Bridge Abutment Design

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D

ESIGN

II

LLUSTRATION

_–

B

RIDGE

A

BUTMENT

D

ESIGN

T Christie,

T Christie, Parsons Brinckerhoff, Bristol, UKParsons Brinckerhoff, Bristol, UK M Glendinning,

M Glendinning, Parsons Brinckerhoff, Cardiff, UKParsons Brinckerhoff, Cardiff, UK J Bennetts,

J Bennetts, Parsons Brinckerhoff, Bristol, UKParsons Brinckerhoff, Bristol, UK S Denton,

S Denton, Parsons Brinckerhoff, Bristol, UKParsons Brinckerhoff, Bristol, UK

Abstract

This paper provides a calculation showing how the heel l

This paper provides a calculation showing how the heel l ength and overall length of the ength and overall length of the basebase slab of a conventional cantilever gravity abutment can be

slab of a conventional cantilever gravity abutment can be determined in accordance with thedetermined in accordance with the requirements of the

requirements of the Eurocodes and relevant non-contradictory informationEurocodes and relevant non-contradictory information[1],[2],[3],[4],[5],[6][1],[2],[3],[4],[5],[6].. Sliding resistance, bearing resistance and overturning stability

Sliding resistance, bearing resistance and overturning stability are all are all considered.considered. The calculations illustrate the requirements of the

The calculations illustrate the requirements of the Eurocodes in regard to loading, partialEurocodes in regard to loading, partial factors, combination of actions and other issues which require

factors, combination of actions and other issues which require a somewhat different approacha somewhat different approach from that used with

from that used with pre-Eurocode designspre-Eurocode designs..

Notation

The symbols us

The symbols used in the calculations are as for the Euroced in the calculations are as for the Eurocode and PD 6694-1. ode and PD 6694-1. Other symbolsOther symbols are defined in the text of the calculations or identified in

are defined in the text of the calculations or identified in the Figure 1.the Figure 1.

The Design Problem

An 8m high, 12m wide abutme

An 8m high, 12m wide abutment of a multispan continuous bridgnt of a multispan continuous bridge is shown in Figure 1. e is shown in Figure 1. It isIt is required to determine the heel length (

required to determine the heel length ( B Bheelheel) and the overall base length () and the overall base length ( B B) of this abutment) of this abutment

necessary to satisfy the requirements of sliding resistance, bearing resistance and overturning necessary to satisfy the requirements of sliding resistance, bearing resistance and overturning stability specified in the Euroc

stability specified in the Eurocodes. odes. The abutment is subject to three notionaThe abutment is subject to three notional 3m wide lanesl 3m wide lanes of traffic surcharge.

of traffic surcharge.

The characteristic actions and soil parameters applied to the

The characteristic actions and soil parameters applied to the abutment are as follows:abutment are as follows: Permanent actions

Permanent actions Weight

Weight of of steel steel beams beams 50 50 kN/mkN/m

Weight

Weight of of concrete concrete deck deck 72 72 kN/mkN/m

Weight

Weight of of surfacing surfacing 36 36 kN/mkN/m

Actions for traffic group gr2 Actions for traffic group gr2 Maximum vertical traffic reaction

Maximum vertical traffic reaction V V traffictraffic 100 100 kN/mkN/m

Uplift due to traffic on adjacent span

Uplift due to traffic on adjacent span U U traffictraffic 30 30 kN/mkN/m

Braking and acceleration action

Braking and acceleration action H H brakingbraking 50 50 kN/mkN/m

UDL surcharge (from PD 6694-1 Table 5)

UDL surcharge (from PD 6694-1 Table 5)   hh 20K20Kaa kN/m²kN/m²

Line load surcharge (from PD

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Soil parameters: Granular backfill

Weight density γbf 18 kN/m²

Angle of shearing resistance  ' bf 35



Clay foundations

Weight density  18 kN/m²

Undrained shear strength cu 100 kN/m²

Angle of shearing resistance  ' 27



Critical state angle of shearing resistance  ' cv 23



Overburden pressure (q) =γbf x Z q q 12 kN/m²

The initial dimensions of the foundations are to be based on traffic load group gr2 in which the characteristic value of the multi-component action is taken as the frequent value of Load Model 1 in combination with the frequent value of the associated surcharge model, together with the characteristic value of the braking and acceleration action, (see the UK National Annex to BS EN 1991-2:2003, NA.2.34.2).

Wind is not required to be considered in combination with traffic model gr2 and thermal actions are not considered to be significant and are therefore neglected in these preliminary calculations.

The water table is well below foundation level and need not be considered, but it is r equired to check sliding resistance and bearing resistance at STR/GEO for both the drained and the undrained condition.

As no explicit settlement calculation is to be carried out at SLS it is required to be

demonstrated that a sufficiently low fraction of the ground strength is mobilised (see BS EN 1997-1:2004, 2.4.8(4)). This requirement will be deemed to be satisfied if the maximum pressure at SLS does not exceed one third of the characteristic resistance (see PD 6694-1, 5.2.2).

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Transverse Dimensions Abutment width W abut= 12m

Notional lane widths W lane= 3m

The traffic on the third notional lane is subject to a 0.5 lane factor so that the effective number of lanes N lane

used in the surcharge calculation is 2.5 (see UK

National Annex to BS EN 1991-2:2003, NA 2.34.2)

Figure 1. Base slab design for a gravity cantilever bridge abutment

Methodology for Preliminary Design

Calculations are carried out "in parallel" for the SLS characteristic combination of actions and for STR/GEO Combinations 1 and 2, using Design Approach 1 (see BS EN 1997-1:2004, 2.4.7.3.4.2). Partial factors on actions are taken from the UK National Annex to BS EN 1990:2002, Table NA.A2.4 (B) and (C), partial factors for soil parameters are from the UK National Annex to BS EN 1997-1:2004, Table A.NA.A.4 andψ factors from the UK National

Annex to BS EN 1990:2002, Table NA.A2.1. The preliminary calculations are carried out on a "metre strip" basis

The following procedure was used for the preliminary design:

1. Calculations were carried out "in parallel" for the SLS characteristic combination and for STR/GEO Combinations 1 and 2. This allowed a side-by-side comparison of the three limit states to be made and repetitive calculations to be minimised.

2. The following actions were calculated:

(a) The total horizontal action on the wall ( H ) due to active earth pressure, traffic surcharge (factored byψ 1) and braking and acceleration (see Table 1).

.

(b) The minimum vertical reaction due to deck reaction (V DL;inf ) and uplift caused by

traffic on remote spans (U ) (see Table 2).

(c) The maximum vertical reaction due to the weight of the deck and traffic (see Table 3). Bheel B Z Y= 1.5 Z q X=0.25 P

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(d) The vertical pressure exerted by the backfill and the base slab (γbf Z ). (For

convenience in these preliminary calculations, the density of the concrete in the base slab and abutment wall was considered to be the same as the density of the backfill (γbf )).

3. The length of the heel ( Bheel) required to provide enough weight to resist sliding for the

drained foundation was found as follows:

The sliding resistance due to the weight of the deck less traffic uplift ( Rvx) was taken

as (V DL;inf - U )tan ' cv. The required sliding resistance due to the weight of the backfill

and abutment was therefore H - Rvx. The weight of the abutment and backfill required

to provide this resistance was therefore equal to ( H - Rvx)/ tan ' cv and this had to equal

Bheelγbf Z . The required value of Bheel therefore equalled ( H - Rvx)/(γbf Ztan ' cv) and this

equals ( H - Rvx)/( μγbf Z ) as in Table 2.

4. As it was recognised that the loads on the toe and the use of the correct density of concrete would increase the sliding resistance, the selected figure of Bheelin Table 2 was taken as

slightly less than the figure of Bheelobtained from the calculation.

5. For undrained foundations the total overall base length for sliding, ( B1) was taken as H d / cu;d

as in Table 2 (see BS EN 1997-1:2004, Equation 6a).

6. The required overall base length is also dependent on other factors such as the requirement to keep the load within the middle third at SLS and within the middle two-thirds at ULS, the bearing resistance for the drained and undrained condition and in some circumstances

(although not for this structure) for resistance to overturning. In all these calculations the eccentricity of the vertical action is required. To obtain this it is convenient to take moments about the back of the heel (point P on Figure 1) rather than the centre of the base, because the bearing resistance calculations are iterative, but the moments about the back of the heel do not alter with varying toe lengths, provided the value of Bheelis not changed. This allows multiple

iterations to be carried out with minimal change to the data.

7. Moments about P were calculated (see Tables 4 and 5). The distance of the line of action from P is eheel, where eheel= M/V and M is the total moment about P and V is the total vertical

load. It can be shown that to satisfy the SLS middle third condition (see PD 6694-1, 5.2.2), the overall base length ( B2) must be 1.5 eheel, and to satisfy the ULS middle two-thirds

condition (see BS EN 1997-1:2004, 6.5.4), the overall base length ( B3) must be 1.2 eheel(see

Table 5).

8. To determine the overall base length ( B) required to provide adequate bearing resistance for the undrained and drained conditions, an iterative calculation with increasing values of B was carried out, starting with the maximum value of the base length found from the sliding

calculations (i.e the largest of B1, B2, or B3) and increasing progressively until the bearing resistance for the undrained and drained conditions drained and the toe pressure limitation at SLS were all satisfied.

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9. The selected value of B and the calculations in Table 6 and 7 are based on the final iteration, that is the minimum value of B necessary to satisfy the bearing resistance

requirements. The calculations largely replicate the equations given in BS EN 1997-1:2004, Annex D.

Notes



The abutment is assumed to be transversely stiff and so the traffic loads can be distributed over the whole width of the abutment (see PD 6694-1, Table 5 Note C)



For convenience in the preliminary design, the density of the concrete in the base slab and wall is considered to be the same as the density of the backfill (  bf ).



It should be noted that the same partial factor  Gis applied to the vertical and

horizontal earth pressure actions (see PD 6694-1, 4.6). This is only likely to be

relevant in a sliding resistance calculation if STR/GEO Combination 1 is more critical than Combination 2.



In these calculations a model factor,  Sd;k = 1.2 has been applied to the horizontal earth

pressure at ULS in order to maintain a similar level of reliability to previous practice (see PD 6694-1, 4.7).



In Tables 1 to 7 the figures given in the SLS column are the characteristic values of material properties and dimensions and the characteristic or representative values of actions per metre width. The figures in the STR/GEO columns are the design values unless otherwise indicated.

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Horizontal actions SLS STR/GEO Comb. 1 Comb. 2 Height of abutment Z Z 8.00 8.00 8.00 m

Partial factor on soil weight  G;sup 1.00 1.35 1.00

Backfill density = γbf;k  G;sup  bf,d 18.0 24.3 18.0 kN/m3

 ' bf;k = 35



; Partial factor  M on tan( ' bf;k )  M 1.00 1.00 1.25

tan-1(tan( ' bf;k )/  M ) =  ' bf;d  ' bf;d 35.0 35.0 29.3

Active pressure coefficient K aincl. ( M )

(1-sin ' bf;d )/(1+sin bf;d ) K a 0.27 0.27 0.34

Model factor  Sd:K  Sd:K 1.00 1.20 1.20

Design active pressure action

 bf;d K a Sd;K Z² /2 = H ap;d H ap;d 156 253 237 kN/m

Surcharge UDL =  hW lane N lane / W abut

= (20K a) x 3 x 2.5/12 =  h;ave  h;ave 3.39 3.39 4.29 kN/m2

Surcharge UDL action  h;avex Z = H sc;udl H sc;udl 27.1 27.1 34.3 kN/m

Surcharge Line Load/m = F K a N lane / W abut

= 2 x 330K ax 2.5/12 = H sc;F

H sc;F 37.3 37.3 47.2 kN/m

Combined surcharge/m H sc;udl+ H sc;F =

H sc;comb H sc;comb 64.4 64.4 81.6 kN/m

Partial factor on surcharge γQ γQ 1.00 1.35 1.15

 1 = 0.75 for surcharge in traffic group grp2  1 0.75 0.75 0.75

Design surcharge = H sc;d = H sc;comb.ψ.γQ H sc;d 48.3 65.2 70.4 kN/m

Characteristic braking action H braking;k H braking;k 50.0 50.0 50.0 kN/m

Partial factor on braking  Q  Q 1.00 1.35 1.15

Braking action /m H braking:d = H braking;k  Q H braking;d 50.0 67.5 57.5 kN/m

TOTAL DESIGN HORIZONTAL

ACTION H d = H ap;d + H sc;d + H braking;d H d 254 386 365 kN/m

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Minimum vertical actions and sliding resistance SLS STR/GEO Comb. 1 Comb. 2 Height of abutment Z Z 8.00 8.00 8.00 m

Characteristic deck weight 50+72+36 = 158 V DL;k 158 158 158 kN/m

Inferior partial factor on deck weight  G;inf 1.00 0.95 1.00

Inferior weight of deck V DL;inf;d 158 150 158 kN/m

Uplift from traffic U k 30.0 30.0 30.0 kN/m

Superior partial factor on uplift  Q;sup 1.00 1.35 1.15

 1= 0.75 for vertical traffic actions in traffic

group grp2  1 0.75 0.75 0.75

Factored uplift from traffic U k. Q = U d U d 22.5 30.4 25.9 kN/m

Minimum vertical loads from deck and

traffic V x;d = V DL;inf;d

–

U d V x;d 136 120 132 kN/m

 ' cv;k = 23



; Partial factor  M on tan( ' cv;k )  M 1.00 1.00 1.25

Coefficient of friction tan( ' cv;k )/  M =  d  d 0.42 0.42 0.34

Sliding resistance due to Vx  d .V x;d = Rvx;d Rvx;d 57.5 50.8 44.9 kN/m

Horizontal action from Table 1, H d H d 254 386 365 kN/m

Reqd resistance from backfill [ H d

–

Rvx;d ] Rreq 197 335 320 kN/m

Density of backfill (Table 1)  bf;d  b;df 18.0 24.3 18.0 kN/m3

Frictional shear stress due to backfill: [ d  bf;d

Z ] 61.1 82.5 48.9 kN/m2

Required Bheel= Rreq / ( d  bf;d Z ) Bheel;req 3.22 4.06 6.55 m

SELECTED VALUE OF HEEL B heel

Rounded down, see Methodology para. (4) B heel 6.25 6.25 6.25 m

cu;k = 100; Partial factor  M on cu;k  cu 1 1 1.4

Undrained shear strength cu:d = cu;k /  cu cu:d 100.0 100.0 71.4 kN/m2

OVERALL BASE LENGTH B1 = H d /cu;d B1 2.54 3.86 5.11 m

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Maximum vertical actions SLS STR/GEO Comb. 1 Comb. 2 Height of abutment Z Z 8.00 8.00 8.00 m

Selected value of Bheel (Table 2) Bheel 6.25 6.25 6.25 m

Partial factor on steelwork  G;sup  G;sup 1.00 1.20 1.00

Weight of steelwork = 50 G;sup 50.0 60.0 50.0 kN/m3

Partial factor on concrete  G;sup  G;sup 1.00 1.35 1.00

Weight of concrete = 72 G;sup 72.0 97.2 72.0 kN/m3

Partial factor on surfacing  G;sup  G;sup 1.00 1.20 1.00

Weight of surfacing = 36 G;sup 36.0 43.2 36.0 kN/m3

Superior weight of deck/m V DL;sup;d V DL;sup;d 158 200 158 kN/m

Characteristic vertical action from traffic

V traffic;k V traffic;k 100.0 100.0 100.0 kN/m

Partial factor on traffic  Q  Q 1.00 1.35 1.15

 1 = 0.75 for vertical traffic actions in traffic

group grp2  1 0.75 0.75 0.75

Design traffic action/m

V traffic;d =V traffic;k  Q  V traffic;d 75.0 101 86.3 kN/m

Density of backfill  bf;d (Table 1)  bf;d 18.0 24.3 18.0 kN/m3

Selected width of heel Bheel (Table 2) Bheel 6.25 6.25 6.25 m

Design weight of backfill/m

V bf;d = V bf;d 900 1215 900 kN/m

TOTAL MAXIMUM VERTICAL LOAD

V max;d = V DL;sup;d + V traffic;d + V bf;d V max;d 1133 1517 1144 kN/m

Table 3. Maximum vertical actions

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Moments about the underside of the base

due to horizontal actions SLS

STR/GEO Comb.

1

Comb. 2 Active Pressure action H ap;d including  Sd;K

(Table 1) H ap;d 156 253 237 kN/m

Lever arm = Z /3 2.67 2.67 2.67 m

Active Moment M ap;d = H ap;d Z/3 M ap;d 416 674 633 kNm

Surcharge UDL action H sc;udl (Table 1) H sc;udl 27.1 27.1 34.3 kN/m

Lever arm = Z /2 4.00 4.00 4.00 m

H sc;udl x Z /2 = M sc;udl M sc;udl 108 108 137 kNm

Surcharge Line Load H sc;F (Table 1) H sc;F 37.3 37.3 47.2 kN/m

Lever arm = Z Z 8.00 8.00 8.00 m

H sc;F Z = M sc;F M sc;F 298 298 378 kNm

Combined surcharge moment M sc;udl + M sc;F M sc;comb 406 406 515 kNm

 Qfor surcharge  Q 1.00 1.35 1.15

 1 = 0.75 for surcharge in traffic group grp2  1 0.75 0.75 0.75

Design surcharge moment M sc;comb Q 1 M sc;d 305 412 444 kNm

Braking action/m H braking;d (Table 1) H braking;d 50.0 67.5 57.5 kN/m

Lever arm for braking ( Z -Y ) = La;b = 8 - 1.5 La;b 6.50 6.50 6.50 m

Braking moment M braking;d = H braking;d x La;b M brakin ;d 325 439 374 kNm

MOMENT DUE TO HORIZONTAL ACTIONS,

M hor;d = M ap;d + M sc;d + M braking;d M hor;d 1046 1525 1451 kNm

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Moments about the back of the heel SLS STR/GEO Comb. 1 Comb. 2

Width of heel Bheel Bheel 6.25 6.25 6.25 m

Distance of deck reactions

behind front of wall X X 0.25 0.25 0.25 m

La;deck = Bheel- X La;deck 6.00 6.00 6.00 m

Superior weight of deck V DL;sup;d (Table 3) V DL;sup;d 158 200 158 kN/m

Deck Moment V DL;sup;d La;deck = M deck;d M deck;d 948 1202 948 kNm

Traffic Load V traffic;d (Table 3) V traffic;d 75.0 101 86.3 kN/m

Traffic Moment V traffic;d La;deck = M traffic;d M traffic;d 450 608 518 kN/m

Weight of backfill V bf;d (Table 2) V bf;d 900 1215 900 kNm

Backfill moment V bf;d Bheel /2 = M bf;d M bf;d 2813 3797 2813 kN/m

Total Moment about heel due to vertical

actions M vert;d = M deck;d + M traffic;d + M bf;d M vert;d 4211 5607 4278 kNm

Moment about base due to horizontal

Actions (Table 4) M hor;d 1046 1525 1451 kNm

Total design moment about heel

M vert;d + M hor;d = M heel;d M heel;d 5257 7131 5729 kNm

Total vertical load V d (Table 3) V d 1133 1517 1144 kN/m

Line of action in front of heel eheel

= M heel/ V eheel 4.64 4.70 5.01 m

Total length B2 required for middle third at

SLS = 1.5 eheel(see PD 6694-1 5.2.2) B2 6.96 m

Total length B3 for middle two thirds at ULS

= 1.2 eheel(see BS EN 1997-1 6.5.4) B3 5.64 6.01 m

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Bearing Resistance

_–

undrained foundation SLS STR/GEO Comb. 1 Comb. 2 Geometry of foundation (m)

Final B (found iteratively) B 8.60 8.60 8.60 m

Heel length Bheel (Table 2) Bheel 6.25 6.25 6.25 m

Transverse width of foundation L L 12.0 12.0 12.0 m

Inclination   0o 0o 0o Partial factors  F applied to   G 1.00 0.95 1.00  M applied to tan   1.00 1.00 1.25  M applied to cu  cu 1.00 1.00 1.40



Mapplied to c  c 1.00 1.00 1.00

Properties of foundation material

Weight density  d (including  G)  d 18.0 17.1 18.0 kN/m3

Angle of shearing resistance  d  d 27.0 27.0 22.2

Cohesion intercept c d c d 0 0 0

Undrained shear strength cu;d cu;d 100.0 100.0 71.4 kN/m2

Applied action

Horizontal actions H d (Table 1) H d 254 386 365 kN/m

Vertical action V d (Table 3) V d 1133 1517 1144 kN/m

Moment about P = M heel;d (Table 4) M heel;d 5257 7131 5729 kNm/m

M heel;d / V = eheel eheel 4.64 4.70 5.01 m

Eccentricity about centre line e = eheel- B /2 e 0.34 0.40 0.71 m

Overburden pressure qd 12.0 12.0 12.0 kN/m2

Effective foundation dimensions (m)

Effective foundation breadth B = B-2e B 7.92 7.80 7.19 m

Effective area for 1m strip design A = B A 7.92 7.80 7.19 m2

Effective transverse width L = L L 12.0 12.0 12.0 m

Undrained bearing resistance (Annex D to BS EN 1997-1 D.3) Bearing parameters for undrained foundations

bc=1-2 /(



+2) bc 1.00 1.00 1.00

sc = 1+0.2( B / L ) sc 1.13 1.13 1.12

ic= ½{1+



(1- H d / A cu;d )} ic 0.91 0.86 0.77

R/A



= (



+2)cu;d bcscic+ qd R/A 543 509 328 kN/m2

V d / A



V d /A 143 195 159 kN/m2 Ratio R/V R / V d 3.79 2.62 2.06 Settlement check Not critical (see Table 7) 1/3( R/A



) at SLS characteristic 181 kN/m2

Max toe pressure (1+6e / B)V d / B 163 kN/m2

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Bearing Resistance

_–

drained foundation SLS STR/GEO Comb. 1 Comb. 2 Effective foundation dimensions

B from Table 6 B 7.92 7.80 7.19 m

L from Table 6 L 12.0 12.0 12.0 m

A per metre width from Table 6 A 7.92 7.80 7.19 m2

Other geometry, partial factors, foundation properties and actions are as Table 6

Bearing parameters for drained foundations

N q= etandtan2 (45+ d /2) N q 13.2 13.2 7.96

N c= ( N q-1)cot  d N c 23.9 23.9 17.1

N  = 2 ( N q-1) tan  , where 



 /2 (rough

base) N  12.4 12.4 5.68

bc= bq

–

(1-bq)/ N ctan  d bc 1.00 1.00 1.00

bq= b = (1 -  tan  d ) bq , b 1.00 1.00 1.00

sq = 1 + ( B / L ) sin  d , for a rectangular

shape sq 1.30 1.29 1.23

s = 1

–

0.3 ( B / L ), for a rectangular shape; s 0.80 0.81 0.82

sc = (sqN q

–

1)/( N q

–

1) for rectangular,

square or circular shape sc 1.32 1.32 1.26

m = (2+ B / L )/(1+ B / L ) m 1.60 1.61 1.63

iq= [1

–

H /(V + A c d cot  d )]m iq 0.67 0.62 0.54

ic= iq

–

(1

–

iq)/ N ctan  d ic 0.64 0.59 0.47

i = [1

–

H /(V + A c dcot  d)]m+1 i 0.52 0.47 0.36

R/A = (Equation from BS EN 1997-1 D.4)

c



d N cbcscic 0.00 0.00 0.00

qd N q bq sqiq 137 128 62.7

0.5



d B



N  bsi 367 311 110

R / A



= sum of above R/A 504 439 172 kN/m2

V d / A V d /A 143 195 159 kN/m

Ratio R/V R / V d 3.52 2.25 1.08

Resistance to limit settlement at SLS

1/3 ( R/A



) at SLS characteristic 168 Limits kN/m2

Max toe pressure (1+6e/B) V d / B 163 satisfied kN/m2

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Final Design

After the preliminary design has been completed a final design should be carried out as given below:

1. Select the final dimensions based on the preliminary values: Bheel = 6.25m and B = 8.6m.

As the weight on the toe has not been included in the preliminary design, Bheel has been

"rounded down" and the overall length (B) may need to be "rounded up".

2. The final selected base slab dimensions should be verified using the correct concrete densities, the loads on the toe and other relevant combinations of actions.

Details of the final design calculations are not included in this paper.

Conclusions

It is difficult to generalise about which combination of actions or which limit states are critical on the basis of calculations for a single bridge because the critical combination is often

determined by the ratio of the bridge span to the abutment height or the ratio of traffic action to the soil actions. It is however clear that horizontal earth pressures are generally critical for

STR/GEO Combination 1 regardless of the bridge proportions because  G for soil is higher

than K a;d / K a;k for most realistic values of  ' . Also, for undrained sliding resistance

Combination 2 is always likely to be critical because  M on cu is higher than K a;d / K a;k for all

realistic values of  ' , and it is also higher than  Qon surcharge braking and acceleration.

For drained sliding resistance, in the calculations presented in this paper, Combination 2 was more critical than Combination 1, primarily because the effects of  G on the weight of soil

were favourable for sliding resistance and unfavourable for horizontal pressure and therefore, to some extent, cancelled each other out in Combination 1. It was however apparent from the calculations that Combination 1 could be critical for sliding for low abutments supporting long spans where braking and acceleration actions were large and earth pressures were small. For bearing pressure, Combination 2 was found to be significantly more critical than

Combination 1 for both drained and undrained foundations and as  Meffects tend to

predominate in bearing resistance calculations it seems probable that Combination 2 will be critical for bearing resistance in most typical abutments and retaining walls. It was also

apparent from supporting calculations that the limitation on toe pressure at SLS is quite severe and that in many cases where it is required to be applied, it will dictate the length of the base. Additional explicit settlement calculations may therefore result in shorter base lengths being required.

Overturning was not found to be an issue for the abutment illustrated in this paper and

although it needs to be verified, it appears that it is unlikely to affect the proportions of typical gravity abutments as bearing failure under the toe would normally precede overturning.

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References

[1] PD 6694-1 Recommendations for the design of structures subject to traffic loading to BS EN 1997-1: 2004, BSi, London, UK

[2] BS EN 1990:2002+A1:2005 Eurocode - Basis of structural design Incorporating corrigenda December 2008 and April 2010, BSi, London, UK

[3] BS EN 1991-2:2003 Eurocode 1: Actions on structures – Part 2: Traffic loads on

bridges, Incorporating Corrigenda December 2004 and February 2010 , BSi, London, UK

[4] BS EN 1997-1:2004 Eurocode 7: Geotechnical design – Part 1: General rules,

Incorporating corrigendum February 2009, BSi, London, UK

[5] NA to BS EN 1990:2002+A1:2005 UK National Annex for Eurocode – Basis of

structural design, Incorporating National Amendment No.1 , BSi, London, UK

[6] NA to BS EN 1991-2:2003 UK National Annex to Eurocode 1: Actions on structures –