windows-1256__bending stresses from external loading on buried pipe

7/27/2019 Windows-1256__bending Stresses From External Loading on Buried Pipe

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BENDING STRESSES FROM EXTERNAL LOADING

ON BURIED PIPE.

By Lawrence Matta, Ph.D., P.E., C.F.E.I. |June 2011 Vol. 238 No. 6

Figure 1: Heavy equipment adding vertical loading to a pipe during repair

operations.

The pipeline industry has long been interested in evaluating the effects of

external loading due to fill and surface loads, such as excavation

equipment, on buried pipes. This interest stems not only from the initial

design of pipeline systems, but also from the need to evaluate changing

loading conditions over the life of the pipeline. Variations in loading

conditions can arise due to the construction of roads and railroads over the

pipeline and one-time events in which, for example, heavy equipment must

cross the pipeline.

The pipeline may also suffer corrosion or damage that requires excavation

and repair. Heavy excavation equipment is often placed directly over a

pipeline during repair work, as shown in Figure 1. Safety while excavating

pressurized pipelines is a serious concern for operating companies. Both
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gas and liquid pipeline companies often specify reduced pressures while

excavating and repairing in-service pipelines.

A common issue is determining what pressures are safe during excavation

and repair procedures. Design codes, regulations and industry publicationsoffer little guidance on what factors should be considered to determine

safe pressures during in-service excavation activities. Surface-loading

conditions and soil overburden result in stresses that should be evaluated

in determining safe excavation pressures near areas of damage or

corrosion. Large concentrated loads, like truck wheel loads, are of primary

concern.

The ALA Guideline for the Design of Buried Steel Pipe presents design

provisions for use in evaluating the integrity of buried pipelines for a range

of applied loads. (ref: Guideline for the Design of Buried Steel Pipe,

American Lifelines Alliance/ASCE/FEMA, 2001.) Its methodology offers an

approach for evaluating the fill and surface-loading effects on buried

pipelines. This approach utilizes the deflection of the pipe, calculated using

a version of the classic Iowa Formula, in estimating the wall-bending

stresses in the pipe. The wall-bending stress is then combined with other

calculated stresses to calculate the overall stress in the pipe.


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Figure 2: Schematic of the deflection of a buried pipe due to verticalloading.

Smith and Watkins pointed out that the Iowa Formula was derived to

predict the ring deflection of flexible culverts, and not as a design equation

to determine the wall thicknesses of pipes. (ref: Smith, G., and Watkins, R.,

The Iowa Formula: Its Use and Misuse when Designing Flexible Pipe,

Proc. of Pipelines 2004 Intl Conf., ASCE, 2004.) It is often used to

estimate wall stresses, however, and determination of the total stress is

important to safety calculations. In this article, the wall-bending stress

calculation and some quirks in its behavior will be discussed.

Pipe materials are classified as being either flexible or rigid. A flexible pipe

has been defined as being able to deflect at least 2% without structural

distress. (ref: Moser, A.P. and Folkman, S., Buried Pipe Design, 3rd Ed.,

McGraw Hill, 2008.) Materials such as steel and most plastics are

considered flexible pipe. Concrete and clay pipes are considered rigid. The

Iowa Formula was developed for use with flexible pipes.

Flexible pipes derive much of their load-carrying capacity from pressure

induced at the sides of the pipe as they deform horizontally outward under

vertical loading. Analysis of the effect of fill weight and surface loading is

therefore a problem of interaction between the pipe and the soil. The Iowa
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Formula describes the interaction of the pipe and soil and the deflection

that results from vertical loading.

Figure 3: Effect of wall thickness ratio on the normalized wall-bending

stress

In his research of the performance of buried flexible pipes, M. G. Spangler

observed that, compared to rigid pipes, flexible pipes provide little inherent

stiffness and perform poorly in 3-edge bearing tests. However, flexible

pipes performed better than predicted by these tests when buried. He

reasoned that the source of strength of the flexible pipe is not the pipe

itself, but is primarily the soil beside the pipe. (ref: Insight into Pipe

Deflection Predictions: An Interview with M.G. Spangler, Sewer Sense No.

17, National Clay Pipe Association, 2004.)

The ability of buried flexible pipe to support vertical loads is based on

support from the soil around the pipe and the restraining force induced onthe sides of the pipe counter to the horizontal deflection. Coupling these

concepts with ring-deflection theory led to the development of the Iowa

Formula in 1941. (ref: Spangler, M.G., The Structural Design of Flexible

Pipe Culverts, Bulletin 153. Iowa State College, Ames, Iowa, 1941.)
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The Iowa Formula was developed to estimate the distortion of a buried

flexible pipe under vertical loading. A sketch of a deflected pipe is shown in

Figure 2. The formula for the deflection can be written as:

The formula has two terms in the denominator, the first of which depends

on the pipe stiffness and the second on the modulus of soil reaction, E.

For thin-walled flexible pipes, the modulus of soil-resistance term tends to

dominate the equation. This term defines the resistance of the soil to

deformation. Unfortunately, E is not a true property of the soil, but instead

depends upon a number of factors including compaction, texture, and fill

depth. E is normally estimated from tables or by testing.

It can be shown that the maximum through-wall circumferential bending

stress can be determined from Eq. 2:
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This stress equation is what is used in the ALA guidelines to account for

the stresses due to ovality of a buried pipe.

Along with the Iowa Formula, Spangler also derived a formula for

determining the wall-bending stress in a vertically loaded pipe with internalpressure. This is often referred to as the Spangler Stress Formula. In this

case, however, he did not include a term to represent the soil support that

resists distortion of the pipe. Warman et al. derived a combined equation

that includes the effects of lateral soil restraint and the distortion-resisting

effects of internal pressure. Inclusion of the pressure term removes some

of the conservatism of the Iowa equation when applied to pressurized

pipes. The wall-bending stress term proposed by Warman et al. can be

written as:

Consider the wall-bending stress without internal pressure, as shown in

Eq. 3. If the ratio of the wall thickness to pipe diameter is set to zero, the

wall-bending stress goes to zero. The wall-bending stress also approaches

zero as the wall thickness ratio increases. A graph showing the calculated

wall stress as a function of the wall thickness ratio is shown in Figure 3

using 500 psi for the value of E. Note that the magnitude of the stress

depends on other terms, but the shape of the curve is determined by the

ratio of E to E.

Again using a value of 500 psi for E and the Youngs modulus of steel

(2.9x106 psi), the maximum stress occurs at t/D of about 0.01. This

roughly corresponds to a 48-inch pipe with a 0.5 inch wall thickness. At
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thicknesses greater than the critical thickness, the stress equation predicts

that the wall stress gets lower as the wall thickness is increased. However,

for thickness ratios below the critical value, using a thicker wall results in a

higher wall-bending stress. This is interesting, in that the thinner the wall is

made, the lower the stress becomes.

Looking at the Iowa Formula in Eq. 1, it can be seen that reducing the wall

thickness to zero results in a finite value of deflection. At this point, the

wall-bending stress is zero, so the soil is carrying the entire vertical load. It

appears that for gravity fed flows, that a hole in the soil does not need a

pipe at all! Unfortunately, there are reasons that we cant get rid of the

pipe. The Iowa Formula assumed that the pipe transfers the vertical load to

the side walls, so without the pipe, the formula doesnt work. Also, ignoringthe wall-bending stress, the vertical load itself will cause the pipe to fail due

to buckling or crushing if the walls get too thin.

Figure 4: Example minimum wall thickness ratio calculation using the wall-

bending stress formula without a pressure term.


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A maximum value of the circumferential stress can be determined by

adding the hoop stress and the wall-bending stress. If the circumferential

stress and its Poisson contribution to the longitudinal stress are used to

calculate the Von Mises stress, the resulting equations can be solved to

determine the minimum acceptable wall thickness ratio as a function of

internal pipe pressure.

As an example, consider a steel pipe 48 inches in diameter. Assume some

combination of burial depth, lag factor, and live-loading to achieve a

vertical pressure at the pipe of about 13 psi. This is a high value of vertical

loading, but it was chosen to illustrate peculiar behavior of the wall-bending

stress equation. In this example, we also assume a modulus of soil

reaction E of 500 psi and constants based on a bedding angle of 30.Using the wall-bending stress equation given in Eq. 3, the minimum

required wall thickness as a function of internal pressure was calculated.

The results are graphed in Figure 4. Wall thickness ratios above and to the

left of the curve are acceptable, below and to the right are beyond the

acceptable stress limit (in this case taken to be 0.6 times the ultimate

tensile strength).

The results show that, for pressures between roughly 160-180 psi internal

pressure, an S-curve occurs where a range of wall thicknesses are not

acceptable while thinner walls are. In our example, at 170 psi internal

pressure, a wall thickness ratio of 0.85% is not acceptable, but a wall

thickness ratio of 0.45% is okay. Based on the pipe diameter of 48 inches,

these correspond to wall thicknesses of 0.408 inches and 0.216 inches,

respectively. This behavior certainly appears unrealistic.

Next we repeat the example, but using the wall-bending stress determined

with Eq. 4, which incorporates the pressure term. Again, the pipe has adiameter of 48 inches and a vertical-loading pressure of 13 psi.

Figure 5 shows the results based on the Iowa Formula with the pressure

term included and the previous results without the pressure term. The

minimum required wall thickness calculated using the hoop stress only

(neglecting the wall-bending stress entirely) is also shown for comparison.


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The results for the calculation using the Iowa Formula with the pressure

term included do not show the strange behavior observed when the

pressure term is not included.

Figure 5: Comparison of minimum wall thickness ratio calculations using

several approaches.

Comparing the results shows that not including the pressure effects in the

wall-bending stress equation leads to calculated wall thicknesses that

become extremely conservative as pressure increases. On the other hand,

comparing the results based on the Iowa Formula with the pressure term

included to the results for hoop stress alone shows that the effect of the

wall-bending stress is not insignificant, and the results become

increasingly different as pressure increases. This indicates that neglecting

the effects of wall-bending stress could result in non-conservative stresscalculations and wall thickness values.

The chart in Figure 5 also shows the calculated wall thickness ratio at the

buckling limit with no internal pressure. This is a performance limit based

on the pipe walls buckling under the vertical load. Since internal pressure


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puts the walls into tension rather than compression, this effect will be

observed for unpressurized pipes or pipes under vacuum. However, since

all pipelines will be unpressurized at some time, this performance limit

must be satisfied for pipes that normally operate pressurized as well.

The buckling limit wall thickness ratio for the example pipe is about 0.48%.

Therefore, for any design pressure less than about 360 psi, the buckling

limit will determine the minimum required wall thickness for the example

pipe. Note that the buckling limit is a function of the vertical load pressure,

which was specifically chosen in this example to be high.

Conclusions

Smith and Watkins pointed out that the Iowa Formula was derived to

predict the ring deflection of flexible culverts, and not as a design equation

to determine the wall thicknesses of pipes. It is, however, widely used in

stress calculations, and is part of the methodology used to predict the

stresses in pipelines due to vertical loading in the ALA Guideline for the

Design of Buried Steel Pipe. The use of the Iowa Formula to calculate the

wall-bending stresses in a pressurized buried pipe is generally

unrealistically conservative, and can, under certain circumstances, lead to

results that behave strangely, particularly for high vertical loading.

Inclusion of a pressure-stiffening term in the stress equation appears to

improve the behavior and remove some of the excessive conservatism

inherent in the Iowa Formula. At high vertical-loading pressures and low

internal pressures, the wall buckling limit may be the dominant factor in the

minimum allowable wall thickness.

Author

Lawrence Matta, Ph.D., is a staff consultant at Stress Engineering,Houston. He received his Ph.D. from Georgia Tech. He is registered in

Texas as a Professional Engineer and is a certified fire and explosion

investigator (CFEI). His experience includes investigation of pipeline

failures and the resulting explosions and fires. He can be reached

[email protected], 281-955-2900.
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windows-1256__bending stresses from external loading on buried pipe

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