Numerical analysis of Concrete Face Rockfill Dams Numerical analysis of Concrete Face Rockfill Dams based on Lade’s model and gradient plasticitybased on Lade’s model and gradient plasticity
P. Dakoulas, E. Stavrotheodorou, A. GiannakopoulosUniversity of Thessaly
Volos, Greece
Realistic prediction of slab performance during impoundment,
creep and dynamic settlements
Motivation:
Campos Novos Dam
Zipingpu Dam
Topics
• Behavior and modelling of rockfill
• Lade’s constitutive model
• A simple gradient plasticity approach
• Numerical model
• Concrete slab performance: o effect of dam heighto effect of rockfill stiffness
• Conclusions
Oroville dam rockfill
Axial Strain, å1,%
0 2 4 6 8 10 12 14
Vo
lum
etr
ic S
tra
in,
å vol,
%
-3
-2
-1
0
1
2
3
Axial Strain, ε1, %
0 2 4 6 8 10 12 14
σ1-
σ3,
kP
a
0
2000
4000
6000
8000
10000
12000
14000
Pyramid dam rockfill
σ3= 4413 kPa
2896
965
207
σ3=207 kPa
965
2896
4413
excellent quality average quality
Axial Strain, ε1,%
0 5 10 15 20 25 30
Vo
lum
etr
ic S
tra
in,
ε vol,
%
0
2
4
6
8
Axial Strain, ε1, %
0 5 10 15 20 25 30
σ1-
σ3,
kP
a
0
2000
4000
6000
8000
10000
12000
14000 σ3= 4413 kPa
2896
965207
σ3=207 kPa
965
28964413
(Marachi et al. 1972)
Lade’s constitutive model for geomaterials
stress-strain relationship with hardening and softening behaviour
yield surfaces at different levels of plastic work and failure surface
(Dakoulas and Sun 1993)
yield surface
3, /pW kNm m
Lade’s constitutive model for geomaterials
The model offers the following advantages:
•Continuous variation of the tangent Young’s modulus based on the stress state during the analysis
•Realistic description of volumetric strains due to shearing
•Realistic handling of the softening behaviour
Simulation of rockfill behavior: isotropic compression
Oroville rockfill Pyramid rockfill
(using Lade’s model implemented in ABAQUS as a user material)
Oroville rockfill behavior: triaxial compression
Pyramid rockfill behavior: triaxial compression
Possible numerical convergence issues
Intense softening behaviour
(e.g. due to major rockfill breaking above a critical confining stress, as in Mohale dam)
Local areas of possible large strain concentration
abutment interface
material zone interface
slope surface
vertical stress, σv, kPa
0 200 400 600 800 1000 1200 1400
vert
ica
l mo
du
lus
Mv,
MP
a
0
20
40
60
80
100
intense softening behaviour
A simple gradient plasticity approach
1/2
2 2 2 2 2 22 1( ) ( ) ( ) ( ) ( ) ( )
23p p p p p p p pq q x y z xy yz zxe de de de de de de de
1/22
21
0
1 rgc l
deviatoric plastic strain:
gradient coefficient: where: 1/22 2 2p p p
q q qr
e e eg
x y z
= gradient of
pqe
0
l = intrinsic length (rockfill size)
= reference strain (limit of elastic range) (Bassani 2001)
A simple gradient plasticity approach
Numerical models of three dams
100 m
200 m
Dam A
Dam B
concrete panels
material zones
Aspect ratio:
L/H = 2
Shape factor:
As/H2 = 2.1
300 m
Dam C
material zones
Numerical models of three dams
Aspect ratio:
L/H = 2
Shape factor:
As/H2 = 2.1
Fiber reinforced concrete based on mixing plain concrete with fc= 37
MPa and steel fiber (Reinforcing Index = 2.5%)
Numerical modelling of concrete slab panels
Geometry: slab width = 15 m
slab thickness = 0.30+0.003 h (h = depth of overlying water)
Material:
Uniaxial compressionUniaxial tension
Elastic Young’s modulus at the end of construction
H= 200m
Oroville rockfill
Pyramid rockfill
2
1 22
161 2a
a a
I v JE Mp
p v p
Elastic Young’s modulus:
,M = model parameters
v = Poisson’s ratio
1 2,I J = stress invariants
ap = atmospheric pressure
Young’s modulus is derived
from unloading test (i.e.
purely elastic behavior)
Distribution of settlements at midsection
H = 300 m -> S/H = 0.40% H = 300 m -> S/H = 1.47%
H = 200 m -> S/H = 0.30%
(measured on Oroville dam S/H=0.31%)
Construction settlements
narrow canyons
Concrete slab deflection after impoundment
Oroville rockfill
Pyramid rockfill
H = 200 m
Slab deflection
after impoundment
after long-term creep and dynamic settlements
Assumption: Max long-term settlements at crest is 50% of max. construction settlement
Tensile plastic strains in the concrete slab
H= 300 m H= 300 m
Compressive stressafter impoundment
H= 200 m
H= 300 m
Compressive stresses after impoundment
H= 200 m
H= 300 m
x
y
Compressive stressafter
long-term settlements
H= 200 m
H= 300 m
Compressive stresses after long-term settlements
x
y
3D strength: 57 MPa
after long-term settlements
Maximum compressive stress vs dam height
after impoundment
Horizontal movement of slab panels after impoundment
Oroville rockfill
Horiz. movement of slab panels after long-term settlements
Oroville rockfill
CONCLUSIONS
• Lade’s model for rockfill allows a realistic simulation of the stress-strain behavior and volumetric strains in a wide range of confining stresses.
• Comparison of measured construction settlements of dams in narrow canyons showed good agreement with the numerical predictions of the study.
• Use of excellent quality rockfill at void ratios 0.2 allows small construction settlements even for the 300 m dam
• Measured slab deflections due to impoundment from 18 CFRDs at various void ratios are in good agreement with the predicted slab deflections
CONCLUSIONS
• The use of excellent quality rockfill at void ratios of 0.2 yields small slab deflections even for the 300 m dam during impoundment and long-term settlements
• Compressive stresses in the slab reach a maximum at about 40% of the height during impoundment, but may reach a larger value near the crest due to long-term settlements
• For the excellent quality rockfill, compressive stresses remain at low levels compared to the strength of concrete
• For the average quality rockfill, compressive stresses become very high, especially after long-term settlements
Thank you for your attention!
AcknowledgementsAcknowledgementsThis research has been co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF)-Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund.
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