A table of most of the equations we have used ( click here for river equations)

Note, the symbols don’t translate with some browsers… I am working on the problem

Basic
Force balance	∑F = 0, or ∑F = ma	The second form is used if there are any accelerations
Hydro or litho static pressure	P = r g d	r is the material density, and d is the depth of burial
Slope stability
Shear stress, parallel to slope at some depth (perpendicular to slope)	Τ = ρ g d sin α	See notes on slope angles and depths
Normal stress, perpendicular to slope	s = rgd cosa
Coefficient of friction	m = tan f	f is the internal angle of friction.  In the absence of cohesion,  f is the angle at which a block will slide.
Factor of Safety for a slice of a potential failure surface	FS =  (seff  tan f + S ) / ts	General form of the FS equation.  The ratio of resisting stresses to driving stresses.  The coefficient of friction is tan f or m.
Factor of Safety for a straight dry slope	FS = (rgd cosa tanf + S) / rgd sina	Where d is the perpendicular to slope depth
Water pressure in a ‘shallow soiled hillslope’	Pw = rw g dwt cosa	Where d is the ‘perpendicular to slope’ depth from the watertable down to the point of interest
Effective pressure	seff  = sn  -  Pw	Normal stress reduction, as a result of water pressure
FS for a wet straight slope, using the ‘shallow soil hillslope’ approx. for water pressure	FS = [((rsgds  + hrwgdwt ) - rwgdwt ) cosa tanf + S] / (rsgds  + hrwgdwt ) sina	Note this only applies directly to the specified type of failure
After failure, the mass will tend to fall at an acceleration of:	a = g (sina - cosa tanf )	This is just the sum of forces divided by the mass. If the slope doesn’t change the acceleration a is a constant.
Useful formula for motion, with constant acceleration	V^2= 2 a L  and  2L = a t^2	Where v is velocity, L is the slide path length, and t is the time since the acceleration (a) was applied
Stress, Strain and Strain Rate
Stress	Force per area	This is a tensorial quantity, with magnitude and two directions
Strain τφ	Change of length with length. Example: a normal strain component (only for very small Dx) exx = Dx / (original length in x) A shear strain is more complex exy = ½ [Dy / (original x) + Dx / (original y) ]	Although dimensionless, this is also a tensor!
Strain rate	Calculation of shear strain rate in a fluid e^oxy = ½ [DVy / Dx + DVx / Dy]	The shear strain rate is determined by gradients in the velocities
Debris flow equations
	A page of debris flow equations here
Two useful velocity equations	V = ( 2 g z ) ^½ V= ( g (R/W) z ) ^½	Where z is the superelevation. The first can be used for water piling up against an obstacle, the 2^nd for water going around a bend of radius R and flow width W.
Convolution for Shallow Soiled Hillslope approximation, and other distributed input to point output processes.		This gives the water table at time ‘t’, at some distance X downslope. The sum runs from sometime in the past (see note below) to time ‘t’, and the time step size (to step thru the sum) is given by Dt. This form only works for constant slope and water velocity. Note, the start time of the sum, is the time in the past when water that is passing the point you are interested in, fell on the top of the hill. In other words: t (lower limit) is [slope length/water velocity], note this is a [past] time.