Numerical modeling of buckling and bending behavior of 2 × 2 pile group in liquefied soil and investigation of improvement solutions

The seismic performance of pile groups in liquefied soils is a critical challenge in foundation engineering, particularly when buckling and bending interact under dynamic loading. This study investigates the behavior of a $$\:2\times\:2$$ pile group using a three-dimensional FLAC3D numerical model that incorporates the Finn–Byrne formulation for excess pore pressure generation and free-field boundaries to minimize wave reflection. Two input motions were applied: a synthetic sinusoidal wave ( $$\:2\:Hz$$ , $$\:4-12\:s$$ , $$\:1\:\text{g}$$ ) and the 1995 Kobe (FUK) earthquake record. Results show that Partial Ground Improvement (PGI) substantially enhanced stability: the maximum bending moment was reduced by $$\:26\%-38\%$$ , the axial force remained below the material yield threshold, and the slenderness ratio shifted from $$\:SR\:\approx\:\:173$$ (long-column elastic buckling) to $$\:SR\:\approx\:\:17$$ (short-column yielding). Consequently, piles with PGI avoided buckling failure, while untreated piles experienced instability. In addition, PGI improved stress redistribution along the pile depth and limited curvature concentrations at the liquefied-nonliquefied interface. Key contributions can be considered as follows: (1) quantitative evidence of how PGI modifies the dominant failure mechanism in pile groups under liquefaction, (2) comparative assessment under both synthetic and real seismic records, and (3) design-oriented interpretation linking slenderness, critical axial load, and bending demands to practical recommendations for earthquake-resistant pile group foundations. The findings highlight PGI as a cost-effective and technically robust countermeasure for improving the seismic reliability of pile-group foundations in liquefied deposits.