A General Analytical Solution for Calculation of Lateral Active Earth Pressure of Narrow Backfills Behind Retaining Walls

ABSTRACT This study presented a general analytical solution for calculation of lateral active earth pressure of narrow backfills behind retaining walls under arbitrary lateral displacement modes. The proposed method innovatively introduced an equivalent friction angle between adjacent horizontal differential elements to characterize the influence of diverse wall displacement modes on stress redistribution within the backfill soils, addressing three critical gaps: (1) universal applicability—a single framework replaced mode‐specific formulations, enabling predictions for any wall displacement mode, including complex drum‐shaped deformations in braced excavations; (2) maximum displacement localization sensitivity—a nonlinear transition law for explicitly accounted for the depth‐dependent influence of maximum wall deflection (), enhancing accuracy for flexible walls; and (3) simplified workflow—the solution required only basic geotechnical and geometric parameters (, , ) and avoided iterative steps, ensuring efficiency for practical design. Validation against finite element simulations and published model tests demonstrated strong agreement across displacement modes. Parametric analyses revealed that the proposed method effectively captured the sensitivity of earth pressure to backfill width (), internal friction angle (), and wall‐soil friction angle (). Notably, when , the solution predicted significantly reduced earth pressures compared to classical theories, emphasizing its advantages in optimizing retaining structure designs for urban excavations adjacent to existing underground facilities.