A comparison of embedded and conventional retaining wall ... · TRANSPORT RESEARCH LABORATORY A comparison of embedded and conventional retaining wall design using Eurocode 7 and

TRANSPORT RESEARCH LABORATORY

A comparison of embedded and conventionalretaining wall design using Eurocode 7 andexisting UK design methods

Prepared for Quality Services (Civil Engineering),Highways Agency

D R Carder

TRL REPORT 320

Transport Research Foundation Group of CompaniesTransport Research Foundation (a company limited by guarantee) trading as TransportResearch Laboratory. Registered in England, Number 3011746.

TRL Limited. Registered in England, Number 3142272.Registered Offices: Old Wokingham Road, Crowthorne, Berkshire, RG45 6AU.

First Published 1998ISSN 0968-4107

Copyright Transport Research Laboratory 1998.

The information contained herein is the property of the TransportResearch Laboratory and does not necessarily reflect the views orpolicies of the customer for whom this report was prepared. Whilstevery effort has been made to ensure that the matter presented in thisreport is relevant, accurate and up-to-date at the time of publication,the Transport Research Laboratory cannot accept any liability for anyerror or omission.

CONTENTS

Page

Executive Summary 1

1 Background 3

Part A: Comparative study for embedded retaining walls 3

2 Introduction 3

3 Ultimate limit state of the soil 3

3.1 Effect of unplanned excavation on wall penetration 4

4 Ultimate limit state of the structural elements 4

5 Serviceability limit state of the structural elements 8

6 Conclusions 11

Part B: Comparative study for reinforced concrete walls 12

7 Introduction 12

8 Factors adopted for limit state design 12

9 Ultimate limit state of the soil 14

10 Ultimate limit state of the structural elements 16

11 Serviceability limit state of the structural elements 16

12 Conclusions 18

Part C: General 19

13 Summary 19

14 Acknowledgements 20

15 References 20

Abstract 21

Related publications 21

iii

iv

1

Executive Summary

The publication of the draft for development of Eurocode 7has given rise to the need for a parametric study comparingdesigns of embedded and conventional retaining walls withthose determined using existing UK design methods. Themethods compared for embedded retaining wall design were:

� EC7 (British Standards Institution, 1995) - draft fordevelopment

� BS8002 (British Standards Institution, 1994)

� BD42 (Design manual for roads and bridges, Volume 2,Section 1) - issued 1994

� CIRIA 104 (Padfield and Mair, 1984)

In addition to the first two of the above design methodswhich were also relevant to conventional construction, thefollowing method was investigated for conventionalretaining wall design:


For this study, design examples of both wall types wereselected which were considered typical of construction onthe national motorway network. Examples for embeddedwalls included both cantilever and walls propped at thetop: L-shaped walls and bridge abutments were consideredfor conventional construction. Sizing of the structures wascarried out by considering the different ultimate limit statemodes of failure and design of the structural elements wasthen established for serviceability and ultimate limit states.The overall designs using the various standards/codes werethen compared to assess their relative merits.

Generally final designs for both embedded andconventional walls were similar when using BS8002 andEC7, although the complexity of EC7 makes its use muchmore difficult and prone to error. Reference should bemade to the report for comparisons between designs usingthe various Departmental Standards and EC7.

Feedback to British Standards Institution on the relativemerits of the draft for development of Eurocode 7 will ensurethat the code is appropriate for UK usage prior to its release.

2

3

1 Background

The publication of the draft for development of Eurocode 7has given rise to the need for a parametric study comparingdesigns of embedded and conventional retaining walls withthose determined using existing UK design methods. In thisreport, design examples of both wall types were selectedwhich were considered typical of construction on thenational motorway network.

In the case of embedded walls, analyses were carried outfor both cantilever and walls propped at the top with aretained height of 7.5m and founded in either cohesionlessor cohesive soil. The design methods employed were:

� EC7 (British Standards Institution, 1995) - draft fordevelopment

� BS8002 (British Standards Institution, 1994)


� CIRIA 104 (Padfield and Mair, 1984)

The design philosophy of the more recent of thesemethods places increasing emphasis on a limit stateapproach with serviceability and ultimate states beingconsidered. For example, EC7 and BS8002 have a limitstate approach with the former using partial factors and thelatter relying mainly on a mobilisation factor on soilstrength. BD42 for embedded walls is also written forcompatibility with limit state principles although it is basedon the lumped factor of safety approach of CIRIA 104.

Conventional wall design was assessed for ‘L-shaped’retaining walls of 2.5m and 7.5m height. The latter resultswere compared with those for a 7.5m high bridge abutmentwhere bridge dead and live loadings were included. Bothcohesionless and cohesive soils were considered as backfillto the structure. In addition to the first three of the abovedesign methods which were also relevant to conventionalconstruction, the following design method was included:


BD30 uses lumped factors of safety when consideringthe serviceability and ultimate limit state of the soil, butemploys partial factors for the limit states of the structuralelements.

Parts A and B of this report contain the comparativestudies for embedded retaining walls and conventionalwalls respectively. Part C contains an overall summary.

Part A: Comparative study for embeddedretaining walls

2 Introduction

A study was undertaken to compare the design ofembedded retaining walls according to CIRIA 104, BD42,BS8002 and EC7. A design example was selected with aretained height of wall (ie. excavation depth in front of thewall) of 7.5m which was typical of that used in highway

schemes. Analyses were carried out both for theunpropped cantilever case and for a wall propped at thetop. Two soils were analysed:

� Granular soil (γ=20kN/m3, c'=0, φ'=30o)

� Cohesive soil (γ=20kN/m3, c'=10kPa, φ'=25o)

The strength values (c',φ') were assumed to be peakvalues from laboratory effective stress testing. In thecohesive case, made ground (c'=0, φ'=30o) to a depth of 1mwas assumed to overlay the clay as this commonly occursin practice and also prevents the development of tensioncracks which are treated slightly differently in the variousdesign methods. The assumption of linear seepage aroundthe wall was used throughout all the analyses. With bothsoil types the most severe condition of a high water tablewas assumed: with the granular soil it was taken at theretained ground surface and in the other case at 1m depthat the granular/cohesive soil interface. In both cases,ground water level was considered to be at excavationlevel in front of the wall.

A uniform surcharge of 10kPa was used on the retainedground as in a highway situation this corresponds to HAloading (BD37, DMRB 1.3) which is a normal requirement. Itmust be noted that BS8002 has a requirement for minimumsurcharge loading of 10kPa of the retained ground and, if HAloading is not required, this will produce a difference in walldesign between the various design methods.

3 Ultimate limit state of the soil

Design for the overall stability of the soil/structure isprimarily used for determining the depth of penetration ofan embedded wall. Comparisons between the requiredpenetrations using different design methods will depend onwhether there is compatibility in the selection of soilparameters. Moderately conservative soil strengthparameters can be used for designs according to CIRIA 104and BD42; these parameters are considered near identical tothe representative or conservative values required byBS8002. Clause 2.4.3 of EC7 defines the characteristic soilstrength value used as a cautious estimate of the mean:Simpson (1994) suggests that in practice this may beessentially similar to the values used in the other designmethods. For the ultimate limit state of the soil, a directcomparison between the penetrations determined bydifferent methods is therefore possible. Table 1 summarisesthe various factors used in the analyses.

Figures 1 and 2 compare the wall penetrations required bythe different design methods for a cantilever wall and wallpropped at the top respectively. Generally the comparisonswere carried out using the wall friction angles of δ

a= 2/3 φ'

design

and δp=½φ'

design recommended by CIRIA 104 (clauses 5.1.2

and 7.3.2) and BD42. However the implications of using thehigher wall friction angles of δ

a=δ

p= 2/3φ'

max permitted under

BS8002 (clause 3.2.6) and δa=δ

p=φ'

design permitted under EC7

(clause 8.5.1) for cast in situ walls are also shown.For the analyses using CIRIA 104 methods the

recommended factors of safety are indicated in Figures 1 and 2.It must be noted however that the overall factor of safety of

4

1.5 adopted for the net total pressure method tends to givethe smallest penetrations as it probably relies on a lessconservative estimate of soil strength parameters (Symonsand Kotera, 1987). For this reason considerable caution isrequired when using this method and BD42 recommendsthat a minimum factor of safety of 2 is employed.

In Figures 1a and 2a for a granular soil (c'=0, φ'=30o), itis useful to compare results from BS8002 and EC7 withthose from the strength factor method when using the samewall friction angles. The mathematics of the analyses arethen similar in using a factor on tanφ' and penetrations forBS8002, EC7 and the strength factor method increase asthis factor changes from 1.2 to 1.25 to 1.5 respectively.

The wall penetrations shown in Figures 1 and 2 aresummarised in Table 2 for granular and cohesive soilsretained by cantilever and propped (at the top) walls. Alsoshown in Table 2 are the depth variances from thepenetration given by BS8002 which has arbitrarily beenselected as the reference. On this basis of the same wallfriction angles, the same surcharge on the retained groundof 10kPa, and no unplanned excavation in front of thewall, the design methods can be arranged in increasingorder of wall penetration as given in Table 3.

Generally it is clear that the net total pressure methodprovides the least penetration and needs to be used withcaution as has been discussed previously. BS8002 tends toreflect the view at the time of writing that retaining walldesign was too conservative and for this reason is the leastconservative of the other methods. EC7 designs provideslightly greater depths of penetration than BS8002. Thestrength factor method of CIRIA 104 was generally themost conservative of the methods in requiring the greatestwall penetrations.

It must be noted that the design methods for cantileverwalls generally assume fixed earth support conditions atthe toe of the wall and an additional penetration may benecessary to ensure this. Guidance on the magnitude ofthis additional penetration is given in CIRIA 104.

3.1 Effect of unplanned excavation on wall penetration

The analyses so far have not taken into account the effectupon the required penetration of any unplanned excavationin front of the wall. BS8002 (clause 3.2.2.2) recommends aminimum depth of unplanned excavation of either 0.5m or10% of the retained wall height, while EC7 (clause 8.3.2.1)gives 10% of the retained height limited to a maximum of0.5m. Figures 3 and 4 evaluate the effect of unplannedexcavation upon the required penetrations for a cantileverwall and wall propped at the top respectively. Figure 3 alsoshows the variation of wall penetration with soil frictionangle for a granular soil, whilst Figure 4 investigates theeffect of changes in soil cohesion for a clay soil.

In Figure 3 the trend of the results is similar in all caseswith a larger wall penetration being needed as the soilstrength decreases. With no unplanned excavation, resultsfrom BS8002 and EC7 are near identical with much smallerpenetrations than required by the strength factor method ofCIRIA 104 which is also employed in BD42. If unplannedexcavation is included, results using BS8002 and EC7 arecloser to those of the strength factor method. Marginallylarger penetrations are then appropriate for designs usingBS8002 as opposed to EC7 because of the slightly largerdepth of unplanned excavation with the former.

Similar conclusions are reached in Figure 4 for a wallpropped at the top and embedded in cohesive soil. Onceagain the results for BS8002 and EC7 which includeunplanned excavations are closer to those of the strengthfactor method (no unplanned excavation). Smalldifferences in penetration arise between BS8002 and EC7because the former uses a factor of 1.2 on c' and the latteruses a factor of 1.6.

4 Ultimate limit state of the structuralelements

The ultimate limit state design of the structural elements wascompared using the respective depths of penetrationdetermined on the basis of linear seepage of water around the

Table 1 Factors used in analysis of ultimate limit state of the soil

CIRIA 104/ BD42

Net total Burland- Strength EC7Soil type CP2 pressure Potts factor BS8002 Case C

Overall factorGranular 2.0 1.5 (2.0) 2.0 1.0 1.0 1.0Cohesive 1.75 1.5 (2.0) 2.0 1.0 1.0 1.0

Factors on tanφ'Granular, 1.0 1.0 1.0 1.5 1.2 1.25φ'=30o φ'

design=21.1o φ'

design=25.7o φ'

design=24.8o

Cohesive, 1.0 1.0 1.0 1.5 1.2 1.25φ'=25o φ'

design=17.3o φ'

design=21.2o φ'

design=20.5o

Factors on c'Cohesive, 1.0 1.0 1.0 1.5 1.2 1.6c'=10kPa c'

design=6.7kPa c'

design=8.3kPa c'

design=6.2kPa

* BD42 factors are indicated in brackets where different.

5

Figure 1 Cantilever wall penetration for 7.5m deep excavation

18 20 22 24 26 28 300

1

2

3

4

5

Depth of wall (m)

Fac

tor

of s

afet

y

(1.5)

(2) (2)

(1.5)

CP2

Strength factor

Net total pressure

Burland-Potts

CIRIA 104methods

(2) - FoS recommended by CIRIA 104- BS8002

- EC7, case C

- BS8002

- EC7, case C

16 18 20 22 24 26 28 300

1

2

3

4

5

Depth of wall (m)

Fac

tor

of s

afet

y

(1.5)

(2)

(1.75)(1.5)

CP2

Strength factor

Net total pressure

Burland-Potts

CIRIA 104methods

- EC7, case C (1.25 < FoS < 1.6)

- EC7, case C (1.25 < FoS < 1.6)

(a) Granular soil,φ'= 30o

(b) Cohesive soil, c'=10kPa and φ'= 25o

Retained side:-Surcharge=10kPaWater table at surface

Retained side:-Surcharge=10kPaWater table at 1m depth

(2) - FoS recommended by CIRIA 104- BS8002

- BS8002

δa = 2/3φ'design, δp = 1/2φ'design

δa = δp = 2/3φ'max

δa = δp = φ'design




6

Figure 2 Penetration for wall propped at top and 7.5m deep excavation

12 13 14 15 16 17 18 190

1

2

3

4

5

6

Depth of wall (m)

Fac

tor

of s

afet

y

(1.5)

(2) (2)

(1.5)

CP2

Strength factor

Net total pressure

Burland-Potts

CIRIA 104methods

11 12 13 14 15 16 17 18 190

1

2

3

4

5

6

Depth of wall (m)

Fac

tor

of s

afet

y

(1.5)

(2)

(1.75)(1.5)

CP2

Strength factor

Net total pressure

Burland-Potts

CIRIA 104methods

(a) Granular soil,φ'=30o

(b) Cohesive soil, c'=10kPa and φ'=25o

Retained side:-Surcharge=10kPaWater table at surface

Retained side:-Surcharge=10kPaWater table at 1m depth

(2) - FoS recommended by CIRIA 104

- BS8002- EC7, case C

- BS8002

- EC7, case C

(2) - FoS recommended by CIRIA 104

- BS8002

- EC7, case C (1.25 < FoS < 1.6)

- BS8002

- EC7, case C (1.25 < FoS < 1.6)







7

Table 2 Wall penetrations calculated by using different design methods

Wall penetration (m) 1 Depth variance from BS8002 (m)

CIRIA 104/ BD42 CIRIA 104/ BD42

Soil Net total Burland Strength EC7 Net total Burland Strength EC7type CP2 pressure -Potts factor BS8002 (Case C) CP2 pressure -Potts factor BS8002 (Case C)

Cantilever wall2

Granular 27.07 21.47 25.91 27.54 22.84 23.65 +4.23 -1.37 +3.07 +4.70 +0.00 +0.81(23.05)3 (21.44)4 (21.82)5 (+0.21)3 (-1.40)4 (-1.02)5

Cohesive 24.85 19.91 26.17 27.51 21.92 23.90 +2.93 -2.01 +4.25 +5.59 0.00 +1.98(21.43)3 (20.70)4 (22.09)5 (-0.49)3 (-1.22)4 (+0.17)5

Wall propped at topGranular 16.53 13.81 15.86 17.13 14.78 15.19 +1.75 -0.97 +1.08 +2.35 0.00 +0.41

(14.34)3 (14.11)4 (14.28)5 (-0.44)3 (-0.67)4 (-0.50)5

Cohesive 15.23 12.65 15.85 16.94 14.03 15.13 +1.20 -1.38 +1.82 +2.91 0.00 +1.10(13.20)3 (13.44)4 (14.23)5 (-0.83)3 (-0.59)4 (+0.20)5

1 δa= φ'

design and δ

p=½φ'

design assumed unless otherwise stated.

2 Wall penetration assumes fixed earth support, a small additional penetration may be necessary to ensure this.3 Numbers in brackets show penetrations when using a minimum factor of safety of 2 for this method as recommended by clause 3.1 (iv) of BD42.4 Numbers in brackets show penetrations when δ

a=δ

p= 2/3φ'

max is used for BS8002 (clause 3.2.6).

5 Numbers in brackets show penetrations when δa=δ

p=φ'

design is used for EC7 (clause 8.5.1).

Table 3 Methods arranged by increasing order of wallpenetration

Granular (c'=0, φ'=30o) Cohesive (c'=10kPa, φ'=25o)

Cantilever Propped at top Cantilever Propped at top

Net total pressure Net total pressure Net total pressure Net total pressureBS8002 BS8002 BS8002 BS8002EC7 EC7 EC7 EC7Burland-Potts Burland-Potts CP2 CP2CP2 CP2 Burland-Potts Burland-PottsStrength factor Strength factor Strength factor Strength factor

20 25 30 35 40 4515

20

25

30

35

Soil friction angle (degrees)

Dep

th o

f wal

l (m

)

- BS8002,- EC7, case C,

- Strength factor, CIRIA 104,

Unplannedexcavation

depth

zero

zero

0.5m0.75m

Retained side:-Surcharge=10kPaWater table at surfaceRetained height=7.5m


δa = δp = 2/3φ'max δa = δp = φ'design

Figure 3 Effect of unplanned excavation upon cantileverwall penetration in granular soil

8

wall and the maximum wall friction angles permitted witheach design method (Table 2). For CIRIA 104 and BD42designs, the strength factor method has been arbitrarilyadopted throughout. For EC7 case B designs, the depth ofwall penetration from case C calculations was adopted.

The depths and magnitudes of the maximum wallbending moments and shears are reported in Table 4 forthe cantilevered structure. If the effect of unplannedexcavation in front of the wall is ignored for BS8002 andEC7, generally BS8002 is then found to be leastconservative with the smallest design moments and shearsin both granular and cohesive soils. For granular soil, theuse of CIRIA 104 with moderately conservativeparameters is most conservative because a load factor of1.5 is employed on the real expected loads (clause 8.3.2,CIRIA 104). With cohesive soils, the latter approachproduces values similar to those with the other designmethods as the use of an unfactored value of c' reducesmoments and shears.

It is worth noting in Table 4 that, with the exception ofthe shear requirements in granular soil, designs using EC7case C are marginally more critical than case B. Thisfinding was also reported by Simpson (1994) for anembedded wall example, although the converse was truewith conventional wall design.

If the effect of unplanned excavation is included forBS8002 and EC7, bending moments calculated from thesecodes are increased by an average of 37% and 23%respectively. In the case of granular soil, these designsusing BS8002 and EC7 then require slightly larger wallbending moment resistance than CIRIA 104 and BD42with no unplanned excavation. With cohesive soil thehighest bending moments are still obtained when using

0 2 4 6 8 10 1213

14

15

16

17

18

19

20

21

Soil cohesion,c' (kPa)

Dep

th o

f wal

l (m

)

Unplannedexcavation

depth

zero

zero

0.5m0.75m

Retained side:-Surcharge=10kPaWater table at 1m depthRetained height=7.5m

zero

- BS8002,

- EC7, case C,- Strength factor, CIRIA 104,


δa = δp = 2/3φ'max δa = δp = φ'design

Figure 4 Effect of unplanned excavation upon proppedwall penetration

worst credible soil parameters with CIRIA 104 and BD42as zero cohesion has a large effect on design values.

Table 5 shows the results calculated in a similar mannerfor walls propped at the top and also includes the designprop load in each case. The prop loads for CIRIA 104,BD42 and EC7 case B given in Table 5 cannot besatisfactorily determined using the design penetrationsfrom Table 2 as force balance does not exist. For thisreason, prop loads were determined in limit equilibriumusing a reduced penetration, although wall bendingmoments and shear forces were then calculated using thisprop load and the full penetration. Because the seepagepath around the wall is different with the smallerpenetration, this does introduce a second order error in thecalculation of prop load which has been neglectedfollowing the approach of clause 8.4.3 of CIRIA 104. Thepartial factors used in the various calculations are given inthe notes to Table 5.

Generally prop loads with CIRIA 104 and BD42 areconsiderably higher than those determined using BS8002and EC7. This is primarily because of the γ

fl of 2 used on

prop loads with the first two methods. Prop loadscalculated using BS8002 and EC7 (both cases B and C) arevery similar for granular soils, however design loadsaccording to EC7 case B are about 30% less than those forcase C in cohesive soil.

For walls propped at the top, there is little difference inshear force in the wall with the different design methods. Ifthe effects of unplanned excavation are ignored, designshears for granular and cohesive soils are all in the rangeof 149-236kN/m. It must be noted however that the shearat the top of the wall at the prop location will also needconsideration.

As with cantilever walls, the bending moment forpropped walls in granular soils is most critical when usingCIRIA 104 and moderately conservative soil parameters.With cohesive soils, the latter approach produces bendingmoments similar to the other methods because of theeffects of using an unfactored value of cohesion. Althoughthere is little difference in bending moment for cases B andC of EC7 in granular soil, values for case B are 33% lowerthan case C with cohesive soil.

5 Serviceability limit state of thestructural elements

Tables 6 and 7 show the magnitudes of wall bendingmoment and shear calculated for the serviceability limitstate using the various design methods for cantilever andwalls propped at the top respectively. In the latter case theprop forces are also shown in Table 7. As with ultimatelimit state design, the respective depths of wall penetrationfor each design method were taken from Table 2.

With both cantilever and propped walls in both soiltypes, serviceability design values for the wall moments/shears and prop loads are the lowest when using EC7. Lowvalues of wall moments and shears are also calculatedbecause of the effect of cohesion in clay soils when usingCIRIA 104 and moderately conservative soil parameters.

9

Table 4 Ultimate limit state design of the structure: cantilever wall

CIRIA 104 BD42 BS80021 EC7

Moder-Case B2 Case C1

ately No 0.75m No 0.5m No 0.5mconser- Worst Worst un- un- un- un- un- un-vative credible credible planned planned planned planned planned plannedpara- para- para- exca- exca- exca- exca- exca- exca-meters meters3 meters3 vation vation vation vation vation vation

Granular soil (φφφφφ'=30o)Maximum bending moment (kNm/m) 48354 40555 44606 3901 5143 3581 4321 4017 4843Depth to maximum bending moment (m) 14.5 15.9 15.9 15.7 17.3 13.5 14.4 16.0 17.0Maximum shear (kN/m) 6694 4955 5456 483 580 545 617 487 552Depth to maximum shear (m) 9.7 10.4 10.4 10.3 11.3 9.3 9.9 10.4 11.1

Cohesive soil (c'=10kPa, φφφφφ'=25o)Maximum bending moment (kNm/m) 28054 40635 44696 2641 3747 2086 2670 3248 4071Depth to maximum bending moment (m) 13.5 16.5 16.5 15.2 17.0 12.7 13.7 16.1 17.3Maximum shear (kN/m) 4364 4815 5296 346 437 358 421 393 457Depth to maximum shear (m) 9.0 10.7 10.7 9.8 10.9 8.6 9.3 10.3 11.1

1 Factored soil parameters used for BS8002 and EC7 case C (see Table 1).2 Unfactored soil parameters and partial factor of 1.35 used for case B following clause 2.4.2(17) and NAD of EC73 Worst credible parameters have been assumed of φ'=27o for granular soil and c'=0 and φ'=25o for cohesive soil4 Calculations using moderately conservative soil parameters (unfactored) include γ

fl of 1.5 following clause 8.3.2 of CIRIA 104

5 Calculations using worst credible soil parameters (unfactored) use γfl of 1 following clause 8.3.2 of CIRIA 104

6 Calculations using worst credible soil parameters (unfactored) include γfl of 1 and γ

f3 of 1.1 following clause 3.6 of BD42

Table 5 Ultimate limit state design of the structure: wall propped at the top


Moder-Case B2 Case C1

ately No 0.75m No 0.5m No 0.5mconser- Worst Worst un- un- un- un- un- un-vative credible credible planned planned planned planned planned plannedpara- para- para- exca- exca- exca- exca- exca- exca-meters meters3 meters3 vation vation vation vation vation vation

Granular soil (φφφφφ'=30o)Maximum bending moment (kNm/m) 16654 14145 11066 1023 1350 912 1102 1044 1261Depth to maximum bending moment (m) 6.6 7.1 6.3 6.4 7.1 5.8 6.2 6.5 6.9Maximum shear (kN/m) 2424 1615 2446 204 246 254 287 205 232Depth to maximum shear (m) 9.8 10.4 10.4 10.4 11.4 9.4 10.2 10.5 11.2Prop force (kN/m) 5107 6097 5368 244 292 2429 2749 247 279

Cohesive soil (c'=10kPa, φφφφφ'=25o)Maximum bending moment (kNm/m) 9674 15105 11896 721 1019 538 690 802 1090Depth to maximum bending moment (m) 6.1 7.3 6.6 6.2 6.8 5.4 5.8 6.0 6.8Maximum shear (kN/m) 1814 1535 2366 149 187 184 214 202 193Depth to maximum shear (m) 8.9 10.7 10.7 9.7 10.9 8.5 9.2 10.4 11.1Prop force (kN/m) 3007 6157 5418 167 216 1409 1689 200 233

1 Factored soil parameters used for BS8002 and EC7 case C (see Table 1).2 Unfactored soil parameters and partial factor of 1.35 used for case B following clause 2.4.2(17) and NAD of EC73 Worst credible parameters have been assumed of φ'=27o for granular soil and c'=0 and φ'=25o for cohesive soil4 Calculations using moderately conservative soil parameters (unfactored) include γ


5 Calculations using worst credible soil parameters (unfactored) use γfl of 1 following clause 8.3.2 of CIRIA 104

6 Calculations using worst credible soil parameters (unfactored) include γfl of 1 and γ

f3 of 1.1 following clause 3.6 of BD42

7 Prop force determined at limit equilibrium using a reduced penetration with allowance of 25% and γfl of 2 then applied (clauses 8.5.2 and C.2.6 of CIRIA 104)

8 Prop force determined at limit equilibrium using a reduced penetration and γfl of 2 and γ

f3 of 1.1 (clause 3.8 of BD42)

9 Prop force determined at limit equilibrium using a reduced penetration (no advice given in EC7)

10

Table 7 Serviceability limit state design of the structure: wall propped at the top


Mod. Worst No 0.75m No 0.5mconservative credible unplanned unplanned unplanned unplannedparameters parameters2 excavation excavation3 excavation excavation3

Granular soil (φφφφφ'=30o)Maximum bending moment (kNm/m) 14434 10055 1023 1350 676 816Depth to maximum bending moment (m) 6.6 6.3 6.4 7.1 5.8 6.2Maximum shear (kN/m) 2104 2225 204 246 188 214Depth to maximum shear (m) 9.8 10.4 10.4 11.4 9.4 10.0Prop force (kN/m) 5106 3657 244 292 1798 2038

Cohesive soil (c'=10kPa, φφφφφ'=25o)Maximum bending moment (kNm/m) 8384 10805 721 1019 398 511Depth to maximum bending moment (m) 6.1 6.6 6.2 6.8 5.4 5.8Maximum shear (kN/m) 1574 2155 149 187 136 158Depth to maximum shear (m) 8.9 10.7 9.7 10.9 8.5 9.2Prop force (kN/m) 3006 3697 167 216 1048 1248

1 EC7 uses unfactored loads and partial factors of 1 on ground properties, clauses 2.4.2(18) and 2.4.3(13)2 Worst credible parameters have been assumed of φ'=27o for granular soil and c'=0 and φ'=25o for cohesive soil3 Serviceability limit state need not include consideration of unplanned excavation; values have been included for completeness4 Calculations using moderately conservative soil parameters (unfactored) include γ


5 Calculations using worst credible soil parameters (unfactored) and γfl of 1 and γ

f3 of 1 following clauses 3.9 and 3.10 of BD42

6 Prop force determined at limit equilibrium using a reduced penetration with allowance of 25% and γfl of 2 then applied (clauses 8.5.2 and C.2.6 of CIRIA 104)

7 Prop force determined at limit equilibrium using a reduced penetration and γfl of 1.5 and γ

f3 of 1 (clause 3.12 of BD42)

8 Prop force determined at limit equilibrium using a reduced penetration (no advice given in EC7)

Table 6 Serviceability limit state design of the structure: cantilever wall


Mod. Worst No 0.75m No 0.5mconservative credible unplanned unplanned unplanned unplannedparameters parameters2 excavation excavation3 excavation excavation3

Granular soil (φφφφφ'=30o)Maximum bending moment (kNm/m) 41904 40555 3901 5143 2652 3200Depth to maximum bending moment (m) 14.5 15.9 15.7 17.3 13.5 14.4Maximum shear (kN/m) 5804 4955 483 580 403 457Depth to maximum shear (m) 9.7 10.4 10.3 11.3 9.3 9.9

Cohesive soil (c'=10kPa, φφφφφ'=25o)Maximum bending moment (kNm/m) 24314 40635 2641 3747 1545 1978Depth to maximum bending moment (m) 13.5 16.5 15.2 17.0 12.7 13.7Maximum shear (kN/m) 3784 4815 346 437 265 312Depth to maximum shear (m) 9.0 10.7 9.8 10.9 8.6 9.3

1 EC7 uses unfactored loads and partial factors of 1 on ground properties, clauses 2.4.2(18) and 2.4.3(13)2 Worst credible parameters have been assumed of φ'=27o for granular soil and c'=0 and φ'=25o for cohesive soil3 Serviceability limit state need not include consideration of unplanned excavation; values have been included for completeness4 Calculations using moderately conservative soil parameters (unfactored) include γ


5 Calculations using worst credible soil parameters (unfactored) and γfl of 1 and γ

f3 of 1 following clauses 3.9 and 3.10 of BD42

11

The effect of unplanned excavation need not be consideredas a normal serviceability requirement. However if it isconsidered for BS8002 and EC7, maximum bending momentsincrease by an average of 37% and 25% respectively.

Comparison of the serviceability limit state results inTables 6 and 7 for structural element design with those forultimate limit state in Tables 4 and 5 indicates that it is thelatter which is more critical with all of the designapproaches. It is important to note that this will notnecessarily be the case when considering walls founded instiff over-consolidated clays. Each of the design methodsrequires that the high in situ stresses in these clays areconsidered, but it is only BD42 (clause 3.10) which givesany significant guidance on design procedures and factorsto be adopted. For this reason it has not been possible toextend this comparative study to cover over-consolidatedclays as, with this one exception, the process woulddepend heavily on engineering judgement.

6 Conclusions

The design of embedded retaining walls according toCIRIA 104, BD42, BS8002 and EC7 has been compared.Design calculations were carried out for both cantileverand walls propped at the top with a retained height of wallof 7.5m. Linear seepage from a high water table in theretained ground around the embedded toe of the wall toexcavation level was assumed throughout. The followingconclusions were reached.

i Consideration of overall stability is used to determinewall penetration. Significant variation in penetration inboth granular and cohesive soil is found with thedifferent design methods even if the same wall frictionangles, surcharge and excavation depths are employed.On this basis, generally the net total pressure method ofCIRIA 104 provides the least penetration and needs tobe used with caution. BS8002 tends to be the next leastconservative of the other design approaches, whereasthe strength factor method (CIRIA 104 and BD42) is themost conservative.

ii If the higher wall friction angles permitted underBS8002 and EC7 are used, penetrations (for bothcantilever and propped walls) reduce by about 5% and7% with the two codes respectively. This reduction ismore than compensated by subsequent increases inpenetration of about 11% and 7% respectively if theeffects of unplanned excavation are then taken intoaccount as specified by BS8002 and EC7. Includingallowance for unplanned excavations is not mandatorywith CIRIA 104 and BD42 although it is clearly goodpractice to take account of the risk.

iii The ultimate limit state design of the structural elementswas compared using the maximum permitted wallfriction angles and the respective penetrationsdetermined with each design method. The followingfindings were established.

a For granular soil and both types of wall, the use ofCIRIA 104 with moderately conservative parameters

to determine bending moments and shears is mostconservative because a load factor of 1.5 is employed.With cohesive soil, the latter approach producesvalues similar to those from the other methodsbecause of the use of an unfactored value of c'.Bending moments calculated using EC7 case C aremarginally more critical than case B designs.

b Generally prop loads with CIRIA 104 and BD42 areconsiderably higher than those determined usingBS8002 and EC7. This is primarily because of the γ

fl

of 2 used on prop loads with the first two methods.Prop loads calculated using BS8002 and EC7 (bothcases B and C) are very similar for granular soils,however design loads according to EC7 case B areabout 30% less than those for case C in cohesive soil.

iv With both cantilever and propped walls in both soil types,serviceability design values for the wall moments/shearsand prop loads are the lowest when using EC7.Comparison of the serviceability limit state results forstructural element design with those for ultimate limitstate indicates that it is the latter which is more criticalwith all of the design approaches. It is important to notethat this will not necessarily be the case when consideringwalls founded in stiff over-consolidated clays. Each of thedesign methods requires that the high in situ stresses inthese clays are considered, but it is only BD42 (clause3.10) which gives any significant guidance on designprocedures and factors to be adopted.

12

Part B: Comparative study for reinforcedconcrete walls

7 Introduction

The second study compared the design of conventionalretaining walls and abutments according to BD30, BS8002and EC7. For this study, design calculations were carriedout for ‘L-shaped’ retaining walls of 2.5m and 7.5mheight. The latter results were compared with those for a7.5m high bridge abutment where bridge dead and liveloadings were included.

Both granular and cohesive soils were considered asbackfill to the structure and the foundation soil wasassumed to have the same properties as the backfill. Thefollowing geotechnical parameters were adopted:

� Granular backfill (γ=20kN/m3, c'=0, φ'=35o)

� Cohesive backfill (γ=20kN/m3, c'=5kPa, φ'=25o)

The strength parameters (c',φ') were assumed to be peakvalues from laboratory effective stress testing. In the caseof the granular backfill, it was assumed that the backfillwas free-draining with the water table below thefoundation of the wall. In the case of the cohesive backfill,with a c' of 5kPa and a surcharge of 10kPa, only shallowtension cracks could develop and no account was thereforetaken of any water pressure build-up in the cracks. Withhigher values of cohesion, water filled tension crackswould need consideration.

In these analyses, a simple case with no backfill in front ofthe wall and hence no passive pressures has been assumedthroughout. For this reason, the effect of unplanned excavationin front of the wall has not been considered. If backfill is placedin front of a wall or abutment the different design requirementsfor unplanned excavation would need evaluation.

As with the embedded wall analyses, a uniform surchargeof 10kPa was used on the retained ground as in a highwaysituation this corresponds to HA loading (clause 5.8.2,BD37, DMRB 1.3) which is a normal requirement. It mustagain be noted that BS8002 has a requirement for minimumsurcharge loading of 10kPa of the retained ground and, ifHA loading is not required, this will produce a difference inwall design between the various codes.

For the calculation of bridge deck loading on the 7.5mhigh abutment, the following deck geometry and loadingswere considered:

� Class of structure: motorway or trunk road

� Deck span of 20m with total deck dead and superimposedloads of 3000kN and 1000kN respectively

� Deck comprising 2 carriageways each including 2 lanesof width 3.65m with a cycle/footpath 1.5m wide

On this basis and after consideration of the various loadcombinations (Table 1, BD37, DMRB 1.3), the followingnominal loads were adopted as summarised in Table 8. Itmust be noted that, for the purpose of simplicity,secondary live loads normally used in design such asaccidental loads, braking and longitudinal loads have notbeen included and a simply supported deck (ie. noeccentricity of loading) was assumed.

Unfactored nominal loads from Table 8 were used forlimit states of the soil for design calculations employingBD30 and BS8002. Ultimate limit state designs accordingto EC7 adopted load factors of 1.35 (assuming the liveloads were persistent and not variable following Table C1of EC1: Part 3) and 1.0 for cases B and C respectively.Factored loads were used in structural element design forBD30 and BS8002. In the case of the first two of thesestandards, an additional factor γ

f3 of 1.1 was used for

calculating moments and shears for ultimate limit statedesign of the structural elements as specified by BS5400:Parts 3 and 4 (implemented by Highways Agency in BD13and BD24 respectively).

8 Factors adopted for limit state design

Calculations for retaining walls and abutments wereperformed to establish the minimum required stablegeometry derived from consideration of overturning andsliding, and maximum and minimum bearing pressures.Following this, maximum bending moments and shearforces have been evaluated for the base and stem of the wall.

Values of friction and adhesion for the wall and base arenot exactly the same as used for embedded walls where thewall is cast in situ against the soil. Table 9 summarises therelevant values and source clauses in each designdocument. No specific advice on values is given in BD30and it has therefore been assumed that, as the other codeswere not available when it was written, the intention inBD30 was to employ values from CP2 (1951) wherenecessary. For the purpose of these examples, it has beenassumed that the only part of the structure cast in situ is thespread-base and the highest permitted friction anglebetween soil and base has therefore been used in assessingthe stability against sliding.

The various factors for use with each limit state have beenidentified for each design method. Table 10 shows the loadfactors employed for analyses using BD30 and referencesthe source clauses in the Highways Agency Standard. ThisStandard uses unfactored soil strength parameters and placesemphasis on using worst credible soil pressures for thedesign of the structural elements by requiring ‘at rest’ ratherthan ‘active’ lateral earth pressures. Measurements by TRLon a pilot scale retaining wall (Carder et al, 1977 & 1980)confirm that on completion of backfilling, lateral pressuresare more realistically based on ‘at rest’ conditions with abulb of higher pressures over the upper part ( 2m) of thewall: the magnitude of this bulb will depend upon the sizeand type of compaction plant, its proximity to the wall, andthe soil type.

Table 8 Nominal loads and factors from BD37

Nominal load γfl for structural design

per metre widthDescription of abutment SLS ULS

Dead load 150 kN/m 1.0 1.15Superimposed dead load 50 kN/m 1.2 1.75Live load (combination) 260 kN/m 1.1 1.3

13

Table 10 Design load factors for retaining walls using BD30

Soil Structural elements

Earth and water pressures SLS1 ULS2 SLS3 ULS4

Retained side Horizontal Live load/ 1.0 1.0 1.0 1.5pressures surcharge use K

ause K

ause K

ouse K

o

Fill 1.0 1.0 1.0 1.5use K

ause K

ause K

ouse K

o

Vertical Live load/ 1.0 1.0 1.05 1.25,6

pressures surcharge

Fill 1.0 1.0 1.05 1.25,6

In front of wall Horizontal Live load/ 1.0 1.0 1.0 1.06

passive pressures surcharge (relieving effect7)

Soil 1.0 1.0 1.0 1.06

(relieving effect7)

Vertical pressures Live load/ 1.0 1.0 1.05 1.05

surcharge (relieving effect7)

Soil 1.0 1.0 1.05 1.05

(relieving effect7)

1 Clauses 5.3.4 and 5.2.5.2, BD302 Clauses 5.3.4 and 5.2.4.2, BD303 Clauses 5.3.3 and 5.2.3, BD304 Clauses 5.3.2 and 5.2.2, BD305 Vertical pressures only used in calculating bending and shear of the base6 Clause 5.8.1.2 of BD377 Clause 5.3.2 of BD30 and clause 5.8.1.3 of BD37

Table 9 Design values of wall/base friction and adhesion under drained conditions

BS8002 EC7 BD30

Wall friction, δw ≈ 2/3φ' < 2/3 φ

crit' No specific advice given, values for

75% of design shear strength Clause 8.5.1(4) cohesionless soil as given in CP2:of soil (or representative valuedetermined by test). δ

soil/concrete= 20o

Clause 3.2.6 CP2,Clause 1.4321

δ <φcrit

' for rough surfaces, Design of base and stem, δ=0.δ = 20o for smooth surfaces. Sliding or tilting, δ=φ.

Clause 2.2.8 CP2,Clause 1.435

δpassive

= ½δsoil/concrete

CP2,Clause 1.452

Wall adhesion, cw

0 0 0Clause 2.2.8 Clause 8.5.1(4) (Cohesionless soil)

Base friction, δb

≈ 2/3φ' φ'design

for cast in situ concrete, No specific advice given,75% of design shear strength 2/3φ'

design for smooth precast foundations. values for cohesionless soil as

of soil (or representative value Clause 6.5.3(8) given in CP2:determined by test).

Clause 3.2.6 φ' for cast in situ concrete,when precast δ

b=δ

w=20o.

δ < φcrit

' for rough surfaces, CP2,Clause 1.4922δ = 20o for smooth surfaces.

Clause 2.2.8

Base adhesion, cb

0 0 0Clause 2.2.8 Clause 6.5.3(8) (Cohesionless soil)

14

As BS8002 uses the most severe earth pressures fordesign by either using a factor (M) of 1.2 on strength orthe critical state strength of the soil, the application of anypartial load factors is not required. It must be noted that, aswith the other design documents, factors are still requiredon material strengths when designing the reinforcedconcrete. BS8002 (clause 3.1.5) highlights the need forcompatibility of deformations with designs for each limitstate. For example, backfilling behind a rigid retainingwall will need designs based on ‘at rest’ earth pressureswith allowance for residual compaction stresses (clause3.3.3.6). Active earth pressures are appropriate to theserviceability design of flexible walls and more generallyto the ultimate limit state design of most walls wheremovement will occur before failure.

Table 11 gives the partial factors for serviceability andultimate limit states of the soil and structural elementsaccording to EC7 with the table notes referring to thesource clauses where appropriate. These partial factors on‘actions’ are used in conjunction with factors on groundproperties as given in Table 2.1 of EC7. For ultimate limitstate design, both cases B and C in Table 2.1 need to beevaluated: normally case B is critical to the design of thestructural elements and case C is critical in terms of overallstability and sizing of the structural elements. Case B usesa factor of 1 on ground properties, whilst case C usesfactors of 1.25 on tanφ', 1.6 on c', and 1.4 on c

u and q

u. As

with BS8002, EC7 suggests that for rigid walls theserviceability earth pressures should be calculated using ‘atrest’ earth pressures (clause 8.5.2) and compaction effectsneed to be taken into account (clause 8.5.5).

9 Ultimate limit state of the soil

The calculations for ultimate limit state of the soil wereused to determine the width of the spread-base for the2.5m and 7.5m high retaining structures and an overviewof the factors used in the analysis is given in Table 12.

Table 13 compares the various widths determined usingthe different design methods for the cases of overturning,sliding and bearing failure. In the latter case, no tensionhas been allowed to develop beneath the base (ie. the lineof thrust has been limited to within the middle third of thebase) and the resulting maximum bearing pressures arealso shown. This approach is not mandatory when usingBS8002 (clause 4.2.2.1) and EC7 (clause 6.5.4) providedthat the ultimate bearing capacity is accurately known.

Table 13 shows that, for both granular and cohesivebackfills, there is little difference in the spread-base widthsdetermined for the overturning mode using BS8002 andEC7 although a larger width is required according to BD30as would be expected because of the lumped factor ofsafety of 2 which is included.

More variation occurs in the minimum widths to preventsliding and this is primarily due to the differences in basefriction angle given in Table 9. Both BD30 (following therecommendations of CP2) and EC7 permit the use of φ'

design

for cast in situ concrete, whilst BS8002 gives a lower value of2/3φ'

max. The required widths for the 7.5m wall are significantly

higher with cohesive rather than granular backfill because ofthe lower φ' and hence base friction angle. With the 2.5m highwall this effect is not so noticeable because of the influence ofcohesion near the top of the wall.

Table 11 Design load factors for retaining walls using EC7

Soil Structural elements

Earth and water pressures SLS1 ULS2 ULS3 SLS1 ULS2 ULS3

Case B Case C Case B Case C

Retained side Horizontal Live load/ 1.0 1.35 1.0 1.0 1.35 1.04

pressures surcharge

Fill 1.0 1.35 1.0 1.0 1.35 1.0

Vertical Live load/ 1.0 1.35 1.0 1.05 1.355 1.04,5

pressures surcharge

Fill 1.0 1.35 1.0 1.05 1.355 1.05

In front of wall Horizontal Live load/ 1.0 1.35 1.0 1.0 1.35 1.04

passive surchargepressures

Soil 1.0 1.35 1.0 1.0 1.35 1.0

Vertical Live load/ 1.0 1.35 1.0 1.05 1.355 1.04,5

pressures surcharge

Soil 1.0 1.35 1.0 1.05 1.355 1.05

1 Clause 2.4.2(18) and partial factors of 1 on ground properties as given by clause 2.4.3(13)2 All earth and water pressures multiplied by 1.35 as overall action is unfavourable, clause 2.4.2 (17) and NAD; partial factors of 1 on ground

properties as Table 2.13 Table 2.1 with partial factors applied to ground properties4 Live load assumed to be persistent with the same factor as a permanent action, Table C1 of EC1 Part35 Vertical pressures only used in calculating bending and shear of the base

15

In Table 13, EC7 values have been calculated using bothcases B and C. In all instances, case C is more critical and itis generally this case that dictates ultimate limit state designand sizing of the elements although the code requiresstability checks to be carried out using case B as well.

It is interesting to note that the spread-base width for a7.5m high bridge abutment is less than that for a wall whenconsidering overturning and sliding modes of failure. Thisis because the dead and live loads from the deck increasethe restoring moment about the wall toe and the verticalforce (ie. hence the sliding resistance) for the two failure

modes respectively. However the additional vertical loadson the abutment require a much higher spread-base widthfor stability in bearing.

In Table 13 the most critical mode of failure has beenhighlighted for both granular and cohesive backfill. Withgranular backfill, failure in bearing tends to dominate withall design methods and therefore requires the largest widthof spread-base. Final design widths are therefore based onthis failure criterion and are marginally lower whendesigning to BD30 than with the other codes andstandards. However it must be noted that the maximumbearing pressure of 330kN/m2 is used in conjunction with alumped factor of safety of 2 with BD30 and at first sight itappears that the width of the base may need to beincreased. For this reason a further investigation of bearingcapacity using the approach of Terzaghi and Peck (1967)and correction factors (i

c, i

q, iγ) for inclination of loading as

given in Annex B of EC7 was undertaken. The bearingcapacity is given by:

Bearing capacity = c'Ncic + q'N

qiq + 0.5γ'bNγiγ

In this equation γ' is the effective unit weight of soilbelow foundation level, q' is the effective overburdenpressure at foundation level, b is the spread-base width,and N

c, N

q, Nγ are bearing capacity factors. The value of c'

used is the value appropriately factored according to thedesign method being employed.

For granular soil, bearing capacity can be conservativelyestimated from the last term in this equation and thedependence of the bearing capacity factor Nγ on the designvalue of φ' is as shown in Table 14. On this basis all thedesigns given in Table 13 were viable with those of EC7

Table 13 Determination of width of spread-base for L-shaped walls: ultimate limit state of the soil

Spread-base width (m)

Granular backfill Cohesive backfill

Bearing/ Final Bearing/ FinalDesign Over- loading design Over- loading designmethod turning Sliding eccentricity1 value turning Sliding eccentricity1 value

(a) 2.5m high retaining wall (0.3m thick stem and base)BD30 1.12 0.96 1.37, max bp2= 121kN/m2 1.37 0.81 1.06 0.98, max bp2= 121kN/m2 1.06BS8002 0.86 0.89 1.48, max bp = 121kN/m2 1.48 0.74 1.23 1.28, max bp = 121kN/m2 1.28EC7, Case B3 0.81 0.55 1.29, max bp = 162kN/m2

1.51 0.60 0.59 1.01, max bp = 162kN/m2

1.45EC7, Case C 0.88 0.73 1.51, max bp = 121kN/m2 0.84 1.14 1.45, max bp = 121kN/m2

(b) 7.5m high retaining wall (0.75m thick stem and base)BD30 3.08 2.51 3.84, max bp2= 330kN/m2 3.84 3.14 4.43 3.91, max bp2= 330kN/m2 4.43BS8002 2.35 2.34 4.14, max bp = 330kN/m2 4.14 2.53 4.45 4.44, max bp = 330kN/m2 4.45EC7, Case B3 2.21 1.19 3.71, max bp = 446kN/m2

4.22 2.32 2.52 3.98, max bp = 446kN/m2

4.66EC7, Case C 2.40 1.89 4.22, max bp = 330kN/m2 2.65 3.71 4.66, max bp = 330kN/m2

(c) 7.5m high bridge abutment (1.2m thick stem and base)BD30 2.45 <1.2 6.38, max bp2= 478kN/m2 6.38 2.52 1.56 6.46, max bp2= 476kN/m2 6.46BS8002 1.43 <1.2 6.70, max bp = 470kN/m2 6.70 1.70 1.57 7.02, max bp = 464kN/m2 7.02EC7, Case B3 1.57 <1.2 6.33, max bp = 646kN/m2

6.80 1.64 <1.2 6.53, max bp = 640kN/m2

7.25EC7, Case C 1.51 <1.2 6.80, max bp = 468kN/m2 1.88 <1.2 7.25, max bp = 459kN/m2

1 For comparative purposes the eccentricity of loading has been limited to within the middle third of the base, ie. no tensions beneath the base. This isnot mandatory in BS8002 and EC7 when ultimate bearing capacity is accurately known

2 Factor of safety of 2 is required on ultimate bearing capacity for BD303 For EC7, unfactored deck and abutment loads used for overturning and sliding as their action is favourable; factor of 1.35 used on them for bearing

failure (unfavourable)

Table 12 Factors used in analysis of ultimate limit stateof the soil

Soil type BD30 BS8002 EC7 EC7Case B Case C

Overall factorGranular 2.0 1.0 1.35* 1.0Cohesive 2.0 1.0 1.35* 1.0

Factors on tanφφφφφ'Granular, 1.0 1.2 1.0 1.25φ'=35o (φ'

design=30.3o) (φ'

design=29.3o)

Cohesive, 1.0 1.2 1.0 1.25φ'=25o (φ'

design=21.2o) (φ'

design=20.5o)

Factors on c'Cohesive, 1.0 1.2 1.0 1.6c'=5kPa (c'

design=4.2kPa) (c'

design=3.1kPa)

* Factor on unfavourable actions (Table 2.1, EC7).

16

case C being the most marginal. The results in Table 14demonstrate that even if the factor of safety of 2 is takeninto account, bearing capacity for a spread-base of thesame width in cohesionless soil calculated using EC7 CaseC is generally the most critical with the lowest value of Nγ.

With cohesive soil, the most critical modes of failurehighlighted in Table 13 are either sliding or bearing. Forretaining walls, the reduction in φ' and hence base frictionmake sliding more critical when using BD30 and BS8002as already discussed. As would be expected bearing failuredominates with all methods when designing a bridgeabutment because of the large vertical pressures producedby the dead and live deck loads.

If the bearing capacity for the cohesive soil is investigatedusing the previous formula, the various factors calculatedare shown in Table 15. If only the N

c and Nγ terms in the

equation are considered, the maximum bearing pressuresfrom Table 13 exceed the ultimate values by 7%-50% forthe various design methods. However if the N

q term is

included and an average effective overburden pressure (q')calculated from both sides of the wall, the bearing capacityis then adequate in all cases.

2.5m high wall because of the influence of cohesion atshallow depth.

Generally there is little difference in maximum momentsand shears determined using BS8002 and EC7, but valuesfor BD30 are significantly higher by a factor of greaterthan 2. This is because BD30 design considers worstcredible stresses and uses a γ

fl factor of 1.5 on K

o lateral

stresses in the backfill whereas the other methods use Ka

stresses as movement, which will relieve stresses, mustoccur before failure.

Comparisons of the moments and shears given in Table 16for case B and C designs according to EC7 verified that, aswould be anticipated, case B designs were normally morecritical although there were a few instances with cohesivebackfills where case C values were marginally higher.

11 Serviceability limit state of the structuralelements

A similar comparison of different design requirements forthe structural elements, but for the serviceability limitstate, is shown in Table 17 for both granular and cohesivebackfill. It must be noted that, with the exception of BD30where K

o stresses were used, stresses appropriate to K

a

conditions were used throughout. For this reason, designsusing BD30 are apparently more conservative than theother design methods as shown in Table 17.

However designs based on Ka are mainly applicable to

flexible walls and, as discussed in Section 8, the designmethods generally require that compaction effects aretaken into account in serviceability design of more rigidwalls. In both BS8002 and EC7, this requirement forincluding compaction stresses in the design of rigid wallsneeds more emphasis. A typical distribution of lateralstress caused by compaction of granular fill based on thefindings of Carder et al (1977) is shown in Figure 5. Thisunfactored stress distribution has been used to calculatebending moments and shear forces on the wall stem andthe results are given in Table 18. This table also shows thevalues from ultimate and serviceability limit statecalculations extracted from Tables 16 and 17.

In Table 18 the most severe case for granular backfilland each method has been highlighted. With the exceptionof BD30, the most severe design condition for the othermethods is the serviceability limit state analysis whichincludes compaction stresses. Designs for rigid walls usingBS8002 and EC7 which do not consider compaction couldtherefore be inherently unsafe.

Generally BD30 makes allowance for worst crediblestresses on rigid walls in ultimate limit state design byusing a factor of 1.5 on K

o which, with the possible

exception of low walls, means that compaction stresses canbe safely accommodated. In the case of the 7.5m high walland bridge abutment however, ultimate limit state valuesexceed by more than 20% the serviceability values whichinclude an allowance for compaction: BD30 wouldtherefore appear overly conservative in this area. Inaddition, the logic of its approach in terms of soilmechanics principles appears questionable.

Table 14 Variation of Nγγγγγ for granular backfill (φφφφφ'max=35o)

Design method φ'design

Nγ

BD301 35o 45BS8002 30.3o 21EC7, Case B 35o 45EC7, Case C 29.3o 18

1 Factor of safety of 2 required on bearing capacity for BD30

Table 15 Variation of Nq, Nγγγγγ and N

c for cohesive backfill

(c'max

=5kPa, φφφφφ'max

=25o)

Design method φ'design

c'design

Nq

Nγ Nc

BD301 25o 5 10.7 9.0 20.7BS8002 21.2o 4.2 7.2 4.9 16.1EC7, Case B 25o 5 10.7 9.0 20.7EC7, Case C 20.5o 3.1 6.7 4.3 15.3

1 Factor of safety of 2 required on bearing capacity for BD30

10 Ultimate limit state of the structuralelements

For the purpose of this comparison, the final values ofspread-base widths (Table 13) determined for the ultimatelimit state of the soil using each design method were usedthroughout. Analyses were then carried out using thefactors relevant to structural design as described in Section 8.The maximum bending moments and shear forcesdetermined in the wall stem and base on this basis for 2.5mand 7.5m high walls and a 7.5m high abutment are givenin Table 16 for both granular and cohesive backfill.

With the 7.5m high structures, wall moments and shearswere greater when the backfill was cohesive because thelarger K-value (due to the lower φ') gave increased lateralstresses at depth. This effect was not noticeable with the

17

Table 16 Ultimate limit state design of the stem and base of L-shaped walls


Wall stem Base1 Wall stem Base1

Spread- Spread-Design base Max bm Max shear Max bm Max shear base Max bm Max shear Max bm Max shearmethod width (m) (kNm/m) (kN/m) (kNm/m) (kN/m) width (m) (kNm/m) (kN/m) (kNm/m) (kN/m)

(a) 2.5m high retaining wall (0.3m thick stem and base)BD302,3 1.37 42 49 -42 44 1.06 7 67 -46 71BS8002 1.48 16 19 -20 15 1.28 11 16 -14 14EC7, Case B

1.5118 21 -22 16

1.459 15 -12 10

EC7, Case C 17 20 -21 15 15 20 -19 15

(b) 7.5m high retaining wall (0.75m thick stem and base)BD302,3 3.84 882 368 -885 300 4.43 1194 498 -1234 330BS8002 4.14 336 140 -416 93 4.45 378 173 -485 94EC7, Case B

4.22 380 158 -470 100

4.66 404 191 -528 91

EC7, Case C 350 146 -434 93 419 186 -536 94

(c) 7.5m high bridge abutment (1.2m thick stem and base)BD302,3,4 6.38 726 323 -1370 5 6.46 983 438 -1643 41BS8002 6.70 277 124 -538 -158 7.02 306 150 -611 -163EC7, Case B

6.80 313 139 -638 -232

7.25 324 165 -702 -249

EC7, Case C 288 129 -558 -160 341 162 -665 -167

1 Base moments and shear forces are determined allowing for bearing pressure distribution beneath base2 BD30 calculations include a factor of 1.5 on K

o stresses, see Table 10

3 Moments and shears include γf3 of 1.1

4 Factors on dead and live deck loads are as given in Table 8

0 20 40 60 80

0

2

4

6

Lateral stress (kPa)

Dep

th (

m)

Ko

2.5m wall

7.5m wall

Figure 5 Envelope of compaction stresses assumed forgranular backfill

18

Table 18 Design bending moments and shear forces in the stem of L-shaped walls with granular backfill: effect ofcompaction stresses

Serviceability limit state: Serviceability limit state:Ultimate limit state1 no allowance for compaction2 allowance for compaction3

Design Spread-base Max bending Max shear Max bending Max shear Max bending Max shearmethod width (m) moment (kNm/m) force (kN/m) moment (kNm/m) force (kN/m) moment (kNm/m) force (kN/m)

(a) 2.5m high retaining wall (0.3m thick stem and base)BD304 1.37 42 49 25 30 48 48BS8002 1.48 16 19 16 19 48 48EC7 1.51 18 21 13 16 48 48

(b) 7.5m high retaining wall (0.75m thick stem and base)BD304 3.84 882 368 534 223 641 241BS8002 4.14 336 140 336 140 641 241EC7 4.22 380 158 281 117 641 241

(c) 7.5m high bridge abutment (1.2m thick stem and base)BD304 6.38 726 323 440 196 539 214BS8002 6.70 277 124 277 124 539 214EC7 6.80 313 139 232 103 539 214

1 From Table 16 : 2. From Table 17 : 3. Compaction stresses superimposed on unfactored Ko stresses : 4. Moments and shears include γ

f3 of 1.1 for uls

Table 17 Serviceability limit state design of the stem and base of L-shaped walls: no allowance for compaction effects


Wall stem Base1 Wall stem Base1

Spread- Spread-Design base Max bm Max shear Max bm Max shear base Max bm Max shear Max bm Max shearmethod width (m) (kNm/m) (kN/m) (kNm/m) (kN/m) width (m) (kNm/m) (kN/m) (kNm/m) (kN/m)

(a) 2.5m high retaining wall (0.3m thick stem and base)BD302 1.37 25 30 -31 27 1.06 34 41 -39 55BS8002 1.48 16 19 -20 15 1.28 11 16 -14 14EC73 1.51 13 16 -17 12 1.45 6 11 -9 7

(b) 7.5m high retaining wall (0.75m thick stem and base)BD302 3.84 534 223 -649 172 4.43 723 302 -902 180BS8002 4.14 336 140 -416 93 4.45 378 172 -485 94EC73 4.22 281 117 -349 74 4.66 299 141 -391 67

(c) 7.5m high bridge abutment (1.2m thick stem and base)BD302,4 6.38 440 196 -779 -122 6.46 596 266 -1014 -90BS8002 6.70 277 124 -547 -175 7.02 306 150 -620 -180EC73 6.80 232 103 -473 -172 7.25 240 122 -520 -184

1 Base moments and shear forces are determined allowing for bearing pressure distribution beneath base2 BD30 calculations use a factor of 1.0 on K

o stresses, see Table 10

3 EC7 uses unfactored loads and partial factors of 1 on ground properties, clauses 2.4.2(18) and 2.4.3(13), see Table 114 Factors on dead and live deck loads are as given in Table 8

19

12 Conclusions

The design of conventional retaining walls and abutmentsaccording to BD30, BS8002 and EC7 has been compared.Design calculations were carried out for ‘L-shaped’retaining walls of 2.5m and 7.5m height. The latter resultswere compared with those for a 7.5m high bridge abutmentwhere bridge dead and live loadings were included. Thefollowing conclusions were reached:

i There is little difference in the spread-base widthdetermined for stability against overturning usingBS8002 and EC7, although a larger width is requiredby BD30 primarily because of the lumped factor ofsafety employed.

ii More variation occurs in the minimum widths toprevent sliding due to the differences in base frictionangle. Generally with granular backfill, BD30 is moreconservative than BS8002 which, in turn, is moreconservative than EC7.

iii With all design methods, failure in bearing tends todominate ultimate limit state design of the soil. Finalspread-base widths are marginally lower whendesigning to BD30 because smaller K

a values for earth

pressure are calculated when using unfactored φ'values for the soil. EC7 (case C) is generally the mostcritical when designing to prevent bearing failure.

iv Generally there is little difference in ultimate momentsand shears determined in the stem and base usingBS8002 and EC7, but values for BD30 aresignificantly higher by a factor of greater than 2. Thisis because BD30 considers worst credible stresses anduses a γ

fl of 1.5 on K

o whereas the other methods use

Ka as movement must occur before failure.

v When no allowance is made for compaction effects,the serviceability moments and shears in the wall stemwere again higher with BD30 because of the use of K

o

stresses. All methods require the use of compactionstresses when designing rigid walls and this proves tobe the critical factor when designing to BS8002 andEC7. More emphasis needs to be placed onhighlighting these clauses within the two codes asotherwise designs could be inherently unsafe. WithBD30, ultimate moments and shears in the wallexceeded by more than 20% the serviceability valueswhich include an allowance for compaction: BD30would thus appear overly conservative in this area.

vi When using EC7 it was verified that case C isnormally critical for ultimate limit state of the soil,whilst case B is more critical for determining ultimatebending moments and shears.

vii Certain aspects of EC7 need either better clarificationor simplification. For example, live deck loading onbridge abutments has been assumed to be persistentwith a partial factor of 1.35 for ultimate limit state caseB, however it could equally well be considered as avariable action with a factor of 1.5. Difficulties alsoarise with decisions on whether some actions arefavourable or unfavourable and more guidance isneeded on this.

viii Further investigation of the effect of passive pressures infront of inverted T-shaped walls is recommended. Thiswill also permit evaluation of the effects of unplannedexcavation in front of conventional retaining walls.

20

Part C: General

13 Summary

This study has compared the design of both embedded andconventional retaining walls undertaken using BS8002,EC7 and Highways Agency design standards. For bothtypes of wall, design examples were selected which wereconsidered typical of construction on the nationalmotorway network. The main points were as follows:

i Generally final designs for both embedded andconventional walls are similar when using BS8002 andEC7, although the complexity of EC7 makes itsimplementation much more difficult and prone to error.

Sizing of the structure

ii For embedded walls, significant variations in wallpenetration are found for overall wall stability.BS8002 and EC7 designs tend to be less conservativethan CIRIA 104 and BD42.

iii For conventional walls, failure in bearing tends todominate ultimate limit state design of the soil. Finalspread-base widths are marginally lower whendesigning to BD30 because smaller K

a values for earth

pressure are calculated when using unfactored φ'values for the soil. EC7 (case C) is generally the mostcritical when designing to prevent bearing failure asbearing capacity factors reduce with factoring φ'.

iv For conventional walls, there is little difference in thespread-base width determined for stability againstoverturning using BS8002 and EC7, although a largerwidth is required by BD30 primarily because of thelumped factor of safety employed. More variationoccurs in the minimum widths to prevent sliding dueto the differences in base friction angle with BD30being more conservative than BS8002 which, in turn,is more conservative than EC7 with granular backfill.

Structural design

v For both embedded and conventional walls, ultimatelimit state bending moments and shears are moresimilar with BS8002 and EC7 than with the HighwaysAgency design standards. This is primarily because forconventional walls BD30 considers worst credible K

o

stresses with a γfl of 1.5, while for embedded walls the

use of zero cohesion for clay soils with BD42 leads toconservatism.

vi For conventional walls, ultimate limit state design usingEC7 case B is more critical than case C for determiningwall bending moments and shears. With embeddedwalls, bending moments and shears from case C may bemarginally more critical than case B designs.

vii For embedded walls propped at the top, prop loads forultimate limit state design with CIRIA 104 and BD42are considerably higher than those determined usingBS8002 and EC7. This is primarily because of the γ

fl

of 2 used on prop loads with the first two methods.Prop loads calculated using BS8002 and EC7 (both

cases B and C) are very similar for granular soils,however design loads according to EC7 case B areabout 30% less than those for case C in cohesive soil.

viii More guidance and emphasis on serviceability designof the structural elements is generally given inHighways Agency standards than in the other designcodes. For example, BD42 includes detailedprocedures for serviceability design of embeddedwalls. For conventional walls, the most severe designcondition is the serviceability analysis which takesaccount of compaction stresses. BD30 routinely usesK

o soil stresses for serviceability design of the wall in

part recognition of this and safety is further assured bythe overly conservative use of worst credible stresseswith a factor of 1.5 on K

o for ultimate limit state.

14 Acknowledgements

The work in this report forms part of the research programof the Civil Engineering Resource Centre and was fundedby Quality Services (Civil Engineering Division) of theHighways Agency. The HA Project Manager is Dr D I Bushof the Structures Design Group.

Thanks are due to Mr N Moss (Babtie Group) andDr G B Card (Card Geotechnics) for their help indeveloping a computer routine for conventional walls andto Mr R R Carder for his help with the routine forembedded walls. The contribution of Mr R Thompson(now of Edge) and Mr C A Holt of Allott & Lomax incarrying out initial design comparisons for conventionalwalls is gratefully acknowledged.

15 References

British Standards Institution (1982). Steel, concrete andcomposite bridges, BS5400 Part 3, Code of practice fordesign of steel bridges. British Standards Institution, London.

British Standards Institution (1990). Steel, concrete andcomposite bridges, BS5400 Part 4, Code of practice for designof concrete bridges. British Standards Institution, London.

British Standards Institution (1994). Code of practice forearth retaining structures BS8002. British StandardsInstitution, London.

British Standards Institution (1994). Eurocode 1: Basis ofdesign and actions on structures, Part 3, ENV 1991-3:1994.British Standards Institution, London.

British Standards Institution (1995). Eurocode 7:Geotechnical design, Part 1, DD ENV 1997-1:1995.British Standards Institution, London.

Carder D R, Pocock R G and Murray R T (1977).Experimental retaining wall facility - lateral stressmeasurements with sand backfill. TRRL LaboratoryReport 766. Transport Research Laboratory, Crowthorne.

21

Carder D R, Murray R T and Krawczyk J V (1980).Earth pressures against an experimental retaining wallbackfilled with silty clay. TRRL Laboratory Report 946.Transport Research Laboratory, Crowthorne.

Design Manual for Roads and Bridges (DMRB).

Volume 1: Section 3 General Design

BD 13/90 Design of steel bridges. Use of BS5400:Part 3. (DMRB 1.3)

BD 24/92 Design of concrete bridges. Use of BS5400:Part 4. (DMRB 1.3.1)

BD 37/88 Loads for highway bridges. Use of BS 5400:Part 2. (DMRB 1.3)

Volume 2: Section 1 Substructures

BD 42/94 Design of embedded retaining walls andbridge abutments (unpropped or propped at the top).(DMRB 2.1)

BD 30/87 Backfilled retaining walls and bridgeabutments. (DMRB2.1)

Institution of Structural Engineers (1951). Earthretaining structures. Civil Engineering Code of PracticeNo 2. Institution of Structural Engineers, London.

Padfield C J and Mair R J (1984). Design of retaining wallsembedded in stiff clay. CIRIA Report 104. ConstructionIndustry Research and Information Association, London.

Simpson B (1994). Eurocode 7. Seminar on BS8002 on11 May. Institution of Structural Engineers, London.

Symons I F and Kotera H (1987). A parametric study ofthe stability of embedded cantilever retaining walls. TRRLResearch Report 116. Transport Research Laboratory,Crowthorne.

Terzaghi K and Peck R B (1967). Soil mechanics inengineering practice. 2nd ed., John Wiley and Sons Inc.,New York. Chapman & Hall Limited, London.

22

Abstract

This report gives the results from comparative studies on the design of embedded and conventional retaining wallsusing Eurocode 7 and existing UK design methods. Design examples for embedded walls included both cantileverand walls propped at the top: L-shaped walls and bridge abutments were considered for conventional construction.Retained heights of the structures were typical of those used on the national motorway network. Sizing of thestructures was carried out by considering the different ultimate limit state modes of failure and design of thestructural elements was then established for serviceability and ultimate limit states. The overall designs using thevarious standards/codes were then compared to assess their relative merits.

Related publications

TRL228 Movement trigger limits when applying the observational method to embedded retaining wallconstruction on highway schemes by G B Card and D R Carder. 1996 (price code E, £20)

TRL213 The effectiveness of berms and raked props as temporary support to retaining walls by D R Carder andS N Bennett. 1996 (price code E, £20)

TRL172 Ground movements caused by different embedded retaining wall construction techniques byD R Carder. 1995 (price code E, £20)

TRL152 Earth pressures against an experimental retaining wall backfilled with Lias Clay by A H Brookes,D R Carder and P Darley. 1995 (price code E, £20)

TRL128 Doubly-propped embedded retaining walls in clay by D J Richards and W Powrie. 1995(price code H, £30)

RR116 A parametric study of the stability of embedded cantilever retaining walls by I F Symons and H Kotera.1987 (price code B, £15)

LR946 Earth pressures against an experimental retaining wall backfilled with silty clay by D R Carder,R T Murray and J V Krawczyk 1980. (price code AA, £10)

LR766 Experimental retaining wall facility — lateral stress measurements with sand backfill by D R Carder,R P Pocock and R T Murray. 1977 (price code AA, £10)

Prices current at January 1998

For further details of these and all other TRL publications, telephone Publication Sales on 01344 770783 or 770784,or visit TRL on the Internet at http://www.trl.co.uk.

Documents

A comparison of embedded and conventional retaining wall ... · TRANSPORT RESEARCH LABORATORY A comparison of embedded and conventional retaining wall design using Eurocode 7 and