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<p>In non-uniform thermal environments, rock fracture behavior is significantly influenced by temperature gradients, localized thermal stresses, and mineral phase transitions, making accurate fracture parameter measurements challenging with conventional experimental methods. To address this, this paper proposes a multi-task (MT) learning approach based on physics-informed neural networks (PINNs), termed MT-PINN, for identifying mixed-mode stress intensity factors (SIFs) in cracked rock specimens under non-uniform temperature fields. First, a heat conduction equation accounting for heat flow disturbances and a thermomechanically coupled phase-field equation incorporating thermal expansion effects are established, which are then embedded into the loss function of a deep neural network framework, constructing the MT-PINN model to predict crack-tip fields and fracture parameters. Second, finite element simulations based on the phase-field method are performed to compute the mechanical response and damage evolution of notched semicircular bending (NSCB) rock specimens under varying non-uniform temperature fields, and the MT-PINN model is trained using datasets generated from these simulations. Finally, three-point bending tests on Fangshan granite NSCB specimens are conducted to measure crack-tip displacement fields and mixed-mode SIFs via digital image correlation, and the practical performance of the PINN model is evaluated. Experimental results are well compared with MT-PINN predictions, demonstrating the model’s effectiveness in identifying rock fracture parameters under non-uniform thermal conditions.</p>

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Identification of rock fracture parameters under non-uniform temperature fields based on physics-informed neural networks

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Yucheng Wu,
  • Wei Liu,
  • Zhiqian Zhang,
  • Bowen Liu,
  • Houlu Sun,
  • Guangjin Wang,
  • Xin Gong

摘要

In non-uniform thermal environments, rock fracture behavior is significantly influenced by temperature gradients, localized thermal stresses, and mineral phase transitions, making accurate fracture parameter measurements challenging with conventional experimental methods. To address this, this paper proposes a multi-task (MT) learning approach based on physics-informed neural networks (PINNs), termed MT-PINN, for identifying mixed-mode stress intensity factors (SIFs) in cracked rock specimens under non-uniform temperature fields. First, a heat conduction equation accounting for heat flow disturbances and a thermomechanically coupled phase-field equation incorporating thermal expansion effects are established, which are then embedded into the loss function of a deep neural network framework, constructing the MT-PINN model to predict crack-tip fields and fracture parameters. Second, finite element simulations based on the phase-field method are performed to compute the mechanical response and damage evolution of notched semicircular bending (NSCB) rock specimens under varying non-uniform temperature fields, and the MT-PINN model is trained using datasets generated from these simulations. Finally, three-point bending tests on Fangshan granite NSCB specimens are conducted to measure crack-tip displacement fields and mixed-mode SIFs via digital image correlation, and the practical performance of the PINN model is evaluated. Experimental results are well compared with MT-PINN predictions, demonstrating the model’s effectiveness in identifying rock fracture parameters under non-uniform thermal conditions.