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Stress corrosion failure of large diameter pressure pipelines of prestressed concrete
Engineering Failure Analysis 8 (2001) 245±261
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Stress corrosion failure of large diameter pressure pipelines of prestressed concrete A. Valiente Departamento de Ciencia de Materiales, Escuela de Ingenieros de Caminos, Canales y Puertos, Universidad PoliteÂcnica de Madrid, Ciudad Universitaria, E-28040 Madrid, Spain Received 21 February 2000; accepted 3 March 2000
Abstract The failure of a 1.5 m diameter prestressed concrete line for water supply was examined. The water pressure opened a hole of 0.5 m2 in the pipe wall by breaking the concrete into fragments and by tensile severing of a number of coils of the wire winding. Flexural and tensile testing of samples of the broken materials showed no damage to the concrete, but showed signi®cant losses of strength and ductility in the prestressing steel wire. The SEM analysis of the external and fracture surfaces of the circumferential wires revealed shallow cracking and corroded areas as expected from a stress corrosion cracking process. The failure analysis presented in this paper shows that such a process was able to exhaust the damage tolerance of the aected tube until the pipeline burst under the work pressures. 7 2001 Elsevier Science Ltd. All rights reserved. Keywords: Damage tolerance; Pipeline failures; Prestressing; Stress corrosion cracking
1. Introduction The prestressing technique is a major ®nding of civil engineering. By this technique, the surplus tensile strength of a material (prestressing steel) is devoted to resisting tensile loads transferred from another material of poor tensile strength (concrete). This composite material requires steels with very high tensile strength, a feature that often entails the risk of low tenacity and sensitivity to processes able to produce localized cracking. As a consequence, the prestressing steel is protected by using non-aggressive concrete constituents and by isolating the steel from the environment by means of an impermeable coating. These protective measures are easy to apply to the structural members of prestressed concrete made in a
E-mail address: [email protected] (A. Valiente). 1350-6307/01/$ - see front matter 7 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 6 3 0 7 ( 0 0 ) 0 0 0 1 0 - 8
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factory, but they must be complemented with careful handling during construction to avoid damage that might cancel out the protection. In accordance with the potential vulnerability of the prestressing steel, the prestressed concrete might be expected to have low damage tolerance, but experience denies this. In practice, a good level of damage tolerance is exhibited by the prestressed concrete consisting of prestressing steel wires embedded in concrete and joined to it throughout their length. This damage tolerance allows a structural member to go on working without failing even though a number of fractures may have occurred in the prestressing steel. The origin of this damage tolerance is the fact that the prestressing force exerted by a wire does not necessarily vanish along all the wire if it breaks, and the remaining wire may be enough to avoid structural failure. Failure does not occur unless damage tolerance be exhausted. Accordingly, the failure analysis presented in this paper is envisaged with the aid of a quantitative assessment of damage tolerance in prestressed concrete. The paper documents and analyzes the failure that arose in a large diameter pressure pipeline of prestressed concrete, a structure whose safety depends on the integrity of large amounts of continuous prestressing steel wire, hundreds of meters per meter of pipeline. Prestressed concrete is widely used in pipelines because it competes economically with steel pipes. The design rules of these pipes are soundly stated [1], but to the author's knowledge no evaluation of damage tolerance as described above is available. Prestressed concrete pipes are made by winding a pretensioned wire onto a concrete core, previously cast, steam cured, and often prestressed longitudinally by straight wires embedded in the core wall along the middle surface. After winding, a concrete or mortar coating is deposited on the core to embed the circumferential wire inside the wall pipe and to increase the thickness of the pipe up to its design value. With the subsequent shrinkage and creep of the core, the prestressing wire loses a proportion of its tensile stress as a part of the prestressing force is transferred to the coating. Eventually, the pipe is load tested and is ready to be put into service. Regarding the mechanical behaviour of the pipe, the circumferential wire works as a thin layer of steel inserted in the concrete of the pipe wall. The thickness of the layer is so small that its contribution to the rigidity of the pipe is insigni®cant, and therefore the external loads are taken almost entirely by the concrete of the core and the coating, with hardly any change in the stress of the circumferential wire. The basic function of this is to produce an initial compressive stress in the concrete, high enough to avoid tensile stresses when adding the stresses due to external loads. The examined failure involves successive fractures of the circumferential prestressing wire as a result of a stress corrosion cracking process. The precautions to assure the integrity of the pipeline were not enough to prevent stress corrosion cracking in all the pipes, and the failure of the pipeline occurred after six years of service. The failed pipe was replaced and no new failure has occurred since then. The evaluation of damage tolerance is based on an estimation of the number of coils of circumferential wire that can become inoperative by stress corrosion cracking before the external loads produce the complete failure of the pipe. 2. Failure description and data design The failure occurred in a 5 km long pressure pipeline for water supply that had been in operation for six years. The pipeline was buried, and the failure was localized in a pipe of 1.5 m inner diameter, 10.5 cm thickness and 5.1 m length. The pipe was composed of a concrete core 8 cm thick, a 5 mm diameter circumferential prestressing wire with a coil spacing of 3.1 cm, and a mortar coating 2.5 cm thick. The pipe was longitudinally prestressed on the middle surface of the wall by 30 prestressing wires of 5 mm diameter uniformly distributed (Fig. 1). When the back®ll was removed and the pipe exposed, a roughly rectangular area of the pipe
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Fig. 1. Geometrical features of the failed pipe.
wall, 1 m long and 0.5 m high, was found to be broken into fragments. This area was just at the end of the pipe forming the spigot joined to the socket of the next pipe (Fig. 2). The pipeline was designed with no surge tank to attenuate the wave pressure produced by the opening and closing of the control valves, given that the maximum pressure due to the water hammer was about 1.5 times the service pressure of 0.5 MPa and coincided with the ®eld proof pressure. The failure of the pipeline can be attributed without doubt to this maximum transient pressure, since it was detected just after operating the valves. The material properties provided by the manufacturer of the prestressed concrete pipes and used as design data are given in Table 1.
Fig. 2. The failed pipe showing the burst area of the wall.
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Table 1 Design material properties of the failed pipe
Elastic modulus Poisson's coecient Yield strength Tensile strength Maximum uniform elongation
Prestressing steel
Concrete
Mortar
Es = 210 GPa ± sY s 1700 MPa sTs 1800 MPa > 2%
E = 35 GPa n 0:2 ± sTc 3:5 MPa ±
E = 35 GPa n 0:2 ± ± ±
3. Material failure analysis Field samples collected from the failed pipe and supplied for testing and observation in the laboratory consisted of fragments of the concrete core detached from the broken area and pieces of prestressing steel cut from the coils of the same area. Most of these coils were found broken, and some of the steel samples collected for the laboratory included the fracture surfaces, and special care was taken to preserve them when removing the coils. After cleaning, the broken steel samples were examined under a low magni®cation microscope and two types of fractures were observed (Fig. 3). The features of the ®rst (Fig. 3a) are typical of the ductile fracture in cold drawing prestressing steel wire: a cup and cone rupture resulting from an advanced necking process. Apart from this, there is no appreciable cracking on the lateral surface of the wire. In contrast, the second type of sample shows the signs of ¯aw-induced fracture common in these steels: an irregular fracture propagation path in the absence of necking. The surface ¯aw whose propagation typically causes this type of fracture in cold drawing prestressing steel wires [2] could not be identi®ed as a feature dierent from the rest of the fracture due to the highly corroded condition of the fracture surfaces when found. Such strong degradation means that the coils fractured in this way broke well before the ®nal failure of the pipeline. On the contrary, a better condition was exhibited by the the fracture surfaces of the coils failed in a ductile way, which means that they had broken as a consequence of the failure of the pipeline.
Fig. 3. The two types of fractures of the prestressing wire observed at the failure site.
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In prestressed concrete made with controlled materials and subjected to the design loads, a damage process involving ¯aw nucleation and ductility loss in the prestressing steel can only be attributed to unexpected fatigue and/or stress corrosion. In this case the loading history allows fatigue to be disregarded, so a stress corrosion cracking process appeared as the most probable explanation of the failure of a number of coils before that of the pipe. The existence of the shallow cracking observed on the lateral surface of these coils, near the broken ends (Fig. 3b), also supports this explanation. In accordance with these data, mechanical testing of the samples was conducted in the laboratory in order to detect any damage in the materials of the pipe by comparing the tensile behaviour experimentally determined just after the failure of the pipe with that assumed at the design stage. Prismatic specimens of 4 cm 4 cm 14 cm having the longer edge parallel to the hoop direction of the pipe were machined from the largest fragments of concrete available. These specimens were tested up to fracture by three point bending and exhibited no anomalous behaviour, failing at a tensile stress of about 5 MPa, as calculated from the bending moment on the basis of the elementary beam theory. This value agrees with the design tensile stress in Table 1. The wire samples were long enough to provide standard prestressing steel specimens, so they were tensile tested without diculty. The entire stress±strain curve was registered over a gauge length of 5 cm by attaching an extensometer to each specimen. The results of the three tests performed are shown in Fig. 4 and largely dier from that of the concrete, as regards the existence of damage. Only one of the specimens exhibited no sign of damage when compared with the design data, since the measured yield strength, tensile strength and maximum uniform elongation are practically the same as those of the manufacturer (Table 1). In the other two specimens these values are lower, specially the maximum uniform elongation. This is not due to divergent stress±strain curves, but to a premature fracture that occurred when plastic deformation had hardly begun. As already mentioned, in prestressing steel wire
Fig. 4. Stress±strain curves of the prestressing wire samples tested in the laboratory.
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[2] such brittle behaviour involves the existence of a surface ¯aw whose size surpasses the damage tolerance of this material. The fracture surfaces of the specimens were in agreement with both the brittle and the ductile behaviour indicated by the stress±strain curves, and con®rmed the existence of surface cracks able to trigger the brittle fracture. The broken ends of the specimens with maximum and minimum ductility (as measured by the maximum uniform elongation) can be seen in Fig. 5. A necking process resulting in a cup and cone fracture produced the failure of the ductile specimen, whereas that of the brittle one was due to a fast propagation fracture prior to any sign of necking. These fractures accurately reproduced that of Fig. 3, namely, that found at the failure site on the wire coils that circumferentially prestressed the burst part of the pipe wall. When the brittle specimens were observed by scanning electron microscopy (Fig. 6), it became apparent that the fracture was triggered by a surface crack developed in the wire before the test. The black colour taken on by the faces of the crack indicated a very long corrosion process in deaerated environment [3] and provided a de®nite proof of the cracking of the prestressing wire before the failure of the pipeline. To summarize the failure analysis of the materials, no damage was found in the concrete, but the cold drawing steel wire for the circumferential prestressing of the failed pipe showed clear signs of stress corrosion cracking. The nucleation and growth of surface cracks on the wire transformed its tensile behaviour from ductile to brittle and could decrease its mechanical strength until causing the failure of some coils under the design stresses. This is not only supported by the ®nding of coils broken prior to the failure of the pipeline, but also by the laboratory ®ndings. As demonstrated by the mechanical testing, the size attained by these cracks was able to produce the brittle fracture of the wire under stresses below the yield strength of the wire. Indeed, an LEFM analysis such as that performed in [4] indicates that a crack only 20% deeper than that of Fig. 6 would have suced to exhaust the strength of the circumferential prestressing wire under normal service conditions. This prediction is based on the estimation of the fracture toughness of the circumferential wire from the failure stress (1400 MPa) and
Fig. 5. Ductile and brittle fractures of the prestressing wire obtained in the tests.
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the crack depth (1.4 mm) of the specimen of Fig. 6. According to this fracture toughness, a crack 1.7 mm deep would cause the fracture of the wire under the work stress of 1080 MPa. 4. Structural failure analysis The failure of a prestressing concrete pipe by the design pressure requires more than one or two inoperative coils, since in practice these pipes are not so vulnerable as this. On the other hand, the fracture of many coils of the burst area was a ductile, not a ¯aw-induced failure, so they failed simultaneously with the concrete core when the two materials were overloaded up to the tensile strength by the applied pressure. Therefore, the number of coils made inoperative by stress corrosion before ®nal failure was much lower than the number contained in the burst area (about 30, according to the coil spacing and the dimensions of the area). From these two limits, it can be stated that a number of inoperative coils ranging between 3 and 10 produced the failure of the pipe under service loading. It remains to be shown that such a ®gure was able to exhaust the damage tolerance of the pipe. To evaluate the damage tolerance of the pipe, a quantitative assessment is required of the stresses due to the loss of the prestressing load resulting from the inoperative coils. The structural design hypothesis is the basis of the assessment. Hence, it is assumed that the three materials (prestressing steel, concrete and mortar) are Hookean, their elastic properties as given in Table 1, and that any length of the pipe remains unchanged when buried. As a consequence of the ®rst assumption, the superposition principle applies for stresses, and accordingly those produced by the loss of prestressing load may be added to
Fig. 6. SEM image of a crack developed in the prestressing wire before the failure.
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that produced by the manufacturing prestressing load, by the permanent external loads (weights and soil forces) and by the water pressure, all of which are available as design data. However, the disappearance of the prestressing load in a short length of pipe does not produce a uniform loading along the pipe, and the corresponding stresses cannot be found as in the design, namely, by assimilating the pipe to be an elastic multilayered ring (see, for instance, [5]). When undamaged, the prestressing circumferential wire produces a load equivalent to a uniform inward pressure extended over all the pipe, so that a number of contiguous inoperative coils would have the same eect as an equal outward pressure acting on the aected length of pipe and superposed on the prestressing load of the entire circumferential wire, on the permanent loads, and on the water pressure. The stresses due to this inward pressure can be obtained from the theory for thin walled pipes under axisymmetrical loading described by Timoshenko in [6], and whose main result is that the stress ®eld in the pipe is the same as that of a rectangular beam on an elastic foundation. This theory is reconstructed in Appendix A to include the eect of the prestressing steel, and is used to evaluate the stress ®eld developed as the prestressing force locally vanishes. Its accuracy for the analyzed pipe is checked in Appendix A by showing the agreement of its predictions for pressure loading with the corresponding design stresses. The load exerted on the pipe by the coils of circumferential prestressing wire prior to any loss is an inward uniform pressure ps acting along all the pipe. This pressure is produced by the tensile stretching of the circumferential wire and its value is given by the coil spacing s, the cross sectional area As and the tensile stress ss0 of the wire, and the radius of the coils, which is identi®ed with the external radius of the concrete core Rc: ps
ss0 As sRc
1
According to this, the loss of the circumferential prestressing load along a length 2Z of the pipe can be substituted by an outward uniform pressure ps applied along the length 2Z on the complete pipe (with all the circumferential wire operative), since this pressure would neutralize the circumferential prestressing load in the length 2Z (see Fig. 7). Indeed, this application of the superposition principle is not strictly valid due to the decrease of rigidity produced by the inoperative circumferential wire in the length 2Z of the pipe, but the dierence is too small to be taken into account, as is shown below. Let Z be the superscript standing for the stresses and displacements due to the application of the outward pressure ps in the length 2Z. In accordance with Appendix A, the stress and displacement ®elds to be found are those of the beam of Fig. 8. If the end eects are disregarded and the origin of the zaxis is placed at the middle at the pressurized length, the displacement solution must be symmetric to the plane z = 0 and remain ®nite for any z value.
Fig. 7. Loading due to inoperative circumferential prestressing wire in a length 2Z of the pipe.
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The values of the constant k to be considered for the lengths jzj < Z and jzj > Z of the beam are dierent, since they are those given by Eq. (A11) with As 0 for jzj < Z and with the design values for jzj > Z: The dierence represents the contribution previously mentioned of the circumferential wire to the rigidity of the pipe and it can be neglected, since it is less than 3%. The radial displacements uZ z of the pipe coincide with the de¯ections of the elastic beam, which are given in [6]: 8 < 2 ÿ eb jzjÿZ cos b jzj ÿ Z ÿ e ÿb jzjZ cos b jzj Z jzjRZ 0 s A s 2 uZ s 2sRc k : e ÿb jzjÿZ cos b jzj ÿ Z ÿ e ÿb jzjZ cos b jzj Z jzjrZ r 3k b4 E 0 t3
3
The circumferential stresses at the concrete core and the mortar coating are obtained by particularizing Eq. (2) in the ®rst Eq. (A3), from which it becomes apparent that the maximum of these stresses at a given cross section (z = constant) occurs, in both the core and the coating, at their respective outer surface, namely at y tc ÿ t=2 for the former and at y t=2 for the latter (tc is the core thickness). The stress of the circumferential prestressing wire is analogously obtained by particularizing Eq. (2) in Eq. (A4), but the result is only meaningful for the length jzjrZ, since at jzjRZ the circumferential wire is inoperative. Fig. 9 is a plot of these three stresses as a function of z for three values of the length 2Z: one, four and ten times the coil spacing s. The geometrical data and material constants of the analyzed pipe were used for the plot and are summarized in Table 2. For the concrete core and the mortar coating, the maximum circumferential stress along the pipe occurs at the middle section of the length 2Z, since the two stresses are the dierence between two amounts respectively proportional to the function uZ z and its second derivative d 2 uZ =dz 2 , which respectively have a maximum and a minimum at z 0: Therefore, the maximum increase of the circumferential stress produced at the concrete core and the mortar coating by the local loss of the Z circumferential prestressing load, are the stresses sZ c and sm given by: 0 sZ c ss
ÿ As E 0 1 ÿ e ÿbZ cos bZ ÿ 2tc ÿ tnRb 2 sin bZ skRRc
4
0 sZ m ss
ÿ As E 0 1 ÿ e ÿbZ cos bZ ÿ tnRb 2 sin bZ skRRc
5
Fig. 8. Equivalent beam for the loading due to inoperative circumferential prestressing wire.
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For the circumferential prestressing wire that remains operative, the maximum stress sZ s occurs at z Z: 0 sZ s ss
As Es 1 ÿ e ÿ2bZ cos 2bZ 2skRRc
6
Fig. 10 shows the plots of Eqs. (4)±(6) particularized for the values of Table 2. The stress ss0 in Eqs. (4)±(6) is that of the prestressing wire in the absence of inoperative coils, and since the coils become inoperative when the pipe is working, the work stress of the undamaged prestressing wire should be used as ss0 : According to the design data, this work stress has a practically uniform value of 1080 MPa when only the permanent loads act on the pipe, and it hardly increases by 3% under the maximum service pressure. Therefore, no signi®cant error is made by identifying ss0 with the stress s0s of the circumferential prestressing wire at the burst area under the permanent loads. Table 3 gives the design circumferential stresses at this area of the pipeline under the service loads. The stresses at the concrete core are the critical ones regarding the integrity of the pipe, since it does fail catastrophically when the concrete core fails. As a design criterion, no circumferential tensile stress is permitted at the core for normal operating conditions, though tension is sometimes permitted under
Fig. 9. Circumferential stresses produced along the pipe by the loss of the circumferential prestressing load in a length 2Z of pipe (maximum values at each cross section).
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255
Table 2 Structural data of the failed pipe Circumferential prestressing steel Coil spacing
Coil radius
Elastic modulus
Cross sectional area
s 3:1 cm
Rc = 83 cm
Es = 210 GPa
As = 19.6 mm2
Thickness
Poisson's ratio
Elastic modulus
E0
tc = 8 cm
n 0:2
E = 35 GPa
E 0 36:5 GPa
Thickness
Poisson's ratio
Elastic modulus
E0
tm = 2.5 cm
n 0:2
E = 35 GPa
E 0 36:5 GPa
Concrete core E 1ÿn 2
Mortar coating E 1ÿn 2
Pipe tE 0 1 R2
As Es stE 0
Thickness
Radius
k
t = 10.5 cm
R = 80.25 cm
k = 6.16 GPa mÿ1
q b 4 E3k0 t3
As E 0 b kRRc
As E 0 skRRc
b 4:57 mÿ1
5.62 10ÿ3
32.4 10ÿ3
transient conditions. Therefore, the safety margin provided by this criterion would be exhausted if the circumferential stress at the core reaches values as high as the tensile stress of the concrete sTc : This occurs with the combinations of pressure and length of pipe with inoperative circumferential wire, which verify: sTc s0c scp sZ c
Fig. 10. Maximum stresses produced by a local loss of circumferential prestressing load.
7
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Table 3 Design values of the circumferential stresses at the burst area
Stress under the permanent loads Stress increase due to a pressure p
Mortar
Concrete
Prestressing steel
s0m ÿ2:0 MPa smp 6:92 p
s0c ÿ4:7 MPa scp 7:14 p
s0s 1080 MPa ssp 41:51 p
where s0c is the design stress in the absence of applied pressure, scp is the increase of design stress due to pressure, and sZ c is given by Eq. (4). For the numerical values of Tables 2 and 3, Eq. (7) becomes: 8 sTc s0c 7:14p 5:62 10 ÿ3 s0s 1 ÿ e ÿbZ cos bZ ÿ 0:184 sin bZ The plot of this relationship between Z and p is shown in Fig. 11 for the values of b, sTc , s0c and s0s given by Tables 1±3. The coil spacing s, also given in Table 2, has been used as the unit of length for the plotted Z values. As seen in the plot, with no circumferential prestressing load along the length occupied by ®ve coils, the stress produced at the core of the pipe by the permanent loads and the transient service pressure equals the tensile strength of the concrete. For the stationary service pressure, this ®gure increases up to eleven coils. 5. Global failure analysis The structural analysis con®rms the critical role of the prestressing wire for the structural integrity of the prestressed concrete pipes used in the pipeline, as well as their damage tolerance when damage
Fig. 11. Failure locus of the failed pipe.
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257
locally cancels out the eect of the circumferential prestressing steel. It has been shown that the safety margin of the pipeline under normal service loading only vanishes if half a dozen successive coils become inoperative. This ®gure is in agreement with the dimensions of the burst area and also with the levels of damage tolerance that the prestressed concrete pipes exhibit in practice. However, it is not a damage level beyond expectation if the circumferential wire is subjected long enough to stress corrosion cracking by an environment suciently aggressive for the steel. The mechanical testing of the ®eld samples showed that they were seriously aected by this type of damage previous to the pipeline failure. The signs of external damage observed in these samples before testing and the damage revealed by testing agreed with the features of that produced by stress corrosion cracking. As stated in Section 3, the crack size necessary to the fracture of the circumferential wire under the operating stress was within the expectations of crack growth suggested by the collected data. This could produce a number of fractures in the burst area so that half a dozen successive coils of wire would become inoperative in this area. The occurrence of these fractures in the circumferential wire does not necessarily imply the loss of the prestressing load along the overall length of each coil severed from the rest of the wire, since a part of the coil can become anchored to the pipe wall by adherence and hold the tensile stress previous to the fractures. In this case the prestressing load exerted by the broken coil on the pipe only vanishes where the coil is free of stress, namely, between the broken ends and the anchorage points. The rest of the coil can produce stresses even at the region of the concrete core embraced by the unstressed wire, but the two sources of such stresses (the residual prestressing load and the anchorage forces) tend to compensate their eects. In conclusion, the reviewed data concerning material condition and damage tolerance allow the failure of the pipeline to be attributed with a high degree of certainty to stress corrosion cracking. However, the design rules for prestressed concrete pipes take into account the high sensibility of the prestressing steel to this phenomenon, and adopt measures to isolate it from aggressive environments. The mortar coating is a protective barrier against these aggressions, and therefore the aggressive environment had to penetrate up to the wire through this barrier by ®nding a cracked or detached zone. The localization of the burst area near the joint of two pipes suggests a possible explanation of how such a zone could develop. The pipeline had to adjust itself to any misalignment by bending horizontally, and no prestressing wire compressed longitudinally the mortar coating to avoid the tensile stress produced by this bending. If such a misalignment indeed occurs, the mortar must be expected to fail near the joint of two pipes, where the bending moment is maximum. The local character of the failure process entailed by this explanation has been con®rmed by the absence of new failures in the repaired pipeline, but the available information only permits speculation upon the subject. 6. Conclusions The case study documented in this investigation contradicts the fairly extended idea that failures in civil engineering always require accumulated errors in design, materials and construction. An indeterminate cause initiated a damage process that culminated in a serious structural failure despite the damage tolerance of the prestressed concrete pipes, which has been quantitatively assessed as a part of the investigation. A prediction is made of how many coils of the circumferential prestressing wire must become inoperative by damage to reduce or annul the safety margin against tensile stresses in the concrete core. However, the good performance shown by the investigation does not alter the fact that the vulnerability of the prestressing steel to some cracking processes transforms the protection of this material into a safety measure of capital importance for the integrity of the pressure pipes of prestressed concrete, so any risk endangering this protection must be avoided. In the failure examined here, some kind of damage in¯icted, perhaps fortuitously, on the mortar coating of the pipe locally broke the
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protective barrier and left the prestressing wire unprotected. This allowed the contact of the wire with aggressive environments and gave place to a stress corrosion cracking process with crack growth rates high enough to achieve the crack size for the brittle fracture of the wire. On reaching the number of fractures necessary to increase the stresses in the concrete core up to the tensile strength, the damage tolerance of the pipe was exhausted and the burst of the pipeline became unavoidable. Acknowledgements The ®nancial support to the author by the Spanish Government (Ministerio de EducacioÂn y Cultura, Research Project PB95-0238) is gratefully acknowledged.
Appendix A The stress analysis of a thin-walled pipe under axisymmetric loading can be reduced to that of a rectangular beam on an elastic foundation by extending the assumptions of the elementary beam theory to the pipe [6]. When the stress tensor is referred to the axial (z ), radial (r ) and circumferential y directions of the pipe, trz is the only non-vanishing shear component due to axisymmetry, whereas the normal radial stress sr is negligible due to the small thickness of the pipe. The axial normal strain ez varies linearly in the radial direction in accordance with the beam theory, and its value at the mean surface of the pipe is assumed to be null since the length of a buried pipeline must hold, so: ez ÿy
d 2u dz 2
A1
where u u z is the radial displacement of the mean surface of the pipe and y the radial distance to this surface. As an additional hypothesis, the circumferential normal strain ey is assumed to be constant in the radial direction, so that its value is given by the radial displacement u and the radius R of the mean surface of the pipe: ey
u R
A2
The absence of normal stress in the radial direction and the strains given by Eqs. (A1) and (A2) determine the normal stresses in the axial and circumferential directions when the Hooke's stress±strain equations are applied. This is the case for the core and the coating of a prestressed concrete pipe provided that concrete and mortar behave as Hookean materials. The stresses so determined would be due to the axisymmetrical load that produces the displacements u u z: For concrete and mortar with the same elastic modulus E and Poisson's coecient n, the Hooke's stress±strain equations yield: d 2u 0 0 u ÿ ny 2 sy E ey ÿ nez E R dz d 2u u A3 sz E ez ÿ ney E y 2 ÿ n dz R p E 0 being the material constant E 0 E= 1 ÿ n 2 : These axisymmetrical loads also change the tensile force of the prestressing steel, since the circumferential and longitudinal wires respectively undergo the
0
0
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259
circumferential and axial strains of the pipe that occur at their localizations in the pipe wall. Therefore, the circumferential wires remain subjected to the strain given by Eq. (A2) and the longitudinal ones to that given by Eq. (A1) for y 0: Since Es is the elastic modulus of the prestressing steel, the tensile stresses ss and ss respectively produced by these strains are: ss Es ey jyys Es
u R
ss Es ez jy0 0
A4
The equations expressing the equilibrium between the applied external forces and the stresses (A3) and (A4) supply the relationship between the displacements u(z ) and the axisymmetrical loads. Fig. A1 shows an elemental part of the pipe wall whose sides are oriented in the axial and circumferential directions, measuring respectively dz and R dy at the mean surface of the wall. The axisymmetrical applied forces and the internal forces and moments acting on the pipe element are depicted in the ®gure. The longitudinal and circumferential applied forces per unit area are q q z and p p z, the internal normal force and bending moment per axial unit length are Ny and My , and the internal normal force, shear force and bending moment per mean circumferential unit length are Nz , Qz and Mz : The equilibrium of forces in the axial and radial direction as well the equilibrium of moments in the circumferential direction result in familiar equations of the elementary beam theory, modi®ed by the presence of the force Ny : dNz R dy qR dy dz 0)
dNz ÿq dz
Fig. A1. Internal and external forces and moments in a pipe under axisymmetrical loading.
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d 2 Mz N y dQz R dy ÿ Ny dy dz pR dy dz 0 ÿp ÿ ) dMz R dy ÿ Qz dzR dy 0 dz 2 R
A5
Now, the internal forces and moments can be found as a function of the displacements u(z ) by integration of the stresses as given by Eqs. (A3) and (A4). The hypothesis of thin wall allows the calculations to be simpli®ed by using the approximation y R R: 1 Nz R dy
t
t
1 Mz R dy
2
t ÿ2
sz y R dy dy
t
2
t ÿ2
t ÿ2
sz dy
2
t ÿ2
t sz y y R dy dy
t
2
2
t ÿ2
E
0
d 2u u ÿ 2yn dz R
t sz y dy
2
t ÿ2
E
0
dy ÿE 0
d 2u u t3 d 2 u y dy ÿE 0 ÿ 2yn 12 dz 2 dz R
2 3 t t 2 2 1 4 ss As u As As 0u 0 t 5 dz E u sy dz dy Es E dy Es Ny t t s Rs dz R s R R ÿ ÿ 2
nt u R
A6
A7
A8
2
and provides a less involved ®nal result after substituting in Eq. (A5): q E0
nt du R dz
A9
t 3 d4 u E 0 t Es As up 2 1 0 E 12 dz4 E st R 0
A10
Once Eq. (A10) has been solved and the function u(z ) found from the applied radial force p(z ), Eq. (A9) gives the longitudinal force exerted by the soil and back®ll to preserve the length of the pipeline. Further, Eq. (A10) is also the dierential equation for the de¯ections of an elastic beam of rectangular cross section, elastic modulus E 0 , thickness t and width unity, resting on an elastic foundation and subjected to a non uniform normal force of value per unit length p(z ). Fig. A2 illustrates the equivalence between this problem and the axisymmetrical original one, the constant k of the elastic foundation being:
Fig. A2. Thin-walled pipe axisymmetrically loaded and equivalent beam.
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Table A1 Circumferential stress increases due to pressure on the basis of Appendix A
Pressure ( p )
Mortar
Concrete
Prestressing steel
smp 7:38 p
scp 7:38 p
ssp 42:50 p
E 0t Es As k 2 1 0 E st R
A11
In order to ascertain the accuracy of this equivalence for the examined prestressed concrete pipe, the stresses due to pressurization are used by comparing those of design, given in Table 3, with those derived from the equivalence. The solution of Eq. (A10) for p constant with no end eect is the trivial one u p=k, and its substitution in Eqs. (A3)±(A5) yields the circumferential stress in the prestressing wire, the concrete core and the mortar coating. The values of these stresses at the outer boundary of each layer are obtained by particularizing the results at y yc for concrete and y t=2 for mortar: u p Es sSp Es R up=k kR yys
sCp E 0
u d 2u p ÿ ny 2 E0 up=k R dz kR yys
sMp E 0
u d 2u p ÿ ny 2 E0 up=k R dz kR
A12
yys
Table A1 gives the numerical results for the data of Table 2 and shows that they agree with those of design (Table 3), since the dierences are lower than 7%. References [1] Stephenson D. Pipeline design for water engineers. Oxford: Elsevier Scienti®c, 1976. [2] Elices M. Fracture of steels for reinforcing and prestressing concrete. In: Sih GC, DiTommaso A, editors. Fracture mechanics of concrete: structural application and numerical calculation. Boston: Martinus Nijho, 1985. p. 226±80. [3] Parkins RN, Elices M, SaÂnchez-GaÂlvez V, Caballero L. Environment sensitive cracking of prestressing steels. Corrosion Science 1982;22:379±405. [4] Valiente A, Elices M. Premature failure of prestressed steel bars. Engineering Failure Analysis 1998;5:219±27. [5] Clarke NWB. Buried pipelines. London: MacLaren, 1968. [6] Timoshenko S. In: Strength of materials Ð part II. 2nd ed. Princeton, NJ: Van Nostrand, 1955.
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Stress corrosion failure of large diameter pressure pipelines of prestressed concrete A. Valiente Departamento de Ciencia de Materiales, Escuela de Ingenieros de Caminos, Canales y Puertos, Universidad PoliteÂcnica de Madrid, Ciudad Universitaria, E-28040 Madrid, Spain Received 21 February 2000; accepted 3 March 2000
Abstract The failure of a 1.5 m diameter prestressed concrete line for water supply was examined. The water pressure opened a hole of 0.5 m2 in the pipe wall by breaking the concrete into fragments and by tensile severing of a number of coils of the wire winding. Flexural and tensile testing of samples of the broken materials showed no damage to the concrete, but showed signi®cant losses of strength and ductility in the prestressing steel wire. The SEM analysis of the external and fracture surfaces of the circumferential wires revealed shallow cracking and corroded areas as expected from a stress corrosion cracking process. The failure analysis presented in this paper shows that such a process was able to exhaust the damage tolerance of the aected tube until the pipeline burst under the work pressures. 7 2001 Elsevier Science Ltd. All rights reserved. Keywords: Damage tolerance; Pipeline failures; Prestressing; Stress corrosion cracking
1. Introduction The prestressing technique is a major ®nding of civil engineering. By this technique, the surplus tensile strength of a material (prestressing steel) is devoted to resisting tensile loads transferred from another material of poor tensile strength (concrete). This composite material requires steels with very high tensile strength, a feature that often entails the risk of low tenacity and sensitivity to processes able to produce localized cracking. As a consequence, the prestressing steel is protected by using non-aggressive concrete constituents and by isolating the steel from the environment by means of an impermeable coating. These protective measures are easy to apply to the structural members of prestressed concrete made in a
E-mail address: [email protected] (A. Valiente). 1350-6307/01/$ - see front matter 7 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 0 - 6 3 0 7 ( 0 0 ) 0 0 0 1 0 - 8
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factory, but they must be complemented with careful handling during construction to avoid damage that might cancel out the protection. In accordance with the potential vulnerability of the prestressing steel, the prestressed concrete might be expected to have low damage tolerance, but experience denies this. In practice, a good level of damage tolerance is exhibited by the prestressed concrete consisting of prestressing steel wires embedded in concrete and joined to it throughout their length. This damage tolerance allows a structural member to go on working without failing even though a number of fractures may have occurred in the prestressing steel. The origin of this damage tolerance is the fact that the prestressing force exerted by a wire does not necessarily vanish along all the wire if it breaks, and the remaining wire may be enough to avoid structural failure. Failure does not occur unless damage tolerance be exhausted. Accordingly, the failure analysis presented in this paper is envisaged with the aid of a quantitative assessment of damage tolerance in prestressed concrete. The paper documents and analyzes the failure that arose in a large diameter pressure pipeline of prestressed concrete, a structure whose safety depends on the integrity of large amounts of continuous prestressing steel wire, hundreds of meters per meter of pipeline. Prestressed concrete is widely used in pipelines because it competes economically with steel pipes. The design rules of these pipes are soundly stated [1], but to the author's knowledge no evaluation of damage tolerance as described above is available. Prestressed concrete pipes are made by winding a pretensioned wire onto a concrete core, previously cast, steam cured, and often prestressed longitudinally by straight wires embedded in the core wall along the middle surface. After winding, a concrete or mortar coating is deposited on the core to embed the circumferential wire inside the wall pipe and to increase the thickness of the pipe up to its design value. With the subsequent shrinkage and creep of the core, the prestressing wire loses a proportion of its tensile stress as a part of the prestressing force is transferred to the coating. Eventually, the pipe is load tested and is ready to be put into service. Regarding the mechanical behaviour of the pipe, the circumferential wire works as a thin layer of steel inserted in the concrete of the pipe wall. The thickness of the layer is so small that its contribution to the rigidity of the pipe is insigni®cant, and therefore the external loads are taken almost entirely by the concrete of the core and the coating, with hardly any change in the stress of the circumferential wire. The basic function of this is to produce an initial compressive stress in the concrete, high enough to avoid tensile stresses when adding the stresses due to external loads. The examined failure involves successive fractures of the circumferential prestressing wire as a result of a stress corrosion cracking process. The precautions to assure the integrity of the pipeline were not enough to prevent stress corrosion cracking in all the pipes, and the failure of the pipeline occurred after six years of service. The failed pipe was replaced and no new failure has occurred since then. The evaluation of damage tolerance is based on an estimation of the number of coils of circumferential wire that can become inoperative by stress corrosion cracking before the external loads produce the complete failure of the pipe. 2. Failure description and data design The failure occurred in a 5 km long pressure pipeline for water supply that had been in operation for six years. The pipeline was buried, and the failure was localized in a pipe of 1.5 m inner diameter, 10.5 cm thickness and 5.1 m length. The pipe was composed of a concrete core 8 cm thick, a 5 mm diameter circumferential prestressing wire with a coil spacing of 3.1 cm, and a mortar coating 2.5 cm thick. The pipe was longitudinally prestressed on the middle surface of the wall by 30 prestressing wires of 5 mm diameter uniformly distributed (Fig. 1). When the back®ll was removed and the pipe exposed, a roughly rectangular area of the pipe
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Fig. 1. Geometrical features of the failed pipe.
wall, 1 m long and 0.5 m high, was found to be broken into fragments. This area was just at the end of the pipe forming the spigot joined to the socket of the next pipe (Fig. 2). The pipeline was designed with no surge tank to attenuate the wave pressure produced by the opening and closing of the control valves, given that the maximum pressure due to the water hammer was about 1.5 times the service pressure of 0.5 MPa and coincided with the ®eld proof pressure. The failure of the pipeline can be attributed without doubt to this maximum transient pressure, since it was detected just after operating the valves. The material properties provided by the manufacturer of the prestressed concrete pipes and used as design data are given in Table 1.
Fig. 2. The failed pipe showing the burst area of the wall.
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Table 1 Design material properties of the failed pipe
Elastic modulus Poisson's coecient Yield strength Tensile strength Maximum uniform elongation
Prestressing steel
Concrete
Mortar
Es = 210 GPa ± sY s 1700 MPa sTs 1800 MPa > 2%
E = 35 GPa n 0:2 ± sTc 3:5 MPa ±
E = 35 GPa n 0:2 ± ± ±
3. Material failure analysis Field samples collected from the failed pipe and supplied for testing and observation in the laboratory consisted of fragments of the concrete core detached from the broken area and pieces of prestressing steel cut from the coils of the same area. Most of these coils were found broken, and some of the steel samples collected for the laboratory included the fracture surfaces, and special care was taken to preserve them when removing the coils. After cleaning, the broken steel samples were examined under a low magni®cation microscope and two types of fractures were observed (Fig. 3). The features of the ®rst (Fig. 3a) are typical of the ductile fracture in cold drawing prestressing steel wire: a cup and cone rupture resulting from an advanced necking process. Apart from this, there is no appreciable cracking on the lateral surface of the wire. In contrast, the second type of sample shows the signs of ¯aw-induced fracture common in these steels: an irregular fracture propagation path in the absence of necking. The surface ¯aw whose propagation typically causes this type of fracture in cold drawing prestressing steel wires [2] could not be identi®ed as a feature dierent from the rest of the fracture due to the highly corroded condition of the fracture surfaces when found. Such strong degradation means that the coils fractured in this way broke well before the ®nal failure of the pipeline. On the contrary, a better condition was exhibited by the the fracture surfaces of the coils failed in a ductile way, which means that they had broken as a consequence of the failure of the pipeline.
Fig. 3. The two types of fractures of the prestressing wire observed at the failure site.
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In prestressed concrete made with controlled materials and subjected to the design loads, a damage process involving ¯aw nucleation and ductility loss in the prestressing steel can only be attributed to unexpected fatigue and/or stress corrosion. In this case the loading history allows fatigue to be disregarded, so a stress corrosion cracking process appeared as the most probable explanation of the failure of a number of coils before that of the pipe. The existence of the shallow cracking observed on the lateral surface of these coils, near the broken ends (Fig. 3b), also supports this explanation. In accordance with these data, mechanical testing of the samples was conducted in the laboratory in order to detect any damage in the materials of the pipe by comparing the tensile behaviour experimentally determined just after the failure of the pipe with that assumed at the design stage. Prismatic specimens of 4 cm 4 cm 14 cm having the longer edge parallel to the hoop direction of the pipe were machined from the largest fragments of concrete available. These specimens were tested up to fracture by three point bending and exhibited no anomalous behaviour, failing at a tensile stress of about 5 MPa, as calculated from the bending moment on the basis of the elementary beam theory. This value agrees with the design tensile stress in Table 1. The wire samples were long enough to provide standard prestressing steel specimens, so they were tensile tested without diculty. The entire stress±strain curve was registered over a gauge length of 5 cm by attaching an extensometer to each specimen. The results of the three tests performed are shown in Fig. 4 and largely dier from that of the concrete, as regards the existence of damage. Only one of the specimens exhibited no sign of damage when compared with the design data, since the measured yield strength, tensile strength and maximum uniform elongation are practically the same as those of the manufacturer (Table 1). In the other two specimens these values are lower, specially the maximum uniform elongation. This is not due to divergent stress±strain curves, but to a premature fracture that occurred when plastic deformation had hardly begun. As already mentioned, in prestressing steel wire
Fig. 4. Stress±strain curves of the prestressing wire samples tested in the laboratory.
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[2] such brittle behaviour involves the existence of a surface ¯aw whose size surpasses the damage tolerance of this material. The fracture surfaces of the specimens were in agreement with both the brittle and the ductile behaviour indicated by the stress±strain curves, and con®rmed the existence of surface cracks able to trigger the brittle fracture. The broken ends of the specimens with maximum and minimum ductility (as measured by the maximum uniform elongation) can be seen in Fig. 5. A necking process resulting in a cup and cone fracture produced the failure of the ductile specimen, whereas that of the brittle one was due to a fast propagation fracture prior to any sign of necking. These fractures accurately reproduced that of Fig. 3, namely, that found at the failure site on the wire coils that circumferentially prestressed the burst part of the pipe wall. When the brittle specimens were observed by scanning electron microscopy (Fig. 6), it became apparent that the fracture was triggered by a surface crack developed in the wire before the test. The black colour taken on by the faces of the crack indicated a very long corrosion process in deaerated environment [3] and provided a de®nite proof of the cracking of the prestressing wire before the failure of the pipeline. To summarize the failure analysis of the materials, no damage was found in the concrete, but the cold drawing steel wire for the circumferential prestressing of the failed pipe showed clear signs of stress corrosion cracking. The nucleation and growth of surface cracks on the wire transformed its tensile behaviour from ductile to brittle and could decrease its mechanical strength until causing the failure of some coils under the design stresses. This is not only supported by the ®nding of coils broken prior to the failure of the pipeline, but also by the laboratory ®ndings. As demonstrated by the mechanical testing, the size attained by these cracks was able to produce the brittle fracture of the wire under stresses below the yield strength of the wire. Indeed, an LEFM analysis such as that performed in [4] indicates that a crack only 20% deeper than that of Fig. 6 would have suced to exhaust the strength of the circumferential prestressing wire under normal service conditions. This prediction is based on the estimation of the fracture toughness of the circumferential wire from the failure stress (1400 MPa) and
Fig. 5. Ductile and brittle fractures of the prestressing wire obtained in the tests.
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the crack depth (1.4 mm) of the specimen of Fig. 6. According to this fracture toughness, a crack 1.7 mm deep would cause the fracture of the wire under the work stress of 1080 MPa. 4. Structural failure analysis The failure of a prestressing concrete pipe by the design pressure requires more than one or two inoperative coils, since in practice these pipes are not so vulnerable as this. On the other hand, the fracture of many coils of the burst area was a ductile, not a ¯aw-induced failure, so they failed simultaneously with the concrete core when the two materials were overloaded up to the tensile strength by the applied pressure. Therefore, the number of coils made inoperative by stress corrosion before ®nal failure was much lower than the number contained in the burst area (about 30, according to the coil spacing and the dimensions of the area). From these two limits, it can be stated that a number of inoperative coils ranging between 3 and 10 produced the failure of the pipe under service loading. It remains to be shown that such a ®gure was able to exhaust the damage tolerance of the pipe. To evaluate the damage tolerance of the pipe, a quantitative assessment is required of the stresses due to the loss of the prestressing load resulting from the inoperative coils. The structural design hypothesis is the basis of the assessment. Hence, it is assumed that the three materials (prestressing steel, concrete and mortar) are Hookean, their elastic properties as given in Table 1, and that any length of the pipe remains unchanged when buried. As a consequence of the ®rst assumption, the superposition principle applies for stresses, and accordingly those produced by the loss of prestressing load may be added to
Fig. 6. SEM image of a crack developed in the prestressing wire before the failure.
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that produced by the manufacturing prestressing load, by the permanent external loads (weights and soil forces) and by the water pressure, all of which are available as design data. However, the disappearance of the prestressing load in a short length of pipe does not produce a uniform loading along the pipe, and the corresponding stresses cannot be found as in the design, namely, by assimilating the pipe to be an elastic multilayered ring (see, for instance, [5]). When undamaged, the prestressing circumferential wire produces a load equivalent to a uniform inward pressure extended over all the pipe, so that a number of contiguous inoperative coils would have the same eect as an equal outward pressure acting on the aected length of pipe and superposed on the prestressing load of the entire circumferential wire, on the permanent loads, and on the water pressure. The stresses due to this inward pressure can be obtained from the theory for thin walled pipes under axisymmetrical loading described by Timoshenko in [6], and whose main result is that the stress ®eld in the pipe is the same as that of a rectangular beam on an elastic foundation. This theory is reconstructed in Appendix A to include the eect of the prestressing steel, and is used to evaluate the stress ®eld developed as the prestressing force locally vanishes. Its accuracy for the analyzed pipe is checked in Appendix A by showing the agreement of its predictions for pressure loading with the corresponding design stresses. The load exerted on the pipe by the coils of circumferential prestressing wire prior to any loss is an inward uniform pressure ps acting along all the pipe. This pressure is produced by the tensile stretching of the circumferential wire and its value is given by the coil spacing s, the cross sectional area As and the tensile stress ss0 of the wire, and the radius of the coils, which is identi®ed with the external radius of the concrete core Rc: ps
ss0 As sRc
1
According to this, the loss of the circumferential prestressing load along a length 2Z of the pipe can be substituted by an outward uniform pressure ps applied along the length 2Z on the complete pipe (with all the circumferential wire operative), since this pressure would neutralize the circumferential prestressing load in the length 2Z (see Fig. 7). Indeed, this application of the superposition principle is not strictly valid due to the decrease of rigidity produced by the inoperative circumferential wire in the length 2Z of the pipe, but the dierence is too small to be taken into account, as is shown below. Let Z be the superscript standing for the stresses and displacements due to the application of the outward pressure ps in the length 2Z. In accordance with Appendix A, the stress and displacement ®elds to be found are those of the beam of Fig. 8. If the end eects are disregarded and the origin of the zaxis is placed at the middle at the pressurized length, the displacement solution must be symmetric to the plane z = 0 and remain ®nite for any z value.
Fig. 7. Loading due to inoperative circumferential prestressing wire in a length 2Z of the pipe.
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The values of the constant k to be considered for the lengths jzj < Z and jzj > Z of the beam are dierent, since they are those given by Eq. (A11) with As 0 for jzj < Z and with the design values for jzj > Z: The dierence represents the contribution previously mentioned of the circumferential wire to the rigidity of the pipe and it can be neglected, since it is less than 3%. The radial displacements uZ z of the pipe coincide with the de¯ections of the elastic beam, which are given in [6]: 8 < 2 ÿ eb jzjÿZ cos b jzj ÿ Z ÿ e ÿb jzjZ cos b jzj Z jzjRZ 0 s A s 2 uZ s 2sRc k : e ÿb jzjÿZ cos b jzj ÿ Z ÿ e ÿb jzjZ cos b jzj Z jzjrZ r 3k b4 E 0 t3
3
The circumferential stresses at the concrete core and the mortar coating are obtained by particularizing Eq. (2) in the ®rst Eq. (A3), from which it becomes apparent that the maximum of these stresses at a given cross section (z = constant) occurs, in both the core and the coating, at their respective outer surface, namely at y tc ÿ t=2 for the former and at y t=2 for the latter (tc is the core thickness). The stress of the circumferential prestressing wire is analogously obtained by particularizing Eq. (2) in Eq. (A4), but the result is only meaningful for the length jzjrZ, since at jzjRZ the circumferential wire is inoperative. Fig. 9 is a plot of these three stresses as a function of z for three values of the length 2Z: one, four and ten times the coil spacing s. The geometrical data and material constants of the analyzed pipe were used for the plot and are summarized in Table 2. For the concrete core and the mortar coating, the maximum circumferential stress along the pipe occurs at the middle section of the length 2Z, since the two stresses are the dierence between two amounts respectively proportional to the function uZ z and its second derivative d 2 uZ =dz 2 , which respectively have a maximum and a minimum at z 0: Therefore, the maximum increase of the circumferential stress produced at the concrete core and the mortar coating by the local loss of the Z circumferential prestressing load, are the stresses sZ c and sm given by: 0 sZ c ss
ÿ As E 0 1 ÿ e ÿbZ cos bZ ÿ 2tc ÿ tnRb 2 sin bZ skRRc
4
0 sZ m ss
ÿ As E 0 1 ÿ e ÿbZ cos bZ ÿ tnRb 2 sin bZ skRRc
5
Fig. 8. Equivalent beam for the loading due to inoperative circumferential prestressing wire.
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For the circumferential prestressing wire that remains operative, the maximum stress sZ s occurs at z Z: 0 sZ s ss
As Es 1 ÿ e ÿ2bZ cos 2bZ 2skRRc
6
Fig. 10 shows the plots of Eqs. (4)±(6) particularized for the values of Table 2. The stress ss0 in Eqs. (4)±(6) is that of the prestressing wire in the absence of inoperative coils, and since the coils become inoperative when the pipe is working, the work stress of the undamaged prestressing wire should be used as ss0 : According to the design data, this work stress has a practically uniform value of 1080 MPa when only the permanent loads act on the pipe, and it hardly increases by 3% under the maximum service pressure. Therefore, no signi®cant error is made by identifying ss0 with the stress s0s of the circumferential prestressing wire at the burst area under the permanent loads. Table 3 gives the design circumferential stresses at this area of the pipeline under the service loads. The stresses at the concrete core are the critical ones regarding the integrity of the pipe, since it does fail catastrophically when the concrete core fails. As a design criterion, no circumferential tensile stress is permitted at the core for normal operating conditions, though tension is sometimes permitted under
Fig. 9. Circumferential stresses produced along the pipe by the loss of the circumferential prestressing load in a length 2Z of pipe (maximum values at each cross section).
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255
Table 2 Structural data of the failed pipe Circumferential prestressing steel Coil spacing
Coil radius
Elastic modulus
Cross sectional area
s 3:1 cm
Rc = 83 cm
Es = 210 GPa
As = 19.6 mm2
Thickness
Poisson's ratio
Elastic modulus
E0
tc = 8 cm
n 0:2
E = 35 GPa
E 0 36:5 GPa
Thickness
Poisson's ratio
Elastic modulus
E0
tm = 2.5 cm
n 0:2
E = 35 GPa
E 0 36:5 GPa
Concrete core E 1ÿn 2
Mortar coating E 1ÿn 2
Pipe tE 0 1 R2
As Es stE 0
Thickness
Radius
k
t = 10.5 cm
R = 80.25 cm
k = 6.16 GPa mÿ1
q b 4 E3k0 t3
As E 0 b kRRc
As E 0 skRRc
b 4:57 mÿ1
5.62 10ÿ3
32.4 10ÿ3
transient conditions. Therefore, the safety margin provided by this criterion would be exhausted if the circumferential stress at the core reaches values as high as the tensile stress of the concrete sTc : This occurs with the combinations of pressure and length of pipe with inoperative circumferential wire, which verify: sTc s0c scp sZ c
Fig. 10. Maximum stresses produced by a local loss of circumferential prestressing load.
7
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Table 3 Design values of the circumferential stresses at the burst area
Stress under the permanent loads Stress increase due to a pressure p
Mortar
Concrete
Prestressing steel
s0m ÿ2:0 MPa smp 6:92 p
s0c ÿ4:7 MPa scp 7:14 p
s0s 1080 MPa ssp 41:51 p
where s0c is the design stress in the absence of applied pressure, scp is the increase of design stress due to pressure, and sZ c is given by Eq. (4). For the numerical values of Tables 2 and 3, Eq. (7) becomes: 8 sTc s0c 7:14p 5:62 10 ÿ3 s0s 1 ÿ e ÿbZ cos bZ ÿ 0:184 sin bZ The plot of this relationship between Z and p is shown in Fig. 11 for the values of b, sTc , s0c and s0s given by Tables 1±3. The coil spacing s, also given in Table 2, has been used as the unit of length for the plotted Z values. As seen in the plot, with no circumferential prestressing load along the length occupied by ®ve coils, the stress produced at the core of the pipe by the permanent loads and the transient service pressure equals the tensile strength of the concrete. For the stationary service pressure, this ®gure increases up to eleven coils. 5. Global failure analysis The structural analysis con®rms the critical role of the prestressing wire for the structural integrity of the prestressed concrete pipes used in the pipeline, as well as their damage tolerance when damage
Fig. 11. Failure locus of the failed pipe.
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257
locally cancels out the eect of the circumferential prestressing steel. It has been shown that the safety margin of the pipeline under normal service loading only vanishes if half a dozen successive coils become inoperative. This ®gure is in agreement with the dimensions of the burst area and also with the levels of damage tolerance that the prestressed concrete pipes exhibit in practice. However, it is not a damage level beyond expectation if the circumferential wire is subjected long enough to stress corrosion cracking by an environment suciently aggressive for the steel. The mechanical testing of the ®eld samples showed that they were seriously aected by this type of damage previous to the pipeline failure. The signs of external damage observed in these samples before testing and the damage revealed by testing agreed with the features of that produced by stress corrosion cracking. As stated in Section 3, the crack size necessary to the fracture of the circumferential wire under the operating stress was within the expectations of crack growth suggested by the collected data. This could produce a number of fractures in the burst area so that half a dozen successive coils of wire would become inoperative in this area. The occurrence of these fractures in the circumferential wire does not necessarily imply the loss of the prestressing load along the overall length of each coil severed from the rest of the wire, since a part of the coil can become anchored to the pipe wall by adherence and hold the tensile stress previous to the fractures. In this case the prestressing load exerted by the broken coil on the pipe only vanishes where the coil is free of stress, namely, between the broken ends and the anchorage points. The rest of the coil can produce stresses even at the region of the concrete core embraced by the unstressed wire, but the two sources of such stresses (the residual prestressing load and the anchorage forces) tend to compensate their eects. In conclusion, the reviewed data concerning material condition and damage tolerance allow the failure of the pipeline to be attributed with a high degree of certainty to stress corrosion cracking. However, the design rules for prestressed concrete pipes take into account the high sensibility of the prestressing steel to this phenomenon, and adopt measures to isolate it from aggressive environments. The mortar coating is a protective barrier against these aggressions, and therefore the aggressive environment had to penetrate up to the wire through this barrier by ®nding a cracked or detached zone. The localization of the burst area near the joint of two pipes suggests a possible explanation of how such a zone could develop. The pipeline had to adjust itself to any misalignment by bending horizontally, and no prestressing wire compressed longitudinally the mortar coating to avoid the tensile stress produced by this bending. If such a misalignment indeed occurs, the mortar must be expected to fail near the joint of two pipes, where the bending moment is maximum. The local character of the failure process entailed by this explanation has been con®rmed by the absence of new failures in the repaired pipeline, but the available information only permits speculation upon the subject. 6. Conclusions The case study documented in this investigation contradicts the fairly extended idea that failures in civil engineering always require accumulated errors in design, materials and construction. An indeterminate cause initiated a damage process that culminated in a serious structural failure despite the damage tolerance of the prestressed concrete pipes, which has been quantitatively assessed as a part of the investigation. A prediction is made of how many coils of the circumferential prestressing wire must become inoperative by damage to reduce or annul the safety margin against tensile stresses in the concrete core. However, the good performance shown by the investigation does not alter the fact that the vulnerability of the prestressing steel to some cracking processes transforms the protection of this material into a safety measure of capital importance for the integrity of the pressure pipes of prestressed concrete, so any risk endangering this protection must be avoided. In the failure examined here, some kind of damage in¯icted, perhaps fortuitously, on the mortar coating of the pipe locally broke the
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protective barrier and left the prestressing wire unprotected. This allowed the contact of the wire with aggressive environments and gave place to a stress corrosion cracking process with crack growth rates high enough to achieve the crack size for the brittle fracture of the wire. On reaching the number of fractures necessary to increase the stresses in the concrete core up to the tensile strength, the damage tolerance of the pipe was exhausted and the burst of the pipeline became unavoidable. Acknowledgements The ®nancial support to the author by the Spanish Government (Ministerio de EducacioÂn y Cultura, Research Project PB95-0238) is gratefully acknowledged.
Appendix A The stress analysis of a thin-walled pipe under axisymmetric loading can be reduced to that of a rectangular beam on an elastic foundation by extending the assumptions of the elementary beam theory to the pipe [6]. When the stress tensor is referred to the axial (z ), radial (r ) and circumferential y directions of the pipe, trz is the only non-vanishing shear component due to axisymmetry, whereas the normal radial stress sr is negligible due to the small thickness of the pipe. The axial normal strain ez varies linearly in the radial direction in accordance with the beam theory, and its value at the mean surface of the pipe is assumed to be null since the length of a buried pipeline must hold, so: ez ÿy
d 2u dz 2
A1
where u u z is the radial displacement of the mean surface of the pipe and y the radial distance to this surface. As an additional hypothesis, the circumferential normal strain ey is assumed to be constant in the radial direction, so that its value is given by the radial displacement u and the radius R of the mean surface of the pipe: ey
u R
A2
The absence of normal stress in the radial direction and the strains given by Eqs. (A1) and (A2) determine the normal stresses in the axial and circumferential directions when the Hooke's stress±strain equations are applied. This is the case for the core and the coating of a prestressed concrete pipe provided that concrete and mortar behave as Hookean materials. The stresses so determined would be due to the axisymmetrical load that produces the displacements u u z: For concrete and mortar with the same elastic modulus E and Poisson's coecient n, the Hooke's stress±strain equations yield: d 2u 0 0 u ÿ ny 2 sy E ey ÿ nez E R dz d 2u u A3 sz E ez ÿ ney E y 2 ÿ n dz R p E 0 being the material constant E 0 E= 1 ÿ n 2 : These axisymmetrical loads also change the tensile force of the prestressing steel, since the circumferential and longitudinal wires respectively undergo the
0
0
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259
circumferential and axial strains of the pipe that occur at their localizations in the pipe wall. Therefore, the circumferential wires remain subjected to the strain given by Eq. (A2) and the longitudinal ones to that given by Eq. (A1) for y 0: Since Es is the elastic modulus of the prestressing steel, the tensile stresses ss and ss respectively produced by these strains are: ss Es ey jyys Es
u R
ss Es ez jy0 0
A4
The equations expressing the equilibrium between the applied external forces and the stresses (A3) and (A4) supply the relationship between the displacements u(z ) and the axisymmetrical loads. Fig. A1 shows an elemental part of the pipe wall whose sides are oriented in the axial and circumferential directions, measuring respectively dz and R dy at the mean surface of the wall. The axisymmetrical applied forces and the internal forces and moments acting on the pipe element are depicted in the ®gure. The longitudinal and circumferential applied forces per unit area are q q z and p p z, the internal normal force and bending moment per axial unit length are Ny and My , and the internal normal force, shear force and bending moment per mean circumferential unit length are Nz , Qz and Mz : The equilibrium of forces in the axial and radial direction as well the equilibrium of moments in the circumferential direction result in familiar equations of the elementary beam theory, modi®ed by the presence of the force Ny : dNz R dy qR dy dz 0)
dNz ÿq dz
Fig. A1. Internal and external forces and moments in a pipe under axisymmetrical loading.
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A. Valiente / Engineering Failure Analysis 8 (2001) 245±261
d 2 Mz N y dQz R dy ÿ Ny dy dz pR dy dz 0 ÿp ÿ ) dMz R dy ÿ Qz dzR dy 0 dz 2 R
A5
Now, the internal forces and moments can be found as a function of the displacements u(z ) by integration of the stresses as given by Eqs. (A3) and (A4). The hypothesis of thin wall allows the calculations to be simpli®ed by using the approximation y R R: 1 Nz R dy
t
t
1 Mz R dy
2
t ÿ2
sz y R dy dy
t
2
t ÿ2
t ÿ2
sz dy
2
t ÿ2
t sz y y R dy dy
t
2
2
t ÿ2
E
0
d 2u u ÿ 2yn dz R
t sz y dy
2
t ÿ2
E
0
dy ÿE 0
d 2u u t3 d 2 u y dy ÿE 0 ÿ 2yn 12 dz 2 dz R
2 3 t t 2 2 1 4 ss As u As As 0u 0 t 5 dz E u sy dz dy Es E dy Es Ny t t s Rs dz R s R R ÿ ÿ 2
nt u R
A6
A7
A8
2
and provides a less involved ®nal result after substituting in Eq. (A5): q E0
nt du R dz
A9
t 3 d4 u E 0 t Es As up 2 1 0 E 12 dz4 E st R 0
A10
Once Eq. (A10) has been solved and the function u(z ) found from the applied radial force p(z ), Eq. (A9) gives the longitudinal force exerted by the soil and back®ll to preserve the length of the pipeline. Further, Eq. (A10) is also the dierential equation for the de¯ections of an elastic beam of rectangular cross section, elastic modulus E 0 , thickness t and width unity, resting on an elastic foundation and subjected to a non uniform normal force of value per unit length p(z ). Fig. A2 illustrates the equivalence between this problem and the axisymmetrical original one, the constant k of the elastic foundation being:
Fig. A2. Thin-walled pipe axisymmetrically loaded and equivalent beam.
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Table A1 Circumferential stress increases due to pressure on the basis of Appendix A
Pressure ( p )
Mortar
Concrete
Prestressing steel
smp 7:38 p
scp 7:38 p
ssp 42:50 p
E 0t Es As k 2 1 0 E st R
A11
In order to ascertain the accuracy of this equivalence for the examined prestressed concrete pipe, the stresses due to pressurization are used by comparing those of design, given in Table 3, with those derived from the equivalence. The solution of Eq. (A10) for p constant with no end eect is the trivial one u p=k, and its substitution in Eqs. (A3)±(A5) yields the circumferential stress in the prestressing wire, the concrete core and the mortar coating. The values of these stresses at the outer boundary of each layer are obtained by particularizing the results at y yc for concrete and y t=2 for mortar: u p Es sSp Es R up=k kR yys
sCp E 0
u d 2u p ÿ ny 2 E0 up=k R dz kR yys
sMp E 0
u d 2u p ÿ ny 2 E0 up=k R dz kR
A12
yys
Table A1 gives the numerical results for the data of Table 2 and shows that they agree with those of design (Table 3), since the dierences are lower than 7%. References [1] Stephenson D. Pipeline design for water engineers. Oxford: Elsevier Scienti®c, 1976. [2] Elices M. Fracture of steels for reinforcing and prestressing concrete. In: Sih GC, DiTommaso A, editors. Fracture mechanics of concrete: structural application and numerical calculation. Boston: Martinus Nijho, 1985. p. 226±80. [3] Parkins RN, Elices M, SaÂnchez-GaÂlvez V, Caballero L. Environment sensitive cracking of prestressing steels. Corrosion Science 1982;22:379±405. [4] Valiente A, Elices M. Premature failure of prestressed steel bars. Engineering Failure Analysis 1998;5:219±27. [5] Clarke NWB. Buried pipelines. London: MacLaren, 1968. [6] Timoshenko S. In: Strength of materials Ð part II. 2nd ed. Princeton, NJ: Van Nostrand, 1955.