6. Structural design – general
6.1 Structural options for basement slabs
In the past, engineers have designed strips of rafts as continuous beams limiting the spread of loads to a small zone on either side of the column lines. The contact pressure distribution under the raft and the loads that are causing the pressure are both dependent on the relative settlements. The relative settlements may be ignored only where the foundation system can be assumed to be rigid or the supporting ground is very stiff. In such cases the loads transmitted from the superstructure may be deemed to be unmodifi ed by settlements. Complete soil-structure interaction may be accounted for by treating the subsoil as part of the structure.
Beams on an elastic foundation
One simplifi cation is to model the raft as series of interconnected beams on an elastic foundation. Using Figure 6.1 as reference, the classical governing equation for plates loaded normal to its plane may be modifi ed to include the upward pressure from the soil and may be stated as follows:
EI (d4w/dx4) = qb = ksbw, where
E = elastic modulus of the material of the beam (i.e. concrete) I = moment of inertia of the beam
q = load intensity of the beam acting downwards
Note that by defi nition the ground pressure q = w ks i.e. the settlement multiplied by modulus of sub-grade reaction.
ks = modulus of sub-grade reaction (MN/m2/m)
(This ‘spring constant’ is a parameter used in rigid pavement design and estimates the support provided to the slab by the underlying layers as illustrated in Figure 6.2. Simply, it is pressure/deformation.
Some typical values are given in Table 6.1).
w = defl ection of the beam b = breadth of the beam
The equation may be solved using a fi nite difference technique which is not suited to hand calculations. Although useful infl uence coeffi cients are presented in some books (e.g. Ray[44]), the calculation process will be tedious in all but very simple cases.
P
x w
Figure 6.1 Idealised soil structure model.
Slab
Spring constantk
Deflection P
Soil type Condition ks range
MN/m2/m
Typical design value ks MN/m2/m
I Rock N/A
II Gravel, sand Dense 100 to 150 Dense 40
III Clay, Sandy clay Stiff 20 to 40 Stiff 30
IV Clay, Sandy clay Firm 10 to 20 Firm 15
V Sand, Silty sand, Clayey sand Loose 10 to 25 Loose 20
VI Silt, Clay, Sandy clay, Silty clay Soft 10
VII Silt, Clay, Sandy clay, Silty clay Very soft 5
Another method that is often used in practice is to represent the soil as series of discrete springs to model the soil-structure interaction. However, the determination of the stiffness of the springs will involve collaboration between the structural engineer and geotechnical specialist. An iterative procedure is commonly adopted.
The geotechnical specialist will take into account that the soil extends beyond the structure and will provide realistic values for spring stiffness. Once the correct spring stiffnesses have been agreed they can be directly used in conjunction with a finite element package for the design.
Finite element analysis
It is modern practice to use a fi nite element package for the design of rafts, where the modulus of elasticity of the soil, Es, the shear modulus, G, and Poisson’s ratio are the principal elastic properties of interest. This is illustrated by the simple raft shown in Figure 6.3. The effect of varying the stiffness of the raft and that of the soil using elastic moduli, Es, of 75 000, 150 000 and 225 000 kN/m2 (‘ 75, 150 and 225 MPa) has been computed using a fi nite element analysis program. The results are shown in Figures 6.4 to 6.6.
For this example, dome-shaped defl ection profi les are realistic and generally will be obtained in full soil-structure models.
Figure 6.2 Relationship between load, defl ection and
modulus of subgrade reaction.
Table 6.1 Typical values of modulus of subgrade reaction, ks
Figure 6.3 A simple raft
RC beam 1 m wide used as raft. Four thickness are considered in the example -0.5 m, 0.7 m, 0.9 m and 1.1 m
1000 kN 1000 kN
8 m
Sub soil simulated by springs -stiffness of springs depends on soil characteristics - values considered in the example are 75, 150 and 225 MPa
Distance from centre line of raft (m)
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick Settlement for 8 m wide rafts of varying thickness
E = 150 MPas
Distance from centre line of raft (m)
-4 -3 -2 -1 0 1 2 3 4
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick 0
Settlement for 8 m wide rafts of varying thickness E = 225 MPas
Distance from centre line of raft (m)
-4 -3 -2 -1 0 1 2 3 4
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick 0
RC beam 1 m wide used as raft. Four thickness are considered in the example -0.5 m, 0.7 m, 0.9 m and 1.1 m
1000 kN 1000 kN
8 m
Sub soil simulated by springs -stiffness of springs depends on soil characteristics - values considered in the example are 75, 150 and 225 MPa
Distance from centre line of raft (m)
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick
Distance from centre line of raft (m)
-4 -3 -2 -1 0 1 2 3 4
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick 0
Distance from centre line of raft (m)
-4 -3 -2 -1 0 1 2 3 4
Plate 0.5 m thick Plate 0.7 m thick Plate 0.9 m thick Plate 1.1 m thick 0
Figure 6.3 A simple raft.
Figure 6.4 Settlement for a simple raft assuming an elastic modulus of Es = 75 MPa.
Typical for clay with cu = 100 kN/m2: stiff clay/
medium dense sands and gravels).
Figure 6.5 Settlement for a simple raft assuming modulus of Es = 150 MPa (Typical for clay cu = 200 kN/m2: very stiff clay/
dense sands and gravels).
Figure 6.6 Settlement for a simple raft assuming modulus of Es = 225 MPa (Typical for clays cu = 300 kN/m2: hard clay/
very dense sands and gravels).
General conclusions
The following general conclusions can be drawn:
For a given soil, increasing the stiffness of the raft reduces the peak settlements and the pressures are distributed more evenly.
In this example, even with the stiffest beam employed, the distribution of settlements (and hence pressure) are far from uniform.
In the permanent condition, basement walls are invariably propped by fl oor construction. Even where large openings occur adjacent to the wall (e.g. ventilation shafts and light wells) it will be possible to prop the wall at intervals against the fl oor.
The fl oor diaphragm will need to distribute the reactions from opposite walls by strut action. Generally this is not a problem in concrete floors unless there are large openings in the fl oor. Generally lateral pressures on opposite faces of the basement will be self-equilibrating. Where there is asymmetry (e.g. where depth of soil retention is unequal), out of balance forces may be transmitted through shear walls and base slab to the ground by friction/adhesion between the walls and the soil behind.
The effects of construction method and sequence must be considered to check if a more critical condition could occur during construction when the wall may not be propped.
Where temporary works such as contiguous or secant piled walls, are required to be incorporated into the permanent works, the type and size of the piles will usually be dictated by preferred methods of work. Issues such as whether the wall will be propped or unpropped, tolerances, availability of plant and whether ground conditions are such that groundwater needs to be cut off all have their infl uence. The contractor will therefore have input into the fi nal design.
Preliminary designs are often made likening the temporary works to a wall or by using proprietary software. Design of piled wall tends to be an iterative process but fi nal design should be undertaken by specialists once all the design and construction parameters are agreed.
These will include:
The requirement for the basement and thus grade of basement required
The depth of the basement
The nature of the soils and the environs to the project
The construction sequence and method of excavation
Any temporary and/or permanent propping requirements.