Example JRC-07Anchored sheet pile wall

Verification of drained strength (limit state GEO)Design Approach 1

Design situationConsider a sheet pile wall that retains Hnom 8.0m= of dense sand with characteristic weight density

γk 20kN

m3= and drained angle of shearing resistance φk 38°= . The ground behind the wall is horizontal and

subject to a blanket surcharge (representing traffic loading) - but, for simplificty, we will assume qk 0kPa= . The

ground is dry.The sheet pile is a Z section with flange thickness tf 8.5mm= , web thickness tw 8.5mm= , web height

h 302mm= , clutch-to-clutch breadth b 670mm= , elastic section modulus Wel 1400cm3

m= , and characteristic

yield strength fyk 355MPa= .

An anchor with ultimate design resistance of Ra,d 130kN

m= will be installed at an angle θ 30°= to the

horizontal to stabilize the wall.

GeometryAllowing for an unplanned excavation in ULS verifications, the design retained height of the wall is:

Hd Hnom min 10% Hnom× 0.5m, ( )+ 8.5 m==

Material properties

Partial factors from Set M1

M2

⎛⎜⎝

⎞⎟⎠: γφ

1

1.25

⎛⎜⎝

⎞⎟⎠

=

Design angle of shearing resistance:

φd atantan φk( )

γφ

⎛⎜⎜⎝

⎞⎟⎟⎠

38.0

32.0

⎛⎜⎝

⎞⎟⎠

°==

Characteristic value of soil's constant-volume angle of shearing resistance is assumed to be:φcv,k 30°=

Design value of soil's constant-volume angle of shearing resistance is:φcv,d min φd φcv,k, ( ) 30 °==

Angle of wall friction is k 0.67= times the soil's constant-volume angle of shearing resistance:δd kφcv,d 20 °==

Earth pressure cofficients from Annex C of EN 1997-1:

Ka,h Kaγ φd δd, 0, 0, ( )→⎯⎯⎯⎯⎯⎯⎯⎯ 0.21

0.26

⎛⎜⎝

⎞⎟⎠

==

Kp,h Kpγ φd δd, 0, 0, ( )→⎯⎯⎯⎯⎯⎯⎯⎯ 7.39

5.18

⎛⎜⎝

⎞⎟⎠

==

Actions

Partial factors from Set A1

A2

⎛⎜⎝

⎞⎟⎠: γG

1.35

1

⎛⎜⎝

⎞⎟⎠

= , γG,fav 1= and γQ1.5

1.3

⎛⎜⎝

⎞⎟⎠

=

'Single source principle' allows γG,fav γG1.35

1

⎛⎜⎝

⎞⎟⎠

==

Ratio of variable and permanent partial factors is:

γQ/GγQ

γG

1.11

1.3

⎛⎜⎝

⎞⎟⎠

==

Assume a depth of embedment d1.38

2.01

⎛⎜⎝

⎞⎟⎠m=

Overturning moment about anchor is:

MEd,dst γG Ka,h1

3γk Hd d+( )3

×1

2γQ/G qk× Hd d+( )2

×+⎡⎢⎣

⎤⎥⎦

×⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯1790

2040

⎛⎜⎝

⎞⎟⎠

kN m

m==

Restoring moment about anchor is:

MEd,stb γG,fav Kp,h1

2γk d2

× Hd2

3d+

⎛⎜⎝

⎞⎟⎠

×⎡⎢⎣

⎤⎥⎦

×⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯1789

2061

⎛⎜⎝

⎞⎟⎠

kN m

m==

Out of balance mnoment is:MEd,dst MEd,stb−

MEd,stb

0.1

1−

⎛⎜⎝

⎞⎟⎠

%=

Active thrust on retained side of wall is:

Pa,Ed γG Ka,h1

2γk Hd d+( )2

× γQ/G qk× Hd d+( )×+⎡⎢⎣

⎤⎥⎦

×⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯272

291

⎛⎜⎝

⎞⎟⎠

kN

m==

Passive thrust thrust on restraining side of wall is:

Pp,Ed γG,fav Kp,h1

2γk d2

×⎛⎜⎝

⎞⎟⎠

×⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯190

209

⎛⎜⎝

⎞⎟⎠

kN

m==

Hence net thrust is:

PEd Pa,Ed Pp,Ed−81.9

81.7

⎛⎜⎝

⎞⎟⎠

kN

m==

Hence axial force transfered to the anchor is:⎛ ⎞

Fa,Ed

max PEd1PEd2

, ⎛⎝

⎞⎠

cos θ( )94.6

kN

m==

The depth of zero shear force in the retaining wall can be found (approximately) from:

zPEd

γG Ka,h1

2× γk

→⎯⎯⎯⎯⎯⎯5.42

5.57

⎛⎜⎝

⎞⎟⎠

m==

... and checked for accuracy using:

Vz,Ed PEd γG Ka,h1

2γk z2

× γQ/G qk× z×+⎛⎜⎝

⎞⎟⎠

×⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

−0.0

0.0

⎛⎜⎝

⎞⎟⎠

kN

m==

Hence the maximum bending moment in the wall is:

MEd PEd z γG Ka,h1

6γk z3

×1

2γQ/G qk× z2

×+⎛⎜⎝

⎞⎟⎠

×−⎡⎢⎣

⎤⎥⎦

→⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯296

303

⎛⎜⎝

⎞⎟⎠

kN m

m==

Maximum bending moment from either combination is:

MEd max MEd1MEd2

, ⎛⎝

⎞⎠

303kN m

m==

Maximum shear force in the wall is:

VEd max PEd1PEd2

, ⎛⎝

⎞⎠

81.9kN

m==

Verifications

Verification of resistance to overturning

'Degree of utilization' Λ

MEd,dst

MEd,stb

100

99

⎛⎜⎝

⎞⎟⎠

%== or 'Overdesign factor' ODFMEd,stb

MEd,dst

1

1.01

⎛⎜⎝

⎞⎟⎠

==

The design is unacceptable if the degree of utilization is > 100% (or overdesign factor is < 1)

Verification of bending resistancePartial factor on yield strength of steel is γM0 1.0= (from EN 1993-1-1)

Factor for reduced shear force in interlocks βB 1.0=

Design bending resistance of sheet pile section is:

Mc,RdβB Wel fyk

γM0497

kN m

m==

'Degree of utilization' Λ

MEd

Mc,Rd61 %== or 'Overdesign factor' ODF

Mc,Rd

MEd1.64==

The design is unacceptable if the degree of utilization is > 100% (or overdesign factor is < 1)

Verification of shear resistanceProjected shear area is:

Avtw h tf−( )

b3724

mm2

m==

Design shear resistance of sheet pile section is:

Vpl,RdAv fyk

3 γM0763.2

kN

m==

'Degree of utilization' Λ

VEd

Vpl,Rd11 %== or 'Overdesign factor' ODF

Vpl,Rd

VEd9.3==

The design is unacceptable if the degree of utilization is > 100% (or overdesign factor is < 1)

Verification of resistance to anchor pull-out

Design pull-out resistance of anchor is: Fa,Rd Ra,d 130kN

m==

'Degree of utilization' Λ

Fa,Ed

Fa,Rd73 %== or 'Overdesign factor' ODF

Fa,Rd

Fa,Ed1.37==

The design is unacceptable if the degree of utilization is > 100% (or overdesign factor is < 1)