## Example (6.1): Analysis and design of a raft for a high rise building

Introduction

The presence of the structure on compressible subsoil causes settlements for the foundation and also for the structure itself. Values of settlements and settlement differences depend not only on the thickness of the compressible soil layer under the foundation, the value and distribution of structure loads, the foundation depth and contact pressure under the foundations but also on the flexural rigidity of the structure.

One of the properties that has a considerable influence on the development of settlement is the rigidity of the superstructure. The more rigid structure has more uniform settlement and conversely, structure that is more flexible has greatest difference in settlement. The entire structure can be defined as the three media: superstructure, foundation and soil. The analysis of the entire structure as one unit is very important to find the deformations and internal forces.

However, most of the practical analyses of structures neglect the interaction among the three media to avoid the three-dimensional analysis and modeling. The structure is designed on the assumption of non-displaceable supports while the foundation is designed on the assumption that there is no connection between columns. Such accurate analysis of the entire structure is extremely complex.

The early studies for consideration the effect of the superstructure were by *Meyerhof *(1953) who suggested an approximate method to evaluate the equivalent stiffness that includes the combined effect of the superstructure and the strip beam foundation. *Kany * (1959) gave the flexural rigidity of a multi-storey frame structure by an empirical formulae. Also, *Kany *(1977) analyzed the structure with foundation using a direct method. *Demeneghi * (1981) used the stiffness method in the structural analysis. *Panayotounakos/ Spyropoulos/ Prassianakis *(1987) presented an exact matrix solution for the static analysis of a multi-storey and multi-column rectangular plexus frame on an elastic foundation in the most general case of response and loading.

At the analysis of foundations with considering the superstructure stiffness, it is required to distinguish between the analysis for plane structures (two-dimensional analysis) and that for space structures (three-dimensional analysis). Further, it is required to distinguish between approximation methods with closed form equations (*Kany *(1974), *Meyerhof * (1953), *Sommer *(1972)) and refined methods such as conventional plane or space frame analysis (*Kany * (1976)), * Finite Elements *(*Meyer *(1977), *Ellner/ Kany * (1976), Zilch (1993), *Kany/ El Gendy * (2000)) or * Finite Differences *(*Bowles *(1974), *Deninger * (1964)).

In addition, many analytical methods are reported for analysis of the entire structure as one unit by using the finite element.

For examples:

*Haddadin *(1971) presented an explicit program for the analysis of the raft on Winkler's foundation including the effects of superstructure rigidity.

*Lee/ Browen *(1972) analyzed a plane frame on a two-dimensional foundation.

*Hain/ Lee *(1974) employed the finite element method to analyze the flexural behavior of a flexible raft foundation taking into account stiffness effect of a framed superstructure. They proposed the use of substructure techniques with finite element formulation to model space frame-raft-soil systems. The supporting soil was represented by either of two types of soil models (Winkler and half-space models).

*Poulos *(1975) formulated the interaction of superstructure and foundation by two sets of equations. The first set links the behavior of the structure and foundation in terms of the applied structural loads and the unknown foundation reactions. The second set links the behavior of the foundation and underlying soil in terms of the unknown foundation reactions.

*Mikhaiel *(1978) considered the effect of shear walls and floors rigidity on the foundation.

*Bobe/ Hertwig/ Seiffert * (1981) considered the plastic behavior of the soil with the effect of the superstructure.

*Lopes/ Gusmao *(1991) analyzed the symmetrical vertical loading with the effect of the superstructure.

*Jessberger/ Yuan/ Thaher/ Ming-bao * (1992) considered the effect of the superstructure in case of raft foundation on a group of piles.

*Zilch *(1993) proposed a method for interaction of superstructure and foundation via iteration.

*Kany/ El Gendy *(2000) proposed an iterative procedure to consider the effect of superstructure rigidity on the foundation. In the procedure, the stiffness of any substructure such as floor slab or foundation, connected by the columns can be represented by equivalent spring constants due to forces and moments at the connection nodes. Consequently the stiffness matrices of the slab floors, columns and foundation remain unaffected during the iteration process.

Description of the problem

This example was carried out to show the influence of flexure rigidity of the superstructure on the settlements, contact pressures for a raft of high rise building. It is required to analysis a raft for the building shown in Figure (6.6) in three simplified sections. The building is a reinforced concrete skeleton structure consists of a cellar and 13 storeys. The floor height is 3 [m] while the bay width is 3.6 [m]. The number of bays is 18. The total building length is 66 [m] while the total width of the cellar basement is 17.55 [m]. The raft thickness is 1.2 [m]. In the following study the raft is analyzed considering subsoil behavior.

Also, a simplification estimation of the superstructure deformations is carried out. In the analysis, settlements and contact pressures are determined in which a comparison is carried out in four cases as:

i) For not stiffened raft

ii) For compound system raft-cellar

iii) For compound system raft-cellar-superstructure

iv) For completely rigid raft

The stiffness of the structure system parallel to the long axis can be determined from the data given in Figures (6.6) and (6.7).