12.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 IX. Mass Wasting Processes 1.Debris Flows Flow types: Debris flow, lahar (volcanic), mud flow (few gravel, no boulders) Flowing mixture of water, clay, silt, sand, gravel, boulder, etc. Flowing is liquefied with about 15% of water by weight. Rheology: function of grain size distribution. Mud flow !non-newtonian fluid Wet grain flow !friction and collisions with pore pressure Most Debris flows: debated if more like fluid mud or more like wet grain flow. Mud flows: - (zuy!!+=µ""( )yzu!!µ"=## 1Visco plastic simplification) Simplification: = constant (f(grain size, H2O%)) = constant (f(grain size, H2O%)) !yµ112.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 MOVIE SHOW (made by USGS in 1984) on Debris Flow Processes 1. Landslides Types of Landslide: Rock avalanches (Blackhawk slide is an example) Rock fall (toppling of blocks) Shallow soil landslides (tabular) Deep bedrock landslides (tabular) Earth flows (slow oozing !reactivations over long time) Rotational slumps Infinite Slope Stability Analysis (initiation of failure) • Assumptions 1. 2-D planar failure at impermeable interface (no side-wall or end effects) 2. Mohr-Coulomb failure criterion 3. Slope-parallel groundwater seepage F !factor of safety F = 1, at failure (or critical) F > 1, stable F < 1, unstable 212.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 where F =strength (resisting force)driving force=st!bwet=c + ("wet# p) tan$%bwetghS!!is the internal friction angle. Infinite slope approximation no end effects, assume parallel seepage (uniform level of saturation) where is internal friction angle. st= c +!tan"i!iMore generally, many factors (including root networks, capillary tension, weathering) influence the effective cohesion; also pore pressures reduce normal stress: st= c'+ (!" p) tan#c 'Fs=stdriving stress! 1!b="bghsin#!b; where is total effective cohesion. at failure (by definition) where is wet soil bulk density. {As derived earlier for unaccelerated fluids and a rigid block on an inclined plane}. Wet bulk density: !b= vs!s+ m(1" vs)!w, where vsis volume fraction solids and m is fraction of soil depth saturated. {normal stress component due to wet weight of soil} !="bgh cos#SKETCH 312.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 Thus write factor of safety equation: Fs=c'+ (!" p) tan#$b=c'+ (%bgh cos&" p) tan#%bghsin&Pore pressure for parallel seepage (part of the “infinite slope approximation”) p =!wgmh cos"Substitute into factor of safety equation: Fs=c'+ (!b" m!w)gh cos#tan$!bghsin#Fs! 1failure 412.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 Implications for Cohesionless soil c ' = 0if cohesionless Fs=(!b" m!w)tan#!btan$Fstan!max=("b# m"w)tan$"b=1 at maximum stable slope, set this and solve for maximum stable slope: If dry, cohesionless, m = 0 and thus: tan!max= tan", !max="Angle of Repose = angle of internal friction! Seepage Forces The above derivation was done in terms of pore pressures. An alternative formulation instead considers stresses due to the action of seepage forces (fluid drag on sediment particles). These are both equivalent – just different ways to cast the problem mathematically. The use of pore pressures was introduced to simplify the mathematics. However, for some problems, recasting in terms of seepage forces yields improved intuition. We Follow the work of Iverson and Major (1986), WRR Seepage Forces can act in both x-and z-directions and thus contribute to both normal and shear stresses. Generally: Normal stress: Driving stress: ( ) ( )zceseepageforghmwb+!"##cos512.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 where ( ) ( )xceseepageforghmwb+!"##sinwbm!!"is buoyant weight of wet soil. (Note we treat only buoyancy, not pore pressures) In the case of parallel seepage, seepage force in (z) = 0; so normal stress is simply the normal component of the buoyant weight (intuitively satisfying) -fseepage=qK!wgIn the x direction: where q is water flux per unit volume, so this is seepage force per unit volume. Darcy’s law: q = K sin!, where K is hydraulic conductivity. {per unit volume} Thus, stress due to seepage force in (x) is = !"singmhw(ie. this is a force per unit area of fseepage=!wgsin"soil, where mh is the height of soil column over which the seepage force acts). If you look at the expression for the shear (driving) stress: ( ) ( )xceseepageforghmwb+!"##sinyou see that the effect of the seepage force is to cancel out the effect of buoyancy – this is why the driving stress is the shear stress due to the full wet weight of the soil. Substituting the seepage force term into the factor of safety equation yields: ( )!"#!""sintancosghghmcFbwbs$+%=The same relation – only a more intuitive, and more general, derivation. Sub-aqueous Slope Stability Consider a talus cone on the sea floor. Cohesionless material, fully saturated (m = 1). Is the angle of repose less than, greater than or equal to the angle of internal friction and why? Recall for dry, cohesionless soil: tan!max= tan"!max=", 612.163/12.463 Surface Processes and Landscape Evolution K. Whipple September, 2004 If you try to address this problem in terms of pore pressures it can be confusing, and most students will guess the angle of repose is reduced due to the lubricating effects of water. However, if you consider the problem in terms of seepage forces, you will realize that there are no seepage forces involved because the water is not moving. Thus from above you can see that both normal forces and shear forces are due simply to the buoyant tan!max= tan"!max="weight of the material, and for cohesionless soil , -- exactly the same underwater, on dry land, on Mars, on the Moon, etc. Non-parallel Seepage Iverson and Major (1986), WRR, exploited the generalized treatment in terms of seepage forces to address the effects of non-parallel seepage on slope stability of cohesionless material under fully saturated conditions (m = 1). This problem is rather nasty in terms of pore pressures, but, as they demonstrated can be rather elegantly treated in terms of seepage forces. They write: ( )[ ]( )[ ]!"##!"##$coscos1sinsin1taniiwtwt%%+%=Where gbt!"=gww!"=b!, , is wet bulk density, i is the magnitude of the seepage force vector and λis its orientation. For