<p>Nonlinear fluid resonance in the gap between a berthed barge and a vertical terminal is studied through both physical laboratory tests and numerical simulations in this work. A modified fully nonlinear potential flow solver is developed by incorporating a quadratic damping term. The study primarily focuses on the effect of asymmetry in the barge draft on either side of the gap, influencing the quadratic damping terms and the fluid-system's nonlinearity. The working principle of quadratic damping term is elucidated through phase dynamics analysis via Hilbert transformation. The sensitivity of the damping coefficient to barge draft, gap width, and incident wave amplitude is examined across a broad parameter space, with the underlying physics clarified by analogy to the general dynamics of a damped forced oscillator. The draft asymmetry across the gap introduces intrinsic structural asymmetry into the fluid system, thereby leading to a distinct softening-type nonlinear stiffness behavior compared to symmetric two-barge configurations. Further harmonic analysis by the Fourier transformation reveals the contributions of the higher order harmonics to the overall responses. Quantified analysis demonstrates the high accuracy of the modified potential flow model in addressing the amplitudes-frequency and phase-frequency responses, instantaneous phase dynamics, the softening stiffness nonlinearity, and higher order harmonics. The physical insights gained offer a deeper understanding of the damping and the nonlinearity of gap resonance problem, and the experimental measurements provide benchmark reference data for potential numerical validations.</p>