Proceedings of the Institution of

Civil Engineers
Structures and Buildings 146
November 2001 Issue 4
Pages 341^352

Paper 12278
Received 11/02/2000
Accepted 19/03/2001

Keywords:
D. G. Cavell P. Waldron
bridges/corrosion/grouting
Dr, Engineer, Mott Professor, The University of
MacDonald, Mott Sheffield, Department of
MacDonald House, Sheffield, Civil & Structural
UK Engineering, Sheffield, UK

Parametric study of the residual strength of deteriorating

simply-supported post-tensioned concrete bridges
D. G. Cavell and P. Waldron

This paper discusses the results of a parametric study of structural capacity of existing bridges of this type, and led to a
the residual strength of deteriorating simply-supported temporary moratorium on their construction (1992–1996) by
post-tensioned bridges of the internally grouted duct the Department of Transport.
type. This was conducted with the use of an analytical
model which was developed to investigate the effects of Tendon corrosion is mainly caused by the ingress of chlorides
tendon failure due to corrosion and regions of grout from de-icing salts through inadequately sealed ducts, normally
voids in post-tensioned concrete beams. The research at the anchorages and between joints in segmental post-
was initiated to address concerns over the remaining tensioned bridges. The most serious event occurred in 1985
structural capacity of deteriorating post-tensioned when the Ynys-y-Gwas, a single-span segmental post-tensioned
bridges following the discovery of a variety of defects bridge collapsed without warning under its own self-weight. In
in post-tensioned bridges during the inspection of the addition, regions of grout voids due to incomplete grouting are
UK’s national stock of post-tensioned concrete bridges. often found at the anchorage and at high points along a duct
The defects, ranging from incompletely grouted ducts profile, exposing the tendons to increased risk of corrosion.
to chloride-induced tendon corrosion and fractures,
may have a detrimental effect on residual strength. The effects of tendon failure in post-tensioned bridges contain-
The findings from this parametric study provide an ing integral grouted tendons have been observed to vary from
understanding of the behaviour of corrosion-damaged one structure to another, depending on the bridge deck
post-tensioned concrete bridges, and will assist in the geometry, prestressing system, integrity of grout within the
development of strategies for extending the lives of such duct and extent of tendon corrosion. The problem faced by
structures through repair and strengthening, so avoiding engineers involved with the assessment of post-tensioned
unnecessary and costly replacement. bridges is that there is a lack of satisfactory analytical models
and guidance on methods to assess residual strength whilst
accounting for the level of damage that has been discovered
NOTATION
during inspection. The problem is compounded by the fact that
fcu characteristic strength of concrete
it is difficult and expensive to determine the condition of the
fps tendon stress
tendons or grout using currently available inspection tech-
Mcr cracking moment
niques. Specialised non-destructive testing methods may prove
Mdec decompression moment
inconclusive as the presence of the steel duct often distorts the
Ms design bending moment at service
results. Visual evidence such as spalling, discoloration or local
Mt design bending moment at ultimate
cracking of concrete which could indicate signs of distress, are
Mu ultimate moment
also lacking. Most investigations have so far been concerned
Vtot total shear resistance
with improving inspection methods to determine the extent of
Vu ultimate shear force
deterioration1, 2 but it still remains difficult to make a complete
d ultimate midspan deflection
and realistic assessment. As a result, there is a risk that some
f coefficient of friction between steel and concrete
bridges found to be suffering from corrosion will be repaired,
fu ultimate midspan curvature
strengthened or replaced unnecessarily, and at great cost. Better
methods are therefore required to determine the level of
1. INTRODUCTION deterioration and the residual structural capacity of these
Inspection of the UK’s entire stock of post-tensioned concrete bridges in order to raise confidence levels.
bridges with internally grouted tendons has revealed a variety
of defects. These include regions of grout voids due to This paper discusses the results of a parametric study using a
inadequate grouting in the tendon ducts, and tendon corrosion sophisticated non-linear analytical model which has been
resulting in localised loss of tendon area and, in extreme cases, developed3, 4 to evaluate the residual strength of deteriorated
tendon fractures. These findings raised concerns over the post-tensioned concrete beams. The principal mechanisms of

Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron 341

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 damage considered are the failure of tendons due to corrosion, length of the tendon. The tendon stress is thus member
and incomplete grouting leading to unbonded tendon dependent, and both the lengths and distribution of grout voids
behaviour. need to be considered in the analysis.

2. COMPUTER MODEL The model assumes that tendons are perfectly bonded in fully
A FORTRAN computer program was written to assess the grouted conditions, and where grout voids exist, the tendons
residual strength of deteriorating simply-supported post- are assumed to be totally unbonded over the void length. The
tensioned beams. The program assumes that the beam is of unbonded tendon theory is only applied where voids exist since
constant cross-section and symmetrical about the vertical axis. the prestressing system is likely to comprise a combination of
fully grouted, poorly grouted and totally ungrouted tendons.
The non-linear model adopts the strain compatibility method The analysis is complex and involves both analysis of the effect
based on the general flexural theory for reinforced and of bonded tendon failure and, where voids exist, analysis of the
prestressed concrete beams.5, 6 Prestress losses due to tendon additional effect of the voids using unbonded tendon theory.
stressing are estimated to BS 5400.7 Non-linear material models Determination of the tendon stresses due to the combined
based on Hognestad’s model for concrete and the trilinear and effects of tendon failure and regions of ungrouted tendons
bilinear equations of BS 81108 are adopted to simulate the requires a number of iterations and use of the appropriate
stress-strain behaviour of concrete, the prestressing tendon and subroutine to analyse each case.
unstressed steel respectively. A partial safety factor gm = 1 was
used throughout to define the actual stress-strain behaviour of When the concrete section is cracked, a non-linear analysis is
concrete, the prestressing steel and any untensioned reinforce- required to determine the moment of resistance. This is
ment. The model also accounts for tensile strength of concrete relatively straight-forward for bonded sections, but for sections
and tension stiffening effects in cracked concrete.9 The shear containing unbonded tendons, a further level of iteration is
resistance is predicted by a truss analogy model,10 which has required. At each iteration, the analysis must be conducted at
been found to be suitable for prestressed beams with both every nodal section along the whole length of the void, and this
bonded and unbonded tendons. may involve analysis of both uncracked and cracked sections.
It is only when all affected voided sections have been analysed
The model was then modified to accommodate damage due to that the stress in the unbonded part of the tendon can be
tendon failure as a result of corrosion, and unbonded tendon determined (the stress is member dependent).
behaviour due to regions of incomplete grouting in the ducts.
In order to include the contribution of failed tendons after Clearly, when there are a number of voids along a tendon, and
re-anchoring in the grout, the model incorporates the at various other tendons, the situation becomes very complex.
established tendon re-anchoring phenomenon to estimate the At a section, there may be more than one unbonded tendon
residual prestress. This was achieved by drawing an analogy and, since unbonded tendon stress is member dependent, the
with prestress transfer in pre-tensioned concrete,11–13 where lengths of the voids have to be considered. The solution for
prestress is developed mainly by friction and the wedging analysis of unbonded tendon behaviour therefore involves a
action of the tendon following cutting. Both linear and highly iterative procedure, and can be time-consuming. Due
exponential expressions (with a friction coefficient) to describe to the large number of iterations involved, the analysis is
the re-anchoring behaviour were considered in this model. susceptible to convergence problems and considerable effort
was given to developing efficient solutions. To determine an
The program requires that the beam to be analysed is appropriate number of segments compatible with a time-
discretised into a number of segments to enable analysis at the efficient analysis without compromising the accuracy of
respective nodal sections. Where there are tendon failures, the solution, a trial section was analysed with the beam described
program assumes an idealised resultant distribution of residual below divided into 20, 40, 80 and 160 segments. The accuracy
prestress. Depending on the number and location of tendon of solution achieved in each case and the analysis time taken
failures, determination of the residual prestress distribution by a PC with a 486 DX2-66 processor was monitored. Sufficient
along the length of a beam can involve an appreciable number accuracy was achieved with 80 segments for a beam of this
of iterations at the respective nodal sections to obtain a span and configuration and this was adopted throughout the
solution which satisfies force and moment equilibrium, and parametric study.
the strain compatibility condition.
3. PARAMETRIC STUDY
To study the effect of incomplete grouting on the ability of A parametric study was conducted utilising this analytical
failed tendons to re-anchor, the model adopts the method model to study the influence of tendon failure due to corrosion
of analysis for internal unbonded post-tensioned beams.14 and the presence of grout voids on residual beam strength.4, 15
The method is similar to that for bonded beams, but the stress A simply-supported post-tensioned beam of 18 m span was
in the unbonded tendon cannot be evaluated from moment analysed representative of those from the replaced deck of
equilibrium and strain compatibility alone since perfect bond the Botley bridge, Oxford, UK. The centre span deck of this
between the tendon and the concrete cannot be assumed along 3 span bridge comprised 51 beams of trapezoidal section, which
the voided regions. Instead, the change in stress in the were longitudinally and transversely post-tensioned (Fig. 1).
unbonded tendon at a given loading depends on the average Following discovery of defective grouting and tendon
change in strain in the adjacent concrete over the unbonded corrosion, the main deck was replaced in 1993. This provided

342 Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron

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 The beam was discretised
610 1829 7315 1524 7315 1829 610 into a number of segments
where sectional analysis
was to be performed.
Commencing with the
analysis of the beam under
its permanent load, the load
was then incrementally
increased until failure, whilst
noting the loads to cause
decompression and first
cracking in the concrete. The
ultimate condition was
Fig. 1. Cross-section of main deck of Botley bridge (all dimensions in mm) assumed to be reached when
either the concrete crushed in
compression, the tendons
the opportunity for a series of tests to be undertaken on yielded or failed before failure of the concrete, or premature
individual beams to investigate tendon re-anchoring,2 the shear failure occurred.
results of which were used to validate this analytical model.

The control beam represents the idealised situation of perfect

The model requires input data of the beam geometry, pre- bond in the absence of corrosion or regions of incomplete
stressing tendons and unstressed steel, material properties, grouting. For this beam, the moments required to cause
loading, locations of tendon failure, and extent of grout voids. decompression and first cracking in the concrete were

The twelve 7 mm wires within

each of the five ducts in each 340 355

beam were idealised as a

single tendon of equivalent
area, and tendons at the same
level were located on the
vertical symmetrical axis
710

(Fig. 2). This eliminates any

biaxial effects from lateral
eccentricity of force follow- 50
ing tendon fracture, which
50
was achieved in practice by
lateral confinement provided 75
by adjacent beams within the 100 100
deck.
375

Tendon fracture due to (a) (b)

corrosion, and regions of
grout voids were modelled in Fig. 2. Cross-section at midspan of Botley beam: (a) actual; (b) idealised (all dimensions in mm)
the beam using the notation
shown in Fig. 3. Some typical
deterioration cases considered
are presented in Table 1. The xc (distance to tendon failure)
study consisted of three parts, 18·0 m
aimed at investigating

Void
. the effect of tendon failure
within a well-grouted duct
(i.e. no voids)
. the effect of tendon failure
and presence of limited
voids within the grout xv lu
. the effect of unbonded
tendons alone due to the
presence of grout voids Fig. 3. Damage modelled in the Botley beam
(i.e. no tendon failures).

Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron 343

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 Case No. Description Number xc: Re-anchoring Tendon Grout xv: Void
of failed m model failure void m length,
tendons level level lu: m

Control 0 ^ ^ ^ ^ ^ ^
Tendon C failure:
P2a quarter point 1 4?5 linear C ^ ^ ^
P2b midspan 1 9?0 linear C ^ ^ ^
P2c anchorage 1 0?0 linear C ^ ^ ^
Tendon D failure:
P3a quarter point 1 4?5 linear D ^ ^ ^
P3b midspan 1 9?0 linear D ^ ^ ^
P3c anchorage 1 0?0 linear D ^ ^ ^
Tendons (D + E) failure:
P4a midspan 2 9?0 linear D, E ^ ^ ^
P4b 1 m from anchorage 2 1?0 linear D, E ^ ^ ^
(nominal links not included)
P4c 1 m from anchorage 2 1?0 linear D, E ^ ^ ^
Failure at anchorage, voids present
P5a Tendon C 1 0?0 linear C C 0?0 9?0
P5b Tendons (D + E) 2 0?0 linear D, E D, E 0?0 9?0
P6a Failure of Tendon C at quarter 1 4?5 linear C C 1?0 4?0
P6b point within presence of 1 4?5 linear C C 1?0 6?0
P6c limited voids 1 4?5 linear C C 1?0 9?0
P6d Failure of Tendon C at quarter 1 4?5 linear C C 5?0 3?0
P6e point, voids within re-anchoring 1 4?5 f = 0?35 C C 5?0 3?0
P6f length 1 4?5 f = 0?20 C C 5?0 3?0
P7a Tendon C totally unbonded 0 ^ ^ ^ C 0?0 18?0
P7b 1 0?0 linear C C 0?0 18?0
P8a Voids near anchorage ends 0 ^ ^ ^ D, E 0?0 4?5
D, E 13?5 4?5
C 0?0 4?5
C 13?5 4?5
A, B 0?0 4?5
A, B 13?5 4?5
P9a Failure of Tendon C at quarter 1 4?5 f = 0?20 C C 0?0 18?0
P9b point, tendon re-anchoring 1 4?5 f = 0?10 C C 0?0 18?0
within poor grout
P10a Failure of Tendons (D + E) at 2 0?0 f = 0?20 D, E D, E 0?0 18?0
P10b anchorage, tendon re-anchoring 2 0?0 f = 0?10 D, E D, E 0?0 18?0
within poor grout

Table 1. List of typical deterioration cases considered

calculated to be 492 kNm and 631 kNm respectively. Failure

occurred at midspan at an ultimate moment of 1242 kNm. 1600

The values of the curvature and deflection at this final stage Ultimate moment and curvature
1400 for P2a and P2c similar
are shown in Table 2 and the corresponding tendon stresses are control beam (Table 2)

1200
recorded in Table 3.
1000
Moment: kNm

Under the original design to CP115,16 the design bending 800

moment at service was estimated to be 601 kNm. If this beam

600 Control
is to serve as a Class 1 member (no tensile stresses permitted) P2a

in accordance with the current bridge code, BS 5400,7 the 400 P2b
P2c
decompression moment of the beam therefore needs to be at 200

least 601 kNm. However, even for the control beam with no 0
0 2 4 6 8 10 12
damage simulated, the predicted decompression moment was Curvature at midspan: 10–6 rad/mm

only 492 kNm. The beam thus did not meet the current
serviceability criteria as a Class 1 member. Table 4 shows the Fig. 4. Moment-curvature diagram for failure of Tendon C
estimated decompression moment normalised against the within a well-grouted duct
design bending moment at service.

344 Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron

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 Case No. Mdec: Mcr: Mu: fu d: Case No. Tendon stresses at ultimate at the section
kNm kNm kNm 10”6: mm with maximum tendon stress: N/mm2
rad/mm
Tendons Tendon Tendons
Control 492 631 1242 10?43 303?5 (D + E) C (A + B)
P2a 349 631 1242 10?43 310?5
Control 1248 1143 1038
P2b 395 531 1127 11?84 212?8
P2a 1256 ^ 924
P2c 492 631 1242 10?43 303?6
P2b 1296 ^ 1187
P3a 323 454 1234 9?87 305?6 P2c 1248 1143 1038
P3b 380 515 1093 11?86 194?6
P3a 1318* 1269 1042
P3c 492 631 1242 10?43 303?6
P3b 1297* 1268 1190
P4a * 399 893 14?76 106?1 P3c 1248 1143 1038
P4b * 631 1242 10?43 303?9
P4a ^ 1349 1313
P4c * 631 1242 10?43 303?9
P4b 1248 1143 1038
P5a 395 531 1127 11?47 324?8 P4c 1248 1143 1038
P5b * 399 892 14?67 444?1
P5a 1295 ^ 1183
P6a 359 493 1242 10?43 330?3 P5b ^ 1347 1311
P6b 389 525 1155 7?85 295?5
P6a 1299 ^ 1043
P6c 395 531 1127 11?47 327?8
P6b 1300 ^ 1159
P6d 349 598 1225 9?87 307?6 P6c 1295 ^ 1183
P6e 453 592 1222 9?89 309?0
P6d 1263 866 1058
P6f 435 574 1210 9?83 309?8
P6e 1265 829 1068
P7a 496 634 1234 10?71 310?5 P6f 1268 724 1078
P7b 395 531 1127 11?47 327?8
P7a 1270 901 1089
P8a 492 631 1117 6?74 208?7 P7b 1295 ^ 1183
P9a 349 631 1242 10?43 318?6 P8a 1041 973 906
P9b 349 627 1242 10?28 322?3
P9a 1256 ^ 924
P10a * 631 1242 10?43 304?4 P9b 1256 1092 1040
P10b * 631 1242 10?43 313?1
P10a 1248 1143 1038
P10b 1248 1143 1038
* Concrete decompressed under beam permanent load
* Stress in the remaining unbroken tendon
Table 2. Results for the deterioration cases considered
Table 3. Tendon stresses at ultimate at the section with the
maximum tendon stress

For Class 2 members, tensile stresses are permitted provided

they do not exceed the design flexural tensile strength of
pffiffiffiffiffiffi
concrete, defined as 0?36 fcu in BS 5400. In the analytical moment of 1242 kNm was similar to that of the control beam,
model, the cracking moment was calculated from the tensile and flexural strength was not compromised since the failed
strength of concrete with a partial safety factor gm = 1. This tendon re-anchored within a relatively short length of 675 mm.
gives a predicted cracking moment normalised against the For failure of the tendon at midspan (case P2b), the residual
design bending moment (Table 4) which is less conservative strength was estimated to be 1127 kNm. In this case, tendon
than that obtained by using the serviceability criteria for failure corresponding to an overall 20% loss of area at midspan
Class 2 members. All further discussion of the beam at the resulted in only a 9?3% loss of strength over the control beam
serviceability limit state thus refers to the cracking limit rather due to redistribution of force from the failed tendon to the
than the Class 2 limit. remaining four tendons. Table 4 indicates that, although the
factor of safety provided by the residual strength compared to
3.1. Effect of tendon failure within a well-grouted duct the design ultimate moment is 1?20, the decompression and
The failure of a tendon within a well-grouted duct is first cracking moments had reduced to 395 kNm and 531 kNm
simulated, assuming that there are no regions of incomplete respectively to give a normalised cracking moment of 0?88.
grouting within the duct. In such a case, it is expected that the
failed tendon will be able to re-anchor within a short distance. In all three cases, failure of Tendon C did not result in shear
In practice, most damage in post-tensioned concrete beams resistance deficiency at any point along the beam. The
normally involves tendon failure within a region of incomplete minimum values of shear capacity normalised against ultimate
grouting, and this is considered later. shear (always at the support unless otherwise indicated) is
recorded in Table 4.
Figure 4 shows the predicted moment-curvature response due
to failure of the central Tendon C at various locations along the A similar response resulted when failure of Tendon D was
beam. It illustrates that neither failure of the tendon at quarter simulated at quarter span, midspan and the anchorage
span (case P2a) nor at the anchorage (case P2c) resulted in a respectively. Failure of this tendon at midspan (case P3b)
reduction in flexural strength. In both cases, the ultimate resulted in a lower residual strength of 1093 kNm (12% loss of

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 Case No. Mdec Mcr Mu V tot 1400

Ms Ms Mt Vu
1200
(Class 1 limit) (cracking limit)
1000

Control 0?82 1?05 1?32 1?87

Moment: kNm
800
P2a 0?81 1?05 1?32 1?87
P2b 0?66 0?88 1?20 2?06 600

P2c 0?82 1?05 1?32 1?78 Control

400 P2b - Tendon C
P3a 0?75 1?05 1?31 1?88 P3b - Tendon D
P4a - Tendons (D+E)
P3b 0?63 0?86 1?16 2?10 200

P3c 0?82 1?05 1?32 1?64

0
0 2 4 6 8 10 12 14 16
P4a ^ 0?66 0?95 2?53 Curvature at midspan: 10–6 rad/mm
P4b ^ 1?05 1?32 0?94*
P4c ^ 1?05 1?32 1?03*
Fig. 5. Moment-curvature diagram for failure of Tendon C,
P5a 0?66 0?88 1?20 1?97 Tendon D or Tendons (D + E) at midspan
P5b ^ 0?66 0?95 1?06
P6a 0?78 1?07 1?32 1?87
P6b 0?70 0?94 1?23 2?01
P6c 0?66 0?88 1?20 2?06
moment-deflection response (Fig. 6), which shows that, even
P6d 0?81 1?02 1?30 1?90 for failure of the tendon at the critical midspan section, no
P6e 0?78 1?01 1?30 1?90
significant increase in deflection was predicted. Even when
P6f 0?75 0?98 1?29 1?92
both the bottom tendons failed (case P4a), the deflection profile
P7a 0?83 1?05 1?31 1?91 hardly departs from the control situation except for a reduction
P7b 0?66 0?88 1?20 1?97
in maximum deflection at the ultimate condition. At this stage,
P8a 0?82 1?05 1?19 2?18 the stress in the remaining tendons had reached values of
P9a 0?81 1?05 1?32 1?87 1349 N/mm2 and 1313 N/mm2, respectively representing 86%
P9b 0?81 1?05 1?32 1?86 and 84% of the ultimate tensile strength (UTS) of the tendon.
P10a ^ 1?05 1?32 0?79
P10b ^ 1?05 1?32 0?79 This study shows that deflection is not significantly affected by
local tendon failure until collapse is imminent, hence deflection
* Values at 1?0 m from left hand support
monitoring is likely to be largely ineffective to detect any local
damage. This behaviour supports the findings of previous
Table 4. Normalised values for serviceability and ultimate
investigators17, 18 that local failure of grouted tendons is not
limit states
necessarily accompanied by visible signs of distress unless
collapse is imminent.

strength) compared to case P2b, due to the greater lever arm of Case P4b simulates failure of the two bottom tendons near the
the lower Tendon D. In this case, the cracking moment reduced anchorage. This area is vulnerable to tendon corrosion
to 515 kNm, giving a normalised cracking moment of 0?86 especially if the duct is not properly sealed against the ingress
(Table 4). When tendon failure occurred away from the critical of chloride-laden water, and localised corrosion resulting in
midspan section, the reduction in flexural strength was severe pitting and tendon failure is possible. In this analysis,
negligible. This is demonstrated by failure of tendon D at the existing shear reinforcement was neglected. It was found
quarter span (case P3a), which gave a residual strength of that the total shear resistance provided by the residual
1234 kNm (0?7% strength reduction), and tendon failure at prestressing force and the concrete alone was marginally
the anchorage (case P3c) where flexural strength was not
compromised.

1400
The failure of both the bottom Tendons (D + E) at midspan is
1200
simulated in case P4a. In this case, it was found that concrete
decompression had already occurred under permanent load 1000

alone, and the beam failed at a much lower moment of P3b

Moment: kNm

800
893 kNm. The flexural strength was significantly reduced in P2b
600 P4a
this case (28% loss of strength), providing a factor of safety of
0?95 (Table 4), but only after the beam had accommodated a 400
Control
P2b - Tendon C
40% overall loss of tendon area at the critical midspan section. 200
P3b - Tendon D
P4a - Tendons (D+E)
The cracking moment reduced to 399 kNm, corresponding to a
0
normalised cracking moment of only 0?66 (Table 4). 0 50 100 150 200 250 300 350
Deflection at midspan: mm

Figure 5 shows the increased midspan curvature associated with Fig. 6. Moment-deflection diagrams for failure of Tendon C,
failure of both bottom tendons compared to that for failure of Tendon D and Tendons (D + E) at midspan
Tendon C or Tendon D alone. The damage is not apparent in the

346 Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron

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 may well be deficient. However, this was found not to be the
600
case as the ultimate condition was reached at a significantly
500
lower strength of 892 kNm and, at this stage, the shear force at
the anchorage did not exceed the shear resistance provided.
Vu = 248 kN
400 P4b: Vtot = 233 kN
Shear force: kN

P4c: Vtot = 256 kN

300 Figure 8 shows the increased deflection and significantly lower

residual strength for case P5b. A similar profile was obtained
200
for the moment-curvature diagram. Although tendon failure
100 Vu occurred at the anchorage in both cases P5a and P5b, the
P4b
P4c
presence of the long length of void did not allow the failed
0
0 2000 4000 6000 8000 10 000 12 000 14 000 16 000 18 000 tendon to re-anchor, and the capacity at midspan was
Length: mm
compromised as if tendon failure occurred at midspan itself.
As a result of reduced cracking moments of 531 kNm and
Fig. 7. Reduced shear resistance provided after failure of
399 kNm for case P5a and P5b respectively, the normalised
Tendons (D + E) near the anchorage
cracking moments were reduced accordingly (Table 4), and case
P5b failed to provide a sufficient factor of safety against
collapse due to reduced flexural strength.
insufficient to resist the shear force near the anchorage (Fig. 7),
indicating that premature shear failure could occur without the In each case, there was an appreciable increase in deflection as
addition of a moderate amount of shear reinforcement. a result of debonding and loss of prestress force over the void
length. The void has the effect of increasing the distance over
For the Botley beams, nominal links (R10 links at 450 mm which tendon failure occurs, resulting in a larger deflection
centres) were provided, somewhat less than the current than that produced due to localised tendon failure within a
minimum shear requirement of BS 5400. Nonetheless, when the well-grouted duct (Fig. 6). This study demonstrates that tendon
nominal links were considered in case P4c, the total shear failure is not necessarily accompanied by significant increase in
resistance was found to be sufficient to resist the shear force deflection unless it loses its prestress force over an appreciable
near the anchorage (Fig. 7), and the normalised shear capacity distance due to poor or incomplete grouting.
was increased from 0?94 to 1?03 (Table 4).
Figure 9 shows the residual prestress distribution at the ultimate
3.2. Effect of tendon failure in the presence of limited condition for case P5a. It indicates that where a void exists
voids within the grout within the re-anchoring length, the tendon is assumed to be
In the analytical model, both the location and length of grout totally unbonded over this length and does not re-anchor until
voids are required to be input. However, this is difficult to sound grout conditions are re-established. As a result, the stress
determine accurately in practice due to the limitations of in the remaining tendons increased significantly in the half of
current inspection techniques. In the field tests on the Botley the beam containing the failed tendon. This is more significant
beams, voids were identified by drilling into the ends of the in case P5b where the concrete had already decompressed as a
ducts, and subsequently pressure tested to determine the void result of failure of the two bottom tendons. Although collapse
volume. Clearly whilst this gives some information, it does not occurred at a much lower moment in this case, the stress in the
determine the precise location or length of grout void. The use remaining tendons in regions containing the failed tendons had
of this analytical model therefore requires engineering judge- already reached a maximum of 1347 N/mm2 (86% UTS) and
ment based on experience and knowledge of the likelihood of 1311 N/mm2 (84% UTS) for Tendons C and (A + B) respectively
void locations. A good estimate can then be made to simulate (Table 3).
the conditions most likely to occur in practice. It is also
expected that the more promising non-destructive test methods
will be sufficiently developed to detect the presence and extent
of grout voids more reliably in the future. There is hence a need 1400

for better inspection methods to make the analysis less subject 1200
to the experience of the user.
1000
Moment: kNm

3.2.1. Effect of void length. The results from the mandatory 800

inspection of post-tensioned bridges indicate that grout voids

600
tend to exist more commonly near the anchorage. It is also in
this region that there is an increased risk of tendon corrosion 400
Control

and fracture due to improperly sealed anchorages. This type of 200

P5a - Tendon C

P5b - Tendon (D+E)

damage is simulated in case P5a for failure of Tendon C at the
0
anchorage, with the presence of a long void extending from the 0 50 100 150 200 250 300 350 400 450
Deflection at midspan: mm
anchorage to midspan. It was found that the shear resistance at
the anchorage was still sufficient to resist the ultimate shear
Fig. 8. Moment-deflection diagrams for failure of Tendon C
force (Table 4) and did not govern failure of the beam. When
and Tendons (D + E) at the anchorage, with the presence of
failure of the two bottom tendons at the anchorage was voids in the grout
simulated in case P5b, it was expected that the shear resistance

Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron 347

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 1400

1400
1200 Remaining

Tendon stress, fps: N/mm2

tendons
1200
1000
Tendon stress, fps: N/mm2

1000
800
800
600
600
Failed
400 tendon
Tendons (D+E)
Tendons (D+E) 400 Tendon C
200 Tendon C Tendons (A+B)
200
Tendons (A+B)
0
0 2000 4000 6000 8000 10 000 12 000 14 000 16 000 18 000 0
Length: mm (a)
1400

Tendon stress, fps: N/mm2

1200
Fig. 9. Tendon stress distribution at the ultimate condition for
Case P5a 1000

800
600
The failure of Tendon C at quarter span within various lengths 400
of grout voids is considered in cases P6a, P6b and P6c. It was
200
found that for case P6a (void length 4 m), the flexural strength
was not compromised and the ultimate condition was reached 0
(b)
at midspan at 1242 kNm. The longer void (length 6 m) in case 1400
P6b caused a 7% loss of strength as the ultimate condition Tendon stress, fps: N/mm2 1200
was reached at the end of the void (but not at midspan). For
1000
case P6c where the void (length 9 m) extends past midspan, the
ultimate moment was reached at midspan instead at 1127 kNm, 800
representing a 9?3% loss of strength. In all three cases, prestress 600
was lost over the entire void length containing the failed
400
tendon. As a result, the moment-deflection profiles (Fig. 10)
indicate some damage, even for case P6a where flexural 200
strength was not compromised. 0
0 4000 8000 12 000 16 000
Length: mm
Figure 11 illustrates the resulting distribution of residual (c)
prestress at the ultimate condition for the three cases
considered here. It indicates that the stress in the remaining
Fig. 11. Tendon stress distributions at the ultimate condition
unbroken tendons increased significantly in the regions of for cases P6a, P6b and P6c: (a) P6a (void length 4 m);
incomplete grouting containing the failed tendon, but also that (b) P6b (void length 6 m); (c) P6c (void length 9 m)
the maximum tendon stress is not necessarily at the critical
midspan section. The maximum tendon stresses are recorded in
Table 3.
of failed tendons, as it affects the distribution of residual
prestress following tendon failure.
This study demonstrates that the length of grout voids in a
beam is an important factor when considering the re-anchoring
3.2.2. Effect of poorly grouted ducts. The grout voids considered
so far have been concerned with a completely ungrouted length
1400 of duct, which would have prevented a failed tendon from
re-anchoring within it. However, visual evidence suggest that
1200
voids often occupy a greater length of poorly grouted duct,
1000 with the tendons partially exposed above the grout. Therefore,
some re-anchoring is possible for tendon failure within a poorly
Moment: kNm

800
grouted duct although a longer length may be required.
600
Control
P6a (void length 4 m)
400
P6b (void length 6 m) Cases P10a and P10b represent the failure of the two bottom
200
P6c (void length 9 m)
tendons at the anchorage in the absence of voids (as opposed to
P5b). However, exponential re-anchoring models with f = 0?2
0
0 50 100 150 200 250 300 350 and f = 0?1 have been adopted to simulate less efficient
Deflection at midspan: mm
re-anchoring within a poorly grouted duct. It was found that
flexural strength was not compromised although the failed
Fig. 10. Moment-deflection diagram for failure of Tendon C at
quarter span within different lengths of grout voids tendons required relatively longer lengths of 4050 mm and
8100 mm respectively to re-anchor compared with 675 mm

348 Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron

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 for P5b (measured from the end of the void). Since some
1400
re-anchoring occurred immediately after tendon failure with no
extensive debonding as in case P5b, the deflection increased 1200

only marginally (Table 2). However, this study revealed

Tendon stress, fps: N/mm2

1000
interesting results when compared with case P5b where a void
was modelled over half the length of the duct, and the failed 800

tendons could not re-anchor until past midspan. As a result, the 600
residual strength was reduced to 892 kNm, but when poor grout
400 Tendons (D+E)
was considered (case P10a and P10b), the flexural strength was Tendon C
not compromised. However, due to higher ultimate load 200 Tendons (A+B)

achieved in cases P10a and P10b, the shear resistance at the 0

anchorage was found to be insufficient to resist the ultimate (b)
1400
shear force (Fig. 12) and premature shear failure was predicted
to occur instead (Table 4). 1200

Tendon stress, fps: N/mm2

1000

800
The failure of Tendon C at quarter span within a poorly grouted
duct (no full voids modelled) is investigated in cases P9a and 600

P9b with f = 0?2 and f = 0?1 respectively. Fig. 13 shows the 400
Tendons (D+E)
Tendon C
tendon stress distribution at the ultimate condition. Compared
Tendons (A+B)
200
to P6a (Fig. 11), the stresses in the remaining tendons in cases
P9a and P9b are slightly lower. This is because the failed tendon 0
0 2000 4000 6000 8000 10 000 12 000 14 000 16 000 18 000
started to re-anchor immediately to contribute to the overall Length: mm
(b)
prestress, resulting in lower stresses in the other tendons.
Although relatively longer re-anchoring lengths of 4050 mm
Fig. 13. Tendon stress distribution at the ultimate condition
and 8100 mm were required for cases P9a and P9b respectively,
for cases P9a and P9b (a) P9a ( f = 0?2) (b) P9b ( f = 0?1)
the residual strengths of the beams were comparable to case
P6a. In fact, as demonstrated in cases P6b and P6c, the presence
of a concentrated void is more critical if it extends a long
distance and does not allow a failed tendon to re-anchor. The re-anchoring model was found not to affect the residual
beam strength significantly, the main difference being the
lower level of residual prestress in Tendon C within the void for
3.2.3. Presence of voids after a failed tendon has started to the poorer grout conditions. Figure 14 illustrates the tendon
re-anchor. Cases P6d, P6e and P6f consider the failure of stress distribution at the ultimate condition for case P6f. Even
Tendon C at quarter span, with grout voids present within the for this worst case, the residual strength was 1210 kNm, only
re-anchoring length after the tendon has started to re-anchor. It 2?6% lower than for the control beam. However the normalised
is assumed that some re-anchoring has already occurred before cracking moment was reduced from 1?05 to 0?98 (Table 4) in
a void is encountered, and that no further re-anchoring is this case.
possible until the end of the void length. Different re-anchoring
models were employed to represent various grout conditions This study demonstrates that the presence of voids after a failed
surrounding the failed tendon. Case P6d represents linear tendon has started to re-anchor is not as critical as tendon
re-anchoring within relatively good grout whilst cases P6e failure within a fully ungrouted region. The main concern is the
and P6f represent exponential re-anchoring with f = 0?35 and condition of the grout and whether it is sufficient in quality
f = 0?2 respectively to simulate poorer grout conditions. and integrity to allow some re-anchoring to occur.

700 1400

600 1200

500 1000
Tendon stress, fps: N/mm2

Vu = 276 kN
P10a: Vtot = 218 kN
Shear force: kN

400 P10b: Vtot = 218 kN Vu 800

P10a

300 P10b 600

200 400 Tendons (D+E)

Tendon C

200 Tendons (A+B)

100

0 0
0 2000 4000 6000 8000 10 000 12 000 14 000 16 000 18 000 0 2000 4000 6000 8000 10 000 12 000 14 000 16 000 18 000
Length: mm Length: mm

Fig. 12. Reduced shear resistance provided after failure of Fig. 14. Tendon stress distribution at the ultimate condition
Tendons (D + E) at the anchorage for case P6f ( f = 0?2)

Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron 349

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 3.3. Effect of unbonded tendons due to the presence available grout. Concern arises when the duct is incompletely
of voids grouted at the anchorage, thus not enabling a failed tendon to
re-anchor in this region.
3.3.1. Totally ungrouted tendon. Inspection of the Botley beams
revealed that one had a totally ungrouted duct. This is Case P8a considers the undesirable situation where voids exist
simulated in Case P7a were the central Tendon C is totally at the anchorage at both ends of the beam for all five tendons.
ungrouted, with the remaining four tendons assumed to be fully The aim was to investigate if the presence of grout voids alone
grouted. In this case, the flexural strength was 1234 kNm, at the anchorage, with no tendon fractures, is detrimental to the
representing only a 0?8% loss of strength. Although the capacity of the beam. In this case, since a relatively long void
ultimate stress in the unbonded tendon (901 N/mm2) was (4?5 m at each end) was modelled for each tendon, the limiting
appreciably different from that in the fully grouted control compressive strain of concrete was reached first at the end of
beam (1143 N/mm2), the reduction in overall strength was the void near midspan, which precipitated an earlier collapse
marginal (Fig. 15). The performance at service was not moment of 1117 kNm (10?1% reduction in strength) as shown
dissimilar from that of the fully grouted beam but as conditions in Fig. 16 but still 19% above the design ultimate moment
approach ultimate, the small loss in strength is apparent. This (Table 4).
behaviour is also demonstrated in the moment-curvature curve,
suggesting that a totally unbonded tendon alone with no 3.4. Analysis times
tendon failure may not cause significant increase in curvature The analysis for P7a required a relatively long run time
or deflection, provided some bonded tendons are present. (about 4?5 h on a PC with a 486 DX2-66 processor) since the
stress in the unbonded tendon is member-dependent and the
If the tendon within this totally ungrouted duct were to fail analysis had to be undertaken at all nodal positions along
anywhere along its length due to corrosion (analysed in case the whole length of the beam at every iteration until a state of
P7b), this would result in a 9?3% loss of strength. This is due to force and moment equilibrium was achieved. Table 5 compares
loss of prestress force over the entire unbonded length as the the time taken for this analysis with those for the other
failed tendon is not able to re-anchor. As a result of loss of deterioration cases considered. It indicates that where a void
prestress force over an extensive length, an increase in was simulated, the analysis time increased significantly
deflection is apparent even from an early stage (Fig. 15). depending on the void length. When no void was simulated, the
time taken for analysis of the beam with grouted (or poorly
This study indicates that voids alone within a duct may not grouted) tendons was always less than 10 minutes.
present a great risk to the integrity of the beam, particularly
when the conditions within it are dry. An ungrouted duct will 4. CONCLUSIONS
however, reduce the capacity of the beam to accommodate Based on the analytical results discussed in this paper, the
further deterioration, as exemplified in case P7b where flexural following conclusions can be made. Significant levels of
strength was compromised due to loss of prestress over the deterioration do not always compromise flexural strength to
whole length of duct following tendon failure at a single the same degree. In the cases considered, tendon failure
point. However, it is only when corrosion is allowed to occur corresponding to an overall 20% loss of tendon area at midspan
(due to ingress of water and chlorides) that the flexural strength resulted in a typical 10% loss of flexural strength. For a 40%
may be significantly affected. overall loss of tendon area, a reduction in strength of 28%
resulted. Where tendon failure occurs away from the critical
3.3.2. Tendons ungrouted at both ends. For the Botley beams, it midspan section, the reduction in strength is further reduced.
was reported that voids in the grout were discovered near the The loss of prestressing force due to tendon failure heavily
anchorage. The integrity of the anchorages are normally of influences the load at which the behaviour of the beam first
secondary concern if the ducts are fully grouted since, in the becomes non-linear. In the analytical model, the effect of
event of failure of the anchorage or the tendon itself at the incomplete grouting was investigated using the theory for
anchorage, the failed tendon is able to re-anchor in the internal unbonded beams. It was found that although the

1400 1400

1200 1200

1000 1000
Moment: kNm
Moment: kNm

P8a
800 800

600 600

Control
400 P7a 400 Control
P7b P8a
200 200

0 0
0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350
Deflection at midspan: mm Deflection at midspan: mm

Fig. 15. Moment-deflection diagram for Tendon C totally Fig. 16. Moment-deflection diagram for the beam with grout
ungrouted along the length of the beam voids present at the anchorage

350 Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron

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 its prestress force over an
Case No. Description Time taken to
run analysis: appreciable distance due to
min the absence of grout. The use
of exponential re-anchoring
Control 7 to model poor or incomplete
Tendon C failure:
grouting conditions results
P2a quarter point 7
P2b midspan 5 in a relatively longer tendon
P2c anchorage 7 re-anchoring length. How-
Tendon D failure: ever, the re-anchoring model
P3a quarter point 7 adopted, whether linear or
P3b midspan 5 exponential, does not signi-
P3c anchorage 7 ficantly affect residual
Tendons (D + E) failure: strength.
P4a midspan 3
P4b near anchorage 7
P4c near anchorage 7 The failure of tendons within
a poorly grouted duct is not as
Failure at anchorage, voids present
P5a Tendon C 31 detrimental as the failure of
P5b Tendons (D + E) 24 tendons within an ungrouted
Tendon C failure, voids present region. This is because some
P6a Failure of Tendon C at quarter point within 20 tendon re-anchoring is
P6b presence of limited voids 24 possible within a poorly
P6c 28 grouted duct but not where a
Tendon C failure, voids within re-anchoring length void exists. In practice, most
P6d Failure of Tendon C at quarter point 19 ducts have been found to be
P6e 17 at least partially grouted and
P6f 17 some immediate tendon
Tendon C totally unbonded re-anchoring is possible. The
P7a No tendon failure 272 presence of voids within the
P7b Tendon C failure 54
grout where a failed tendon
Voids near anchorage ends had started to re-anchor was
P8a No tendon failure 95 found to be of secondary
Tendon C failure within poor grout concern compared to the
P9a Failure of Tendon C at quarter point, tendon 7 failure of a tendon within a
P9b re-anchoring within poor grout 7
fully ungrouted region. The
Tendons (D + E) failure within poor grout condition of the grout and
P10a Failure of Tendons (D + E) at anchorage, 7 whether it is sufficient in
P10b tendon re-anchoring within poor grout 7
quality and integrity as
to permit some partial
Table 5. Time taken to analyse the deterioration cases considered
re-anchoring to occur, will
determine the re-anchoring
behaviour of the failed
tendon in this case. The
presence of grout voids alone (no tendon failure) may not anchorages have been shown to be a potential point of
significantly affect flexural strength, the presence of voids will, weakness due to their vulnerability to corrosion. However, a
however, reduce the capacity of the beam to accommodate relatively high percentage of tendon loss of area may be
further deterioration. For instance, failure of a tendon in a accommodated before the shear resistance is found to be
grouted duct will result in a local reduction in prestress which deficient (40% loss of overall tendon area in the case
may be insignificant if it occurs at non-critical sections, considered here).
whereas a similar defect in an ungrouted duct will cause a loss
of prestress over the whole length of the tendon and may The understanding provided by this study of the behaviour of
significantly reduce load capacity. deteriorating post-tensioned concrete bridges will assist in the
management of the deterioration process and development of
The presence of voids at or near to a tendon fracture will affect strategies for extending the lives of such structures through
the ability of a failed tendon to re-anchor fully. This may have repair and strengthening, so avoiding unnecessary demolition.
a profound effect on residual strength, particularly when a duct
contains long or continuous voids. The length and distribution 5. ACKNOWLEDGEMENTS
of grout voids along the beam are important factors when The authors gratefully acknowledge the financial support of
considering loss of strength. The deflection profile of a beam is the Engineering and Physical Sciences Research Council
not significantly affected by local failure of a grouted tendon (Grant No. GR/J/45169) and the contribution of Oxfordshire
until collapse is imminent. Thus monitoring of deflection may County Council in providing the original design calculations
not reveal signs of distress unless the failed tendon has lost and access to the demolished bridge beams.

Structures and Buildings 146 Issue 4 Parametric study of the residual strength of bridges Cavell 0 Waldron 351

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 REFERENCES 11. AMERICAN CONCRETE INSTITUTE. Building Code Requirements
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Department of Civil and Structural Engineering, 1997. Bridges. Proceedings of the 5th International Conference on
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Please email, fax or post your discussion contributions to the secretary: email: lyn.richards@ice.org.uk; fax: +44 (0)20 7799 1325;
or post to Lyn Richards, Journals Department, Institution of Civil Engineers, 1^7 Great George Street, London SW1P 3AA.

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