Soil friction angle

All soil moves over time due to many factors; gravity, slope of the ground, slope of the underlying rock, soil content and consistency, and the amount of water in the soil, whether it is in a earthquake zone etc.

You might look into "angle of repose". It is widely documented for various materials.

Friction Angles in Sand

The following typical correlation may be used to estimate the soil friction angle, φ:

φ = N/4 + 28

As an alternative, the procedure described in shall be used. The maximum Ф value shall be limited to 35 degrees for silty sand (A-2-4) and 38 degrees for clean sand (A-3), unless higher friction angles are statistically supported by laboratory shear strength test results.

Various published correlations estimate the angle of internal friction, φ, of cohesionless soils based on SPT-N values and effective overburden pressure. Some of these correlations are widely accepted whereas, others are more likely to overestimate triaxial test data. In the absence of laboratory shear strength testing, φ estimates for cohesionless soils, based on SPT-N, These values are based on SPT-N values obtained at an effective overburden pressure of one ton per square foot. The correction factor, C, may be used to "correct" N values obtained at overburden pressures other than 1 tsf.

Once I get the friction angle how to calculate the co-efficient of friction between soil and the pipe?

Umm, or you could get the friction angle directly from shear testing of representative samples, rather than attempting to estimate it from the variety of equations indirectly correlating it to field tests. The coefficient of friction between any material and soil is something that is tested for, for common materials it should be available through a little research online. There is not any specific estimator equations for coefficient of friction with soil for all materials, it is specific to the application, structure, materials, and surface.

The "friction angle" or the direction of friction is always opposite the direction of motion of an object. Since the ground may be moving instead of the pipe, it would be the direction of motion of the dirt.

Usually I would use the friction between the soil and the steel (assuming steel corrugated) and this is typically 1/2 the soil friction angle itself say 17 degrees for clean sand, 22 degrees for a good gravel.