rock scour: past, present and future - seprem · rock scour: past, present and future george w....
Post on 02-Sep-2018
221 Views
Preview:
TRANSCRIPT
Rock Scour: Rock Scour:
Past, Present and Future Past, Present and Future
George W. Annandale, D.Ing, P.E.George W. Annandale, D.Ing, P.E.
Engineering and Hydrosystems Inc.Engineering and Hydrosystems Inc.
Denver, Colorado Denver, Colorado
OutlineOutline
�� Introduction Introduction
�� Rock Scour ProcessRock Scour Process�� Jet Hydraulics Jet Hydraulics
�� Scour Resistance of Rock Scour Resistance of Rock
�� Methods of Analysis Methods of Analysis �� PastPast
�� PresentPresent
�� Future Future
�� Plunge Pool Design Plunge Pool Design
�� Summary Summary
Bartlett Dam, Arizona
Bartlett Dam, Arizona
30m Scour in Granite
Turbulent JetTurbulent Jet
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Fluctuating Pressures and ResonanceFluctuating Pressures and Resonance
-6
-4
-2
0
2
4
6
1 11 21 31 41 51 61 71 81 91
Time [5 msec/unit]
Pre
ssu
re [
m]
excitation at fissure entry
end of fissure
middle of fissure
Sinusoidal pressure excitation
at entry of fissureFissure
length
= 10 m
Resonance conditions at
middle of fissure
Resonance conditions at end of fissure
Impacting high velocity jet
Sinusoidal pressure excitation
at entry of fissureFissure
length
= 10 m
Resonance conditions at
middle of fissure
Resonance conditions at end of fissure
Impacting high velocity jet
Bollaert 2002
RockRock--Water InteractionWater Interaction
2
3
4
6
5
Aerated jet impact
Macro-turbulent energy dissipation
Interface pressure fluctuations
Pressure propagation-hydrojacking
Uplift of rock entities
Downstream displacement
1
q,Vβ
ht
y dm
p
1
2
3
4
5
6
H
2
3
4
6
5
Aerated jet impact
Macro-turbulent energy dissipation
Interface pressure fluctuations
Pressure propagation-hydrojacking
Uplift of rock entities
Downstream displacement
1
q,Vβ
ht
y dm
p
1
2
3
44
5
6
H
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Bollaert 2002
HydraulicsHydraulics
�� Fluctuating Pressures Fluctuating Pressures
�� Entrained Air Entrained Air
�� Resonance Resonance
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
f = c / 4L
C = 1000 m/s 100 m/s
approx 25 Hz
Rock Breakup ProcessesRock Breakup Processes
�� Brittle Fracture Brittle Fracture
�� Fatigue Failure Fatigue Failure
�� Removal of Intact Rock BlocksRemoval of Intact Rock Blocks
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Brittle Fracture / FatigueBrittle Fracture / FatigueClose-ended Fissures
impacted by
Pressure Fluctuations
Brittle Fracture
or
Fatigue Failure
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Brittle Fracture and Brittle Fracture and
SubSub--Critical Failure Critical Failure
Stress Intensity KI
Fracture
Toughness KI,insitu
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Removal of Intact RockRemoval of Intact Rock
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
Fluctuating Uplift Force
Friction
Downward Force
Santa Santa LuziaLuzia DamDam
76m Drop 134m76m Drop 134m33/s/s
~7 m
Introduction Introduction Introduction Scour Process Analysis Analysis Analysis Design Design Design SummarySummarySummary
OutlineOutline
�� Introduction Introduction
�� Rock Scour ProcessRock Scour Process�� Jet Hydraulics Jet Hydraulics
�� Scour Resistance of Rock Scour Resistance of Rock
�� Methods of Analysis Methods of Analysis �� PastPast
�� PresentPresent
�� FutureFuture
�� Plunge Pool Design Plunge Pool Design
�� Summary Summary
Analysis TechniquesAnalysis Techniques
Rigorous Mathematical
Modeling
Semi-Empirical Methods
Empirical Methods Increased Understanding
Increased Complexity
Increased Value
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Past: Empirical MethodsPast: Empirical Methods
�� VeroneseVeronese (1937)(1937)
�� YildizYildiz and and UzucekUzucek (1994)(1994)
�� Mason and Mason and ArumuganArumugan
(1985)(1985)
54.0225.0
s 90.1Y qH=
αcos90.1Y 54.0225.0
s qH=
zv
wyx
sdg
hHqKY =
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
NearNear--Prototype TestingPrototype Testing
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Empirical MethodsEmpirical Methods
y = 1.0983x
R2 = 0.5345
y = 0.6856x
R2 = 0.4358
0
0.5
1
1.5
2
0 0.5 1 1.5 2
Experimental Erosion Elevation (m)
Pre
dic
ted
Ero
sio
n E
lev
ati
on
(m
)Yildiz
Mason Prototype
Identity Line
Linear (Mason Prototype)
Linear (Yildiz)
Current: SemiCurrent: Semi--EmpiricalEmpirical
�� Quantify Relative Magnitude of Erosive Quantify Relative Magnitude of Erosive
Capacity of Water Capacity of Water
�� Quantify Relative Magnitude of Ability of Rock Quantify Relative Magnitude of Ability of Rock
to Resist Scour to Resist Scour
�� Scour Threshold Relationship based on Field Scour Threshold Relationship based on Field
Data and NearData and Near--Prototype Validation Prototype Validation
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Essence of Erosion ProcessEssence of Erosion Process
Jacking Dislodgment Displacement
Fluctuating
pressures
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Fluctuating Pressures and ResonanceFluctuating Pressures and Resonance
-6
-4
-2
0
2
4
6
1 11 21 31 41 51 61 71 81 91
Time [5 msec/unit]
Pre
ssu
re [
m]
excitation at fissure entry
end of fissure
middle of fissure
Sinusoidal pressure excitation
at entry of fissureFissure
length
= 10 m
Resonance conditions at
middle of fissure
Resonance conditions at end of fissure
Impacting high velocity jet
Sinusoidal pressure excitation
at entry of fissureFissure
length
= 10 m
Resonance conditions at
middle of fissure
Resonance conditions at end of fissure
Impacting high velocity jet
Erosive Power of WaterErosive Power of Water
160
180
200
220
240
260
280
300
320
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Rate of Energy Dissipation (W/m2)
Std
. D
ev
iati
on
of
Pre
ss
ure
Flu
ctu
ati
on
s (
Pa
)
P = γ . Q . ∆E
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Annandale 1995
Estimation of Stream PowerEstimation of Stream Power
HQ
A
P= ρgQH/A
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Turbulent JetTurbulent Jet
?
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Plunging Jet Footprint?Plunging Jet Footprint?
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Rock ResistanceRock Resistance
�� Principal Elements Principal Elements
�� GeoGeo--mechanical Index mechanical Index
�� Scour Scour ThreholdThrehold
MMss -- Intact Material StrengthIntact Material Strength
�� Water jet likely to scour Water jet likely to scour ““perfect clayperfect clay”” easier than easier than
““perfect rockperfect rock””
�� Intact Material Strength of latter is greaterIntact Material Strength of latter is greater
�� Therefore greater resistanceTherefore greater resistance
Perfect Rock Perfect Clay
Water Jets
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
KKbb -- Block SizeBlock Size
More Difficult to Erode Easier to Erode
Large Blocks
Small Blocks
or particles
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Block Size and ShapeBlock Size and Shape
Elongated slabs of
rock
Equi-sided blocks of
rock
Flow direction
Removal of blocks by flowing water is
easier than removal of elongated
blocks.
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
FrictionFriction
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
FrictionFriction
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
FrictionFriction
+ Effects of Gouge
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
OrientationOrientation
Dip Direction
Dip
Plane of discontinuity
Intersection between plane of
discontinuity and horizontal plane
(also known as the strike)
Dip
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
OrientationOrientation
Flow penetrates underneath
rock and removes it from bed.
Increased difficulty to remove rock by
flowing water.
Rock dipped in direction of flow Rock dipped against direction of flow.
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility of RockErodibility of Rock
FactorsFactors
�� Mass Strength Mass Strength
�� Block Size Block Size
�� InterInter--block Shear Strengthblock Shear Strength
�� Relative Dip and Dip Direction Relative Dip and Dip Direction
Primary
Secondary
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility IndexErodibility Index
K = Ms . Kb . Kd . Js
Mass Strength Number
Block Size Number
Joint Shear Strength
Number
Ground Structure
Number
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility IndexErodibility Index
Erosion ThresholdErosion Threshold
0.10
1.00
10.00
100.00
1000.00
10000.00
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
Erodibility Index
Str
eam
Po
wer
KW
/m2
Scour
No Scour
Scour-CSU
Threshold
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Seismic VelocitySeismic Velocity
Erosion ThresholdErosion Threshold
0.01
0.10
1.00
10.00
100.00
1000.00
10000.00
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
Erodibility Index
Str
ea
m P
ow
er
KW
/m2
Scour
No Scour
Scour-CSU
D9, D10 and
D11
Extremely Hard
Ripping and
Blasting
Very Hard
RippingHard RippingEasy RippingPower Tools
Hand Pick and
Spade
D7 and D8D5 and D6D3 and D5
Seismic Velocities (p-wave)
3,600 - 3,800
ft/sec
3,000 ft/sec
1,200 ft/sec
CASE 590M
Refusal
2,000 ft/sec
3,500 ft/sec
2,500 ft/sec
A
2 3 4 5 6 71
Ex
ca
va
tio
n
Cla
ss
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Gibson Dam Gibson Dam
MontanaMontana
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Gibson DamGibson Dam
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Gibson DamGibson Dam
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Gibson DamGibson Dam
0.1
1
10
100
1000
10000
0.01 0.1 1 10 100 1000 10000 100000
Erodibility Index
Str
eam
Po
wer
KW
/m2
Stream Power at lower
abutment
Stream power at
upper abutment
Fractured rock
where scour was
observed
Concrete
Competent rock
where no scour
was observed
NO EROSION
EROSION
Erosion threshold line
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility IndexErodibility Index
Simulated RockSimulated Rock
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility IndexErodibility Index
Granular MaterialGranular Material
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility IndexErodibility Index
Failure of Simulated RockFailure of Simulated Rock
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Erodibility Index MethodErodibility Index Method
Simulated Rock: VerificationSimulated Rock: VerificationErosion Threshold for a Variety of Earth Materials
0.10
1.00
10.00
100.00
1000.00
10000.00
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
Erodibility Index
Str
ea
m P
ow
er
KW
/m2
Scour-SCS
No Scour-SCS
Scour-CSU
Threshold
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
San San RoqueRoque
PhilippinesPhilippines
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
San San RoqueRoque
PhilippinesPhilippines
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Future: Computer ModelingFuture: Computer Modeling
�� Simulate Fluctuating Pressures Simulate Fluctuating Pressures
�� Air Entrainment Air Entrainment -- Resonance Resonance
�� Rock Failure Rock Failure
�� Brittle Fracture Brittle Fracture
�� Fatigue Failure Fatigue Failure
�� Direct Removal of Rock Blocks Direct Removal of Rock Blocks
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Experimental installation Experimental installation Experimental installation Experimental installation –––– Lausanne, Switzerland Lausanne, Switzerland Lausanne, Switzerland Lausanne, Switzerland
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
Pressure FluctuationsPressure Fluctuations
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Design Design Design SummarySummarySummary
OutlineOutline
�� Introduction Introduction
�� Rock Scour ProcessRock Scour Process�� Jet Hydraulics Jet Hydraulics
�� Scour Resistance of Rock Scour Resistance of Rock
�� Methods of Analysis Methods of Analysis �� PastPast
�� PresentPresent
�� Future Future
�� Plunge Pool Design Plunge Pool Design
�� Summary Summary
Plunge Pool Design Options Plunge Pool Design Options
�� Plunge Pools: Energy Dissipaters Plunge Pools: Energy Dissipaters
�� PrePre--formed formed
�� SelfSelf--formedformed
�� Hardened Hardened
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Plunge Pool Design ApproachPlunge Pool Design Approach
�� Plunge Pool Scour Plunge Pool Scour AssessmentAssessment
�� Jet Modification Jet Modification
�� Plunge Pool PrePlunge Pool Pre--FormingForming
�� Plunge Pool Boundary Plunge Pool Boundary Modification Modification �� Rock Modification Rock Modification
�� Lining Lining
�� Is it a Problem & to What Is it a Problem & to What Extent?Extent?
�� L/Lb > 2L/Lb > 2
�� Scour Analysis; How Deep?Scour Analysis; How Deep?
�� Mass Strength & Block SizeMass Strength & Block Size
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Plunge Pool PrePlunge Pool Pre--FormingForming
Minimum DepthMinimum Depth
( )25
0.113
2requiredY H q
g= ⋅ ⋅
Hq
Yrequired
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Puerta 2004
Plunge Pool PrePlunge Pool Pre--FormingForming
Appropriate Pool DepthAppropriate Pool Depth
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Erodibility IndexErodibility Index
Erosion ThresholdErosion Threshold
0.10
1.00
10.00
100.00
1000.00
10000.00
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04
Erodibility Index
Str
eam
Po
wer
KW
/m2
Scour
No Scour
Scour-CSU
Threshold
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Plunge Pool Scour AssessmentPlunge Pool Scour Assessment
Hydrology & Hydraulics Material Properties: Geology and Geotechnical
Ele
vation
Elevat
ion
El
ev
ation
Scour Depth Calculation
Stream Power
Stream Power
Stream Power
Available Stream
Power
Threshold Required Stream
Power
Plunge Pool WSEOriginal Riverbed
Maximum Scour Elevation
ThresholdRequired Stream
Power
Available Stream Power
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Plunge Pool Boundary ModificationPlunge Pool Boundary Modification
�� Rock Anchors Rock Anchors
�� Lining Lining
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Rock AnchorsRock Anchors
Mass Strength
Block Size
Tensioned
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
LiningLiningMass Strength
Block Size
Tensioned Anchors
Concrete Lining
Jet
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Concrete Lining DesignConcrete Lining Design
�� WeightWeight
�� Brittle Fracture Brittle Fracture
�� Fatigue Fatigue
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
ExampleExample
Introduction Introduction Introduction Scour ProcessScour ProcessScour Process Analysis Analysis Analysis Design SummarySummarySummary
Scour Assessment: ValidationScour Assessment: Validation
Bull Run Dam No. 2: Erodibility Index
540
550
560
570
580
590
600
610
620
0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0
Power per Unit Area (kW/m^2)
Ele
va
tio
n (
ft)
40000 cfs Discharge
30000 cfs Discharge
25100 cfs Discharge
20000 cfs Discharge
Calibration
Max Rock Resistance
Min Rock Resistance
Fault Zone
Flow 3
Flow
4
Flow 5
Sedimentary
Interbed
highly weathered basalt
vesicular basalt
pillow lava
claystone, sandstone, tuff:
cemented and non-cemented
vesicular basalt
altered/weathered basalt
vesicular basalt
General Stratigraphic Column
Approximate Current Stilling
Pool Level (Bottom)
Stilling Pool Elevation = 690' Jet Erosive Power
20000cfs 25100cfs 30000cfs 40000cfs
From "A" to "B" is the Probable
Range of Material Resistance
for Flow 3 After Calibration
BA
Fault Zone Resistance
Scour AssessmentScour Assessment
~ 677'
~ 627'
~ 597'
~ 594'
~ 573'
Flow 1
Flow 2
Flow 3
Flow 4
Flow 5
Sedimentary Interbed
WSE ~ 695'
Stilling Pool Level 1964
Approximate Current
Stilling Pool Level
Approximate
Jet Centerline
Jet Spread (~14°)
Probable Scour from
40,000 cfs Event
40'
40'
NW SEGeneral Cross Section Showing Scour Potential:
Bull Run Dam No. 2*
*General profile (i.e. ground surface, flow locations, etc.) taken from Shannon & Wilson, Inc. report (July 1978)
Cross Section C - C`.
Probable Scour from 30,000cfs
Event (Line "A")
No Significant Scour for 30,000cfs Event
(If Material Resistance is Closer to Line "B"
Conduits 3 & 5
~613'
Scour Assessment: Scour Assessment: BackrollerBackroller
~5' of Scour Observed Along
Fault Zone Beneath Spillway
Associated with 1964 Event
d
d = Diameter of Backroller;
As the Amount of Scour
Increases, so does the Diameter
Protective Concrete Slab Beneath Spillway
Backroller
Flow Length = p *d
Scour Assessment: Scour Assessment: BackrollerBackroller
Protective Concrete Slab Beneath Spillway
22'
5'7'
Existing Scour Hole
(25,100 cfs - 1964)
Probable Scour from
30,000 cfs Event
Probable Scour from
40,000 cfs Event
Mitigation DesignMitigation Design
d = Depth of Pool =
Diameter of Eddy
d
Approximate
Jet Centerline
Jet Spread (~14°)Flow Length of the
Macroturbulent Eddy = p *d
Jet Thickness
Optional Protection MeasuresOptional Protection MeasuresPrePre--Forming + Maintain Plunge Pool ElevationForming + Maintain Plunge Pool Elevation
Flow 5 ~ 572 ft
Excavation
Concrete Wall with Rock Bolts
WSE = 690 ft
Optional Protection MeasuresOptional Protection MeasuresLining + Increase Plunge Pool ElevationLining + Increase Plunge Pool Elevation
WSE = 695 ft
Concrete Slab with Rock Bolts
Optional ProtectionOptional ProtectionLining + Riprap + Increase Plunge Pool ElevationLining + Riprap + Increase Plunge Pool Elevation
WSE = 695 ft
Concrete Slab with Rock Bolts Covering Jet
Impingement Zone and Fault Zone
Riprap with D50 ~ 3.5 ft
OutlineOutline
�� Introduction Introduction
�� Rock Scour ProcessRock Scour Process�� Jet Hydraulics Jet Hydraulics
�� Scour Resistance of Rock Scour Resistance of Rock
�� Methods of Analysis Methods of Analysis �� PastPast
�� PresentPresent
�� Future Future
�� Plunge Pool Design Plunge Pool Design
�� Summary Summary
SummarySummary
�� Reviewed Rock Scour Analysis MethodsReviewed Rock Scour Analysis Methods
�� Past: Empirical Past: Empirical
�� Present: SemiPresent: Semi--Empirical Empirical �� Quantify Rock and Erosive CapacityQuantify Rock and Erosive Capacity
�� Scour Threshold for RockScour Threshold for Rock
�� Erodibility Index MethodErodibility Index Method
�� Field and NearField and Near--Prototype Validation Prototype Validation
�� Future: Computer Simulation Future: Computer Simulation �� Rock: Brittle Fracture, Fatigue and Block RemovalRock: Brittle Fracture, Fatigue and Block Removal
�� Hydraulics: Air, Pressure Fluctuations and ResonanceHydraulics: Air, Pressure Fluctuations and Resonance
Summary Summary
�� Plunge Pool DesignPlunge Pool Design
�� Self Formed Self Formed
�� PrePre--FormedFormed
�� Hardened Hardened
�� Example Example
top related