Front. Phys. Frontiers in Physics Front. Phys. 2296-424X Frontiers Media S.A. 1753194 10.3389/fphy.2026.1753194 Brief Research Report Visualization of thermal interference effects in energy piles using transparent soil Li et al. 10.3389/fphy.2026.1753194 Li Renrong 1 Writing - review and editing Writing - original draft Liu Yancheng 1 * Software Writing - review and editing Conceptualization Zhou Yang 2 Writing - review and editing Software Conceptualization College of Civil Engineering, Jiangsu Open University, Nanjing, Jiangsu, China Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, Jiangsu, China Correspondence: Yancheng Liu, 2584702214@qq.com 04 03 2026 2026 14 1753194 24 11 2025 14 02 2026 18 02 2026 Copyright © 2026 Li, Liu and Zhou. 2026 Li, Liu and Zhou https://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Thermal interference between adjacent energy piles in group configurations can significantly reduce system efficiency. Conventional temperature monitoring methods rely on discrete sensors, which fail to capture the continuous spatial evolution of soil temperature fields. This study developed a non-contact visualization method for temperature fields based on transparent soil and digital image processing technology to investigate the thermal interference effects surrounding energy piles. The transparent soil was composed of fused quartz sand and a refractive index-matched pore fluid (mineral oil and dodecane at a mass ratio of 4:1). By calibrating the functional relationship between normalized pixel intensity and temperature, non-contact measurement of the soil temperature field was achieved. The temperature distributions under single pile and double pile conditions with different pile spacings (2–6 times pile diameter D) were investigated, and a thermal interference coefficient was introduced to quantify the thermal interaction between piles. The results indicate that when the pile spacing is within 4D, variations in spacing have a significant impact on the thermal interference effect. When the spacing increases to 6D, the thermal interference coefficient decreases to 2.5%. The proposed visualization technique successfully reveals the spatial pattern of thermal interference and provides quantitative references for energy pile group design. Limitations regarding scale effects, thermal property mismatch, cyclic loading, 3D heat transfer, calibration uncertainty, and groundwater advection are discussed to guide future research.

 energy pile temperature field thermal interference transparent soil visualization The author(s) declared that financial support was received for this work and/or its publication. The work presented in this paper was supported by the University Natural Science Foundation of Jiangsu Province (Grant No. 24KJB560003), the Science and Technology Projects of Jiangsu Province Construction System (Grant No. 2024ZD038), and Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University (Grant No. 2024004). section-at-acceptance Interdisciplinary Physics Introduction

Energy piles, which integrate the geothermal heat pump technology with traditional piles, have opened new avenues for the exploitation and utilization of shallow geothermal energy [1–3]. Energy piles serve the dual functions of bearing structural loads and facilitating heat exchange, corresponding to their mechanical and thermal performance, respectively. As load-bearing components, ensuring the structural safety of energy piles has driven significant research interest in their mechanical behavior [4–6]. The heat exchange efficiency is another critical indicator for assessing whether energy piles meet design requirements. Numerous studies have explored the factors influencing the thermal performance of energy piles, such as the properties of the heat exchange fluid [7, 8], characteristics of the heat exchange pipe [9, 10], attributes of the pile and soil [1, 11, 12], and operational conditions [13, 14].

In practical engineering applications, energy piles are typically installed in group configurations. Research on the thermal performance of energy pile groups has shown that the average heat transfer rate per pile within a group is often lower than that of a single isolated pile [2, 15]. This reduction is attributed to thermal interference between adjacent piles when their spacing falls within the individual pile’s thermal influence zone, thereby impairing the overall heat transfer efficiency of the group. Theoretical analyses based on temperature response functions also indicate that small pile spacing significantly degrades the heat transfer performance of pile groups as a result of this thermal interference [7, 16]. Numerical simulations have further confirmed that the operation of energy pile groups diminishes their long-term heat exchange capacity by altering the temperature field in the surrounding soil [17, 18]. Therefore, investigating the evolution of the soil temperature surrounding energy piles and analyzing the mechanisms underlying thermal interference are of considerable importance.

Conventional studies on soil temperature fields often rely on embedded temperature sensors, which are limited by discrete spatial measurements and failed to capture the continuous spatial evolution of soil temperature fields. Recently, visualization techniques utilizing transparent soil materials have been developed to overcome this limitation. Saturated sand can be simulated using silica sand and refractive index-matched liquids [19, 20], while clayey soil behavior can be modeled using solid particulate materials such as silica powder, laponite, and carbomer [21, 22]. Combined with digital image processing, these transparent soil techniques have been successfully applied in model tests, facilitating the investigation of various geotechnical engineering challenges, such as structure and soil displacement [23]. Temperature variations induce changes in the refractive index of the pore fluid within transparent soil [24], affecting its light transmission properties. This principle allows for the quantification of temperature fields by establishing a correlation between image pixel intensity and temperature. Several previous studies validated the feasibility of this approach for studying soil temperature fields by observing the thermal distribution around the energy pile in transparent soil [25–27], while mainly focused on rectangular energy piles, excluding circular sections, and simplified the internal pipe configuration.

This study aims to apply transparent soil technology to visualize the distribution of the soil temperature around energy piles and analyze the phenomenon of thermal interference between energy piles. By calibrating the relationship between normalized pixel intensity of transparent soil images and temperature, the distribution of temperature around energy piles is obtained. Focusing specifically on the heat transfer process involving double energy piles, this research seeks to elucidate the patterns and mechanisms governing thermal interference between adjacent piles.

 Methods Background of transparent soil

Transparent soil is an innovative soil simulant composed of transparent solid particles and a pore fluid with matching refractive index [28, 29]. Transparent soil can be used to model natural soil and enable direct visual observation and analysis of relevant scientific issues [27, 28]. When the refractive index of the pore fluid aligns with that of the solid particles, light scattering at the solid-liquid interface due to refractive index differences is minimized, thereby enhancing the overall transparency of the material. As the discrepancy between the refractive indices of the pore fluid and solid particles increases, the transparency of the synthetic soil decreases accordingly. The refractive index, defined as the ratio of the speed of light in a vacuum to that in a medium, is a dimensionless quantity that describes how light propagates through a material. A higher refractive index indicates a stronger ability to bend incident light. Temperature is one of the key factors influencing the refractive index of materials. Variations in temperature can alter the density of certain materials, thus affecting the speed of light through them. Since the density of solid materials changes minimally with temperature, their refractive indices are generally considered unaffected by thermal variations. In contrast, the influence of temperature on the refractive index of liquid materials cannot be overlooked.

Saturated transparent sand is composed of fused quartz sand and a pore liquid with the same refractive index. The particle size range is 0.1–1.0 mm. The pore liquid consists of mineral oil and dodecane in a mass ratio of 4:1, and its refractive index is the same as that of fused quartz (1.4585 in a 20 °C environment). The physical and mechanical properties are listed in Table 1.

Properties of the transparent soil.

Parameters Unit Value
Coefficient of uniformity, C u - 3.51
Coefficient of curvature, C c - 1.14
Maximum dry weight, γ d,max kN/m3 10.07
Minimum dry weight, γ d,min kN/m3 12.58
Saturated unit weight, γ sat kN/m3 18.37
Thermal conductivity, K W/(m·K) 0.785
Specific heat capacity, c J/kg·K 2097.90

The transparent soil used in this study has lower thermal conductivity than typical natural soils (1.5–2.5 W/mK for typical sandy soil, 1.0–1.8 W/mK for typical clay soil). This means heat diffusion is slower in the model, and thermal interference appears more confined than in reality.

Figure 1a shows the transparency characteristics of transparent soil at different temperatures. To facilitate the observation of transparency variations in transparent soil, a black background panel is typically placed behind the model container to enhance visual contrast. In Figure 1a, the images of transparent soil are composed of numerous pixels, with each pixel’s color and brightness quantifiable as a corresponding pixel intensity value ranging from 0 to 255. The pixel intensity value of 0 represents pure black, 255 represents pure white, and values between correspond to varying shades of gray.

(a) Behaviors of transparent soil under different temperature; (b) layout of transparent soil test system.

Composite image showing two sets of experimental setups. The top row displays three side-by-side photographs of an observation area in a reference soil sample at 20, 30, and 40 degrees Celsius with corresponding pixel intensities (PI) of 60, 72, and 95, where boxes indicate observation areas and references. The bottom row presents a labeled schematic cross-section of a water bath experiment with transparent soil and model piles, dimensions annotated, alongside a labeled photograph of the physical setup showing a model box inside a water bath within a darkroom, with lighting and camera indicated.

As observed in Figure 1a, a reference object is embedded within the transparent soil mass. When the transparency of the transparent soil changes with temperature, the clarity of the reference object viewed through the transparent soil also varies accordingly. The results demonstrate that the transparent soil achieves optimal transparency at 20 °C, allowing clear observation of the embedded reference object and relatively distinct visualization of the black background panel. The corresponding pixel intensity value at this state is approximately 60, which is the average pixel intensity value at that state. As the temperature of the transparent soil gradually increases, the difference in refractive indices between the pore fluid and solid particles grows, leading to reduced transparency. This results in progressively diminished clarity of the reference object and increased blurring of the black background panel, accompanied by a gradual rise in pixel intensity values. When the temperature reaches 40 °C, only the faint outline of the reference object remains discernible while the black background panel becomes largely indistinguishable, with the corresponding average pixel intensity increasing to approximately 95. These findings indicate that the relationship between pixel intensity and transparent soil temperature enables visual observation of the temperature field distribution within the transparent soil mass.

 Test arrangement

Figure 1b shows a schematic diagram of the experimental setup for visualizing the temperature field of energy piles. The system can be divided into two main parts, the model box system and the image acquisition system, as detailed below.

Model box system

The model box system consists of a constant-temperature water bath and a transparent soil model box. The water bath measures 400 mm (length) × 200 mm (width) × 230 mm (height) and is maintained at a constant temperature by a temperature control system to provide a stable thermal boundary for the transparent soil model box. The transparent soil model box measures 300 mm (length) × 100 mm (width) × 400 mm (height) and is positioned at the center of the water bath. Model energy piles are uniformly arranged in the central area of the model box. To minimize boundary effects, the minimum distance from the pile center to the sidewall of the model box is greater than three times the pile diameter [27]. The model energy piles are made of hollow copper tubes with an outer diameter of 15 mm and a wall thickness of 0.5 mm, embedded to an effective depth of 150 mm in the transparent soil. A U-shaped copper tube with an outer diameter of 4 mm and a wall thickness of 0.5 mm is used as the heat exchange tube inside the pile, and the pile is filled with epoxy resin. The heat exchange tube is connected to the temperature control system, allowing regulation of the inlet water temperature. To verify the accuracy of the temperature observations in the transparent soil, several temperature sensors are installed. Additionally, to reduce the influence of surface reflection from the model energy piles on the observations, the pile surfaces are coated in black. The indoor temperature was maintained at a constant 20 °C throughout the test.

Considering the scale effects, the model piles are significantly smaller than full-scale energy piles. Direct geometric scaling is not appropriate for heat transfer; instead, Fourier number (F 0) similarity is preserved to match the thermal diffusion time scale. The test duration is scaled such that the dimensionless time (F 0 = αt/L 2, where α is thermal diffusivity, t is time, and L is pile diameter) in the model corresponds to that in prototype conditions. This approach enables qualitative and semi-quantitative extrapolation of thermal interference trends. However, advective and multiphase effects are not scaled and require separate investigation.

 Image acquisition system

A high-definition camera is positioned directly in front of the model tank and connected to a computer for timed image capture during experiments. The experiment is highly sensitive to light, and even minor variations in illumination can affect the results. Therefore, the tests are conducted in a stable, light-shielded darkroom environment. Two LED lights of the same power are symmetrically arranged on either side of the tank to provide uniform and consistent lighting conditions.

 Results and discussion Temperature calibration and verification Temperature calibration

To quantify the relationship between pixel intensity in captured transparent soil images and temperature, temperature calibration is required. During the calibration process, temperature sensors embedded in the transparent soil sample provide temperature measurements. The transparent soil model box containing these sensors is placed in a constant-temperature water bath, with a black background panel positioned behind the model box. Using a temperature control system, the water tank temperature is gradually increased from 20 °C to 40 °C. This heating process is divided into 20 stages, with each stage raising the temperature by 1 °C. After reaching each target temperature, the system is maintained at that level for 10 min before proceeding to the next stage. Pixel intensity values are obtained through image processing of the collected images. Since pixel intensity is highly sensitive to variations in lighting conditions, normalization according to Equation 1 is applied to minimize the influence of illumination changes [27, 28]: P I N = P I − P I 20 P I 40 − P I 20 where PI N is the normalized pixel intensity, PI is the observed pixel intensity, PI 20 and PI 40 correspond to the observed pixel intensities of transparent soil at 20 °C and 40 °C, respectively.

The relationship between normalized pixel intensity and temperature, as obtained from the temperature calibration tests, is shown in Figure 2a. The results indicate that the normalized pixel intensity of the transparent soil increases gradually with rising temperature, following a logarithmic function. Specifically, when the temperature is below 30 °C, the increase in normalized pixel intensity per unit temperature is relatively small. However, when the temperature exceeds 30 °C, the rate of increase becomes significantly larger. Previous studies have conducted similar temperature calibration experiments on transparent soils, and their results are also presented in Figure 2a for comparison. [28] used transparent soil composed of fused quartz sand with a mixture of Baby Oil and Krystol 40, while [27] employed fused quartz sand with a blend of white mineral oil and paraffin. In the study by [28], the normalized pixel intensity exhibited a linear relationship with temperature. In contrast, the results of [27] show a trend similar to that observed in this study, with only a modest increase in normalized pixel intensity within the 20 °C–30 °C range. Although the transparent soil used in this study and in [27] was prepared with the same materials, differences in the proportions of the constituent materials may account for the variations observed in the intensity-temperature relationship. Therefore, even for transparent soils composed of the same materials, previous temperature calibration results cannot be directly applied, and new calibration tests should be conducted accordingly.

(a) Calibration of the relationship between the normalized pixel intensity and temperature; (b) temperature distribution of the surrounding transparent soil at different times; (c) verification of the temperature change in transparent soil.

Panel (a) displays a line graph relating temperature to normalized pixel intensity for three studies, showing a positive correlation with a fitted equation. Panel (b) contains thermal images of soil temperature distribution at five, fifteen, thirty, sixty, and one hundred twenty minutes, ranging from zero to twenty degrees Celsius. Panel (c) presents a line chart comparing soil temperature changes at two locations over time, measured by pixel intensity and temperature sensors, with a schematic of the measurement points.

The relationship between normalized pixel intensity and temperature for the transparent soil in this study can be expressed by Equation 2: T = 20 · P I N 0.7 + 1 where T is the temperature of transparent soil, PI N is the normalized pixel intensity.

 Temperature verification

To validate the reliability of using transparent soil for visualizing the temperature field around energy piles, a preliminary test was conducted to observe the temperature distribution in transparent soil containing two model energy piles. The transparent soil model box was placed in a constant-temperature water bath maintained at 20 °C, and the inlet water temperature of the model energy piles was set to 40 °C. During the test, images of the transparent soil were captured, and the transparent soil temperature around the piles was derived based on the calibrated relationship between pixel intensity and temperature. Figure 2b illustrates the evolution of the temperature distribution in the transparent soil around the piles during the experiment. In the initial stage, the thermal influence radius of the energy piles was relatively limited, with a distinct boundary between the temperature fields of the two piles and no significant thermal overlap. As the test proceeded, the thermal influence radius gradually expanded, and a temperature interference effect began to develop between the two piles. Due to this effect, the temperature spread more rapidly in the region between the piles compared to the outer regions. By 15 min, the thermal influence radius between the piles had reached approximately 2.5 times the pile diameter (D), whereas it was only about 1 time the pile diameter on the outer sides. With further testing, the interference effect continued to develop but at a gradually decreasing rate. After approximately 120 min, the temperature field around the twin piles stabilized, with the influence range extending to about 2.5 times the pile diameter. As shown in Figure 2b, the transparent soil temperature decreased horizontally with increasing distance from the piles, while the vertical temperature remained generally consistent at the same horizontal distance. To further minimize the subtle influences of impurities in the transparent soil and fluctuations in lighting conditions, the average temperature at the same horizontal distance from the pile wall was used as the representative temperature for that location.

To quantify the temperature variation around the energy piles after thermal interference, the overlapping temperature zone between the two piles in Figure 2b was analyzed. The transparent soil temperatures at the pile wall and at a distance of two times the pile diameter from the wall within this zone were extracted and plotted over time, as shown in Figure 2c. The results indicate that the temperature increased rapidly during the initial stage of the test, then rose at a gradually decreasing rate before eventually stabilizing. After approximately 120 min, the temperature had largely stabilized, with cumulative temperature increases of about 8 °C at the pile wall and 15 °C at the location two times the pile diameter away. To validate the accuracy of the transparent soil observations, temperature sensors were embedded in the soil during the test, and the corresponding measured values are also presented in Figure 2c. As shown in the figure, the observed temperatures from the pixel intensity of transparent soil were slightly lower than the sensor measurements in the early stage, but the difference between the two gradually diminished over time. After about 30 min, the observed and measured values were in close agreement, confirming the feasibility of using transparent soil testing to analyze temperature changes around energy piles.

 Thermal interference analysis

The above studies have verified the feasibility of visualizing the temperature field around piles using transparent soil, and preliminary tests have observed the thermal interference effect between energy piles. As this effect varies with pile spacing, it is necessary to visually analyze the temperature distribution around piles under different spacing conditions. A series of visual experiments were conducted using transparent soil for a single energy pile and for double energy piles with different spacings (2, 3, 4, and 6 times the pile diameter D). Figure 3a shows the temperature distributions around the piles under single pile and double pile operation. It can be observed that the thermal interference effect between the piles varies significantly with different spacings. When the pile spacing is 2D, the temperature of transparent soil between the double piles is the highest, and the interference effect is pronounced. As the pile spacing increases, the thermal interference effect gradually weakens.

(a) Temperature distribution and interaction around pile in transparent soil; (b) distribution of horizontal temperature around the pile; (c) variation of thermal interference effects for different pile spacings.

Five thermal maps across the top show temperature distributions around single and double piles at varying pile spacings labeled as single, 2D, 3D, 4D, and 6D, with a color scale from zero to twenty degrees Celsius. Bottom left graph (b) plots temperature against clear distance from the pile shaft for single and double pile configurations, indicating decreasing temperature with increased pile spacing. Bottom right graph (c) shows thermal interference coefficient versus pile spacing at different time intervals using colored symbols, highlighting steeper and gradual changes and including schematic diagrams for context.

In order to more systematically analyze the influence of pile spacing on the temperature field around the piles, the temperature distribution along the horizontal direction under different pile spacings was plotted based on temperature data from the region between the two piles in Figure 3a, taking the left side of the symmetry axis as an example, as shown in Figure 3b. The results show that when the pile spacing is small, the thermal interference response is significant, resulting in higher temperatures around the piles. As the pile spacing increases, the temperature around the piles gradually decreases, and the distribution gradually approaches that of the single pile case.

In Figure 3b, the difference in temperature between the double-pile and single-pile cases indicates the thermal interference caused by the additional pile. This interference can affect the heat transfer efficiency of energy piles. This study focuses on the temperature variation at the pile-soil interface (i.e., the pile shaft). To enable a systematic comparison of thermal interference under different pile spacings, the temperature increment at the pile-soil interface was normalized by the corresponding value in the single-pile case. This normalization yields a dimensionless thermal interference coefficient, which isolates the effect of pile spacing from absolute temperature variations and facilitates the evaluation of heat transfer efficiency. To quantify the effect of pile spacing on the thermal interference, the temperature increments under different pile spacings were normalized: using the temperature change in the single pile case as a reference, the temperature increment for each pile spacing was divided by this value, defining the thermal interference coefficient (kth) to reflect the heat transfer efficiency of the energy piles: k t h = Δ T t − Δ T o Δ T t × 100 % where △T o and △T t are the changes in temperature of the transparent soil surrounding the single pile and between the double piles, respectively.

Figure 3c illustrates the variation pattern of the thermal interference coefficient under different pile spacing conditions. Two characteristic parts can be clearly identified from Figure 3c. When the pile spacing is within 4 times the pile diameter (4D), the thermal interference coefficient exhibits a steep decline, decreasing rapidly with increasing pile spacing. Specifically, at a pile spacing of 2D, the thermal interference coefficient is approximately 18%. When the pile spacing increases to 4D, the coefficient drops to about 6%. This trend indicates that within this range, pile spacing is a sensitive parameter affecting the heat exchange performance of energy piles. Minor adjustments in pile spacing can lead to significant changes in the thermal interference coefficient, reflecting the dominant role of thermal interaction between piles during this stage. When the pile spacing exceeds 4D, the thermal interference coefficient enters a phase of gradual decline, with a noticeably reduced rate of decrease. As the pile spacing further increases to 6D, the thermal interference coefficient is only approximately 2.5%, indicating that the thermal interference effect between piles has significantly weakened, and further increasing the pile spacing has a limited effect on improving thermal interference. This phenomenon can be understood from the spatial decay law of thermal interference effects: as the pile spacing increases, the mutual influence range of the temperature fields around the piles decreases, leading to reduced efficiency in thermal interference transmission.

Furthermore, Figure 3c also reveals the evolution characteristics of the thermal interference coefficient under different operating durations. Under all pile spacing conditions, the thermal interference coefficient gradually increases over time, and the increment within the same period is larger for smaller pile spacings. This time dependent behavior can be attributed to the continuous expansion of the thermal influence radius during the operation of energy piles, resulting in interference between the temperature fields around the piles. Particularly under small pile spacing conditions, temperature interference is more pronounced, and the accumulation rate of thermal interference is faster. The above findings have important implications for the engineering design of energy pile groups. For layouts with small pile spacing, such as when closely spaced retaining piles are also used as energy piles, activating all piles as energy piles may lead to significant thermal interference, thereby reducing the overall heat exchange efficiency of the system. Therefore, in practical engineering, an intermittent application strategy should be considered. By rationally configuring the number and location of energy piles, the heat exchange performance can be optimized and meet the energy requirements.

 Conclusion

The present study, through transparent soil model testing, successfully achieved visual observation of the temperature field around energy piles and systematically analyzed the thermal interference effects between piles. The main conclusions are as follows:

A logarithmic relationship was established between the normalized pixel intensity of transparent soil images and temperature. Validation experiments confirmed the feasibility and accuracy of the transparent soil-based temperature field visualization method.

The thermal interference effect between energy piles exhibits a nonlinear relationship with pile spacing. The thermal interference coefficient accumulates gradually over operation time, with a higher accumulation rate under smaller spacing conditions. When the pile spacing is within 4D, the thermal interference coefficient decreases steeply and is highly sensitive to changes in spacing. When the spacing exceeds 4D, it enters a gradual decline part, where the thermal interference effect is significantly attenuated. When the spacing increases to 6D, the thermal interference coefficient decreases to 2.5%.

The current experimental configuration approximates plane thermal diffusion and does not resolve vertical temperature gradients along the pile shaft. This 2D simplification may overestimate horizontal interference if significant axial heat flow occurs. Future work should extend to 3D transparent soil models or hybrid numerical-experimental approaches that incorporate full-scale geometric effects.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

 Author contributions

RL: Writing – review and editing, Writing – original draft. YL: Software, Writing – review and editing, Conceptualization. YZ: Writing – review and editing, Software, Conceptualization.

 Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

 Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Edited by: Riccardo Meucci, National Research Council (CNR), Italy

Reviewed by: Njitacke Tabekoueng Zeric, University of Buea, Cameroon

Hui Li, Wenzhou University, China