Discussion of 'Thrust Restraint Design of Concrete Pressure Pipe' by Mehdi S. Zarghamee, Daniel W. Eggers, Rasko P. Ojdrovic, and Daniel P. Valentine

摘要

The authors are to be complimented on their development of a design procedure for restraint of pressure-induced thrust at bends in pipelines, using concrete pressure pipe, which includes the effects of soil resistance to lateral movement of tied-pipe. The authors' procedure is a needed extension of a beam-on-elastic-foundation design procedure for thrust restraint of fiberglass-reinforced plastic pipe and fittings developed in the late 1970s (Ameron 1980), but it is found to be lacking in some respects. Throughout this discussion, DELTA is substituted for the authors' theta for compatibility with AWWA (1996). In the authors' Eq. (3) the third term, 2kl'_b delta cos~2(DELTA/2) referred to herein as T_3, represents passive soil-pressure forces that act on the bend to resist thrust T. The fourth term of Eq. (3) 2f_ul_b sin(A/2) referred to herein as T_4, represents friction forces that act on the bend to resist thrust. Both terms are incorrect because they are not based on movement of the bend into the soil in the direction of the thrust force and because' all bends are treated as having only a single mitered joint. The correct third term is T'_3=k deltal_k where l_k is the effective length of the projection of the outer surface of the entire bend on a plane perpendicular to T. That projection is a rectangle of length 2l_b cos(DELTA/2) and width D_o, with half ellipses appended to its ends. The major axis of the ellipses is D_o and the minor axis is D_o sin(DELTA/2). The effective projected length, which is equal to the projected area divided by D_o, is l_k=2l_b cos(DELTA/2) + (pi/4)D_o sin (DELTA/2). The correct fourth term is T'_4 = f_(mu)l_(mu) where l_(mu) is the sum of the centerline lengths of each of the mitered sections of the bend. Using the guidelines for the design of mitered bends in AWWA (1996), l_(mu)=2(l_b-R tan(DELTA/2) + (n_s-l)R tan(theta/2)), where l_b is equal to L_1 from Table 1 of AWWA (1996), R is the radius of the bend, n_s is the number of mitered sections and theta = DELTA/(n_s-l). For D_o= 1,829 mm (72 in.) values of T'_3/T_3 range from 0.9 to 1.4 for values of A from 7.5 deg to 90 deg and R from 1.0D_o to 2.5D_O. Values of T'_4/T_4 range from 15.3 to 2.0 over the same ranges of DELTA and R. The differences represented by the ratios, especially T'_4/T_4, are significant.