Determining the freezing state and frozen section thickness is fundamental to assessing the development of artificial frozen walls but is commonly difficult or inaccurate because of a limited number and fixed position of thermometer holes under complex field conditions. We report a novel experimental design that measures soil temperature, water content, and ultrasonic properties to monitor movement of the cryofront (0°C isotherm), water migration, and acoustic parameters during progressive upward freezing of fine sand under laboratory conditions. Ultrasonic testing during different stages of freezing revealed changes in three acoustic parameters (wave velocity, wave amplitude, and frequency spectrum). As the cryofront ascended through the sand at different water contents, wave velocity continually increased, whereas wave amplitude initially decreased and then increased. Wave velocity measurements revealed the cryofront position during freezing, but measurements of wave amplitude did not. The frequency components indicated the frequency of different evolving freezing regions during upward freezing and the freezing state of fine sand during later stages of freezing. The freezing state can be evaluated on the basis of single vs multiple peaks and the kurtosis of frequency spectrum change. An equation developed to predict the thickness of the frozen section and tested against measured values in the laboratory and field showed accuracies of 86.84–99.33%. The equation is used successfully to estimate frozen wall thickness in artificially frozen fine sand in Guangzhou, China.

Fractal characteristics and the fractal dimension are widely used in the description and characterization of rock fracture networks. They are important tools for coal mining, oil and gas transportation, and other engineering problems. However, due to the complexity of rock fracture networks and the difficulty in directly applying the limit definition of the fractal dimension, the definition and application of the fractal dimension have become hot topics in related projects. In this paper, the traditional fractal calculation methods were reviewed. Using the traditional fractal theory and the head/tail breaks method, a new fractal dimension quantization model was established as a simple method of fractal calculation. This simple method of fractal calculation was used to calculate the fractal dimensions of three rock fracture networks. Through comparison with the box-counting dimension calculation results, it was verified that the model could calculate the fractal dimension of the fracture length of rock fracture networks, as well as quantify it accurately and effectively. In addition, we found a number of similarities between rock fracture networks and urban road traffic networks in GIS. The application of the space syntax metric to rock fracture networks prevents controversy with respect to the definition of the axis and it showed a good effect. Using the space syntax metric as a parameter can better reflect the space relationship of rock fractures than length. Through the calculation of the fractal dimension of the connection value and control value, it was found that the trend of the length fractal dimension was the same as that of the control value, whereas the fractal dimension of the connection value was the opposite. This further verifies the applicability of the space syntax metric in rock fracture networks.

Determining the development of artificial frozen walls by present methods is challenging where substantial seepage occurs because fixed monitoring points only indicate physical properties in small areas. Here we use ultrasonic acoustic methods to determine the physical properties between two freezing pipes during freezing. Sensitivity analysis indicates that wave velocity is sensitive to physical properties, and the sensitivity rank is water content > temperature > density. The attenuation coefficient has a low sensitivity to physical parameters, whereas dominant frequency is sensitive to temperature and water content but insensitive to density. Wave velocity increases with temperature and density in a quadratic relationship, and with water content in a linear relationship. Dominant frequency increases with temperature and water content in a quadratic relationship. A multiple regression model of wave velocity and dominant frequency established by stepwise regression can be used to predict the relationship between wave velocity and temperature of frozen fine sand in different areas where the soil properties are similar to those reported here. Wave velocity and dominant frequency measured in the laboratory can be used to predict the relationship between acoustic parameters and temperature in field conditions after curve move based on the first data point from field measurements. The procedure of curve moving involves calculating the difference in value of the first data point between laboratory and field measurements at the same temperature level, and then moving the predicted curve of the laboratory test upward or downward according to the difference. Supplementary material: Experimental datasets are available at https://doi.org/10.6084/m9.figshare.12268970