To address the inherent randomness of soil properties, this article introduces an innovative approach, the Spectral Feynman-Kac Method (SFKM), to solve the one-dimensional (1D) consolidation problem under double drainage boundary conditions. By integrating the Feynman-Kac formula with the Karhunen-Loève (KL) expansion, the SFKM models the soil properties as random fields and provides probabilistic solutions to a stochastic differential equation (SDE) corresponding to the 1D consolidation equation using Monte Carlo (MC) simulations. In this work, the coefficient of consolidation (cv) is treated as a random field with an exponential covariance function to model the spatial correlation. The random field of cv is then incorporated into the SDE, which provides the solutions to the 1D consolidation equation when simulated under the drainage boundary conditions. Compared with the analytical solution, the excess pore water pressure profiles obtained from the SFKM framework show strong alignment, demonstrating the effectiveness of the adopted approach. It is deciphered that the SFKM framework offers a more realistic and robust approach to soil consolidation analysis, accounting for the spatial variability of soils.