The node-based smoothed particle finite element method (NS-PFEM) offers high computational efficiency but is numerically unstable due to possible spurious low-energy mode in direct nodal integration (NI). Moreover, the NS-PFEM has not been applied to hydromechanical coupled analysis. This study proposes an implicit stabilised T3 element-based NS-PFEM (stabilised node-based smoothed particle finite element method [SNS-PFEM]) for solving fully hydromechanical coupled geotechnical problems that (1) adopts the stable NI based on multiple stress points over the smooth domain to resolve the NI instability of NS-PFEM, (2) implements the polynomial pressure projection (PPP) technique in the NI framework to cure possible spurious pore pressure oscillation in the undrained or incompressible limit and (3) expresses the NI for assembling coefficient matrices and calculating internal force in SNS-PFEM with PPP as closed analytical expressions, guaranteeing computational accuracy and efficiency. Four classical benchmark tests (1D Terzaghi's consolidation, Mandel's problem, 2D strip footing consolidation and foundation on a vertical cut) are simulated and compared with analytical solutions or results from other numerical methods to validate the correctness and efficiency of the proposed approach. Finally, penetration of strip footing into soft soil is investigated, showing the outstanding performance the proposed approach can offer for large deformation problems. All results demonstrate that the proposed SNS-PFEM with PPP is capable of tracking hydromechanical coupled geotechnical problems under small and large deformation with different drainage capacities.

中文翻译：

---

具有稳定节点积分和多项式压力投影的新型耦合 NS-PFEM 用于岩土工程问题

基于节点的平滑粒子有限元法 (NS-PFEM) 提供了很高的计算效率，但由于直接节点积分 (NI) 中可能存在虚假的低能量模式，因此数值不稳定。此外，NS-PFEM 尚未应用于流体力学耦合分析。本研究提出了一种基于隐式稳定 T3 单元的 NS-PFEM（基于稳定节点的平滑粒子有限元法 [SNS-PFEM]），用于解决（1）基于多个应力点的稳定 NI解决 NS-PFEM 的 NI 不稳定性的平滑域，(2) 在 NI 框架中实施多项式压力投影 (PPP) 技术，以消除在不排水或不可压缩极限中可能出现的虚假孔隙压力振荡； (3) 用 PPP 表示用于组装系数矩阵和计算 SNS-PFEM 中内力的 NI作为封闭的解析表达式，保证了计算的准确性和效率。模拟了四个经典基准测试（一维 Terzaghi 固结、Mandel 问题、二维条形基础固结和垂直切割基础），并与解析解或其他数值方法的结果进行比较，以验证所提出方法的正确性和效率。最后，研究了条形基础对软土的渗透，展示了所提出的方法可以为大变形问题提供的出色性能。所有结果表明，所提出的具有 PPP 的 SNS-PFEM 能够跟踪具有不同排水能力的小变形和大变形下的流体力学耦合岩土工程问题。