Eurocode 7 and Slope Design - Decoding the Eurocodes

1 1 EurocodeEurocode7 and Slope Design7 and Slope DesignEngineering Sustainable Slopes10thJune 2008 Andrew Harris (Geomantix)Outline of presentationOutline of presentation Principles of EC7 for Slope engineering Implications of partial factor system for slopes Use of existing charts and software Conclusion2 Principles of EC7 for Slope engineeringPrinciples of EC7 for Slope engineeringScope of sections 11 and 12 Scope of sections 11 and 12 of EN 1992of EN 1992--11 Scope Section 11 covers overall stability of the ground and movements in the ground related to foundations, retaining structures, natural slopes, embankments.

2 And excavations Section 12 covers embankments for small dams and infrastructure3 Application of partial factors and Application of partial factors and tolerancestolerancesdFrepFF =kdMXX ={},,dEdddEEFXa ={},,ddddRRFXaR =ActionsResistancesEffects of actionsMaterial propertiesdnomaaa= Geometrical parametersVerification of strengthVerification of strengthVerification of strength is expressed in Eurocode 7 by:Ed= Design effect of actionsRd= Design resistance corresponding to that effectddER 4 Limits states for slopes and Limits states for slopes and embankmentsembankmentsLimit states for slopes in generalLimit states for slopes in general Limit states for slopes include.

3 Loss of overall stability of the ground and associated structures Excessive movement Loss of serviceability5 Verification of strength for GEO/STRV erification of strength for GEO/STRD esign Approaches for STR/GEOD esign Approaches for STR/GEO (1)P The manner in which equations are applied shall be determined using one of three Design Approaches Design Approaches apply ONLY to STR and GEO limit states Each nation can choose which one (or more) to allow only Design Approach 1 is to be used in the UK In simplest terms, the Design approaches apply factors to the ApproachesDesign ApproachesStructural actions (or effects)& material propertiesActions (or effects)& resistancesMaterial propertiesActionsCombination 2 Combination 1321 Design ApproachPartial factors for limit states GEO/STR Partial factors for limit states GEO/STR (DA1) Slopes(DA1) Slopes ReEarth resistance (Re) (0) RhSliding resistance (Rh) cEffective cohesion (c ) cuUndrained shear strength (cu) RvBearing resistance (Rv) Weight density ( )

4 QuUnconfined compressive strength (qu) Shearing resistance (tan )Symbol(0) QUnfavourableVariable action (Q)( G,fav) GUnfavourablePermanent action (G)R1M2A2 Combination 2 Parameter7 Design Approach 1 for Design Approach 1 for slopes and embankmentsslopes and embankmentsImplications of partial factor system Implications of partial factor system for slopesfor slopes8 stability of infinitely long slopeStability of infinitely long slopeImplications of partial factor system for slopesInfinitely long Slope overlying Infinitely long Slope overlying permeablepermeableand impermeable rockand impermeable rock9 Equations for infinite slopeEquations for infinite Slope Traditional definition of factors of safety()

5 21costansin cosuwwucrHFHhrH + ==Applying partial factorsApplying partial factors The Design effect of actions may be taken as: The Design resistance may be taken as:Rd = c d+ (1 ru) vdcos2 tan d= c k+ (1 ru) G kH cos2 tan k ddER ==sin cossin cosdvdGkEH Re Re c10 Applying partial factorsApplying partial factorsor the Design resistance may be taken as:Rd = c k+ (1 ru) G;fav kH cos2 tan k As long as Rdis at least as great as Edthe requirements of EN 1997-1 are satisfied Re cEffect of favourable or unfavourableEffect of favourable or unfavourable EN 1997-1 applies different partial factors to favourable and unfavourable = c G, GCombination 2 Combination 1 Design Approach 1 Individual partial factor11 Unfavourable/favourableUnfavourable/favo urable In the Edterm the action due to the self-weight of the soil is unfavourable and should be multiplied by G= In the Rdterm the self-weight is favourable and may be multiplied by G.

6 Fav= If this is assumed then Combination 1 always governs for effective stress analysis with an equivalent overall factor of safety of However, is it logical to multiply the same action by different partial factors?Single source principleSingle source principleEN 1997-1 Clause Note Unfavourable (or destabilising) and favourable (or stabilising) permanent actions may in some situations be considered as coming from a single source. If they are considered so, a single partial factor may be applied to the sum of these actions or to the sum of their If self weight is considered unfavourable when assessing both the Design effect of the actions and the Design resistance, Combination 2 governs for all effective stress cases In this case the equivalent factor of safety for the Slope is except for very low angles of friction and provided there are no variable actions Is this large enough?

7 Unfavourable/favourable? Unfavourable/favourable? (1:3 Slope (1:3 Slope , , rruu= ))F = = = of a finite slopeStability of a finite slopeImplications of partial factor system for slopesKey features of circular slip analysisKey features of circular slip analysis14 BishopBishop s s RoutineRoutine (aka (aka SimplifiedSimplified ) ) MethodMethod()(){}()tansectan1tansiniiii iiiiiiiii iicbW Q ubFFWQ ++ + =+ partial factors applied to material propertiespartial factors unfavourable or favourable?partial factors unfavourable on variable actionsApplying partial factors to BishopApplying partial factors to Bishop s Methods Method In principle the same approach may be adopted as for infinite slopes It is complicated by the iterative nature of circular slip analysis (or non-circular) It is less clear what parts of the equation are favourable or unfavourable- eg when is negative the self-weight of the slip reduces the overturning moment There is therefore no fully logical way of applying Gand G.

8 Fav15 Use of existing charts and softwareUse of existing charts and softwareTraditional stability chart for infinite Traditional stability chart for infinite Slope (1:3 slopeslope (1:3 Slope , , rruu= ))16 Design Approaches compared Design Approaches compared (1:3 Slope (1:3 Slope , , rruu= ))Infinite Slope Infinite Slope -- Design chart for Design chart for Design Approach 1 Design Approach 1 ((rruu= ) from Bond & Harris (2008)) from Bond & Harris (2008)17 Slope stability softwareSlope stability software Standard Slope stability software does not allow different factors to be applied to different parts of the relevant equations Combination 1 may be approximated by multiplying the weight density of the soil be and any applied variable action by = This applies the unfavourable partial factor to both the favourable and unfavourable elements of the equationsSoftware (cont)Software (cont) Combination 2 is relatively easy to accommodate as the strength parameters may be factored on input.

9 Any variable action may be multiplied by Provided the critical surface has a factor of safety greater or equal to then the requirements of EN 1997-1 are satisfied In principle the results of a DA1-1 and DA1-2 analysis should be compared to identify which is most critical, but it is clear that DA1-2 will govern18 ConclusionConclusionEurocode 7 and Slope DesignSummary of key points 1 Summary of key points 1 Unless the Single Source Principle is invoked, Eurocode 7 requires different partial factors to be applied to unfavourable and favourable actions, which is not possible with typical limit equilibrium Slope stability calculations For Design Approach 1, Combination 2 governs the Design of slopes and embankments for practical values of soil shearing resistance 19 Summary of key points 2 Summary of key points 2 As Combination 2 governs is the equivalent factor of safety = adequate?

10 The logical approach to limit equilibrium Slope stability problems is to factor strength, thus EC7 makes little change EC7 defines the minimum required levels of safety, it may be necessary to use higher partial factorsDecoding Eurocode 7 Decoding Eurocode 7 Book published Autumn 2008 by Spon in hardback with colour section Authors Andrew Bond (Geocentrix) and Andy Harris (Geomantix) Web: Key features Covers EN 1997-1 and -2, plus relevant parts of other Eurocodes Also covers associated execution and testing standards Explains key principles and application rules with real-life case studies Material extensively tested on training courses over 5 years ISBN 978041540948320 Decoding the EurocodesDecoding the Eurocodes blogblog Web log (blog) started May 2006 Website.