Historically, safety factors have been used as a measurement of safety versus failure. The design values have been established for materials and then a factor or multiplier has been applied to assure that the material does not approach the design value established. But how safe are these values for the final design?
This paper will look at safety factors based on design criteria for AWWA standard water pipe. We discuss how the safety factor is established and how that applies to the actual design of the pipe. We will look at how the actual pipe material is supplied versus the value used for the design. The paper will also discuss the relevancy of how the safety factor affects the final design.
The conclusion of the paper will explain how the safety factor is just a guide for the engineer to use in the evaluation of AWWA water pipe. There are many design factors that are involved that must be considered when designing a piping system.
How do you evaluate them and what do they mean?
When an engineer designs a water pipeline, they commonly utilize design standards such as American Water Works Association (AWWA) standards to specify the minimum requirements for the pipeline. The minimum requirements include some assumed safety factor for the pipeline conditions. What does that really mean?
A commonly accepted definition of safety factor is a term used to describe the ultimate structural capacity of a system beyond the expected loads or actual loads. The term design factor is often used interchangeably although they are calculated differently. Essentially, safety factor is how much stronger the system is than it is required to be for intended loads.
AWWA does not have a standard definition for safety factor or design factor and it is left to the particular standard to define those terms. The pipe standards all use internal pressure for the basis of safety factor. For this paper, safety factor will be described as some divisor applied to the material strength (typically minimum specified yield strength rather than ultimate tensile strength, hence offering more hidden safety factor) used for the pipe design for internal pressure stresses. Design factor will be the inverse of a safety factor. Simply put, the allowable material stress for internal pressure design is the minimum specified yield strength divided by the safety factor. Or, the allowable material stress is the minimum specified yield strength times the design factor.
Risk is equal to probability of failure times consequence of failure. A safety factor is a design decision that weighs the risk vs. the cost of failure. Cost could be money, but it also could be political, loss of service, or worst yet, loss of life. The risk is not always the same for all pipelines.
Table 1 below is for water pipes for various types of materials which are allowed by AWWA.
Table 1 – Water Pipe Safety Factors
|M41 – Ductile Iron
C150 – DIP
|Uses Safety Factor on specified yield strength against working pressure plus 100 psi surge pressure
Uses Safety Factor on specified yield strength against working pressure plus 100 psi surge pressure
|M11 – Steel Pipe
C200 – Steel Pipe
C220 – Stainless Steel Pipe
|Uses Design Factor on specified yield for working pressure
Uses Design Factor on specified yield and surge Pressure
Refers to M11 for guidance
|M23 – PVC Pipe
C900 – PVC Pipe
C905 – PVC Pipe
(14” – 48”)
|Uses Safety Factor for distribution mains on projected tensile strength
Uses Safety Factor for transmission mains on projected tensile strength
Uses Safety Factor on categorized long-term tensile strength
Uses Design Factor on categorized long-term tensile strength
|M45 – FRP Pipe
C950 – FRP Pipe
|Uses Safety Factor against long-term tensile strength
Uses Safety Factor against long-term tensile strength
|M55 – HDPE Pipe
C906 – HDPE Pipe
(4” – 63”)
|Uses Design Factor on long-term tensile strength
Uses Design Factor on long-term tensile strength
As can be seen, Safety Factors and Design Factors are described differently for each pipe material. DIP and Steel Pipe standards have an apparent Safety Factor of 2:1. FRP Pipe standards are 1.8:1 and HDPE Pipe standards do not discuss Safety Factor but utilize a Design Factor of 0.63. Furthermore, HDPE standards go on to mention that the Design Factor for HDPE is not the inverse of the Safety Factor! However, there are variances within the conditions that are being analyzed for the various pipe materials.
These Safety Factors are based on internal working pressure and for DIP and Steel Pipe are applied against the minimum yield strength of the material.1 In this instance, the apparent safety factor is 2 (as the material strength utilized is the yield strength, not the ultimate strength). For the plastic pipe materials, the Safety Factor or the Design Factor is applied against the long term (extrapolated 50-year) tensile strength of the material and could be considered a “true” Safety Factor as the factor is derived from the ultimate strength of the material.
The formula for stress from internal pressure is consistent and is:
t = PD/2S
t = pipe wall thickness – inches
P = internal pressure – psi
D = internal pipe diameter – inches
S = allowable design stress (either the material yield or tensile strength divided by the Safety Factor from Table 1 or the material yield or tensile strength times the Design Factor from Table 1)
It would appear that the risk of failure for DIP, Steel Pipe and PVC Pipe materials are equivalent but FRP Pipe and HDPE Pipe materials appear to have a greater risk. This is not necessarily so. Are the stress values for the materials measured the same? Is the design control internal pressure? We will look at these two questions and present some considerations.
Many pipe products are designed based on a maximum allowable stress. The material used for the pipe manufacturing is tested and the actual strength of the material utilized is then known. If the actual tested material strength is above the minimum specified value, then the wall thickness required is calculated using the specified minimum stress value as the maximum allowable stress for the design. Therefore, if the actual material that was tested for the pipe is higher than the minimum required value for design there is an additional safety factor. This is how Steel, Stainless Steel and DIP pipe materials are designed. For PVC, FRP and HDPE Pipe materials, the tests cannot be completed to allow manufacturing to proceed in a timely manner. These products take a statistical average approach to determine the value to be used in the internal pressure calculation. And, the statistical average is based on an extrapolated 50-year material tensile strength developed from 10,000-hour material tests. More notable is that the value is a moving target and not static as it is with DIP and steel, making the prediction after the 10,000-hour test an unverifiable educated guess.
Probabilistic methods have two recognized ways to evaluate. Some like the observation and experience method. An example is flipping a coin. This method says the probability of heads is 1 out of 2 or 0.5, commonly referred to as 50%. Others identified probability as the characterization of data according to statistical rules. They would evaluate flipping the coin based on a Stanford study which put the statistical average at 51 percent that the side up was more likely. For engineering these two methods need to work hand in hand.
How does this apply to pipe material safety factors? Let us use HDPE as the comparison as it has the lowest listed AWWA safety factor at 1.59 (based on the specified design factor of 0.63). To obtain the long-term hydrostatic strength (LTHS) of the HDPE for design of the pipe wall thickness, a standard material composition of at least 18 samples is tested for over 10,000 hours (11.4 years) at 73 degrees. The LTHS is then extrapolated using a best fit to 50-years life. By definition 50% of the pipe samples will have a higher strength and 50% will have a lower strength. ASTM D2837 directly address the variability of the material strength by placing a constraint on the lower confidence limit (LCL) of the material via the LCL ratio of:
LCL/LTHS ≥ .85
ASTM D2837 then bases the confidence level based on the number of specimens tested and the desired confidence level to get the lower confidence level of 97.5%
I can add more statistical parts of the formula about C906 restriction which change the LCL ratio to 90% which explains that the mean strength, by itself, has no relevance in the discussion.
The above explanation of the testing shows why you cannot test the actual material sample for the HDPE pipe because there is a 10,000-hour time frame which is extrapolated out to 50 years. And there is a chance that the actual material used to manufacture the pipe could have an actual strength less than the value utilized in the design. But we will most likely never know as we couldn’t prove or disprove the value for 50 years.
There is one more point to make about the testing of the different materials. That point is about accuracy and precision. Accuracy and precision are not the same thing. See Figure 1 below:
Steel/Stainless Steel and DIP for water pipe are tested on the material that is being used for that project. The values used to calculate the wall thickness are therefore precise because you cannot have a material with less than the minimum specified strength and used in the internal pressure calculation. The material is tested on a machine that is regularly calibrated and is therefore accurate.
HDPE material as described above has an element of inaccuracy and element of imprecision due to the necessary method of testing.
This information is also complicated by significant figures. Steel samples are done on a calibrated machine and must exceed the value being used for the design calculation. Since they exceed the value used in the design they are “accurate” to the design value to the last digit used. By using statistical averaging and extrapolation the significant digits are difficult to determine.
Design Controlled by Other Design Constraints
Figure 2 is the from ASCE MOP No. 79 for penstocks. As can be seen there are numerous items that could control the design. Many of these are not considered in AWWA water pipe design methodologies.
For AWWA water pipe, the design control is usually limited to a few design considerations. Internal pressure is most discussed when talking about Safety Factors. There are numerous other restraints that must be evaluated. For buried pipe there is a restraint on the external load that the pipe can handle. In rare cases, an external radial water pressure combined with an internal negative pressure (vacuum) will control the design. these other design considerations can control the design and therefore how “safe” your pipe design might be. Steel Pipe is a flexible pipe and Figure 3 below gives a pictorial example of how the three most common design controls for buried Steel Pipe are different as the conditions change.
The control for the design of the thickness of the pipe can be changed by the grade of material used in the internal pressure design. Or, in some cases by the depth of cover over the top of the pipe. In this case, the type of soil and its placement compaction are very important. Finally, the handling stiffness to protect the cement mortar lining during shipping and installation could be the design control.
Above we have discussed the variables in design when internal pressure controls the design. Now we will look at another major design consideration that is when the pipe is buried.
Buried Pipe Design
Buried pipe design is used to control the deflection and/or collapse of the pipe under the load developed by the soil on top of the pipe. Flexible pipe design per AWWA uses some derivation of the Modified Iowa formula to predict deflection of the pipe. This formula from AWWA M11 is a combination of the pipe stiffness and the stiffness developed by the soil envelope around the pipe.
The formula is:
Δ = Predicted deflection (inch)
Dl = Long term deflection lag factor (unitless)
K = Bedding constant = 0.1 (unitless)
W = Total earth and live load per unit pipe length (pounds/inch of pipe)
r = Radius of the pipe (inch)
EI = Pipe wall stiffness (inch-pounds)
E’ = Modulus of soil reaction (pounds per square inch)
E’ is the stiffness of the soil envelope surrounding the pipe and varies with type of soil, compaction of soil, and depth of cover.2 E’ is not a material property and cannot be uniquely measured. It is based on actual observed test data. The problem is that soil is not consistent. It will vary over the length of a pipeline. This becomes very apparent when looking at the E’ for various different pipe material design manuals. The E’ from AWWA Manual M41 for ductile iron lists an E’ of 700 psi for 90% compacted coarse grain soils no depth variation. The E’ from AWWA M11 for steel pipe lists an E’ of 1,000 psi for the same soil and compaction at 5 feet of cover and E’ of 1,700 psi for 15 to 20 feet of cover and AWWA Manual M55 for HDPE pipe lists an E’ of 2,000 psi for the same soil and compaction with no depth variations.
This formula is usually calculated to a percentage to two decimal places. This shows an answer with very good precision but based on the input it does not have the same accuracy. Remember, soils are quite imprecise.
But, looking at safety factors against external load again, the design of external load is typically based on the damage of a unique element of the pipe. For instance, to protect cement mortar lining in Steel Pipe from excessive cracking, the predicted deflection is limited to 3% or less (not 3.00%), which yields a Safety Factor against incipient fragmenting of the cement mortar lining of approximately 2 or a Safety Factor against collapse of approximately 7. To protect plastic pipe materials from collapse, the predicted deflection is limited to 5% or even as high as 7.5%, which then yields a Safety Factor against pipe collapse of 4.
Finally, in addition when considering external loads, DIP and FRP pipe both look at excessive bending of the pipe wall in order to prevent rupture in that loading scenario. It is difficult to assess a true Safety Factor for this condition, hence we will not go further.
The above discussion brings us back to what is the safety factor of a water pipe designed to AWWA standards and consequently what are the risk evaluations. The engineer must look at both the probability of failure as a characterization of the data according to statistical rules along with the risk of failure, such as diameter or criticality of service, based on observation and experience. A 6” water line and a 60” water line do not have the same risk. An irrigation line and a water line suppling water for critical infrastructure do not have the same risk. Steel pipe has a long history of success in the water industry. The steel material has known and measurable strengths in a wide range of temperatures and the tested material strength is required to be higher than the minimum design strength. It has a history of maintaining that strength for over 100 years. It is conservatively designed for buried conditions and is unparalleled for use in above ground applications with an unlimited flexibility for fitting design. It’s strength to weight ratio makes it the product of choice in beam applications. In all designs for internal pressure, it is the pipe material with a safety factor that is always more than 2:1. For other design controls it is very conservatively designed and has a long history of success. You never have to worry what is “my” real safety factor.
1 DIP adds 100 psi to the working pressure to allow for surge while Steel Pipe utilizes a higher allowable stress when considering the surge condition.
2 Plastic pipe design uses a combination of embedment E’ along with a native soil E’.
- Steel Water Pipe