Comparison of Different Approaches for the Calculation of the Integrated Zone and the Cross-over Value in Amplitude Sweep Tests

In soil rheology, the amplitude sweep test (AST) simulates dynamic stresses by means of either increasing shear strain or shear stress and returns information on the viscoelasticity and shear resistance of soils. The dimensionless Integral Z, I_z, is used to compare the microstructural soil stability, based upon the loss factor, tan⁡δ. Sandy, silty, loamy, and clayey topsoil-samples, equilibrated to defined matric potentials, were subjected to ASTs and pedotransfer functions were derived to test the suitability of soil physical and chemical parameters to estimate the value of I_z. The current approach to the calculation of I_z and of the shear strain and stress values at the cross-over (CO, i.e., where the storage modulus (G') equals the loss modulus (G'')) on the base of the commercial software RheoPlus was found to be unprecise due to data simplifications and varying assumptions regarding data interpolation. The deviation of the values at the CO and of I_z of the two calculation methods was evaluated. Considering 132 soil samples, I_z values ranged from 6.8 to 79.4, and the mean value and standard deviation of the difference between the values of I_z as calculated by RheoPlus and those calculated as defined by Markgraf et al. (2009) were 0.78 and 1.49, respectively. No difference was found for soil samples with loss factor values smaller than 1 in the complete strain range. A neglectable difference was found for most samples because the loss factor values behind the ‘cross-over' were close to 1 and not significantly altered when set to 1. The results underline, that despite the simplifications that were made for the calculations of the rheological parameter, the resulting values of most of the considered samples, do not differ in an unacceptable manner. For the considered soils and matric potentials, the derived pedotransfer functions are applicable to estimate the values of I_z from soil chemical and physical properties such as the soil matric potential, and sand, clay, and soil organic carbon contents.