# Stiffness Parameters of Soil Material Models

## Technical Article on the Topic Structural Analysis Using Dlubal Software

• ### Technical Article

The Geotechnical Analysis add-on provides RFEM with additional specific soil material models that are able to suitably represent complex soil material behavior. This technical article is an introduction to show how the stress-dependent stiffness of soil material models can be determined.

#### Introduction

Soil shows a highly nonlinear material behavior. One of its significant properties is the stress dependence of the soil stiffness. The nonlinear elastic soil material model is appropriate for representing this stress-dependent stiffness.

Once the "Soil" material type is set in the program and the nonlinear elastic "Isotropic | Soil | Nonlinear Elastic (Solids)” material model is selected, a specific input tab is available (Image 1).

#### Stress Dependence of Stiffness

The tab above (Image 1) provides a schematic representation of the stress-strain relation of soil in the dialog graphic. The stress dependence used is expressed for the oedometric modulus with the following equation, according to . It corresponds to the approach used in the hardening soil model.

$$Eoed=Eoed,ref·σ3+c·cotφpref+c·cotφm$$

The shear strengths (φ and c, see 1 in Image 1) can be taken directly from the geotechnical report of the respective project. Moreover, the following parameters (see 2 in Image 1) are required.

• Eoed,ref - reference value of oedometric tangent modulus
• pref - reference stress
• m - exponent for stress dependence

The stress dependence is controlled by the exponent m, which can be measured in both the oedometer test and the triaxial test. Typical values for sand are m = 0.5 and for clay, m = 1.0. The reference value of the model's initial loading stiffness Eoed,ref can be derived from the constrained moduli of the geotechnical report by means of pref and m.

#### Determination of Parameters Eoed,ref, pref & m

This section will now show how to determine the parameters for the material model using an example. Geotechnical investigation for our example shows the following soil layers.

The calculation is carried out using the following steps:

• 1. Determination of available stresses in initial state

Based on the layers' soil properties and the layer heights, the effective overburden pressure σv‘ can be determined for the respective depth.

• 2. Stiffness of soil according to geotechnical report

The soil stiffness profile along the depth is known from the geotechnical report.

• 3. Stiffness calculated by formula of material model

The parameters of the material model are set in such a way that the stiffness profile resulting from the material model shows a satisfactory agreement with that of the expert assessment.

The stresses and stiffnesses shown in the table in Image 3 are the result for the present example.

#### Result

Image 4 below shows the distribution of the oedometric stiffness over depth in the initial stress state, as derived from the formula of the material model and used in the FE analysis. The stiffness profile from the geotechnical report is shown for comparison.

It becomes clear that the stiffness values Eoed applied represent the stiffness profile of the geotechnical report appropriately.

#### Author #### Dipl.-Ing. Juliane Stopper-Akdag

Product Engineering & Customer Support

Ms. Stopper provides technical support for our customers and is responsible for the development of products for geotechnical engineering.

#### Reference

  German Geotechnical Society: Empfehlungen des Arbeitskreises Numerik in der Geotechnik – EANG. Ernst & Sohn. Berlin. 2014  T. Schanz, P. A. Vermeer and P. G. Bonnier. The hardening soil model: Formulation and verification, pages 281–296. , 1999. 