## 3 Analysis of Results
### Analysis of Properties of Red Sandstone Specimens with Different Orientations
#### 3.2.1 Ultrasonic Characterization of Red Sandstone Specimens
From the Z-axis direction, that is, from the analysis of the measurement point height, the ultrasonic wave velocity value of the red sandstone decreases with the rise in the height of the measurement point. The characteristic parameters of the CT grayscale histogram corresponding to it also change with certain regularity, in which the average grayscale, maximum probability grayscale level, and probability of the grayscale level being greater than 200 decrease with the rise in the height of the measurement point with a significant change trend, while the average amount of information and the third-order center moment have the opposite trend. Neither uniformity nor standard deviation changed significantly, probably due to the large amount of data and the existence of a certain pattern in their distribution. In general, the grayscale distribution of CT images and its features change with the height of the measurement points, along with the ultrasonic wave velocity values, which can generally be used to define the degree of degradation, so it can be assumed that there is a correlation between the CT grayscale image features and the degree of degradation. In terms of the average gray level, the maximum probability gray level, and the probability of a gray level greater than 200, the smaller the overall gray level of the CT grayscale image, i.e., the darker the image, the greater the degradation of the red sandstone specimen. 2. Specific analysis of the degree of degradation of horizontally oriented red sandstone specimens. In the above analysis, it was found that there is a correlation between the characteristics of CT grayscale images and the degree of degradation of red sandstone in the longitudinal direction. However, the results of ultrasonic tests showed that there are different values of ultrasonic wave velocity in the horizontal direction in the same layer, so it can be understood that the erosion along different directions is different, i.e., the degree of degradation is different, and this section will apply the above analysis method to corroborate this conclusion. For accurate comparison, the grayscale distribution maps of the CT images of each layer are projected onto the X-Z and Y-Z planes, respectively, with the X, Y, and Z directions consistent with the definitions in Figure 2. The projection of the X-Z plane characterizes the grayscale distribution along the X-axis direction and, to some extent, the propagation characteristics of the ultrasound waves. The Y-Z plane, on the other hand, characterizes the propagation of ultrasonic waves in the Y-axis direction. The differences in ultrasonic waves in the X and Y directions and the grayscale distribution under different layers are analyzed below. Since the top surface of specimen S is non-horizontal and inconsistent in height, only four ultrasonic wave data are collected in the Y direction, so only four sets of data are compared and analyzed here, i.e., the data corresponding to the \(L1\) to \(L4\) layers. From the horizontal plane, when in the same level, the overall gray level of the gray distribution projection map on the X-Z plane is smaller than the projection on the Y-Z plane, and the gray level of the gray distribution projection map on the Y-Z plane is significantly more than that on the X-Z plane, as shown in Figure 9. The occurrence of degradation phenomena such as defects, cracks, and so on will result in the gray value of