Design - Cellular Raft.

Introduction
Cellular rafts are used where valuable increases in bearing capacity can be achieved by the removal of overburden or where severe bending moments may be induced due to mining activity, seismic loadings, etc.

The cellular form in such situations can perform two functions (see Fig. 13.31).

The foundation while being economic for such situations is one of the most expensive foundation types used.

Fig. 13.31 Cellular raft.

Sizing the design
In the case of overburden removal the depth required may relate more to the excavation required to produce adequate reduction in load than to the bending moment resistance of the cellular form (see Fig. 13.32).

Fig. 13.32 Raft depth dictated by bearing
requirements.

On the other hand it is more common for the raft depth to relate to the moments likely to be induced and the reduced overburden load to be a resulting bonus. For example, a raft designed to resist seismic loads or mining subsidence may need to be designed to span two-thirds of its total length and to cantilever one-third of its length. Similarly rafts on variable ground subjected to large differential settlements may require such design parameters. This requirement  on a building plan which is restricted to say 20 m on any one side can produce very large shear forces and bending moments thus requiring deep rectangular, I or box sections.

The size of these beams can often be reduced by jointing buildings into smaller units (see Chapter 6). Cellular rafts or other rafts which are formed from beams crossing at right angles are difficult to assess since loads are resisted in two directions by the framework. The designer must start by calculating the design column loads and relating these to the overall plan and ground pressures.

The calculations for the ground pressures based upon the centre of gravity of the loads and the relative stiffness of the raft foundation is then considered. In the case of the cellular raft a stiff raft would normally be assumed (see Fig. 13.33). With reference to Fig. 13.33, the centre of gravity of the load would be calculated in the normal way and the resultant load would be the total addition of the loads on the frame- work for the design conditions being considered.

Fig. 13.33 Centre of gravity of load on stiff raft.

The ground pressures at the corners of the raft would then be determined. Assume the resultant total load to be T, the total area to be A, the moment in each of the two directions to be Mx and My, the eccentricity in each direction to be ex and ey, and the section modulus in those directions assum- ing symmetrical plan to be Zx and Zy. The stress at each corner would equal

Mx and My, being the resultant moments, equal T × ex and  T × ey, respectively (see Figs 13.34 and 10.18).

Fig. 10.18 Foundation in biaxial bending.

As usual in design calculations these theoretical pressures will not necessarily be achieved on site and the difficulty then arises when the engineer tries to assess the actual ground pressures. These pressures will be dependent on the sub- strata, the flexibility of the raft, the actual loads occurring at any time and the time at which these pressures are considered relative to the original application of the load.

None of these conditions can be assessed accurately nor is it necessary to do so. The procedure to be adopted is for the engineer to apply the art of foundation design in producing calculations and details for the raft. This means taking consideration of these variables as part of the refinement of the design at the detailing stage. Adjustments must be made  to sections, reinforcement, location of joints and to the number of beams on plan to produce a more realistic and practical solution. The authors make no apology for suggesting that foundation engineering is an art as well as  a science since they have learnt this art from long and bitter
experience. The engineer doing this exercise therefore would begin by preparing a rough layout from practical experience indicating rough sizes likely to be required.

Assumptions are then made, for example:

(1) The raft will be assumed to be stiff.
(2) The bearing pressure will be assumed to be trapezoidal, as indicated in Fig. 13.34.
(3) The load from the structure will be assumed to be fixed at the design load for the analysis.
(4) The reactions to each beam line will be assumed to be proportional to the bearing area and ground pressure on that line and when both directions are totalled they must be equal to the applied load at that point from the structure.

Fig. 13.34 Corner pressure below stiff raft with
resultant load as Fig. 13.3.

Many methods of analysing foundations have been proposed, some assuming springs below the foundations, some assuming uniform bearing pressure, some assuming non- linear bearing pressures, some trying to take into account the stiffness of the raft foundation.

At the end of the day the experienced engineer fully under- stands that all these calculated methods, while being  reasonable and theoretically logical, are not realistic. The foundation which the engineer designs will not sit on the soil which was taken to the laboratory for testing, it will  not for its total life be resisting the loads calculated, it willnot be of the stiffness assumed, it will not be subjected to
the settlements or movements anticipated by calculation.

With all this in mind the engineer uses analysis as one of the tools in the kit bag. The above knowledge produced by design and calculation is taken into account and the design adjusted in a direction which is more realistic.

To achieve this practical engineers will often make simple assumptions to produce a quicker analysis while satisfying themselves of the foundation requirements without the need for complicated and often less accurate methods of analysis. A typical design approach for a cellular raft is shown in the following example.