A General Dynamic Model for the Resonant Column/Quasi-Static Torsional Shear Apparatus
A new model is proposed that allows for more general boundary conditions at both the active and passive ends of resonant column apparatus, especially those incorporated within the resonant column/quasi-static torsional shear devices. The improved three-degree-of-freedom model can be used in order to obtain more accurate measurements of the dynamic properties of tested soils when the base and the reaction mass of the apparatus are not perfectly fixed. This becomes particularly important in the hybrid resonant column/quasistatic torsional shear apparatus where the load cell located below the bottom platen provides additional flexibility to the passive end and the inertia of the reaction mass of the Hardin-type oscillator is relatively small. The analysis confirmed that use of the model is particularly important if the natural frequency of the soil-apparatus system is close to that of the passive end or reaction system, and that the calculated modulus and damping values can be highly inaccurate if simplified boundary conditions are assumed. Such situations especially occur when very soft soils, very stiff soils, or rock specimens are tested. The solution was programmed in a spreadsheet where both the shear modulus (G) and the damping ratio (D) are established for a given set of measurements and apparatus constants. In order to obtain the necessary apparatus constants, calibration procedures are presented for a resonant column/quasi-static apparatus. Comparison of existing models and the new solution to the observed response for a rubber testing specimen showed that the three-degree-of-freedom assumption is more accurate in modelling the apparatus boundary conditions.