Theoretical Background
The constrained modulus method represents the mutual interaction between the foundation slab and the soil through an iterative coupling of soil contact stresses, settlements, and subgrade reaction moduli.
Initial subgrade reaction values are used for a first FE calculation to determine the soil contact stress distribution. Subsequently, settlements are calculated in the elastic half-space according to Boussinesq, integrating stresses layer by layer. Updated vertical and shear-effective subgrade reaction moduli are then derived, for which another FE calculation is performed. This iteration is repeated until changes in settlements and stresses fall below the convergence threshold.
For further information, see the online manual for the Geotechnical Analysis add-on:
Scope of Analysis
A static analysis considering soil-structure interaction by applying the constrained modulus method is to be performed for the illustrated foundation slab.
Subsoil Modeling
The input for the subsoil structure is carried out in the steps
- Creating soil materials based on library material
- Describing the subsoil structure using boring logs
- Creating the soil massif.
The following image series briefly and concisely summarizes the process. A detailed description of the procedure can be found in the technical article KB 1699 | Creating Soil Body from Soil Samples in RFEM 6:
1. Constrained Modulus Method as Subsoil Modeling Type
The basis for applying the constrained modulus method is the soil massif.
In the "Type of subsoil modeling" field of the soil massif, the numerical method for subsoil modeling can then be selected.
In the drop-down menu, select the constrained modulus method (1).
An additional "Settings" section (2) appears, consolidating further settings and options.
2. Surfaces to be Supported
In the settings for the constrained modulus method, assign the surfaces to be supported. In this example, the default settings are adopted for the other settings.
The input can be confirmed with "OK". The subsoil structure is now fully modeled.
3. Generated Support
The constrained modulus method generates the surface support as well as line supports on the boundary lines.
The created supports are listed in the types for surfaces or lines and are displayed graphically on the model. The stiffness coefficients of the support are determined during the static analysis.
Analysis
In this example, the load combinations are to be generated by the assistant so that the constrained modulus method is performed for the combinations of the quasi-permanent design situation.
For all other design situations, the support from the associated quasi-permanent combination is to be adopted.
This is set accordingly in the combination wizard, as the following image series shows.
The generated load combinations are illustrated as examples in the following image series.
The constrained modulus method is active for all load combinations of the quasi-permanent situation. For all combinations of the other design situations, however, the adoption of the support from the associated quasi-permanent load combination is set. A static analysis without the constrained modulus method is performed for these.
The model can now be calculated.
Results
After the static analysis, you can select the "Elastic foundation coefficients" result for surfaces in the Results navigator, so that the calculated subgrade reaction moduli Cu,z, Cvx,z and Cv,yz are displayed graphically, as shown in the following image.
Furthermore, under Support reactions, the result for the "Elastic foundation coefficients" of the line supports can be selected and thus displayed in the graphic.
Conclusion
Using the constrained modulus method allows for efficient consideration of the soil-structure interaction, thereby significantly improving the result quality of the finite element analysis compared to constant surface bedding.