IX. Mass Wasting Processes

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1 IX. Mass Wasting Processes 1. Deris Flows Flow types: Deris flow, lahar (volcanic), mud flow (few gravel, no oulders) Flowing mixture of water, clay, silt, sand, gravel, oulder, etc. Flowing is liquefied with aout 15% of water y weight. Rheology: function of grain size distriution. Mud flow non-newtonian fluid Wet grain flow friction and collisions with pore pressure Most Deris flows: deated if more like fluid mud or more like wet grain flow. Mud flows: Visco- plastic ( simplification) u " " y + µ z # u 1 ( " y ) # z µ Simplification: y constant (f(grain size, H 2 O%)) µ constant (f(grain size, H 2 O%)) 1

edrock landslides (taular) Earth flows (slow oozing reactivations over long time) Rotational slumps Infinite Slope Staility Analysis (initiation of

2 MOVIE SHOW (made y USGS in 1984) on Deris Flow Processes 1. Landslides Types of Landslide: Rock avalanches (Blackhawk slide is an example) Rock fall (toppling of locks) Shallow soil landslides (taular) Deep edrock landslides (taular) Earth flows (slow oozing reactivations over long time) Rotational slumps Infinite Slope Staility Analysis (initiation of failure) Assumptions 1. 2-D planar failure at impermeale interface (no side-wall or end effects) 2. Mohr-Coulom failure criterion 3. Slope-parallel groundwater seepage F factor of safety F 1, at failure (or critical) F > 1, stale F < 1, unstale 2

3 F strength (resisting force) driving force where is the internal friction angle. s t c + (" # p)tan$ wet wet % wet ghs Infinite slope approximation level of saturation) no end effects, assume parallel seepage (uniform s t c + tan" i where i is internal friction angle. More generally, many factors (including root networks, capillary tension, weathering) influence the effective cohesion; also pore pressures reduce normal stress: s t c'+ ( " p)tan# ; where c' is total effective cohesion. s F s t driving stress 1 at failure (y definition) " ghsin# where is wet soil ulk density. {As derived earlier for unaccelerated fluids and a rigid lock on an inclined plane}. Wet ulk density: v s s + m(1" v s ) w, where v s is volume fraction solids and m is fraction of soil depth saturated. " ghcos# {normal stress component due to wet weight of soil} SKETCH 3

4 Thus write factor of safety equation: F s c'+ ( " p)tan# c'+ (% ghcos& " p)tan# $ % ghsin& Pore pressure for parallel seepage (part of the infinite slope approximation ) p w gmhcos" Sustitute into factor of safety equation: F s c'+ ( " m w )gh cos# tan$ ghsin# F s 1 failure 4

5 Implications for Cohesionless soil c' 0 if cohesionless F s ( " m w )tan# tan$ F s 1 at maximum stale slope, set this and solve for maximum stale slope: tan max (" # m" w )tan$ " If dry, cohesionless, m 0 and thus: Seepage Forces tan max tan", max " Angle of Repose angle of internal friction The aove 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 oth equivalent just different ways to cast the prolem mathematically. The use of pore pressures was introduced to simplify the mathematics. However, for some prolems, recasting in terms of seepage forces yields improved intuition. We Follow the work of Iverson and Major (1986), WRR Seepage Forces can act in oth x- and z-directions and thus contriute to oth normal and shear stresses. Generally: Normal stress: (# # ) gh cos" seepageforce( z) m w + Driving stress: 5

6 (# # ) gh sin" seepageforce( x) m w + where " m w is uoyant weight of wet soil. (Note we treat only uoyancy, not pore pressures) In the case of parallel seepage, seepage force in (z) 0; so normal stress is simply the normal component of the uoyant weight (intuitively satisfying) In the x-direction: f seepage q K wg 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. f seepage w gsin" {per unit volume} Thus, stress due to seepage force in (x) is " gmh sin (ie. this is a force per unit area of 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: (# # ) gh sin" seepageforce( x) m w + you see that the effect of the seepage force is to cancel out the effect of uoyancy this is why the driving stress is the shear stress due to the full wet weight of the soil. w Sustituting the seepage force term into the factor of safety equation yields: F s c% + (" $ m" ) " gh sin w gh cos tan# The same relation only a more intuitive, and more general, derivation. Su-aqueous Slope Staility 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 " 6

7 If you try to address this prolem in terms of pore pressures it can e confusing, and most students will guess the angle of repose is reduced due to the luricating effects of water. However, if you consider the prolem in terms of seepage forces, you will realize that there are no seepage forces involved ecause the water is not moving. Thus from aove you can see that oth normal forces and shear forces are due simply to the uoyant weight of the material, and for cohesionless soil tan max tan", max " -- 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 staility of cohesionless material under fully saturated conditions (m 1). This prolem is rather nasty in terms of pore pressures, ut, as they demonstrated can e rather elegantly treated in terms of seepage forces. They write: tan$ [( # t # w )% 1] sin" + i sin [( # # )% 1] cos" % i cos t w Where " t g, " w w g, is wet ulk density, i is the magnitude of the seepage force vector and λ is its orientation. For parallel seepage λ 90º and i sin. SKETCH This readily confirms that the solution for parallel seepage is correct (same as we had aove for case m 1 and c 0). From analysis of their equation aove, Iverson and Major (1986) can discover generally what seepage directions are most destailizing to the slope. What is your intuitive ranking: vertical down, horizontal out, normal down, parallel seepage directions and why? Normal down: increases staility. No effect on shear stress, counteracts normal uoyancy. Vertical down: no net effect. Slightly increases normal stress, and equally increases shear stress. Parallel: decreases staility. No effect on normal stresses, ut counteracts uoyancy in shear stress. 7

8 Horizontal: most destailizing. Decreases normal stress and increases shear stress. Condition expected at ase of slopes this is one of the main deviations in nature from conditions assumed in the Infinite Slope Staility Analysis considered aove. Flow Convergence and Soil Saturation Levels Iida (1984), Japanese Geomorphological Union considered the other major deviation in nature from conditions assumed in the Infinite Slope Staility Analysis: Flow convergence dictated y surface topography. FIGURE: Iida, 1984 definition sketch: prolem formulation Assume unsaturated flow/storage is negligile; write relation conservation of mass (water) ( t) Ia( t) ( t) Vdarcy hsat ( t) Vdarcy" z( t) cos z ( t) cos q( t) q q " V darcy 8

9 q(t) is discharge/unit width, I rainfall intensity, a(t) contriuting area, Δz(t) saturation level, and V darcy is the Darcian velocity For a straight slope (no convergence), constant slope (α) Vdarcy a( t) Vxt ; V x cos " V darcy K sin p V x is horizontal component of interstitial velocity (porosity correction relates Darcy velocity to true interstitial fluid velocity, cosine term gives the horizontal component of fluid velocity), λ p porosity, and K hydraulic conductivity Why is V darcy K sin? Darcy s Law # V darcy " K l Parallel Seepage: {Darcy s Law} " x " z ; " l cos #" # z cos cos tan sin # l # x 9

10 V darcy K sin V x K sin" cos" p Comine aove relations into conservation of mass: q t Ia t ; z ( t) cos" q( t) to write: q ( ) ( ) IK sin" cos" ( t) t " z ( t) It p p V darcy Steady-state solution (Δz max ; t T c ) T L V c x L" p K sin cos max ( T ) " z " z c IL K sin cos For convergent (ε > 0) topography Recall that arc length Lε; Δa average arc length x ΔL 10

11 q 1 a [" L + "( L + L) ] L 2 L ; L Vxt &( V xt + )' + # a( t) $ ' Vxt $ 2 % " IK sin ) cos) &' V t ( $ p % 2 # " x ( t) + t ' z It ( V t ) $ p % 2 & x # ( t) + " Comparison to the solutions for non-convergent topography (planar hillside), we see that the depth of saturation is enhanced y a factor of 1 & ' Vxt # $ +, due to the effects of convergence. % 2 " Steady-state solution (Δz max ; t T c ) Recall L T V c x L" p K sin cos ' z max ' z IT ( L * $ % 2 IL ( L K sin) cos) $ % 2 c & # & # ( T ) + + " c p " At steady state, the saturation enhancement factor can e written entirely in terms of morphologic variales: 11

12 1 & ' L # $ + % 2 " Note, if storm is rief (T s < T c ), peak Δz occurs after the storm ends, ut is of lesser magnitude than Δz max FIGURE: Iida, 1984: Δz(t) vs. ε Limitations of infinite slope staility analysis - Neglects 3-D effects - Neglects stress-field rotations (Anderson and Sitar, 1995) - Neglects flow through shallow edrock fractures - Seismic loading affects oth driving stress and pore pressures 12

Landslides & Debris Flows

T.#Perron# #12.001# #Landslides#&#Debris#Flows# 1# Landslides & Debris Flows Many geologic processes, including those shaping the land surface, are slowacting, involving feedbacks that operate over many