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Supplemental Figures for Shield-Tunnel Seismic Damage Reconstruction

Supplemental Materials (Figs. S1-S16) for the manuscript:

Surrogate-Accelerated Computation of Seismic Damage Fields in Shield Tunnels
Wencan Guan

This repository contains sixteen high-resolution supplemental figures supporting the numerical validation, seismic damage-field analysis, sparse reconstruction, surrogate comparison, and spatial fidelity evaluation presented in the manuscript.

Dataset Description

A single elasto-plastic time-history analysis of a tunnel-soil system can require several hours of computation. The underlying study investigates whether surrogate models fitted to sparse samples of simulated damage fields can accelerate this computation while preserving the field peaks that govern structural assessment of the tunnel lining.

Three reconstruction mechanisms are evaluated using the same reference fields, observation locations, and performance metrics:

  1. A mechanics-informed non-stationary Gaussian process with homoscedastic noise.
  2. A mechanics-informed non-stationary Gaussian process with geometrically prescribed heteroscedastic noise.
  3. An untrained deep image prior.

The methods are compared across three field quantities and four seismic instants using a common set of 3,200 observation points.

The reference fields originate from a plane-strain finite-element model of a shield tunnel embedded in soil. In the constitutive model, the Mohr-Coulomb cohesion, friction angle, and dilation angle degrade with accumulated equivalent plastic strain. Damage is therefore generated at the constitutive level rather than introduced through post-processing.

Figure Gallery

Figure S1: Dynamic-model validation

Verification of the dynamic model using an independent elastic case. Equivalent stress distributions in the soil and tunnel lining are shown at five time instants.

Figure S1: Dynamic-model validation


Figure S2: Evolution of the reference damage fields

Reference results for all six field measures at four recorded seismic instants.

Figure S2: Evolution of the reference damage fields


Figure S3: Effect of the damage constitutive law

Difference in equivalent plastic strain between simulations performed with and without the damage constitutive law.

Figure S3: Effect of the damage constitutive law


Figure S4: Faster-softening case

Damage-field evolution for the constitutive configuration with faster material softening.

Figure S4: Faster-softening case


Figure S5: Reconstruction of equivalent plastic strain

Sparse reconstruction of the equivalent plastic-strain field at all four seismic instants.

Figure S5: Reconstruction of equivalent plastic strain


Figure S6: Reconstruction of the damage field

Sparse reconstruction of the damage field at all four seismic instants.

Figure S6: Reconstruction of the damage field


Figure S7: Reconstruction of plastic dissipation

Sparse reconstruction of the plastic-dissipation field at all four seismic instants.

Figure S7: Reconstruction of plastic dissipation


Figure S8: Deep-image-prior early-stopping audit

Early-stopping analysis for the deep image prior across all twelve reconstructed frames.

Figure S8: Deep-image-prior early-stopping audit


Figure S9: Gradient sharpness ratio

Spatial gradient sharpness ratio for the three reconstructed field quantities, including the reference fields.

Figure S9: Gradient sharpness ratio


Figure S10: Signed relative error

Signed relative-error distributions for the three reconstructed field quantities, including the reference fields.

Figure S10: Signed relative error


Figure S11: Damage-front orientation error

Damage-front orientation errors for the three reconstructed field quantities, including the reference fields.

Figure S11: Damage-front orientation error


Figure S12: Local peak fidelity

Local peak-fidelity evaluation for the three reconstructed field quantities, including the reference fields.

Figure S12: Local peak fidelity


Figure S13: Neural-network surrogate on an independent case

Performance of the neural-network surrogate when evaluated on an independent case.

Figure S13: Neural-network surrogate


Figure S14: Stationary-kernel surrogates on an independent case

Performance of stationary-kernel surrogate models when evaluated on an independent case.

Figure S14: Stationary-kernel surrogates


Figure S15: Predicted-versus-reference comparison

Predicted-versus-reference scatter plots for six surrogate configurations and two field quantities.

Figure S15: Predicted-versus-reference comparison


Figure S16: Best-performing surrogate by element

Element-wise assignment of the best-performing surrogate model.

Figure S16: Best-performing surrogate by element

File Index

Figure File Description
S1 S01_validation_stress.png Independent elastic validation case
S2 S02_damage_evolution_full.png Reference damage-field evolution
S3 S03_depeq_difference.png Plastic-strain difference
S4 S04_faster_softening.png Faster-softening case
S5 S05_recon_kappa_allframes.png Equivalent plastic-strain reconstruction
S6 S06_recon_D_allframes.png Damage-field reconstruction
S7 S07_recon_Wp_allframes.png Plastic-dissipation reconstruction
S8 S08_dip_earlystop.png Deep-image-prior early-stopping audit
S9 S09_gsr_allfields.png Gradient sharpness ratio
S10 S10_relerr_allfields.png Signed relative error
S11 S11_orient_allfields.png Damage-front orientation error
S12 S12_lpf_allfields.png Local peak fidelity
S13 S13_nn_independent.png Neural-network surrogate
S14 S14_kernels_independent.png Stationary-kernel surrogates
S15 S15_scatter_both.png Predicted-versus-reference scatter
S16 S16_dominance_map.png Best-performing surrogate by element

All figure files are located in the figs_supp directory.

Figure Production

The figures were rendered with Matplotlib at 300 dpi using cached finite-element and reconstruction results. No numerical model was rerun specifically to create this supplemental dataset.

Field plots were produced using tricontourf on the unstructured finite-element mesh. The tunnel opening was masked, and a focus window of approximately +/-6 m was used. A shared color scale was applied within each comparison row to ensure consistent visual interpretation.

Intended Use

This dataset is intended for:

  • Reproducibility and visual inspection of the manuscript results.
  • Comparison of sparse field-reconstruction methods.
  • Evaluation of spatial fidelity metrics.
  • Research and teaching in earthquake, tunnel, and computational engineering.
  • Development of surrogate models for finite-element field data.

Limitations

These files contain rendered supplemental figures rather than the complete finite-element model, raw simulation database, or executable reconstruction code. Numerical values should therefore not be extracted from the images when the original computational data are required.

The manuscript is currently under review. The bibliographic information in this dataset card will be updated after publication.

License

The supplemental figures are released under the Creative Commons Attribution 4.0 International License.

You may share and adapt the material provided that appropriate credit is given.

Citation

Until the final publication reference becomes available, please cite this dataset as:

@dataset{guan2026shield_tunnel_supplement,
  author    = {Guan, Wencan},
  title     = {Supplemental Figures for Surrogate-Accelerated Computation
               of Seismic Damage Fields in Shield Tunnels},
  year      = {2026},
  publisher = {Hugging Face},
  url       = {https://huggingface.co/datasets/guanwencan/ASCE_JCCV},
  license   = {CC BY 4.0}
}

Contact

Profile Information
Wencan Guan Wencan Guan

School of Civil Engineering, Tongji University
Institute of Structural Mechanics, Bauhaus-Universität Weimar

ORCID: 0009-0005-9398-1331
Hugging Face: guanwencan
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