Physics based scour model applied to Tucurui Dam (Brazil)

Transcription

AquaVision engineering
Design and consulting in hydraulic,
geotechnic and environmental engineering
Physics based scour model applied to
Tucurui Dam (Brazil)
Dr Erik Bollaert
Prof. Bela Petry
AquaVision Engineering Ltd.
Engineering Consultant
CH–1024 ECUBLENS
SWITZERLAND
Delft
THE NETHERLANDS
E-mail: [email protected]
Web: http://www.aquavision-eng.ch
Physical processes of rock scour formation
Physical-mechanical processes
1
2
3
4
5
6
Vi, Di
free
falling
jet
δout
Z
Process 2. Diffusive shear layer: Jet module
Falling jet impact
Vj
Diffusive 2-phase shear-layer
Bottom pressure fluctuations
Progressive joint break-up
Dynamic ejection blocks
Transport/mounding
Falling
Jet
module
Jet core
6
Plunge
Pool
module
2
Y
t
Cp C’
p
shear
layer
Developed
jet
Dj,Dout
aerated
pool
4-6 x Dj
Y
1 Vj
h
Dj
Rock joint
Developed jet impact
mounding
3
Rock
Mass
module
5 CI
Γ+
4
Cmaxpd, ∆pc, fc, CI
Process 4. Progressive joint break-up by fatigue: LEFM model
Sj2
Sj1
y
Process 5. Dynamic ejection blocks: Uplift model
x
r θ crac
k tip
αj1 αj2
ej2
Griffith (1920)
Irwin (1957)
Paris et al.
(1961)
∫ (Fu − Fo − G b − Fsh ) ⋅ dt = m ⋅ V∆tpulse
0
G b = ∀ ⋅ (γ r − γ w ) =
x 2b
y
x
KI
σ ij =
2 πr
z
zb
xb
r
a
z
a
stress field
W
σy
stress singularity
⋅ z b ⋅ (γ r − γ w )
V∆tpulse = 2 ⋅ g ⋅ h up
xb
σy
KI
Lj1
∆tpulse
I ∆tpulse =
σy
mode I
⋅ f ij (θ ) + higher order terms
 a 
K I = σ max ⋅ π ⋅ a ⋅ f 

W
∆a c =
∫ (f ⋅ C ⋅ S max ⋅ S a
tf
m
n
)
+ υ ⋅ e bS ⋅ dt
0
(after Costin & Holcomb 1981)
-
KI = f (pressure distribution)
KI = f (in-situ stress field)
KIdyn = f (pressurization rate)
f (a/W) = f (geometry fissure) planar, …
KIc = fracture toughness value
- literature
- tests
Grady & Kipp (1980)
Haimson & Zhao (1991)
Zhao & Li (2000)
Zhao (2000)
Zhang et al. (2000)
m]
Experimental facility at EPFL, Switzerland
+1
0.001m
a
0.80m
d
Absolute pressure [10
14
Pressure at pool bottom (a)
Pressure at joint end (d)
12
fundamental period = 1/fres
10
8
6
4
2
spike
0
0
0.01m
peak
0.05
0.1
Time [sec]
0.15
0.2
Experimental facility at EPFL, Switzerland
Comprehensive Scour Model (CSM) (Bollaert, 2002)
- use of dynamic pressures at plunge pool bottoms
- computation of transient pressures inside rock mass
- comparison with resistance of rock mass against fracturing
- computation of net uplift pressures on single rock blocks
- comparison with resistance of blocks against uplift
1
2
3
4
5
6
Vi, Di
free
falling
jet
δout
Z
Falling jet impact
Diffusive 2-phase shear-layer
Bottom pressure fluctuations
Progressive joint break-up
Dynamic ejection blocks
Transport/mounding
Falling
Jet
module
1 Vj
New engineering model
for evaluation of ultimate scour
and time evolution of scour formation
Dj,Dout
h
aerated
pool
6
2
Y
t
Modules:
1. falling jet
2. plunge pool
3. rock mass
- hydrodynamic forces in rock
- resistance criteria of fractured rock
Cp C’
p
mounding
3
Rock
Mass
module
5 CI
4
Cmaxpd,
Plunge
Pool
module
∆pc, fc, CI
Γ+
Falling jet and plunge pool modules
Falling jet
Di
Vi
v’
θ1
Di
θ = 0.5·(θ1 + θ2)
θ2
Vi
D j = Di ⋅
Vj
u’
θ
vz
D out = D i + 2 ⋅ δ out ⋅ L
vx
Vi
Z
δout
Dj
δin = 0.5–1 %
δin
δout = 3–4 %
Vj
αout
Dj
δout ∝ Tu
ε
Ds
Plunge pool
1.0
- centerline mean (Cpa) and
fluctuating (C’
pa) dynamic
pressures
0.8
Y
δout
t2
zsc
∆x
xult
1.2
- Y/Dj ratio
Dout
0.4
Franzetti & Tanda (1987)
Ervine et al. (1997)
0.35
0.3
JET STABILITY
<<
Cpa
[-] 0.6
0.4
5% < Tu
3% < Tu < 5%
0.2
1% < Tu < 3%
Tu < 1%
core jet
developed jet
0.0
C pa
C pa
 Dj 

= 38.4 ⋅ (1 − α i ) ⋅ 

Y


= 0.85
0
2
2
4
6
8
10 12
Y/Dj [-]
14
16
18
20 0
2
4
6
8 10 12 14 16 18 20 22 24
Y/Dj [-]
for Y/Dj > 4-6
3
for Y/Dj < 4-6
C 'pa
2
 Y 




 − 0.0079 ⋅  Y  + 0.0716 ⋅  Y  + 0.0583
= 0.0022 ⋅ 
Dj 
Dj 
 Dj 






0.25
0.2
0.15
0.1
0.05
0
C'pa
[-]
Rock mass module: Hydrodynamic forces
1.) Maximum dynamic pressure Cmaxp in a closed-end joint
⋅
φ ⋅ V j2
2g
(
+
= γ ⋅ C pa + Γ ⋅ C
C+
'
pa
)⋅
+
+
'
Γ = C pd / C pa
Pmax [Pa ] = γ ⋅ C
max
pd
24
φ ⋅ Vj2
2g
20
maximum curve
16
12
8
minimum curve
4
pd
ratio at pool bottom
0
0
2
4
6
8
10 12
Y/Dj [-]
14
16
18
20
3.) Characteristic frequency of pressures fc in a closed-end joint
fc [Hz] ~ 10 –100
c [m/s] = 4·Lj·f c ~ 100 –200
Air concentration at jet impact αi [%]
2.) Characteristic amplitude of pressures ∆pc in a closed-end joint
60
50
40
L/Dj >>
30
20
air concentration inside I-joint αj
10
0
5
10
15
20
Vj [m/s]
25
30
35
4.) Maximum dynamic impulsion CmaxI in an open-end joint
1.6
1.4
1.2
pup = Cup · V2/2g
Iup = pup·∆tup =
∆tup = Tup · 2L/c
Cup·Tup·(V2L/gc)
=
CI·(V2L/gc)
[m.s]
1.0
CΙ
0.8
[-]
0.6
0.4
2
 Y


 − 0.119 ⋅  Y  + 1.22
C I = 0.0035 ⋅ 
 Dj 
 Dj 




0.2
0.0
0
2
4
6
8
10 12
Y/Dj [-]
14
16
18
20
Semi-elliptical (EL)
Rock mass module: Fracture Mechanics Method
(100 cyc/s) (50 cyc/s)
N° days
N° days m/cyc
for 1 m
for 1 m
10-6
Single-edge (SE)
5.10-7
e
KI
φ
aB e
1
a
K B
I
1
10 -7
5.10 -8
10
10
10-8
5.10-9
100
(Cmax
p)
4. Time-dependent crack propagation (∆pc, fc))
KI < KI ins
da
m
= Cr⋅ (∆K I ) r
dN
10-9
5.10 -10
1. Stress Intensity at crack tip
 a 
Cmax
KI = σ
a
f
⋅
π
⋅
⋅


max p
W
2. Fracture toughness of rock
KI ins, T = A · (1.2 to 1.5) · T
+ (0.054·σc) + B
KI ins, UCS = C · (1.2 to 1.5) · UCS + (0.054·σc) + D
3. Instantaneous crack propagation
KI > KI ins
Westerley Granite
Fatigue law
100
σwater
2.0
1.0
1.5
0.5
0.6 0.7 0.8 0.9 1
∆K I
2.5
K Ic
K I / KIc
1
1.5
2
∆Κ
5
10
1.E-04
crack propagation rate [m/cycle]
σwater
W
crack propagation rate
W
2c
1.E-05
1.E-06
(3.
gabbro m = 12.2
1.E-07
granite m = 11.9
1.E-08
dolerite m = 9.9
marble, limestone m = 8.8
1.E-09
sandstone m = 4.8
sandstone m = 3.0
1.E-10
Rock mass module: Dynamic Impulsion Method
Fu
Fo
Gb
Fsh
∆tpulse
I ∆tpulse =
∫ (Fu − Fo − G b − Fsh ) ⋅ dt = m ⋅ V∆tpulse
0
G b = ∀ ⋅ (γ r − γ w ) = x 2b ⋅ z b ⋅ (γ r − γ w )
=
=
=
=
underpressures
overpressures
weight of rock block
shear and interlocking forces
V∆tpulse = 2 ⋅ g ⋅ h up
y
x
Fo(x, t)
z
xb
zb
xb
Gb
Fsh(t,ej)
Fu(x, t, ej1(t), ej2(t))
x
Tocantins-Araguaia basin
Tucurui Dam plunge pool (Brazil)
Tocantins
River
- catchment area Tocantins River 758’000 km2 (7.5 % of land mass of Brazil)
- Tocantins River has a total length of 2’500 km
- average annual flow rate of 10’900 cms
- dry season in September-October
- peak flooding during February-April (average monthly flows of 50’000 cms)
Tucurui Dam plunge pool (Brazil)
ear
th
d
am
rockfill dam
Tucurui Dam Complex
140
Core of jet
Outer limits of turbulent air-water shear layer
120
Centerline of jet
Tailwater level downstream
100
Rockbed
80
Elevation (m a.s.l.)
- 86 m high rockfill dam on Tocantins River
- 6’900 m long main dam wall
- meta-sedimentary rock at spillway
- 2nd largest spillway worldwide (110’000 m3/s)
- pre-excavated plunge pool at – 40 m
- almost no scour since dam construction
- 23 rectangular gates 21 m x 20 m wide
- floods during 3 months / year (Feb-April)
intake and
power house
spillway
m
l da
l
i
f
th
ear
(35m radius, angle of 32°)
Flip
bucket
60
High-velocity
Jet impact
40
20
0
Pre-excavated
plunge pool
-20
-40
-60
-80
-100
-80
-60
-40
-20
0
20
40
60
Distance (m)
80
100
120
140
160
180
200
Rock mass properties
Fault structures
Plan view geology
spillway
meta-sedimentary rock
(Cadman et al. 1982)
Meta-sedimentary rock
- Unconfined Compressive Strength of intact rock = ~ 125 MPa
- multiple families of faults, joints
- one major fault through the center of the riverbed
- very complex situation (lithology –tectonic structure –faults)
- near-horizontal bedding, sliding stability
Rock mass properties
Property
Unconfined Compressive Strength
Density rock
Ratio horizontal/vertical stresses
Symbol
UCS
γr
K0
CONSERV
50
2600
2-3
AVERAGE
75
2700
2-3
BENEF
125
2800
2-3
Unity
MPa
kg/m3
-
Typical maximum joint length
Vertical persistence of joint
Form of rock joint
Tightness of joints
Total number of joint sets
Typical rock block length
Typical rock block width
Typical rock block height
L
P
Nj
lb
bb
zb
1
0.25
single-edge
tight
3+
1
1
0.5
1
0.25
elliptical
tight
3
1
1
0.75
1
0.25
circular
tight
2+
1
1
1
m
m
m
m
Joint wave celerity
Fatigue sensibility
Fatigue coefficient
c
m
C
150
8
1.00E-07
125
9
1.00E-07
100
10
1.00E-07
Semi-elliptical (EL)
Circular (C)
W
2c
m/s
-
Single-edge (SE)
y
x
W
b
xb
z
b
zb
e
KI
σwater
φ
aB e
aB
K
I
σwater
xblb
Flooding and bathymetric surveys (1969-2001)
Flooding survey (available since 1969)
- 1969 – 1980: statistical analysis based on Tucurui
and Itupiranga about 175 km upstream,
PMF = 90’000 cms
- 1978-1980: 3 major flood events during dam
construction, up to 68’000 cms
- 1980-present: more detailed flood analysis, PMF =
110’000 cms, somewhat conservative,
maximum peak since dam construction
= 43’000 cms (Jan 1990)
Bathymetric survey
Survey 1 (1984)
Sedimentation along right hand side of plunge pool due
to 3 yrs of river diversion during dam construction
1997
bottom
Survey 2 (1985)
No specific issues, only left hand isde of basin has been
surveyed due to strong turbulent vortices
Survey 3 (1986)
Former sediment deposits washed away. Slight erosion
(max. 5 m) along two local areas of plunge pool bottom
and problaby related to removal of partially detached
(blasting) rock blocks.
Survey 4 (1997)
Same erosion in same areas as found during the 1986
survey. No specific issues to notice.
Survey 1986 (ICOLD, 2002)
Laboratory model tests
Figure 1.- Scour formation in plunge pool following laboratory test with gravel and 100’000 cms (Large
Brazilian Spillways, ICOLD, Petry et al., 2002)
- discharges between 15’000 and 100’000 cms
- plunge pool bottoms at elevations of -15m, -25m, -40m
- pool at -40m:
no erosion for discharges of up to 50’000 cms (calibration model)
erosion until – 65m for discharge of 100’000 cms
Application of Comprehensive Scour Model
Falling jet at Tucurui Dam
The jet at Tucurui Dam is issuing from a chute with flip bucket. As such, numerical computations
have first been performed of the air-water flow characteristics along the chute. The water surface
line for a 110’000 m3/s is presented in Figure 4.
The flow velocity at the lip of the flip bucket equals 27.8 m/s, for a total flow depth of about
8 m. The upstream water level is 75.3 m a.s.l. and the downstream plunge pool water level is at 4.4
m a.s.l. The jet is thus of rectangular shape with a width of 20m and an issuance thickness of 8m.
Second, the jet characteristics at impact in the tailwater depth have been defined based on
ballistics accounting for air drag. As such, the jet velocity at impact has been computed at 37.9 m/s
for an inner jet core diameter of about 6.9 m. Its turbulence intensity has been estimated at 8 % and
its air concentration at impact at 40 %, corresponding to very turbulent air-water jets.
80
140
Core of jet
Outer limits of turbulent air-water shear layer
120
Cen terline of jet
70
Ta ilwater level downstream
100
Rockbed
80
Elevation (m a.s.l.)
60
50
Vi = 27.8 m/s
40
Flip
bucket
60
High-velocity
Jet impact
40
20
0
Pre-excavated
plunge pool
-20
30
-40
-60
20
0
10
20
30
40
50
60
70
80
90
-80
-100
-80
-60
-40
-20
0
20
40
60
80
100
Distance (m)
Plunge pool diffusion at Tucurui Dam
The diffusion of the jet through the pool water depth is presented in Figure 2. Significant spread of
the jet is computed, with an outer jet diameter at impact in the pool of about 20m. The jet core
vanishes before impacting the plunge pool bottom, corresponding to fully developed jet conditions.
120
140
160
180
200
Application of Comprehensive Scour Model
Results of computations
Table 2a.- Scour elevations as a function of time duration of flood following a 100’000 m3/s flood event at
Tucurui Dam (CSM model)
SCOUR ELEVATION COMPUTATIONS
Hours
96
192
720
1500
5760
57600
TIME
Days
Months
4
0.1
8
0.3
30
1.0
62.5
2.1
240
8.0
2400
80.0
Years
0.01
0.02
0.08
0.17
0.67
6.67
BENEF
-40.4
-40.4
-40.4
-40.4
-40.4
-41.3
-42.6
-47.5
CFM
AVER
-53.6
-53.6
-54.3
-54.9
-56.4
-59.2
CONS
-61.6
-62.6
-64.1
-65.0
-67.2
-74.3
CONS
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
-93.9
DI
AVER
AVER
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
-78.9
BENEF
BENEF
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
-63.2
Table 2b.- Scour elevations as a function of time duration of flood following a 50’000 m3/s flood event at
Tucurui Dam (CSM model)
SCOUR ELEVATION COMPUTATIONS
Hours
96
192
720
1500
5760
57600
TIME
Days
Months
4
0.1
8
0.3
30
1.0
62.5
2.1
240
8.0
2400
80.0
Years
0.01
0.02
0.08
0.17
0.67
6.67
BENEF
-40.6
-40.6
-40.6
-40.6
-40.6
-40.6
CFM
AVER
-40.6
-40.6
-40.6
-40.6
-40.6
-40.6
CONS
-40.6
-40.6
-40.6
-40.6
-40.6
-40.6
CONS
-45.1
-45.1
-45.1
-45.1
-45.1
-45.1
DI
AVER
-40.0
-40.0
-40.0
-40.0
-40.0
-40.0
BENEF
-40.0
-40.0
-40.0
-40.0
-40.0
-40.0
Conclusions
1.
2.
3.
4.
Almost no scour formation for 100’000 cms and under beneficial parametric assumptions
Small scour forms under average parametric assumptions and for 100’000 cms (10m of scour formation)
The laboratory model tests are probably somewhat on the conservative side (25m of socur formation)
For a completely broken up rock mass (detached blocks with depth), significant scour would form, however not plausible

Physics based scour model applied to Tucurui Dam (Brazil)

Transcription

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