Stability of earthworks to Eurocode 7 (print) · 2 May-09 Eurocode 7 and earthworks ©2009...

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Stability of earthworks to Eurocode 7

Dr Andrew Bond (Geocentrix)

May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 2

‘Trinity’ of geotechnical standards

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Introducing earthworks into the trinity

Slope stability to Eurocode 7


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Design: overlap with Eurocode 7

Section 11 Overall stabilitySection 12 Embankments

§x.1 General (2/2 paragraphs)§x.2 Limit states (2/2)§x.3 Actions and design situations (6/8)§x.4 Design and construction considerations (11/13)§x.5 Ultimate limit state design (26/7)§x.6 Serviceability limit state design (3/4)§11.7 Monitoring (2)/§12.7 Supervision and Monitoring (5)

ScopeSection 11 covers overall stability of the ground and movements in

the ground related to foundations, retaining structures, naturalslopes, embankments, and excavations

Section 12 covers embankments for small dams and infrastructure


Verification of strength

Verification of strength is expressed in Eurocode 7 by:

Ed = design effect of actionsRd = design resistance corresponding to that effect

This requirement applies to limit state GEO:“Failure or excessive deformation of the ground, in which the strength

of soil or rock is significant in providing resistance’EN 1997-1 §2.4.7.1(1)P

…and to ultimate limit state STR“Internal failure or excessive deformation of the structure or structural

elements … in which the strength of structural materials is significant in providing resistance”

EN 1997-1 §2.4.7.1(1)P

≤d dE R

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Verification of strength for GEO/STR


Partial factors for limit states GEO/STR for persistent/transient design situations, as recommended by EN 1997-1

SlopesWalls

(1.0)

R4

VariesPile resistance1.11.4γReEarth resistance

(Re)

1.11.4

1.0

1.4

Material factors

1.0

M1

(0)1.3

(0)1.51.0

1.35A1

Action factors

1.0A2

1.25

M2

γRhSliding resistance (Rh)

γcEffective cohesion (c’)γcuUndrained shear strength (cu)

1.01.0γRvBearing resistance (Rv)γγWeight density (γ)

γquUnconfined compressive strength (qu)

γφShearing resistance (tan φ)

Sym-bol

-FavourableγQUnfavourableVariable

action (Q)

(γG,fav)FavourableγGUnfavourablePermanent

action (G)

R3R2R1

Resistance factorsParameter

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Design Approaches for STR/GEO

§2.4.7.3.4.1(1)P The manner in which equations [above] are applied shall be determined using one of three Design Approaches

Design Approaches apply ONLY to STR and GEO limit statesEach nation can choose which one (or more) to allow

NA.4 … only Design Approach 1 is to be used in the UKIn simplest terms, the design approaches apply factors to the following…

A1/A2 + M2 + R3A1 + M1 + R2A2 + M2 + R1A1 + M1 + R1

Structural actions (or effects)& material properties

Actions (or effects)& resistances

Material properties

ActionsCombination 2Combination 1

321Design Approach


National choice of Design Approach

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Example: stability of infinitely long slope



Infinitely long slope overlying permeable and impermeable rock

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Analysis of infinitely long slope overlying permeable and impermeable rock

( ) 21 cos tansin cosγ β ϕ

γ β βγγ

′ + −=

=

u

w wu

c r HF

HhrH

( ) 2sin cos 1 cos tanβ β β ϕγ′

= = − − ucN F rH


Traditional stability chart for 1:3 slope with ru = 0.5H = 2.5m, ϕ = 30°, γ = 20 kN/m3, F = 1.0 → c’ =6.5 kPa

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Characteristic stability number based on Eurocode 7

( ) ( ) 2sin cos 1 cos tanϕ

γ γγ γ γ β β β ϕγ γ

⎛ ⎞′= ≥ − −⎜ ⎟⎜ ⎟

⎝ ⎠

k G ck G c Re u k

k

cN rH

≤d dE R

sin cos sin cosσ β β γ γ β β= =d vd G kE H

( )( )( ) 2

2

tan1 cos1 cos tan ϕ

ϕγ γ βγ γσ β ϕ

γ γ

⎛ ⎞⎛ ⎞′+ − ⎜ ⎟⎜ ⎟ ⎜ ⎟′ + − ⎝ ⎠ ⎝ ⎠= =

k ku G k

cd u vd dd

Re Re

c r Hc r

R

( ) ( ), 2sin cos 1 cos tanϕ

γ γγ γ γ β β β ϕ

γ γ⎛ ⎞′

= ≥ − −⎜ ⎟⎜ ⎟⎝ ⎠

G fav ckk G c Re u k

k

cN rH


Eurocode 7 stability chart for 1:3 slope with ru = 0.5Design Approaches compared

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Design chart for infinitely long slope using Design Approach 1 with ru = 0.5 (from Bond & Harris, 2008)


Design chart for finite slope using Design Approach 1 with ru = 0.3 (from Bond & Harris, 2008)

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Summary of key points



Summary of key points

Most countries in Europe have chosen Design Approach 1 or 3 for slope stability design

In Design Approach 1, slope stability is governed by Combination 2 over the practical range of soil shear resistances

Design Approach 1 Combination 2 gives near identical results to Design Approach 3

The use of Design Approach 2 for slope stability is ambiguous and potentially unsafe

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‘Decoding Eurocode 7’ by Bond and Harris (2008)

Book published August 2008Key features

Covers ENs 1997-1 and -2, plus relevant parts of other EurocodesAlso covers associated execution and testing standardsExplains key principlesIllustrates application rules with real-life case studiesMaterial extensively tested on training courses over 5 years

Authors Andrew Bond (Geocentrix) and Andy Harris (Geomantix)Published by Taylor and Francis in hardback, with colour sectionISBN: 9780415409483

Website: www.decodingeurocode7.com

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