Model Test on Thermomechanical Behavior of Deeply Buried Pipe Energy Pile Under Different Temperature Loads and Mechanical Loads

Abstract

Deeply buried pipe energy pile (DBP-EP) offers the capability to harness geothermal energy from significantly deeper subterranean layers than those available inside buried pipe energy pile (IBP-EP). Despite its potential, there is a notable scarcity of research on the thermomechanical behavior of DBP-EP. This study meticulously observed the thermal variations in the soil surrounding the DBP-EP, the mechanical response of the pile itself, the earth pressure at the pile toe, and the displacement occurring at the pile’s top during the heating phase across various operational conditions. The findings show that for every 1 °C increase in inlet temperature, the temperature difference between the inlet and outlet increases by about 0.27 °C. The method of load application at the pile top during heating markedly influences the frictional resistance along the pile’s sides. Furthermore, When the pile top load rises from 0.26 kN to 0.78 kN, the observed vertical load at the pile foot decreases by 2.2–8.51%. This indicates that the increase in the pile top load reduces the downdrag effect on the sandy soil near the pile toe. This reduction subsequently diminishes the impact of vertical loads on the pile toe. Notably, after continuous operation for 8 h, the rate of increase in pile top displacement for DBP-EP shows a decline. Additionally, for every 1 °C rise in the inlet water temperature, the final displacement at the pile top diminishes by approximately 0.03‰D. This research endeavors to furnish a robust theoretical foundation for the structural design and practical engineering applications for DBP-EP.

1. Introduction

Currently, there is a diversity of approaches to geothermal energy development [1,2]. Inside buried pipe energy pile (IBP-EP) has become an important method of extracting geothermal energy from the ground source side [3,4]. The pile foundation is used as a heat exchange well, which is connected to the heat pump system through a collector pipe, and the heat pump unit extracts the ground-side thermal energy, which is difficult to utilize directly using geotechnical methods, to supply heat or cold to buildings and other infrastructures [5,6]. At present, the research on IBP-EP tends to be limited, and more scholars focus on energy pile improvement technology. Many energy pile improvement techniques have been proposed, with a focus on improving the energy pile body material [7,8,9,10,11,12], the pile structure [13,14,15,16,17] and the construction process [18,19,20,21]. The deeply buried pipe energy pile (DBP-EP) technology [22] requires the heat exchanger pipe to extend out of the pile into a deep well at the bottom of the pile, with the upper part of the heat exchanger pipe wrapped in pile concrete and the lower part wrapped in backfill. The DBP-EP can be designed with different depths of the pile bottom well to meet different heat transfer needs, making the structure form more flexible. Compared with IBP-EP, DBP-EP is divided into a pile foundation portion and a deep well portion along the depth direction, and the heat transfer mechanism along the depth direction is variable along the cross-section and along the heat transfer medium, as shown in Figure 1. DBP-EP can obtain deeper geothermal energy and can independently satisfy the energy demand of the upper structure. The DBP-EP construction process is flexible, and the construction of the pile foundation casting and the drilling of the heat exchanger pipe can be operated separately, so compared with the construction process for pre-buried IBP-EP heat exchanger pipes, the process for the DBP-EP pipes has a broader application prospect. However, relatively few studies have been conducted on DBP-EP, and only the heat transfer performance of DBP-EP has been analyzed under hot and cold cycles [23,24,25], seepage conditions [26,27], and intermittent operation [28]. The effects of different temperature loads and mechanical loads on the thermomechanical behavior of DBP-EP during the heating process are not known.

In recent years, the thermomechanical behavior of energy piles has become a major research focus, with numerous thermomechanical response tests being conducted by scholars, both domestically and internationally. These studies have shown that the additional thermal stress and strain caused by the thermal expansion of the pile body during operation cannot be ignored [16,29]. The heat exchanger tube within the energy pile facilitates heat exchange, leading to uneven temperature stress distribution throughout the pile, a phenomenon confirmed by the thermomechanical response tests conducted by Laloui et al. [30] and Bao et al. [13]. Wu et al. [31] introduced the thermal stress concentration factor to evaluate the inhomogeneity of thermal stresses within energy piles and analyzed the relative impact of various factors contributing to this inhomogeneity. Bourne-Webb et al. [32] found that assuming a uniform temperature distribution within the pile results in expansion or contraction near the “zero point” of the pile. Model tests, including centrifugal and indoor model tests, have become a popular method among scholars for studying the thermomechanical response of energy piles. Stewart et al. [33] and Goode et al. [34] used centrifugal modeling tests to investigate these responses, confirming the feasibility of such tests and highlighting the significant impact of the end restraints on the stress–strain behavior of piles. The research team of Yang et al. [9,35,36] conducted extensive thermomechanical response tests using indoor modeling and numerical simulations. They validated the feasibility of indoor modeling tests by considering various thermomechanical parameters, such as loading conditions, operational modes, pile material, and layout configurations. Liu et al. [37] conducted comparative modeling tests on IBP-EP and improved energy piles and discovered that pre-burying heat exchanger tubes within steel tubes has a minimal impact on the structural safety of the piles, but it reduces their heat exchange capacity. Yin et al. [38] and Liu et al. [7] performed modeling tests on helical energy piles to investigate their thermomechanical behavior under both summer and winter conditions. Chang et al. [19] and Cao et al. [20] conducted thermomechanical response tests on static drill rooted energy piles using modeling tests that considered the surrounding soil and the effects of different heating methods. Guo et al. [8] carried out field tests on PHC energy piles to examine their thermomechanical behavior under various operational conditions. Ding et al. [39] studied the effects of asymmetric thermal loading on energy pile groups over long-term operation by modeling a three-dimensional energy pile group. They analyzed the pile–soil–slab interaction by comparing the ratios of thermal expansion coefficients, pile–soil stiffness, and slab–soil stiffness. Kong et al. [40,41] found that multiple cycles of heating and cooling cause continuous accumulation of pile settlement, as demonstrated through their modeling experiments.

Mechanical loading also influences the thermomechanical behavior of energy piles. Yavari et al. [42] performed thermomechanical response experiments on energy piles situated in dry sand via modeling tests, revealing that heating the tops of the piles while maintaining constant axial loads leads to bulging and causes irreversible settlement at the tops. In a separate study, Song et al. [43] explored the thermomechanical performance of energy piles subjected to prolonged inclined mechanical loads by creating a three-dimensional model. Bao et al. [44], along with Song et al. [45] and Nguyen et al. [46], executed thermomechanical response experiments on energy piles using indoor models, which considered a range of operating conditions, constraints, and soil parameters. Chen et al. [47] investigated the horizontal bearing behavior of energy piles within sandy soil through modeling tests and found that both heating and cooling elevate the soil pressure in front of the piles. Khoshbakht et al. [48] assessed the load-displacement response of energy piles via numerical simulations to evaluate alterations in their bearing capacity. Ai et al. [49] formulated a three-dimensional model for an energy pile group subjected to vertical loading in saturated soil, examining how pile spacing, arrangement, loading duration, soil layering, and the modulus ratio of the soil skeleton affect the thermomechanical behavior of the pile group. The research indicates that mechanical load significantly influences the thermomechanical behavior of energy piles during the heating process. The application of mechanical loads complicates the study of the thermomechanical behavior of energy piles, so more thermal response tests on energy piles should be carried out.

The above analysis indicates that the changes in the thermomechanical behavior of DBP-EP during the heating process are complex due to the combined effects of temperature and mechanical loads. To investigate this thermomechanical behavior, this paper establishes a single-pile model test for DBP-EP and conducts thermomechanical response tests on a single DBP-EP pile. To achieve a more precise simulation of real working conditions, a steady load is applied to the upper section of the pile, while circulating water is introduced during the testing phase. This study meticulously observed the thermal variations in the soil surrounding the DBP-EP, the mechanical response of the pile itself, the earth pressure at the pile toe, and the displacement occurring at the pile’s top during the heating phase across various operational conditions. The results obtained from this research are intended to serve as a theoretical foundation for both structural design and practical engineering applications for the DBP-EP system.

2. Overview of the DBP-EP Model Test

2.1. DBP-EP and Soil Condition

The experimental location for this study is situated at the snow and ice melting test base of Hubei University of Technology in Wuhan, China, as illustrated in Figure 2. The dimensions of the model tank measure 1200 mm × 1200 mm × 1200 mm, with its internal surface insulated using 50 mm thick extrusion board. The test pile consists of a prefabricated model measuring 1000 mm in length, maintaining a scaling ratio of 1:25 between the pile and the heat exchanger pipe. The materials used for the mold of the pile body comprise a PVC plastic pipe with an inner diameter of 0.1 mm and a steel pipe with an inner diameter of 30 mm, along with a 3D-printed base and an accompanying 3D-printed components to secure the upper steel pipe centered within the setup. When assembled, the PVC exterior needs to be reinforced with wire, and after the assembly is completed, cement mortar is poured into the mold, and the ratio of cement mortar is water–sand–cement = 0.23:1.1:0.3. The pipe embedded within the pile is made of copper, featuring an outer diameter of 6 mm, an inner diameter of 4.8 mm, and a total length of 8000 mm. Given that the DBP-EP in situ testing focuses solely on the thermal response of the heat exchanger tubes that extend from the pile’s body, these tubes are positioned horizontally during this test to maintain a consistent length for the circulating liquid heat exchanger pathway. The constant load at the top of the pile was applied by weights, with a single weight of 100 N. A separate 3D-printed model was fabricated as the base of the loading plate, and space was reserved at the bottom of the model for the heat exchanger tubes and the sensor lines. The top loading plate is an aluminum square plate with a weight of 66 N. The weights and micrometer are placed on top of the plate.

The pile was placed in the center of the model tank; the layout of the measurement points inside the pile and the soil conditions around the pile are shown in Figure 3. One group of temperature probes, T_A, was embedded in the pile, and six groups of temperature probes, T_B, T_C, T_D, T_E, T_F and T_G, were embedded around the pile. The T_A group of temperature probes was fixed on the side surface of the steel pipe before pouring the pile, and the probes were poured into the pile, along with the steel pipe. In the T_B group, the temperature probes were affixed to the lateral surface of the pile body, allowing for direct measurement of temperature variations from that specific location. In contrast, the temperature probes utilized in the T_C, T_E, T_F, and T_G groups were secured to steel reinforcement bars and embedded within the soil body. This setup facilitates comprehensive temperature monitoring throughout the surrounding environment of the pile. Furthermore, four temperature sensors were arranged at the upper and lower parts of the energy pile, specifically located at the entrance and exit of the heat exchange tube. These probes play a crucial role in tracking the temperature fluctuations of the circulating water within the heat exchange system, ensuring that the inlet water maintains a consistent temperature. Furthermore, the earth pressure monitoring system incorporates two pressure cells, with a diameter of 28 mm and a thickness of 10 mm. The pressure cells are embedded in layers on the bottom of the pile during the sand filling process. The temperature probes at T_A, T_B, T_C, T_D, T_E, T_F, and T_G were placed from 50 mm below the surface of the earth, and the spacing between each of the temperature probes along the depth direction was 200 mm. The pile strain gauges were only deployed inside and on the side of the pile; S_A and S_B were symmetrically arranged with the T_A and T_B temperature probes. The earth pressure cells P₁ and P₂ are symmetrically distributed along the center at the bottom of the pile, with an effective burial depth of about 950 mm. Two micrometers, with a range of 0–30 mm and a resolution of 0.001 mm, were used to measure the pile top displacement. The test temperature data acquisition instrument was a Keysight-DAQ970A (Kimballton, IA, USA), and the strain gauge and earth pressure cell data acquisition instrument was a uT7130.

2.2. Details of DBP-EP Thermomechanical Response Test

The model test was conducted over a period of 35 days, and the test conditions are shown in

Table 1. Operating conditions.

Operating Temperature (°C)	Constant Load on Pile Top (kN)	Operating Condition Number
$T_{in}=30$	$F_{top}=0$	1-1
	$F_{top}=0.26$	1-2
	$F_{top}=0.78$	1-3
$T_{in}=35$	$F_{top}=0$	2-1
	$F_{top}=0.26$	2-2
	$F_{top}=0.78$	2-3
$T_{in}=40$	$F_{top}=0$	3-1
	$F_{top}=0.26$	3-2
	$F_{top}=0.78$	3-3

. The single test was carried out from 8 a.m. to 8 a.m., for a total of 24 h. The air temperature range during the test was 21–26 °C, and the water temperature range was 19–24 °C. The water temperature was regulated using a water bath pot to maintain a steady inlet temperature. To perform the DBP-EP thermomechanical response test, six sets of testing conditions were implemented. Before the test was carried out, a constant load was applied to the top of the pile, and the constant loads on the top of the pile were 0 kN, 0.26 kN, and 0.78 kN, respectively. After the top of the pile was completely stabilized by displacement, circulating water at 30 °C, 35 °C, and 40 °C was injected into the heat exchanger pipe, which was used to simulate the summer working conditions. Temperature probe, strain gauge, earth pressure cell, and micrometer readings were recorded at the same time. The soil temperature recovery time between tests was not less than 2 days to ensure that the soil temperature returned to the initial temperature.

3. DBP-EP Pile Soil Thermal Response Test

DBP-EP Thermal Response Analysis

Figure 4a illustrates the temperature variation of the heat exchanger tube along the depth direction over time. During the entire heating process, the water inlet temperature remains constant after the circulating water is introduced for one hour. As the circulating water moves through the heat exchanger tube, there is a noticeable change in temperature along the depth of the tube. Specifically, the temperature at the inlet side experiences a gradual decrease. This decline in temperature is consistent as the water travels deeper into the tube. Conversely, on the outlet side, the temperature shows a steady increase as it moves along the same depth direction. This contrasting thermal behavior highlights the effective heat transfer process occurring within the heat exchanger, where the circulating water relinquishes heat on its way in, while the outgoing water emerges at a lower temperature. This indicates that the circulating water continuously exchanges heat with the pile body as it flows through the heat exchanger tube. As the inlet temperature increases, the difference in temperature between the inlet and outlet also expands. When the inlet temperature increased from 30 °C to 35 °C, the temperature difference between the inlet and outlet increased by 1.27 °C. When the inlet temperature increased from 35 °C to 40 °C, the temperature difference between the inlet and outlet increased by 1.47 °C. It is worth noting that for every 1 °C increase in temperature, the temperature difference between the inlet and outlet increased by approximately 0.27 °C. Illustrated in Figure 4b is the variation in pile temperature with depth as time progresses. The pile temperature gradually increases over time, with the rate of change diminishing after 8 h. The temperature inside the pile is higher than the temperature at the pile side, and notably, the difference between these temperatures increases as the inlet temperature rises. The average temperature at the pile end was greater compared to the overall average temperature of the pile body as time increased, as shown in

Table 2. Difference between the temperature at the end of the pile and the average temperature of the pile as a whole.

Operating Temperature (°C)	$\mathit{t}$ = 2 h		$\mathit{t}$ = 8 h		$\mathit{t}$ = 24 h
	$\mathit{d}$ = 0.015 m	$\mathit{d}$ = 0.05 m	$\mathit{d}$ = 0.015 m	$\mathit{d}$ = 0.05 m	$\mathit{d}$ = 0.015 m	$\mathit{d}$ = 0.05 m
$T_{in}=30$	−0.046 °C	0.154 °C	−0.099 °C	0.0188 °C	0.0324 °C	0.226 °C
$T_{in}=35$	0.469 °C	0.657 °C	0.575 °C	0.843 °C	0.186 °C	0.422 °C
$T_{in}=40$	0.794 °C	0.844 °C	0.692 °C	0.840 °C	0.840 °C	1.123 °C

. This is different from the findings reported in the IBP-EP thermal response tests [30,31,50], and this discrepancy may be attributed to the fact that DBP-EP requires the heat exchanger tubes to extend downward at the end of the piles, and thus, the temperatures are greater at the end of the piles. This suggests that more heat buildup occurs inside the pile when DBP-EP is introduced at a higher inlet water temperature, which could be more pronounced if the number of heat exchanger tubes increases.

Figure 5 illustrates the temperature variation of the pile–soil interface along the horizontal direction during the operation of the DBP-EP system. It can be observed that the energy pile generates a thermal exchange, leading to changes in the temperature of the surrounding soil. The data presented in the figure indicate that the operation of the energy pile has a significant impact on the temperature of the adjacent soil. Furthermore, it is evident that the extent of the temperature variations in the soil is correlated with the horizontal distance from the energy pile, suggesting that the thermal influence diminishes as the temperature point moves further away from the pile. Combined with the average temperature change curve in the horizontal direction in the figure, it can be observed that the closer the pile, the greater the degree of perturbation; with the growth of the horizontal distance, this perturbation is gradually reduced until it disappears, which is here called the radius of the temperature impact, i.e., the range of energy pile operation which can be affected. With the increase of the water inlet temperature, the temperature influence radius of the pile body gradually increases.

4. DBP-EP Pile Soil Thermomechanical Response Test

4.1. DBP-EP Thermomechanical Response Analysis

4.1.1. DBP-EP Axial Observation Strain Analysis

Figure 6a,c,e illustrates the variation in axial observed strain along the depth of the pile. In contrast, Figure 6b,d,f displays the changes in axial observed strain on the lateral surface of the pile at varying depths. These sets of figures correspond to three different constant load conditions applied at the top of the pile: 0 kN, 0.26 kN, and 0.78 kN, respectively. The data indicate that the change in axial strain within the pile is significant at the onset of DBP-EP operation. Over time, the rate of change in axial strain decreases, but the total amount of axial strain continues to increase. Additionally, the axial strain in the pile rises with an increase in the inlet water temperature. Because the strain gauges inside the pile are installed outside the steel pipe, covered by concrete, and located closer to the heat exchanger pipe, the changes in strain are more pronounced inside the pile compared to on its side. Nonetheless, the general trend of axial strains inside the pile and on its side is similar. When the pile top is unrestrained, the axial strains measured at both ends exceed those in the central region, and the axial strain at the base diminishes because of the restraining influence of the adjacent sand and soil. Conversely, when the pile top is restrained, a comparable pattern occurs; however, the axial strain at the top of the pile decreases due to the effects of the steady load applied at that location.

Compared with IBP-EP [30], the overall axially observed strain change trend of DBP-EP is roughly similar to that of IBP-EP, but the axially observed strain change at the pile toe is not the same as that of IBP-EP due to the unique structural form of DBP-EP.

4.1.2. DBP-EP Side Friction Resistance Analysis

Figure 7 illustrates the variations in lateral friction force for DBP-EP piles across various working conditions, where constant loads of 0 kN, 0.26 kN, and 0.78 kN are applied to the top of the pile. The calculation of the lateral friction force for the piles is derived from the observed axial strain, Young’s modulus, and the cross-sectional area of the pile. Here, the axial observed strain represents the average of the strains measured across each pile cross-section. The positive lateral friction is specified to indicate the upward displacement of the pile, and negative friction is used to indicate the downward displacement of the pile.

$$f={\displaystyle \frac{E\left(A_i{\overline{\epsilon }}_i-A_{i+1}{\overline{\epsilon }}_{i+1}\right)}{\pi D{L}_i}}$$

(1)

In this context, $f$ represents the mean side friction of the pile ($\mathrm{k}\mathrm{P}\mathrm{a}$), $A_i$ denotes the cross-sectional area of the i-th segment of the energy pile (${\mathrm{m}}^2$), $\overline{{\epsilon }_i}$ indicates the average axial observed strain at the i-th cross-section ($\mu \epsilon$), $E$ signifies the modulus of elasticity of the material used for the pile, $L_i$ refers to the length of the pile segment located between the i-th and the (i + 1)-th cross-sections ($\mathrm{m}$), and $D$ represents the diameter of the pile’s cross-section ($\mathrm{m}$).

As illustrated in Figure 7, the resistance against friction on the side of the pile steadily rises as the duration of DBP-EP operations lengthens. Furthermore, the side friction resistance of the pile also escalates with an increase in the water temperature at the inlet. Analyzing the variations in the side friction resistance curve reveals a consistent overall trend: negative friction resistance is present in the upper section of the pile, whereas positive friction resistance can be found in the lower section. The structural configuration of DBP-EP affects these behaviors, leading to thermal expansion and upward displacement of the surrounding soil beneath the pile. However, due to the overlying soil pressure exerted by gravity, the upward displacement of the soil is constrained, preventing this expansion and extrusion from affecting the middle and upper soil layers around the pile. Consequently, negative friction resistance is generated near the bottom of the pile. The variation in side friction resistance at the top of the pile is primarily influenced by the pile top load, which to some extent, inhibits the formation of negative friction resistance.

Table 3. Difference in side friction resistance at the pile end for different time periods.

Operating Condition Number	$\mathit{t}$$=0 \mathbf{h}\mathbf{–}\mathit{t}$ = 2 h	$\mathit{t}$$=2 \mathbf{h}\mathbf{–}\mathit{t}$ = 8 h	$\mathit{t}$$=8 \mathbf{h}\mathbf{–}\mathit{t}$ = 24 h
1-1	−9.555 kPa	−10.314 kPa	−25.62 kPa
1-2	2.94 kPa	−7.284 kPa	2.181 kPa
1-3	8.085 kPa	−6.125 kPa	−1.501 kPa
2-1	−19.643 kPa	−15.674 kPa	−71.425 kPa
2-2	−53.637 kPa	2.701 kPa	−74.002 kPa
2-3	−28.555 kPa	3.235 kPa	−49.465 kPa
3-1	−29.418 kPa	−77.396 kPa	−35.064 kPa
3-2	−52.571 kPa	−70.78 kPa	−0.274 kPa
3-3	−93.731 kPa	−29.988 kPa	0.797 kPa

shows the difference in side friction resistance at the pile end for different time periods. Analysis of the data shows that the pile top load inhibits the generation of negative frictional resistance at the pile end for the same inlet temperature. This occurs because the constant load at the pile top was applied before the tests were conducted, causing the sandy soil around the pile bottom to become denser. The negative frictional resistance at the pile end gradually increased with the increase of operation time, which indicated that the generation of negative frictional resistance at the pile end was affected by the temperature of the incoming water. Compared with IBP-EP, the trend of side friction resistance of DBP-EP is roughly similar to that of IBP-EP. Kong et al. [16] and Fang et al. [50] also reported that negative friction resistance would be generated at the bottom of the pile through thermal response tests on energy piles using field tests. The difference is that the overall frictional resistance of DBP-EP is larger than that of IBP-EP, which may be due to the higher temperature change of DBP-EP resulting in greater radial thermal expansion of the pile body, which increases the pile–soil contact area, thus leading to an increase in side friction resistance. Additionally, the manner in which the load is applied at the top of the pile also plays a significant role in influencing the pile side friction resistance. These factors collectively contribute to the differing behaviors exhibited by IBP-EP and DBP-EP in terms of pile side friction characteristics. Therefore, attention should be paid to the effect of the pile top load on the thermal behavior of energy piles in practical engineering applications, as DBP-EP will cause greater radial thermal expansion of the pile body and increase the pile–soil contact area, while the pile side friction resistance will be greater under the combined effect of the pile top load.

4.2. DBP-EP Pile Toe Earth Pressure Analysis

Figure 8 demonstrates the changes in earth pressure at the base of the pile, along with the proportion of the end bearing capacity under varying working conditions, with fixed loads of 0.26 kN and 0.78 kN applied at the top of the pile. For this experiment, it is presumed that the earth pressure distribution at the pile’s underside is uniform. The vertical load is calculated based on the earth pressure readings obtained from the pressure gauge, utilizing the specific equations outlined in Ref. [16], as follows:

$$F_{toe}={\sigma }_{toe}{A}_{toe}$$

(2)

In this context, $F_{toe}$ represents the vertical load at the base of the pile ($\mathrm{k}\mathrm{N})$, ${\sigma }_{toe}$ denotes the earth pressure occurring at the pile’s toe ($\mathrm{k}\mathrm{P}\mathrm{a}$) and $A_{toe}$ refers to the effective bearing area of the pile toe (${\mathrm{m}}^2$). This approach serves merely as an estimated approximation of the DBP-EP vertical load; therefore, additional analysis utilizing more sophisticated sensors and techniques is necessary.

The bar graphs presented in Figure 8 illustrate the real vertical loads at the toe of the pile within the DBP-EP system across various operational conditions after 24 h. As the temperature of the water intake escalates, the vertical load at the pile toe progressively rises. Nonetheless, if the constant load applied at the top of the pile is increased, the increase in the vertical load at the toe of the pile becomes less significant for the same water intake temperature. Specifically, when the pile top load is raised from 0.26 kN to 0.78 kN, the vertical load variations at the pile toe are recorded as −0.004 kN, 0.009 kN, and 0.004 kN, respectively. This indicates that with an increase in the constant load applied at the top of the pile, the influence of the water intake temperature on the vertical load at the toe decreases.

The end bearing capacity [16] can be calculated from the pile toe and pile top vertical loads, as follows:

$$\gamma ={\displaystyle \frac{F_{toe}}{F_{top}}}$$

(3)

In this context, $\gamma$ is the percentage of end bearing capacity ($\%$), and $F_{top}$ is the constant load applied at the pile top ($\mathrm{k}\mathrm{N}$).

The line graph in Figure 8 shows the DBP-EP end-loading percentage under different operating conditions after 24 h. The end-bearing percentage gradually increases with the rise in inlet temperature. The primary reason for this phenomenon is the downdrag effect exerted by the surrounding soil during the energy pile’s operation [50]. This downward pull results in the displacement of sandy soil near the pile toe, which subsequently causes a reallocation of a portion of the vertical load that was originally carried by the adjacent sandy soil to the pile toe. As a result, the heightened vertical load at the pile toe signifies a fraction of the load that ought to have been sustained by the neighboring sandy soil. With the increase in load on the pile top, there is a gradual reduction in the proportion of end-bearing capacity. In particular, when the load at the top of the pile rises from 0.26 kN to 0.78 kN, the observed percentage reduction in the vertical load at the pile toe is 2.2%, 4.76%, and 8.51%, respectively, revealing a multiplicative trend in the decrease. This implies that as the load on the pile top escalates, the influence of the downdrag effects from the sandy soil surrounding the pile toe on the vertical load at the toe lessen. This may be due to the fact that the pile end is an open cross-section, which reduces the contact area between the pile end and the soil, so that the soil around the pile carries more load. Therefore, for the practical engineering application of DBP-EP, the load applied to the top of the pile can weaken the influence of soil drag effect on the pile end, thus enhancing the bearing capacity of the pile.

4.3. DBP-EP Pile Top Displacement Analysis

Figure 9 illustrates the changes in pile top displacement over time under various operating conditions, specifically with constant pile top loads of 0 kN, 0.26 kN, and 0.78 kN. The data presented in the graph reveal that during the initial phase of the DBP-EP operation, there is a rapid increase in pile top displacement. However, this rate of increase begins to decline significantly after approximately 8 h of operation. Moreover, it is observed that as the magnitude of the constant load applied to the pile top increases, the resulting pile top displacement correspondingly decreases. A particularly noteworthy observation is that when the constant load is set at 0.78 kN, the pile top displacement stabilizes after around 2 h. This stabilization effect can be attributed to the constant load’s ability to limit the axial elongation that results from the thermal expansion of the pile during the initial stages of energy pile operation. Nonetheless, as the operation proceeds, the thermal expansion of the pile gradually begins to surpass the restrictions imposed by the constant load, ultimately leading to the attainment of a stable state after approximately 24 h.

As the constant load at the top of the pile is raised from 0 kN to 0.26 kN, the corresponding final displacement of the pile top is reduced by 0.31‰D, 0.46‰D, and 0.65‰D, respectively. In a similar fashion, increasing the constant load from 0.26 kN to 0.78 kN results in decreases of 0.36‰D, 0.47‰D, and 0.66‰D in the final displacement. Notably, for each 1 °C rise in the temperature of the inlet water, the final displacement at the pile top diminishes by roughly 0.03‰D. A review of this data indicates that substantial displacements at the top of the pile can be reduced by modifying the water inlet temperature, adjusting the load on the pile top, and ensuring the selection of suitable operating conditions.

5. Conclusions

In this paper, the thermomechanical behavior of DBP-EP under different temperature loads and mechanical loads are investigated, and the changing rules of the thermal variations in the soil surrounding the DBP-EP, the mechanical response of the pile itself, the earth pressure at the pile toe, and the displacement occurring at the pile’s top during the heating phase across various operational conditions are analyzed by means of indoor model tests. The following conclusions were obtained:

• By examining the mechanical response of DBP-EP and monitoring the variations in side friction resistance at the base of the pile over time under various top load conditions, it becomes evident that when the pile top remains unrestrained, the side friction resistance at the pile’s bottom exhibits a gradual upward trend. In contrast, when the top of the pile is restrained, the alterations in side friction resistance at the bottom exhibit minimal changes. This phenomenon can be attributed to the application of a consistent load on the pile’s top prior to the commencement of the test, leading to a densified state of the sandy soil surrounding the base. This indicates that the approach of applying the top load during the heating of energy piles may influence thermomechanical behavior, to a certain degree.
• When the DBP-EP is subjected to temperature load, it is observed that the influence of the inlet temperature on the vertical load at the pile toe diminishes progressively as the constant load applied at the top of the pile increases. Specifically, the end bearing capacity—representing the resistance provided by the soil at the pile tip—shows a gradual decline in percentages in relation to the growing load at the top of the pile. When the pile top load is increased from 0.26 kN to 0.78 kN, the percentage decrease in the vertical load at the pile toe is 2.2%, 4.76%, and 8.51%, respectively, and it can be found that the percentage decrease increases multiplicatively. Such findings suggest that as the load atop the pile intensifies, the downdrag effect exerted by the sandy soil encircling the pile toe on the vertical load at that location gradually diminishes.
• As the operational duration of DBP-EP increases, the rate of pile top displacement rises more rapidly during the initial phase of operation. Subsequently, after approximately 8 h of running, this rate of displacement growth gradually declines. Once the pile stabilizes after 24 h of operation, it is observed that for every 1 °C rise in inlet temperature, the final displacement of the pile top reduces by roughly 0.03‰D. This indicates that altering the inlet temperature and the load on the pile top, along with choosing suitable operational conditions, can effectively prevent significant displacement of the pile top.

The above conclusions summarize the thermodynamic behavior of DBP-EP under different temperature loads and mechanical loads. It can be found that the thermodynamic behavior of DBP-EP is also affected by various factors, such as pile material, soil type, and operation mode. Therefore, it is necessary to carry out further related research in the future to provide guidance and suggestions for the practical engineering applications for DBP-EP.