Macroscopic properties of granular materials are important in modeling a variety of flow and transport phenomena in many fields of science. Determination of these parameters has always been an issue among both researchers and engineers, mainly in view of tortuosity and permeability. This paper presents analytical functions for the tortuosity and permeability of monosized sphere arrays based on a volume averaging approach and eliminates some ambiguities by modification of the original representative elementary volume model. Veracity of the proposed formulations has been illustrated through comparisons with the latest available results on the subject. Good agreement is found.

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Flow through the pores of granular materials has many instances in practice. Therefore, it is interesting to realize how some parameters, such as the shape of the particles affect the passing flow. Following the recent mathematical theory proposed by the authors, this paper deals with the issue of how tortuosity and permeability are influenced by the particle shape. Comparison of the results with the experimental data reveals the competency of the theory in predicting the impact of particle geometry.

In this paper, mesh-free Element-Free Galerkin method has been utilized for analysis of axisymmetric problems. To this aim, basic formulations and assumptions of the method for the case of axisymmetry are derived, and a simple problem of linearly elastic solid mechanics is taken as a benchmark for controlling the consistency of the proposed formulation as well as its accuracy in comparison to FEM. Two different norms for error estimation, i.e. displacement & stress norm, have been addressed in this study. Eventually, using these two norms, a parametric study has been performed on critical factors to demonstrate suitable parametric values. The numerical results show high dependency of the predicted values to the selection of these parameters.

SUMMARY Tunnels constructed using New Austrian Tunnelling Method (NATM) are always based on certain round (unsupported) advance lengths, after which, the temporary lining is placed. The settlement of the ground surface resulting from such construction is of high significance in design and practice. The existing data in this respect, however, is scarce. It is the aim of this paper to propose a semi‐analytical procedure based on three‐dimensional finite element analyses to predict the maximum surface settlement of the ground in NATM tunnels under different combinations of tunnel diameter, overburden depth, round length and soil and lining properties. The comparison of the results with three case histories of real tunnels reveals reasonable accuracy of the present solution. Copyright © 2012 John Wiley & Sons, Ltd.