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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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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 3
Introducing earthworks into the trinity
Slope stability to Eurocode 7
Stability of earthworks to Eurocode 7
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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 5
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
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 6
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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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 7
Verification of strength for GEO/STR
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 8
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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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 9
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
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 10
National choice of Design Approach
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Example: stability of infinitely long slope
Stability of earthworks to Eurocode 7
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 12
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
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 14
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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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 15
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
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 16
Eurocode 7 stability chart for 1:3 slope with ru = 0.5Design Approaches compared
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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 17
Design chart for infinitely long slope using Design Approach 1 with ru = 0.5 (from Bond & Harris, 2008)
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 18
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
Stability of earthworks to Eurocode 7
May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 20
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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May-09 Eurocode 7 and earthworks ©2009 Geocentrix Ltd. All rights reserved 21
‘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