lecture 06 - di prisco
DESCRIPTION
Prefabricated tunnel segments class in Politecnico di Milano ItaliaTRANSCRIPT
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Prefabricated tunnel segments
SFRC solution
M. di Prisco
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2
Outline
transient phases during segment production
bending resistance in FRC structures
shear resistance in FRC structures
KRd factor
TBM jack pushing: strut and tie model with and
without fibres, 2D and 3 D conditions
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Considering additional loads due to:
Adhesion: 2 kN/m2
Humidity: 0.5 kN/m3
Dynamic increasing factor: 20% Wc
DEMOULDING AND FIRST HANDLING
ACCIDENTAL SETTINGS
STOCKPILING
Considering additional load:
Dynamic increasing factor:
60% Wc
Considering both:
External
Internal
Disalignment
Structural design models for transient stages
Scheme 1 Scheme 2
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ACCIDENTAL SETTINGS
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7.7.3 Verification of safety (ULS)
7.7.3.1 Bending and/or axial compression in linear members
(1) The bending failure is considered when one of the following
conditions is obtained (see Fig.XX.7):
• attainment of the maximum compressive strain in the FRC, ecu;
• attainment of the maximum tensile strain in the steel (if present), esu;
• attainment of the maximum tensile strain in the FRC, eFu.
M
Fue
sue
cue
Asl
cdf
Ftsf / F
Rd
NSd
cd·f
Ftuf / F
·xx
y
hardening softening
Bending of FRC structures
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For FRC structures without the minimum reinforcement
du(wu) ≥ 20 dSLS
dpeak ≥ 5 dSLS
Du ultimate displacement
dpeak displacement at the maximum load
dSLS displacement at service load computed by performing a
linear elastic analysis with the assumptions of uncracked
condition and initial elastic Young’s modulus.
P
PU
UPEAKSLS
Displacement
SLSP
Load
MAX
P
crack formationP
CRPu > Pcr
or
Structural constraints to remove bars
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Not Post-tensioned beams
30
30 30
30
R0
2 x
S0
3 x
Experimental programme
Post-tensioned beams
30
30
30
30
S1
3 x 3 x
30
30
P1
2 x 2 x
P2 30
30
Total: 15 beams (6 typologies)
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M2
fck [MPa] 60
Cement CEM I 52.5R
[kg/m3]
400
Agg. < 12mm
[kg/m3]
569
Agg. < 8mm [kg/m3] 403
Agg. < 4mm [kg/m3] 676
Filler [kg/m3] 96
Plasticizer/cement 2.2%
Water /binder 0.39
F4
Df [mm] 0.8
Lf [mm] 60
Aspect ratio 75
Tensile Strength [Mpa] 1192
Type hooked
end
Class 4a
Fibre dispersion
Mechanical properties
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Test modelling: uniaxial constitutive relationships
0 0.02 0.04 0.06
0
400
800
1200
1600
2000
[MPa]
e
steel
Model Code 90
a = 0.83
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Test modelling: FE approach
S2C
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Reliability of the model
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Reliability of the models
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peak
m =1
SLE
507.43.1/3.5
SLS
peak
d
d
0 30 60 90 120
d [ m m ]
0
100
200
300
400
P [ k N ]
R0B
S1C
S0A
R0
30
30
30
30
S1
Constraint check
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Example: beam in FRC 300x300x3000 mm
MPa2.15.1/)f45.0(f k,1Rd,Fts
MPa13.05.1/)f2.0f5.0(f k,1Rk,3Rd,Ftu
02.0Fu e
mm5.2)l02.0;mm5.2min(w csu
kNm57.66
hhb)ff(
2
hhbfM FtudFtsdFtudRd
kN08,17KM2P RdRdu
Class 4a:
Rigid-plastic method
MPa44.0)5.1*3/()f(f k,3Rd,Fu Linear softening method
mm300lcs
0083.0300/5.2h/wuu
mm25.6)2/(1500 uu d
fR1k= 4 MPa; fR3k= 2 MPa
kNmh
bhfM FtudRd 62
kNm6.153.1*12K*2*MP RdRdu
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k mf f ks
0
1
2
3
4
5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
CTODm [mm]
No
min
al S
tre
ss
s
N [
MP
a]
Load vs. Central deflection
0
50
100
150
200
250
300
350
0 1 2 3 4 5 6
Central deflection [mm]
Lo
ad
[k
N]
Slab P22 50/0,75 Vf=0,38 %
Slab P21 50/0,75 Vf=0,38 %
Slab P20 50/0,75 Vf=0,38 %
di Prisco, M., Failla, C., Plizzari, G.A., Toniolo, G
(2004).
P = P (fm)
P = P (fk)
the key role of the scattering
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the key role of the scattering
4.1max,
max,
k
m
m
k
f
f
P
PPRd = KRd P(fFd)
2 5
V V0
KRd = KRd (V/V0 , Pmax/Pcr) =
tests
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CONCRETE RETAINING (cantilever) WALL
Surcharge
Load condition
35
SLS
SLU
d
d
%15.0: srebar
MC (2010) classification of SFRC:
Class “2b” - Vf = 25kg/m3
SLS
SLU
Material design values
Courtesy by Giovanni Plizzari
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Models for members without shear reinforcement:
MC 90 and EC2 approach
Zsutty, T. C., 1968, Beam shear strength prediction by analysis
of existing data, ACI Journal, November 1968, Vol. 65, No. 11,
pp. 943-951
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13
W
FtukRd,F 1 ck cp
c ctk
0 18100 1 7 5 0 15 [tensioni in MPa]
f.V k . f . b d
f
Shear resistance without shear
reinforcement
w = 1.5
MC 90 and EC2 approach
Prestressing (EC2)
Concrete strength
Reinforcement ratio
Size effect
Area of cross section
VR,c = C∙b∙d∙k∙1/3∙fck1/3+ Cp∙b∙d∙cp
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21
Muttoni, A., 2003, : Introduction to SIA 262 code,
Documentation SIA, D 0182, Zürich, Switzerland, pp.
5–9.
Preliminary design, non
governing failure modes
Typical design
Assessment of critical existing
structures, design of special
cases
Multi level approach to shear
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Models for members with shear reinforcement (girders):
compression strut strength
Brittleness
effect
Strain
effect 1f
303/1
ckcf
fck in MPa
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Girders (crushing of compression struts)
Vecchio, F. J. and Collins, M. P., 1986, The
modified compression field theory for reinforced
concrete elements subjected to shear, ACI
Journal, 83, March-April, pp. 219-231
Strain
effect
ke
Sigrist V., 2011, Generalized Stress Field
Approach for Analysis of Beams in Shear, ACI
Structural Journal, V. 108 (4), pp. 479-487.
ke
Brittleness
effect
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The levels-of-approximation approach:
shear in girders with transverse reinforcement
Level I
Level II
Level III
Level IV
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(7.7-7))
(7.7-8))
1d16
32k75.0
g
dg
mm125.010002.0w
700029
45
xu
xmin
min
e
e
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26
Shear resistance : validation
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Verification at SLS
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esh
Crack width limitations at SLS
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31 ENGINEERING FRAMEWORK
Tunnel Boaring Machine – TBM -
Structural problems
Advancing direction
Hydraulic jack
Shield
Cutter head
Tunnel Ring
splitting
hydraulic
jacks
hydraulic
jacks
in-plane actions
(placing situation)
spalling
hydrauli
c jacks
Schnütgen 2000
- general assumptions and
strut and tie models
- diffusion effects associated
to local pressures
- validity limits of FRC ties in
Strut and Tie Models
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D-REGIONS
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Strut and tie model
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Strut and tie model
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D-regions for geometrical
discontinuities
Strut and tie model
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D-regions for statical and/or
geometrical discontinuities
Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and Tie model
Strut and tie model
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Basic concepts
Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Superposition of two models
Strut and tie model
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Strut and tie model
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Minimum complementar energy with Su 0
Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
By J. Schlaich and K. Schäfer, 1991: “Design and detailing of
structural concrete using strut and tie models
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Strut and tie model
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Strut and tie model
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Strut and tie model
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check lb
Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
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Strut and tie model
![Page 90: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/90.jpg)
90
Courtesy by J. Walraven
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The case of a deep beam
![Page 92: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/92.jpg)
The case of a deep beam
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The case of a deep beam
![Page 94: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/94.jpg)
The case of a deep beam
![Page 95: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/95.jpg)
The case of a deep beam
![Page 96: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/96.jpg)
The case of a deep beam
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Strut and tie model
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Strut and tie model
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Strut and tie model
![Page 100: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/100.jpg)
Engineering problem
![Page 101: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/101.jpg)
Model Code ‘90 Approach
12
2
111
* 6.013.0 hbfb
bhbf ctcc
cc
yk
21
sxx
f
f
b6.0h
A
ccx2
2
11
*cc fb6.0
b
b1bf3.0
x
cc
cc
bb
bb
f
f
12
12
2
12
*
![Page 102: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/102.jpg)
Materials
Plain concrete
(PC)
SFRC
Cement Type: CEM I 42.5 (300
Kg/m3)
Aggregates 8/16: 1035 kg/m3
Aggregates 0/8: 207 kg/m3
Aggregates 0/5: 828 kg/m3
w/c ratio: 0.6
Dmax aggregates : 16 mm
Super-plasticizer: 1%
Rcm=34.64 MPa
Fiber length (l): 60 mm
Fiber diameter (d): 0.8 mm
Aspect ratio (l/d): 75
Fiber content: 25 kg/m3
SFRC shape bottle strut
![Page 103: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/103.jpg)
Mechanical characterization of SFRC
150
150
600
150 96 96150
1 221
Provini sui quali viene effettuata la prova di compressione
Provini sui quali viene effettuata la prova di trazione indiretta
Specimen for compression tests
Specimen for splitting tests
Test number Average value
MPa Standard dev.
MPa
Uniaxial compression tests (Rc)
Uniaxial compression tests
reduced friction (fc)
Splitting tests (fct,sp)
12
12
12
40.97
32.23
2.98
2.368
3.319
0.215
Uniaxial
compression tests
reduced friction (fc)
Splitting
tests (fct,sp)
![Page 104: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/104.jpg)
Mechanical characterization of SFRC
a
P/2 P/2
CTOD
b
hN
0.6mm 2.4mmCTOD
N=b·hN
2
feq0.6-3
feq0-0.6
fIf
b = 150 mm
hN = 105 mm
a = 150 mm
fIf=4.30 MPa
feq0-0.6=3.45 MPa
feq0.6-3=3.31 MPa D0= feq0-0.6 / fIf =0.81
D1= feq0.6-3 / feq0-0.6 =0.97
![Page 105: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/105.jpg)
Experimental set-up
a
b
b
t
b = 270 mm
t = 60 mm
=b/a
-250 -200 -150 -100 -50 0 50
x (N/mm2)
0
100
200
300
z (m
m)
b/c=1
b/c=1.5
b/c=2
b/c=2.5
b/c=3
30
13
5/1
60
30
27
0
LVDT
LVDT
LVDT
a
d d
4.0
60
dd
LV
DT
LV
DT
LV
DT
27
0
270
135
30 30
(a) (b)
dd
30
13
5/1
60
30
27
0
LVDT
LVDT
LVDT
a
d d
4.0
60
dd
LV
DT
LV
DT
LV
DT
27
0
270
135
30 30
(a) (b)
dd
1
1.5
2
2.5
3
Z
(mm)
![Page 106: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/106.jpg)
Experimental tests
PC =b/a=1-1.5-2-3 SFRC =b/a=1-1.5-2-2.5-3
3 nominally identical tests
2 standard tests 1 moirè test
Front Front Rear Rear +
![Page 107: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/107.jpg)
Test results
0 1 2 3
D [mm]
0
100
200
300
400
500
P [
KN
]
FRC1_media
PC1_media
0 0.5 1 1.5 2
D [mm]
0
100
200
300
400
P [K
N] FRC1.5_media
PC1.5_media
0 1 2 3
D [mm]
0
100
200
300
P [K
N]
FRC2_media
PC2_media
0 1 2 3
D [mm]
0
50
100
150
200
250
P [
KN
]
C3_ media
P3 _media
SFRC
PC = 1 = 1.5
= 2 = 3
P
d P
d
d
d
P
P
[kN, mm]
P
P
d
![Page 108: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/108.jpg)
Crack Patterns
PC SFRC
=1
=2
=3
![Page 109: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/109.jpg)
Test results - COD
0 0.4 0.8 1.2 1.6 2
0
0.4
0.8
1.2
1.6
top
middle
bottom
D [mm]
COD[mm] PC
= 1
0 0.4 0.8 1.2
0
1
2
3
top
middle
bottom
D [mm]
COD[mm]
PC
= 2
0 0.4 0.8 1.2
0
1
2
3
top
middle
bottom
D [mm]
COD[mm] PC
= 3
0 0.4 0.8 1.2 1.6 2
0
1
2
3
top
middle
bottom
D [mm]
COD[mm] SFRC
= 1
0 0.4 0.8 1.2 1.6 2
0
1
2
3
top
middle
bottom
D [mm]
COD[mm] SFRC
= 2
0 0.4 0.8 1.2 1.6 2
0
1
2
3
top
middle
bottom
D [mm]
COD[mm] SFRC
= 3
D
![Page 110: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/110.jpg)
Concentrated pression
1 1.5 2 2.5 3
0
0.4
0.8
1.2
SFRC w=1.5mm
SFRC w=0.3mm
PC w=1.5mm
PC w=0.3mm
pa/fcm
1 1.5 2 2.5 3
0.4
0.8
1.2
SFRC load peak
SFRC first cracking
PC load peak
PC first cracking
pa/fcm
Pre-peak Post-peak
pa/fcm
![Page 111: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/111.jpg)
Concentrated pression
1 1.5 2 2.5 3
0.4
0.8
1.2
1.6
Load peak
First cracking
w=1.5mm
Model Code
pa/peak(=1)
PC
1 1.5 2 2.5 3
0
0.4
0.8
1.2
1.6
2
Load peak
w=0.3mm
w=1.5mm
Model Code =3.42%
pa/peak(=1)
SFRCpa/ppeak (β=1)
no valley
![Page 112: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/112.jpg)
Design prediction models
b/2
f Tt
a/4
a/2
b/4
b/2
b
pat/2
fcm
xx
T=As fy
fcm
pat/2
b
b/2
b/4
a/2
a/4pa*a*t/2 pa*a*t/2
Reinforced
concrete SFRC
fFtu
![Page 113: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/113.jpg)
Design prediction (t=60mm)
1 1.5 2 2.5 3
0
0.4
0.8
1.2
1.6
2
1
1+1
exp SFRC w=1.5mm
SFRC design
pa/fcm
18
1+16
![Page 114: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/114.jpg)
HPFRC
Fiber length (l): 13 mm
Fiber diameter (d): 0.16 mm
Aspect ratio (l/d): 80
Fiber content: 1.28% by volume
Component Conetnt
Cement Type I 52.5 600 kg/m3
Water 200 l/m3
Sand 0-2mm 983 kg/m3
Slag 500 kg/m3
Superplasticizer 33 l/m3
Fibres 100 kg/m3
![Page 115: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/115.jpg)
Mechanical characterization of HPFRC
Uniaxial compression strength (fcc)
First cracking strength (fIf)
110 N/mm2
11.05 N/mm2
SLS residual strength (feq1) 14.09 N/mm2
ULS residual strength (feq2) 14.00 N/mm2
Italian Standard CNR DT 204
![Page 116: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/116.jpg)
Experimental set-up
a
b
b
t
b = 270 mm
t = 60 mm
=b/a = 1 / 1.5 / 2 / 3
-250 -200 -150 -100 -50 0 50
x (N/mm2)
0
100
200
300
z (m
m)
b/c=1
b/c=1.5
b/c=2
b/c=2.5
b/c=3
30
13
5/1
60
30
27
0
LVDT
LVDT
LVDT
a
d d
4.0
60
dd
LV
DT
LV
DT
LV
DT
27
0
270
135
30 30
(a) (b)
dd
30
13
5/1
60
30
27
0
LVDT
LVDT
LVDT
a
d d
4.0
60
dd
LV
DT
LV
DT
LV
DT
27
0
270
135
30 30
(a) (b)
dd
1
1.5
2
2.5
3
Z
(mm)
3 Nominally identical tests
x (MPa)
![Page 117: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/117.jpg)
Test results
= 1 P
P
d
![Page 118: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/118.jpg)
Test results
= 1.5 P
P
d
![Page 119: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/119.jpg)
Test results
= 2 P
P
d
![Page 120: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/120.jpg)
Test results
= 3 P
P
d
![Page 121: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/121.jpg)
Test results
P
P
d
![Page 122: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/122.jpg)
Comparison with SFRC
![Page 123: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/123.jpg)
b/a c,max/fc
NSC HSC UHSC UHPC-1-HT UHPC-2-HT
2.3 0.89 0.6 0.41 0.87 0.96
4.7 1.18 0.59 0.38 1.04 1.44
6.9 1.75 0.73 0.56 1.28 1.66
10.7 2.48 1.15 0.81 1.73 2.22
by T. Leutbecher, E. Fehling, 2012
Bottle shaped strut
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Size effect
![Page 125: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/125.jpg)
Stati tensionali diffusivi
2.3
0
1.5
0
0
0
15 0.07
1 1.3 0.1
e
sp
i bp
e
e
P
b e l
e
e k
h
a
a
a
1.2
1.0
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Stati tensionali diffusivi
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Basic anchorage length
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Trasmission length
Design anch. length
Development length
Development length
![Page 129: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/129.jpg)
1 2 2 1 1
1
1
2
2 /
bs sd
bs
bs bs bs bs
n n t n t
N Fz
N b l
bs bursting
Fsd = design force for each
tendon
1= 1.1 safety factor
(overstressing by
overpumping)
bpt2
bptbsbs
bsbs
ll6.0hl
hl
Bursting
(indirect anchorage)
(direct anchorage)
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131
D-region stresses
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132
Structural design for damage mechanisms
TBM MAX THRUST ACTION
MEAN COMPRESSION ON THE RING
LOCAL COMPRESSION UNDER THE JACK PLATE
BURSTING STRESS IN RADIAL AND CIRCUMFERENTIAL DIRECTION
Concrete check under compression:
c.m = 11.29 MPa < 42 MPa = fcd,sfrc
c = 33.26 MPa < 94 MPa = fcd,hpfrcc
c = 73.20 MPa < 94 MPa = fcd,hpfrcc
QuickTime™ e undecompressore
sono necessari per visualizzare quest'immagine.
cr = 1.77 MPa
ct = 1.16 MPa
fctk = 2.87 MPa
<
![Page 133: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/133.jpg)
0
50
100
150
200
0 1 2 3 4 5 6 7 8 9 10
Displacement (mm)
Lo
ad
(kN
)
Type B
Type B
Type A
Type C
A
courtesy by Meda, 2012
PANAMA tunnel 133
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134
Structural design for damage mechanisms
GASKETS
SHEAR-OFF OF THE MOUNTING GROOVE EDGES
Shear action:
Shear bearing capacity of unreinforced concrete:
Vsc 12.0 kN m1
Vsc 1.35 p 0.0085 m
Vrdct
fctk0.05
c
0.04 m
Vrdct 56kN m1
TENSILE SPLITTING STRESSES
Design max tensile splitting stress:
Tensile strength of un-reinforced concrete:
ct,d Zsd
0.5 0.8ds
ct,d 0.46 MPa
Rd ,ct fctk ,0.05
c
Rd,ct 1.39 MPa
<
lcg= 0.0085 m
il = 0.04 m
< Zsd = Design transverse tensile force
2.80
![Page 135: Lecture 06 - Di Prisco](https://reader031.vdocuments.us/reader031/viewer/2022021322/577c7d471a28abe0549e1fbb/html5/thumbnails/135.jpg)
Selection of the Concrete Composition
(by R. Gettu et al. – BEFIB 2004)
Requirements
• 28-day characteristic compressive strength of at least 40 MPa.
• Early-age (4-6 hours) mean compressive strength of at least 25 MPa.
• 28-day mean equivalent flexural strength of at least 2.9 MPa.
Practical Considerations
• Adequate “placeability” with 30 kg/m3 of steel fibers.
• Maximum cement content of 400 kg/m3.
• Cement and aggregates should be those normally used in the
prefabrication plant.
135
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Composition and Properties
(by R. Gettu et al. – BEFIB 2004)
Component kg/m3
Cement CEM I 52.5R 400
Sand 0/5 mm 745
Gravel 5/14 mm 558
Grava 12/22 mm 559
Water 132.2
Superplasticizer 4.8
Property Test result
Slump after 20 minutes from casting
3 cm
Density of fresh concrete 2430 kg/m3
28-day cylinder strength 62,8 MPa (±2,4%)
at 4+0,5 hours
18,7 MPa (±3,7%)
at 5+0,5 hours
25,0 MPa (±3,1%)
Compressive strength with accelerated curing
at 6+0,5 hours
28,2 MPa (±2,4%)
136
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Selection of Fiber Type
(by R. Gettu et al. – BEFIB 2004)
Toughness Characterization
Belgian standard was
chosen for determining the
equivalent flexural strength
(deflection limit of 1.5 mm).
• Toughness evaluated with
different fibers.
• Fibers had lengths of 50-60
mm and diameters of 0.75-
1.0 mm.
0 1 2 3 4
Flecha (mm)
0
10
20
30
40
50
Carga (
kN
)
Dramix 80/60
Dramix 65/60
Wirand 1.0/50
Novocon 1060
Duoloc 47×1.0
Tests with 45 kg/m3 of fibres
Midspan deflection (mm)
Load (
kN
)
137
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Evaluation of Possible Use of Fibers
as the only reinforcement (by R. Gettu et al. 2004)
• More than 3 km of tunnel lining has been constructed with rebar + fibre reinforcement. • Is the total substitution of bar reinforcement with fibers cost-effective, in this project? • Yes, if the required performance can be obtained with a dosage of about 60 kg/m3. Duration of study ≤ 4 months
138
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Performance of the Tunnel Lining
(by R. Gettu et al. – BEFIB 2004)
Requirements
• Adequate flexural strength during demolding and
storage in order to avoid cracking.
• Resistance against cracking or crushing due to the
reactions of the actuators of the tunnelling machine
during the boring operation.
• Ability to resist the soil pressure during service.
139
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Numerical Analysis: Level of stresses
High tensile stresses can occur when the supports are eccentric during storage by piling.
Posibles eccentricidades respecto el eje de apoyoPossible eccentricities between supports
140
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Eccentricities in the reaction of the actuators of the tunelling machine, especially in the radial direction, can generate high localized tensile
stresses.
Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Numerical Analysis: Level of stresses
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The low tensile stresses obtained in the analyses motivated further study of the possibility of using steel fibres as the only reinforcement of the concrete in the segments.
Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Numerical Analysis: Level of stresses
During service, the soil pressure can generate compressive stresses of up to 17 MPa. The maximum values of tensile stress are less than 1 MPa.
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Material
Characterization
• Comparison of the
performance of
different fibres.
• Evaluation of
reference
compressive and
flexural strengths,
and toughness.
• Accelerated curing
was simulated in a
environmental
chamber.
0 0.25 0.5 0.75 1 1.25 1.5
Flecha (mm)
0
10
20
30
40
Ca
rga
(k
N)
Dramix 80/60 BN
Dramix 65/60 BN
Wirand 50x1 mm
Novocon HE 1060
Duoloc 47×1.0
Dramix 80/60
Dramix 65/60
WirandDuoloc Novocon
Deflection (mm)
Loa
d (
kN
)
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Material
Characterization
• Comparison of the
performance of
different fibres.
• Evaluation of
reference
compressive and
flexural strengths,
and toughness.
• Accelerated curing
was simulated in a
environmental
chamber.
0 0.5 1 1.5 2 2.5 3
Flecha (mm)
0
20
40
60
Ca
rga
(k
N)
60 kg/m3
45 kg/m3
30 kg/m3
Deflection (mm)
Loa
d (
kN
)
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing: Stacking
No cracking occurs in the SFRC segments when the eccentricity of the supports is equal to or less than 50 cm, even when all the segments of a ring are piled at the age of 4 days.
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing:
Flexure
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing: Flexure
For small crack openings (less than 0.2 mm), the segment with 60 kg/m3 of fibres has similar load-carrying capacity as the segment with conventional rebars.
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing: Flexure
For small crack openings (less than 0.2 mm), the segment with 60 kg/m3 of fibres has similar load-carrying capacity as the segment with conventional rebars.
Tensile displacement or crack opening (mm)
Load (
kN
)
Load (
kN
)
Tensile displacement or crack opening (mm)
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing: In-Plane Compression
Some local cracking appears. The behaviour is similar for the SFRC and reference panels.
LVDT cara
encofrada
LVDT cara
regleada
LVDT lateral 1
LVDT lateral 2
Plato de carga (excéntrica) 540 x 120 x 10 mm
Plato de carga continuo 540 x 180 x 10 mm
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Real-Scale Structural Testing: Contact at Joints
Splitting cracks occur at high loads. Slightly more cracking is seen in SFRC specimens.
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Quality Assurance Requirements:
• Fibre quality (dimensions, hooks, tensile strength and elastic
modulus, surface quality)
• Batching and Mixing (homogeneity, slump/workability)
• Fibre content in fresh concrete
• Toughness requirement of SFRC
• Placing should not affect the homogeneity of the concrete
• Vibration should be regulated to avoid preferential orientation and
segregation of fibers
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Tunnel Lining of Section 4
(by R. Gettu et al. – BEFIB 2004)
Quality Check of Cast Segment
4 cores extracted perpendicular to the curved surface (radial direction) and
4 cores extracted from the flat edges, one from the middle of each side
Radial core
Core extracted from flat face
10 cm 20 c
m
To check preferential
orientation:
Fibre count made on
halved core. Differences
should not be more than
10% of the lower value. To check segregation:
Cores are crushed, fibres
are separated and
weighed. The fibre
content should not vary
by more than 5% from
the specified value.
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Tunnel Segments: Non Linear Analyses, Fiber FF1-45
0
5000
10000
15000
20000
25000
0 0,5 1 1,5 2 2,5 3 3,5
Displacement [mm]
Lo
ad
[kN
]
Service Load
Max.
Load
Service Load =3000x4=12000 kN Segment is already cracked
Splitting cracks in radial and tangential direction in the loaded zones
Barcelona Metro: further structural analyses
(by Plizzari et al. Università di Brescia, 2005) 153
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Staffe 8/200 mm
Aree di carico
dei martinetti
4 Staffe sotto
le zone di carico
31
5
4
Sezione longitudinale
23
4
Sezione trasversale
50Pilastrino
10 14
450
100 100
500
35
0
Original Design
Proposal
Vantages: 1) smaller encumbrance
2) simpler construction
3) simpler casting
Barcelona Metro: further structural analyses (by
Plizzari et al. Università di Brescia, 2005) 154
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0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
CMOD [mm]
No
min
al
str
ess [
MP
a]
CM
OD
1
CM
OD
2
CM
OD
3
CM
OD
4
fR1fR2
fR3
fR4
Type A
Type C
Type B
PANAMA tunnel
courtesy by Meda, 2012
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0
50
100
150
200
250
-1000 0 1000 2000 3000 4000 5000 6000 7000 8000
N [kN]
M [
kN
m]
Serviceability conditions
courtesy by Meda, 2012
PANAMA tunnel 156
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0
50
100
150
200
0 1 2 3 4 5 6 7 8 9 10
Displacement (mm)
Lo
ad
(kN
)
Type B
Type B
Type A
Type C
A
courtesy by Meda, 2012
PANAMA tunnel 157