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<p>The pre-peak stage of three-point bending in pre-cracked sandstone reflects the coupled development of crack-tip localization and internal damage. It is therefore important for fracture-parameter evaluation and stability assessment. In this study, a frame-level multimodal framework was established by combining digital image correlation (DIC), acoustic emission (AE), and load–displacement data. Crack initiation was identified from combined DIC, AE, and mechanical evidence and was treated as a short process interval rather than a single point. For representative 0° specimens, water saturation reduced the crack-initiation fracture toughness by up to 72%, mainly because of the reduction in crack-tip surface energy. To integrate the three time-series data streams, a two-anchor process-domain alignment strategy was adopted, and a 28-dimensional frame-level feature vector was constructed. Gradient boosting regression reconstructed the load–displacement response from the pre-peak stage to the peak, reaching a coefficient of determination (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({R}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>) of 0.924 over the full interval and 0.795 in the high-load regime. Shapley additive explanations (SHAP) analysis showed that aligned displacement dominated the prediction, while water condition, DIC-based localization features, and flaw inclination mainly controlled the response correction and modulation. Together, these results quantitatively link local multimodal fracture observations to the global pre-peak response and peak-response-based fracture-parameter estimation. The framework supports post-test characterization of fracture evolution and stability-related interpretation across water conditions and flaw inclinations.</p>

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Reconstruction and Prediction of Pre-peak Load–Displacement Curves in Pre-cracked Sandstone Fracture Using Multimodal Fusion

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Xingping Lai,
  • Taiqi Li,
  • Jiantao Cao,
  • Zheng Wu,
  • Feng Cui,
  • Pengfei Shan,
  • Baoxu Yan,
  • Shuai Zhang

摘要

The pre-peak stage of three-point bending in pre-cracked sandstone reflects the coupled development of crack-tip localization and internal damage. It is therefore important for fracture-parameter evaluation and stability assessment. In this study, a frame-level multimodal framework was established by combining digital image correlation (DIC), acoustic emission (AE), and load–displacement data. Crack initiation was identified from combined DIC, AE, and mechanical evidence and was treated as a short process interval rather than a single point. For representative 0° specimens, water saturation reduced the crack-initiation fracture toughness by up to 72%, mainly because of the reduction in crack-tip surface energy. To integrate the three time-series data streams, a two-anchor process-domain alignment strategy was adopted, and a 28-dimensional frame-level feature vector was constructed. Gradient boosting regression reconstructed the load–displacement response from the pre-peak stage to the peak, reaching a coefficient of determination ( \({R}^{2}\) R 2 ) of 0.924 over the full interval and 0.795 in the high-load regime. Shapley additive explanations (SHAP) analysis showed that aligned displacement dominated the prediction, while water condition, DIC-based localization features, and flaw inclination mainly controlled the response correction and modulation. Together, these results quantitatively link local multimodal fracture observations to the global pre-peak response and peak-response-based fracture-parameter estimation. The framework supports post-test characterization of fracture evolution and stability-related interpretation across water conditions and flaw inclinations.