Maximum and minimum void ratios (emax and emin) of granular soils are commonly used as indicators of many engineering properties. However, few methods, apart from laboratory tests, are available to provide a rapid estimation of both emax and emin. In this study, we present a theoretical model to map the densest and the loosest packing configurations of granular soils onto the void space. A corresponding numerical procedure that can predict both emax and emin of granular soils with arbitrary grain size distributions is proposed. The capacity of the proposed method is evaluated by predicting the maximum and minimum void ratios of medium to fine mixed graded sands with different contents of fines. The influence of the grain size distribution, characterized quantitatively by uniformity parameter and the fractal dimension, on emax and emin is discussed using the proposed method. Moreover, application of this method in understanding the controlling mechanism for the void ratio change during grain crushing is presented.
In this note, two different approaches are used to estimate the entrainment-flux to surface-flux ratio for a sheared convective
boundary layer (CBL); both are derived under the framework of the first-order jump model (FOM). That suggested by Sun and
Wang (SW approach) has the advantage that there is no empirical constant included, though the dynamics are described in an
implicit manner. The second, which was proposed by Kim et al. and Pino et al. (KP approach), explicitly characterizes the
dynamics of the sheared entrainment, but uncertainties are induced through the empirical constants. Their performances in
parameterizing the CBL growth rate are compared and discussed, and a new value of the parameter A3 in the KP approach is suggested. Large-eddy simulation (LES) data are employed to test both approaches: simulations are conducted
for the CBL growing under varying conditions of surface roughness, free-atmospheric stratification, and wind shear, and data
used when the turbulence is in steady state. The predicted entrainment rates in each case are tested against the LES data.
The results show that the SW approach describes the evolution of the sheared CBL quite well, and the KP approach also reproduces
the growth of the CBL reasonably, so long as the value of A3 is modified to 0.6. 相似文献