Mechanical Properties of Granular Soils: Triaxial versus Plane Strain Investigations

The paper compares the pre-failure behavior of granular soils investigated in the classical triaxial apparatus and in the true triaxial apparatus, under plane strain conditions. Both experiments are described within the framework of an incremental model of the pre-failure behavior of sands. The methods of tensor algebra are used to compare theoretical predictions with experimental results. The analysis presented deals with the pre-failure deformations of fully drained sand, as well as with its undrained behavior, including static liquefaction and the specific behavior of an initially dilative soil. Some key questions of soil mechanics are discussed, for instance, whether soil parameters determined from one configuration, such as triaxial conditions, can be applied in other cases.

Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method

This work is devoted to a comparison of different methods determining stop-bands in 1D and 2D periodic heterogeneous media. For a 1D case, the well-known dispersion equation is studied via asymptotic approach. In particular, we show how homogenized solutions can be obtained by elementary series used up to any higher-order. We illustrate and discuss a possible application of asymptotic series regarding parameters other than wavelength and frequency. In addition, we study antiplane elastic shear waves propagating in the plane through a spatially infinite periodic composite material consisting of an infinite matrix and a square lattice of circular inclusions. In order to solve the problem, a homogenization method matched with asymptotic solution on the cell with inclusion of the large volume fracture is proposed and successfully applied. First and second approximation terms of the averaging method provide the estimation of the first stop-band. For validity and comparison with other approaches, we have also applied the Fourier method. The Fourier method is shown to work well for relatively small inclusions, i.e., when the inclusion-associated parameters and matrices slightly differ from each other. However, for evidently contrasting structures and for large inclusions, a higher-order homogenization method is advantageous. Therefore, a higher-order homogenization method and the Fourier analysis can be treated as mutually complementary.