� Note 8
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Level 2
TheStructuralEngineer
Technical
December 2013
Technical Guidance Note
Designing a pile-cap Introduction
Pile-caps are elements that transfer the actions from the superstructure of a building, bridge etc. into piles. They can be considered to be a form of pyramid truss that spreads the axial and bending forces from a vertical element into the piles on which the pile caps sit. Another way to describe them would be as a transfer structure that accommodates tolerances of the piles and spreads the axial force from a concentrated column or wall into one or more piles. This Technical Guidance Note concerns the design of pile-caps for small groups of piles e.g. 2-4 piles. It relies on the strut and tie method to determine the amount of reinforcement required in the pile-cap; which is dependent upon the depth of the cap, the magnitude of the axial load being placed upon it, the cap’s concrete strength and the pile size and spacing. Larger pile-caps are influenced by differential settlement across the base, which complicates their analysis and design. As such, these aspects of pile-cap design will be covered in a future guidance note.
Pile-cap design
ICON LEGEND
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Pile-cap design
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Applied practice practice
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Worked example
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Further reading
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Web resources
2 �Figure Setting out of piles within 2, 3 and 4 pile pile-caps
Pile-caps spread the axial force from the superstructure through to piles at an angle, which determines the depth of the pile-cap. This angle is typically 45º, but can be no shallower than 21.8º and is set from the edge of the element that is being supported by the pile-cap, such as a column. Figure 1 indicates how the vertical action N is is spread through the pile-cap down to the heads of the piles. The layout of piles is largely determined from the magnitude and location of actions they are to support from the superstructure. 1 �Figure Spread of axial forces through 3 pile pile-cap
They are grouped together based on the pile’s capacity to support axial forces that can be either tension or compression, depending on the direction of the axial forces induced into the pile-cap from actions generated by the superstructure. The location of piles with reference to the point of axial force application should be symmetrical. The proximity of piles to one another is at least 3 × diameter of the pile. For pile-caps with 1 or 2 piles, some restraint needs to be provided orthogonally to the pile(s), which is usually achieved via ground beams. Figure 2 provides guidance on the location of piles in 2, 3 and 4 pile pile-caps where s is the spacing between piles. Due to the setting out tolerances for the placement of piles, the edge of a pile cap should be no less than 150mm from the edge of a pile. This allows for the variances for the as-built location of the pile over the
3 �Figure Influence of tolerance of pile location on pile-cap extent
75mm wide tolerance for pile location
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Determining axial forces in piles within pile-caps When a pile-cap is supporting an axial force
N that is placed within the centroid of the pile group, the axial force in each pile is defined as:
N n Pile cut-off level
4 �Figure Placement of bottom reinforcement in pile-cap vs. pile 5 �Figure Extent of anchorage of tension reinforcement in pile-cap
Anchorage of tension reinforcement
Where: n is the number of piles. This only applies to pile groups that have a maximum of 5 piles. Larger pile groups are influenced by differential displacement of the piles. This results in an increase in magnitude of axial force in the piles in the extremity of the pile-cap when compared to the piles that are closer to the centroid of the group. In some cases, the layout of the piles and the stiffness of the pile-cap can result in the piles closer to the centroid being more exposed to higher forces than those at the perimeter.
Centre of pile
Partial factors
idealised one, plus cover to reinforcement (Figure 3). Once cut down, the head of the pile penetrates the soffi t of the cap by at least 75mm. This affects the placement of the bottom reinforcement as it needs t o over-sail the heads of the piles (Figure 4).
When designing a pile-cap, STR partial factors apply (as opposed to GEO) as the pile-cap does not have any direct interaction with the soil. BS EN 1990 defines the partial factors for STR as follows:
Figure 6 shows the forces that pass through a pile-cap into the piles and how the strut and tie method is applied to it. It indicates how the depth of the pile-cap determines the magnitude of the forces within the concrete and the tension reinforcement. Typically the angle of the truss is set at 45º, which is then used to determine the depth of the pile-cap. Further iterations of this angle may be necessary as the size of the pile-cap is altered and/or the element it is supporting is modified to overcome geometry constraints and other extraneous design criteria. This can result in having a shallower angle that increases the tension in the reinforcement as does the compression stress in the struts within the pile-cap. When the location of the axial force is not eccentric, the applied tension force between each pile can be calculated using Table 1. The tension reinforcement As required in the pile-cap is defined as:
A s =
T 0.87 f yk
Where f yk is the tension strength of the reinforcement, which is typically 500 N/mm2
G k,j is the partial factor for permanent actions (e.g. self-weight of the structure) and has a value of 1.35
6 �Figure Truss action within a pile-cap showing compression struts
Q k,1 is the leading frequent variable action (e.g. occupancy and furniture) and has a value of 1.5
Another factor that determines the on-plan size of a pile-cap with respect to the pile location, is the requirement to ensure that all tension reinforcement in the base of the pile-cap is suffi ciently anchored. This is explained further in Clause 9.8.1 in BS EN 1992-1-1. This claus e also allow s for the fact when the pile-cap is subjected to compression forces, the area immediately above the pile is in compression. This form of stress can be taken into account when determining the required anchorage lengths for the tension reinforcement. Figure 5 shows the extent at which the anchorage should be relative to the pile.
"The edge of a pile cap should be no less than 150mm from the edge of a pile"
Q k,2 is the accompanying quasi-permanent variable action (e.g. wind)
ψ0 is the factor for the accompanying quasipermanent value of a variable action, which is drawn from Table A1.1 of BS EN 1990 The effect of design action on a pile-cap foundation N or Ed is defined as:
N = E d = G k, j + Q k,1 + } 0 Q k,2 Further guidance on partial factors can be gained from Technical Guidance Notes 2-5 (Level 1).
Table 1: Tensile force between piles Number of piles
Tensile force between piles (T)
2
Nl 2d
3
2 Nl 9d
4
Nl 4d
Design of tension reinforcement There are two analysis methods used when designing pile-caps. One is the strut and tie system that assumes the reinforcement within the pile-cap is acting as if it were part of a truss, with the compression stresses being withstood by the concrete and the tension by the steel reinforcement. This method is applicable for pile-caps with less than 6 piles and is therefore the focus of this note. The premise of this method is summarised in Clause 5.6.4 and 6.5 in BS EN 1992-1-1.
Note: l is half the distance between centroid of the pile group and the centre of vertical element the pile-cap is supporting; d is the distance between top of the pile-cap and top of the piles
� Note 8
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Level 2
TheStructuralEngineer
Technical
December 2013
Technical Guidance Note
Node checks on strut and tie models
Design of shear reinforcement
There is a need to check the strength of the struts within pile-caps as the vertical action is applied to them. These checks are applicable to all strut and tie models, but they are especially relevant to pile-caps.
A critical shear plane adjacent to the vertical element that the pile-cap is supporting needs to be checked to determine whether or not it fails in shear. The plane’s location is based on the distance av , which is the dimension from the face of the vertical element the pile-cap is supporting and the face of a pile plus 0.2 × the pile diameter. This plane’s location is further explained in Figure 7.
There are the two different types of node that can exist within a pile-cap, relating to the types of forces present: ‘CCT’ (tension) nodes and ‘CCC’ (compression) nodes. The compressive strength at the pile head needs to be checked for either CCC or CCT nodes, depending on how the action from the superstructure is being applied to the pile-cap. In Clause 6.5.4 of BS EN 1992-1-1 the compressive strength of CCC nodes are defined as:
v Rd,max
= k 1 of cd
Where: k1 is the factor applied to node compressive strength and is taken to be 1.0 in the UK o is
the strength reduction factor for concrete cracked in shear and is defined as:
f ck 1 - 250
a
k
f ck is the concrete cylinder compressive
The shear resistance is determined based on the enhanced shear capacity of the pilecap near the point of support i.e. the head of the pile. The applied shear force V Ed can be reduced by the ratio of the depth of the pile-cap to the distance to the critical shear plane. Additionally, the shear at the face of the vertical element that is fixed to the pilecap needs to be checked.
Provided V ed ≤ V Rd,c then no additional reinforcement to resist shear over the minimum is required. The minimum area of shear reinforcement V Rd,c(min) is defined as:
V Rd,c (min) = 0.035k 3 2 f ck1
An additional check with respect to shear is required at the face of the vertical element the pile-cap supports. The shear resistance V Rd,max is defined as:
V Rd,max = 0.5v 1 fcd pd v1 is the shear strength of the concrete in N/mm2, which is defined as:
f ck 0.6 1 - 250
:
V Rd,c = 0.12k (100tf ck)
vertical element the pile-cap is supporting This is defined as:
f ck 0.5v 1 1.5 pd
a k
3
p is the perimeter length of the vertical Where: k is defined as:
1+
element of the superstructure
d is the depth of the pile-cap
200 d
Pile-cap reinforcement detailing
which must be ≤ 2 and d is the effective depth of the pile-cap and is expressed in mm
strength in N/mm 2
f cd is the design value of the concrete’s compressive strength and is defined as:
a cc
c f m ck
cc
αcc is the factor that takes into account the
long term effects on compressive strength and is taken to be 0.85 in the UK
D
f cd is the applied shear at the face of the
The shear resistance of the pile-cap is defined as: 1
2
ρ is defined as:
A s bd which must be ≤ 0.02 and As is the provided area of tensile reinforcement and b is the width of the pile-cap
f ck is the concrete cylinder compressive strength in N/mm 2
There are several unique detailing requirements that are specific to pilecaps. The anchorage length of the tension reinforcement is dependent on the bond conditions between the concrete and the steel. In the case of pile-caps, a good condition bond requires the reinforcement to be located within the 250mm depth of the concrete pour. For anything placed outside of that zone the bond is considered to be 'poor'. For more information on this see Clause 8.4.2 in BS EN 1992-1-1. Table 2 provides anchorage lengths for reinforcement bars based on
γC is the partial safety factor for concrete and
varies depending on the nature of the action being applied to it. In the permanent condition this is taken to be 1.5, but for accidental condition it is 1.2.
Table 2: Typical anchorage length of tension bars in pile-caps Length of bar in diameters Bond conditions
For CCT nodes, the compressive strength of the node is defined as:
v Rd,max
= k 2 of cd
Where: k2 is the factor applied to node compressive strength where a tension force is present and is taken to be 0.85 in the UK This node force is compared against the applied force onto the pile. This typically becomes critical in shallow pile caps due to the increase in applied forces.
f ck/f cu = 25/30N/mm
f ck/f cu
2
f ck/f cu
f ck/f cu =
= 28/35N/mm2
= 30/37N/mm2
32/40N/mm2
Good
40
37
36
34
Poor
48
45
43
41
Table 3: Values of f ctm vs. concrete strength class Concrete strength class f ck/f cu in N/mm2
Axial tensile strength f ctm in N/mm2
25/30
28/35
30/37
32/40
2.6
2.7
2.9
3.1
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concrete strength and bond conditions. A more accurate tension reinforcement anchorage length can be calculated using the guidance provided in Clause 8.4.3 of EN 19921-1. The minimum diameter of reinforcement used in a pile-cap is 8mm. The minimum area of tension reinforcement in the pile-cap As,min is defined thus:
A s,min = 0.26b t d (f ctm /f yk) Where: bt is the average width of the tension area above the piles
d is the effective depth of the pile-cap f ctm is axial tensile strength of concrete (which can be found in Table 3) 7 �Figure Critical shear plane location in a 4 pile pile-cap
Eurocode 0.
Applied practice BS EN 1990-1 Eurocode 0: Basis of Design BS EN 1992-1-1 Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings BS EN 1992-1-1 UK National Annex to Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules for Buildings BS EN 1997-1 Eurocode 7: Geotechnical Design – Part 1 General Rules BS EN 1997-1 UK National Annex to Eurocode 7: Geotechnical Design – Part 1 General Rules
Worked example A 350mm x 350mm concrete column has an axial design action of 3250 kN. Design a 3 pile pile-cap to support the column. The piles are 400mm diameter cylindrical concrete piles. The pile-cap’s concrete is to be grade 30/37 with 500 N/mm 2 high tensile steel reinforcement. The column is placed in the centroid of the pile group.
� Note 8
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Level 2
TheStructuralEngineer
Technical
December 2013
Technical Guidance Note
Glossary and further reading Critical shear plane – location in a pile-cap at which shear failure is most likely to occur.
Ground beam – horizontal element suspended between ground bearing elements and/or pile-caps.
Strut and tie method – Analysis concept that models the compressive strength of concrete as a strut, and tension strength of the reinforcement as a tie.
Further Reading The Institution of Structural Engineers (2012) Technical Guidance Notes 1-5 (Level 1) The Structural Engineer 90 (1-3) Reynolds C. E., Steedman J. C. and Threlfall A. J. (2007) Reynold’s Reinforced Concrete Designer’s Handbook (11th ed.) Oxford, UK: Taylor & Francis The Institution of Structural Engineers (2006) Standard Method of Detailing Structural Concrete: A manual for best practice (3rd ed.) London: The Institution of Structural Engineers Mosley W. H., Hulse R. and Bungey J.H. (2012) Reinforced Concrete Design to Eurocode 2 (7th ed.) Basingstoke, UK: Palgrave MacMillan Viggiani C., Manolini A. and Russo G. (2011) Piles and Pile Foundations Abingdon, Oxford, UK: Spon Press Tomlinson M. and Woodward J. (2007) Pile Design and Construction Practice (5th ed.) Boca Raton, Florida: CRC Press The Institution of Structural Engineers (2006) Manual for the Design of Concrete Building Structures to Eurocode 2 London: The Institution of Structural Engineers Webster R. and Brooker O. (2007) How to design concrete structures using Eurocode 2 – Part 6. Foundations [Online] Available at: www.concretecentre.com/pdf/ publicationlibrary/how2_foundations.pdf (Accessed: November 2013)
Eurocode 0.
Web resources The Concrete Centre: www.concretecentre.com/
