SPECIALTY WORKSHOP: SITES TRAINING AND INTRODUCTION TO WINDAM ASDSO Dam Safety 2008 PART 2 – SITES...

SPECIALTY WORKSHOP: SPECIALTY WORKSHOP: SITES TRAINING AND SITES TRAINING AND

INTRODUCTION TO WINDAM INTRODUCTION TO WINDAM

ASDSO Dam Safety 2008ASDSO Dam Safety 2008

PART 2 – SITES EARTH SPILLWAYPART 2 – SITES EARTH SPILLWAY EVALUATION EVALUATION

B.B. Earth Spillway Integrity AnalysisEarth Spillway Integrity Analysisiii. Phase 3 (Headcut Advance)iii. Phase 3 (Headcut Advance)

3 PHASE Spillway Erosion Model

1. SURFACE EROSION (Cover Destruction)

3. HEADCUT ADVANCE

2. CONCENTRATED FLOW EROSION

HEADCUT ADVANCE

OBJECTIVES

• Phase 3

– Inputs and equations

– Relation of downcutting to headward advance

– Concept of multiple materials and weakest line of attack

– Concept of unraveling (implications of threshold-rate governing relations)

OBJECTIVES

• Phase 3

– Inputs and equations

– Relation of downcutting to headward advance

– Concept of multiple materials and weakest line of attack

– Concept of unraveling (implications of threshold-rate governing relations)

DOWNCUTTING andHEADCUT ADVANCE

dX/dt

d/dt

Parameters Impacting Phase 3 ErosionParameters Impacting Phase 3 Erosion

Multiple materials may be exposed in a single headcut face.

Downcutting controlled by the material exposed at the base for the time step.

Headcut advance controlled by the materials exposed on the headcut face.

SITESSITESAUXILIARY SPILLWAY EROSION

PHASE 3 INPUT PARAMETERSPHASE 3 INPUT PARAMETERS

DOWNCUTTINGDOWNCUTTING

• PARTICLE DIAMETERPARTICLE DIAMETER• DRY BULK DENSITYDRY BULK DENSITY• PERCENT CLAY orPERCENT CLAY or• kkdd DETACHMENT COEFFICIENT DETACHMENT COEFFICIENT

HEADCUT ADVANCEHEADCUT ADVANCE

• KKhh HEADCUT ERODIBILITY INDEX HEADCUT ERODIBILITY INDEX

SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3

DOWNCUTTINGDOWNCUTTING

eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582

dd//ddt = kt = kdd((ee--cc))

HEADCUT ADVANCEHEADCUT ADVANCE

ddX/X/ddt = C (A - At = C (A - Aoo))

A = (qH)A = (qH)1/31/3

(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)

SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3

DOWNCUTTINGDOWNCUTTING

eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582

dd//ddt = kt = kdd((ee--cc))

HEADCUT ADVANCEHEADCUT ADVANCE

ddX/X/ddt = C (A - At = C (A - Aoo))

A = (qH)A = (qH)1/31/3

(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)

SURFACE DETACHMENTSURFACE DETACHMENT

.

rr = detachment rate = detachment rate

kkd d = coefficient of = coefficient of

detachmentdetachmentee = effective stress = effective stress

cc = critical tractive = critical tractive

stressstress

.

a = exponent (~ 1)a = exponent (~ 1)

rr = k = kdd ( (ee - - cc))aa

Effective Stress, e

c

00

Det

achm

ent R

ate,

r

kd

1

• EFFECTIVE STRESS AT THE HEADCUT BASEEFFECTIVE STRESS AT THE HEADCUT BASE

e= dc 0.011(H/dc)0.582

H

dc

e

PHASE 3PHASE 3Headcut DeepeningHeadcut Deepening

H

CRITICAL STRESS for

Detachment

Critical stress based on loose particle condition for all materials.

DETACHMENT RATE COEFFICIENTDETACHMENT RATE COEFFICIENT

The detachment rate coefficient may be externally determined and entered directly in SITES or estimated by SITES from soil properties.

SITESSITESAUXILIARY SPILLWAY EROSION: PHASE 3

DOWNCUTTINGDOWNCUTTING

eeddcc0.011 (H/d0.011 (H/dcc))0.5820.582

dd//ddt = kt = kdd((ee--cc))

HEADCUT ADVANCEHEADCUT ADVANCE

ddX/X/ddt = C (A - At = C (A - Aoo))

A = (qH)A = (qH)1/31/3

(NEH Part 628 Dams Ch 51 Eq 51-9)(NEH Part 628 Dams Ch 51 Eq 51-9)

HEADCUT MIGRATION

dx/dt = C (A - Adx/dt = C (A - Aoo))dX/dt = rate of headcut

migration,

C = material dependent advance rate coefficient,

A = hydraulic attack, and

Ao = material-dependent threshold.

HYDRAULIC ATTACK

q

H

A = (qH)1/3

MATERIAL-DEPENDENTPARAMETERS

AAOO & C are a function of & C are a function of

KKhh = headcut erodibility = headcut erodibility

indexindex

AAOO = =

189 K189 Khh1/21/2exp(-3.23/ln(101Kexp(-3.23/ln(101Khh))))[[ ]]1/31/3

00 KKhh< 0.01< 0.01

KKhh> 0.01> 0.01__

ANDAND

C =C =

- 0.79 ln(K- 0.79 ln(Khh) + 3.04 K) + 3.04 Khh< 18.2< 18.2

0.75 K0.75 Kh h > 18.2> 18.2__

HEADCUT ERODIBILITYINDEX, Kh

KKhh= M= MSS x K x Kbb x K x Kdd x J x JSS

MMSS= material strength number= material strength number

of the earth material.of the earth material.KKbb= block or particle size.= block or particle size.

KKdd= discontinuity or inter-= discontinuity or inter-

particle bond shearparticle bond shear strength number.strength number.JJss= relative ground structure= relative ground structure

number.number.

Kb

Kd

Condition of the Joints• Rough or smooth• Open or closed• Gap size• material in joints

Js

Block size

Orientationto the flow

Kh = 0.01

DESCRIPTION: SM, very loose sand with little bonding

SITE: Buck and Doe Run 33, Missouri

COMMENT: Eroding material in spillway breach: deep deposit

Kh = 0.17

DESCRIPTION: CL , stiff

SITE: Rush Creek 12R, Oklahoma

COMMENT: Eroding material in headcut face.

Kh = 0.5

DESCRIPTION: Disintegrated shale

SITE: West Fork Point Remove 5, Arkansas

COMMENT: Eroding material in Gully Bank.

Kh = 20

DESCRIPTION: Jointed Sandstone

SITE: West Fork Pint Remove 5, Arkansas

COMMENT: Material remaining below surface erosion some minor detachment by flow.

Kh = 35000

DESCRIPTION: Massive rock (ryolite)

SITE: Painted Rock Dam, Arizona

COMMENT: Spillway outlet, negligible erosion.

OBJECTIVES

• Phase 3

– Inputs and equations

– Relation of downcutting to headward advance

– Concept of multiple materials and weakest line of attack

– Concept of unraveling (implications of threshold-rate governing relations)

SITES erosion material parameters include surface detachment coefficient kd and the headcut erodibility index Kh

kd

Kh = 20

DESCRIPTION: Jointed SandstoneSITE: West Fork Pint Remove 5, ArkansasCOMMENT: Material remaining below surface erosion some minor detachment by flow.

dX/dt

d/dt

H

OBJECTIVES

• Phase 3

– Inputs and equations

– Relation of downcutting to headward advance

– Concept of multiple materials and weakest line of attack

– Concept of unraveling (implications of threshold-rate governing relations)

KKhh for MULTIPLE MATERIALS for MULTIPLE MATERIALS

hi

h2

h3 Kh3

Kh2

Kh1

htotal

Kh = exp { }hi ln( Kh )i

h1

Auxiliary Spillway Profile ReachesAuxiliary Spillway Profile Reaches

1 2 3 4 5 6 7 8

INLET CREST EXIT

Auxiliary Spillway Profile ReachesAuxiliary Spillway Profile Reaches

1 2 3 4 5 6 7 8

INLET CREST EXIT

Reaches from the crest to valley floor are considered in integrity analysis.

SPILLWAY GEOLOGY

STATION

EL

EV

AT

ION

, ft

, ft

All materials in spillway to elevation of valley floor are described along a weakest path.

ERODED PROFILEE

LE

VA

TIO

N

STATION, ft

, ft

The eroded profile plotted in output is a composite of all headcuts considered while evaluating breach potential.

file: a:\claystr.bmp

OBJECTIVES

• Phase 3

– Inputs and equations

– Relation of downcutting to headward advance

– Concept of multiple materials and weakest line of attack

– Concept of unraveling (implications of threshold-rate governing relations)