Model Behavior
The nonlinear elastic model is characterized by hyperbolic nonlinear elastic behavior. A corresponding stress-strain relation is illustrated in the following image.
A. Reversible, Elastic Stress States
The model shows elastic behavior whose stress-strain relation is characterized by a variable modulus of elasticity. It describes soil behavior for oedometer conditions; that is, conditions in which the horizontal displacements are negligible compared to the vertical ones.
B. Stiffness
Stress dependency:
The material model is capable of modeling the stress dependence of soil stiffness. Soil exhibits higher stiffness for higher stresses. This property is represented by the function for the oedometric modulus as follows:
The following characteristic values are required for the shear strength parameters c and φ for modeling the stress dependency.
| Variable | Meaning |
|---|---|
| Eoed,ref | Tangent modulus determined from the oedometer test for a specific reference stress value. |
| pref | Reference stress for the stiffness modulus. |
| m | Exponent that controls the stress dependency of the stiffness modulus. It can be measured in both the oedometer test and the triaxial test. |
Load direction dependency:
Furthermore, the material model takes into account the stiffness dependence on the load path. Soil shows significantly higher stiffness in the case of unloading and reloading compared to initial loading. This property is achieved by a modified oedometric modulus for unloading and reloading, which is calculated as follows:
Small strain stiffness:
In the material model, it is possible to activate the consideration of higher stiffness in the range of small strains (“small strain stiffness”). The small strains form an additional state variable for this purpose. The image below shows a schematic illustration of the stiffness dependency on the mobilized strains.
C. Irreversible, Plastic Stress States
The model does not reflect failure criteria and plasticity.
Suitability
The nonlinear elastic model described above can represent essential soil properties, such as stress dependency and the dependency of stiffness on the loading path, and is therefore suitable for deformation analysis. It is valid for problems where the assumption of oedometric conditions applies, as well as for stress states that are far from the load limit.
Application areas include settlement calculations for shallow foundations and under embankments with a distance to failure.