The only way to estimate a phi anlge is from experience in the area in question. Most geotechnical text books give ranges of phi angles based on the material and the kind of deposit it is (i.e., terrace, residual, or alluvial).
Usually the backfill is granular material and is well draining to eliminate any hydrostatic pressure. But for native soils usually I have performed unconsolidated-undrained triaxial tests to obtain cohesion and a friction angle for cohesive soils and a direct shear test (consolidated-drained)...
