03 Bond Design of Gravity Walls

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Background & Applications

GEOTECHNICAL DESIGN wi th worked examples 13-14 June 2013, Dublin

Retaining structures I– es gn o grav yw ll

Dr Andrew Bond

Director, Geocentrix Ltd

Chairman TC250/SC7



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w wor e examp es - une, u n

Outline of talk

Scope and contents

Basis of design for gravity walls

Verification of strength

e n orce concre e wa s

Mass gravity walls

Reinforced fill walls

Veri ication o servicea i ity

Supervision, monitoring, and maintenance

Summary of key points

©2005-13 Geocentrix Ltd. All rights reserved2



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Retaining structures I –

desi n of ravit walls

SCOPE AND CONTENTS



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Scope of EN 1997-1 Section 9 Retaining

Gravity walls

Walls of stone or lain or reinforced concrete havin a base with orwithout a heel, ledge, or buttress

The weight of the wall itself … plays a significant role in the support ofthe retained material

e.g. concrete gravity walls; spread footing r.c. walls; buttress wallsEmbedded walls – to be covered later

Com osite retainin structures

Walls composed of elements of the above two types

e.g. double sheet pile wall cofferdams; earth structures reinforced by

tendons eotextiles or routin structures with multi le rows ofground anchorages or soil nails

Silos are covered by EN 1991-4




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Contents of EN 1997-1 Section 9 Retaining

Section 9 applies to retaining structures supporting ground (i.e. soil,rock or backfill) and/or water

§9.1 General (6 paragraphs)

§9.2 Limit states (4)

§9.3 Actions, geometrical data and design situations (26)§9.4 Design and construction considerations (10)

9.5 Determination of earth ressures 23

§9.6 Water pressures (5)

§9.7 Ultimate limit state design (26)

.

Many provisions from Section 6, ‘Spread foundations’ also apply to




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Contents of EN 1997-1’s Annexes for retaining

Annex C of Eurocode 7 Part 1 provides informative text relevant toretaining structures

Annex C Sample procedures to determine earth pressures (21

§C.1 Limit values of earth pressure (3 paragraphs)

§C.2 Analytical procedure for obtaining limiting active and passive earth

§C.3 Movements to mobilise earth pressures (4)




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DESIGN SITUATIONS AND LIMIT



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Limit modes for overall stability and. .




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Anticipated and unplanned excavations. . . .

Design geometry shall accountfor anticipated excavation or

Wall type For normal site control

H

possible scour in front of theretaining structure

For ULS verifications:

Cantilever 10% H

Supported 10% height below lowestprop

Maximum 0.5 m

= + Δd nomH H H




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Water levels §9.6(3)

When it retains medium or lowpermeability (mainly fine)soils, the wall should bedesigned for a water levelabove formation level

Without reliable drainage, waterlevel should normally betaken at the surface of the

. . w =

With reliable drainage, waterlevel may be assumed to be

. .dw > 0) + maintenancerequirement




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Should water pressures be factored?. . .

For ultimate limit states (ULSs)…

design values [of groundwater pressures] shall represent the mostunfavourable values that could occur during the design lifetime of

the structure

For serviceability limit states (SLSs)…design values shall be the most unfavourable values which couldoccur in normal circumstances

[EN 1997-1 §2.4.6.1(6)P]

Design values of ground-water pressures may be derived either byapplying partial factors to characteristic water pressures or by

applying a safety margin to the characteristic water level…

[EN 1997-1 §2.4.6.1(8)]




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Possible ways of treating water pressures ,

a es gn wa er eve s or an es gn s ua ons

(b) Characteristic water pressures for SLS design situation

Design pressures for ULS, with... c no ac or app e γ = .

(d) factor on permanent actions (γG = 1.35)

(e) factor on permanent actions (γG = 1.35) applied to normal water level and


γQ = .

(f) factor on variable actions (γQ = 1.5)



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Providing a balance between reliability and,

“When partial factors γG

> 1.0 are applied to effective earthpressures, then pore water pressures should also be multiplied by

γG > 1.0 but calculated from highest normal (i.e. serviceability)water levels – i.e. no safety margin is applied (Design Water

Condition 1)

“When partial factors γG = 1.0 are applied [they should be] multipliedb = 1.0 but calculated from hi hest ossible i.e. ultimate

water levels – after an appropriate safety margin has been applied(Design Water Condition 2)”




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Recommended treatment of water pressures,




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BASIS OF DESIGN FOR GRAVITY



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Verification of strength for GEO/STR ,




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Design Approaches explained

Design Approach

Combination 1 Combination 2

Actions Material Actions/effects Structuralproperties & resistances actions/effects

& materialproperties

A1 + M1 + R1 A2 + M2 + R1 A1 + M1 + R2 A1/A2 + M2 + R3

(Major) factors >> 1.0; (minor) factors > 1.0- =

M1-M2 = factors on material propertiesR1-R3 = factors on resistances

©2013. Author name. All rights reserved17



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Partial factors for GEO/STR (DA1): footings,,

Parameter Symbol Combination 1 Combination 2

A1 M1 R1 A2 M2 R1

Permanent action (G)Unfavourable γG 1.35

1.0Favourable (γG,fav) 1.0

Unfavourable 1.5 1.3Variable action (Q)

Favourable - (0) (0)

Shearing resistance (tan ϕ) γϕ1.25

’

1.0

c

Undrained shear strength (cu) γcu1.4

Unconfined compressive strength (qu) γqu

γ

Bearing resistance (Rv) γRv

1.0 1.0Sliding resistance (Rh) γRh


Factors given for persistent and transient design situations



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Partial factors for GEO/STR (DAs 2/3):, ,

Parameter Symbol Design Approach 2 Design Approach 3

A1 M1 R2 A1# A2* M2 R3

Permanentaction (G)

Unfavourable γG 1.351.35 1.0

Favourable (γG,fav) 1.0

Variable action Unfavourable γQ 1.5 1.5 1.3

Favourable - (0) (0)

Shearing resistance (tan ϕ) γϕ1.25

Effective cohesion (c’) γc

. u γcu

1.4Unconfined comp. str. (qu) γqu

Weight density (γ) γγ 1.0

Bearin resistance R 1.4

1.0Sliding resistance (Rh) γRh 1.1

Earth resistance (Re) wallsγRe

1.4

Earth resistance (Re) slopes 1.1


Factors given for persistent and transient design situations#

Applied to structural actions; *applied to geotechnical actions



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National choice of Design Approach for,




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Retaining structures I –desi n of ravit walls

VERIFICATION OF STRENGTH:. .



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Earth pressures on a reinforced concrete wall ,




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Active and passive limit states (Annex C)

Eurocode 7 Part 1 (+Corrigendum 1) gives expressions for

active/passive earth pressures:

σ γ ⎛ ⎞

= + − − + +⎜ ⎟∫ 2 (1 / )z

a a aK dz q u c K a c u

σ γ ⎛ ⎞= + − + + +⎜ ⎟∫ 2 (1 / )

z

p p pK dz q u c K a c u

σa(z), σp(z) = active/passive stress normal to wall at depth z

=a p

γ = weight density of retained ground; c = ground cohesion

q = vertical surface load; z = distance down face of wall


a = wa a es on



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Rankine’s earth pressure coefficient

Earth pressure coefficient for active conditions, assuming a Rankine

zone forms between the back of the wall and the virtual plane:

β

β β ϕ β

⎛ ⎞− −⎜ ⎟=

2 2

,a

cos cos cosK cos

Ka,β = active earth pressure coefficient for inclined thrust (= σ’ β / σ’ v)

ϕ + −cos cos cos

ϕ = angle of shearing of soil; β = angle of inclination of groundsurface

σ’ = inclined effective stress; σ’ = vertical effective stressWhen β = 0, this reduces to the more familiar:

ϕ −=

1 ina

sK




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At rest earth pressures

Earth pressure coefficient for at-rest conditions:

= = ’ ’

0 (1 sin ) (1 sin )K OCRϕ β = − × × +

ϕ = angle of shearing of soil;OCR = overconsolidation ratio (= σ’ v,max / σ’ v)

σ’ h = horizontal effective stress; σ’ v = vertical effective stress

,movement of structure is less than 0.05% of H

Expression is a combination of Meyerhof’s equation for K0 and Kezdi’s




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VERIFICATION OF STRENGTH:



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Earth pressures on a mass gravity wall ,




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Charts of Kerisel and Absi’s earth pressure

Charts are not attributed, but

come from Kerisel and Absi’swork. They are the same asappear in BS 8002

Kerisel and Absi assumed lo -

spiral failure surfaces andhence their charts give upperbound values of Ka and K

Charts are given for walls withvertical faces only

, ,a

p

f K

ϕ ϕ ϕ

=⎬ ⎨ ⎬⎪ ⎩ ⎭⎭




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‘New’ formulation for active and passive earth

z

a a a acK dz u K q K cγ σ γ ⎛ ⎞

′ = − + −⎜ ⎟ ( )cos cosa

n

K K

γ

β β θ ⎫⎪

= × × −⎬0

z

p p pq pcK dz u K q K cγ σ γ ⎛ ⎞

′ = − + +⎜ ⎟∫

pγ

aK ⎫cosn

pqK

= ×

⎪⎭

β ϕ β

ϕ

− ⎛ ⎞−= −⎜ ⎟±⎝ ⎠

m1 sin

2 cossin

tm ( )1 cot

ac

n pc

K K

ϕ = − ×⎬⎪⎭

2( )tan1 sin sin(2 )

1 sin sin(2 )t wm mw

n

t

mK e

m β θ ϕ ϕ ϕ

ϕ ϕ

± + − −± × ±=

× ±m

δ ϕ δ

ϕ

− ⎛ ⎞= ⎜ ⎟

⎝ ⎠m m

1 sin2 cos

sinwm




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Charts of Brinch Hansen’s earth pressure,




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VERIFICATION OF STRENGTH:



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No single design method accepted throughout

Eurocode 7 … does not cover the detailed design of reinforced fill

structures. The values of the partial factors … given in EN 1997-1have not been calibrated for reinforced fill structures

[Foreword to EN 14475]

Design of reinforced fill structures is currently carried out to nationalstandards (such as BS 8006)

, , , .delayed the development of a single design method acceptedthroughout Europe

prov es gu ance on e execu on o re n orcestructures

It is hoped that a future European standard will cover design




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VERIFICATION OF



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Verification of serviceability

Verification of serviceability is expressed in Eurocode 7 by:

Ed = design effect of actions (e.g. displacement, distortion)

d d

d . .

For ‘conventional structures founded on clays’, Eurocode 7 allows

calculation for bearing resistance satisfies:

kR

Ek = characteristic effects of actions; Ek = characteristic resistance

γ ,

k

R SLS


γR,SLS = a partial resistance factor ≥ 3.0



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SUPERVISION, MONITORING,



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Supervision of construction (Annex J)

Selected (general) items from checklist in Annex J on supervision of

construction:Verification of ground conditions and of the location and general lay-out

of the structure

Ground-water flow and pore-water pressure regime; effects ofdewatering on ground-water table; effectiveness of measures to

control seepage inflow; corrosion potentialMovements, yielding, stability of excavation walls and base; temporary

suppor sys ems; e ec s on near y u ngs an u es;measurement of soil pressures on retaining structures and of pore-water pressure variations resulting from excavation or loading


E d



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Supervision water flow and pore-water

Selected items from checklist in Annex J on water flow and pore-

water pressuresAdequacy of systems to control pore-water pressures in aquifers where

excess pressure could affect stability of base of excavation, includingartesian pressures beneath the excavation; disposal of water fromewater ng systems; epress on o groun -water ta e t roug out

entire excavation to prevent boiling or quick conditions, piping anddisturbance of formation by construction equipment; diversion andremoval of rainfall or other surface water

Control of dewatering to avoid disturbance of adjoining structures orareas; observations of piezometric levels; effectiveness, operation and

maintenance of water recharge systemsSettlement of adjoining structures or areas

Effectiveness of sub-horizontal borehole drains


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Monitoring and maintenance (Annex J)

Selected items from checklist in Annex J on performance monitoring:

Settlement at established time intervals of buildings and otherstructures including those due to effects of vibrations onmetastable soils

Lateral displacement and distortions, especially those related to fillsand stock iles soil su orted structures such as buildin s or lar etanks; deep trenches

Piezometric levels under buildings or in adjoining areas, especially ifdeep drainage or permanent dewatering systems are installed or if

Deflection or displacement of retaining structures considering: normalbackfill loadings; effects of stockpiles; fills or other surface

loadings; water pressuresFlow measurements from drains

Water tightness

(No specific guidance given for maintenance)




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SUMMARY OF KEY POINTS

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Summary of key points

Design of gravity walls to Eurocode 7 involves checking that the

ground beneath the wall has sufficient:bearing resistance to withstand inclined, eccentric actions

sliding resistance to withstand horizontal and inclined actions

stabilit to avoid to lin

stiffness to prevent unacceptable settlement or tilt

satisfying the inequalities:

, , p st st


E d



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blo .eurocode7.com

www.decodingeurocode2.comwww.decodin eurocode7.com

DECODING THE EUROCODES

E d



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eurocodes.jrc.ec.europa.eu

03 Bond Design of Gravity Walls

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