A methodology for post-processing the four-point beam bending data and computing stiffness modulus using harmonic analysis

Abstract

The computation of modulus of bituminous mixes from a beam bending test conforming to an undamaged yet steady state is not straightforward. The most widely used practice of choosing the 50th or 100th cycle, for modulus computation, does not ensure that the material response has reached a steady state, crossing the initial transient stage of drastic modulus reduction. In the current study, it is analytically shown that the material retardation time governs the attainment of a steady state response. The study proposes a methodology for post-processing the four-point beam bending test data so as to identify the cycles that could result in a sensible computation of material modulus. The experimental investigations involve four-point beam bending (4-PB) tests carried out on four bituminous mixes, prepared using an unmodified and three modified binders. The 4-PB tests are carried out at 20 oC, 10 Hz frequency at strain levels of 200, 400, 600 and 800 micro-strains. The harmonics of the input/output waveform has been used to identify the cycles that can be used for the computation of a material modulus, and the modulus is computed from the Lissajous plots (stress–strain plots) of the cycles prior to damage initiation. Based on harmonic analysis, the current study specifies a range of modulus for each mix at various strain levels, and the values are further compared with the modulus computed using the conventional post-processing procedure. It is observed that the conventional procedure of using the stiffness modulus at 100th cycle results in higher values of modulus than the ones computed using the proposed post-processing method, as a consequence of the transient response of the material before attaining a steady state.