GGU-UNDERPIN: Structural system

The structural analysis required to determine the state variables (displacement, moment, shear force and normal force) is by means of a rod construction module, which treats the underpinning wall and any anchors and struts as a single structural system. The wall is taken into consideration as a rod construction, running along the centroid of the underpinning wall.

The stiffness EI of the underpinning wall is acquired from E·d³/12, where d is the horizontal thickness of the wall in the section under consideration. The stiffness of each element is assumed as constant, where the thickness is the thickness at the centre of the section. The remaining values of any anchors or struts can be specified before beginning the analysis.

If anchors or struts exist in the system, the point of acting is automatically placed in the centroid axis. The force components acting on the front and rear of the wall, such as soil weight, water pressure, loads, etc. produce a moment around the centroid axis, which GGU-UNDERPIN takes into consideration as a continuously distributed moment load on the rod axis.

The theoretical principles of the rod construction module can be traced back to an article by Duddeck/Ahrens (Betonkalender 1976 (Concrete Calendar), Volume 2). Basically, this is a finite element method based on the displacement method. The division of the wall and the struts into rod sections (finite elements) can be controlled by input (see "System/Depth subdivisions" menu item).

Using FEM produces equation systems in which the number of unknown is a function of the number of rods. The solution to the equation system is acquired in GGU-UNDERPIN using Cholesky's method, which is also employed in other GGU programs and is numerically highly stable. Nor have there been any numerical difficulties reported from other GGU applications.

Amongst the results of the rod construction analysis are the shear forces Q and the normal forces N with regard to the rod construction axis. In a post-processing calculation these forces are converted to the horizontal force H and the vertical force V.