1. EARTH EROSION THEORY SITES WORKSHOP: March 31 – April 2, 2009 Phoenix, AZ

2. EROSION IS ONE OF THE LEAST RELIABLY DEFINED ELEMENTS OF MANY HYDRAULIC PROJECTS. THEREFORE, DESCRIPTION OF EROSION AND PREDICTION OF NONSCOURING VELOCITIES IS ONE OF THE MOST IMPORTANT PROBLEMS OF HYDRAULICS AND RIVER MORPHOLOGY. MIRTSKHOULAVA, TS. E., 1991 MIRTSKHOULAVA, TS. E., 1991

3. Earthen Auxiliary Spillways

4. Earthen Dam Embankments

5. Use fundamental relations of the dominant physical processes in SITES integrity and WINDAMb breach analysis. SITES (spillway breach) SITES (spillway breach) Phases of erosionPhases of erosion Material ParametersMaterial Parameters ErodibilityErodibility Fundamental relation Fundamental relation kd prediction kd prediction Kd measurement (JET) Kd measurement (JET) Headcut Erodibility IndexHeadcut Erodibility Index Fundamental relation Fundamental relation Typical values Typical values WINDAMb (embankment breach) WINDAMb (embankment breach) Stages of erosionStages of erosion Fundamental relationsFundamental relations Impact of CompactionImpact of Compaction

6. Use fundamental relations of the dominant physical processes in SITES integrity and WINDAMb breach analysis. SITES (spillway breach) SITES (spillway breach) Phases of erosionPhases of erosion Material ParametersMaterial Parameters ErodibilityErodibility Fundamental relation Fundamental relation kd prediction kd prediction Kd measurement (JET) Kd measurement (JET) Headcut Erodibility IndexHeadcut Erodibility Index Fundamental relation Fundamental relation Typical values Typical values WINDAMb (embankment breach) WINDAMb (embankment breach) Stages of erosionStages of erosion Fundamental relationsFundamental relations Impact of CompactionImpact of Compaction

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

8. 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. SITES material dependent parameters include surface detachment coefficient k d and the headcut erodibility index K h

9. 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

10. 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

11. Several methods are available for testing of soils. 1.Flume tests 2.Jet erosion tests 3.Rotating cylinder test 4.Soil dispersion test 5.Hole or crack tests 6.Erosion Function Apparatus (Wan and Fell, 2004) (Wan and Fell, 2004)

12. Large flume tests in which the soil material makes up a significant length of the bed are the most reliable erosion tests. (Partheniades, 1968)

13. Erosion Test Results from Literature (Temple and Hanson, 1994)

14. ERODIBILTY

15. Summary of Factors to compute Kd  Dry Density,  d  Percent finer than 2  (% clay)  Number is inversely related to resistance to erosion – low value is high resistance, high value is low resistance  Note units are in ft/hr of downward erosion per unit applied stress of lb/ft 2

16. Estimating erodibility coefficient, k d : Factors cited in the literature that influence soil erodibility: FactorFluid Properties Gradation (%Clay, %Silt, %Sand)Hydraulic Stress Clay TypeWater Chemistry DensityWater Temperature Plasticity Index Pore Chemistry Dispersion/SAR Cementation Slaking Structure Permeability Water Content Temperature. Warning: Using equations to estimate erodibility parameters are crude at best.

17. Several methods are available for testing of soils. 1.Flume tests 2.Jet erosion tests 3.Rotating cylinder test 4.Soil dispersion test 5.Hole or crack tests 6.Erosion Function Apparatus (Wan and Fell, 2004) (Wan and Fell, 2004) JET

18. ESSENTIAL CRITERIA OF AN EROSION TEST BASED ON SOUND HYDRAULIC PRINCIPLES BASED ON KNOWLEDGE OF MATERIALS REPEATABLE AND CONSISTANT APPLICABLE IN CURRENT EQUATIONS APPLICABLE TO FIELD AND LAB TESTING SIMPLE, QUICK, AND INEXPENSIVE

20. oo Where: The stress distribution beneath a submerged Jet was used to develop a method applicable to current equations (Hanson and Cook, 2004). The peak stress is a function of the: 1)diameter of the orifice, 2)distance from the orifice, and 3)pressure on the orifice.

21. J J The rate of scour beneath the submerged jet was formulated similar to the excess stress equation (Hanson and Cook, 2004).

22. A dimensionless time function was used to iteratively determine k d. J J

23. The apparatus was made smaller for greater convenience and has found application in many settings.

24. Jet Erosion Test in NY Spillway

25. Resources   Chapter 51, Part 628, NRCS National Engineering Handbook – Earth Spillway Erosion Model   ASTM D5852, Erodibility Determination of Soil in the Field or in the Laboratory by the Jet Index Method   ASABE Paper No. 02219 Non-vertical JET apparatus for measuring streambank erodibility. Hanson, Cook, and Simon 2002.   ASABE Journal of Applied Engineering in Agriculture. Apparatus, test procedures, and analytical methods to measure soil erodibility in-situ. Hanson and Cook Vol 20(4), 2004.

26. dX/dt d  /dt H

27. 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.

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

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

30. 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 _

31. 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.

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

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

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

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

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

37. 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

38. Typical values for the Kh Factor 0.2 0.01 0.5 10 Hard Rock Soft or Jointed Rock Weathered Rock Soil

39. Weathered Rock Poor Quality Rock 0.2

40. 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

42. file: a:\claystr.bmp

43. Headcut Erodibility Index National Engineering Handbook 210-VI-NEH Chapter 52 Field Procedures Guide for the Headcut Erodibility Index Field Procedures Guide for the Headcut Erodibility Index Appendix 52B - Headcut Erodibility Index Flow ChartAppendix 52B - Headcut Erodibility Index Flow Chart Appendix 52C – Field Data SheetsAppendix 52C – Field Data Sheets

44. Use fundamental relations of the dominant physical processes in SITES integrity and WINDAMb breach analysis. SITES (spillway breach) SITES (spillway breach) Phases of erosionPhases of erosion Material ParametersMaterial Parameters ErodibilityErodibility Fundamental relation Fundamental relation kd prediction kd prediction Kd measurement (JET) Kd measurement (JET) Headcut Erodibility IndexHeadcut Erodibility Index Fundamental relation Fundamental relation Typical values Typical values WINDAMb (embankment breach) WINDAMb (embankment breach) Stages of erosionStages of erosion Fundamental relationsFundamental relations Impact of CompactionImpact of Compaction

45. 1) HEADCUT FORMATION 2) HEADCUT ADVANCE (through crest) 2) HEADCUT ADVANCE (through crest) WINDAM 4 STAGE Breach Erosion Model 3) HEADCUT ADVANCE (into reservoir) 3) HEADCUT ADVANCE (into reservoir) 4) BREACH WIDENING 4) BREACH WIDENING

46. Key Embankment Erosion Processes Surface Detachment Impinging Jet Scour Widening dY/dt dY/dt dW/dt Headcut Migration dX/dt

47. Surface Detachment dY/dt dY/dt = E r = k d (  e –  c ) a E r = Erosion rate,  e = Hydraulic Stress,  ds k d = erodibility coefficient,  c = critical stress a = exponent (often assumed ~1) a = exponent (often assumed ~1) cccc kdkdkdkd d References Hutchinson, 1972 Hutchinson, 1972 Temple, 1984 Temple, 1984 Hanson, 1989 Hanson, 1989 SURFACE DETACHMENT

48. IMPINGING JET SCOUR dY/dt = E r = k d (  e –  c )  e = Hydraulic Stress  =  d c 0.011(H/d c ) 0.582 (NEH Part 628 Dams Ch 51 Eq 51-9) Impinging Jet Scour dY/dt References Robinson, 1992 Robinson, 1992 Stein and Nett, 1997 Stein and Nett, 1997 Hanson et al. 2002 Hanson et al. 2002 dcdcdcdc H

49. dW/dt = 1.4k d (  e –  c )  e =  g(d c 1/3 n) 2 References Visser, 1998 Visser, 1998 Annondale, 2004 Annondale, 2004 Hunt et al., 2005, 2006 Hunt et al., 2005, 2006 Widening dW/dt WIDENING

50. Headcut Migration dX/dt HEADCUT MIGRATION dX/dt = Hk d (  e –  c )/[2E v ] E v = Vertical erosion E v = Vertical erosion required for failure. Requires  T & c u References Robinson & Hanson, 1994 Robinson & Hanson, 1994 Hanson et al., 2001 Hanson et al., 2001

51.  r = k d (  e -  c )  T = W T /V T c u = q u /2

52. IMPACT & ASSESMENT OF COMPACTION

53. Water Content, WC% Dry Density, lb/ft 3 Standard Compaction Curve 95% of Maximum Dry Density Line Maximum Dry Density Optimum Water Content -2%+4% Reference Density Specification Acceptable Zone of Compaction

54. Hammer Soil Mold Laboratory tests. Compact four to five samples at a range of water contents, say 10%, 12%, 14%, 16%, and 18% @ each compaction energy

55. Submergence Tank Sample Point Gage Jet Tube Deflection Plate Lid Laboratory JET Apparatus.

56. Dry of optimum, rapid erosion @ Optimum, slow erosion Wet of optimum, slow erosion

57. Soil Grain Size PIUSCS % Sand % Sand > 75  m % Clay <2  m 2636NPSM 3252617CL Soil 2 Soil 3 Laboratory JET results comparing erodibility of two soil materials prepared at standard compaction effort.

58. Soil Grain Size PIUSCS % Sand % Sand > 75  m % Clay <2  m 2636NPSM 3252617CL Laboratory JET results comparing erodibility of two soil materials prepared at standard compaction effort.

59. A series of compaction curve results for different compaction efforts for a CL soil material.Soil Grain Size a PIUSCS % Sand % Sand > 75  m % Clay <2  m 25 E3515CL

60. Headcut Migration Flume Test Set-up Headcut Migration Data Results Compactive Effort ~ 4000 ft-lb/ft 3 WC% = 9.2% WC% = 14.4% Compactive Effort Low Medium High~ 4000 ft-lb/ft 3

61. Flume Tests High Compaction Approx. dd QHAdv Rtqu  bulk Meas kdComp Eff TestMC%lb/ft^3cfsftft/minlb/ft^2lb/ft^3cm^3/N-sft-lb/ft^3 40.092104.854.143.990.294120811417.6224000 130.1238114.8257.653.960.0809624261290.5384000 60.141111.755.624.110.008218551280.5214000 150.148112.9488.053.240.006323331300.564000 80.1423111.755.164.040.0183417321273.5054000 110.1593111.0756.523.80.00598421290. 9374000

62. Lab Prepared samples and flume samples

63. Headcut Migration dX/dt HEADCUT MIGRATION dX/dt = Hk d (  e –  c )/[2E v ] E v = Vertical erosion E v = Vertical erosion required for failure. Requires  T & c u References Robinson & Hanson, 1994 Robinson & Hanson, 1994 Hanson et al., 2001 Hanson et al., 2001

65. Laboratory Steep Channel Embankment Breach Widening Discharge Model Flume Tests Algorithms Phase 1 Failure Headcut Development Headcut Migration Widening Discharge Data Sets ARS Lab Data Case Studies Additional Data Model Comparisons SIMBA WINDAM a) allowable overtopping b) breach Computer Models NWS Breach, HR Breach, FireFox, & others Erodibility Algorithms Phase 1 Failure Headcut Development Headcut Migration Widening Discharge SIMBA Computer Models Internal Erosion Failure Studies

66. Resources   Transactions of ASABE. Headcut migration analysis of a compacted soil, Hanson, Robinson, and Cook Vol 40(2), 1997.   Transactions of ASABE. Prediction of headcut migration using a deterministic approach, Hanson, Robinson, and Cook. Vol 44(3), 2001.   Transactions of ASABE. Physical modeling of overtopping erosion and breach formation of cohesive embankments, Hanson, Cook, and Hunt. Vol 48(5), 2005.   ASABE Journal of Applied Engineering in Agriculture. Lessons learned using laboratory JET method to measure soil erodibility of compacted soils, Hanson and Hunt, Vol 23(3), 2007.

67. EROSION IS ONE OF THE LEAST RELIABLY DEFINED ELEMENTS OF MANY HYDRAULIC PROJECTS. THEREFORE, DESCRIPTION OF EROSION AND PREDICTION OF NONSCOURING VELOCITIES IS ONE OF THE MOST IMPORTANT PROBLEMS OF HYDRAULICS AND RIVER MORPHOLOGY. MIRTSKHOULAVA, TS. E., 1991 MIRTSKHOULAVA, TS. E., 1991