www.aarsleff.comNOM Oct 2015 1
DGF møde, 29.10.2015 i Øst, DTU, Kgs. Lyngby
Geoteknikerens hverdag
Multi anchored sheet pile wall in soft clay standing on rock
by
Kristoffer Lauridsen, COWI
Carsten S. Sørensen, COWI
Søren Juel Christensen, Aarsleff
Ole Møller, Aarsleff
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Multi anchored sheet pile wall in soft clay standing on rock
Scope
1. To compare design approaches (DAs) and partial coefficients
of the Nordic countries (on the agenda for NMGEC7 meeting
in Reykjavik on 21-22nd August 2015)
2. To evaluate different modelling and effect of prestress of
anchors
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Multi anchored sheet pile wall in soft clay standing on rock
Agenda
• ULS analysis with LEM
fixed support
elastic support without pre-stress
elastic support with pre-stress
• ULS analysis with FEM
with pre-stress
• SLS analysis with FEM
with pre-stress
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison of DAs and partial coefficients
Parameters for LEM analysis
Fill: rough wall
/’ = 18/10 kN/m3
’ = 35
Soft clay: smooth wall
’ = 6 kN/m3
cu = 7 kN/m2 + 1,2 kN/m2 x z
= 0
Till: rough wall
/’ = 10 kN/m3
’ = 38
Hydrostatic water pressure
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison of DAs and partial coefficients
NMGEC7 - meeting Reykjavik 2015 Encl. 1
Retaining wall ULS - LEM earth pressure calculation
DA3 DK NA, LC4
Parameter c' cu G Q
Partial coefficient 1,2 1,2 1,8 1,0 1,5
Id Soil level depth, z ' 'k 'd rough
[m] [m] [kN/m3] [ ] [ ] k K(k) Kp(k) Kc(k)
1 Fill 0,0 0,0 18 -35 -30,3 1,0 0,26 0,27 1,25
1 Fill -2,0 2,0 18 -35 -30,3 1,0 0,26 0,27 1,25
2 Soft clay -2,0 2,0 6 0 0,0 0,0 1,00 1,00 2,00
2 Soft clay -9,0 9,0 6 0 0,0 0,0 1,00 1,00 2,00
3 Till -9,0 9,0 10 -38 -33,1 1,0 0,23 0,24 1,17
3 Till -10,0 10,0 10 -38 -33,1 1,0 0,23 0,24 1,17
Soil parameters, M
Earth pressure coefficients
Actions, F
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison of DAs and partial coefficients
NMGEC7 - meeting Reykjavik 2015
Retaining wall ULS - LEM earth pressure calculationC:\Users\nom\Desktop\NMGEC7\[Nordic LEM earth pressure.xlsx]DK DA3 LC4
DA3 DK NA, LC4
Parameter c' cu G Q surface load, pk = 10 kN/m2
Partial coefficient 1,2 1,2 1,8 1,0 1,5
Id Soil level depth, z ' 'k 'd c'k c'd cuk cud u s'vd pd ed ed + u
[m] [m] [kN/m3] [ ] [ ] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [kN/m2]
1 Fill 0,0 0,0 18 -35 -30,3 0 0,0 0 0 15 4,05 4,05
1 Fill -2,0 2,0 18 -35 -30,3 0 0,0 0 0 36 15 13,52 13,52
2 Soft clay -2,0 2,0 6 0 0,0 0 0,0 7,0 3,9 0 36 15 43,22 43,22
2 Soft clay -9,0 9,0 6 0 0,0 0 0,0 15,4 8,6 70 78 15 75,89 145,89
3 Till -9,0 9,0 10 -38 -33,1 10 8,3 0 70 78 15 11,83 81,83
3 Till -10,0 10,0 10 -38 -33,1 10 8,3 0 80 88 15 14,14 94,14
Soil parameters, M Actions, F
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison of DAs and partial coefficients
Total earth- and water pressure = 767 kN/m
by DK NA, LC 4
-10,0
-9,0
-8,0
-7,0
-6,0
-5,0
-4,0
-3,0
-2,0
-1,0
0,0
0 50 100 150 200
[kN/m2]
LEM earth + water pressure
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Multi anchored sheet pile wall in soft clay standing on rock
Structural analysis of wall … and anchors
• ULS analysis with LEM
fixed support
elastic support without pre-stress
elastic support with pre-stress
• AZ 50
I = 121.060 cm4/m, g = 253 kg/m2
Wel = 5015 cm3/m
Wpl = 5816 cm3/m
• AZ 19-700
I = 39.380 cm4/m, g = 114 kg/m2
Wel = 1870 cm3/m
Wpl = 2206 cm3/m
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Multi anchored sheet pile wall in soft clay standing on rock
Structural analysis of wall … and anchors
Spring constant of anchors: LL
EAN
L
LE
A
NE
s
per anchor per meter horizontal
Id Level c Ø0,62" A EA v L EA/L EA/L/c EA/L/c x cos(v)
Unit [m] [m] n [mm2] [kN] [ ] [m] [kN/mm] [kN/mm/m] [kN/mm/m]
Upper -1,0 3,5 6 900 189.000 45 12,73 14,85 4,24 3,00
Mid -3,5 3,5 6 900 189.000 45 9,19 20,56 5,87 4,15
Lower -7,0 2,4 7 1050 220.500 45 4,24 51,97 21,66 15,31
Note
c horizontal distance between anchors
n number of Ø0,62" strands, each with 150 mm2 cross sectional area
E = 210.000 N/mm2
v inclination to horizontal
L axial length from anchor point at sheet pile wall down to top of rock at level -10
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Multi anchored sheet pile wall in soft clay standing on rock
Structural analysis of wall … and anchors
Capacity of anchors and max. proof load Pp
axial per axial per horizontal
Id Level c Ø0,62" Nyk Nuk anchor meter per meter
Unit [m] [m] n [kN] [kN] [kN] [kN/m] [kN/m]
Upper -1,0 3,5 6 1494 1674 1339 383 271
Mid -3,5 3,5 6 1494 1674 1339 383 271
Lower -7,0 2,4 7 1743 1953 1562 651 460
Note
fyk 1660 MPa yield stress
fuk 1860 MPa tensile strength
Pp proof load ≤ min {0,8 fuk; 0,95 fyk) x A
Structural strength
Characteristic
Max possible Proof load Pp
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: a) stiff support
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
mm Deflection
a) AZ50, stiff support
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: a) stiff support
-150
-100
-50
0
50
100
150
200
250
300
350
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
kNm/m Bending moment
a) Stiff support
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: b) elastic support, AZ50, no pre-stress
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
mm Deflection
a) AZ50, stiff support
b) AZ50 no PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: b) elastic support, AZ50, no pre-stress
-150
-100
-50
0
50
100
150
200
250
300
350
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
kNm/m Bending moment
a) Stiff support
b) AZ50 no PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: c1) Finish pre-stress, AZ50
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
mm Deflection
a) AZ50, stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: c1) Finish pre-stress, AZ50
-150
-100
-50
0
50
100
150
200
250
300
350
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
kNm/m Bending moment
a) Stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: c2) Finish pre-stress, AZ19-700
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
mm Deflection
a) AZ50, stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
c2) AZ19 FIn PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: c2) Finish pre-stress, AZ19-700
-150
-100
-50
0
50
100
150
200
250
300
350
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
kNm/m Bending moment
a) Stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
c2) AZ19 FIn PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: d) DK pre-stress, AZ19-700
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
mm Deflection
a) AZ50, stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
c2) AZ19 FIn PS
d) AZ19 DK PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: d) DK pre-stress, AZ19-700
-150
-100
-50
0
50
100
150
200
250
300
350
0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0
kNm/m Bending moment
a) Stiff support
b) AZ50 no PS
c1) AZ50 Fin PS
c2) AZ19 FIn PS
d) AZ19 DK PS
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: Anchor loads, horizontal
Anchor / support A1 A2 A3 Rock bolt Total
Level -1,0 -3,5 -7,0 -10,0
Unit kN/m kN/m kN/m kN/m kN/m
a) stiff, FULS,d 17 206 422 123 768
b) AZ50, no PS, FULS,d 107 135 305 220 767
c1) AZ50, Fin PS, P0 81 101 162 344
c1) AZ50, Fin PS, FULS,d 99 145 308 215 767
c1) AZ50, Fin PS, FULS,d/P0 1,22 1,44 1,90
c2) AZ19, Fin PS, P0 81 101 162 344
c2) AZ19, Fin PS, FULS,d 76 149 369 174 768
c2) AZ19, Fin PS, FULS,d / P0 0,94 1,48 2,28
d) AZ19, DK PS, P0 60 100 100 260
d) AZ19, DK PS, FULS,d 71 165 350 182 768
d) AZ19, DK PS, FULS,d / P0 1,18 1,65 3,50
Max Pp (horizontal) 271 271 460
RGEO ,d = Max Pp / 1,3 = 208 208 354
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: Anchor loads, horizontal
0 100 200 300 400 500
a) stiff, FULS,d
b) AZ50, no PS, FULS,d
c1) AZ50, Fin PS, FULS,d
c2) AZ19, Fin PS, FULS,d
d) AZ19, DK PS, FULS,d
kN/m
Final load on anchors and rock bolts
A1 (-1,0)
A2 (-3,5)
A3 (-7,0)
Rock bolts (-10,0)
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: Anchor loads, axial + rock bolt
Anchor / support A1 A2 A3 Rock bolt
Level -1,0 -3,5 -7,0 -10,0
c-c (m) 3,5 3,5 2,4 1,0
Inclination, v ( ) 45,0 45,0 45,0 0,0
Unit kN kN kN kN
a) stiff, FULS,d 84 1020 1432 123
b) AZ50, no PS, FULS,d 530 668 1035 220
c1) AZ50, Fin PS, P0 401 500 550
c1) AZ50, Fin PS, FULS,d 490 718 1045 215
c1) AZ50, Fin PS, FULS,d/P0 1,22 1,44 1,90
c2) AZ19, Fin PS, P0 401 500 550
c2) AZ19, Fin PS, FULS,d 376 738 1252 174
c2) AZ19, Fin PS, FULS,d / P0 0,94 1,48 2,28
d) AZ19, DK PS, P0 297 495 339
d) AZ19, DK PS, FULS,d 351 817 1188 182
d) AZ19, DK PS, FULS,d / P0 1,18 1,65 3,50
Max Pp 1339 1339 1562
RGEO ,d = Max Pp / 1,3 = 1030 1030 1202
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Multi anchored sheet pile wall in soft clay standing on rock
LEM: Anchor loads, axial
0 200 400 600 800 1000 1200 1400 1600
a) stiff, FULS,d
b) AZ50, no PS, FULS,d
c1) AZ50, Fin PS, FULS,d
c2) AZ19, Fin PS, FULS,d
d) AZ19, DK PS, FULS,d
kN
Final load on anchors and rock bolts
A1 (-1,0)
A2 (-3,5)
A3 (-7,0)
Rock bolts (-10,0)
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Multi anchored sheet pile wall in soft clay standing on rock
LEM vs FEM
LEM: Limit Equilibrium Method
Influence of ration of stiffness between wall and anchors (no stiff support)
No soil-structure interaction, constant plastic earth pressure
FEM: Finite Element Method
compatibility between strains and stresses in the soil
elasto-plastic soil structure interaction
Plaxis vs. NovaPoint Geocalc? MC model?
modelling of rock bolt support
ULS with pre-stress? AZ50 vs. AZ19-700 ?
SLS with pre-stress? Final anchor loads (FServ;k vs. FULS;d c.f. new Ch. 8)
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Multi anchored sheet pile wall in soft clay standing on rock
FEM
The FEM model:
Finland uses NovaPoint Geocalc computer programme
)1(
1
' nk
n
a
va OCRmM
s
ss
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Multi anchored sheet pile wall in soft clay standing on rock
FEM
The FEM model:
In the Plaxis model a Mohr-coulomb material model was utilized, with a
depth(stress) depended stiffness and strength.
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Multi anchored sheet pile wall in soft clay standing on rock
FEM
The calculation phases:
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Multi anchored sheet pile wall in soft clay standing on rock
FEM
Modelling of the rock bolt:
Several approaches where tested:
best approach: to applied a fixity at the foot of the sheet pile wall
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Multi anchored sheet pile wall in soft clay standing on rock
FEM ULS
A1: 910kN/anchor
A2: N/A
A3: N/A
A1: 901kN/anchor
A2: 675kN/anchor
A3: N/A
A1: 861kN/anchor
A2: 598 kN/anchor
A3: 545 kN/anchor
Calculated ULS LK4 anchor forces:
c1) AZ50 with Finish prestress
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Multi anchored sheet pile wall in soft clay standing on rock
FEM ULS
Bending moment during excavation
-12
-10
-8
-6
-4
-2
0
-100 0 100 200 300 400 500 600 700
DEPT
H [
M]
BENDINGMOMENT
[KNM/M]
1. excav
2. excav
3. excav
Final excavation
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison between LEM and FEM results
AZ 50 with Finish prestress, final stage
axial anchor loads
horizontal (shear) force on rock bolt
Pre-stress P0
LEM ULS FEM ULS FEM SLS
A1 401 400 400
A2 500 500 500
A3 550 550 550
Rockbolt 0 kN/m 0 kN/m 0 kN/m
Final Anchor Loads Pa
LEM ULS FEM ULS FEM SLS
A1 490 861 663
A2 718 598 620
A3 1045 545 562
Rockbolt 215 kN/m 433 kN/m 319 kN/m
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Multi anchored sheet pile wall in soft clay standing on rock
Comparison between LEM and FEM results
Bending moment at the final stage (AZ50 with Finish pre-stress)
-12
-10
-8
-6
-4
-2
00 100 200 300 400 500 600
Depth
[m
]
[kNm/m]
FEM ULS
LEM ULS
SLS FEM
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Multi anchored sheet pile wall in soft clay standing on rock
FEM
Deformations during excavation
-12
-10
-8
-6
-4
-2
00,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07
Depth
[m
]
Displacement [m]
1. excav
2. excav
3. excav
Final excav
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Multi anchored sheet pile wall in soft clay standing on rock
Findings
• Big effect of pre-stress on deformation by LEM, not by FEM
• Effects of very soft clay, near failure during excavations by FEM
• Bending moments by FEM twice the moments by LEM
• Adverse tendency of anchor loads by LEM compared to FEM
Max at the bottom by LEM. Max at the top by FEM.
The reason for this is:
in spite of the relatively stiff (short) lower anchors, the effect of staged
construction by FEM and the wall rotating (~ rigid) around the foot (fixed by
the rock bolt) leads to bigger upper anchor loads and
the LEM is only carried out for the final stage with no superposed section
forces (pre bending) from previous stages.
• FEM: SLS anchor loads > ULS anchor loads for mid and lower anchors