1 Introduction

For the past few decades, the artificial ground freezing (AGF) method has been widely adopted as an eco-friendly temporary ground support technique in various engineering projects, such as tunnel excavation [12, 23, 28, 30, 35, 38, 40], mining [45], and containment of hazardous wastes [3, 6]. Frozen soil can be formed by heat transfer from the soil to freezing pipes. This increases the stiffness or strength and decreases the hydraulic conductivity of soil [2, 5, 18, 21, 36]. Brine and liquid nitrogen are the two most commonly used refrigerants in AGF, which extract the heat energy of the ground while circulating through the freezing pipe. Because of the vaporization characteristics of liquid nitrogen after heat extraction, AGF by injecting liquid nitrogen is called an open system, whereas AGF by circulating brine is called a closed system [38, 46].

The low boiling point (− 196 °C) of liquid nitrogen freezes the surrounding soil faster than brine, which has a higher temperature (− 40 to − 20 °C) during circulation. However, because liquid nitrogen is typically not reusable, the open system is more expensive than the closed system for achieving a target volume of frozen soil. Therefore, a hybrid method, combining open and closed systems, is occasionally employed to form a frozen wall quickly using the open system (typically within a few days), followed by maintaining the frozen wall for a relatively long period using the closed system (lasting several months) [32, 39, 40]. The hybrid method, which may provide a significant economic benefit over the open system itself, combines the advantages of the two freezing systems [50].

For the effective performance of the hybrid method, the initial formation of the frozen soil by injecting liquid nitrogen is critical. Therefore, the formation of frozen walls by injecting liquid nitrogen under various thermal and hydraulic conditions was investigated to provide insights into the effective implementation of AGF under such conditions [20, 23, 26, 27, 34, 48].

The economic constraint of liquid nitrogen may be compensated by circulating liquid nitrogen in the two freezing pipes instead of releasing the partially gasified liquid nitrogen after an initial injection. This scenario can be achieved when the liquid nitrogen is only partially gasified, indicating that it still holds significant potential to extract heat from the ground during the second injection. The opportunity to reuse partially gasified liquid nitrogen can be enhanced when the freezing pipe is positioned at a relatively shallow depth. Although this approach is feasible in practical applications, the potential for reusing liquid nitrogen in AGF has not been thoroughly documented. Therefore, the objective of this study is to investigate the applicability of reusing liquid nitrogen through a field experiment. The efficiency of the reused liquid nitrogen after the initial circulation was assessed based on the observed temperature near the sub-freezing pipes during the second injection. The elapsed time for freezing and the freezing duration obtained from the temperature data were evaluated to quantitatively describe the reusability of liquid nitrogen in AGF.

2 Experimental program

2.1 Testbed description

The AGF field experiment was performed in Ganghwa-gun, Incheon, Republic of Korea, 600 m from the Yellow Sea (Fig. 1a). To obtain the comprehensive geological profile of the testbed, boring and standard penetration tests (SPTs) were conducted at three locations, each located 10 m apart from the freezing pipes, as shown in Fig. 1b, c. Boring was performed up to a depth of 10 m using an NX-core-sized hole with an outer diameter of 76 mm. The geological profiles of the three boreholes, along with N values measured at every 1 m depth, are shown in Fig. 1b. In this figure, the SPT-N values are presented with depth, expressed as blow counts per penetration depth of 300 mm.

Fig. 1
figure 1

Plan view and geologic profile of the testbed

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The site investigations revealed a surface fill layer composed of clayey silt from the surface to the depth of 1 m. Additionally, the sedimentary layer, mostly composed of clayey silt, was located below the fill layer (Fig. 1b). The soil layer from the surface to the depth of 5 m (where the freezing pipes were installed) was classified as very soft or soft ground by the SPT-N values of 1–7. The groundwater level was determined during the boring process by measuring the distance between the ground surface and the water level in the boreholes. It was observed that the groundwater levels were almost similar, at 2 m, in all three boreholes (see GWL in Fig. 1b). This observation suggests a static condition of the groundwater in the testbed, indicating minimal or no water flow.

Laboratory tests were performed on the undisturbed samples obtained from the borehole BH-2 to evaluate the soil properties of the testbed (Table 1). The salinity of the pore water was measured because the test bed was adjacent to the sea. However, the salinity of the testbed across all depths (2–10 m) was approximately 0, indicating that the effect of salinity on ground freezing was negligible (since an increase in salinity lowers the freezing point of pore water [8]). This also suggests that the salt water wedge did not affect the experimental results, as the freezing pipes were installed up to a depth of 5 m in this study. The water content range was 22.6–36.7%, and most of the soil samples passed the #200 sieve (opening size of 75 µm). From the measured liquid limit (LL) and plasticity index (PI), all samples were classified as ML (silt with low plasticity) in accordance with the unified soil classification system (USCS). However, the sample obtained at the depth interval of 0–0.8 m was classified as CL (clay with high plasticity).

Table 1 Soil properties of testbed obtained from undisturbed samples
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The thermal conductivity of soil affects the ground freezing rate significantly [37]. Previous experimental and theoretical studies have documented that the thermal conductivity of frozen soils is approximately twice that of unfrozen soils [17, 25]. This implies that heat conduction from the freezing pipe to the soil near the freezing pipe becomes faster as the freezing front propagates. To investigate the thermal characteristics at the testbed, the thermal conductivities of the unfrozen and frozen soils were measured using QTM-500 (Kyoto Electronics) by adopting the transient hot-wire method. The sampled clayey silt was placed in a mold (100 (length) × 50 (width) × 20 (height) mm) to measure the thermal conductivity of the sample using a QTM-500 (Kyoto Electronics Manufacturing Co., Ltd.) equipped with a 95 × 40 mm flat probe. The thermal conductivity of the unfrozen soil was measured in the laboratory at an ambient temperature of 15 °C. As for the frozen soil, the specimens in the mold were placed in a freezer at − 10 °C for 24 h before measuring the thermal conductivity. The preliminary result ensured the freezing of the entire specimen at a temperature lower than 0 °C when the specimen was placed in the freezer for more than 10 h. To minimize the thawing effect on measuring thermal conductivity, the model and probe were placed in a freezer during the measurement. Table 2 shows the measured thermal conductivities of the unfrozen and frozen testbed soils. Note that the higher thermal conductivity of frozen soils than that of unfrozen soils, presented in Table 2, is consistent with the results presented in the literature [7, 37, 43].

Table 2 Thermal conductivity of unfrozen and frozen soils at the testbed
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2.2 Overview of application of recycled liquid nitrogen

The liquid nitrogen stored in a storage tank was injected into three freezing pipes (named as the main freezing pipes) installed up to 5 m deep to extract heat from the ground through the freezing pipes. To investigate the reusability of liquid nitrogen, the outlet of the main freezing pipes was connected to the adjacent freezing pipes with the identical dimensions (referred to as the sub-freezing pipes in this study) installed 1 m away from the main freezing pipes (Fig. 2b). Then, the second heat extraction was induced through the sub-freezing pipes, followed by releasing gasified nitrogen after the second heat extraction.

Fig. 2
figure 2

Configuration of freezing pipes and flow of liquid nitrogen in the field experiment

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The distance between the freezing pipes (1 m) was consistent to form a typical target thickness of the frozen wall employed in AGF [14, 24, 29]. The length and diameter of the outer freezing pipe were 5.2 m and 89.1 mm, and those of the inner freezing pipe were 5.3 m and 21.7 mm, respectively. Because ground freezing involves a phase change process from pore water to ice, the characteristics of ground freezing, such as freezing rate, vary depending on the degree of saturation and groundwater flow [10, 11, 19]. To freeze the saturated soil below the groundwater table (2 m), the freezing pipe was thermally insulated up to the depth of 2 m from the ground surface (Fig. 2a).

As shown in Fig. 2b, the injection of liquid nitrogen was divided into four steps. (1) The liquid nitrogen stored in the tank was transported to the freezing system to control the flow rate of liquid nitrogen. (2) The liquid nitrogen was injected into the three main freezing pipes with an injection pressure of ~ 5 bar for primary heat extraction. (3) The liquid nitrogen from the main freezing pipes was re-injected into the sub-freezing pipes for additional heat extraction. (4) The gasified nitrogen was discharged into the atmosphere.

To monitor temperature changes during the injection of liquid nitrogen, 33 temperature-measuring holes were installed at 0.25 m intervals near the freezing pipes (Fig. 3). Thermocouples were installed at every 0.5 m between the depth of 1.5–6.0 m in the temperature-measuring holes and 0.5–5.0 m in the freezing pipes. The discharge temperature of nitrogen after the secondary injection remained constant through the automatic valve installed in the freezing system at approximately − 120 °C. The automatic valve was closed when the discharge temperature of nitrogen dropped below − 120 °C to ensure sufficient heat extraction from the ground. When the discharge temperature exceeded − 120 °C after sufficient heat extraction, the valve opened automatically and liquid nitrogen was injected into the freezing pipe. Note that the configuration of temperature-measuring holes was selected to monitor the formation of a frozen wall with a thickness of 1 m.

Fig. 3
figure 3

Schematic of the freezing system for injecting and discharging liquid nitrogen

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The arrangement of the temperature-measuring holes can be divided into two groups, as shown in Fig. 4. Frozen soil was formed by a single main freezing pipe (main only in Fig. 3). A single sub-freezing pipe (sub-only in Fig. 3) at both ends of the layout, as illustrated in Fig. 3, were selected as the first group (Fig. 4a). The second group represented the formation of a frozen wall between two adjacent freezing pipes. The temperature evolution at the temperature-measuring holes for the following three scenarios was investigated: freezing between the two main freezing pipes, freezing between the two sub-freezing pipes, and freezing between the main and sub-freezing pipes. To monitor the temperature evolution and freezing time of the ground for the two groups, the distance between the six freezing pipes was 1 m, and the distances between the freezing pipes and temperature-measuring holes were 25, 50, 55.9, and 70.7 cm (Fig. 3). Liquid nitrogen was injected for 5 days (120 h) while maintaining the discharge temperature of − 120 °C.

Fig. 4
figure 4

Arrangement of freezing pipes and temperature-measuring holes. a Freezing near the single freezing pipe (first group) and b freezing between two freezing pipes (second group)

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3 Experimental program

3.1 Monitored temperature at temperature-measuring holes

During the field experiment, a liquid nitrogen tank having a capacity of 16 tons was recharged twice a day. A total of 32.364 tons of liquid nitrogen was consumed under 5 bars for 5 days. The daily consumption of liquid nitrogen is presented in Table 3.

Table 3 Liquid nitrogen consumption
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Figures 5, 6, 7, 8, and 9 illustrate the evolution of temperature at the freezing pipe outer wall and the ground during the injection of liquid nitrogen for the five scenarios. The main freezing pipe only (Fig. 5), sub-freezing pipe only (Fig. 6), two main freezing pipes (Fig. 7), two sub-freezing pipes (Fig. 8), and main and sub-freezing pipes (Fig. 9) are denoted as main-only setup, sub-only setup, main-main setup, sub-sub setup, and main-sub setup, respectively, in the following text. As shown in Figs. 5a, 7a, b, and 9a, the temperatures measured at the outer walls of the freezing pipes at depths of 4 and 5 m were relatively consistent during the injection, whereas a higher temperature at the depth of 3 m than at depths of 4 and 5 m was observed for the first two days. The temperature at the depth of 3 m was consistent with that at the depths of 4 and 5 m after the elapsed time greater than 2 days. This indicates significant heat extraction in the middle of the main freezing pipes during the formation of frozen soil near the freezing pipes. A consistent temperature after 2 days at the depths of 3, 4, and 5 m implies an identical rate of heat extraction. This occurred after a certain volume of soil froze near the freezing pipe. Additionally, the relatively low temperature of − 120 °C at the depth of 5 m in the sub-freezing pipe indicates the possibility of partially gasified liquid nitrogen after the initial circulation. Although liquid nitrogen was completely gasified in the sub-freezing pipe, − 120 °C might be sufficient to freeze the soil near the sub-freezing pipe.

Fig. 5
figure 5

Temperature evolution during injection of liquid nitrogen for single main freezing pipe. a Main freezing pipe; At b 25 cm; c 50 cm; d 55.9 cm; and e 70.7 cm from freezing pipe

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Fig. 6
figure 6

Temperature evolution during injection of liquid nitrogen for single sub-freezing pipe. a Sub-freezing pipe; At b 25 cm, c 50 cm, d 55.9 cm, and e 70.7 cm from freezing pipe

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Fig. 7
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Temperature evolution during injection of liquid nitrogen for two main freezing pipes. a Main freezing pipe 1; b Main freezing pipe 2; At c 25 cm, d 50 cm, e 55.9 cm, and f 70.7 cm from freezing pipe

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Fig. 8
figure 8

Temperature evolution during injection of liquid nitrogen for two sub-freezing pipes. a Sub-freezing pipe 1; b Sub-freezing pipe 2; At c 25 cm, d 50 cm, e 55.9 cm, and f 70.7 cm from freezing pipe

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Fig. 9
figure 9

Temperature evolution during injection of liquid nitrogen between main freezing pipe and sub-freezing pipe. a Main freezing pipe; b Sub-freezing pipe; At c 25 cm from main freezing pipe, d 25 cm from sub-freezing pipe, e 50 cm from freezing pipe, f 55.9 cm from freezing pipe, and g 70.7 cm from freezing pipe

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It should be noted that the phase of liquid nitrogen in the freezing pipe was not directly identified in this study. However, the high injection pressure of 5 bar applied into the main freezing pipes and the lower monitored temperature at shallower depths in the sub-freezing pipes indicate the boiling point of liquid nitrogen under high pressure and the occurrence of heat extraction in the sub-freezing pipes. This implies that the liquid nitrogen was likely partially gasified after the initial injection. Additionally, it is worth mentioning that the temperature of liquid nitrogen in the freezing pipes was likely lower than the monitored temperature because the thermocouples were attached to the outside of the freezing pipes. Because heat extraction was initiated at the bottom of the freezing pipe when the injected liquid nitrogen flowed upward through the outer freezing pipe (Fig. 2a), the monitored temperature data at the main and sub-freezing pipes were in the order of depth of 1 m > 2 m > 3 m > 4 m > 5 m.

In all temperature-measuring holes, the dominant heat extraction from the soil occurred in the radial direction (refer to Figs. 5, 6, 7, 8, and 9). The dominant heat extraction from the soil occurred in the radial direction. Additionally, the lowest temperature was observed at the depth of 4 m, implying that the semi-spherical shape of the frozen soil near the freezing pipe was formed with a maximum radial distance at the depth of 4 m. For the first group (main-only and sub-only setups), an above-zero temperature at the depth of 5 m at the distance of 25 cm (Figs. 5b and 6b) indicates that heat conduction from the ground temperature below 5 m impeded the radial formation of frozen soil at the depth of 5 m.

The temperature corresponding to the elapsed time of 5 days at the depth of 4 m for D = 25 cm was in the order of sub-only setup (Fig. 6b) > main-only setup (Fig. 5b) ≈ sub-sub setup (Fig. 8c) > main-sub setup (Fig. 9c) > main-main setup (Fig. 7c). This indicates that the most rapid and slowest heat extraction and formation of frozen soil occurs in the main-main setup and sub-freezing pipe only cases, respectively. Similar temperature values (approximately − 76 °C) at the distance of 25 cm for the cases of main-only and sub-sub setups indicate that the evolution of frozen soil between the two freezing pipes with the circulation of reused liquid nitrogen may have similar performance in freezing soils at a relatively short distance (25 cm) from the freezing pipe. On the other hand, lower temperatures were observed for the sub-sub setup (Fig. 8d, e, f) than those for the main-only setup (Fig. 5c, d, e) at the distances of 50, 55.9, and 70.7 cm. This suggests a higher freezing efficiency for the sub-sub setup than the main-only setup at these specific distances. The observed below-zero temperature at the distance of 50 cm for sub-only setup (Fig. 6c) implies that liquid nitrogen can be reused within a 3 m depth interval (heat extraction from 2 to 5 m) between the freezing pipe and surrounding soil at a flow rate of 6.473 ton/day (Table 3). The chance of efficient reuse can be increased at a high flow rate and short depth interval of heat extraction.

3.2 Freezing rate from the experimental observations

The freezing rate of the soil was evaluated using Eq. (1) for a quantitative representation of the temperature measurements presented in Figs. 5, 6, 7, 8 and 9. Here, the freezing pipe was assumed to be an infinite line heat source, where the formation of a cylindrical frozen body surrounding the freezing pipe was anticipated. The radius of the cylindrical frozen body increases during refrigerant injection, and the freezing rate in the radial direction can be defined as the one-dimensional freezing rate of the ground [13]. The one-dimensional freezing rate of the ground (vf (L/T)) can be expressed as follows:

$$v_f = \frac{r_f }{t},$$
(1)

where vf (L/T) is the one-dimensional freezing rate in the radial direction, rf (L) is the radius of the frozen body (distance from the freezing pipe), and t (T) is the required freezing time (time required to reach the sub-zero temperature in temperature-measuring holes). Table 4 summarizes the one-dimensional freezing rate, evaluated from the monitored temperature at the depth of 4 m (representing averaged freezing rates for a given radius of the frozen body).

Table 4 One-dimensional freezing rate according to the freezing temperature at 4 m below the ground surface
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Table 4 summarizes the one-dimensional freezing rate evaluated from the monitored temperature at the depth of 4 m (averaged freezing rates for a given radius of the frozen body). As shown in Table 4, the frozen soil near the single main freezing pipe had a radius larger than 70.7 cm, whereas that formed by the single sub-freezing pipe was less than 55.9 cm. This can be attributed to the different temperatures at the freezing pipes between main-only setup (− 160 °C) and sub-only setup (− 80 °C) (Figs. 5a, 6a). Additionally, a value of vf for main-only corresponding to the distance of 50 cm higher by 1.74 times than that for sub-only indicates a higher heat extraction rate resulting from the lower temperature at the freezing pipe. Similar to the cases of single freezing pipes (main-only and sub-only setups), the case of main-main setup showed higher vf than the sub-sub and main-sub setups for all radii of frozen soil because of the lower temperature at the freezing pipe. For the main-sub setup, a higher value of vf in the main freezing pipe was observed than that in the sub-freezing pipe, implying that the freezing front propagated faster from the main freezing pipe than from the sub-freezing pipe. However, the higher values of vf for the main-sub setup than for the main-main setup at the distance of 25 cm were counter intuitive. This was most likely because the temperature-measuring hole was slightly inclined toward the freezing pipe in the case of main-sub setup.

Overall, the values of vf decreased as the radius of frozen soil increased, except in the case of sub-only setup (Table 4). This is because the contact area between the frozen soil and unfrozen soil is proportional to the squared radius of the frozen soil. This decreases the rate of heat extraction in the radial direction. Because the temperature of the freezing pipe at the depth of 4 m was almost consistent during the experiment, the results presented in Table 4 indicate the anticipated evolution of the frozen soil near the freezing pipe. However, as the radius of the frozen soil increased, a more rapid decrease in vf for the sub-sub setup case was observed than for the main-main setup, indicating that the vf value is a function of temperature at the freezing pipe. The higher temperature of the freezing pipe for the sub-sub setup resulted in lower freezing efficiency after forming a certain radius of frozen soil.

Assuming the frozen soil near the freezing pipe to be circle-shaped in the plane view, the formation of a frozen wall between the two freezing pipes can be divided into four stages, as shown in Fig. 10. (1) The radius of frozen soil was 25 cm around each freezing pipe. (2) The radius of frozen soil was 50 cm where two frozen masses were first encountered. (3) The thickness of frozen wall was 50 cm. (4) The target thickness (1 m) of the frozen wall was achieved. The schematic drawings illustrated in Fig. 10 indicate the relationship between the monitored temperature and thickness of the frozen sample. For example, the monitored temperature at a distance of 70.7 cm corresponds to the thickness of the frozen wall becoming 1 m (Fig. 10d).

Fig. 10
figure 10

Formation of frozen wall in four stages: a Stage 1, b Stage 2, c Stage 3, and d Stage 4

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The observed temperatures presented in Figs. 7f, 8f, and 9g demonstrate that a 1-m-thick frozen wall was obtained at the depths of 3 and 4 m in all three scenarios (the cases of main-main, sub-sub, and main-sub setups) after 5 days of injecting liquid nitrogen. However, only the case of main-main setup could achieve a 1-m-thick frozen wall at the depth of 5 m. This implies the thickest frozen wall in the vertical direction was formed in the main-main setup. Furthermore, the observed sub-zero temperature at relatively short elapsed time at all depths for main-main setup (Fig. 7f) results in the most rapid formation of the 1-m-thick frozen wall, and a thickness greater than 1 m can be anticipated after injecting liquid nitrogen for more than 5 days.

3.3 Elapsed time for freezing

The reuse of liquid nitrogen can be assessed by evaluating the elapsed freezing time (te) and freezing duration (Tfr) from the temperature data shown in Figs. 5, 6, 7, 8 and 9. The mathematical expressions for te and Tfr are as follows:

$$t_e = t_{pn(1)} - t_s$$
(2)
$$T_{{\text{fr}}} = T_T - t_{pn(1)} - \sum \limits_i (t_{np\left( i \right)} - t_{pn\left( i \right)} ),$$
(3)

where tpn(i) is the ith time at which the measured temperature changed to sub-zero, ts is the starting time of liquid nitrogen injection (0 in this study), TT is the overall time (5 days in this study), and tnp(i) is the ith time at which the measured temperature changed back to above zero.

The evaluated te and Tfr values for the five scenarios are presented in Table 5 and illustrated in Figs. 11 and 12, respectively. Overall, at all depths, the case of sub-only setup showed the highest te and lowest Tfr values, whereas the main-main setup showed the lowest te and highest Tfr values among the five scenarios. The missing values of te for the sub-only case at 55.9 and 70.7 cm from the freezing pipe and the te values at 50 cm from the freezing pipe at the depths of 3 and 4 m indicate that a semi-spherical shape (or ovoid shape) of frozen soil was formed (no values at the depths of 2 and 5 m) with a radius of frozen mass of 50 cm. The te and Tfr values presented in Figs. 11 and 12 indicate that a single sub-freezing pipe can be utilized to form relatively small-sized frozen soil with a low freezing rate.

Table 5 te and Tfr values of all experimental conditions (corresponding to Figs. 11 and 12)
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Fig. 11
figure 11

Evaluated elapsed freezing time for five scenarios at a distance of a 25 cm, b 50 cm, c 55.9 cm, and d 70.7 cm from freezing pipe. The missing data represents above-zero temperature for 5 days of injection

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Fig. 12
figure 12

Evaluated freezing duration for five scenarios at a distance of a 25 cm, b 50 cm, c 55.9 cm, and d 70.7 cm from freezing pipe. The missing data represents above-zero temperature for 5 days of injection

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The semi-spherical shape of the formed frozen soil was induced by dominant heat extraction from the range of 3–4 m depth of the 5-m-long freezing pipe with thermal insulation up to 2 m. This led to the most dominant heat extraction in the vertical direction and the most rapid growth of frozen soil at the depths of 3 and 4 m.

3.4 Implications of experimental observations

Adopting liquid nitrogen provided rapid freezing with a sufficient increase in the strength and stiffness of soils. However, the high cost of liquid nitrogen limits the application of the open-system AGF [9, 16, 42]. Although liquid nitrogen can be reused after initial injection when the outlet temperature is below zero, no study investigated the reuse of liquid nitrogen for secondary injection in the AGF method.

The monitored temperatures presented in Figs. 5, 6, 7, 8, and 9 reveal the favorable applicability of reusing liquid nitrogen after the initial injection. The monitored temperatures around the two sub-freezing pipes and the main-sub freezing pipes also indicate the capability of forming a 1-m-thick frozen wall after 3 days by reusing liquid nitrogen. The relatively short required time (1.6 days for forming a 1-m-thick frozen wall) for the two main freezing pipes indicates that the typical practice of AGF using the first injection of liquid nitrogen only should be adopted in case of forming thick frozen walls in a short time. Nevertheless, because the target frozen wall thickness of 1 m is commonly adopted in AGF specifications for underground construction [14, 24, 29], the results presented in this study demonstrate the applicability of reusing liquid nitrogen for developing frozen walls for various construction projects.

The experimental observations presented in this study demonstrated the reusability of liquid nitrogen, though this is limited to saturated silty deposits. However, it’s worth noting that AGF can be applied to soil deposits with a water content higher than 15% [22, 41], suggesting that liquid nitrogen could potentially be reused in many types of soil deposits located below the groundwater level. Previous studies reported that the rate of heat extraction in the freezing process depends on several factors, such as soil type [1, 15, 47], degree of ice saturation [51], configuration and material of freezing pipes [14, 29], pore water salinity [31, 49], flow rate and direction of groundwater [20, 27, 33], geochemical aspects [44], and injection rate [4]. Further investigations are required to assess the reuse of liquid nitrogen under various field conditions.

3.5 Cost estimation for forming 1-m-thick frozen wall between two freezing pipes

In this study, approximately 30% of cost reduction would be anticipated by reusing the liquid nitrogen. For example, the estimated costs to achieve D = 70.7 cm are approximately $2,715 for using only liquid nitrogen and $1928 for the scenario of reusing liquid nitrogen. This estimation assumed that the consumption of liquid nitrogen in the reusing scenario is half that of using liquid nitrogen only. The calculation was based on a unit price of liquid nitrogen at $200 per ton, the average te values in Table 5 for the main-main and sub-sub setups, and the daily consumption rate of 6.473 ton/day as indicated in Table 3. An even higher cost was estimated for the circulation of brine mainly because of the need for installing a freezing plant. The abovementioned calculation results imply significant cost benefits in AGF-related projects by reusing liquid nitrogen for forming a 1-m-thick frozen wall.

The accurate cost estimation of AGF projects is challenging and depends on many factors such as the number of freezing pipes, seepage flow, freezing duration, target freezing volume (or thickness), installation process, and transportation. Therefore, injecting liquid nitrogen into all freezing pipes might be more beneficial than reusing liquid nitrogen for the project with a high operational cost per day (e.g., labor) (reusing liquid nitrogen requires one or two days longer to form a 1-m-thick frozen wall compared with injecting liquid nitrogen). Nevertheless, the material-wise cost estimation indicates the reuse of liquid nitrogen is beneficial for large AGF-related projects, which require the installation of hundreds of freezing pipes. Note that the circulation of brine may be a cost-beneficial method for maintaining a frozen mass of soils for relatively long projects because of low material-related costs (cost without freezing plant).

4 Conclusion

This study investigated the reusability of liquid nitrogen by performing a field experiment under five scenarios: main-only, sub-only, main-main, sub-sub, and main-sub setups. The freezing of silty deposits near the freezing pipes (or between the two freezing pipes) was assessed from the monitored temperature up to the depth of 5 m. Additionally, the freezing rate, elapsed freezing time, and freezing duration were evaluated for quantitative representation and applicability of reusing liquid nitrogen after the initial injection. Based on the monitored temperature data at the temperature-measuring holes, freezing rate, elapsed freezing time, and freezing duration, the following conclusions were obtained:

  1. 1.

    The monitored temperature of − 120 °C at the depth of 5 m for the sub-freezing pipe indicates that the temperature of nitrogen after the initial injection was sufficiently low to freeze the surrounding soil.

  2. 2.

    The highest rate of heat extraction was observed at the main-main setup, while the lowest rate was observed at the sub-only setup. Additionally, a similar rate of heat extraction for the main-only and sub-sub setups indicates the efficiency of additional sub-freezing pipes in the formation of the frozen soil.

  3. 3.

    The sub-zero temperatures observed at the temperature-measuring hole that is located between two sub-freezing pipes implies that a 1-m-thick frozen wall can be formed by injecting reused liquid nitrogen into the two adjacent sub-freezing pipes with 1 m interval.

  4. 4.

    The observed temperature data at the temperature-measuring holes, one-dimensional freezing rate in the radial direction, elapsed freezing time, and freezing duration indicates the applicability of reusing liquid nitrogen in silty deposits. Further investigations are required to verify the efficiency of reusing liquid nitrogen under various hydrogeological conditions and the arrangement of freezing pipes.

  5. 5.

    The results presented in this study suggest a significant potential for reusing liquid nitrogen on construction sites, which could substantially reduce the cost of AGF. Traditionally, AGF using liquid nitrogen without reuse has been regarded as one of the high-cost ground improvement methods.