Every horizontal or vertical pipe bend in a storm drain, culvert, inverted siphon or other pipe structure shall be analyzed for stability. As the momentum of flow changes around a bend, forces are exerted on the bend that must be countered by the pipe walls, soil pressure, pipe joints, and friction. When the dynamic thrust exceeds the allowable force on any of these resistance devices, a thrust block is installed at the bend. A thrust block typically consists of a rough block of concrete poured around the outside of a pipe bend in direct contact with the outer wall of the pipe.
The thrust force on a pipe bend is calculated by vector components (x, y, and z) to simplify the process. In the equations below, “x” represents the horizontal direction of flow upstream of the bend, “y” represents the horizontal direction of flow normal to “x,” and “z” represents the vertical direction along which gravity acts. Equations 28.36-14 through 28.36-16 are adapted from Roberson et al., 1998, using conservation of momentum to find reaction forces. Pipe cross-sectional area and internal pressure are assumed to be constant through the bend, with pressure assumed to equal the surcharge depth above the pipe crown, if applicable.
| (28.36-14) |
| (28.36-15) |
| (28.36-16) |
Where:
FR | = | Reaction force required to hold bend in place, lbf |
ρ | = | Density of water ≅ 62.4 lbs/ft3 |
Q | = | Flow rate in pipe, cfs |
V1x | = | Average pipe velocity upstream of the bend, fps |
V2x | = | V1x cos θ, V2y = V1x sin θ, V2z = V1x sin θ |
p | = | Internal pipe pressure, psf |
g | = | Gravitational constant, 32.17 ft./s2 |
A | = | Cross-sectional flow area of pipe, sf |
θ | = | Total bend angle (vertical or horizontal) |
Wbend | = | Weight of the pipe in the bend, lbs. |
Wwater | = | Weight of the water in the bend, lbs. |
Subscripts 1 and 2 indicate conditions just upstream and just downstream of the bend. |
In addition to soil bearing pressure, force on a bend is resisted by friction between the pipe and the soil. A sliding coefficient of 0.35 is recommended for purposes of calculating the friction force (USBR 1974).
Where calculations indicate that sliding or displacement of a horizontal bend may occur, a thrust block is installed to increase the effective bearing area on the soil such that the load is adequately dispersed. Vertical bends may require an anchor block to provide additional weight to resist the resultant vertical force. Calculation of resisting forces for a vertical bend may include full pipe weight and anchor block weight, but shall not include the weight of earth cover on the bend. This allows for safe operation of the pipe even with reduction or removal of cover material (USBR 1974).
(Res. 40-08 (§ 905.2), 3-19-08)