Keywords: micro and macro levels, transformation field analysis, distinct state concept, unified concept, homogenization, localization.

The main objective of the paper is the development of a procedure leading to the overall material properties of soil from a knowledge of the properties of the constituents. In the development of the homogenization procedures for non-linear materials both the homogenization step itself (from local variables to overall ones) and the often more complicated localization step from overall controlled quantities to the corresponding local ones have to be defined. The nonlinear problems of localization and homogenization are of a great importance today.

The numerical model will be based on transformation field analysis (TFA) [1,2], linked with Desai´s distinct state concept (DSC) [3,4], which provides a description of material properties of soil, such as plasticity, creep, and damage.

A typical damage model is described in [6]. Coupled modelling has been used in [7], where other applications on this topic are referred to. Note that the experimental scale models originate in publications [8,9]. One of the most important approaches to homogenization is described in [5]. There also the finite element implementation is shown.

In the present paper the micro-macro solution of the overall properties of soil is discussed. The eigenstrains serve as additional parameters in Hooke's law for expressing plastic, viscoplastic, creep, wetting, swelling and other behaviour of inclusions in the material under observation. Generalized transformation field analysis is introduced using the distinct state concept, which extends the improvement of elastic states (involved in TFA) to nonlinear states. Both methods together with classical averaging approaches provide powerful tools for determining the overall material properties of soil. Because the influence of aggressive components can be involved in the procedure proposed, e.g. local watering of soil, or freezing, the overall material properties can be stated.

A very important consequence follows from this approach. The numerical models can be connected with results from experimental tests and the averaging procedure, correct governing equations, constitutive equations and other phenomena can be improved using eigenparameters. On the other hand, the numerical results may also show the way to direct the experiments. Then the experiments can be repeated with improved starting assumptions in the scale models, which are mostly used for experiments, it is the physically equivalent material. This is why a mutual influence mathematical-experimental model is expected. Such a procedure is called coupled modelling, which is a type of back analysis.

In numerical analysis it is assumed that principal directions, normal and shear, can be separated in soil material. The numerical analysis of a typical unit cell shows that for normal loading the material properties in a normal direction decreases faster than in shear direction. The opposite assertion is valid for shear loading.

1

G.J. Dvorak, P. Procházka, "Thick-walled Composite Cylinders with Optimal Fiber Prestress", Composites, Part B, 27B, 643-649, 1996. doi:10.1016/S1359-8368(96)00001-7

2

G.J. Dvorak, P. Proch'azka, S. Srinivas, "Design and Fabrication of Submerged Cylindrical Laminates", Part I doi:10.1016/S0020-7683(98)00181-4, Part II doi:10.1016/S0020-7683(98)00182-6 , Int. J. Solids & Structures, 1248-1295, 1999.

3

C.S. Desai, "A Consistent Finite Element Technique for Work-Softening Behavior", J.T. Oden et al. (eds.), Int. Conf. on Comp. Meth. in Nonlinear Mechanics, Univ. of Arizona, 45-54, 1974.

4

C.S. Desai, "Constitutive Modeling Using the Disturbed State Concept", Chapter 8, Continuum Models for Materials with Microstructure, ed. H. Mulhaus, John Wiley & Sons, UK, 1994.

5

Suquet, P.M. "Homogenization Techniques for Composite Media", Lecture Notes in Physics 272, eds. E. Sanchez-Palencia and A. Zaoui, 1985, Springer-Verlag Berlin, 194-278.

6

L.M. Kachanov, "Introduction to Continuum Damage Mechanics", Martinus Nijhoff Publishers, Dordrecht, Netherlands, 1987.

7

P. Procházka, J. Trcková, "Coupled modeling of Concrete Tunnel Lining", Our World in Concrete and Structures, Singapore, 125-132, 2000.

8

J. Kozešník, "Theory of similarity and modelling", Academia, Prague, 1983.

9

Stilborg, B., Stephensson, O., Swan, G. "Three-dimensional physical model technology applicable to the scaling of underground structures", 40th Int. Conf. on Rock Mech. Vol. 2, Montreux, 655-662, 1979.

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