arriving at the design value of actions that occur simultaneously is referred to as load combination.
Combinations 1 and 2
In any design that involves geotechnical actions (e.g. lateral earth pressures), BS EN 1990 and the National Annex to BS EN 1997-1 require consideration of two separate combinations of loads (i.e. two sets of partial factors). These partial load factors are associated with partial factors for soil properties leading to ‘Combination 1’ and
‘Combination 2’ factors at ultimate limit state (See Table 8.2). The structure and the soil are required to resist the action effects caused by both combinations.
In principle the ULS of STR and GEO are examined. Combinations 1 and 2 equate to 'combinations' or 'sets' B and C required by BS EN 1990 when considering the STR/EQU cases. Combination 1 is often said to make the structure critical and Combination 2 the soil but both combinations should be checked.
For each combination of loads, action effects should be calculated using the design values of actions obtained by applying partial factors (γF) to representative values and the appropriate geotechnical properties (and actions) derived by applying partial factors (γM) to values of soil parameters. All the loads that occur in a load case should be classifi ed as either permanent or variable. Earth pressures should be considered as permanent actions. For water pressures, see below.
The ‘Combination 1’ and ‘Combination 2’ values of γF and γM are shown in Table 8.2.
Partial factors γM (soil parameters) and γR (resistances) are used to obtain ground resistance values. The National Annex[11a] should be consulted for values of γR.
8.2 Load combinations and partial factors
Action Stabilising – favourable Destabilising – unfavourable
Permanent G 0.9 1.1
Variable Q 0.0 1.5
Note
According to Eurocode 7 and its National Annex [11a], favourable factors for UPL and HYD are similar, butunfavourable G,unfav = 1.1 for UPL and 1.335 for HYD.
Table 8.1 Partial factors for loads for equilibrium check (EQU)[6a]
As noted earlier, lateral earth pressures on retaining structures is obtained using design values of the effective angle of shearing resistance φd'. However, the value of φd' depends on the partial factor for the soil parameter γM and so for the two combinations to be considered γφ varies. Thus the partial factor for material governs the design value of the load. In design calculations values of φd' should be established for each
combination.
γF for ground water
Eurocode 7 treats ground water as a permanent action, therefore, at ‘normal’ water levels and using Combination 1, γF = γG = 1.35. However, γF for 'abnormal' water levels bear some discussion.
With respect to the water pressure derived on the basis of design water table at ground surface, it is tempting to suggest a value of 1.0 should be applied (e.g. using Combination 2). However, this may not be strictly suffi cient for design of the structure.
BS EN 1990 states that the purpose of the partial factor γF is to:
a) account for the unfavourable deviation of the action values from the representative values;
b) the modelling effects of actions; and c) in some cases the modelling of actions.
Other reasons usually accepted, although not stated in BS EN 1990, are unforeseen redistribution of stresses and variations of geometry of the structure or its elements, as this affects the determination of the action effects. Using a design water table at ground surface only deals with purpose a) noted above. Therefore a value greater than 1.0 is required after uncertainties of the value of actions have been addressed. In Table 2.1 BS 8110-1:1997 gives some guidance. It recommends a value of 1.2 when the maximum credible level for the water can be clearly defined; otherwise a value of 1.4 is recommended. Thus when uncertainties in the value actions are removed, the normal load factor is reduced by (1.4/1.2) = 1.17. If the same margin is applied to the γF normally applied to permanent actions, the reduced value would be (1.35/1.17) = 1.15.
Table 8.2
Load combinations and partial factors (ULS). Combination Partial factors on actions, F Partial factors on soil properties, M
G,unfav G,fav Q φ# c' cu
1 1.35*^ 1.00 1.50 1.00 1.00 1.00 1.00
2 1.00 1.00 1.30 1.25 1.25 1.40 1.00
Note
Values for piles not shown: refer to BS EN 1997-1 Annex A.
There are three design approaches in Eurocode 7[11]. The UK National Annex[11a] adopts design approach 1 (DA1). DA1 requires the consideration of two combinations of partial factors for both actions and soil parameters in order to compare ultimate loads with ultimate soil resistance. The two combinations are detailed in BS EN 1990 Annex A: Tables A1.2(B) & A1.2(C).
Key
# φ is applied to tan φ.
* Eurocode 7 treats groundwater as a permanent action. However, as detailed below, it is recommended that a G,unfav factor of 1.35 is applied to water pressure from water in ‘normal’ conditions and in a separate verifi cation, a Q,unfav factor of 1.20 (or 0) is applied to pressure from water at the most unfavourable level that could occur during the lifetime of the structure (i.e. usually, at surface level).
^ For compaction pressures, partial factor F is presumed = G.
This fi gure is in line with the UK NA[55a] to BS EN 1991-4 Silos and tanks[55] which states that for the liquid induced actions γQ may be taken to equal 1.20 during operation, applied to the stored liquid at the maximum design liquid level.
Thus, on the above basis, it is recommended that for ULS verifi cation γF = γG,unfav = 1.35 should be applied to ‘normal’ ground water levels and γF = γQ= 1.20 should be applied to pressure from water at the most unfavourable level that could occur during the lifetime of the structure (i.e. at surface level or, where the ground water level is known with confi dence, at the ground water level plus a margin based on knowledge of the site and soil conditions). The ground water levels and appropriate partial factors are illustrated in Figure 8.1.
Figure 8.1 Ground water levels and partial factors for ground water to be used
in design. Ground surface
Margin D used in design is based on knowledge of site and soil conditions cannot be assured D should be taken to ground surface level.
Case 2 Free draining soil or where efficient long term drainage can be assured
a) Where long term water table has been established as being low or
b) where long term water table level has not been established with confidence but no water table is noted during the ground investigation.
Case 3 Medium and low permeability soils and long term water table level has not been established with confidence but no water table is noted during the ground investigation.
γw H γw H γw
γw
γw γw
Verifi cation should be carried out using BS EN 1992-1-1 and BS EN 1992-1-2. Analysis of a vertical section is usually undertaken: the form of the actions and resulting bending moment diagram for a typical propped wall situation is shown in Figure 8.2. Analysis should, however, also take account of continuity with suspended fl oor slabs and the possible three-dimensional nature of basement structures, including interactions between wall and base slab elements.
When the aspect ratio (wall length/ wall height) is less than about 1.5, external pressures on walls may be resisted by a combination of horizontal and vertical moments. Appendix A4 provides charts for design in the vertical and horizontal directions.
Moment transfer between walls at corners should be considered and the walls should be suitably reinforced. Figures 8.2 and 8.3 illustrate some typical cases.
It is normal practice fi rst to design the completed structure and then verify it for the action effects during different stages of construction, based on the assumed sequence of construction and stipulated propping requirements. If the contractor wishes to change the method of construction the design would normally be reappraised by the contractor and modifi ed to the satisfaction of the designer.
When considering shear, care should be exercised in taking advantage of any axial compression caused by earth pressures. It will be safe to ignore it. Concise Eurocode 2[56]
and the compendium, How to design concrete structures using Eurocode 2[57] provide useful guidance on the ULS design of concrete elements.