GGU-SLAB: Constrained modulus method

The following condition must be met to employ the constrained modulus method:

Deflection curve of slab = settlement depression of elastic-isotropic half-space

The constrained modulus method therefore requires an iteration process, in contrast to the subgrade reaction modulus method. In the first step, the settlements (elastic-isotropic half-space) at all FEM mesh nodes resulting from a constant load of 1 kN/m² on the FEM elements are calculated. The settlement resulting from the triangle loads must be determined for every FEM mesh node. For example, a mesh comprising 512 triangles and 289 nodes requires

512 · 289 = 147,968 (!) settlement calculations.

The Boussinesq equation is numerically integrated for the settlement calculation because there is currently no analytical solution to this problem. The pressures exercised on the nodes (in the first step = 1 kN/m²; in all following iteration steps = k_s · w) are divided by the calculated settlements in order to acquire the subgrade reaction modulus for each node. Following this a calculation is performed using the subgrade reaction modulus method including determination of the node displacements. If the slab differential settlements deviate from the user-defined settlement given at the start of analysis, the iteration is continued.

The constrained modulus method employs a limiting depth corresponding to the base of the
constrained modulus profile. Alternatively, the limiting depth can be calculated to DIN 4019. To do this, the appropriate check box must be activated in the "System/Analyse" dialog box.