Chapter 4 – Effects of Surge Pressures
Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Chapter 4 – Problem 4.3
4.3 Consider a 3000 mm diameter mild steel pipeline. Compute the thickness required for this pipeline to withstand the following pressure and installation conditions:
a. A working pressure of 10 bar, a positive surge pressure of 15 bar, and a full vacuum where the pipeline is installed above ground on concrete saddles 3m apart.
b. Explain whether the thickness of the pipeline should be increased, decreased, or kept the same for the same pressure conditions described in part (a) but with the pipeline buried above the water table in a trench with a well-compacted soil all around it and with a soil overburden of 1.2m.
c. Same as part (a) except the pipeline must withstand 1/3 vacuum instead of full vacuum. This assumes that the pipeline has an elaborate air management system that limits the extreme negative pressures within the pipeline to 1/3 vacuum level.
d. Same as part (a) except the pipeline must withstand 2/3 vacuum instead of a full vacuum.
Solution:
a. A working pressure of 10 bar, a positive surge pressure of 15 bar, and full vacuum where the pipeline is installed above ground on concrete saddles 3m apart.
For positive pressures, the equation (Eq. 4.1) for the normal stress in thin-walled pipelines applies. AWWA M11 recommends that the design stress (σ) in Eq. 4.1 should be 50 percent of the specified minimum yield strength of the pipe material when computing the thickness (e) to withstand the working pressure (i.e., the pressure that stresses the pipe material throughout its life). AWWA M11 permits the use of higher percentage (not exceeding 75%) of the specified minimum yield strength when computing the pipe thickness needed to withstand transient pressures (pressures that last for few seconds to a few minutes at a time).
From Table 4.1, the specified minimum yield strength for mild steel is 250 MPa. It should be noted that there are multiple grades of mild steel and the correct value of the specified minimum yield strength appropriate for that grade should be obtained from the steel plate supplier.
Using a 50% specified minimum yield strength of 250 MPa as the design stress (i.e., σ = 125 MPa), the minimum thickness (e) required to withstand a 10 bar (P = 1.0 MPa) working pressure = 12 mm.
Using a 60% specified minimum yield strength of 250 MPa as the design stress (i.e., σ = 150 MPa), the minimum thickness (e) required to withstand a 15 bar (P = 1.5 MPa) surge pressure = 15 mm.
AWWA M11 also recommends the following equation (the well-known Timoshenko equation) to compute the collapse pressure for unreinforced circular pipes with no additional support from the soil:
where Pc is collapse pressure in kPa (gage), E is Young’s modulus of the pipe material in kPa, ν is Poisson’s ratio, e is pipe thickness in mm, and D is pipe diameter in mm.
The term Pc in the above equation represents the pressure acting on the outer shell of the pipeline as a result of external loads only (assuming atmospheric pressure is acting on the inner shell of the pipeline) as shown in Figure 4.2. For example, if a short section of an open-ended pipe (where the inside pressure is atmospheric) is placed on stable ground without any supports from the surroundings, and if the external load is 0 (i.e., Pc = 0 kPa gage), then the theoretical pipe thickness required is 0. If Pc is greater than 0, then the thickness required is some finite positive value.
If the internal pressure is below atmospheric level, Pc should be modified to reflect the sub-atmospheric pressure acting on the inner shell. For example, if the pressure due to an external load (an uncompacted soil load, for example) is 20 kPa (gage), and the internal pressure is -50 kPa (gage) or -0.5 bar (gage), then Pc = 20 – (-50) = 70 kPa (gage). If the pressure due to an external load is 0 kPa (gage) and the internal pressure is a full vacuum of -101.325 kPa (gage) or 0 kPa (abs), then Pc = 0 – (-101.325) = 101.325 kPa (gage).
Note that Pc and E in the above equation may be expressed in other units as long as both are expressed in the same units. Likewise, e and D may be expressed in other units as long as both use the same units.
Assuming that the Young’s modulus (E=205 GPa or 205000000 kPa) and the Poisson’s ratio (ν = 0.28) shown in Table D.1 apply to the mild steel plate used in this example, the thickness required to withstand full vacuum pressure of 0 kPa (abs) or -101.325 kPa (gage) converted to Pc = 101.325 kPa (gage) is 18 mm.
In summary, the thickness required to withstand a 10 bar working pressure is 12 mm, 15 bar surge pressure the thickness is 15 mm, and for a full vacuum the thickness is 18 mm. Therefore, the minimum design thickness for the 3000 mm pipeline should be 18 mm to withstand these pressure conditions.
b. Explain whether the thickness of the pipeline should be increased, decreased, or kept the same for the pressure conditions described in part (a) but with the pipeline buried above the water table in a trench with a well-compacted soil all around the pipe circumference
When a pipeline with certain thickness is placed in a trench and is surrounded by well-compacted soil, its strength against collapse by buckling (Figure 4.2) increases substantially compared to its strength against collapse by buckling without any support for the same thickness. Therefore, it is possible to reduce the thickness from the minimum required 18 mm by embedding the pipeline in a trench surrounded by well-compacted soil. However, the selection of soil used for compaction, the bedding requirements, the levels of compaction, the quality control requirements that ensure that the required levels of compaction are met all around the pipe circumference (especially at the haunches) require design by a qualified engineer along with field inspections to ensure the pipeline can safely withstand the required internal vacuum pressures and external load, lest the pipeline lose capacity (or collapse completely) due to buckling.
c. Same as part (a) except the pipeline must withstand 1/3 vacuum instead of a full vacuum.
A full vacuum is 0 kPa (abs) or -101.325 kPa (gage) and a zero vacuum (atmospheric pressure) is 101.325 kPa (abs) or 0 kPa (gage). Accordingly, 1/3 vacuum is 67.55 kPa (abs) or -33.775 kPa (gage), and therefore the collapse pressure Pc = 0 – (-33.775) = 33.775 kPa (gage).
The pipe thickness required to withstand Pc = 33.775 kPa (gage) is 12.25 mm.
In summary, the thickness required to withstand a 10 bar working pressure is 12 mm, the thickness required to withstand a 15 bar surge pressure is 15 mm, and the thickness required to withstand a 1/3 vacuum is 12.25 mm. Therefore, the minimum design thickness for the 3000 mm pipeline should be 15 mm.
d. Same as part (a) except the pipeline must withstand 2/3 vacuum instead of a full vacuum.
2/3 vacuum is 33.775 kPa (abs) or -67.55 kPa (gage), and therefore Pc = 0 – (-67.55) = 67.55 kPa (gage).
The pipe thickness required to withstand Pc = 67.55 kPa (gage) is 15.67 mm.
In summary, the thickness required to withstand a 10 bar working pressure is 12 mm, the thickness required to withstand a 15 bar surge pressure is 15 mm, and the thickness required to withstand a 2/3 vacuum is 15.67 mm. Therefore, the minimum design thickness for the 3000 mm pipeline is 15.67 mm.
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