⚡ electrical engineering

Damage prediction of shield tunnel structures driven by numerical simulation and machine learning

This study proposes a reliable damage prediction framework for shield tunnels that integrates a high-fidelity numerical model, validated against experiments to reveal a three-stage failure process, with a particle swarm optimization-enhanced long short-term memory network to accurately predict crack width evolution under ultimate loading conditions.

Original authors: Yang Yu, Haishuang Guan, Shuang Gao, Chunbing Guo, Yanyu Meng

Published 2026-09-28

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CC BY 4.0

Original authors: Yang Yu, Haishuang Guan, Shuang Gao, Chunbing Guo, Yanyu Meng

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

Beneath the bustling streets of modern cities lies a vast, silent network of tunnels that carry millions of people every day. These shield tunnels, built to last for a century, are engineered to withstand the immense pressure of the earth and the weight of the city above. However, they are not immune to the slow, creeping forces of time and stress. When a tunnel is pushed beyond its limits, perhaps by a sudden shift in the ground or an unexpected load, the concrete rings that form its walls begin to crack. Understanding exactly how these cracks start, grow, and eventually lead to structural failure is critical for keeping the metro safe. Engineers have long relied on physical tests and complex computer simulations to predict these failures, but the behavior of cracking concrete is so intricate that even the best simulations can struggle to capture every detail. To bridge this gap, researchers are now turning to a new approach that combines the precision of physics-based modeling with the pattern-recognition power of artificial intelligence.

A team of researchers from Beihua University in China has developed a new method to predict exactly how much a shield tunnel will crack under extreme stress. They began by building a highly detailed digital twin of a real tunnel segment, modeled after a project in Shanghai. This was not a simple sketch; it was a sophisticated computer model that accounted for the specific way concrete behaves when it is pulled apart, the presence of steel bars hidden inside the walls, and the complex joints where the concrete rings connect. The researchers also included the effect of manholes, which create weak spots in the structure, and the friction between the bolts holding the rings together. To ensure their digital model was trustworthy, they ran a virtual test that mimicked a real-world experiment where a full-size tunnel segment was squeezed until it broke. The computer's predictions matched the physical experiment almost perfectly, confirming that the digital model could accurately simulate the tunnel's journey from a healthy state to a broken one.

With a reliable digital model in hand, the team ran thousands of simulations to watch the tunnel fail in slow motion. They observed that the structure does not collapse all at once; instead, it passes through three distinct phases. First, the tunnel behaves like a stiff spring, bending slightly but returning to its original shape. As the load increases, the concrete begins to develop tiny cracks, marking a transition into a second phase where damage is local and manageable. Finally, if the pressure continues to rise, the cracks multiply and spread rapidly, the steel bars inside begin to bend permanently, and the structure enters a stage of global failure. The researchers found that the tunnel could withstand a load of up to 420 kilonewtons before reaching this critical point of collapse. At this stage, the cracks on the surface had widened to over 4 millimeters, and the steel reinforcement had yielded, meaning it had stretched beyond its ability to recover.

The true innovation of this study lies in what the researchers did next. Instead of just stopping at the simulation, they used the data generated from these virtual failures to teach a computer how to predict the future. They employed a type of artificial intelligence known as a long short-term memory network, which is particularly good at understanding sequences of events over time, much like how a person remembers a story by recalling the order of events. However, these computer networks have many settings that need to be tuned perfectly to work well. To solve this, the team used a particle swarm optimization algorithm, a method inspired by how birds flock together to find the best food source. This algorithm automatically searched for the perfect combination of settings for the neural network, ensuring it could learn the complex patterns of crack growth as efficiently as possible.

The result was a new prediction tool that could forecast the width of cracks in a shield tunnel with remarkable accuracy. When tested against data it had never seen before, this new system outperformed several other common artificial intelligence models. It predicted the crack width with an error margin of just 0.1033 millimeters and matched the actual data with a high degree of certainty. The study demonstrates that by combining the physical laws of engineering with the learning power of machine intelligence, it is possible to create a robust system for monitoring tunnel health. This approach offers a way to identify potential dangers before they become catastrophic, providing engineers with a reliable guide to maintain the safety of the underground transit systems that cities depend on. The findings suggest that such a hybrid model can serve as a vital tool for the long-term protection of infrastructure, turning complex data into clear, actionable insights for keeping the world moving safely beneath our feet.

Technical Summary: Damage Prediction of Shield Tunnel Structures Driven by Numerical Simulation and Machine Learning

Problem Statement

Shield tunnels are critical permanent infrastructure designed for service lives up to 100 years. However, they are vulnerable to disturbances from surrounding construction activities (e.g., surcharge loading, adjacent excavation) and seismic events, which can lead to segment cracking, joint dislocation, and in severe cases, global instability. While extensive research exists on simplified analytical methods and numerical simulations for shield tunnel performance, there is a notable gap in predictive research focusing specifically on the failure and damage evolution of shield tunnels under ultimate loading conditions. Existing machine learning applications in tunnel engineering have predominantly addressed settlement and deformation problems, leaving the prediction of structural failure processes and crack width evolution under extreme loads largely unexplored.

Methodology

The study proposes a hybrid framework integrating high-fidelity numerical simulation with machine learning to predict damage evolution. The methodology proceeds through four distinct stages:

1. Refined Numerical Modeling

A detailed three-dimensional numerical model of a shield tunnel segment was developed based on the Shanghai Metro tunnel project dimensions (6.2 m outer diameter, 0.35 m thickness).

Constitutive Modeling: Concrete nonlinearity was represented using a total strain crack model (specifically the rotating crack model) to accurately capture behavior under combined tension, compression, and shear.
Structural Details: The model explicitly considered local manhole weakening, multiple contact interfaces (simulated with interface elements for sliding/rotation), and embedded reinforcement (simulated via truss elements).
Validation: The model's reliability was verified against full-scale experimental results, showing good agreement in load-displacement responses.

2. Failure Simulation and Data Generation

Failure simulations were conducted under ultimate bearing conditions to elucidate structural stress, deformation, and reinforcement stress evolution.

Loading Protocol: A two-stage loading process was applied, simulating radial loads at the crown, invert, and haunches until structural bearing failure occurred.
Data Extraction: The simulations generated detailed data on crack width evolution, which served as the key indicator for damage prediction. The dataset captured the step-like evolution of cracks due to the brittle nature of concrete.

3. Machine Learning Framework (PSO-LSTM)

To predict the crack width evolution time series, a Long Short-Term Memory (LSTM) network was selected as the base predictive model due to its capability in handling long-term dependencies in time series data.

Optimization: A Particle Swarm Optimization (PSO) algorithm was employed to optimize critical LSTM hyperparameters, including the number of hidden units, the initial learning rate, and the L2 regularization coefficient.
Training: The PSO algorithm iteratively updated particle positions and velocities to identify the global optimum, minimizing prediction error.

4. Comparative Evaluation

The proposed PSO-LSTM model was trained and tested using the numerical simulation dataset. Its performance was quantitatively compared against three other models: a Backpropagation (BP) neural network, a Convolutional Neural Network (CNN), and a conventional LSTM model. Evaluation metrics included Root Mean Square Error (RMSE) and the Coefficient of Determination ( $R^2$ ).

Key Results

Numerical Simulation Findings

Failure Stages: The structural failure process was divided into three stages:
1. Linear Elastic Stage: Up to 230 kN (crack width ~0.11 mm).
2. Local Damage Stage: 230 kN to 420 kN (crack width up to 3.16 mm).
3. Global Failure Stage: >420 kN (crack width up to 4.37 mm).
Damage Characteristics: Tensile failure dominated the damage pattern. Cracks initiated at the inner sides of the crown and invert, propagating to the haunches. Local collapse occurred at segment joints, and the ultimate bearing capacity was determined to be 420 kN.
Reinforcement Behavior: The internal reinforcement experienced progressive tensile stress concentration, eventually reaching yield strength (335 MPa) at structural failure.

Machine Learning Performance

Optimal Configuration: Sensitivity analysis identified 15 particles and 30 PSO iterations as optimal settings. A 7:3 data split (training:testing) yielded the best performance.
Prediction Accuracy: The PSO-LSTM model achieved an RMSE of 0.1033 and an $R^2$ of 0.9487.
Comparative Superiority: The PSO-LSTM model outperformed the BP, CNN, and conventional LSTM models in both accuracy and stability. The BP model exhibited overfitting, while the PSO-LSTM model demonstrated superior capability in capturing the complex dynamic characteristics of damage evolution without evident overfitting.

Significance and Claims

The paper claims that the proposed approach provides effective guidance for monitoring and protection of metro tunnels. By integrating high-fidelity numerical simulation with an optimized machine learning model, the study offers a reliable method to predict crack width evolution under ultimate loading conditions.

The authors assert that this framework contributes to improving operational safety by enabling the early identification of potential catastrophic risks and supporting decisions regarding timely repair or reinforcement. The study emphasizes that the PSO-LSTM model provides a robust and credible basis for tunnel operation and maintenance, addressing the limitation of existing methods that focus primarily on settlement rather than ultimate failure mechanisms.