Detection of the freezing state and frozen section thickness of fine sand by ultrasonic testing

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.

determining the freezing state and frozen section thickness during freezing is fundamental to assessing the development of artificial frozen walls.
Several methods have been used to measure the freezing state and frozen section thickness with varying success. Real-time temperature monitoring 7 and theoretical derivation of stationary temperature fields 8 were used in the 1950s-1960s, whereas numerical simulations of nonstationary temperature fields have developed in recent decades (e.g., 9,10 ). However, the freezing state and frozen section thicknesses predicted from these methods often differ from actual conditions at many sites with high groundwater seepage and geologic structures such as faults, cavities and interbedded strata, because the shape of frozen walls becomes irregular in these conditions. Ground-penetrating radar (GPR) has also been used to determine the freezing state and thickness of frozen walls, 11 although its results are affected by steel freezing pipes and a limited detection depth (3-30 m). Overall, therefore, a more accurate detection method is needed to determine the frozen wall thickness and freezing state. To this end, the present study investigates the use of ultrasonic testing.
Ultrasonic testing is an effective technique to identify the physical and mechanical parameters of frozen soil in the laboratory because soils that are fully or partially saturated with water experience large variations in acoustic parameters when they freeze (e.g., [12][13][14][15]. Several previous studies have investigated the relationships between acoustic parameters and physical mechanical properties of frozen soil (e.g., [16][17][18][19][20][21][22] ). Wang et al., 16 18 Li et al., 19 and Huang et al., 20 used wave velocity to evaluate the physical and mechanical properties of frozen silty clay. Their results indicate that changes in the physical mechanical properties of frozen soils can be measured indirectly by ultrasonic waves. 23 However, these studies focus on the change of acoustic parameters of frozen soil rather than soil that is freezing progressively. Therefore, there remain questions arising from the responses of acoustic parameters from progressively freezing soil, which is the basis of determining the freezing state and frozen section thickness of artificial freezing walls.
Here, 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. This enables us to determine how acoustic parameters vary during progressive upward freezing and elucidate how ultrasonic testing can be used to estimate the freezing state and frozen section thickness. This work is part of a larger project examining the acoustic parameters and physical properties of frozen fine sand. 23 2 | MATERIALS AND METHODS

| Soil properties and specimen preparation
Sand was obtained from 16 m depth at Baiyun Airport, Guangzhou, China. The physical properties of the sand, measured in the laboratory after transport from the field, 24 were: bulk density = 1.87 g/cm 3 , water content = 10.31%, and freezing temperature = −0.2 C. The sand is fine-grained (Table 1).
Soil specimens in this study comprise remolded samples. Following the industrial standard of the People's Republic of China, 25 sand was dried in an oven at 105 C for 48 h. The dry sand was then mixed with a specific amount of water to achieve the required uniform water content. Next, loose moist sand was compacted into a PVC pipe (72 mm high and 85 mm in diameter) to meet the required uniform density. Sand temperature was measured by cylindrical platinum resistance thermometers (Pt100) manufactured by Heraeus Co Ltd. The Pt100 temperature sensors (diameter 4 mm and length 15 mm) were calibrated to an accuracy of ±0.1 C in an ice-water bath, then embedded in the specimens at heights of 35, 45, 55 and 70 mm above the base ( Figure 1a). Finally, rubber insulation (30 mm thick) was wrapped around each specimen, except for the bottom, to minimize the influence of external temperature.

| Monitoring strategy
Our monitoring strategy relied on instrumenting sand samples with Pt100 temperature sensor arrays and a nonmetal ultrasonic measuring system, NM-4A (manufactured by KangKeRui Ultrasonic Engineering Co., Ltd). This allowed us to measure temperature and acoustic parameters at different stages of freezing, as the cryofront ascended to specific heights above the base of the specimens.
Ultrasonic testing during freezing involved four steps. First, the ultrasonic apparatus was calibrated before measurement 26 to calculate the inherent time delay t 0 . A thin film of petroleum jelly was used to ensure good acoustical coupling between the sand

Research Highlight
• Wave velocity, unlike wave amplitude, can reveal the cryofront position during partial freezing of fine sand.
• The frequency components during later stages of freezing can reveal the frequency of different freezing regions.
• Single and multiple peaks in the frequency spectrum and wave velocity during different stages of freezing can identify the freezing state.
• An equation is proposed to calculate the thickness of the frozen section, and it can be used to predict frozen wall thickness of fine sand in the laboratory and field. sample and acoustic transducers and to eliminate any air pockets between them. The apparatus was then used to measure freezing of the sand specimen in a DWB thermostatically controlled tank, which can provide constant temperatures from −40 to 30 C, based on the arrival time of the cryofront at specific heights. Next, an ultrasonic wave propagated through the sample and acoustic parameters were recorded. Finally, acoustic parameters were calculated, including wave velocity, wave amplitude, and frequency spectrum based on ultrasonic theories. 27,28 The gravimetric water content of the sand was measured when the cryofront had reached four specified heights (35, 45, 55 and 70 mm) to determine water migration. At each height, one specimen of soil was divided into horizontal subsamples 1 cm thick. Unfrozen soil was sampled from the PVC pipe with a soil sampler geotome, and underlying frozen soil was sampled with a knife. Each subsample was weighed, dried in an oven (105 C) for 24 h, reweighed and the moisture content was calculated. Overall, the moisture content was determined from four soil specimens for each of three water contents (7.31, 10.31, and 13.31%), giving a total of 12 specimens.    6) The moisture content of the frozen and unfrozen sand was measured in 1-cm vertical increments. (7) The variation of wave velocity, amplitude, and frequency spectrum at different freezing periods was compared and analyzed.

| Ultrasonic parameters
The ultrasonic parameters determined in this study are wave velocity, head wave amplitude, and frequency spectrum. The velocity of compressional and shear waves indicates the physical properties of frozen soil and can be measured directly in the laboratory (e.g., 16,17 ). The compressional wave (p wave) velocity was the main acoustic parameter measured in this study because it is easier to obtain than shear wave velocity under field conditions. The p wave velocity (V p , km/s) is expressed as: where L is the length of the specimen (mm), t p is the travel time of the first wave in frozen soil (μs), and t 0 is the inherent time delay (μs).
The head wave (i.e., first wave) amplitude (A h ) represents the energy magnitude of the head receiving wave and can be recorded automatically by a supersonic test meter. 21 Changes in transmitted amplitude show the variation in contact area between soil particles and can be used to estimate the amount of compaction, changes in void ratio, and associated changes in normal stress (e.g., [29][30][31] ). An increase in contact area between the particles leads to an increase in values of transmitted amplitude through the soil specimen. 31 F I G U R E 2 Flowchart showing the stages in the experimental procedure The frequency spectrum can be calculated by a fast Fourier transform (FFT), which converts data from the time domain into the frequency domain of waveforms (e.g., [32][33][34][35][36]. The frequency spectrum of receiving ultrasonic waves relates to the changes in volume and distribution of inter-particle pores in a soil. 21 Pyrak-Nolte et al. 37 found that fractures and flaws filter the high-frequency content of the transmitted wave. Therefore, the frequency spectrum can determine whether particular frequency components are present in the analyzed signal at different freezing periods, because water migration during progressive upward freezing can lead to variation in the distribution of inter-particle pores. A wavelet transform was used to eliminate high-frequency noise signals from the original signals and to improve the signal characteristics substantially, because ultrasonic waves are nonstable and transient (e.g., 21,38,39 ). The db5 wavelet was selected to disassemble the receiving wave signals into five levels. After wavelet transformation, with the cutoff frequency set at 100 kHz, the reconstructed effective signals were processed by an FFT, to obtain the distribution of the frequency spectrum of fine sand at different stages during progressive upward freezing.

| Changes in water content
Vertical profiles of water content change (Δω) in the sand specimens during upward freezing are presented in Figure 4. The change is shown relative to initially uniform vertical profiles (normalized to 0% in 1. Unfrozen sand with decreased water content. In region 1, the mass of water declined more in specimens with higher initial water content. For example, maximum declines of 0.856, 1.224, and 1.856% were determined for initial water contents of 7.31, 10.31, and 13.31%, respectively, when the cryofront reached 55 mm height. 2. Frozen sand with decreased water content. In region 2, the temperature was below 0 C and the mass of water was less than that of the initial water content. The maximum decreases in water content for different initial moisture contents ( 3. Frozen sand with increased water content. In region 3, the temperature was below 0 C and the mass of water was more than that of the initial water content. Increases in moisture content were greater for specimens with initially greater water contents. The average temperature of region 3 was distinctly lower than that of region 2 and the mass of water increased gradually with depth. Ice crystals were visible in almost all of region 3 during freezing. The crystals were up to a few millimeters in length or diameter ( Figure 6). During later stages of freezing (cryofront at 55-70 mm height), much of sample was frozen, and therefore the rate of increase in wave velocity decreased (Figure 8a). In addition, the bulk, shear modulus, and strength of frozen soil is higher with higher water content in the frozen regions 2 and 3. 16 Thus, when the cryofront arrived at 55 mm and 70 mm height, the wave velocity in the specimen with an initial water content of 13.31% was distinctly greater than that of 10.31%, which in turn exceeded that of 7.31%. led to an increased contact area between the sand particles because ice crystals occupied more of the pore volume and formed new interparticle contact areas in frozen sections. However, the reduction of water in the unfrozen section resulted in more air among the sand grains and less inter-particle contact area. Therefore, a change of wave amplitude indicates that the function of unfrozen section is greater than the frozen section during most of the freezing period. In summary, wave amplitude decreased during early stages of freezing and increased during later stages, which indicates that wave amplitude cannot be used as a method to calculate the cryofront position during upward freezing.

| Ultrasonic frequency-domain characteristics
The distribution of the frequency spectrum during upward freezing was obtained by FFT after wavelet transform (Section 2.4) and is summarized in Figure 9.
where f i and f p are the values of discrete frequency and peak frequency, respectively (kHz), and A i is the discrete frequency amplitude (db).
As shown in Figure 10  during later stages of freezing, a single-peak frequency spectrum or KFS value that is higher than during early stages is abnormal and indicates that the cryofront moved slowly, which may be caused by cold source shortage or limited heat transfer. In addition, a multiplepeak frequency spectrum or a KFS value that is very low during early stages of freezing is abnormal, which indicates that the cryofront has moved faster than normal, which may be caused by lower initial temperature or low source temperature. More generally, single-peak and multiple-peak frequency spectra and KFS values could be used as evaluation methods to identify the freezing state of progressively frozen sand.
Our laboratory results can be compared with field observations obtained during artificial ground freezing engineering at Baiyun Airport, Guangzhou, China, where the average depth of the groundwater table was 4.37 m. As shown in Figure 11, the frozen soil at The trend of the receiving frequency spectrum of fine sand measured in the field (Figure 12a) is similar to that measured in the laboratory ( Figure 9). The frequency spectrum of undisturbed sand in the field is a single peak. During the earlier stages of freezing (0-24 days), the dominant frequency was slightly lower than that of undisturbed soil. The morphology of the frequency spectrum became multi-peaked during later stages of freezing (24-60 days). Therefore, the gradual change from a single-peak frequency spectrum to a multiple-peak one can demonstrate that the frozen wall developed normally.
The trend of KFS of fine sand calculated in the field (Figure 12b) is similar to that calculated in the laboratory ( Figure 10). KFS decreased gradually as freezing time increased, and the minimum value of KFS is 0.0883 when the cryofront arrived at J 2 (60 days). However, when the cryofront arrived at J 2 ( Figure 11) the frequency components of the field results are more complex and KFS is higher than laboratory results. The main reason for this is that underground water continually supplies water into unfrozen soil in the field, whereas such water supply was absent in the laboratory.

| Variation of wave velocity
The trend of wave velocity of progressively frozen fine sand measured in the field is also similar to that of wave velocity measured in the laboratory (Figure 12b). The rate of increase of V p during the early stages of freezing (0-24 days) is lower than that during middle stages (24-42 days). During later stages of freezing (42-60 days), the rate of increase of V p decreases. The wave velocity value measured in the field is higher than that in the laboratory, mainly because formation pressure had compacted the frozen soil in the field, whereas frozen soil was measured under unloaded conditions in the laboratory. Therefore, if lower wave velocity is measured during later stages of freezing, especially if the measured value is similar to that of undisturbed soil, it can be considered to indicate an abnormal freezing state that reflects the slow movement of a cryofront.

| Frozen section thickness of laboratory test
As shown in Figure 13, the specimen that was progressive frozen in the laboratory can be divided into frozen and unfrozen sections according to the cryofront position because the partially frozen layer (temperature range: −0.2 to 0 C) in progressively frozen sand is so thin that it has little impact on the accuracy of the calculation of frozen section thickness. The total travel time of the head wave in the specimen τ p (μs) can be expressed as: where S is the length of the specimen (mm), S f is the thickness of the frozen section (mm), v f is the average wave velocity of the frozen section (km/s) and v u is the average wave velocity of the unfrozen section (km/s).

By rearranging Equation 3
, we obtain the value of the frozen section thickness as: The relationship between wave velocity and temperature of fine sand at different water contents under constant temperature was measured in the laboratory (Figure 14). 23 Wave velocity increases slightly as temperature decreases before fine sand freezes. Therefore, the average wave velocity of the unfrozen section v u can be treated as the wave velocity of undisturbed soil, which can be measured before freezing. However, wave velocity increases sharply as temperature decreases below 0 C, which demonstrates that the average wave velocity of the frozen section v f changes significantly during progressive freezing. section thickness S f and v f (Figure 15) is based on inputting values of S, τ p and v u into Equation 4. The predicted frozen section thickness S f of specimens at different water contents decreases steadily as wave velocity increases, but the slope of the relationship is low. This indicates that the sensitivity of S f to v f is low at different water contents.
For the purpose of prediction, v f can be approximated to wave velocity at −10 C because the design average temperature in the field is usually −10 C. The predicted results of frozen section thickness thus given are presented in Table 2 values of frozen wall thickness in the field are given in Table 3. Measured values of frozen wall thickness in Table 3 were obtained by a temperature sensor (diameter 4 mm and length 30 mm) in steel pipes J 1 and J 2 , where the thickness is determined for sand whose temperature is <0 C ( Figure 16). Table 3

| CONCLUSIONS
The following conclusions are drawn from this study: