ABSTRACT
M. G. Spangler was the first to predic t the ring deflection of buried flexible circular pipes. His Iowa Formula is:
Dx = Df KsWcr 3/(EI+0.061E'r3)
where (See Figure B-1.) Dx = horizontal increase in diameter due to
vertical soil pressure P, P = vertical soil pressure on top of pipe, D = vert ical decrease in diameter which
Spangler assumed to be equal to D x, d = ring deflection = D/D , D = mean circular diameter of the pipe, r = D/2 = mean radius of the pipe, Df = deflection lag factor which can be
incorporated into a time-dependent soil modulus and can be ignored (Spangler assumed Df = 1.5.),
Ks = bedding factor. Spangler found it can vary from 0.083 to 0.110 depending upon the bedding angle, a . (A reasonable assumption is Ks = 0.1.)
Figure B-1 Assumed loads on a flexible ring in Spangler's Iowa Formula.
