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EARTH EROSION THEORY

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

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EARTH EROSION THEORY

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  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

  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) • Phases of erosion • Material Parameters • Erodibility • Fundamental relation • kd prediction • Kd measurement (JET) • Headcut Erodibility Index • Fundamental relation • Typical values • WINDAMb (embankment breach) • Stages of erosion • Fundamental relations • Impact of Compaction

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

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

  8. kd SITES material dependent parameters include surface detachment coefficient kd and the headcut erodibility index Kh Kh = 20 DESCRIPTION: Jointed Sandstone SITE: West Fork Pint Remove 5, Arkansas COMMENT: Material remaining below surface erosion some minor detachment by flow.

  9. kd 1 Detachment Rate, er tc 0 0 Effective Stress, te SURFACE DETACHMENT . r = kd (e - c)a . r = detachment rate kd = coefficient of detachment e = effective stress c = critical tractive stress a = exponent (~ 1)

  10. kd 1 Detachment Rate, er tc 0 0 Effective Stress, te SURFACE DETACHMENT . r = kd(e - c)a . r = detachment rate kd = coefficient of detachment e = effective stress c = critical tractive stress a = exponent (~ 1)

  11. Several methods are available for testing of soils. • Flume tests • Jet erosion tests • Rotating cylinder test • Soil dispersion test • Hole or crack tests • Erosion Function Apparatus • (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, gd • Percent finer than 2m (% 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/ft2

  16. Estimating erodibility coefficient, kd: Factors cited in the literature that influence soil erodibility: Factor Fluid Properties Gradation (%Clay, %Silt, %Sand) Hydraulic Stress Clay Type Water Chemistry Density Water 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. • Flume tests • Jet erosion tests • Rotating cylinder test • Soil dispersion test • Hole or crack tests • Erosion Function Apparatus • (Wan and Fell, 2004) JET

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

  19. 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: • diameter of the orifice, • distance from the orifice, and • pressure on the orifice. Where: o o

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

  21. A dimensionless time function was used to iteratively determine kd. J J

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

  23. Jet Erosion Test in NY Spillway

  24. 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.

  25. H dX/dt de/dt

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

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

  28. MATERIAL-DEPENDENT PARAMETERS AO & C are a function of Kh = headcut erodibility index

  29. [ _ 189 Kh1/2exp(-3.23/ln(101Kh)) ]1/3 Kh> 0.01 AO = 0 Kh< 0.01 AND - 0.79 ln(Kh) + 3.04 Kh< 18.2 C = 0.75 Kh > 18.2 _

  30. HEADCUT ERODIBILITY INDEX, Kh Kh= MS x Kb x Kd x JS MS= material strength number of the earth material. Kb= block or particle size. Kd= discontinuity or inter- particle bond shear strength number. Js= relative ground structure number.

  31. Condition of the Joints • Rough or smooth • Open or closed • Gap size • material in joints Block size Kb Kd Orientation to the flow Js

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

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

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

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

  36. 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

  37. Typical values for the KhFactor 0.01 Soil 0.2 Weathered Rock 0.5 Soft or Jointed Rock 10 Hard Rock

  38. Soil Weathered Rock Poor Quality Rock 0.2

  39. Kh for MULTIPLE MATERIALS { } hi ln( Kh )i Kh = exp hi h1 Kh1 htotal h2 Kh2 h3 Kh3

  40. file: a:\claystr.bmp

  41. Headcut Erodibility IndexNational Engineering Handbook 210-VI-NEH Chapter 52 • Field Procedures Guide for the Headcut Erodibility Index • Appendix 52B - Headcut Erodibility Index Flow Chart • Appendix 52C – Field Data Sheets

  42. Use fundamental relations of the dominant physical processes in SITES integrity and WINDAMb breach analysis. • SITES (spillway breach) • Phases of erosion • Material Parameters • Erodibility • Fundamental relation • kd prediction • Kd measurement (JET) • Headcut Erodibility Index • Fundamental relation • Typical values • WINDAMb (embankment breach) • Stages of erosion • Fundamental relations • Impact of Compaction

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

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

  45. kd SURFACE DETACHMENT Surface Detachment tc d dY/dt dY/dt = Er = kd(te – tc)a Er = Erosion rate, te = Hydraulic Stress, gds kd= erodibility coefficient, tc = critical stress a = exponent (often assumed ~1) • References • Hutchinson, 1972 • Temple, 1984 • Hanson, 1989

  46. IMPINGING JET SCOUR Impinging Jet Scour dc H dY/dt • References • Robinson, 1992 • Stein and Nett, 1997 • Hanson et al. 2002 dY/dt = Er = kd(te – tc) te = Hydraulic Stress  =  dc0.011(H/dc)0.582 (NEH Part 628 Dams Ch 51 Eq 51-9)

  47. WIDENING Widening dW/dt dW/dt = 1.4kd(te – tc) te = gg(dc1/3n)2 • References • Visser, 1998 • Annondale, 2004 • Hunt et al., 2005, 2006

  48. HEADCUT MIGRATION Headcut Migration dX/dt dX/dt = Hkd(te – tc)/[2Ev] Ev= Vertical erosion required for failure. Requires gT & cu • References • Robinson & Hanson, 1994 • Hanson et al., 2001

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