Retaining Walls and Geotechnical Design to Eurocode 7 Summary

EUROCODE 7

Retaining Walls and Geotechnical Design to Eurocode 7 Dr Ian Smith Head of School School of Engineering and the Built Environment Edinburgh Napier University

EUROCODE 7

Geotechnical design by calculation Processes involved: Establish design values of actions and geometrical data

Establish design values of ground properties and resistances

Define limit that must not be exceeded (e.g. bearing resistance)

Perform relevant geotechnical analysis

Show, by calculation, that limit will not be exceeded

EUROCODE 7

Geotechnical design by calculation Processes involved: Establish design values of actions and geometrical data

Establish design values of ground properties and resistances

Define limit that must not be exceeded (e.g. bearing resistance)

Perform relevant geotechnical analysis

Show, by calculation, that limit will not be exceeded

EUROCODE 7

Geotechnical design by calculation Actions: • An action action is given given the general general symbol, symbol, F. F. • Acti Actions ons can be permanent permanent (persiste (persistent) nt) or variable variable (transient), accidental, or seismic. • Pers Persisten istentt actions actions are are denoted denoted by FG. Transient actions are denoted by FQ. • Pers Persisten istentt action actions s can can be either “fav “favourab ourable” le” or “unfavourable”. • Transient actions are always always considered considered as unfavourable.

EUROCODE 7

Geotechnical design by calculation Ground properties: • Geotechnical parameters should be established with consideration consideration given to published data and local and general experience… • Clauses 2.4.3(3) 2.4.3(3) to (6) (6) give guidance on how the parameters parameters should be considered in the design process. • Mater Material ial properties properties are are given the general general symbol, symbol, X. • Characteristic values of material properties are given the general symbol, Xk.

EUROCODE 7

Partial factors of safety Provided in EN 1997-1 Nationally Determined Parameters (NDPs) provided in National Annexe Symbols:  Actions:

General: F

Permanent: G Transient: Q

Materials:

General: M

Soil properties: cu, , etc.

Resistance:

General: R

Bearing resistance: Rv

NB geotechnical engineers already use “” for unit weight (weight density).

EUROCODE 7

Design values These are obtained by combining the characteristic value with the appropriate partial factor of safety.

i.e. characteristic value design value partial factor of safety

EUROCODE 7

Geotechnical design by calculation Representative action Fk

Characteristic material property, e.g. c'

The design is all about Multiplied by

F

Divided by

values

Actions: (loads, forces etc.)

and

Design action Fd

M

values

Material Properties (c, tan , etc.) Design material property, e.g. c'd

Geotechnical Analysis

Design effect of actions, Ed

Design Resistance, Rd Verify

EUROCODE 7

Design values of actions

Characteristic action



representative action

(Fk)



design action

(Frep) Correlation factor, 

(Fd)



design effects of action (Ed)

Partial factor of safety, F

i.e. Frep = Fk   Fd = Frep  F

(  1.0;  = 1.0 for persistent actions)

EUROCODE 7

Design values of geotech params Characteristic geotechnical Parameter  (Mk)

Partial factor of safety, M

i.e.

 M d  

Design geotechnical Parameter 

 M k     M 

(Md)

EUROCODE 7

Design effects of actions (i) i) During the verification of geotechnical strength (i.e. GEO limit state) some effects of the actions will depend on the strength of the ground in addition to the magnitude of the applied action and the dimensions of the structure. Thus, the effect of an action in the GEO limit state is a function of the action, the material properties and the geometrical dimensions. i.e. Ed = E{Fd; Xd; ad} where Ed is the design effect of the action, and Fd is the design action; Xd is the design material property; ad is the design dimension, and where E{…} indicates that the effect, E is a function of the terms in the parenthesis.

EUROCODE 7

Design effects of actions (ii) During the verification of static equilibrium (i.e. EQU limit state) some effects of the actions (both destabilising and stabilising) will depend on the strength of the ground in addition to the magnitude of the applied action and the dimensions of the structure. Thus, the effect of an action in the EQU limit state, whether it be a stabilising or a destabilising action, is a function of the action, the material properties and the geometrical dimensions. i.e. Edst;d = E{Fd; Xd; ad}dst where Edst;d is the design effect of the destabilising action, and Estb;d = E{Fd; Xd; ad}stb where Estb;d is the design effect of the stabilising action.

EUROCODE 7

Design resistances Equation 6.6 in EN 1990:2002 indicates that the design resistance depends on material properties and the structural dimension. However, in geotechnical design, many resistances depend on the magnitude of the actions and so EN 1997-1:2004 2.4.7.3.3 redefines Equation 6.6 to include the contribution made by the design action. The clause actually offers three methods of establishing the design resistance,

 Rd    RF d  ; X d  ; a d  

or

 Rd  

 RF d  ; X k  ; a d      R

or

 RF  ; X  ; a   Rd     d  d  d     R

 Annex B of Eurocode 7 Part 1 offers guidance on which of the 3 formulae above to use for each design approach.

EUROCODE 7

The five ultimate limit states Eurocode 7 lists five ultimate limit states to consider: • Verification of static equilibrium (EQU) • Verification of (structural) strength (STR) • Verification of (ground) strength (GEO) • Verification of resistance to uplift (UPL) • Verification of resistance to heave failure due to seepage (HYD)

EUROCODE 7

Ultimate limit states ULS for Stability:

EQU

UPL

HYD

Loss of static equilibrium

Uplift by water pressure

Hydraulic heave/erosion

ULS for Strength:

GEO

STR

EUROCODE 7

Equilibrium (EQU) limit state Loss of static equilibrium

EQU: loss of equilibrium of the structure or the supporting ground when considered as a rigid body and where the internal strength of the structure and the ground do not provide resistance.

Limit state is satisfied if the sum of the design values of the effects of destabilising actions (Edst;d) is less than or equal to the sum of the design values of the effects of the stabilising actions (Estb;d) together with any contribution through the resistance of the ground around the structure (Td), i.e.

Edst;d ≤ Estb;d + Td.

EUROCODE 7

Geotechnical (GEO) limit state Failure of the ground

GEO: failure or excessive deformation of the ground, where the soil or rock is significant in providing resistance.

This limit state is satisfied if the design effect of the actions (E d) is less than or equal to the design resistance (Rd), i.e.

Ed ≤ Rd

EUROCODE 7

Structural (STR) limit state Internal failure of structure

STR: failure or excessive deformation of the structure, where the strength of the structural material is significant in providing resistance.

 As with GEO limit state, the STR limit state is satisfied if the design effect of the actions (E d) is less than or equal to the design resistance (Rd), i.e.

Ed ≤ Rd

EUROCODE 7

Uplift (UPL) limit state Uplift by water pressure

UPL: the loss of equilibrium of the structure or the supporting ground by vertical uplift due to water pressures (buoyancy) or other actions.

This limit state is verified by checking that the sum of the design permanent and variable destabilising vertical actions (Vdst;d) is less than or equal to the sum of the design stabilising permanent vertical action (Gstb;d) and any additional resistance to uplift (Rd). i.e.

Vdst;d ≤ Gstb;d + Rd.

EUROCODE 7

Hydraulic (HYD) limit state Hydraulic heave/erosion

UPL: hydraulic heave, internal erosion and piping in the ground as might be experienced, for example, at the base of a braced excavation.

This limit state is verified by checking that the design total pore water pressure (u dst;d) or seepage force (Sdst;d) at the base of the soil column under investigation is less than or equal to the total vertical stress ( stb;d) at the bottom of the column, or the submerged unit weight (G'stb;d) of the same column. i.e.

udst;d ≤ stb;d

or

Sdst;d ≤ G'stb;d.

EUROCODE 7

ULS for retaining structures

(a) Overturning (Eurocode 7 EQU limit state)

(b) Bearing failure (Eurocode 7 GEO limit state)

(d) Ground failure (Eurocode 7 GEO limit state)

(c) Forward sliding (Eurocode 7 GEO limit state)

(e) Structural failure (Eurocode 7 STR limit state)

EUROCODE 7

EQU limit state Destabilising actions and effects

Stabilising actions and effects

Representative destabilising actions, Fdst; rep

Representative stabilising actions, Fstb; rep

Partial factors,

Partial factors,

F dst

F stb

Design destabilising actions, Fdst;d

Design stabilising actions, Fstb;d

GEOTECHNICAL ANALYSIS

Design effect of destabilising actions, Edst;d

Design effect of stabilising actions, Estb;d

EUROCODE 7

EQU limit state example Overturning

q

Pq W

Pa

EUROCODE 7

GEO limit state

Partial factors,

 Ac ti ons and effects

Material properties and resistance

Representative actions, Frep

Characteristic material properties, Xk

Partial factors,

F

Design actions, F d

Design material properties, Xd

GEOTECHNICAL ANALYSIS

Design effect of actions, Ed

Design resistance, R d

Verify E

 ≤

R

M

EUROCODE 7

GEO/STR Limit states Three Design Approaches are offered - to reflect national choice

The design approach followed reflects whether the safety is applied to the material properties, the actions or the resistances. Design Approach 1:

Combination 1: A1 + M1 + R1 †Combination 2: A2 + M2 + R1

Design Approach 2: Design Approach 3:

A1 + M1 + R2 A* + M2 + R3

 A*: use set A1 on structural actions, set A2 on geotechnical actions †

For axially loaded piles, DA1, Combination 2 is: A2 + (M1 or M2) + R4

The UK National Annex states that Design Approach 1 shall be used.

EUROCODE 7

GEO/STR Limit states GEO/STR - Partial factor sets Parameter  Permanent action (G)

Variable action (Q)

Symbol

A1

A2

Unfavourable

G

1.35

1.0

Favourable

G

1.0

1.0

Unfavourable

Q

1.5

1.3

-

-

-

A

1.0

1.0

-

-

-

Favourable Accidental action (A)

Unfavourable Favourable

M1

M2

R1

R2

R3

Coefficient of shearing resistance (tan ')



'

1.0

1.25

Effective cohesion (c')

c'

1.0

1.25

Undrained shear strength (c u)

cu

1.0

1.4

Unconfined compressive strength (q u)

qu

1.0

1.4

Weight density ( )



1.0

1.0

Bearing resistance (R v)

Rv

1.0

1.4

1.0

Sliding resistance (R h)

Rh

1.0

1.1

1.0

Earth resistance (R e)

Re

1.0

1.4

1.0

EUROCODE 7

Representation of degree of safety Over-design factor:

Degree of utilisation:



 Rd   E d 



 E d   Rd 

EUROCODE 7

GEO limit state examples sliding…

… and bearing

Gfav Gunfav

Qunfav

Gunfav Gunfav

Ed Ed Rd

R

Qunfav

EUROCODE 7

Retaining wall design Covered in Section 9 of Eurocode 7 Part 1 (1)P The provisions of this Section shall apply to structures, which retain ground comprising soil, rock or backfill and water. Material is retained if it is kept at a slope steeper than it would eventually adopt if no structure were present. Retaining structures include all types of wall and support systems in which structural elements have forces imposed by the retained material.

EN 1997-1:2004 9.1.1(1)P

EUROCODE 7

Retaining wall design Limit states The limit states to be considered are listed in 9.2(1) and are: • loss of overall stability; • failure of a structural element such as a wall, anchorage, wale or strut or failure of the connection between such elements; • combined failure in the ground and in the structural element; • failure by hydraulic heave and piping; • movement of the retaining structure, which may cause collapse or affect the appearance or  • efficient use of the structure or nearby structures or services, which rely on it; • unacceptable leakage through or beneath the wall; • unacceptable transport of soil particles through or beneath the wall; • unacceptable change in the ground-water regime.

EUROCODE 7

Retaining wall design Plus… Gravity walls: bearing resistance failure of the soil below the base; failure by sliding at the base; failure by toppling; Embedded walls: failure by rotation or translation of the wall or parts thereof; failure by lack of vertical equilibrium. EN 1997-1:2004 9.2(1)

EUROCODE 7

Ultimate limit states

(a) Overturning (Eurocode 7 EQU limit state)

(b) Bearing failure (Eurocode 7 GEO limit state)

(d) Ground failure (Eurocode 7 GEO limit state)

(c) Forward sliding (Eurocode 7 GEO limit state)

(e) Structural failure (Eurocode 7 STR limit state)

EUROCODE 7

Ultimate limit states Must also consider overall stability (Section 11)…

EUROCODE 7

Future unplanned excavation (2) In ultimate limit state calculations in which the stability of a retaining wall depends on the ground resistance in front of the structure, the level of the resisting soil should be lowered below the nominally expected level by an amount a. … — for a cantilever wall, a should equal 10 % of the wall height above excavation level, limited to a maximum of 0,5 m; — for a supported wall, a should equal 10 % of the distance between the lowest support and the excavation level, limited to a maximum of 0,5 m. EN 1997-1:2004 9.3.2.2(2) (3) Smaller values of a, including 0, may be used when the surface level is specified to be controlled reliably throughout the appropriate execution period.

EUROCODE 7

Gravity walls When Rankine’s conditions do not apply... Charts for both horizontal and inclined retained surfaces are given in Annex C. 1.0 1 0.9 0.8 0.7 0.6 0.5

0.4

Ka 0.3

0.2

δ / φ' = 0 δ / φ' = 0.66 δ / φ' = 1 0.1 0

5

10

15

20

25

Design values of

30

'

35

40

45

EUROCODE 7

Example Surcharge, q = 20 kPa 1.8 m

2

4.0 m 1

Retained fill: c' = 0; ' = 32  = 18 kN/m3

K a      h = 22.4 kPa

K a  q = 6.2 kPa

2.0 m 3

= 26.7 kPa 1.0 m

Foundation soil: c' = 0; ' = 28  = 20 kN/m3

7.4 kPa 34.1 kPa

2.6 m

Check the overturning (EQU) and sliding (GEO) (using Design Approach 1) limit states.

EUROCODE 7

Embedded walls

EUROCODE 7

Embedded walls Cantilever wall – pressure distribution q = 10kPa

h

0.1h; > 0.5m

Pq1 Pa1 d 

Pp1

d 0

O

K  pd 0 K ad 

K a(h+d 0)

Pq2 K  p(h+d)

Pa2

Pp2

EUROCODE 7

Embedded walls Cantilever wall – simplified pressure distribution

Pq 

P p

Pa R 

K  pd 0

K a(h+d 0)

h+d 0 3

EUROCODE 7

Passive resistance Favourable action:

P p ;d   P p ;k     G ; fav or 

Resistance:

P p ;d  

P p ;k    Re

EUROCODE 7

Passive resistance

Design Approach 1

2

3

Combination 1

Combination 2

G;fav

1.0

1.0

1.0

1.0

Re

1.0

1.0

1.4

1.0

i.e. only concerns Design Approach 2

EUROCODE 7

Passive resistance but what about for embedded walls?… Single Source Principle…

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 effects. EN 1997-1:2004 2.4.2 Note to (9)P

EUROCODE 7

Passive resistance

P p

Pa

“uncertainty” in Pp = “uncertainty” in Pa

i.e.

if Pa is a permanent unfavourable action, so must be Pp (Single source principle)