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.