmented gravel were calculated.