The following describes a method for designing uncased pipeline crossings of highways without compromising the structural integrity of the pipeline.
Pipeline codes (specifically CSA Z662-96) usually permit uncased pipeline crossings of highways, provided that the pipeline is installed at a great enough depth (usually a minimum of 1.2 metres) and that a thicker wall pipe is used within the right-of-way.
Historical Background
During the past two decades, the state-of-the-art of pipeline design has advanced significantly. The design of buried pipelines under vehicular crossings is rather unique in that it also involves soil-structure interaction. Casing of pipeline crossings under roads and railroads was a common practice in the past. Technological improvements in the manufacturing process, construction, and the protection of pipelines have reduced the need for casing. The current practice is to utilize uncased crossings whenever possible.
On the basis of studies sponsored by the American Society of Civil Engineers, and the independent research conducted by M.G. Spangler, a design procedure was developed and introduced in a paper presented on June 3, 1964, at the annual conference of the American Water Works Association. The Spangler method, often referred to as the ‘‘Iowa Formula,’’
has become the most widely accepted procedure for the design of uncased pipeline vehicular crossings.
Design Procedures
The design of an uncased pipeline crossing must be adequate to provide the following:
1. Sufficient support for the soil, the road surface, and the live loads over the pipe.
2. Sufficient rigidity so that excessive flattening of the pipe does not occur.
3. Sufficient strength so that combinations of internal and external forces do not cause failure of the pipe.
The adopted basic theories are commonly those credited to Marston and Spangler.
Marston’s equation has been proven to be conservative. (All design equations are provided at the end of this section.) The analysis of pipeline crossings can be broken down into two main categories: the determination of forces acting on the pipe and determination of the stress and deformations in the pipe section due to the combinations of the forces acting on the pipe. These are detailed below.
Determination of Forces Acting on the Pipe
In this category, the forces include the pipe’s internal pressure and the external pressure acting on the pipe due to the weight of the soil above it, as well as the wheel loads.
(a) Internal Pressure
The internal pressure is normally known for an operating pipeline or can be calculated using the expression given in the codes for design pressure [see Equation (7-7)]. Included in this expression is a design factor known as the class location factor which limits the internal stress level on the basis of population density adjacent to a pipeline.
(b) Soil Load
To calculate the soil load, Marston’s theory can be used. Included in Marston’s formula is a design parameter called the load coefficient, Cd. It is a function of the ratio of the height of the backfill or earth above the pipe to the width of the ditch or diameter of the bored hole.
It is also a function of the internal friction of the soil backfill and the coefficient of friction between the backfill and the sides of the ditch. Marston recognized five different classes of soil in the development of his original formula. The generally accepted factor used today in design involving highway subsoil material is the soil class, which Marston labelled
‘‘ordinary maximum for clay (thoroughly wet).’’ Values of the load coefficient can be found in Figure 7-45.
(c) Wheel Loads
Vehicle wheel loads are considered as concentrated loads applied at the roadway surface and the load on the buried pipe, including impact loading, is calculated using the Boussinesq Point Load Formula. An influence coefficient, CT, is included in this formula, which represents the fractional part of the wheel load that is transmitted through the soil to
the buried pipe, and is based on Holl’s integration of the Boussinesq equation. This influence coefficient is dependent upon the length and width of the section of pipe under consideration, its depth below the roadway surface, and the position of the point of application of the wheel load with respect to the area in plan of the pipe section. The area on which the load is calculated is a projection of the pipe section on a horizontal plane through the top of the pipe. The influence coefficient can be found in Figure 7-46. Impact factors for vehicles operating on unpaved roads or those paved with a flexible-type surface range from 1.5 to 2.0; for rigid pavements it is taken to be 1.0.
Determination of Stresses and Deformations
A buried pipe under a road crossing is subjected to the hoop stress caused by internal pressure and circumferential bending stress due to the external static and dynamic loads. The bending stresses are assumed to be algebraically additive to the tensile hoop stress due to internal pressure. Also, flexible pipes are characterized by their ability to deform extensively without rupture of the pipe wall. They could fail by excessive deflection rather than by rupture. Therefore, design procedures are also directed toward predicting the pipe deflection under load. These stresses are as follows:
(a) Hoop Stress (Sh)
The hoop stress in the pipe is computed using Barlow’s Formula (Sh) [see Equation (7-1)], which establishes a relationship between the tensile strength, the internal pressure, and the nominal dimensions of a pipe.
(b) Circumferential Bending Stress (Sb)
Stresses in the pipe caused by external loads can be computed using Spangler’s Formula. Included in this formula are bending and deflection parameters, Kb and Kz which are dependent upon the distribution of load over the top half of the pipe and the resultant distribution of the bottom reaction. The load distribution over the top half of the pipe may be considered as uniform. The bottom reaction, however, depends largely upon the extent to which the pipe settles into, and is supported by, the soil at the bottom of the trench or bored hole. For bored installations, the bottom reaction may be considered to occur over an arc of 908. For an open trench installation, the bottom reaction is generally assumed to occur over an arc of 308.
(c) Deformations
Pipe deflections may be calculated by using the Iowa Formula (Spangler’s), and ignoring the support of the soil. The pipe, therefore, acts as an elastic ring having no effective lateral soil support and the deflection is controlled entirely by the elastic resistance to bending of the pipe wall.
Design Equations
Marston’s Formula for soil load on an assumed rigid pipe:
Wd ¼ cd B2d ð7 103Þ
Boussinesq’s Point Load Formula for wheel load:
WL¼cTI
L P ð7 104Þ
Figure 7-45. Values of load coefficient Cd(Trench Fill) [Spangler et al., 1964]
Figure 7-46. Influence value Ifor concentrated or uniform surcharge of limited extent
Barlow’s Formula for hoop stress:
Sh ¼PiR
t ð7 105Þ
Spangler’s Formula for circumferential bending stress:
Sb ¼ 6 KbWeREt
Et3þ 24KzPiR3 ð7 106Þ
IOWA Formula (Spangler’s) for pipe deflections:
¼ 12 KzWeR3
Et3þ 24 KzPiR3 ð7 107Þ Nomenclature:
B = pipe diameter, m
Bd= width of trench at the top of a pipe (i.e., effective width), m Cd= load coefficient for fill load
CT= Influence coefficient for a single concentrated load = 4I
E = Young’s Modulus, MPa
Sb= circumferential bending stress in a thin steel pipe wall, MPa Sh= tensile hoop stress in a steel pipe, MPa
I = impact factor for live loads, varies as function of buried depth. API RP1102, recommends 1.75 for railroads and 1.5 for highways each decreasing by 0.3 per foot of depth below five (5) feet until the factor equals 1.0 I= Influence value
Kb= bending parameter Kz= deflection parameter
L = length of pipe (taken as 0.91 m), m P = wheel load, kg
Pi= internal pressure in pipeline, MPa R = outside radius of pipe, mm
t = pipe wall thickness, mm Wd= soil dead load on the pipe, N/m
We= total external load on the pipe, N/m (includes the soil dead load and the vehicle wheel live load)
WL= wheel live load on the pipe, N/m
= maximum vertical deflection in pipe, mm = unit weight of soil, kg/m3
Sample Calculation Given:
p Pipe diameter = 610 mm p Pipe wall thickness = 12.7 mm p Pipe grade = 359 MPa
p Class location = 1
p Internal pressure = 8450 kPa
p Depth of cover = 1.2 m (min. per code) p Wheel load = 9,072 kg
p Unit weight of soil = 1,922 kg/m3 p Young’s modulus = 200 103MPa
Determine the combined circumferential stress and vertical deflection in the pipe due to internal pressure and external loads.
(a) Calculate the soil load:
p Trench width, assume Bd= 0.61 + 0.34 = 0.95 m p Depth of cover, H = 1.2 m
p H/Bd= 1.2/0.95 = 1.26
Then, using Figure 7-45, Cd= 1.07, from curve D for ‘‘ordinary maximum for clay.’’
Therefore, using Equation (7-103), the soil dead load on the pipe is:
Wd= 1.07 1,922 9.81 0.952= 18,208 N/m (b) Calculate the wheel load on the pipe. (See Figure 7-47).
Consider the load to be acting on an area:
B L = 0.61 m 0.91 m Using Figure 7-46:
m¼ B
2H¼ 0:61
2 1:2¼ 0:254 n¼ L
2H ¼ 0:91
2 1:2¼ 0:379 which gives I= 0.038 and CT= 4 I= 0.152.
Figure 7-47. Wheel load on the pipe
Therefore, using an impact factor of 1.5 within Equation (7-104), the wheel live load on the pipe is:
WL¼0:152 1:5 9; 072 9:81
0:91 ¼ 22; 298 N=M
(c) Calculate the hoop stress due to internal pressure and the circumferential bending stress due to external loads to give the combined stress in the pipe:
Sh ¼8; 450 103 305
12:7 ¼ 203 MPa
This is lower than the maximum limit of 0.6 SMYS (= 215 MPa) required for uncased crossings in Class 1 location.
The circumferential bending stress is given by Equation (7-106) where (see below), for an open trench installation, the bending and deflection parameter Kband Kzare 0.235 and 0.108, respectively.
From Equation (7-106), Sbwhen calculated will be found to be 43 MPa.
Parameters Width of Uniform Crossing Construction Deflection Kz Moment Kb
Reaction (Degrees)
0 Consolidated rock 0.110 0.294
30 Open trench 0.108 0.235
90 Bored 0.096 0.157
Therefore, the combined stress is:
Shþ Sb ¼ 203 þ 43 ¼ 246 MPa ¼ 0:69 SMYS
This is lower than the maximum limit of 0.72 SMYS permitted in a Class 1 location for the pipe sections adjacent to the crossing. This ensures that the uncased pipeline within the crossing operates at a lower stress level and has a higher factor of safety than the pipe sections adjacent to the crossing.
(d) Calculate the vertical deflection (with no internal pressure to give the worst loading condition):
Using Equation (7-107), the vertical deflection of the pipe is:
¼ 120:108 18;208 þ 22;298ð Þ1033053
20010612:73þ 240:1088:451063053 ¼ 1:44 mm
¼ 0:24% of the nominal pipe diameter
This is within the limit of 3% of nominal pipe diameter for vertical deflection as recommended by Spangler.