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APPENDIX A
FORMULAE AND SAMPLE CALCULATIONS
Pipe Installation (Fused)
The fused polyethylene (PE) pipe can be pulled by a cable attached to a pulling head fastened to the
pipe. This prevents damage to the PE pipe. The length of the fused pipe which can be pulled will vary
depending upon field conditions and ease of access to the area. In general, the maximum pulling length
for small diameter pipe, 12 inch and smaller, is normally limited to 1000 feet, and for larger pipe, about
500 feet. Longer lengths have been pulled, however, all conditions must be determined. The various
pulling forces and lengths information is desirable for design and estimating purposes. The maximum
force that can be applied to a pipe on level ground can be determined by the following formula:
Pt = (smax) A (1)
Where Pt = maximum pulling force (lb)
smax = maximum allowable tensile stress, 1000 psi
A = cross sectional area of pipe, in^2
Note: HDPE primary properties are specified by cell classification per ASTM D
- Tensile strength is normally cell class 4 which is 3000 to 3500 psi. The allowable tensile stress of 1000 psi provides a design factor of approximately 3 to compensate for installation stresses.
The following formula can be used to determine the pulling length:
L = Pt fa
Where L = pulling length (feet)
f = friction coefficient (0.5)
Sample Calculations:
- 1000 feet of 12 inch, SDR 26 is being pulled over smooth ground with a 5o^ slope. What is the pulling force? t = 0.490 inches d = 12.75 - 0.49 = 12.26 C = Bd A = Cxt = p^ x 12.26 x 0.49 = 18.87 in^2 Pt = 1000 x 18.87 = 18,870 lbs.
Pipe weight per foot: V = A x 12 = 18.87 (12) = 226.44 in 3
Weight = 226.44 (0.955) 0.0361 = 7.8 lbs/ft
The maximum straight line of pipe that should be pulled (assuming f = 0.5) is:
L = 18,
L = 4838 feet
Note: The maximum radius of curvature should be limited to maximum axial strain properties of the pipe, as discussed below.
See figure A1 for pit trench configuration
EXAMPLE:
PE pipe Do = 24.00 inches Height of cover, H = 12 feet
R = 50 (24) = 1200 inches (100 feet)
L $ [12 (2 x 100 - 12)]1/2^ = [12 (188)]1/ L # [2256]1/2^ = 47.50 Use 48 feet
Pipe Installation (Gasketed)
The gasketed pipe joint segments can be pushed and/or pulled into the existing pipeline from an
insertion pit. The pipe joints should be inserted with spigot end first and the bell end trailing. The
push/pull bearing plate should be applied against the flat surface of the bell step, to avoid damaging the
bell, especially on plastic pipe (HDPE). The maximum pushing and/or pulling length is determined by
the longitudinal compressive strength of the pipe and this varies with type of material and its design.
The access pit should be approximately 5 to 10 feet longer than the standard 20 foot pipe segment
lengths. The width of the pit should be 2 to 4 feet wider than the diameter of the existing pipe.
In general, the maximum push/pull lengths for 18-inch and larger slipliner pipe is normally limited
to 1000 feet in a dry sewer and about twice that in an active flowing sewer.
The existing pipeline condition, i.e., alignment and grade changes, structural and corrosion conditions, etc., must be determined prior to the installation. The maximum push/pull force to be applied can be determined by the following formula.
Pc = smax A (6)
Pc = maximum push/pull force, lbs.
smax = maximum allowable compressive stress psi
A = cross sectional area* of pipe, in 2
- located at minimal cross section
From Roark, axial compressive stress, psi
smax = 0.3 Et (7) r(SF)
E = use initial tensile or compressive modulus
t = minimum wall thickness, in.
r = mean radius, in
SF = Safety Factor usually 2.0 - 4.0 (for materials)
The following formula can be used to determine the push/pull length.
L = Pc fa^ (SF)
Where L = estimated push/pull length (feet)
f = friction coefficient (= 0.5 in dry & = 0.25 in wet)
a (^) = pipe weight (lbs/ft)
Sample Calculation:
- Determine the estimated force needed and length of 36-inch inner profile wall HDPE pipe (RSC 160) that can be pushed/pulled through a dewatered (dry) 42-inch RCP pipeline. Pipe weighs 42 lbs/ft. Zbar = 0.
Do = 39.44 in I = 0.277 I = t 3 /12 t = 1.492 in.
smax = 0.3 Et r(SF)
E = 113,000 psi
t = 1.492 in (effective)
r = (39.44 - 1.49) / 2 = 18.975 in.
SF = 2.
smax = 0.3 (113,000) 1.492 = 1333 psi 18.975 (2.0)
Force needed:
Pc = Fmax A
smax = 1333 psi, A = B dt = B (37.492) 1.492 = 175.
Pc = 1333 (175.73) = 234,248 lbs
L = 234,248 = 5578 Ft. 0.5 (42) (2.0)
- Determine the estimated force needed and length of 36-inch diameter exterior profile wall HDPE pipe (RSC 160) that can be pushed/pulled through a dry 42-inch RCP. Pipe weighs 42 lbs/lf.
From Roark Axial Compressive Stress = 0.3 E t r (SF)
E = 113,000 psi (initial tensile modulus) t = 0.36 inches (wall thickness raceway) SF = 2, r = (36 + 0.36) / 2 = 18.18 inches
Axial Comp. Stress = 0.3 (113,000) 0.36 = 336 psi 18.18 (2) From Formula (6)
Pc = 336 (π x 36.36 x 0.36) = 13.817 lbs.
The profile wall does not make contact along its entire surface. Adjusted friction values are: f = 0.3 (dry) and f = 0.1 (wet). When using HDPE Pipe, the normal friction factors should be used, i.e., f = 0.5 and 0.25.
From Formula (7)
L = 13,817 = 658 feet 0.25 (42) (2)
- Sample Calculation:
Determine the estimated force needed and length of 36-inch RPM pipe that can be pushed/pulled through a dry 42-inch RCP. The axial compressive stress of the RPM pipe is 14,000 psi. The pipe stiffness is 36 psi having a wall thickness of 0.72 inches.
Pipe weighs 71 lbs/lf.
Do = 38.3 inches, t = 0.72, Effective t = 0.45 inches
From Formula (6)
P = 14,000 (π x 37.4 x 0.45) P = 740,222 lbs (w/o SF) and P = 185,055 lbs (w/4 to 1 - SF) Force used
From Formula (7)
L = 185,055 = 2606 feet - length 0.5 (71) (2)
Hydrostatic Loads
When there is a possibility of groundwater level above the pipe, the level and its duration should be estimated, and pipe of sufficient wall thickness to withstand the pressure, without collapsing, should be used. It should be noted that an appropriate safety factor of 2 should be used. The following basic equation should be used to determine needed wall thickness:
P = 24 Ea I (8) (1-μ^2 )d^3 (FS)
Note: Apply an appropriate Safety Factor (normally 2.0)
The following product material Poisson ratios should be used:
Material Poisson Ratio HDPE 0. PVC 0. RPM 0. CIPP 0. Steel 0. DIP 0.
The following product material initial flexural modulus (Ei) values should be modified for apparent long
term values (Ea):
Material Ei (Initial-psi) HDPE 113, PVC 400, RPM 1.5 x 10^6 CIPP 300, Steel 30 x 10^6 * DIP 24 x 10^6 *
- Initial and long term assumed to be the same.
When slipliner pipe is subjected to a constant on-going loading, the following apparent modulus values
should be used.
Material Ea (long term - psi)* HDPE 24, PVC 113, RPM 0.75 x 10^6 CIPP 150, Steel 30 x 10^6 ** DIP 24 x 10 6 **
- Long term values set at 50 years, determine by long term stress regression testing.
** The wall thickness should be increased for corrosion allowance, usually 0.08 inch or greater.
Pg = Safe Grouting pressure (psi)
Ei = Initial modulus
From ASTM D-
EI = 0.0186 (PS)d 3
PS = Ei I (18) 0.0186 d^3
Ei I = 0.0186 PS (19) d^3
Pg = 24 (0.0186) PS = 0.446 PS (20) (1-μ^2 ) (1-μ^2 )
Refer to material ratio table for the following calculation examples. It is recommended that a factor of safety of at least 1.5 be applied to the grouting pressures.
Material Poisson Effect FS Effect
HDPE 0.558 PS 0.37 PS PVC 0.519 PS 0.35 PS RPM 0.491 PS 0.33 PS Steel 0.491 PS 0.33 PS DIP 0.491 PS 0.33 PS
Useful approximate conversion relationships are as follows:
Dimensional ratio (DR) to pipe stiffness (PS)
PS = 4.47 Ei (21) (DR-1)^3
Ring Stiffness Constant (RSC) to pipe stiffness (PS)
PS = 6 (RSC) (22)
D
Safe grouting pressure (Pg) = FS Effect
Try an RSC 100. The pipe is 36.00 inches I.D., having an I = 0.277 in^4 /in. and an effective wall thickness of 1.493 inches. The centroid of the section is Z = 0.7965.
d = Di + 2Z = 36 + 2 (0.7965) = 37.593 inches
Di is inside diameter
From Formula (8)
P = 24 (24,000) 0.277 = 3.75 psi (0.80) (37.593)^3
Use a FS = 2.
P = 3.75 (2.31) = 4.33 ft.
The pipe strength will not prevent long term collapse. it is necessary to grout annular space or use a stiffer pipe. Grouting annular space provides approximately 6 times more buckling resistance.
From Formula (22)
PS = 6 (100) = 16.67 psi (initial) 36
From Formula (20) including adjustment effects
Pg = 0.37 (16.67) = 6.17 psi
It should be noted that the maximum OD of the liner pipe must be less than the ID of the existing pipe and also meet its alignment. The selected liner wall is H=1.593 inches.
OD = 36 + 3.186 = 39.186 inches (ok)
- A 36-inch RPM pipe sliplined into an existing 42-inch RCP pipe. The pipe is 20 feet deep with 10 feet of groundwater over the pipe.
Try a PS of 36 psi. Pipe is 38.30 inches OD having wall thickness of 0.72 inches.
d = 38.30 - 0.72 = 37.58 in. Ea = 750,000 psi
From Formula (9)
P = 2 (750,000) 0. 3 = 11.59 psi (1-0. 2 ) 37. 3
Use a FS = 2.
P = 11.59 (2.31) = 13.39 feet (ok)
Grouting the annulus provides 6 times more buckling resistance. The safe pressure for grouting the annulus would be;
From Formula (20) including adjustment effects
Pg = 0.33 PS = 0.33 (36) = 12 psi
It should be noted that the maximum OD of the liner pipe must be less than the ID of the existing pipe and also meet its alignment. The selected liner wall is 0.72 inches.
OD = 36.86 + 1.44 = 38.30 inches (ok)
- A 42-inch Cured-in-place-Pipe (CIPP) will be inverted into an existing 42-inch RCP pipe. The pipe is 20 feet deep with 10 feet of groundwater over the pipe.
Try a CIPP having a wall thickness of 0.75 inches. The method of placing CIPP inside the existing pipe wall negates the necessity for grouting the annular space. Therefore, Formulae (13) or (15) may be used directly for determining the buckling resistance.
From Formula (13)
P = 2 (7) 150,000 (0.75)^3 = 12.84 psi (1 - 0.l3^2 ) (41.25)^3
P = 12.84 (2.31) = 14.83 ft. (ok) 2.0 (FS)
From Formula (15)
DR = 42 = 56
t = (12 x 0.004)1/3^ = (0.048)1/3^ = 0.36 in.
The mean diameter of the PVC liner is:
d = 42 - 0.36 = 41.74 in.
From Formula (8):
P = 2344 (140,000) 0.004 = 9.92 psi (22.9 ft.) 0.91 (41.74)^3
This provides satisfactory long term buckling strength.
The effective pipe stiffness is:
PS = Ei I = 420,000 (0.004) = 1.24 psi 0.0186d 3 0.0186 (41.74) 3
Safe grouting pressure (Pg) = FS Effect
Pg = 0.35 (1.24) = 0.43 psi
This will be done by multi-stage careful grouting.
Flow Comparisons
The sliplining rehabilitation methods all reduce the remaining available waterway cross section for
hydraulics. Plastic pipe manufacturers claim Manning flow characteristics at n = 0.010. This value has
not been substantiated under long term sewer flow conditions, nor can they be attained except in
laboratory conditions with extremely high Reynolds Numbers. Further, under field conditions actual
"n" value for plastic pipes are for all practical purposes, the same as VCP and RCP. No reduction of
"n" value shall be used for any material.
For comparative purposes, various rehabilitation methods are illustrated below showing relative
performance for lining an existing 42-inch pipeline.
Material Inside Diameter (in.) Flow Ratio
HDPE (Solid Wall) 33.78 0.
HDPE (Profile Wall) 36.00 0.
RPM 36.86 0.
CIPP 40.50 1.000 (Minimum reduction)
When gravity flow sewer pipes are half full, or full, the velocities are equal. The volume of flow in a half full sewer is 2 that of a full flow sewer. The flow ratio for the tabulated values above are based on pipe inside diameter to the 3/8 power. (Reference should be made to the NCPI Handbook)
