发表机构
King Mongkut’s University of Technology Thonburi（泰国皇家理工大学吞武里分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出无标签物理信息神经网络求解空间变异边坡可靠性，结合神经算子快速预测安全系数与破坏模式，并验证了失效概率的一致性。
AI 中文摘要
本文提出了一种无标签物理信息神经网络（PINN），用于非关联Mohr-Coulomb塑性模型的增量强度折减，以分析空间变异$c$-$\phi$边坡的可靠性。该PINN在有限元网格上以虚功损失进行训练，并在图形处理单元上同时求解多个随机场。在均质边坡的求解预算固定下，它在52个随机场上复现了Abaqus安全系数的均方根误差在2%至3%以内，并将破坏机制定位在相同的薄弱区域，但带内塑性应变分辨率不足。仅基于PINN解训练的神经算子可在数秒内预测一百万个场的安全系数、位移路径和破坏模式。整个流程中不涉及有限元解：蒙特卡洛场、重要性样本和算子训练数据均来自PINN，Abaqus仅用于验证结果。蒙特卡洛模拟、一阶可靠性方法、重要性抽样和算子给出的失效概率一致，对于所研究的边坡低至$10^{-3}$，但安全系数3%的离散度会使$10^{-3}$的概率膨胀至多两倍，且绝对值针对单一网格。异质Bishop分析给出的失效概率分别低2.6倍和8.3倍，尽管其临界圆遵循PINN机制，因为安全系数的微小差异在尾部被放大。该算子还提供了失效条件下的破坏机制和位移响应。
英文摘要
This paper proposes a label-free physics-informed neural network (PINN) for non-associated Mohr-Coulomb plasticity with incremental strength reduction for the reliability of spatially variable $c$-$ϕ$ slopes. The PINN is trained with a virtual-work loss on the finite-element mesh and solves many random fields at once on a graphics processing unit. With a solver budget fixed on the homogeneous slopes, it reproduces the Abaqus factor of safety within 2 to 3% root-mean-square on 52 random fields and locates the failure mechanism in the same weak zones, with the plastic strain in the band under-resolved. A neural operator trained only on the PINN solutions predicts the factor of safety, displacement path and failure mode of a million fields in seconds. No finite-element solution enters the pipeline: Monte Carlo fields, importance samples and operator training data come from the PINN, and Abaqus serves only to verify the result. Monte Carlo simulation, the first-order reliability method, importance sampling and the operator give consistent failure probabilities down to $10^{-3}$ for the slope studied, but a 3% scatter in the factor of safety inflates a probability of $10^{-3}$ by up to a factor of two, and the absolute values refer to one mesh. A heterogeneous Bishop analysis gives failure probabilities 2.6 and 8.3 times lower although its critical circles follow the PINN mechanism, because a small difference in the factor of safety is amplified in the tail. The operator also yields the failure mechanism and displacement response conditional on failure.
