1. SPECIALTY WORKSHOP: SITES TRAINING AND INTRODUCTION TO WINDAM ASDSO Dam Safety 2008 PART 2 – SITES EARTH SPILLWAY EVALUATION EVALUATION B. Earth Spillway Integrity Analysis iii. Phase 3 (Headcut Advance)

2. 3 PHASE Spillway Erosion Model 1.SURFACE EROSION (Cover Destruction) 3. HEADCUT ADVANCE 2. CONCENTRATED FLOW EROSION

3. HEADCUT ADVANCE

4. 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)

5. 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)

6. DOWNCUTTING and HEADCUT ADVANCE dX/dt d  /dt

7. Parameters 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.

8. SITES AUXILIARY SPILLWAY EROSION PHASE 3 INPUT PARAMETERS DOWNCUTTING PARTICLE DIAMETER PARTICLE DIAMETER DRY BULK DENSITY DRY BULK DENSITY PERCENT CLAY or PERCENT CLAY or k d DETACHMENT COEFFICIENT k d DETACHMENT COEFFICIENT HEADCUT ADVANCE K h HEADCUT ERODIBILITY INDEX K h HEADCUT ERODIBILITY INDEX

9. SITES AUXILIARY SPILLWAY EROSION: PHASE 3 DOWNCUTTING  e  d c 0.011 (H/d c ) 0.582 d  /dt = k d (  e -  c ) HEADCUT ADVANCE dX/dt = C (A - A o ) A = (qH) 1/3 (NEH Part 628 Dams Ch 51 Eq 51-9)

10. SITES AUXILIARY SPILLWAY EROSION: PHASE 3 DOWNCUTTING  e  d c 0.011 (H/d c ) 0.582 d  /dt = k d (  e -  c ) HEADCUT ADVANCE dX/dt = C (A - A o ) A = (qH) 1/3 (NEH Part 628 Dams Ch 51 Eq 51-9)

11. SURFACE DETACHMENT.  r = detachment rate k d = coefficient of detachment detachment  e = effective stress  c = critical tractive stress stress. a = exponent (~ 1)  r = k d (  e -  c ) a Effective Stress,  e cc 0 0 Detachment Rate,  r kdkd 1

12. EFFECTIVE STRESS AT THE HEADCUT BASE EFFECTIVE STRESS AT THE HEADCUT BASE   e =  d c 0.011(H/d c ) 0.582  H dcdc   e PHASE 3 Headcut Deepening H

13. CRITICAL STRESS for Detachment Critical stress based on loose particle condition for all materials.

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

15. SITES AUXILIARY SPILLWAY EROSION: PHASE 3 DOWNCUTTING  e  d c 0.011 (H/d c ) 0.582 d  /dt = k d (  e -  c ) HEADCUT ADVANCE dX/dt = C (A - A o ) A = (qH) 1/3 (NEH Part 628 Dams Ch 51 Eq 51-9)

16. HEADCUT MIGRATION dx/dt = C (A - A o ) dX/dt = rate of headcut migration, C = material dependent advance rate coefficient, A = hydraulic attack, and A o = material-dependent threshold.

17. HYDRAULIC ATTACK q H A = (qH) 1/3

18. MATERIAL-DEPENDENT PARAMETERS A O & C are a function of K h = headcut erodibility index

19. AO =AO =AO =AO = 189 K h 1/2 exp(-3.23/ln(101K h )) [ ] 1/3 0 K h < 0.01 K h > 0.01 _ AND C = - 0.79 ln(K h ) + 3.04 K h < 18.2 0.75 K h > 18.2 _

20. HEADCUT ERODIBILITY INDEX, K h K h = M S x K b x K d x J S M S = material strength number of the earth material. of the earth material. K b = block or particle size. K d = discontinuity or inter- particle bond shear particle bond shear strength number. strength number. J s = relative ground structure number. number.

21. KbKb KdKd Condition of the Joints Rough or smooth Open or closed Gap size material in joints JsJs Block size Orientation to the flow

22. K h = 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

23. K h = 0.17 DESCRIPTION: CL, stiff SITE: Rush Creek 12R, Oklahoma COMMENT: Eroding material in headcut face.

24. K h = 0.5 DESCRIPTION: Disintegrated shale SITE: West Fork Point Remove 5, Arkansas COMMENT: Eroding material in Gully Bank.

25. K h = 20 DESCRIPTION: Jointed Sandstone SITE: West Fork Pint Remove 5, Arkansas COMMENT: Material remaining below surface erosion some minor detachment by flow.

26. K h = 35000 DESCRIPTION: Massive rock (ryolite) SITE: Painted Rock Dam, Arizona COMMENT: Spillway outlet, negligible erosion.

27. 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)

28. SITES erosion material parameters include surface detachment coefficient k d and the headcut erodibility index K h kdkd K h = 20 DESCRIPTION: Jointed Sandstone SITE: West Fork Pint Remove 5, Arkansas COMMENT: Material remaining below surface erosion some minor detachment by flow.

29. dX/dt d  /dt H

30. 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)

31. K h for MULTIPLE MATERIALS hihi h2h2 h3h3 K h3 K h2 K h1 h total K h = exp { } h i ln( K h ) i h1h1

33. Auxiliary Spillway Profile Reaches 1234567 8 INLETCRESTEXIT

34. Auxiliary Spillway Profile Reaches 1234567 8 INLETCRESTEXIT Reaches from the crest to valley floor are considered in integrity analysis.

35. SPILLWAY GEOLOGY STATION ELEVATION, ft All materials in spillway to elevation of valley floor are described along a weakest path.

36. ERODED PROFILE ELEVATION STATION, ft The eroded profile plotted in output is a composite of all headcuts considered while evaluating breach potential.

37. file: a:\claystr.bmp

39. 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)