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Eurocode 7 and New Design Challenges / University College London, 19 March 2013

S C I E N C E P A S S I O N T E C H N O L O G Y

COMPARISON OF EC DESIGN

APPROACHES FOR NUMERICAL

ANALYSIS OF DEEP EXCAVATIONS

Helmut F. Schweiger

Computational Geotechnics GroupInstitute for Soil Mechanics and Foundation Engineering

Graz University of Technology

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Comparison of EC7 design approaches for numerical analysis of deep excavations

Introduction

Eurocode 7 Design Approaches

Benchmark Example

Excavation in sand

Excavation in soft clay-Comparison of constitutive model and design approaches

Issues from simplified case histories

Deep excavation in soft clay

Deep excavation in stiff clay

Wall with prestressed anchorsNATM tunnel

-Comparison of design approaches

Summary and discussion

Introduction EC7 Design Approaches Benchmark Examples Simplified Case Histories Summary / Discussion

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Application of numerical methods for ultimate limit state design in

general and in accordance with Eurocode7 is a much discussed

issue and work in progress

what design approach is best suitable for numerical methods?

at what stage should "partial factors" be introduced (if at all)?

should we use the same design approach for numerical andconventional analysis (for a given type of problem)?

should we use finite element analysis for ULS-design?see also (with emphasis mainly on deep excavations), e.g.: Schweiger (2009, 2010), Simpson (2007),

Schweiger (2005), Lo (2003), Bauduin, De Vos & Frank (2003), Simpson (2000), Bauduin, De Vos &

Simpson (2000)

With respect to numerical modelling there is a significant difference between

calculating a factor of safety

performing a calculation with factored material parameters according to EC7


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Actions F

Permanentunfavourable

1) Variable

2)

Designapproach

G QDA1/1 1.35 1.50DA1/2 1.00 1.30DA2 1.35 1.50

DA3Geot.

3): 1.00

Struct.4):1.35

1.301.50

Partial factors for actions according to EC7

(can be changed in National Annex)

for deep excavation andtunnelling problems this

means that earth pressure

has to be factored

in numerical analysis

not feasible

alternatively effects ofactions can be factored

(e.g. bending moments,

strut forces)

> commonly referred to

as DA2*

PARTIAL FACTORS EC7


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Partial factors for soil properties and resistances according to EC7

DA1/1 and DA1/2: two analysis required

Soil properties M Resistances

tan c cu Unit weight Passive Anchor

Designapproach

c cu F R;e a

DA1/1 1.00 1.00 1.00 1.00 1.00 1.10DA1/2 1.25 1.25 1.40 1.00 1.00 1.10DA2 1.00 1.00 1.00 1.00 1.40 1.10DA3 1.25 1.25 1.40 1.00 1.00 1.00

PARTIAL FACTORS EC7


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EC7 design approaches in combination with numerical methods:

DA2:

Analysis is performed in terms of characteristic material parameters

Partial factors applied to loads (feasible only for e.g. foundation problems)

DA2*:

Analysis is performed in terms of characteristic material parameters Partial factors applied to effects of actions (e.g. bending moments)

> This is straightforward for numerical analysis

DA3:

Option 1:

Analysis is performed in terms of designmaterial parameters

> perform all excavation steps with factored values for soil strength

Option 2:

Analysis is performed in terms of characteristicmaterial parameters but for

all construction steps a check with reduced strength parameters is made


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excavation level 1

excavation level 2

final excavation level

Option 2 for DA3:perform excavation step 1

with unfactored values for soil strength

> reduce tanto tanunfact / > check for failure


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excavation level 1

excavation level 2





perform excavation step 2with unfactored values for soil strength(start from results for excavation step 1 with

unfactored properties)



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excavation level 1

excavation level 2





N.B. Serviceability limit state obtained as well








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EXCAVATION IN SAND

Phases:

1: Initial stresses (K0= 1 - sin')

2: Sheet pile wall (wished-in-place)> displacements set to 0

3: Excavation 1 to -2.00 m

4: Activation of strut at -1.50 m

5: GW-lowering to -6.0 m



8: Surcharge 15 kPA (variable load)


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Constitutive models compared:

Hardening Soil (small) model*Mohr-Coulomb model

1E-5 0.0001 0.001 0.01

Shear strain [-]

0

10000

20000

30000

40000

SecantmodulusG[kN/m]

HS-Small

Hardin & Drnevich

* MC failure criterion

EXCAVATION IN SAND


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Parameter Meaning Value

[kN/m] Unit weight (unsaturated) 18

r [kN/m] Unit weight (saturated) 20

[] Friction angle 41

c [kPa] Cohesion 0

[] Angle of dilatancy 15ur [-] Poissons ratio unloading-reloading 0.20

E50re

[kPa] Secant modulus for primary triaxial loading 30 000

Eoedre

[kPa] Tangent modulus for oedometric loading 30 000

Eurre

[kPa] Secant modulus for un- and reloading 90 000

m [-] Exponent of the Ohde/Janbu law 0.55

pref

[kPa] Reference stress for the stiffness parameters 100K0

nc [-] Coefficient of earth pressure at rest (NC) 1-sin()

Rf [-] Failure ratio 0.90

Tension [kPa] Tensile strength 0

G0 [kPa] Small-strain shear modulus 112 500

0,7 [-] Reference shear strain where Gsec=0.7G0 0.0002

Parameters for HSS-model

EXCAVATION IN SAND


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horizontal wall displacement [mm]

-6-303691215

depthbelow

surface[m]

0

1

2

3

4

5

6

7

8

9

HS

HSS

MC

bending moments [kNm/m]

-80 -60 -40 -20 0 20 40

depthbelow

surface[m]

0

1

2

3

4

5

6

7

8

9

HS

HSS

MC

EXCAVATION IN SAND


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DA2*:

Permanent loads: G= 1.35

Variable loads: Q= 1.50

All soil factors = 1.0

surchargepermanent= 10 kPa

surchargevariable= 15 kPa

DA3:



Strength: c= = 1.25

> ' = 28.35 ( = 12)


> surchargevariable= 15 kPa > 19.5 kPa

Initial stresses (DA3):

K0c= 1sin(41) = 0.344 (based on characteristic ')

Note: if an advanced model is used, where

strength depends on e.g. density then thisapproach cannot be used.

It becomes more complex but can still be

done, see:

Potts and Zdravkovic

Accounting for partial material factors in

numerical analysis, Geotechnique 2012

EC7 PARTIAL FACTORS


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Difference in maximum design bending

moment between DA2 and DA3 smallerfor HSS model than for MC model (in

this particular example)

Mdesign, DA2*= M1x 1.35 + (M2M1) x 1.5

M1

bending moment excluding variable load

M2 bending moment including variable load


-100 -80 -60 -40 -20 0 20 40 60

depthbelow

surface[m]

0

1

2

3

4

5

6

7

8

9

HSS-DA3

MC-DA3

HSS-DA2

MC-DA2

COMPARISON OF RESULTS


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design approach

DA2 DA3

designstrutforce[kN/m]

0

20

40

60

80

100

120

140

160

180

200

MC

HSS

DA2Strut force after

excavation

Strut force

due to load

Design strut

force

MC 78 21.6 138

HSS 108.6 23.1 181

DA3Strut force after

excavation

Strut force

due to load

Design strut

force

MC 122 39 161

HSS 140 36 176

138

181 176161



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Phases:

1: Initial stresses (K0= 1 - sin')

2: Sheet pile wall (wished-in-place)

> displacements set to 0


4: Activation of strut at -1.50 m



7: Surcharge 15 kPa (variable load)

EXCAVATION IN CLAY


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Undrained analysis with "Method B"(undrained strength parameters):

cu= 23.9 kPa at -2.0m

cu= 2.1 kPa/m

Parameters for HSS-model

"Method A":

undrained analysis witheffective strength parameters

Parameter Meaning Value

[kN/m] Unit weight (unsaturated) 15

sat [kN/m] Unit weight (saturated) 16

'[] Friction angle (Mohr-Coulomb) 27

c [kPa] Cohesion (Mohr-Coulomb) 15

[] Angle of dilatancy 0

ur [-] Poissons ratio unloading-reloading 0.20E50

ref [kPa] Secant modulus for primary triaxial loading 4 300

Eoedref

[kPa] Tangent modulus for oedometric loading 1 800

Eurref

[kPa] Secant modulus for un- and reloading 14 400

m [-] Exponent of the Ohde/Janbu law 0.90

pref [kPa] Reference stress for the stiffness parameters 100

K0nc

[-] Coefficient of earth pressure at rest (NC) 1-sin()

Rf [-] Failure ratio 0.90t [kPa] Tensile strength 0

G0 [kPa] Small-strain shear modulus 25 000

0.7 [-] Reference shear strain where Gsec=0.7G0 0.0003

EXCAVATION IN CLAY


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Comparison of constitutive models

horizontal wall displacement [mm]

-100102030405060

depthbelow

surface[m]

0

1

2

3

4

5

6

7

8

9

10

11

HS

HSS

MC

SS

distance from wall [m]

0 10 20 30 40 50 60 70

surf

acedisplacement[mm]

-30

-20

-10

0

10

20

30

40

50

60

HS

HSS

MC

SS

EXCAVATION IN CLAY


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DA2*:



All soil factors = 1.0


surchargevariable= 15 kPa

DA3:



Strength: c= = 1.25

> ' = 22.2

> c' = 12 kPa

> surchargevariable= 15 kPa > 19.5 kPa

Undrained strength: cu= 1.40

cu= 17.1 kPa at -2.0m, cu= 1.5 kPa/m

Initial stresses (DA3):

K0c= 1sin(27) = 0.546 (based on characteristic ')

EC7 PARTIAL FACTORS


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Difference resulting from choice of

constitutive model much larger than

difference between DA2 and DA3

Note: undrained strength for "Method B"

is chosen such that cuis the same for

Methods A and B for MC-model and this

value is also used for the HSS analysis

using Method B

design bending moments [kNm/m]

-250 -200 -150 -100 -50 0 50

depthbelow

surface[m]

0

1

2

3

4

5

6

7

8

9

10

11

HSS_DA2-A

MC_DA2-A

HSS_DA2-B

MC_DA2-B

HSS_DA3-A

MC_DA3-A

HSS_DA3-B

MC_DA3-B



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design approach

DA2 DA3

designstrut

force[kN/m]

0

50

100

150

200

250

HSS-A

MC-A

HSS-B

MC-B

DA2strut force after

excavation

strut force

due to load

design

strut force

MC 95.7 13.7 150

HSS 121 19.6 193

MC_B 100.6 15.3 159

HSS_B 121.4 19.4 193

DA3strut force after

excavation

strut force

due to load

design

strut force

MC 101.4 21.1 123

HSS 140.2 35.3 176

MC_B 116.7 35.1 152

HSS_B 161.9 43.8 206

193

150159

193

176

206

123

152



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Diaphragm Wallt = 46.7 m

Chalk

London Clay d = 66.7 m

+ 10.0 m

- 33.0 m

P 7

P 6

P 5

P 4

P 3

P 2

P 1

- 27.0 m

- 22.5 m

- 17.5 m

- 12.5 m

- 7.5 m

- 3.0 m

+ 2.5 m

+ 6.5 m

+ 13.7 m

- 53.0 m

Excavation Level

Prop Level

GWT + 6.5 m

17.5 m

1.2 m

stiff clay


CASE HISTORY - STIFF CLAY

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-3000 -2000 -1000 0 1000

d

epthbelow

surface[m]

0

5

10

15

20

25

30

35

40

45

50

DA2

DA2

DA3

DA3

DA2*1.35

DA2*1.35

Partial factor on strength parametersdoes not influence bending moments

significantly > higher design values

for DA2*


CASE HISTORY - STIFF CLAY

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Prestressed

ground anchors


DIAPHRAGM WALL WITH PRESTRESSED GROUND ANCHORS

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max. bendingmoment

kNm/m

anchor forcelayer 1

(kN/m)

anchor forcelayer 2

(kN/m)

anchor forcelayer 3

(kN/m)

factor of

safety

characteristic 658 334 756 755 1.57

x 1.35 (DA2*) 888 451 1021 1020

DA3 867 358 805 766 1.26

Only sligthly increased as compared to prestress forces

Increase in anchor force due to factored soil strength < 10%

Consequence: anchor forces DA2* >> DA3

bending moments are not so much different

N.B. effect of water is fully factored in DA2* but not in DA3


DIAPHRAGM WALL WITH PRESTRESSED GROUND ANCHORS

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GW-Table -4.0 m

Excavation

steps surface 0.0 m

-2.0 m

Final excavation -33.0 m

Strut levels(Prestress forces)

10.0 m

-18.5 m

-5.0 m

-12.0 m

-8.5 m

-15.5 m

-22.5 m

-25.0 m

-27.5 mJGP 1: 2 m

JGP 2: 3 m-36 m

-40 m

-1.0 m (200)

-4.0 m (550)

-7.5 m (650)

-11.0 m (600)

-14.5 m (700)

-17.5 m (700)

-21.0 m (800)

-24.0 m (850)

-27.0 m (800)

FILLK0= 0.5

MARINE CLAY

K0= 0.625

OLD ALLUVIUM SW2

K0= 0.46

-38.0 m

-30.0 m (700)

0.8 m

-31.0 m

-45.0 m

OLD ALLUVIUM CZ

K0= 0.46


CASE HISTORY - SOFT CLAY

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-3000 -2000 -1000 0 1000 2000 3000

d

epthbelow

surface[m

]

0

5

10

15

20

25

30

35

40

MC_DA2c

MC_DA2c

MC_DA2d

MC_DA2d

MC_DA3_A

MC_DA3_A

MC_DA3_B

MC_DA3_B

MC_DA3_A2

MC_DA3_A2

wall deflection [mm]

-40-20020406080100120140160180200

depthbelow

surface[m]

0

5

10

15

20

25

30

35

40

MC_DA2_A

MC_DA2_B

MC_DA3_A

MC_DA3_B

MC_DA3_A2

Note: Analysis A2

> partial factor on

stiffness of soil layers


CASE HISTORY - SOFT CLAY

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Phases:

Step 0: Initial stresses (K0= 1.25)

Step 1: Pre-relaxation top heading (55%)

Step 2: Full excavation top heading with

lining in place (shotcrete "young")

Step 3: Pre-relaxation bench (35%, shotcrete

top heading > "old"))

Step 4: Full excavation bench with lining inplace (shotcrete bench "young")

Step 5: Pre-relaxation invert (20%, shotcrete

bench > "old"))

Step 6: Full excavation invert with lining in

place (shotcrete invert "young")


NATM TUNNEL

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design approach

DA2 DA3ma

ximum

designbendingm

oment[kNm/m]

0

20

40

60

80

100

HSS

MC

HS

SS

design approach

DA2 DA3

designnormalforce

[kN/m]

0

200

400

600

800

1000

1200

1400 HSSMC

HS

SS

Normal force in lining smaller for DA3?


NATM TUNNEL

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DA3 DA2

Vertical displacements

DA3: possibly pre-relaxation factors have to be modified too


NATM TUNNEL

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EC7 - ULS-design approaches using FEM: Different design approaches (DA2 / DA3) will lead to

different design (true also for conventional analysis)

Choice of constitutive model may have larger influence than

choice of design approach

It seems that difference between DA2 and DA3 is less

pronounced for advanced constitutive models

Application of numerical methods complying with EC7

requirements is in general possible, but

results of numerical analysis depend on constitutive model and othermodelling assumptions

not all failure modes required to be checked by EC7 are easily covered,

but is this really required?

Structural elements have to be considered in a consistent manner


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Arguments forDA2 (DA2*), againstDA3

"Real" soil is considered

"Limit state" of working load conditions are obtained, only one

analysis required (not exactly true if variable loads are present)

Unrealistic system behaviour (e.g. struts in tension) is avoided

Arguments againstDA2 (DA2*), forDA3

Partial factor should be placed where one of the uncertaintyis > soil

parameters Soil is load and resistance > not always clear cut, automatically taken

into account in DA3/DA1

Some critical mechanisms may be missed in DA2*


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