Under internal water flow, hydraulic earth structures (such as dikes, levees, or dams and their foundations) can incur a migration of the finest particles of their constitutive soil. This migration may be the cause of modifications of hydraulic properties and degradation of mechanical strength of these structures. The study realized by [Marot, 2012] on clayey sand specimens underlines the influence of specimen length on critical hydraulic gradient and also on the rate of erosion. To investigate the effect of the height of cohesionless specimen and the effect of the hydraulic loading history on suffusion process, a series of suffusion tests was performed on assemblies of glass beads. These tests were conducted in a large oedo-permeameter device developed in our laboratory [Sail, 2011]. The specimens were subjected to an axial load and a downward seepage flow with a constant hydraulic gradient, increased in several steps. Two processes of erosion were observed during the tests. First, a suffusion process characterized by a diffuse departure of fine particles is occurring gradually over a long time period. This suffusion process can be accompanied by a local excess of pore pressure preceding a localized blowout developing quickly. Hydraulic shear stress concept and erosion power concept are used to characterize suffusion development. Results reveal that suffusion and localized blowout are two time–dependent processes. Thus an interpretation based on unique or average values of hydraulic loading and induced erosion rate cannot lead to an accurate characterization of the soil erodibility. By the mean of an energy analysis of tests, the suffusion characterization is independent of specimen length and not influenced by the loading history.