Abstract: Based on Terzaghi’s one-dimensional consolidation theory applied to partially drained boundaries, conventional models often prescribe an exponential decay function (E-function) to represent boundary pore-water pressure. While this approach effectively reconciles Terzaghi’s boundary and initial conditions, it generates a physical paradox: at t = 0, the drainage boundary exhibits a nonzero rate of change of pore-water pressure, implying an instantaneous drainage velocity that contradicts the assumed initial undrained state. In this work, we revisit the physical basis of boundary conditions and derive a novel decay function for boundary pore-water pressure that simultaneously satisfies the initial condition of zero drainage velocity and the prescribed boundary constraint. This new formulation yields a mathematically consistent one-dimensional consolidation model for saturated soils with a partially permeable drainage boundary.Analytical solutions are obtained by applying Fourier integral transforms in the spatial coordinate and Laplace transforms in time. A key feature of the model is the introduction of a dimensionless parameter, α, which continuously controls drainage capacity. When α is set near 500, the boundary pore-water pressure decays almost instantaneously to zero, recovering the classical fully drained condition and Terzaghi’s original solution. Conversely, as α approaches 0.01, the boundary behaves as undrained, with pore-water pressure remaining effectively constant over time. Under identical α values and at any given dimensionless time, the pore-water pressures predicted by our model exceed those computed with the conventional E-function boundary condition. Correspondingly, the predicted consolidation time is longest for our solution, intermediate for the E-function condition, and shortest for Terzaghi’s fully drained case. Parametric studies further illustrate the sensitivity of consolidation rates to α and provide practical guidance for selecting boundary functions in geotechnical design.Results demonstrate that physically grounded boundary conditions are critical for accurately capturing consolidation mechanisms and timing. This work thus offers a robust reference for developing and calibrating one-dimensional consolidation models. Future research may extend the analysis to include soil relaxation and creep effects, which remain outside the scope of Terzaghi’s original theory.