long term & short term Pile capacity 1

[Enhineyero]

Hi all is there an equation for long term and short term pile capacity?

I thought pile capacity are checked in the same manner as with shallow footings: (critical service load combination) / (allowable soil bearing capacity, with FS of 3)

I check pile capacity using: (Qb+Qps)/FS-(a)Qns. Where in Qb is end bearing, Qps is positive skin friction, "a" is mobilization factor for negative friction, Qns is negative skin friction. FS = 2.0~2.5

then i saw a colleague's calculation and it has long term and short-term case.

Long term: (Qb/FS1+Qps/FS2)-(a)Qns , where FS1 is factor of safety for positive skin friction, FS2 factor of safety for end bearing

short term: (Qb+Qps)/FS

has any one done this kind of checking. May i know your reference?

I usually use bowles geo book to do my foundation design. and so far i cant this checking in the book.