⚡ electrical engineering

Flow rate and leakage-channel geometry govern thermal anomalies in tunnel lining blocks

Through laboratory experiments and 3D modeling, this study demonstrates that water flow rate and leakage-channel geometry critically govern the intensity, spatial distribution, and temporal dynamics of thermal anomalies in tunnel lining blocks, necessitating location-specific interpretation of temperature data.

Original authors: Jiabao Wang, Quanyi Xie, Xiang Jia, Xiaohan Li, Lizhi Zhou, Jianhong Wang, Jian Liu

Published 2026-10-28

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CC BY 4.0

Original authors: Jiabao Wang, Quanyi Xie, Xiang Jia, Xiaohan Li, Lizhi Zhou, Jianhong Wang, Jian Liu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Underground tunnels are marvels of engineering, but they face a persistent enemy: water. When groundwater finds a way through the concrete walls that hold back the earth, it does more than just create a wet spot. The moving water carries heat away from the rock and concrete, creating a cold signature that can be felt on the surface. For engineers, spotting these temperature drops is a promising way to find hidden leaks before they cause serious damage. However, reading these thermal clues is tricky. The shape and size of the cold patch depend on how fast the water is moving and the exact path it takes through cracks and gaps behind the wall. If the water flows through a straight crack or a jagged, shifting channel, the resulting cold spot looks different, making it hard to tell exactly what is happening underground just by looking at a temperature map.

To untangle this problem, a team of researchers at Shandong University set out to understand how the speed of leaking water and the geometry of the leak path control the temperature patterns on a tunnel wall. They built a physical model to mimic a section of a tunnel lining, using two large blocks of concrete stacked on top of each other to represent a common joint where leaks often occur. Inside this setup, they created narrow, water-filled channels to simulate the hidden pathways where groundwater might seep through. By pumping water at different speeds and adjusting the position and angle of these channels, they could watch how the cold water spread through the concrete. They paired these physical experiments with a detailed computer simulation that tracked the movement of heat and water, allowing them to test many more scenarios than would be possible in the lab alone.

The researchers found that the speed of the water is a dominant factor in how cold the tunnel wall gets. When the water flows slowly, the cooling effect stays concentrated near the top where the water enters. But as the flow rate increases, the cold water travels further down the channel and spreads its chill deeper into the lower part of the concrete structure. This means that a faster leak creates a larger, more widespread cold zone. However, there is a limit to this effect; once the water flows fast enough, the temperature near the inlet stops dropping significantly because the concrete there is already as cold as the water itself. The most striking discovery, however, came from looking at the shape of the leak path. When the researchers shifted the lower channel sideways relative to the upper one, the cold zone did not simply move in a straight line. Instead, the cooling effect redistributed itself in complex ways. Some spots on the wall became much colder as the channel moved, while others became warmer, showing that the location of the cold spot is highly sensitive to the exact alignment of the leak.

In contrast to the dramatic changes caused by shifting the channel sideways, rotating the channel slightly had very little impact on the temperature pattern observed on the surface. Turning the lower channel by thirty or sixty degrees changed the temperature by only a tiny fraction of a degree, a difference so small it would be difficult to detect without precise instruments. This suggests that for the purpose of finding leaks, the horizontal position of the leak path matters far more than its slight angular tilt. The study also revealed that time plays a crucial role in how these cold spots develop. Points on the concrete closest to the water channel cooled down very quickly, dropping most of their temperature in the first few hours. Points further away cooled much more slowly, continuing to drop in temperature long after the initial rush. This means there is no single moment when the temperature pattern stabilizes; the wall is constantly changing as the cold spreads.

These findings help engineers understand that a thermal image of a tunnel is not a simple snapshot of a single leak. The cold patch seen on the surface is the result of a dynamic interaction between how fast the water is flowing and the specific, often irregular, path it takes through the rock and concrete. While the computer models and lab tests provided a clear picture of these mechanics, the researchers note that applying this knowledge to real-world tunnels will require further validation. The models assumed a perfect, straight channel and constant material properties, whereas real tunnels have complex, messy cracks and varying conditions. Nevertheless, the work establishes a vital foundation: to accurately diagnose a leak, one must look at both the intensity of the cooling and the specific timing of how that cold spreads, recognizing that the shape of the cold spot tells a story about the hidden geometry of the leak itself.

Technical Summary: Flow rate and leakage-channel geometry govern thermal anomalies in tunnel lining blocks

Problem Statement
Water leakage remains a persistent serviceability and durability issue in underground tunnels, particularly in drill-and-blast tunnels where leakage pathways are heterogeneous, involving discrete fractures, construction joints, and imperfect contact zones. While leakage is often detected via surface wet marks, these visual indicators do not reveal the underlying leakage-channel morphology or seepage intensity. Although temperature is a promising indicator because leakage water transports heat via advection while the lining responds via conduction, current detection methods are largely image-driven. They identify thermal anomalies but often fail to explain how specific leakage parameters—such as flow rate, channel offset, and channel orientation—dictate the shape, amplitude, and temporal evolution of these thermal signatures. There is a need for a mechanism-based interpretation that links leakage hydraulics and channel geometry to spatiotemporal temperature-field evolution.

Methodology
This study employed a combined experimental and numerical approach to investigate leakage-induced thermal anomalies in a simplified two-block tunnel lining system.

Experimental Setup: Laboratory tests were conducted using two C50 concrete blocks (1.0 m × 0.5 m × 0.5 m each) stacked to simulate a local lining region. A steel-lined box simulated a pressurized groundwater environment. Three benchmark configurations (Models A–C) were tested with varying flow rates (100–150 mL/min), channel offsets (100–200 mm), and rotation angles (0° and 30°). Twenty-five PT1000 sensors arranged in a 5×5 array monitored temperatures over a 6-hour period with 10-second sampling intervals.
Numerical Modeling: A three-dimensional fracture-flow and heat-transfer model was developed in COMSOL Multiphysics. The model coupled the Fracture Flow interface with Heat Transfer in Solids and Fluids. It utilized a Darcy-type fracture formulation with a 0.5 mm aperture and assumed homogeneous material properties. The numerical domain replicated the two-block geometry but densified the monitoring array to 45 points to capture finer spatial gradients.
Validation and Analysis: The numerical model was validated against the 6-hour experimental data using Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and the squared Pearson correlation coefficient ( $R^2$ ). Following validation, one-factor numerical analyses were performed over a 24-hour period to isolate the effects of flow rate (10–200 mL/min), channel offset (0–400 mm), and channel rotation (0°–60°) on both spatial temperature distributions and transient cooling histories.

Key Results
The study quantified how leakage intensity and channel geometry govern thermal responses:

Model Validation: The numerical model successfully captured the principal spatial temperature contrasts and transient cooling responses observed in the experiments. Across 30 monitoring histories, RMSE values ranged from 0.226 to 0.952 °C, and MAPE values ranged from 1.126% to 4.508%. However, temporal correlation ( $R^2$ ) varied significantly by location, ranging from <0.001 to 0.994, indicating that while magnitude errors were modest, the timing of responses was location-dependent.
Flow Rate Effects: Increasing the flow rate from 10 to 200 mL/min intensified cooling and extended the spatial reach of the low-temperature zone along the leakage channel. However, near the inlet, the reduction in temperature exhibited diminishing returns as local temperatures approached the inlet water temperature (10 °C).
Channel Offset Effects: Increasing the horizontal offset between the upper and lower channels redistributed cooling laterally. This produced location-dependent and sometimes non-monotonic temperature responses. For instance, at certain monitoring points, increasing the offset initially lowered temperatures before raising them as the cooling zone shifted away. This effect was significantly stronger than that of channel rotation.
Channel Rotation Effects: Rotating the lower channel about the vertical axis (0° to 60°) had a comparatively weak effect on the central monitoring section. Maximum temperature differences across rotation angles were approximately 0.15 °C, suggesting that rotation is a less sensitive thermal discriminator than flow rate or offset for the specific geometry and observation section studied.
Transient Evolution: Cooling rates were not uniform across the monitoring section. Points near the channel and interface connection responded rapidly (accounting for ~95% of total 24-hour cooling within the first 6 hours), while more distant points exhibited delayed responses. This indicates that no single stabilization time exists for the monitoring section; rapid near-channel cooling coexists with delayed conduction-driven cooling elsewhere.

Significance and Limitations
The paper claims that its findings support a location-specific interpretation of internal thermal responses, moving beyond phenomenological recognition toward mechanism-based understanding. By demonstrating that flow rate and channel offset significantly alter the spatial footprint and temporal development of thermal anomalies, the study provides a basis for linking surface thermography to hidden leakage parameters.

However, the authors maintain a modest stance regarding the immediate applicability of these results:

The study focuses on a local monitoring section of two concrete blocks and does not assume that a temperature pattern uniquely identifies the underlying leakage condition.
The experimental validation covers only the first 6 hours; the 24-hour results are predictions beyond the experimental window and do not establish experimentally verified late-time equilibrium.
The small temperature differences caused by channel rotation require further numerical refinement and experimental resolution to be considered robust quantitative signatures.
The transferability of these findings to full-scale tunnel systems with variable lining thickness, groundwater temperatures, ventilation, and complex channel connectivity requires further validation.

Ultimately, the study establishes a validated framework for simulating leakage-induced thermal anomalies but emphasizes that surface thermography and quantitative leakage estimation based on these mechanisms require further validation.

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