1. Last Lecture Chemical weathering: main driver is acidic water When common rock forming minerals are weathered the typical reaction results in some loss of cations and the production of clays Because silicate mineral weathering consumes CO 2, weathering can influence global climate

2. Sediment transport on hillslopes Hillslope hydrology Slope stability Today’s lecture

3. What might the rate of these processes depend on? Physical Weathering

4. Two prevailing theories: Physical Weathering

5. alpha Quantifying Physical Weathering Rates Cosmogenic Radionuclides: neutron CRNs produced in rock and soil We know how fast Can give age / erosion rate

6. Heimsath et al., 1999 Coastal California Heimsath et al. 2000 SE Australia Does soil production vary with soil depth?

7. Heimsath et al. 2001 Oregon Coast Range Wilkinson et al. 2005 Blue Mountains, Australia Does soil production vary with soil depth? YES! Evidence for both peaked and exponential soil production functions depending on where you are

8. Stability vs Instability

9. p = Production rate W = Production rate when there is no soil  = A length that tells you how much the production rate decreases with increasing soil thickness h = Soil thickness PlaceW in mm/yr  in m Reference Australia (1)0.1430.238 Heimsath et al., Quat. Int., 2001 California0.0770.435 Heimsath et al. Geomorph. 1999 Oregon0.2680.333 Heimsath et al. ESPL 2001 Australia (2)0.0530.5 Heimsath et al., Geology 2000 This is what the soil production function looks like

13. Natural erosion rates can on sloping lands range from 1 metre per million years to several mm per year (1 mm/yr = 1km/million years) Disturbance (e.g., humans) can raise rates by 100 times or more! Soil can be stripped in decades Human Disturbance

14. If you strip the soil, how long does it take to recover? Mass balance: The rate of change of soil thickness is equal to the rate of soil production minus the rate of erosion: Human Disturbance

15. Take a very simple situation. You strip away all the soil, and then you manage to reduce the erosion rate to zero: Time it takes soil to recover 0

16. Take a very simple situation. You strip away all the soil, and then you manage to reduce the erosion rate to zero: And remember, soil production is a function of depth: Time it takes soil to recover 0

17. So putting these two together you get: It turns out you can solve this equation, to find out how long it takes for the soil to reach some thickness h: Time it takes soil to recover

18. H = 0.2m h = 0.5m 1230 yrs4296 yrs 1530 yrs7990 yrs 2460 yrs8590 yrs 3060 yrs16000 yrs So soil conservation is important because once it is gone, it is gone for a very long time! How long does it take?

19. Late Holocene (last 4ka) uplift/subsidence rates (mm/yr) Late Holocene surface change Shennan and Horton (2001), J. Quat Sci., 17, 511-526.

20. Late Holocene surface change Fastest rate of soil production measured ->0.1-0.2 mm/yr) We shouldn’t expect the same background erosion rates all over the UK

21. So Fastest rate of soil production measured - >0.1-0.2 mm/yr) We shouldn’t expect the same background erosion rates all over the UK

23. Soil mantled landscapeBedrock landscape Relative balance between erosion and production of soil http://static.panoramio.com/photos/original/147837.jpg Transport limited Weathering limited Weathering can make sediment available for transport: then what?

24. Mobile Soil Bedrock/Saprolite Soil Production Erosion Soil Mantled Landscape: Soil Production > Erosion

25. It rains. What happens?

26. Infiltration rates Also: – Tropical rainforest in Australia: 1350 mm/hr – Oregon Coast Range 5400 mm/hr

27. Rain rate < infiltration capacity

28. All rain goes into soil

29. Shallow subsurface storm flow

30. Saturation overland flow

31. Rain rate > infiltration capacity: overland flow

32. SOF (and piping)

33. Partial area and distributed hydrologic models Lyon et al. Hyd. Proc. 2004

34. Montgomery et al, WRR, 1997 Coos bay, Oregon

35. Patterns of saturation Montgomery et al, WRR, 1997

36. Saturation in Vermont

37. Convergent and Divergent areas

38. What happens during a storm? Example storm hydrograph

39. Understanding saturation on hillslopes Important for hydrology Also for slope stability Why are these the bits that are saturated? Water collects, but soil is thicker. Can we make predictions????

40. Predicting saturation If you cant get this right, you’ve got no chance of predicting basin response to storms because of this

41. Predicting saturation Also you won’t be able to predict this

42. Predicting saturation or this (as we’ll see later in this lecture)

43. Darcy’s law Rate of water coming from tube proportional to change in height/distance

44. Darcy’s law q = K(  h/L) K is just a constant of proportionality q is the ‘Darcy velocity’

45. Darcy Assume that water in soil flows parallel to the soil surface

46. The components of the Darcy equation

47. trigonometry q = K(  h/L)

48. trigonometry q = K(  h/L)  h/L=?

49. Water flux q = K(  h/L)  h/L=sin(  ) So q = K sin(  )

50. Darcy’s law Assume that water in soil flows parallel to the soil surface

51. Slope correction But we want to know flow of water horizontally Why? It is just more convenient.

52. trigonometry

53. Water flux, corrected

54. Some simple box models: It rains Imagine this as a box

55. Some simple box models: It rains Imagine this as a box

56. Some simple box models: It rains Imagine this as a box Water comes in Water goes out

57. Some simple box models: It rains Imagine this as a box Coming in: Rain Going out: Overland flow Evaporation Groundwater flow Deep flow Nothing coming in From the right because It is a drainage divide

58. Going in, coming out Coming in: p*L Where p is precipitation rate and L is length of box Going out: r*L Where r is the return flow rate

59. Going in, coming out Going out et*L Where et is evapotranspiration rate q SSF *d SSF Where q is the Darcy velocity and d is the depth of shallow subsurface flow

60. What about in 3D?

61. 3D You define where you want water to flow out Follow lines of steepest descent upslope

62. 3D This gives you a contributing area, A

63. What about what goes out? Volume going out is: q SSF *d SSF *b q SSF

64. Okay, lets do things in volumes per time Coming in: p*A Where p is precipitation rate and L is length of box Going out: r*A Where r is the return flow rate

65. Okay, lets do things in volumes per time Going out et*A Where et is evapotranspiration rate q SSF *b*d SSF Where q is the Darcy velocity and d is the depth of shallow subsurface flow

66. If there is no change in the amount of water in the box, what goes in must come out p*A=et*A+r*A+ q SSF *b*d SSF This is a bit ugly. Lets name something the water supply, call it ‘w’, and let it be equal to the precipitation minus the evapotranspiration and return flow: w = p-et-r

67. If there is no change in the amount of water in the box, what goes in must come out w*A = q SSF *b*d SSF Okay, all this equation says is that the water supplied to the hillslope must equal the water leaving the hillslope from Horton overland flow and shallow subsurface flow

68. w*A = q SSF *b*d SSF But wait! We know q SSF = K*sin(  )*cos(  ) If there is no change in the amount of water in the box, what goes in must come out q = K(  h/L)  h/L=sin(  ) So q = K sin(  )

69. Implications Can solve for the depth of water at a given supply rate in the soil

70. Implications How much water can a hillslope transport before overland flow occurs? Max water supply rate is:

71. How much water can a hillslope transport before overland flow occurs? Increase KIncrease w Increase d soil Increase w Increase  Increase w (up to a point) Increase ADecrease w w max = K*sin(  )*cos(  )*b*d Soil /A

72. Some numbers A/b (in metres) – divergent slope ~1-10 – Planar slope ~10-200 – Convergent slope ~100-100,000 Soil thickness: 0-3m K in cm/hr – Silt: 0.01 – Sand: 40

73. Result: prediction of saturation during a rainstorm

74. So why did we go to all that trouble?

75. Creep vs. Overland flow Zone where creep dominates (Convex) Zone where overland flow dominates (Concave) Exfiltration and overland flow Creep processes lead to hillslopes with different curvature than overland flow.

76. Landslides and Debris Flows

77. Why do landslides occur?

78. Resolution of forces acting on a slope W N t S a W: weight of material N: normal force acting perpendicular to slope t: shear force acting parallel to slope S: shear strength (resistance to shear) a: slope angle Friction/shear strength depends on the normal force! Pore water reduces both normal force and frictional resistance to sliding Landslides

79. Force balance Start by looking at W

80. Forces W = g*  s *L*d s

81. Driving and resisting forces Shear tries to get the block to slide downhill This is resisted by friction

82. Stresses: Force divided by area

84. Resisting stress Friction resists sliding The friction is a function of the effective normal stress R =  eff *tan(  ) tan(  ) is the friction slope

85. Resisting stress Effective normal stress: buoyant weight of the soil mass – W buoyant = W soil –W water  eff = cos(  )*(W soil -W water )

86. So, balance the forces: At the limit of stability, friction and cohesion just balance shear stress:  = C r +  eff *tan(  ) There is something called the ‘factor of safety’. It is the ratio between resisting forces and forces compelling the soil to move downslope: FS = (C r +  eff *tan(  ))/ 

87. So, balance the forces: FS = (C r +  eff *tan(  ))/  or The depth of water in soil at the failure point is equal to:

88. Rainfall rate for failure Can solve for the depth of water at a given supply rate in the soil

89. Rainfall rate for failure This is the supply rate at failure Now you can get a good idea of how much rain you need to get one of these:

90. But wait… Supply rate that fills soil: Must be larger than the supply rate to cause failure

91. A few typical values Typical root cohesion: 500-15000N/m 2 Typical tan(  ): 0.8  w = 1000 kg/m 3  s = 1500-1900 kg/m 3 K in cm/hr – Silt: 0.01 – Sand: 40

92. Can the hillslope fail at all? If the slope is still stabile once it fills with water, it won’t fail at all. This is the equation for the factor of safety if the soil is saturated (that is d w = d s )

93. So this can be applied all over the landscape

94. There is tension between the amount of water available and the steepness of the hillslope

95. Conclusions 4 runoff mechanisms Slope stability: depends on gradient, amount of water, cohesion, and soil thickness You should familiarize yourself with the stability equations (we use them in practicals ! Reading: Get it here: http://eps.berkeley.edu/development/view_person.php?uid=1164&page=81 http://eps.berkeley.edu/development/view_person.php?uid=1164&page=81