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