If you take Ko=1-sin(phi) and Ka=tan^2(45-phi/2), you get the ratio Ko/Ka ranging from 1.35, to 1.5 to 1.65 for friction angles of 20, 30 and 40 degrees. I just use 1.5.
I used this approach in graduate school and it was well received by Prof. Duncan for an assignment involving at rest earth pressure on a sloping backfill. I have no other reference, except that's what I've done for the last 20 years. No broken walls yet!
f-d
¡papá gordo ain’t no madre flaca!