In a recent paper, Wu et al. (Journal of Fluid Mechanics 542, 281(2005)) have developed a novel experimental and theoretical approach to investigate the dynamic lift forces generated in the rapid compression of highly compressible porous media, (e.g. snow layer), where a porous cylinder-piston apparatus was used to measure the pore air pressure generation and a consolidation theory was developed to capture the pore pressure relaxation process. In the current study, we extend Wu et al.'s approach to various porous materials such as synthetic fibers. A complete redesign of the previous experimental setup was done, where an accelerometer and a displacement sensor were employed to capture the motion of the piston. The pore pressure relaxation during the rapid compaction of the porous material was measured. The consolidation theory developed by Wu et al. was modified by introducing the damping effect from the solid phase of the materials. One uses Carman-Kozeny's relationship to describe the change of the permeability as a function of compression. By comparing the theoretical results with the experimental data, we evaluated the damping effect of the soft fibers as well as that of the pore air pressure for two different synthetic fibers, A and B. The experimental and heoretical approach presented herein has provided an important methodology in quantifying the contributions of different forces in the lift generation in soft porous media and is in extension of the previous studies done by Wu and others.