1

Session 4

Risk and Reliability

Design of Retaining Structures

Slopes, Overall Stability and

Embankments

(Blarney Castle)

2

Session 4a

Risk and reliability

3

Complexity and Geotechnical Risk

• The complexity of a geotechnical design situation and the geotechnical risks involved are due to the geotechnical hazards and the vulnerability of the structure being designed

• When assessing the complexity of a design situation, the following factors related to geotechnical hazards should be considered (Clause 2.1(2)):

– Ground conditions– Groundwater situation– Regional seismicity– Influence of the environment

• And the following factors relating to the vulnerability of a structure:– Nature and size of the structure and its elements– Surroundings

• The concept of three Geotechnical Categories is offered as a method to assess the complexity (Clause 2.1(10))

4

Geotechnical Categories and Risk Factors

HighModerateLowGeotechnical Risk

High risk of damage to neighbouring structures or services

Possible risk of damage to neighbouring structures or services due, for example, to excavations or piling

Negligible risk of damage to or from neighbouring structures or services and negligible risk for life

Surroundings

Very large or unusual structures and structures involving abnormal risks. Very sensitive structures in seismic areas

Conventional types of structures with no abnormal risks

Small and relatively simple structures or construction. Insensitive structures in seismic areas

Nature and size of the structure and its elements

HighModerateLowVulnerability

Complex or difficult environmental factors requiring special design methods

Environmental factors covered by routine design methods

Negligible risk of problems due to surface water, subsidence, hazardous chemicals, etc.

Influence of the environment

Areas of high earthquake hazardModerate earthquake hazard where seismic design code (EC8) may be used

Areas with no or very low earthquake hazard

Regional seismicity

High groundwater pressures and except-ional groundwater conditions, e.g. multi-layered strata with variable permeability

No risk of damage without prior warning to structures due to groundwater lowering or drainage. No exceptional water tightness requirements

No excavations below water table, except where experience indicates this will not cause problems

Groundwater situation

Unusual or exceptionally difficult ground conditions requiring non routine investigations and tests

Ground conditions and properties can be determined from routine investigations and tests.

Known from comparable experience to be straightforward. Not involving soft, loose or compressible soil, loose fill or sloping ground.

Ground conditions

HighModerateLow

Geotechnical ComplexityGeotechnicalhazards

GC3GC2GC1

Geotechnical CategoriesRisk Factors

5

Expertise, Investigations, Design Methods and Structural Types related to Geotechnical Categories

• Very large buildings• Large bridges• Deep excavations• Embankments on soft ground•Tunnels in soft or highly permeable ground

Conventional:• Spread and pile foundations• Walls and other retaining structures• Bridge piers and abutments• Embankments and earthworks• Ground anchors and other support systems• Tunnels in hard, non-fractured rock

• Simple 1 and 2 storey structures and agricultural buildings having maximum design column load of 250kN and maximum design wall load of 100kN/m• Retaining walls and excavation supports where ground level difference does not exceed 2m• Small excavations for drainage and pipes

Examples of structures

More sophisticated analysesRoutine calculations for stability and deformations based on design procedures in EC7

Prescriptive measures and simplified design procedures, e.g. design bearing pressures based on experience or published presumed bearing pressures. Stability or deformation calculations may not be necessary.

Design procedures

Additional more sophisticated investigations and laboratory tests

Routine investigations involving borings, field and laboratory tests

Qualitative investigations including trial pits

Geotechnical investigations

Experienced geotechnical specialist

Experienced qualified personPerson with appropriate comparable experience

Expertise requiredGC3GC2GC1

Geotechnical Categories

6

Reliability

• All Eurocodes based on reliability analyses – i.e. aim to achieve structures with a certain target probability of failure:– 1x10-6 in 1 year for a ULS– 2x10-3 for an SLS– β = 3.8

• Target reliability achieved through:– Use of characteristic loads– Selection of characteristic parameter values– Choice of appropriate partial factor values

• Hence appropriate selection of characteristic values is essential to obtain the required reliability for geotechnical designs

7

Reliability Analyses

The reliability of the ULS design of a spread foundation was investigated for:• Different loading conditions• Different failure mechanism • Different characteristic values – 5% fractile or 95% confidence in mean• Auto-correlation length δv• Correlated and uncorrelated c’ – tanφ’ values

8

Example Details

• Loading conditions• Results shown for Load Case 1

• FORM analysis and β values

9

Failure Mechanism

• Choice of depth to select soil parameter values

10

Calculated β Values

40.037.535.032.530.027.525.0

8

7

6

5

4

3

2

1

φ

β

3.8

DA1DA2DA3FOS = 2FOS = 3

'40.037.535.032.530.027.525.0

8

7

6

5

4

3

2

1

φ

β

3.8

DA1DA2DA3FOS = 2FOS = 3

'

Assumptions:• Uncorrelated c’ - tanφ’• δv = 2m• V (tanφ’) = 15%• φ’k = 5% fractile

Result• β generally < 3.8

Assumptions:• Correlated c’ - tanφ’• δv = 2m• V (tanφ’) = 15%• φ’k = 95% of mean

Result• β generally > 3.8

11

Discussion

Any questions

12

Session 4b

Design of Retaining Structures

(Carton House)

13

Scope

• Requirements in Section 9: Retaining Structures of Eurocode 7 apply to structures which retain ground comprising soil, rock or backfill and water at a slope steeper than it would eventually adopt if no structure were present

• Main types are gravity walls and embedded walls

• Eurocode 7 also covers composite walls which are defined in Eurocode 7 as walls as composed of elements from the above two types of wall. A large variety of such walls exists and examples include double sheet pile wall cofferdams, earth structures reinforced by tendons, geotextilesor grouting and structures with multiple rows of ground anchorages or soil nails

• Pressures in silos are not covered by Eurocode 7 but by EN1991-4

14

Relevant CEN Standards

• Eurocode 7 refers to the following CEN standards that are relevant to the design and construction (execution) of retaining walls

• EN 1997-3: Part 53-Pt 5 Design of Steel Structures - Piling (EN 1993-5:1997)

• Execution standard –Execution of special geotechnical work

• EN 1538 - Diaphragm Walls

• EN 12063 - Sheet pile walls

• EN 1536 - Bored Piles

15

Table 9 2

For fill, the nature of the materials available and the means used to compact them adjacent to the wall

The stability of borings or slurry trench panels while they are open

For sheet piling, their drivability without loss of interlock

The appearance and durability of the wall and any anchorages

Access for maintenance of the wall and any associated drainage measures

The ductility of structural components

The ability to carry vertical load

The practicality of excavating beneath any propping of retaining walls

The practicality of forming ground anchorages in adjacent ground

The practicality of constructing the wall to form a water cut-off

The required degree of water tightness of the finished wall

The effects of constructing the wall including:• Temporary support to the sides of the excavation• Changes in in-situ stresses and resulting ground movements caused by the

wall excavation and its construction• Disturbance of the ground due to driving and boring operations• Provision of access for construction

CheckedItems to be considered

Table 9 2

Construction Considerations

16

Pressures and Forces on Retaining Walls

• The following five different types of earth pressure are considered in the sub-sections of Clause 9.5:– At rest earth pressure (C9.5.2)– Limiting values of earth pressure (C9.5.3)– Intermediate values of earth pressure (C9.5.4)– Earth pressure due to compaction (C9.5.5)– Water pressure (C9.5.6)

• Backfill – density estimated from knowledge of available material. GDR shall specify verification checks

• Use conservative backfill density values to avoid excessive site testing• Surcharges – consideration should be taken of increased surcharge

due to repetition of load• Wave and ice forces, seepage forces, collision forces, temperature

effects

17

At rest earth pressures – K0 valuesFactors to be considered

• Stress history

• May assume at rest conditions if wall movement is < 5 x 10-4 x h for normally consolidated soil (Clause 9.5.2(2))

• For overconsolidated soil – except for high OCR values (Clause 9.5.2(3))

• Horizontal coefficient of earth pressure K0 = (1-sinφ') √ OCR

• For sloping ground (Clause 9.5.2(4))

• K0;β = K0 (1+sinβ)

Limiting Values• Ka and Kp values obtained from charts and equations in Annex C

• Equations for earth pressure in Annex C are useful for numericalanalyses

Determination of Earth Pressures

18

Water Pressures

• For silts and clays - The ground water level shall be assumed to be at surface of retained material unless reliable drainage system or infiltration is prevented

• Effects of water filled tension cracks shall be considered where no special drainage or flow prevention measures are installed (principle)

19

Points to Note• Earth pressures include the pressure from soil and weathered rock and

water pressures

• The single source principle applies to DA1 and DA3, although not expressly stated in Eurocode 7

– i.e. the same partial action factors are applied to earth pressures on opposite sides of the wall

• DA3 is as DA1.C2 but with partial factors of 1.35 &1.5 on permanent and variable structural actions

• The partial factor is applied to the net water force, although this not expressly stated in EC7, this is very important for DA2 and to DA1.C1 in some design situations

• DA1.C1 may not apply a safety margin against overall stability of an retaining structure in particular design situations

• Need to demonstrate vertical equilibrium can be achieved

20

• Mobilised wall friction δ– Concrete or steel sheet pile: dd = k φcv,d

– k ≤ 2/3 for precast concrete or steel sheet piling

– k =1.0 may be assumed for concrete cast to soil

– No adhesion or friction resistance for steel sheet pile in clay under undrained conditions immediately after driving.

Wall Friction

21

Allowance for Unplanned Excavations

• For embedded cantilever walls, ∆a = 10% of its height and for a supported wall ∆a = 10% of the height beneath the lowest support with ∆a limited to a maximum of 0.5m. Smaller values may be used where the surface level is specified to be controlled [C9.3.2.2(3)] or larger values where the surface level is particularly uncertain

• (Clause 9.3.2.2(4))

• No overdig allowance for SLS check

22

Design Methods and Considerations

• Design methods– Calculation– Prescriptive measures– Experimental models and load tests– Observational method

• Observational method specifically mentioned

• γF and γR are strictly applied to actions (forces) and not to pressures but in practice it is more convenient to apply factors to pressures

• Design should guard against brittle failure• The SLS design values of the earth pressures at not necessarily the limiting

values• Deflection must not cause damage to adjacent structures (note: SLS not

necessary in some circumstances)• Drainage systems must have maintenance in place or demonstrated to work

effectively without maintenance

23EmbeddedFailure by lack of vertical equilibrium

EmbeddedFailure by rotation or translation of the wall or parts thereof

Gravity and compositeFailure by toppling of the wall

Gravity and compositeFailure by sliding at the base of the wall

Gravity and compositeBearing resistance failure of the soil below the base

All typesUnacceptable change to the flow of groundwater

All typesUnacceptable leakage through or beneath the wall

All typesMovements of the retaining structure which may cause collapse or affect structure, nearby structures or services

All typesCombined failure in ground and in structural element

All typesFailure of structural element e.g. wall, anchor, strut, connection

All typesLoss of overall stability

CheckedRetaining structure typeLimit states to be considered

Limit states to be Considered

24

Actions and Resistances

Geotechnical Action• Eurocode 7 defines a geotechnical action as an action transmitted to the

structure by the ground, fill, standing water or ground-water (Clause 1.5.2.1)

Passive Earth Pressure• The passive earth pressure, PP acting on resistance side of a gravity wall

should be considered as an earth resistance (Table A.13) when considering base sliding and as a favourable geotechnical action (Table A3) when considering bearing failure

Design water levels/pressures• The design value of the water table is generally taken as the worst

reasonable scenario. An alternative approach is to consider the variations in the water level as a variable action and the apply appropriate partial factor

25

Design Actions

DA1.C1 & DA2• In DA1.C1 and DA2, design values of action are obtained by applying γF to the

characteristic values of non geotechnical actions e.g. self weight of the wall Fd = γF Fkand to geotechnical actions obtained from the characteristic values of the ground parameters Fd = γFF(Xk) or alternatively to the effect of actions Ed = γEE(Fk,Xk,ad)

DA1.C2 & DA3• In DA1.C2 and DA3, design values are obtained by applying γF to the characteristic

values of non geotechnical actions Fd = γF Fk and the design values of geotechnical actions are obtained by factoring the ground parameters Fd = γF F(Xk / γm)

Effects of actions• Where the application of the partial values to geotechnical actions gives

unreasonable results, the partial factors for actions can be applied directly to the effect of actions, e.g. BM or SF, calculated using representative values of the actions(Clause 2.4.7.3.2(2))

26

Embedded Wall

OΣabout OBM = 0

• Need to find:– The minimum length of wall penetration to prevent rotational failure and

vertical equilibrium, and– The distribution of effects of the actions (BMs, SF) and the magnitude of

the support reactions (anchors, props)

• Analyse using limit equilibrium method (LEM) assuming ‘free earth support’ for ‘tied back’ (single) sheet pile wall

27

Analysis of Tied-Back Sheet Pile Wall

6.0m

4.0m

d

∆ = 0.5m

a) Problem geometry

Silty sand

levelDesign

d

gravelCoarse

Surcharge = 20kPa

Tie Rod

Tidallag = 0.6m

1.5m

8Active

b) Calculation model

4

5Passive

7

3

1

2

6

28

Earth Pressure Equations – DA1.C1, DA1.C2 & DA3

pa,d' + u = γGunfav [Ka,d (σv – ua) - 2ck'√Ka,d ,/ γM + ua] + γQunfavKa,d q

pp,d' + u = γGunfav [Kp,d (σv – ub) + 2ck'√Kp,d / γm + ub] / γR

• Single source princiiple used for DA1 and DA3

• Use of net pressure not necessary when using single source principle as γR = 1.0

• Useful for FE analyses

Aua

UNIFORM SOIL ck' φk'

Bub

29

Earth Pressure Equations – DA2

• Single source principle not used• Net water pressure force used

pad' = γG,unfav [Ka,k (σv – ua) - 2ck'√Ka,k/γM + (ua - ub)] + γQunfav q

pp,d' = γG,fav [Kp,k (σv – ub) +2ck'√Kp,k / γM] / γR

Aua - ub

Uniform Soil . ck' , φk'

B

30

Calculation Stages

• Compute the design earth pressure

• Determine the sheet pile length by taking moments about the tie rod

• Determine the design tie rod force by balancing horizontal forces

• Determine the bending moments using the design earth pressure values.

31

Design φ’ values

DA3 M3 γcu=1.4; γc'=1.25; γφ'=1.25

atan(tan32/1.25) = 26.58oatan(tan35/1.25) = 29.26oDA3

atan(tan32/1.0) = 32oatan(tan35/1.0) = 35oDA2

atan(tan32/1.25) = 26.58oatan(tan35/1.25) = 29.26oDA1.C2

atan(tan32/1.0) = 32oatan(tan35/1.0) =35oDA1.C1

Sandy Siltφd' (γφ')

Granular Backfillφd' (γφ')

Design earth pressures are obtained using design φ’ values

32

Informative Annex C – Ka & KP

33

26.58

0.35

4.2

32.0

0.28

6.1

φd' (o)

Ka

KP

Silty Sand(γk = 18kN/m3)

29.26

0.31

-

35

0.25

-

φd' (o)

Ka

KP

Granular backfill(γk = 22kN/m3)

DA1.C2& DA3

DA1.C1& DA2

DrainedParameterSoil

Design Parameters

34

Approximation for Seepage Water Pressures

Gravel

Silty sand d

∆H

L

γw∆HL/(L+D) γw∆d/(L+D)

35

Earth Pressure Equations – DA1.C1

pad' + u = 1.35 [Kad (σv – ua) + ua] + 1.5 q

pPd ' + u = 1.35 [KPd (σv – ub) + ub]/1.0

Aua

Bub

ck'=0 for both soils

d

361.35*{6.1*[4.5*10+18*d-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}

1.35*[10*4.5]

0

1.35*{0.28*[22*10+18*(d+0.5)-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}+1.5* 0.28*20

1.35*[0.28* (22*10-4.6*10)+4.6*10]+ 1.5* 0.28*20

1.35*[0.25* (22*10-4.6*10)+4.6*10]+ 1.5* 0.25*20

1.35*0.25* 22*5.4+ 1.5* 0.25*20

1.35*0.25* 22*1.5+ 1.5* 0.25*20

1.5* 0.25*20

DA1:C1

384.21(d=4.32m)

8

60.87

06

212.86(d=4.32m)

5

136.274+

128.334

47.603

18.632

7.51

ID

0

6

10

1515

1.5

5.4

1010

0

2

4

6

8

10

12

14

16

-150 -100 -50 0 50 100 150 200 2501

2

3

44+

5

6

7

8

DA1.C1

37

Vertical equilibrium

• Vertical downward force due to active pressure

• Σ{1.35 x Kad x (σv'-q) + 1.5Kad q} x ∆L x tanδ = 254.2 kN/m

• Vertical upward force due to passive pressure

• Σ{1.35 x KPd x (σv')} x ∆L x tanδ = 243 kN/m

• If there were a significant difference, change δ, on generally the active side as sheet piles tends to move down [Frank et al., 2004]

Horizontal equilibrium• Design anchor force

• Td = Pa;d- PP;d = 296.9 kN/m

Vertical and Horizontal Equilibrium

38

TIED SHEET PILE RETAINING WALL

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

DEPTH (m)

SHEA

R F

OR

CE

kN/m

BENDING MOMENT DIAGRAM

-1200.0

-1000.0

-800.0

-600.0

-400.0

-200.0

0.0

200.0

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

DEPTH (m)

BEN

DIN

G M

OM

ENT

(kN

m/m

)

Shear Force and BM

DA1.C1

Td= 296.9 kN/m

391.0*{4.2*[4.5*10+18*d-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}

1.0*10*4.5

0

1.0*{0.35*[22*10+18*(d+0.5)-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}+1.3* 0.35*20

1.0*[0.35* (22*10-4.6*10)+4.6*10]+ 1.3* 0.35*20

1.0*[0.31* (22*10-4.6*10)+4.6*10]+ 1.3* 0.31*20

1.0*0.31 * 22*5.4+ 1.3* 0.31*20

1.0*0.31* 22*1.5+ 1.3* 0.31*20

1.3* 0.31*20

DA1:C2

321.73(d=6.56m)

8

457

06

204.34(d=6.56m)

5

116.04+

108.04

44.893

18.292

8.061

ID

0

6

10

1515

1.5

5.4

1010

0

2

4

6

8

10

12

14

16

-150 -100 -50 0 50 100 150 200 2501

2

3

44+

5

6

7

8

DA1.C2

40

Td= 321.3 kN/m

TIED SHEET PILE RETAINING WALL

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

DEPTH (m)

SHEA

R F

OR

CE

kN

BENDING MOMENT DIAGRAM

-1400.0

-1200.0

-1000.0

-800.0

-600.0

-400.0

-200.0

0.0

200.0

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

DEPTH (m)

BEN

DIN

G M

OM

ENT

(kN

m

Shear Force and BM

DA1.C2

41

Summary DA1

277225277Sd kN/m

125112511045*MdkNm/m

321.3321.3296.9Td kN/m

17.117.114.8Length (m)

DA1DA1.C2DA1.C1

* If Md from DA1.C1 were > that from DA1.C2 could reduce it by carrying out a FE or other soil/structure analysis for longer length.

42

Earth Pressure Equations – DA2

p’ad + u = 1.35[Kad (σv – ua)+(ua-ub]+1.5q

A

ua

Bub

p’Pd + u = 1.0[KPd (σv – ub)]/1.4

ck‘ = 0 for both soils

d

Net water pressure

43

0

06

65.79

0

0

2

4

6

8

10

12

14

16

18

20

05101520

Net water pressure kPa

Dep

th (m

)

0

6

17.25

6

10.5

17.25

10.5

1.5

5.4

1010

0

2

4

6

8

10

12

14

16

18

20

-150 -100 -50 0 50 100 150 200 2501

2

3

44+

5

6

7

8

X

Y

Earth and Water Pressures – DA2

44

58.11.35*(0.25*(22*6-0.6*10)+0.6*10)+1.5*0.25*20X

222.3(d=6.74m)

1.0*[6.1*{4.5*10+18*d-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2*d+0.5))}]/1.48

0

0

1.35*[0.28*{22*10+18*(d+0.5)-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2*d+0.5))}]+1.5* 0.28*20

1.35*[0.28*{22*10+18*(0.5)-((0.5+4.6)*10-0.6*(0.5)*10/(2*d+0.5))}+(0.6*10-0.6*(0.5)*10/(2*d+0.5))]+1.5* 0.28*20

1.35*[0.28* (22*10-4.6*10)+ 0.6*10]+1.5* 0.28*20

1.35*[0.25* (22*10-4.6*10)+ 0.6*10]+1.5* 0.25*20

1.35*0.25* 22*5.4+ 1.5* 0.25*20

1.35*0.25* 22*1.5+ 1.5* 0.25*20

1.5* 0.25*20

DA2

07

06

97.2(d=6.74m)

5

83.58Y

82.34+

74.334

47.63

18.62

7.51

ID

0

6

17.25

6

10.5

17.25

10.5

1.5

5.4

1010

0

2

4

6

8

10

12

14

16

18

20

-150 -100 -50 0 50 100 150 200 2501

2

3

44+

5

6

7

8

X

Y

DA2

45

TIED SHEET PILE RETAINING WALL

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

0.00 5.00 10.00 15.00 20.00

DEPTH (m)

SHEA

R F

OR

CE

kN

BENDING MOMENT DIAGRAM

-1600.0-1400.0-1200.0-1000.0-800.0-600.0-400.0-200.0

0.0200.0

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

DEPTH (m)

BEN

DIN

G M

OM

ENT

(kN

m

Shear Force and BM

DA2

Td= 347 kN/m

461.0*{4.2*[4.5*10+18*d-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}

1.0*10*4.5

0

1.0*{0.35*[22*10+18*(d+0.5)-((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))]+((d+0.5+4.6)*10-0.6*(d+0.5)*10/(2d+0.5))}+1.3* 0.35*20

1.0*[0.35* (22*10-4.6*10)+4.6*10]+ 1.3* 0.35*20

1.0*[0.31* (22*10-4.6*10)+4.6*10]+ 1.3* 0.31*20

1.0*0.31 * 22*5.4+ 1.3* 0.31*20

1.0*0.31* 22*1.5+ 1.3* 0.31*20

1.3* 0.31*20

DA3

321.73(d=6.56m)

8

457

06

204.34(d=6.56m)

5

116.04+

108.04

44.893

18.292

8.061

ID

0

6

10

1515

1.5

5.4

1010

0

2

4

6

8

10

12

14

16

-150 -100 -50 0 50 100 150 200 2501

2

3

44+

5

6

7

8

DA3

47

TIED SHEET PILE RETAINING WALL

-400.00

-300.00

-200.00

-100.00

0.00

100.00

200.00

300.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

DEPTH (m)

SHEA

R F

OR

CE

kN

BENDING MOMENT DIAGRAM

-1400.0

-1200.0

-1000.0

-800.0

-600.0

-400.0

-200.0

0.0

200.0

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

DEPTH (m)

BEN

DIN

G M

OM

ENT

(kN

m

Shear Force and BM

DA3

Td= 321.3 kN/m

48

277328277Sd kN/m

125112591251Md kNm/m

321.3347321.3Td kN/m

17.117.2517.1Length (m)

DA3DA2DA1

Summary of Results

49

Reinforced Cantilever Gravity Retaining Wall

Coarse grained backfill

Surcharge = 20kPa

0.5m1.0m

a) Problem geometry

levelDesign B

Glacial till

5.2m

1.6m5.0m

2.0m0.3m

Waterlevel

A

0.4m

7 4

Uplift

b) Calculation model

B

6

5

1

2

3

A

• Design against bearing and sliding failure as for a spread foundation

50

Discussion

Any Questions

51

Session 4c

Slopes, Overall Stability and Embankments

52

Slopes and Overall Stability

• Eurocode 7 has no separate section on the design of slopes

• Instead there is a separate Section 11 on Overall Stability

- Overall stability situations are where there is loss of overall stability of the ground and associated structures or where excessive movements in the ground cause damage or loss of serviceability in neighbouring structures, roads or services

- Typical structures for which an analysis of overall stability should be performed (and mentioned in relevant sections of Eurocode 7):

- Retaining structures- Excavations, slopes and embankments- Foundations on sloping ground. natural slopes or embankments- Foundations near an excavation, cut or buried structure, or shore

• It is stated that a slope analysis should verify the overall moment and vertical stability of the sliding mass. If horizontal equilibrium is not checked, interslice forces should be assumed to be horizontal

– This means that Bishop’s method is acceptable, but not Fellenius’ method

53

Overall Stability Failure Modes

- Examples of overall failure modes involving ground failure around retaining structures presented in Section 11

54

Comments on Overall Stability

Unfavourable weight

SurchargeFavourable weight

Centre of rotation

Wf

Slip surface

Wu

• Typical slope stability design situation• No specific inequality to be satisfied is given in Eurocode 7• It could analysed be in terms of forces or moments or both• No calculation model is given• Finite elements can be used but no guidance given• DA2 is generally not used for slopes

55

Design of Slopes Using DA1

Both DA1.C1 and DA1.C2 should be considered, but DA1.C2 normallycontrols if no structural element or soil reinforcement is involved

For undrained conditions:

DA1.C1 γG = 1.35, γQ= 1.5, γcu = 1.0

DA1.C2 γG = 1.0, γQ= 1.3, γcu = 1.4

Drained conditions

In DA1.C1 an increase in the vertical load generally increases the resistance, leaving the margin of safety relatively unchanged. Thus DA1.C2, where γG = 1.0, γQ = 1.3, γc‘, γφ‘, = 1.25, governs

Single source principle is applied – i.e. both unfavourable and favourable components of the same load, e.g. soil weight, are treated as if they act as a single load

56

W = 150kN

β = 20ο

Interface propertiescu,k = 40 kPac‘k = 5 kPaφ‘k = 35o

Undrained ConditionsDA1.C1 Fd = 1.35x150xsin20 = 69.3 kN/m; Rd = (40/1.0)x1.75 = 70 kN/m Fd < Rd OKDA1.C2 Fd = 1.0x150xsin20 = 51.3 kN/m; Rd = (40/1.4)x1.75 = 50 kN/m Fd > Rd Fail

Drained Conditions

DA1.C1 Fd = 1.35x150xsin20 = 69.3 kN/mRd = (5/1.0)x1.75 +1.35x150xcos20x(tan35/1.0) = 8.75 + 133.2 = 142kN/m OK

DA1.C2 Fd = 1.0x150xsin20 = 51.3kN/mRd = (5/1.25)x1.75 +1.0x150xcos20x(tan35/1.25) = 7.0 + 98.7= 105.7kN/m OK

L = 1.75m

DA1 Design Example

Sliding stability of a block on a slope

Design sliding resistance, Rd

Undrained: ( cu,k /γM) x LDrained: (c‘k/γM) x L + N tan φ‘k /γM)

57

Sliding Stability of an Infinite Slope

S

Rd

d

Ground s u rface

W eak clay layer

Slip p lane

1.8m

c = 25kP auk

30

Hard s tratum

0

Design situation:- Hard stratum resting on a weak layer

Equilibrium requirement:- Design sliding force, Sd ≤ Design resisting force, Rd

58

Infinite Slope with Seepage

β

Slip plane

β

hz

bcos

b

For water table at the surface:

Traditional design

βγφγ

tan'tan'

sat

F =

If F = 1.25

γsat tan β ≤ γ’ (tanφ’/ 1.25)

i.e Eurocode 7 condition

59

Slope Stability Analysis Using Method of Slices

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80

x Axis

y A

xis

Radius, r

Eurocode 7 requirements when using the method of slices:- Both vertical and moment equilibrium should be checked, and- If horizontal equilibrium is not checked, then the interslice forces shall

be assumed to be horizontal- This means some simpler methods not acceptable

Centre of rotation

60

Details of different methods of slices from SLOPE/W

Note:- Not acceptable methods

- Acceptable methods

61

Bishop’s Simplified Method of Slices

mobm;

'k

mobm;

'''

'

mob γTanφN'

γc

FTanφN

Fcτ +=+=

Design Procedure:

DA1.C1Apply γG = 1.35 to permanent actions, incl. soil weight force via the soil weight density and γQ = 1.5 to variable actions and check that γ m;mob = F ≥ 1.0

DA1.C2Apply γG= 1.0 to permanent actions, incl. soil weight force via the soil weight density and γQ=1.3 to variable actions and check that γm;mob = F ≥ 1.25

∑∑ +

−+=

mobm

k

kGGk

Gmobm TanTan

SecTanubWbcWSin

;

''

; '1

])([1

γφα

αϕγγαγ

γ

62

Slope Stability Analysis Example Using Method of Slices

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70 80

x Axis

y A

xisCentre of slip circle at:X=28Y= 35

Radius, r

6 slices

63

Stability Analyses Using DA1.C1

F = γM, mob ≥ 1.0 so OK according to DA1.C1

1.333021F=

1692.0831269.36Sum2813.617

283.87941.716461487.26788.082692494.82660.9916060.3437.96814.0413465.4185926

347.48231.350681469.33768.082692503.65560.6424760.3622.64814.0413467.7034745

350.5631.181649414.24248.082692312.48660.3698260.3640.39074.0413467.9229874

322.21041.058424341.03538.08269293.438990.1240450.3559.40794.0413466.9210593

258.40370.946233244.518.082692-61.2029-0.1142470.3397.68344.0413464.9201852

129.54450.823941106.7378.082692-73.8447-0.3594130.3155.51854.0413461.9240931

A/BBAc'bγGWsinααruWbhSlice

1.33356F=

A = [c'b + W (1 - ru) tanφ') ] secαB = 1 + tanφ‘ tanα / F

64

Stability Analyses Using DA1.C2

F = γM, mob ≥ 1.25 so OK according to DA1.C2

1.349115F=

1268.528940.2668Sum2813.617

213.57281.707931364.76768.082692366.53820.9916060.3437.96814.0413465.4185926

260.13621.346506350.27488.082692373.07820.6424760.3622.64814.0413467.7034745

262.05791.179486309.09378.082692231.47150.3698260.3640.39074.0413467.9229874

240.82781.057729254.73058.08269269.214070.1240450.3559.40794.0413466.9210593

193.50840.946873183.22788.082692-45.33546-0.114250.3397.68344.0413464.9201852

98.425350.82603781.303028.082692-54.69977-0.359410.3155.51854.0413461.9240931

A/BBAc'bWsinααruWbhSlice

1.349628F=

A = [c'b + W (1 - ru) tanφ') ] secαB = 1 + tanφ‘ tanα / F

65

Stability of an Anchored Excavation

• In this situation the anchor imposes a stabilizing action on the excavation

• Hence DA1.C1 should be checked

• It may control the design

66

Slope Design Using DA3

Slope design using DA3 is the same as DA1.C2 since actions on the soil (e.g. structural actions Gk, Qk, traffic loads, etc.) are treated as geotechnical actions, likethe soil weight Wk, and the A1 partial action factors γG=1.0; γQ=1.3 are applied.

However, in a bearing analysis of thefoundations the structural loads are treated as structural actions and the A2, i.e. DA1.C1partial action factorsγG=1.35; γQ=1.5, are used

Is this slope stability orbearing resistance?

Gk, Qk

Wk

67

Design of Embankments

• Section 12: Embankments of EN 1997 provides the principles and requirements for the design of embankments for small dams and for infrastructure projects, such as road embankments

– No definition is given for the word “small” but Frank et al. state that it may be appropriate to assume “small dams” include dams (and embankments for infrastructure) up to a height of approximately 10m

• A long list of possible limit states, both GEO and HYD types, that should be checked is provided including:

– Loss of overall stability– Failure in the embankment slope or crest– Failure by internal erosion– Failure by surface erosion or scour– Excessive deformation– Deformations caused by hydraulic actions

• Limit states involving adjacent structures, roads and services are included in the list

68

Particular Aspects Regarding Embankment Design

• Since embankments are constructed by placing fill and sometimes involve ground improvement, the provisions in Section 5 should be applied

• For embankments on ground with low strength and high compressibility, EN 1997-1 states that the construction process shall be specified, i.e. in Geotechnical Design Report, to ensure that the bearing resistance is not exceeded or excessive movements do not occur during construction

• Since the behaviour of embankments on soft ground during construction is usually monitored to ensure failure does not occur, it is often appropriate to use the Observational Method for design

• The importance of both supervision and monitoring in the case of embankments is demonstrated by the fact that there is a separate sub-section on the supervision of the construction of embankments and the monitoring of embankments during and after construction in Section 12

• The only other section of Eurocode 7 that has provisions for both supervision and monitoring is the section on ground anchorages

69

Conclusions

• Sections 11 and 12 set out the provisions for designing against overall stability and for the design of embankments

• The focus is on the relevant limit states to be checked

• No calculation models are provided

• When using method of slices for slope stability, some simplified methods not acceptable

• The relevance and importance of other sections of EN 1997-1 is demonstrated, for example:– The section on Fill and Ground Improvement– The sub-section on the Observational Method– The sub-section on the Geotechnical Design Report– The section on Supervision and Monitoring

70

Discussion

Any questions

71

Tomorrow

- Special Features of Soil- Geotechnical Design

Triangle- Associated CEN

Standards- Implementation and Future Development- Tutorial Examples