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Hillslope morphology Ch 8

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Hillslope Types Soil-mantled Soil-mantled –Transport-limited –Shape: smooth, rounded Bare bedrock or thin soils Bare bedrock or thin soils –Weathering-limited –Shape: steep, irregular, jagged = f(weathering mode, relief) lithology, climate structure

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of Hillslope Evolution

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Hillslope Process The transportation of regolith drives hillslope shape The transportation of regolith drives hillslope shape –Regolith: generated by the weathering of bedrock Transportation is a function of Transportation is a function of –Slope –Position on the hillslope (how far from crest) –Boundary condition at the toe Continuous vs Episodic Continuous vs Episodic Climate Climate

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Continuous and Episodic Processes Creep (gravity - continuous) Creep (gravity - continuous) Landslides/Rockfall/Debris Flows (gravity - episodic) Landslides/Rockfall/Debris Flows (gravity - episodic) Solifluction/gelifluction (gravity – continuous) Solifluction/gelifluction (gravity – continuous) Gophers (biological – continuous) Gophers (biological – continuous) Tree throw/downfall (biological - episodic) Tree throw/downfall (biological - episodic)

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Model of hillslope evolution (Kirkby, 1985)

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sequence of change on a fault scarp, Nevada (Wallace, 1977)

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Why are hillslopes convex? Regolith produced between D and A is transported by creep All regolith produced between D and B must be transported past B If this motion is linearly related to slope, the resulting hillslope form is convex and parabolic The amount of regolith that must be passed increases linearly with distance from the crest So slope must increase linearly as well

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The rate of change of regolith mass = rate of regolith inputs – rate of regolith outputs units of mass per unit time Mass of regolith = density x volume = x Rdxdy = INPUTS Weathering rate (production) + Mass flux from the x and y directions - Mass flux out of the x and y directions OUTPUTS Mass flux, Qx Regolith thickness, R Weathering rate, W dot

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Conservation of mass on a hillslope in 1 dimension Regolith thickness as a function of time Weathering rate mass flux downslope (x-direction) What drives the rate of regolith production? What processes are involved in moving regolith downslope?

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If Qx is a function of distance and slope, When diffusion dominates, m = 0, then Diffusion equation for a hillslope Landscape diffusivity constant In words, the rate of change of regolith thickness is a function of the rate of change of slope (curvature) Conservation of mass on a hillslope in 1d

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Diffusion and hillslopes Landscape dominated by diffusive erosion processes have rounded edges Landscape dominated by diffusive erosion processes have rounded edges –Diffusion attacks sharp corners Diffusion combines Diffusion combines –Conservation of mass –How mass flux responds to driving variables

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Diffusion smooths topography In regions of high curvature, regolith will either be thickened or thinned the fastest In regions of high curvature, regolith will either be thickened or thinned the fastest –Creating smooth slopes Only works because we chose a transport rule where mass flux (Qx) was a function of slope only Only works because we chose a transport rule where mass flux (Qx) was a function of slope only –Flowing water is not a diffusive process

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The shape of a parabola If you solve the diffusion eqn, you get If you solve the diffusion eqn, you get Integrating twice results in the eqn for a parabola This hillslope shape must arise if regolith is produced everywhere at the same rate. This is why hillslopes are convex.

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diffusive (slope dependent) transport leads to convex hillslopes advective transport depends on slope and water flow transports sediment creates valleys

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Diffusive Roundup Creep Creep Frost heave Frost heave Solifluction Solifluction Rain splash Rain splash They all round the landscape They all have a linear dependence on local slope

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Hillslope Question 1 On a hillslope with a weathering rate of 20 microns/yr and an effective hillslope diffusivity of 0.02 m 2 /yr, what is the expected curvature of the hillslope? The channels at the edge of the hillslope are 200 m from the hillcrest. On a hillslope with a weathering rate of 20 microns/yr and an effective hillslope diffusivity of 0.02 m 2 /yr, what is the expected curvature of the hillslope? The channels at the edge of the hillslope are 200 m from the hillcrest. –What are we given? –L = 200m. – =0.02 m 2 /yr, –W-dot = 20(10 -6 )m/yr –Density of rock = ~2700 kg/m3 –Bulk density of regolith =~ 2000 kg/m3 –Eqn for curvature What is the hillslope profile if the summit of the hillslope, at x=0, is 1000 m.?

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Non-diffusive Hillslope Processes aka Mass wasting Landslides Landslides –Fast or slow –Wet or dry –Set the location of channel heads –Define the tips of the channel network –Stochastic –A threshold system Elements of a landslide Elements of a landslide –Slope, material properties, degree of saturation, presence/absence of trees/vegetation also flowing water (advective)

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Analysis of slope stability For a single boulder, Resisting force (resists downslope motion) = Wcos Driving force (promotes downslope motion) = Wsin Case 1: Forces acting on a particle resting on a slope surface debris overlying a slide(failure) plane

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Analysis of slope stability What forces are acting on the slab at time of failure? What forces are acting on the slab at time of failure? All forces generated are weight All forces generated are weight –exactly balanced, no accel. slab of regolith over area, A

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For a block of soil, Pressure acting perpendicular to plane = normal stress Pressure acting in the downslope direction = shear stress at failure, internal friction = slope angle Selby, 1993 shear normal

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Shear Strength, S Properties of material that resist gravity forces Properties of material that resist gravity forces Driving force = resisting force Driving force = resisting force –Resisting = Strength + Friction – S = c + σ’(tan ) Coulomb Equation Strength = cohesion + effective normal stress times angle of internal friction Strength = cohesion + effective normal stress times angle of internal friction Cohesion varies with material and condition Cohesion varies with material and condition –Quartzite, clay, wet sand, dry sand… Effective normal stress varies with saturation Effective normal stress varies with saturation –Dry, moist(?), saturated –Normal stress-water pressure varies with material from 90° (quartzite) to ~33° (granular materials) to <10° (clay).

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Factor of Safety FS = Resisting/Driving = Shear Strength/Shear Stress FS = Resisting/Driving = Shear Strength/Shear Stress –If strength exceeds stress (FS>>1), the slope is “stable”. –If strength ≈ stress (FS>1), the slope is metastable. –If stress minutely exceeds strength (FS≤1), the slope is unstable and failure occurs.

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DRY WET

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Slope stability question 1 Consider a long linear hillslope with a slope angle of 25°. It has soil that is 1 m thick, and a shear test on the soil reveals its internal angle of friction is 31°, a cohesion (including roots) of 5000 Pa, and a porosity of 35%. Consider a long linear hillslope with a slope angle of 25°. It has soil that is 1 m thick, and a shear test on the soil reveals its internal angle of friction is 31°, a cohesion (including roots) of 5000 Pa, and a porosity of 35%. Perform a stability analysis on this slope. Is it stable? Perform a stability analysis on this slope. Is it stable? resisting driving 25 o

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