Mass Wasting and Hillslope Processes I Hillslope Physics Physical Properties of Regolith A Basics of Slope Stability 1 Fundamental Terms a Energy ability to do physical work 1 Mechanical Energy a Potential Energy energy of position Ep mgh where Ep potential energy joules m mass kg g acceleration due to gravity 9 8 m sec2 h height of material above reference surface m Units 1 J 1 kg m2 sec2 b Kinetic Energy energy of motion Ek 0 5mV2 where Ek kinetic energy joules m mass kg V velocity m sec Units 1 J 1 kg m2 sec2 b Force push or pull action on a mass of material Newton s Second Law F ma where F force newtons m mass kg a acceleration m sec2 Units 1 N 1 kg m sec2 c Weight pulling force of the Earth under the influence of gravity Wt F mg where Wt weight N F force N m mass kg g acceleration due to gravity 9 8 m sec2 d Stress Force acting per unit surface area stress F A where stress is in N m2 A area m x m m2 39 e Work displacement of mass when acted upon by force e g sliding mass of regolith W Fd where W work J F force N 1 kg m sec2 d distance of mass displacement m Units 1 J 1 N m 1 kg m2 sec2 2 Forces acting on Slope Material Particle on Slope Equations Wt shear force parallel to slope N normal force perpendicular to slope N slope angle relative to horizontal plane degrees weight of particle or mass of material N Wt mg weight of particle N Wt cos normal force N Wt sin shear force N 40 Mass on Slope Equations Note here we assume that a mass of regolith overlies a potential failure plane The failure plane is a surface in 3 d with area Thus forces are applied per unit area resulting in stresses h shear stress parallel to failure plane N m2 normal stress perpendicular to failure plane N m2 slope angle relative to horizontal plane degrees specific weight of mass Wt volume N m3 thickness of regolith above failure plane m Wt mg kg m sec2 N Wt volume N m3 specific weight h cos2 normal stress N m2 h cos sin shear stress N m2 41 In Class Activity Force Analysis of Particle on Slope Model 1 2 3 Choose our class favorite block of rock sample and set up the inclined plane Determine the mass of our block of rock sample by using the balance in the room Using the appropriate equations listed above calculate the force vectors and fill in the table below Show your calculations in the space provided Mass of Rock Block kg Weight of Rock Block N Slope Angle Degrees Normal Force N Shear Force N 0 10 20 30 40 50 60 Given that shear force is oriented downslope and normal force is oriented perpendicular to slope answer the following questions 4 A Which of the two forces will drive the rock block downslope when it fails B Which of the two forces will tend to resist downslope movement of the rock block C Intuitively when do you think the block will begin sliding down the slope choose 1 shear normal shear normal shear normal Place the rock block on the inclined plane and determine the critical angle at which it slides down the slope Calculate the following Critical Angle of Rock Block Sliding degrees Critical Normal Force at Critical Angle N Critical Shear Force at Critical Angle N D How do your inclined plane results compare to your prediction in question C above E List some ideas as to why your results turned out like they did What other physical factors have not been accounted for in our set of equations slope analysis 42 B Other Physical Properties Effecting Slope Stability 1 Driving and Resisting Forces a Driving Force Shear Stress discussed above b Resisting Force Shear Strength 1 2 Shear Strength measure of resistance of slope to shear motion or failure Slope Stability Ratio Slope Safety Factor dimensionless ratio F resisting force driving force shear strength shear stress F 1 Strength Stress Stable Slope F 1 Strength Stress Unstable Slope F 1 Slope Failure Threshold 3 Shear Strength Factors Coulomb Equation a Internal Friction of Material 1 plane friction resisting force at grain boundaries 2 interlocking friction resisting force at irregular grain boundaries grains forced to move up and over one another b Effective Normal Stress 1 Normal Stress force perpendicular to failure plane 2 Effective Normal Stress accounts for internal pore pressure of material a Pore Pressure in Granular Material i dry material pore pressure 0 ii fully saturated material pore pressure is positive a positive hydraulic lift iii partially saturated material pore presssure is negative a suction between grains due to surface tension of water and capillary force c Cohesion force of molecular attraction between grains and particles a clay high cohesive force due to electrostatic attraction at molecular level b sand gravel noncohesive due to lack of electrostatic attraction c Cohesion Factor also includes vegetative root strength 43 Coulomb Equation Measure of Total Shear Strength S c tan where S total shear strength N m2 c cohesion N m2 effective normal stress N m2 angle of internal friction so F S Safety Factor F 1 slope failure F 1 Slope stability F 1 slope failure threshold 44 In Class Exercise A 3 6 m thick mass of regolith rests on top of a sloping bedrock surface The hillslope angle is 8 degrees A geotechnical engineering firm conducted an in situ slope stability analysis with the following results regolith cohesion 2155 N m2 effective normal stress 71855 N m2 angle of internal friction 10o specific weight of regolith 25921 N m3 Calculate the safety factor for the slope show your work Questions 1 Is the slope stable or unstable with respect to shear strength vs shear stress Why 2 What slope stability factors could easily be changed say during the course of a week that would result in driving the slope to a critical threshold Do some thinking and hypothesizing here Directly relate your ideas to the pertinent equations used to calculate slope stability 45 II Mass Wasting Processes and Classification A Stages of weathering and crustal denudation 1 Weathering fragmentation diminution of bedrock a Chemical Processes b Physical Processes 2 Mass Wasting mass movement of weathered rock materials downslope under the force of gravity gravity transfer 3 Erosion and transportation of sediment by surface waters This process can be viewed as a continuum at any given time there exists unweathered material hill slpe material in storage on slopes sediment in transport and sediment in temporary storage along drainage system networks B Components of mass wasting process 1 Gravity and potential energy created by crustal relief a generally