ec2 guide_foundations_rev2 - stare.pdf

Revision 2/OB 07 March 2005

How to use Eurocode 2: Foundations R Webster xxx xxxx xxxx, O Brooker BEng CEng MICE

Introduction Common Intro. for all publications - TBC

Eurocode 7: Geotechnical Design All foundations should be designed so the soil safely resists the actions applied to the structure. The design of any foundation consists of two elements, the geotechnical design and the structural design of the foundation itself. However, for some foundations (eg flexible rafts) the effect of the interaction between the soil and structure may be critical and must also be considered. Geotechnical design is covered by Eurocode 71, which supersedes BS 59302 BS 80023 & BS 80044. Eurocode 7 marks a significant change in geotechnical design in that limit state principles are usedand this should ensure there are no anomalies between the Eurocodes. There are two parts to the code, Part 1: General rules and Part 2: Ground investigation and testing.

The essential features of Eurocode 7 relating to foundation design are discussed in this guide. It should be emphasised this guide only covers the design of simple foundations which is a small part of the scope of Eurocode 7. The guide should not be relied on for general guidance on the code.

Limit states The following ultimate limit states (ULS) should be satisfied for geotechnical design, they each have there own combinations of actions*:

EQU Loss of equilibrium STR Internal failure or excessive deformation of the structure or structural member GEO Failure due to excessive deformation of the ground UPL loss of equilibrium due to uplift by water pressure HYD Failure caused by hydraulic gradients

In addition the serviceability limit state (SLS) should be satisfied. However, it will usually be clear that one of the limit states will governs the design and therefore it will not be necessary to carry out checks for each of them.

Spread Foundations The design of spread foundations is covered by section 6 of Eurocode 7 Part 1 and this gives three methods for design:

1. Direct method analysis is carried out for each limit state 2. Indirect method experience and testing used to determine serviceability limit state parameters which also

satisfy all relevant limit states 3. Prescriptive method in which a presumed bearing resistance is used.

Traditionally, for most spread foundations in the UK, settlement has been taken as the governing criteria, and allowable bearing pressures have been used to limit settlement this philosophy can be continued to be used under the indirect and prescriptive methods. The indirect method should be used where a Geotechnical Design Report (Site Investigation report) has been commissioned and bearing resistances which are based on the serviceability limit state have been provided in the interpretive reporting. The prescriptive method may be used where calculation of the soil properties is not possible or necessary and can be used as long as conservative rules of design are used. Therefore reference can continue to made to Table 1 of BS 8004 (see Table 1) to determine presumed (allowable) bearing pressures.

* For an explanation of Eurocode Terminology please refer to How to use Eurocode 2: Introduction


Pad foundations For a concentrically loaded pad foundation the size can be determined by dividing the characteristic SLS actions by the presumed bearing resistance to give the minimum plan area of the base. This will ensure the settlement is within acceptable limits and the GEO ULS is not exceeded.

Where there is a moment applied to the base the pressure distribution under the base should assessed to ensure that the maximum pressure does not exceed the presumed bearing resistance (see Figure 1). If the eccentricity is greater than L/6 then the pressure distribution should be modified because no tension can occur between the base and the soil, in this case the designer should satisfy himself that there will be no adverse consequences (eg excessive rotation of the base)

Where the base is subject to significant moments then the EQU ULS should also be checked, assuming the potential overturning of the base is due to the variable action from the wind, the following combination should be used (the variable imposed action is not considered to contribute to the stability of the structure):

0.9 Gk + 1.5 Qk,w EQU Combination

Where Gk is the stabilising characteristic permanent action Qk,w is the destabilising characteristic variable wind action

For a reinforced concrete pad foundation the critical bending moments for design of bottom reinforcement are located at the column faces. Both beam shear and punching shear should then be checked at the locations

L

L

L = width of base

Figure 1:

(from BS 8004)


shown in figure 2. For punching shear the ground reaction within the perimeter may be deducted from the column load (Expression 6.48, Eurocode 2). If the basic shear stress is exceeded, the designer should increase the depth of the base, alternatively, but less desirably, the amount of main reinforcement could be increased or shear links could be provided.

The moments and shear forces should be assessed using the STR combination, which can be taken as:

1.25 Gk + 1.5 Qk STR Combination

provided that the permanent actions do not exceed 4.5 times the variable actions and that storage areas are not included. For further details on combinations and where there is more than one variable action reference should be made to the How to use Eurocode 2: Introduction guide in this series.

Figure 2: Shear checks for pad foundations RAFT FOUNDATIONS

The current methods for analysing raft foundations may still to be used i.e. the raft is treated as being inverted, with the bearing pressure acting as a uniformly distributed load and the columns as reactions. The presumed bearing pressure should be obtained from the interpretive Geotechnical Design Report. Where the raft is flexible (e.g. when L/h < 10) the interaction between the soil and structure should be considered and the advice of a geotechnical specialist obtained. As above the structure should be designed for the STR ULS.

Piled Foundations For the purpose of this guide it is assumed that the pile design will be carried out by a specialist piling contractor. However, the actions on the piles must be clearly conveyed to the pile designer, and these should be broken down into the permanent actions and each of the applicable variable actions (e.g. imposed and wind actions). The pile designer can then carry out the structural and geotechnical design of the piles.

A concentrically loaded pilecap should be designed for the STR combination of actions, which can be taken as:

1.25 Gk + 1.5 Qk STR Combination

provided that the permanent actions do not exceed 4.5 times the variable actions and that storage areas are not included. For further details on combinations, where the pilecap is subject to moments or where there is more than one variable action, reference should be made to the How to use Eurocode 2: Introduction5 guide in this series.

Where moments are applied to the pilcap the EQU combination should also be used to check the piles can resist the overturning forces. These EQU loads must also be clearly conveyed to the pile designer; liaison may be required with pile designer to ensure the piles are designed for the correct forces.

A pilecap may be treated as a beam in bending or by using the truss analogy, both methods for determining the design forces in a pilecap are well documented in text books. Rules for using the strut and tie method are covered in sections 5.6.4 and 6.5 of Eurocode 2, although these do not differ significantly from current practice


Both beam shear and punching shear should then be checked as shown in figure 3. If the basic shear stress is exceeded, the designer should increase the depth of the base, alternatively, but less desirably, the amount of main reinforcement could be increased or shear links could be provided.

Figure 3: Critical Shear perimeters for piles Care should be taken that main bars are fully anchored. As a minimum, a full anchorage should be provided from the inner face of piles, large radius bends may be required.

Flexural Capacity Eurocode 2 offers alternative methods for determining the stress-strain relationship of concrete. For simplicity and familiarity the method presented here is the simplified rectangular stress block which is very similar to that found in BS 8110 (see figure 1).

Eurocode 2 gives recommendations for the design of concrete up to grade C90/105, however, the factors, and , modify the strength capacity for concretes above grade C50/60. For the purpose of this guide only concrete up to grade C50/60 is considered. It is important to note that concrete strength is based on the cylinder strength and not the cube strength (eg for grade C28/35 the cylinder strength is 28 MPa, whereas the cube strength is 35 MPa).

As with BS 8110, K can be determined from the design ultimate moment, concrete strength and the width and depth of the section. K is similarly dependant of the amount of redistribution carried out. Knowing K and K and the lever arm, the area of reinforcement can be determined using formulae derived from the stress block (see Figure 5). Finally, checks can be carried out to ensure that the area of reinforcement is within the maximum and minimum areas permitted by the code. Note that minimum area of reinforcement is greater than under BS 8110 where the cylinder strength is over 25 MPa. Selected symbols are given in Table 2.

Figure 4: Simplified Rectangular Stress Block from Eurocode 2

Table 2: Selected Symbols Symbol Definition Value x Depth to neutral axis (d-z)/0.4 xmax Limiting value for depth to neutral axis ( - 0.4)d where 1.0 d Effective depth d2 Effective depth to compression reinforcement Ratio of the redistributed moment to the elastic

bending moment

As Area of tension steel As2 Area of compression steel fcd Design value of concrete compressive strength cc fck/c fck Characteristic cylinder strength of concrete cc Coefficient taking account of long term effects 0.85 for the resistance of flexural

0.8


on compressive strength and of unfavourable effects resulting from the way load is applied

and axial forces. 1.0 for the resistance of shear forces. (From UK National Annex)

fyk Characteristic yield strength of reinforcement 500 MPa for grade XXX fyd Design yield strength of reinforcement fyk/m = 435 MPa for grade XXX fctm Mean value of axial tensile strength 0.30 fck(2/3) for fck C50/60 (from

Table 3.1, Eurocode 2) m Partial factor for material properties 1.15 for reinforcement (y)

1.5 for concrete (c) Ac Cross sectional area of concrete b.h K Factor to take account of the different structural

systems See table 7.4N

leff Effective length of member See section 5.3.2.2 (1)


Determine K and K from: K = M & K = 0.6 0.18 0.21 where 1.0 (bd2fck)

(Refer to Table 4 for values of K)

Is K K ? Compression reinforcement

required

No compression reinforcement required

Yes

No

Calculate lever arm Z from [ ]'53.3112

Kdz += Calculate lever arm Z from [ ] dKdz 95.053.3112

+= (Refer to Table 5 for values of z/d)

Calculate compression reinforcement required from

( )22

2..)'(

ddfdbfKKA

sc

cks

= where fsc = 700((x-d2)/x) fyd

Calculate tension reinforcement required from

yd

scs

yd

cks f

fAzfdbfKA 2

2

...' +=

Calculate tension reinforcement required from As = M

fyd.z

Check minimum reinforcement requirements: As,min = 0.26 fctm bt d where fck 25

fyk (Refer to Table 6 for values of fctm)

Check maximum reinforcement requirements As,max = 0.04 Ac for tension of compression reinforcement outside lap locations

Concrete grade C50/60? Outside scope of this guide

Yes

No

START

Figure 5: Procedure for Determining Flexural Reinforcement


Table 4: Values for K

% Redistribution K 1.00 0 0.2052 0.95 5 0.1931 0.90 10 0.1800 0.85 15 0.1661 0.80 20 0.1512 0.75 25 0.1355 0.70 30 0.1188

Table 5: z/d for singly reinforced rectangular

sections K z/d

0.010 0.991 0.015 0.987 .020 0.982 0.025 0.977 0.030 0.973 0.035 0.968 0.040 0.963 0.045 0.959 0.050 0.954 0.055 0.949 0.060 0.944 0.065 0.939 0.070 0.934 0.075 0.929 0.080 0.924 0.085 0.918 0.090 0.913 0.095 0.908 0.100 0.902 0.105 0.897 0.110 0.891 0.115 0.885 0.120 0.880 0.125 0.874 0.130 0.868 0.135 0.862 0.140 0.856 0.145 0.849 0.150 0.843 0.155 0.836 0.160 0.830 0.165 0.823 0.170 0.816 0.175 0.809 0.180 0.802 0.185 0.795 0.190 0.787 0.195 0.779 0.200 0.771

Table 6: Values of fctm

fck fctm


25 2.6 28 2.8 30 2.9 32 3.0 35 3.2 40 3.5 45 3.8 50 4.1

Deflection Deflection is rarely critical for foundation elements and is therefore not considered any further in this guide. For circumstances where deflection should be checked, refer to the guidance in the How to use Eurocode 2: Beams6.

Design for beam shear Eurocode 2 introduces the strut inclination method for shear capacity checks. In this method the shear is resisted by concrete struts acting in compression and shear reinforcement acting as ties. The angle of the concrete strut varies depending on the shear force applied (see Figure 6). The procedure for determining the shear capacity of a section is shown in Figure 7 together with a commentary for those unfamiliar with the method. As with BS 8110, there is a maximum permitted shear capacity, vRd,max, but this is not restricted to 5 MPa as in BS 8110. For most foundations shear reinforcement is not used and therefore a the concrete shear stress without shear reinforcement should also be checked.

Figure 6: Strut Inclination Method


Table 7: Values for vRd,max fck vRd,max 20 3.31 25 4.05 28 4.48 30 4.75 32 5.02 35 5.42 40 6.05 45 6.64 50 7.20

Table 8: vRd,c resistance of members without shear reinforcement, MPa Effective depth, d (mm) l 200 225 250 275 300 350 400 450 500 600 750*

0.25% 0.54 0.52 0.50 0.48 0.47 0.45 0.43 0.41 0.40 0.38 0.36 0.50% 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.49 0.48 0.47 0.45 0.75% 0.68 0.66 0.64 0.63 0.62 0.59 0.58 0.56 0.55 0.53 0.51 1.00% 0.75 0.72 0.71 0.69 0.68 0.65 0.64 0.62 0.61 0.59 0.57 1.25% 0.80 0.78 0.76 0.74 0.73 0.71 0.69 0.67 0.66 0.63 0.61 1.50% 0.85 0.83 0.81 0.79 0.78 0.75 0.73 0.71 0.70 0.67 0.65

Determine concrete shear stress capacity (without shear reinforcement)

( ) ckckl fkfkv cRd 2331 035.010012.0, = Where k = 1 + (200/d) 2 & l = As /(bd) 0.02

Shear reinforcement required - typically not used in foundations except for 2 pile pilecaps. Redesign section.

Determine maximum shear capacity of beam vRd,max = 0.18 fck(1-fck/250)

Is vRd,max < vEd, ? Redesign section

No

Yes

No shear reinforcement required. Check complete

vRd,max occurs when cot = 1.0. is the angle of the concrete strut from the horizontal (see figure 4). The formula is derived from expression 6.9 in the code, refer to table 7 for values of vRd,max

vEd = shear stress at d from face of support (VEd/(bwd) where VEd is design value of shear forces at ULS)

For shear reinforcement design refer to How to use Eurocode 2: Beams

Is vRd,c > vEd? No

Yes

Expression 6.2 from code. Where d < 200mm, K = 2.0 See Table 8 for values of vRdc

Commentary START

Figure 7: Procedure for Determining Shear Capacity


1.75% 0.90 0.87 0.85 0.83 0.82 0.79 0.77 0.75 0.73 0.71 0.68 2.00% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71 2.50% 0.94 0.91 0.89 0.87 0.85 0.82 0.80 0.78 0.77 0.74 0.71

k 2.000 1.943 1.894 1.853 1.816 1.756 1.707 1.667 1.632 1.577 1.516 Note: This table has been prepared for fck = 30, where 1 exceed 0.40% the following factors may be used: fck 25 28 32 35 40 45 50factor 0.94 0.98 1.02 1.05 1.10 1.14 1.19 * Note: For depths greater than 750 calculate vRd,c directly.

Design for punching shear Eurocode 2 provides specific guidance on the design of foundations for punching shear (see section 6.4.4 (2)), which varies from that given for slabs. In Eurocode 2 the shear perimeter has rounded corners for and the forces directly resisted by the ground should be deducted (to avoid unnecessarily conservative designs). However, the critical perimeter cannot be readily determined, therefore, it will be necessary to find it iteratively. Alternatively, a spreadsheet could be used e.g.TCC spreadsheet xxxxxx7. The procedure for determining the punching shear requirements are shown in Figure 8 together with a commentary. It is worth noting that the shear capacity of an unreinforced section varies slightly from that for the beam shear and punching shear for a slab.


Determine concrete punching shear capacity (without shear reinforcement) from:

( ) ckckl fadkf

adkvRd

23

31 07.010024.0 =

Where k = 1 + (200/deff) 2, l = (ly.lz) 0.02 and a = distance from edge of column to perimeter

Punching shear reinforcement required not recommended for foundations.

Determine value of factor

Is vEd,max < vRD,max? Redesign foundation

No

Yes

is a factor to allow for the additional shear stress that arises from applied moments. = 1.0 for concentrically loaded foundations. Refer to expressions 6.38 to 6.42 of the code where moments are applied.

u1 can be assessed from Figure 6.13 in code, or from the following: u1,sq = 2(cx + cy) + 4d for rectangular column

where cx & cy are column dimensions u1,cir = ( + 4d)

where is column diameter.

Is vEd < vRD,c at critical perimeter?

No

Yes

Due to the deduction of the ground reaction the location of the critical perimeter varies. It should be found iteratively or by using a spreadsheet (eg TCC spreadsheet xxxxxxx{ref}). Typically, the critical perimeter will be found at 0.5 to 1.0 times the effective depth. The area within a perimeter for a square column is 4d2 + cx.cy + 4cxd + 4cyd

Commentary START

Figure 8: Procedure for Determining Punching Shear Capacity

Determine value of vEd, (design shear stress) from: vEd = (VEd - VEd) (u1.deff) where u1 is length of control perimeter.

Derived from expression 6.38 in the code. VEd is the design value of the applied shear forces at ULS, VEd is the upward pressure from the soil minus the self weight of the base within the perimeter. deff = (dy + dz)/2 where dy and dz are the effective depths in orthogonal directions.

Determine value of vRd,max vRd,max is related to concrete strength - refer to Table 7

Determine value of vEd,max (design shear stress at face of column) from: vEd,max = (VEd - VEd) (ui.deff) where ui is perimeter of column

No shear reinforcement required. Check complete

Has the critical perimeter been established?

No

Yes

Repeat for a range of perimeters.

Expression 6.50 from code. ly.lz are the reinforcement ratios in two orthogonal directions for fully bonded tension steel, taken over a width equal to column width plus 3d each side.


Rules for spacing and quantity of reinforcement Minimum area of principal reinforcement The minimum area of reinforcement is As,min = 0.26 fctm bt d/fyk but not less than 0.0013bt.d

Maximum area of reinforcement The maximum area of tension or compression reinforcement, outside lap locations should not exceed As,max = 0.04 Ac

Minimum spacing of reinforcement The minimum spacing of bars should be the greater of:

Bar diameter Aggregate size plus 5 mm 20 mm

Further Guidance xxxxx

References

1 BRITISH STANDARDS INSTITUTION Eurocode 7: Geotechnical Design. BS EN 1997, 2005 2 BRITISH STANDARDS INSTITUTION Code of Practice for Site Investigation. BS 5930, 1999 3 BRITISH STANDARDS INSTITUTION Code of Practice for Earth Retaining Structures. BS 8002, 1994 4 BRITISH STANDARDS INSTITUTION Code of Practice for Foundations. BS 8004, 1986 5 THE CONCRETE CENTRE How to use Eurocode 2: Introduction, 2005 6 THE CONCRETE CENTRE How to use Eurocode 2: Beams, 2005 7 THE CONCRETE CENTRE Spreadsheets for Eurocode 2, 2005

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