$\backslash$table$[[,$A$,$B$,$C$],[1,$Factor of Safety Spreadsheet,$],[2,$Variable,Value,Units$],[3,$Cohesion,$1100,$N$/$m$2],[4,$Density of Regolith,$2200,$kg$/$m$3],[5,$Depth of Regolith,$10\mathrm{.}0,$m$],[6,$Angle of Internal Friction,$15,$degrees$],[7,$Slope,$14,$degrees$],[8,$Depth of water,$0\mathrm{.}0,$meters$],[9,,,],[10,$Constant,Value,Units$],[11,$Gravity,$9\mathrm{.}8,$m$/$s$2],[12,$Density of Water,$1000,$kg$/$m$3],[13,,,],[14,,,],[15,$Shear Strength,$57153\mathrm{.}83,],[16,$Shear Stress,$52158\mathrm{.}36,],[17,,,],[18,$Factor of Safety,$1\mathrm{.}10,]]$The variables are highlighted in yellow and constants are shown below. Click on the cell to the right of $$shear strength$($B$15)$ and create an expression that will calculate the shear strength. Repeat this process for the cell to the right of $$shear stress$$ and $$factor of safety.$$ Note that all angles will need to be converted to radians by multiplying by PI and dividing by $180.$ To do this in Excel you$$ll need to multiply by the quantity PI$()/180.$

Now we will consider the more intrinsic variables, i$.$e$.$ variables that are specific to a material or a site, but that could change from location to location. These include regolith cohesion, the angle of internal friction and slope.

i$.$ Regolith Cohesion:

a$.$ How does the factor of safety change if the regolith cohesion value is increased by $1000$ times from its original value? NOTE: This would be similar to saying that the unit was rock instead of sediment. Does the slope become more stable or less stable?

b$.$ How does this compare to the response to a change in regolith cohesion in question $2$i and why is the response different?

ii$.$ Angle of Internal Friction

a$.$ How does the factor of safety change if the angle of internal friction increases by a factor of $2($this would be the equivalent of changing the material from loose sand to semi$-$consolidated sediment$)?$ Does the slope become more stable or less stable?

b$.$ Why does FS change in this way? Use the mathematical relationships between variables in your explanation.

iii. Slope:

a$.$ How does the factor of safety change if the slope is steeper by a factor of $2?$ Does the material become more or less likely to fail?

b$.$ Why does FS change in this way? Use the mathematical relationships between variables in your explanation.

$4.$ Provide a summary of the results of your sensitivity analysis. In this summary you should use the results of your analysis to conclude which variables are most important in determining slope stability. Also address which factors included here are the least important and provide an explanation as to why.

$5.$ The factor of safety doesn$$t change a lot when cohesion changes $($i$.$e$.,$ the factor of safety is not highly sensitive to changes in cohesion$).$ But, when might changes in cohesion still be very important in causing slope failure?

$6.$ Where else in your study of geoscience might a sensitivity analysis provide insight?