Toutanji 2001.pdf

Thin-Walled Structures 39 (2001) 153–165
www.elsevier.com/locate/tws
Stress modeling of pipelines strengthened with
advanced composites materials
Houssam Toutanji *
, Sean Dempsey
Department of Civil and Environmental Engineering, University of Alabama in Huntsville, Huntsville,
AL 35899, USA
Received 13 June 2000; received in revised form 26 October 2000; accepted 26 October 2000
Abstract
Fiber reinforced polymer composites (FRPC) have established a strong position as an effec-
tive mean for the repair and rehabilitation of infrastructure. However, the use of FRP in the
repair and rehabilitation of pipelines is a new concept that has the potential to improve the
way we repair pipelines. The purpose of this paper is to discuss the benefits of using FRPC
and to provide stress expressions on the interaction between the different stresses exerted on
pipe walls and the effects of FRPC sheets on the circumferential stresses of damaged pipe
walls. The effects of three different FRPC sheets: Glass FRP (GFRP), Aramid FRP (AFRP),
and Carbon FRP (CFRP) on the performance of pipe walls will be compared analytically.
Results show that carbon fiber composites perform better than glass or aramid in improving the
ultimate internal pressure capacity of pipes, and therefore, significantly enhance the strength,
durability, and corrosive properties.  2001 Elsevier Science Ltd. All rights reserved.
Keywords: Advanced composites; Corrosion; Durability; Fiber reinforced polymer composites
1. Introduction and background
Engineers are faced with the ongoing task of rehabilitating pipelines due to damage
caused by many environmental and load factors that occur. Not only defects in the
original material or in the manufacturing and installation process such as cracks
during loading, shipping, unloading, or storage cause damage to pipes but also, site
conditions that accelerate corrosion such as fluctuating ground water, low soil resis-
* Corresponding author. Tel.: +1-256-824-6370; fax: +1-256-824-6724.
E-mail address: toutanji@cee.uah.edu (H. Toutanji).
0263-8231/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved.
PII: S0263-8231(00)00049-5

154 H. Toutanji, S. Dempsey / Thin-Walled Structures 39 (2001) 153–165
Nomenclature
sf hoop stress due to internal fluid pressure
p internal fluid pressure
r radius of pipe
t thickness of pipe wall
ss bending stress due to soil load
Cd calculation coefficient for earth load
g unit weight of soil backfill (N/mm3
)
Bd width of ditch at the level of top of pipe
E modulus of elasticity of pipe
km bending moment coefficient dependent on the distribution of vertical
load and reaction
kd a deflection coefficient dependent on the distribution of vertical load
and reaction
st bending stress due to traffic load
Ic impact factor
Ct surface impact load coefficient
F wheel load on surface
A effective length of pipe on which load is computed
sm the maximum circumferential tensile stress at the critical sections
d maximum defect depth
k a multiplying constant
T time at exposures
n an exponential constant
tt thickness of pipe wall and FRP sheets
tivity, and high soil alkalinity. By utilizing conventional rehabilitation methods such
as shortcrete, polymer concrete composites, and the trenchless method, concrete pipe-
lines and manhole rehabilitation in the US is estimated between $1 and 1.5 billion,
and natural gas pipeline rehabilitation is estimated at $530 million. With the ever
increasing uncertainty in the reliability of these existing repair methods, there is a
need for the development of a rapid and cost effective method of repairing pipelines
without excavation of overlaying soil and/or replacement of pipe sections. This need
has led to the potential use of advanced composite materials.
Advanced composites are lightweight, they have a high specific strength, they
provide a long corrosive resistance, and have a high level of durability. With an
increased tailorability and rapid installation, advanced composites do not require soil
excavation, removal of existing pipe, and are easy to carry into and applied onto
existing pipe surfaces. Pipe diameter is not excessively decreased and flow capacity
has been known to increase in some cases due to the smooth final coating that causes
less friction than some pipe material such as concrete [1].

155
H. Toutanji, S. Dempsey / Thin-Walled Structures 39 (2001) 153–165
1.1. Composite application schemes
Currently two methods of applying FRP to damaged pipes exist. First, adhesion
of pultruded sections, which is most appropriate for simple shapes and has relatively
even substrate, consists of a prefabricated composite section adhesively bonded to
the pipe surface. Second, wet lay-up, which is most appropriate for complex shapes
or uneven surfaces, or when very high bond strength is required consists of the
addition of composites to existing pipe using in situ processing techniques. Both
methods require a clean dry pipe surface with an average ambient temperature of
65°F (18°C) to apply adhesives to the pipe [1].
Winding machines to wrap hollow bodies with thermoplastic composite tapes have
been on the market for many years, and are used in the production of ultralight
military tanks and in the aerospace industry. The operation is carried out in a work-
shop, by placing the tape on a thin-walled cylinder that rotates around its axis. The
winding is consolidated by heating the tape above the melting temperature of the
matrix resin, usually by flame or laser beam, just before setting it in place. Such a
technique, however, cannot be used to repair gas pipelines for several reasons. The
most obvious reasons are that the hollow body cannot be rotated, the use of free
flames and high-pressure oxygen–hydrogen bottles close to a damaged pipeline are
not allowed for safety reasons, the use of a laser beam would require equipment that
cannot be operated in the field, and the adaptation of the existing hooping machines
would be too complex. To overcome these difficulties, a relatively simple orbiting
winding machine that requires the pipe to be excavated and its operation carried out
in a workshop, was developed. This winding machine can be transported and
mounted on the pipe to be repaired in situ. These machines wind the composite
tape with pretensions of up to 1500 N and delivery speeds of up to 60 m/min. The
circumferential pretensions applied during the winding converts into radial stress.
This in turn counterbalances the internal pressure (Fig. 1) [2].
Fig. 1. Schematic of the repairing (a) and section of the wound pipe (b).

2. Theoretical model and analysis
2.1. Theoretical model
Pressurized underground pipelines must resist both internal and external pressures.
To determine the effect of FRP repairs on a pipe wall, stress expressions will have
to be developed and applied to undamaged pipe, damaged pipe, and FRP reinforced
damaged pipes. This will in turn produce an overall expression for the maximum
circumferential tensile stress at a critical section that contains different loading such
as soil, traffic, and internal pressure. Pipelines that withstand loads such as traffic
loads, are subjected to externally applied stresses that are not uniform on any specific
cross section nor are they uniform along the length of the pipe. In this theoretical
model, the support and loading variations along a run of pipe will be assumed to
be indistinguishable at a specific cross section where the longitudinal load variation
will be ignored. It will also be assumed that the pipeline will remain at a constant and
uniform temperature with its cross section in a state of plain strain (i.e. longitudinal
movements or deformations being ignored) [3].
Pipelines are not only faced with internal and external pressures, but are also
subjected to internal and external corrosion. With either a uniform or localized nat-
ure, corrosion affects the pipe wall thickness. Literature review shows that one diffi-
cult aspect of repair of pipe walls is the problem of uncertainty in predicting the
location rate of corrosion [3]. This problem should be of consideration for both
proper design practices and for making decisions about pipeline maintenance and
repair strategies.
2.2. Wall stresses in underground pressurized undamaged pipes
The effects of stresses exerted by external soil pressure and by internal fluid press-
ure on underground-pressurized pipelines should be considered. Internal pressure
produces uniform circumferential tension across the wall if the wall thickness is
comparatively small and the density of the fluid carried in the pipeline is small
relative to the fluid pressure. Bending stresses both in the longitudinal and circumfer-
ential directions are produced by external loads. This circumferential stress is the
main focus since the pipe is assumed uniformly loaded and supported along its
length. Circumferential bending stresses are usually less critical on the sides of a
pipe where they are of higher importance on the top and bottom of the pipe [4]. If
the pipe wall stresses remain within the elastic range of the material, the circumfer-
ential bending stresses in the pipe wall due to the external loads are assumed to be
algebraically additive to the tensile circumferential (i.e. hoop) stress produced by the
internal pressure.
The circumferential stress due to internal pressure can be estimated using the
following expression
sf⫽
pr
t
(1)

157
where it is assumed that t¿r and where sf=hoop stress due to internal fluid pressure;
p=internal fluid pressure; r=radius of pipe; and t=thickness of pipe wall.
The bending stress in the circumferential direction produced in the pipe wall by
the external soil loading can be estimated using Eq. (2) [5]
ss⫽
6kmCdgB2
dEtr
Et3
+24kdpr3 (2)
where ss=bending stress due to soil load (MPa); Cd=calculation coefficient for earth
load; g=unit weight of soil backfill (N/mm3
); Bd=width of ditch at the level of top
of pipe (m); E=modulus of elasticity of pipe (MPa); km=bending moment coefficient
dependent on the distribution of vertical load and reaction (MPa); and kd=a deflection
coefficient dependent on the distribution of vertical load and reaction.
When an external traffic load such as roadway, railway, or airplane traffic exist,
the resulting circumferential bending stresses produced in the pipe wall may be esti-
mate from
st⫽
1
A
6kmIcCtFEtr
(Et3
+24kdPr3
)
(3)
where st=bending stress due to traffic load (MPa); Ic=impact factor; Ct=surface
impact load coefficient; F=wheel load on surface (N); and A=effective length of pipe
on which load is computed (m).
The maximum circumferential tensile stress sm at the critical sections can be
expressed by the following if the pipe wall remains in the elastic range under load
sm⫽sf⫹ss⫹st (4)
sm⫽
pr
t
⫹
6kmCdgB2
dEtr
Et3
+24kdpr3
⫹
6kmIcCtFEtr
A(Et3
+24kdPr3
)
(5)
2.3. Wall stresses in underground pressurized damaged pipes
Internal corrosion is dependent on the pipes internal fluid properties and their
interaction with the pipes own material. This interaction between the fluid properties
and pipe material may cause potential and/or chemical changes as the fluid flows
through the pipeline. Evidence shows that internally uniform corrosion is less likely
to occur, where localized corrosion on the surrounding exterior surface is more likely.
External corrosion is dependent on the localized condition, including the soil type,
rate of oxygen depletion and replenishment, soil water or moisture and its movement,
and presence and effectiveness of any corrosion protection measures. The loss of
pipe wall thickness due to corrosion may be relatively uniform in extent or localized,
but does not occur at a constant rate over the design life of the pipe. Protective
properties of the corrosion product improve after the initial corrosive period. This
initial period of wall thickness corrosion is due to the corrosion products that are

formed on the pipe surface being porous and their protective properties being poor.
The corrosion rates after this initial period gradually decreases and in some cases
stabilizes. Thus, with time the loss of wall thickness increases. Developing
expressions with a function of time in a general corrosive case, whether this means
weight loss, deepest pit or localized depth, or average pit or localized depth, can be
modeled empirically by a power law [6].
d⫽kTn
(6)
This law should be understood as an engineering viewpoint rather than a scientific
viewpoint where d=maximum defect depth; k=a multiplying constant; T=time at
exposures; and n=an exponential constant. For soil conditions, corrosion of steel, k
ranges from 0.1 to 0.5 and n may vary from 0.4 to 1.2 [6].
Applying this power law to the previous circumferential stress Eqs. (1)–(3), can
be estimated using the following expressions. The circumferential stress equation
due to internal pressure then becomes the following expression when applied to a
damaged pipe
sf⫽
pr
t−d
(7)
The bending stress in the circumferential direction produced in the pipe wall by
the external soil loading is then expressed by
ss⫽
6kmCdgB2
dE(t−d)r
E(t−d)3
+24kdpr3
(8)
Therefore, the circumferential bending stress produced in the pipe wall with an
external traffic load is expressed by
st⫽
6kmIcCtFE(t−d)r
A(E(t−d)3
+24kdpr3
)
(9)
2.4. Wall stresses in underground pressurized frp reinforced damaged steel pipes
Applying the properties, equations, and theory behind the wall stresses in under-
ground pressurized damaged pipes, expressions are developed to include the addition
of fiber reinforced polymer composites (FRP) for repair and rehabilitation of pipe-
lines. Using FRP to repair and rehabilitate damaged pipe causes t (thickness of pipe)
to change. The following expression takes into consideration FRP addition and is
substituted for t as tt [7].

159
Fig. 2. Circumferential stresses due to soil load, traffic load, and internal pressure in pipe without defects.
tt⫽(ts⫺d)冋1⫹
EFRPtFRP
Es(ts−d)册 (11)
Thus, with the consideration of FRP addition to the pipe wall thickness, the follow-
ing expressions are developed for the circumferential stress due to internal pressure
and the bending stress in the circumferential direction produced in the pipe wall by
the external soil loading
sf⫽
pr
(ts−d)冋1+
EFRPtFRP
Es(ts−d)册
(12)
ss⫽
6kmCdgB2
dEsttr
Et3
t +24kdpr3 (13)

Fig. 3. Circumferential stresses due to soil load, traffic load, and internal pressure in damaged pipes.
The circumferential bending stress produced in the pipe wall with an external traffic
load with the addition to the FRP sheets
st⫽
6kmIcCtFEttr
A(Et3
t +24kdpr3
)
where tt⫽(ts⫺d)⫹ntFRP (14)
2.5. Example application and analysis
The purpose of this example application is to illustrate that the basis of this model
is realistic and solid. To generate the circumferential stress analytical curves, it is
necessary to know the internal fluid pressure, the pipe radius, the various constants,
the elastic modulus, and the thickness of fiber sheets. This and other necessary data
to use in conjunction to the developed model are provided in Tables 1 and 2. Table
1 summarizes the constraints and mechanical properties of a given length of pipe to

161
Fig. 4. Circumferential stresses due to soil load, traffic load, and internal pressure in CFRP repaired
damaged pipes.
develop plotted curves stresses due to soil, traffic, and internal pressure. Table 2
shows the mechanical properties of FRP sheets.
The analytical results obtained from the model are shown in Figs. 2–5. Fig. 2
shows the comparison of circumferential stresses due to soil load, traffic load, and
internal pressure in an undamaged pipe, Fig. 3 shows the same comparisons but in
a damaged pipe. As expected, a pipe without defects withstand higher stresses due
to soil and traffic loads and lower stresses due to internal pressure than a pipe with
defects. For example, in the pipe without defect, the circumferential stress due to
internal pressure is 182.4 MPa with an internal pressure of 4 MPa, whereas in the
damaged pipe, the stresses are 304 and 4 MPa respectively. The circumferential
stress due to traffic in the pipe without defects at an internal pressure of 4 MPa is
112.6 MPa, whereas in the damaged pipe the stress is 77.7 MPa.
The question is “what benefits do FRP composite sheets provide in a pipe circum-
ferential stresses?” and if they do provide benefit “what type of FRP sheet (CFRP,
GFRP, or AFRP) has a greater ultimate internal pressure?” Fig. 4 shows, as an
example, the circumferential stresses of the CFRP repaired damaged pipe due to the

Fig. 5. Comparison between circumferential stress and internal pressure in pipe without defect, pipe
with defect, and (GFRP, CFRP, and AFRP) repaired damaged pipe.
soil and traffic loads as well as to internal pressure. The curve shows a significant
increase in the stresses due to soil and traffic loads and a decrease in the stress due
to internal pressure when compared to Fig. 3.
Fig. 5 shows a comparison between the maximum circumferential stress, sm, (
sf+ss+st) and internal pressure in pipe without defect, pipe with defect, and GFRP,
CFRP, and AFRP repaired damaged pipe. The curve shows the benefits that FRP
sheets provide for the pipe strength with CFRP. Fig. 6 compares the undamaged
pipe, damaged pipe, and pipes repaired with the three different FRP sheets, to their
ultimate internal pressure (MPa). Again it is clear that the pipe repaired with carbon
fiber sheets has a higher stress threshold than those repaired with glass or aramid fib-
ers.

163
Table 1
Mechanical properties and constraints of a given length of pipe
Symbol Description Value
r Pipe radius, (mm) 228
t Pipe wall thickness, (mm) 5
Km Bending moment coefficient 0.235
Cd Calculation coefficient for earth load 1.32
g Unit Weight of soil, (N/mm2
) 18.85×10−6
Bd Width of ditch at the level of top of pipe, (mm) 762
E Module elasticity of pipe, (N/mm2
) 200,000
kd Deflection coefficient 0.108
Ic Impact factor 1.5
Ct Surface load coefficient 0.12
F Wheel load on surface, (N) 267,000
d Maximum defect depth, (mm) 2
A Effective length of pipe, (mm) 914
Table 2
Mechanical properties of FRP sheets
Specimens Thickness, t (mm) Hoop strength (MPa) Modulus of elasticity
(GPa)
Glass 0.118 1500 74
Aramid 0.193 2100 120
Carbon 0.165 300 400
3. Conclusion
This paper concentrates on establishing fiber reinforced polymer composites as an
effective mean for the repair and rehabilitation of pipelines. This objective was
reached by developing a theoretical model with stress expressions and circumfer-
ential stress curves. The stress expressions were developed to study the interaction
between the different stresses exerted on pipe walls and the effects of FRP sheets
on the circumferential tensile stress of damaged pipe walls. The stress curves dis-
played the maximum circumferential tensile stresses due to soil loads, traffic loads
and the pipes internal pressure. These curves were analyzed and their results showed
that carbon fiber sheet provides a better performance than glass or aramid in improv-
ing the ultimate internal pressure capacity of pipes. This study was focused on the
application of fiber reinforced polymer on steel pipes. Steel may corrode in the pres-
ence of carbon fiber material. However, earlier studies have not shown any visible
degradation when polymeric material contacts steel. Thus, before applying FRP on
damaged steel pipe walls, the walls must be free of corrosion and well coated to
prevent the contact between FRP and the steel.

Fig. 6. Comparison between pipe status and ultimate internal pressure in pipe without defect, pipe with
defect, and (GFRP, CFRP, and AFRP) repaired damaged pipes.
Acknowledgements
The authors would like to acknowledge the financial support of the National
Science Foundation CAREER Grant No. CMS-9796326.
References
[1] Fortner B. Main line mending. Civil Engng Mag 1999;July:42–5.
[2] Frassine R. Long-term performance of a polymer composite repair system for gas pipelines. In:
Advances in Polymer Technology, vol. 16, no. 1. New York: John Wiley and Sons Inc, 1997:33–43.
[3] Ahammed M, Melchers RE. Reliability of underground pipelines subject to corrosion. ASCE J Trans-
port Engng 1994;120(6):989–1002.
[4] Stephenson D. Pipeline design for water engineers. Amsterdam: Elsevier, 1976.
[5] Spangler MG, Handy RL. Soil engineering, 4th ed. New York: Harper and Row, 1982.
[6] Kucera V, Mattsson E. Atmospheric corrosion. In: Mansfield F, editor. Proceedings: Corrosion Mech-
anics. New York: Marcel Dekker Inc, 1987.

165
[7] Toutanji HA. Stress–strain characteristics of concrete columns externally confined with advanced fiber
composite sheets. ACI J Mat 1999;96(3):397–404.

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