Bridge Abutment Design

T Christie, M Glendinning, J Bennetts, S Denton 1

DESIGN ILLUSTRATION  – BRIDGE ABUTMENT DESIGN

T Christie, Parsons Brinckerhoff, Bristol, UK M Glendinning, Parsons Brinckerhoff, Cardiff, UK J Bennetts, Parsons Brinckerhoff, Bristol, UK S Denton, Parsons Brinckerhoff, Bristol, UK

Abstract This paper provides a calculation showing how the heel l ength and overall length of the base slab of a conventional cantilever gravity abutment can be determined in accordance with the [1],[2],[3],[4],[5],[6] requirements of the Eurocodes and relevant non-contradictory information . Sliding resistance, bearing resistance and overturning stability are all considered. The calculations illustrate the requirements of the Eurocodes in regard to loading, partial factors, combination of actions and other issues which require a somewhat different approach from that used with pre-Eurocode designs. designs.

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

The Design Problem An 8m high, 12m wide abutment abutment of a multispan continuous bridge bridge is shown in Figure 1. It is required to determine the heel length ( Bheel) and the overall base length ( B) of this abutment necessary to satisfy the requirements of sliding resistance, bearing resistance and overturning stability specified in the Eurocodes. Eurocodes. The abutment is subject to three notional notional 3m wide lanes of traffic surcharge. The characteristic actions and soil parameters applied to the abutment are as follows: Permanent actions Weight of steel beams Weight of concrete deck Weight of surfacing Actions for traffic group gr2 Maximum vertical traffic reaction Uplift due to traffic on adjacent span Braking and acceleration action UDL surcharge (from PD 6694-1 Table 5) Line load surcharge (from PD 6694-1 Table 5)

50 72 36

V traffic 100 traffic U traffic 30 traffic  H braking 50 braking  h 20Ka F  2 x 330 K a

kN/m kN/m kN/m

kN/m kN/m kN/m kN/m² kN/lane

T Christie, M Glendinning, J Bennetts, S Denton 2

Soil parameters: Granular backfill Weight density Angle of shearing resistance Clay foundations Weight density Undrained shear strength Angle of shearing resistance Critical state angle of shearing resistance Overburden pressure ( q) = γbf  x  Z q

kN/m²

 ' bf 

18 35

  cu  '   ' cv q

18 100 27 23 12

kN/m² kN/m²

γbf 

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).

T Christie, M Glendinning, J Bennetts, S Denton 3

Transverse Dimensions

Abutment width W abut = 12m

Y= 1.5

Notional lane widths W lane = 3m  X=0.25

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 19912:2003, NA 2.34.2 )

 Z 

 Z q P  Bheel  B

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 and ψ  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 by ψ 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).

T Christie, M Glendinning, J Bennetts, S Denton 4

(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  Bheel in Table 2 was taken as slightly less than the figure of  Bheel obtained 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 t han 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  Bheel is 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.

T Christie, M Glendinning, J Bennetts, S Denton 5

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  G is 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.

T Christie, M Glendinning, J Bennetts, S Denton 6

Horizontal actions

SLS

Height of abutment  Z 

STR/GEO Comb. Comb. 1 2

 Z 

8.00

8.00

8.00

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

  M 

1.00

1.00

1.25

 ' bf;d 

35.0

35.0

29.3

 K  a

0.27

0.27

0.34

 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 / Wa  but  = (20K a) x 3 x 2.5/12 =  h;ave

 h;ave

3.39

3.39

4.29

kN/m

 H sc;udl

27.1

27.1

34.3

kN/m

 H sc;F 

37.3

37.3

47.2

kN/m

 H sc;comb

64.4

64.4

81.6

kN/m

γQ

1.00

1.35

1.15

 1

0.75

0.75

0.75

 H  sc;d 

48.3

65.2

70.4

kN/m

 H braking;k 

50.0

50.0

50.0

kN/m

 Q

1.00

1.35

1.15

 H  braking;d 

50.0

67.5

57.5

kN/m

 H  d 

254

386

365

kN/m

 ' bf;k  = 35;

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

-1

tan (tan( ' bf;k )/  M    ) =  ' bf;d  Active pressure coefficient K  a incl. (  M ) (1-sin ' bf;d )/(1+sin bf;d ) Model factor  Sd:K 

Surcharge UDL action  h;ave x Z  = H sc;udl

m

kN/m

Surcharge Line Load/m = F K a N lane / W abut  = 2 x 330K a x 2.5/12 =  H sc;F  Combined surcharge/m  H sc;udl + H sc;F  =  H sc;comb Partial factor on surcharge

γQ

 1 = 0.75 for surcharge in traffic group grp2 Design surcharge = H sc;d =  H sc;comb.ψ.γQ

Characteristic braking action H braking;k  Partial factor on braking  Q Braking action /m  H braking:d = H braking;k  Q TOTAL DESIGN HORIZONTAL ACTION  H d  = H ap;d  + H sc;d  + H braking;d 

Table 1. Horizontal actions

3

2

T Christie, M Glendinning, J Bennetts, S Denton 7

Minimum vertical actions and sliding resistance

Height of abutment  Z 

SLS

STR/GEO Comb. Comb. 1 2

 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

V  DL;inf;d 

158

150

158

kN/m

U k 

30.0

30.0

30.0

kN/m

 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

  M 

1.00

1.00

1.25

 d 

0.42

0.42

0.34

 Rvx;d 

57.5

50.8

44.9

kN/m

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

 b;df 

18.0

24.3

18.0

kN/m

3

61.1

82.5

48.9

kN/m

2

 Bheel;req

3.22

4.06

6.55

m

 B heel 

6.25

6.25

6.25

m

Inferior weight of deck  Uplift from traffic Superior partial factor on uplift

 ' cv;k  = 23;

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

  =  d  Coefficient of friction tan( ' cv;k )/  M  Sliding resistance due to V x  d .V  x;d  = Rvx;d 

Horizontal action from Table 1,  H d 

Required Bheel= Rreq / ( d   bf;d  Z ) SELECTED VALUE OF HEEL  B heel  Rounded down, see Methodology para. (4)

Partial factor   M  on cu;k 

 cu

1

1

1.4

Undrained shear strength cu:d  = cu;k  / c  u

cu:d 

100.0

100.0

71.4

kN/m

OVERALL BASE LENGTH B1 = H d /c   u;d 

 B1

2.54

3.86

5.11

m

cu;k = 100;

Table 2. Minimum vertical actions and sliding resistance

2

T Christie, M Glendinning, J Bennetts, S Denton 8

Maximum vertical actions

Height of abutment  Z 

SLS

STR/GEO Comb. Comb. 1 2

 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

50.0

60.0

50.0 kN/m

1.00

1.35

1.00

72.0

97.2

72.0 kN/m

1.00

1.20

1.00

36.0

43.2

36.0 kN/m

V  DL;sup;d 

158

200

158 kN/m

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

V  traffic;d 

75.0

101

86.3 kN/m

 bf;d 

18.0

24.3

18.0 kN/m

 Bheel

6.25

6.25

6.25 m

V bf;d 

900

1215

900 kN/m

V  max;d 

1133

1517

1144 kN/m

Weight of steelwork = 50 G;sup Partial factor on concrete  G;sup

 G;sup

Weight of concrete = 72 G;sup Partial factor on surfacing  G;sup

 G;sup

Weight of surfacing = 36 G;sup Superior weight of deck/m V  DL;sup;d 

Characteristic vertical action from traffic V traffic;k 

Design traffic action/m V  traffic;d  =V traffic;k   Q  

Density of backfill  bf;d  (Table 1) Selected width of heel  Bheel (Table 2) Design weight of backfill/m V  bf;d =  bf;d  Z B heel  TOTAL MAXIMUM VERTICAL LOAD V  max;d  = V  DL;sup;d  + V traffic;d + V bf;d 

Table 3. Maximum vertical actions

3

3

3

3

T Christie, M Glendinning, J Bennetts, S Denton 9

Moments about the underside of the base due to horizontal actions

Active Pressure action  H ap;d  including  Sd;K  (Table 1)

SLS

 H ap;d 

Lever arm = Z   /3

STR/GEO Comb. Comb. 1 2

156

253

237

kN/m

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

4.00

4.00

4.00

m

 M sc;udl

108

108

137

kNm

 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

 M sc;comb

406

406

515

kNm

 Q for surcharge

 Q

1.00

1.35

1.15

 1 = 0.75 for surcharge in traffic group grp2

 1

0.75

0.75

0.75

 M  sc;d 

305

412

444

kNm

 H braking;d 

50.0

67.5

57.5

kN/m

 La;b

6.50

6.50

6.50

m

325

439

374

kNm

1046

1525

1451

kNm

Lever arm = Z   /2  H sc;udl x Z   /2 = M sc;udl

Surcharge Line Load  H sc;F  (Table 1)

Combined surcharge moment  M sc;udl + M sc;F 

Design surcharge moment  M sc;comb Q 1

Braking action/m H braking;d  (Table 1) Lever arm for braking ( Z -Y ) = La;b = 8 - 1.5 Braking moment M  braking;d  = H braking;d x La;b MOMENT DUE TO HORIZONTAL ACTIONS,  M  hor;d  = M ap;d  + M sc;d  + M braking;d 

 M  brakin

;d 

 M  hor;d 

Table 4. Moments about the underside of the base due to horizontal actions

T Christie, M Glendinning, J Bennetts, S Denton10

Moments about the back of the heel

Width of heel Bheel

SLS

STR/GEO Comb. Comb. 1 2

 Bheel

6.25

6.25

6.25

m

 X 

0.25

0.25

0.25

m

La;deck 

6.00

6.00

6.00

m

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

 M traffic;d 

450

608

518

kN/m

V bf;d 

900

1215

900

kNm

 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

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

Total length B3 for middle two thirds at ULS = 1.2 eheel (see BS EN 1997-1 6.5.4)

 B3

Distance of deck reactions behind front of wall X   La;deck  = Bheel - X

Superior weight of deck  V  DL;sup;d  (Table 3)

Traffic Moment V traffic;d  La;deck  = M traffic;d  Weight of backfill V bf;d  (Table 2) Backfill moment V bf;d  Bheel /2 = M bf;d 

Total vertical load V d  (Table 3)

m

5.64

6.01

Table 5. Moments about the back of the heel (Position P on Figure 1)

m

T Christie, M Glendinning, J Bennetts, S Denton11

Bearing Resistance  –  undrained foundation Geometry of foundation (m) Final B (found iteratively) Heel length Bheel (Table 2) Transverse width of foundation  L Inclination   Partial factors  F  applied to     M applied to tan    M applied to cu M applied to c  Properties of foundation material Weight density  d  (including  G) Angle of shearing resistance  d  Cohesion intercept c d  Undrained shear strength cu;d  Applied action Horizontal actions H d  (Table 1) Vertical action V d  (Table 3) Moment about P = M heel;d  (Table 4)  M heel;d  / V = eheel Eccentricity about centre line e = eheel - B /2 Overburden pressure Effective foundation dimensions (m) Effective foundation breadth B = B-2e Effective area for 1m strip design  A = B  Effective transverse width  L = L Undrained bearing resistance (Annex D to BS EN 1997-1 D.3) Bearing parameters for undrained foundations bc = 1-2   /(+2) sc = 1+0.2( B  /   L ) ic = ½{1+(1- H d /    A cu;d )}  R/A = (+2)cu;d bc sc ic + qd  V d /     A Ratio R/V  Settlement check 1/3( R/A) at SLS characteristic

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

SLS

 B

STR/GEO Comb. Comb. 1 2

m m m

 Bheel  L  

8.60 6.25 12.0 o 0

8.60 6.25 12.0 o 0

8.60 6.25 12.0 o 0

 G     cu  c 

1.00 1.00 1.00 1.00

0.95 1.00 1.00 1.00

1.00 1.25 1.40 1.00

 d   d  c d  cu;d 

18.0 27.0 0 100.0

17.1 27.0 0 100.0

18.0 22.2 0 71.4

kN/m

 H d  V d   M heel;d  eheel e qd 

254 1133 5257 4.64 0.34 12.0

386 1517 7131 4.70 0.40 12.0

365 1144 5729 5.01 0.71 12.0

kN/m kN/m kNm/m m m 2 kN/m

 B   A   L 

7.92 7.92 12.0

7.80 7.80 12.0

7.19 7.19 12.0

m 2 m m

bc sc ic  R/A  V d /A      R / V  d 

1.00 1.13 0.91 543 143 3.79

1.00 1.13 0.86 509 195 2.62

1.00 1.12 0.77 328 159 2.06

181

Not critical (see Table 7)

163

Table 6. Bearing Resistance – undrained foundation

3

2

kN/m

2

kN/m 2 kN/m

2

kN/m

2

kN/m

T Christie, M Glendinning, J Bennetts, S Denton12

Bearing Resistance  –  drained foundation

SLS

STR/GEO Comb. Comb. 1 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 Other geometry, partial factors, foundation properties and actions are as Table 6

 A 

7.92

7.80

7.19

m

 N q

13.2

13.2

7.96

 N c

23.9

23.9

17.1

 N  

12.4

12.4

5.68

bc

1.00

1.00

1.00

bq , b 

1.00

1.00

1.00

sq

1.30

1.29

1.23

2

Bearing parameters for drained foundations tand

 N q = e

2

tan (45+ d  /2)

 N c = ( N q-1)cot  d   /2 (rough  N   = 2 ( N q-1) tan  , where      base) bc = bq  –  (1-bq)/   N c tan  d  bq = b  = (1 -  tan  d ) sq = 1 + ( B /  L ) sin  d , for a rectangular shape s  = 1  –  0.3 ( B  /   L ), for a rectangular shape; sc = (sq N q  –  1)/( N q –  1) for rectangular, square or circular shape

s 

0.80

0.81

0.82

sc

1.32

1.32

1.26

m = (2+ B  /   L )/(1+ B  /   L )

m

1.60

1.61

1.63

iq

0.67

0.62

0.54

ic

0.64

0.59

0.47

i 

0.52

0.47

0.36

cd N c bc sc ic

0.00

0.00

0.00

qd N q bq sq iq

137

128

62.7

0.5 d B N  b s i

367

311

110

 R/A 

504

439

172

kN/m

V d  /A 

143

195

159

kN/m

 R / V  d 

3.52

2.25

1.08

iq = [1  –  H   /(V + A c d cot  d )]

m

ic = iq  –  (1  –  iq)/   N c tan  d  i = [1  –  H   /(V + A c dcot  d)]

m+1

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

 R /   A = sum of above V d /   A  Ratio R/V 

2

Resistance to limit settlement at SLS 2

1/3 ( R/A) at SLS characteristic

168

Limits

kN/m

 B Max toe pressure (1+6e/B) V d / 

163

satisfied

kN/m

Table 7. Bearing Resistance – drained foundation

2

T Christie, M Glendinning, J Bennetts, S Denton13

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  / Ka  ;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  / Ka  ;k  for all realistic values of  ' , and it is also higher than  Q on 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  M effects 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.

T Christie, M Glendinning, J Bennetts, S Denton14

References [1] [2] [3]

[4] [5] [6]

PD 6694-1 Recommendations for the design of structures subject to traffic loading to  BS EN 1997-1: 2004, BSi, London, UK BS EN 1990:2002+A1:2005 Eurocode - Basis of structural design Incorporating corrigenda December 2008 and April 2010 , BSi, London, UK 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 BS EN 1997-1:2004 Eurocode 7: Geotechnical design  –  Part 1: General rules,  Incorporating corrigendum February 2009 , BSi, London, UK 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 NA to BS EN 1991-2:2003 UK National Annex to Eurocode 1: Actions on structures  –  Part 2: Traffic loads on bridges, Incorporating Corrigendum No. 1 , BSi, London, UK