Basic data

The following material parameters are required for all material models.

Unit weight γ – the bulk weight of a dry soil (soil above the ground water table, GWT) is assumed. The bulk weight of a soil below the GWT is calculated from other parameters introduced in section "Uplift".

Modulus of elasticity E

The modulus of elasticity describes the material stiffness that is assumed constant over the entire loading interval. In case of soils this assumption is, however, valid only for a very narrow interval of recoverable deformations. Modulus of elasticity E has no significant effect on soil behavior for nonlinear models after satisfying plasticity condition.

A straightforward answer to what definition and what value of this material parameter (initial, tangent, secant…) one should use in a given material model is, unfortunately, not available. To select a given type of modulus one needs know the soil behavior in the analyzed geotechnical task and to assign a particular magnitude the results from a triaxial test for corresponding stress paths are necessary. Nevertheless, certain recommendations can be provided.

The following interpretation of Young’s modulus E of elasticity is available:

-	instantaneous modulus E0 in case of small loads (assumption o linear dependence of strain and stress) or when instantaneous settlement is calculated
-	secant modulus E50  is determined for a reference stress equal to 50% of stress at the onset of failure (used for example when analyzing spread foundations)
-	deformation modulus Edef is determined from a loading curve derived experimentally, it is required when using the modified elastic model (this model assumes different behavior for loading and unloading) – using this modulus when solving the problem of soil unloading (e.g., underground structures, heaving of bottom a foundation ditch) leads to larger deformations than when using the elastic modulus Eu determined from unloading branch r of the loading curve – an approximate relation is applicable:

-	oedometric modulus Eoed which depends on the level of stress in the soil should be used depending on the expected range of stress in the soil may experience – the relation between Edef and Eoed is provided by:

where:	ν	-	Poisson’s number
	Edef	-	deformation (secant) modulus

-	modulus of elasticity Eur determined from the unloading branch is used when solving the problem of soil unloading (excavations) – must be defined when using the modified elastic model

The values of modules of elasticity should be determined, if possible, from a triaxial experiment. If other methods (penetration tests, piesometers, etc.) are used then it becomes necessary to introduce some correlation coefficients described in literature.

For actual modeling we recommend to perform an elastic analysis first and check the resulting strain field – such strains according to Hookes’s law are linearly dependent on the applied load and the used elastic modulus. If the resulting strains (displacements) are already too large the user should reassess the magnitude of the originally applied elastic modulus.

Poisson number ν – coefficient of transverse contraction is in the case elastic homogeneous material loaded by normal stress in one direction given by:

where:	εy	-	vertical strain
	εx	-	horizontal strain

The Poisson number is relatively easy to determine. To select its value one may take advantage of the built-in soil database. If small loads are assumed and the instantaneous modulus E₀is used, then also the value of the Poisson number ν₀ determined for the initial loading should be employed.