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PRESTRESSED CONCRETE INTEGRAL ABUTMENT BRIDGES
WITH REINFORCED CONCRETE PILES
David Gama
Department of Civil Engineering, Architecture and Georesources, IST, Technical University of Lisbon
Av. Rovisco Pais, 1049-001 Lisbon, Portugal. [email protected]
October 2012
__________________________________________________________________________________________
ABSTRACT: Integral Abutment Bridges (IABs), especially with abutments supported on reinforced concrete
piles, are bridges for which the limits of use are not yet completely clarified, mostly due to the fact that they are
dependent on a great number of factors – ranging from the constraints and design options, to the level of
approximation used in structural analysis. On the other hand, and although IABs are cost effective designs in
term of maintenance, in prestressed concrete IABs, additional prestressing force is needed, compared to what is
expected for non-integral bridges, resulting in increased initial costs. This paper presents the results of a
parametric study of the influence of the design variables, usual in this type of structures, on the possibilities of
their use in lenghts up to 200m and on their structural behaviour and prestressing force design. The parametric
study was based on numerical modelling, where four levels of approximation were established for structural
analysis, permitting to analyse the structure with analyses ranging from simple, linear-elastic, to complex, taking
into account material non-linearity for both concrete and soil. The results obtained indicate that, even with the
important limitation of crack control in the abutment piles, in general, the use of adequate design options and
levels of approximation, should allow a wider use of IABs with reinforced concrete piles, in bridges with lengths
up to 200 meters, although, comparing with non-integral designs, an additional average amount of up to 30% of
prestressing force is to be expected, for bridges of such extensions. Keywords: Prestressed concrete bridges, integral abutment bridges, reinforced concrete piles, imposed
deformations, soil-structure interaction, levels of approximation.
__________________________________________________________________________________________
1. INTRODUCTION
IABs are structures with no bearings or expansion joints,
in which the transmission of loads from the deck to the
elements of the substructure is made monolithically. The
main problems in this type of design result from the
cyclical contraction and expansion movements of the
bridge, due to creep, shrinkage and thermal variations in
the deck. In the case of contraction two main problems
arise: (i) the restriction to deck shortening, resulting in the
reduction of the compression state in this element over
time (Fig. 1 a)), thus creating a need for an additional
amount of prestressing force and (ii) the bending stresses
in the vertical elements resulting from the imposed
deformations (Fig. 1 b)), being a limitation to the
serviceability design. In this case, and particularly for
bridges with greater lengths, taking the cracking effect -
i.e. the non-linear concrete behaviour - into account in
structural analysis, can become relevant, as stresses due
to imposed deformations depend on the stiffness of the
structure. Furthermore, and as in both situations the
concrete visco-elastic properties result in a relaxation of
the stresses induced in the structural elements over time,
this aspect should also be considered.
a) Compression state in the deck vs time (P-prestress)
b) Contraction movement: imposed deformations on
vertical elements
Figure 1
time
Com
pre
ssio
n s
tate
in t
he
dec
k
Pt=t0
Temperature
creep, shrinkage
t0
P∞
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
2
Although in the case of contraction it is necessary to warrant
the equilibrium of the active earth pressures due to abutment
movements, it is in the case of expansion (Fig. 2) that earth
pressures can become a limitation. This is, in fact, the main
problem related to the expansion movements in IABs.
Consequently, it is necessary to properly take into account the
soil-structure interaction, the main difficulty being the
prediction of the effects of the cyclical abutment movements
on the behaviour of the approach embankments. These effects
lead, on the medium term, to important passive earth
pressures, even for minor abutment displacements towards
the approach embankments. In some cases, they can even reach the limit passive value, after a few years. Amidst
the attempts to predict earth pressures in IABs, Kerokoski´s proposal [1] can be singled out, based on which, the
author approximates in a very reasonable way results obtained from IABs instrumentation.
The most common, among the variety of design types existing for IABs, is the
one in which the abutments are founded on a single row of piles (Fig. 3), mainly
of steel in the United States [2] - a country where the use of IABs is established -
. However, in some countries, where IABs are still seldom used (as is the case of
Portugal), there is a traditional use of reinforced concrete piles in non-integral
bridges, and, therefore, a tendency for their use in IABs [3]. With this in view,
and considering the limited amount of published material concerning the use of
this type of piles in IABs, a parametric study was made. The aim of the study
was to relate the project constraints and the design options of prestressed
concrete IABs using reinforced concrete piles, with: (i) the possibilities of use in
lenghts up to 200m; (ii) their structural response and (iii) the additional
prestressing force necessary, compared to the need in non-integral designs. This
study also aimed to establish levels of approximation for structural analysis, in order to understand when – i.e. in
which combination of design variables – it will become necessary to resort to complex analyses, and when
simpler ones can be used, considering both concrete behaviour and soil-structure interaction.
2. PARAMETRIC STUDY
2.1. Basic data
As base case for the parametric study a bridge
design commonly used in overcrossings and
viaducts was considered (Fig. 4). A prestressed
concrete road bridge with spans of l=30.0m and
lateral spans of 0.5l=15.0m. The slab of the
deck has a width of 6.0m, the depth of the cross
section is 1.2m and is supported by: (i) piers
with a height of 8.0m, circular cross section of
1.0m, monolithically connected to the
superstructure and with a spread footing
foundation; (ii) abutments with a rectangular
cross section 6.0m wide, and a depth of 1.0m
(if founded on three 0.6m piles) or 1.4m (if
founded on three 1.0m piles), monolithically connected to the superstructure. The prestress tendon layout is
similar to what would be adopted in non-integral designs, namely without the consideration of any eccentricity at
the deck extremities. The concrete of the deck is class C35/45 and for the rest of the bridge members C30/37.
The reinforcing steel is A500NR, and the prestressing steel A1670/1860. The exposure classes are XC4 for piers,
deck and abutments and XC2 for the foundation elements. The approach embankments have the height of the
abutments. Only straight, unskewed and symmetrical bridges were considered, to limit the scope of the study.
Figure 4. Base case for the parametric study
Figure 3. Single row of piles
supporting an IAB
abutment
Figure 2. Expansion movement: Earth pressures
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
3
2.2. Study parameters
The design variables are divided in three categories: (A) project constraints, (B) design options and (C)
constructive processes (Table 1 and Fig. 4). Each considered design variable can affect: (i) the quantification of
secondary loads (QSL) – shrinkage, creep or uniform temperature -; (ii) the magnitude of the earth pressures
(QEP) and/or (iii) the structural behaviour (SB). The prestressing force calculations are affected equally by the
magnitude of secondary loads and by the design options.
Table 1. Design variables: Project constraints (A); Design options (B); Constructive processes (C)
(A) Project Constraints Parameters Variation Affects
A1 - Bridge location Ambient temperature [ºC] -10 to -20/+30 QSL
Relative Humidity (RH) [%] 50 to 75 QSL
A2 - Bridge length L [m] up to 210
A3 - Geotechnical (foundations) Soil stiffness (Ksoil) Table 2 SB
(B) Design Options Parameters Variation Affects
B1- Type of deck: concrete slab /
concrete beam
Average compressive stress in concrete due
to prestressing force ( ̅) [MPa] 3; 5 QSL
Notional thickness (h0) [mm] 300; 500 QSL
B2 - Cast-in-place / Precast Deck Time at deck/abutment connection [days] 15; 100 QSL
B3 - Concrete composition Cement type [CEM] N; R QSL
B4 - Abutment height H [m] 2 to 4 SB/QEP
B5 - Pile bending stiffness Diameter ( ) [m] 0.6; 1.0 SB
B6 - Geotechnical characteristics of
approach embankments
Angle of internal friction ( ´) [º] 38º to 43º QEP
Dry unit weight ( ) [kN/m3] 19,5 to 22
(C) Constructive Processes Parameters Variation Affects
C1 - Age of concrete at prestressing t0 [days] 15 to 30 QSL
Table 2. Soil properties, for the definition of elastic-linear models and ´p-y` curves (from [10]).
Description [kN/m3] ´ [°] kpy [kN/m3] cu [kN/m2] [-]
Medium dense sand (MDSand) 18,0 34 24400 - -
Dense sand (DSand) 19,5 38 61000 - -
Overconsolidated clay (OClay) 17,0 - - 100 0,005
2.3. Loads
A characteristic combination of actions was used. The vertical loads - dead loads and live loads – were
quantified according to the EN1991-2 [4]. The secondary loads were quantified according to the EN1991-1-5 [5]
and the EN1992-1-1 [6], and were considered in the structural analysis as a uniform temperature equivalent
( ). For were distinguished: (i) bridge contraction, where
,
for which minimum ( ) and maximum (
) limits were defined, depending on the design variables
A1, B1, B2 and B3 and also (ii) the bridge expansion, where
which depends only on A1.
For uniform temperature ( ), and for the effects of contraction ºC and
ºC were
considered. For the expansion situation only ºC was taken into account. To model the effect of deck
shortening resulting from prestress – elastic and due to creep ( ) - were considered: (i)
ºC, corresponding to h0=300mm, RH=75%, t0=28 days and ̅ and (ii) ºC
corresponding to h0=500mm, ̅ , RH=50% and t0=15 days. To model shrinkage ( ) were considered:
(i) ºC, corresponding to a precast deck, with h0=300mm, RH=75% and CEM N and (ii)
ºC, corresponding to a cast-in-place deck, with h0=500mm, CEM R, and RH=50%.
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
4
Thus were defined a range of values representative of imposed deformations on the deck, corresponding, for
contraction to: ºC;
ºC and ºC, and in the case of expansion to:
ºC.
2.4. Numerical model and levels of approximation
The structural analysis software SAP2000 [7] was used to model the structure, with a 2D finite-element model
(FEM), as in the case of straight and unskewed IABs, it provides results that are very similar to those of a 3D
FEM [8]. Four analysis models were used, corresponding to four levels of approximation (LoA), for each of
which the level of accuracy used in the modelling procedure varies, depending on: (i) soil-pile interaction; (ii)
backfill-abutment interaction (earth pressures) and (iii) material behaviour of concrete (cracking effect).
For LoA I (Fig. 5 a)) were used: (i) linear-elastic springs; (ii) triangular earth pressure distribution obtained on
the basis of the Caquot-Kérisel theory and (iii) linear-elastic analysis, based on the uncracked bending stiffness
(EI) of the structural elements. For LoA II (Fig. 5 b)) were used: (i) linear-elastic springs; (ii) triangular earth
pressure distribution obtained on the basis of the Kerokoski proposal for the definition of earth pressures on
IABs [1] and (iii) linear-elastic analysis based on a bending stiffness secant (EIsec) to the structural elements
average moment-curvature relationship (M- m) [9], in order to indirectly take into account the effect of concrete
cracking in structural analysis, which results in the reduction of bending stiffness. For LoA III (Fig. 5 c)) were
used: (i) linear-elastic springs; (ii) force-deflection elastic-plastic springs based on the Kerokoski proposal and
(iii) first order non-linear analysis based on the structural elements M- m, in order to take into account the effect
of concrete cracking directly. For LoA IV (Fig. 5 d)) were used: (i) non-linear springs based on the ´p-y` curves
method [10]; (ii) force-deflection elastic-plastic springs based on the Kerokoski proposal and (iii) first order non-
linear analysis based on the structural elements M- m.
In all LoA, to evaluate the stresses caused by time-dependent effects, the age-adjusted effective modulus method
was used ( ), with
[11], as, in this context, there is no advantage in the use of step-by-step
methods, as discussed in [9]. Given that the reduction of takes on different values, according to the
duration of the application of the time-dependent effects: (i) infinite time for shrinkage and creep, and (ii)
seasonal for thermal effects, as simplification a weighted average of loads was considered, admitting a unique
reduction to the modulus of elasticity of concrete, .
LoA I LoA II LoA III LoA IV
Figure 5. Levels of approximation established for structural analysis
2.5. Influence of design variables on the structural behaviour
In this paragraph, the influence of design variables A3, B4 and B5 in structural behaviour will be examined. The
response of the structure is not very sensitive to variations in the remaining design variables, which affect mostly
the quantification of loads (see §2.2). The structural behaviour will be analysed in terms of: (i) IABs flexural
response and (ii) the restriction to deck axial shortening, reflecting in the need for additional prestressing force,
compared to a non-integral bridge, for a specific design criteria.
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
5
2.5.1 Presentation and interpretation of results: the indicators used
Fig. 6 shows the points in the bending moment diagrams that will serve as basis to evaluate the influence of the
design variables on the flexural response: (i) ; (ii)
and (iii) . To make the results relative, and
given that the design of IABs is conditioned by the crack control in structural elements [9], the ratio /
was used, where: (i) is the design in-service bending moment ( =max( ; ) for the piles and
= for the deck) and (ii) the maximum bending moment that can be induced in the piles, for crack
widths of wk=0.3mm, which is the limiting value according to EN1992-2 [9], for exposure classes XC2 and
XC4. The sign (positive or negative) of the bending moments used to analyse the results is associated to the
orientation of the bending moment diagram shown in Fig. 6, resulting from bridge contraction. For expansion,
and in order to keep the nomenclature of the bending moments’ signs, it was considered that the bending
moment diagrams would be inversely orientated to what is indicated on Fig 4. The values for were obtained
based on a detailing of reinforcement with =As/Ac=2%, on the piles’ axial loading and the values for based
in linear-elastic analyses, ´p-y` curves method for pile-structure interaction and elastic-plastic relationships based
on the Kerokoski model, for the backfill-abutment interaction.
Figure 6. Notable points to assess structural behaviour
To evaluate the influence of the design variables in prestress, the results are presented in terms of the additional
prestressing force percentage, compared to a non-integral bridge, to verify the decompression criteria, given: (i)
the portion of the prestressing force in equilibrium on the vertical elements, at time t0, and (ii) the reduction, over
time, of the deck compression state, resulting from the restriction to its axial shortening.
2.5.2 B4 - Height of abutments
Contrary to the results obtained for the remaining design variables, the flexural response on the piles and
abutments to the alteration of H is highly dependent on the type of bridge movement.
For contraction movements, as much in as in
there is little
response to the considered variations of H. Basically, only depending on
H are: (i) the inflection point, increasing in depth with the rise of H, and,
more particularly, (ii) the part of the bending moment diagram in
equilibrium on the piles, as shown in Fig. 7. As will be observed, the
negative bending moments are mainly influenced by the ratio between the
stiffnesses EI of piles and deck - EIpiles/EIdeck - (§2.5.3), contrarily to the
positive bending moments, which are more sensitive to variations in the
stiffness of the soil (§2.5.4). Therefore, H - for contraction – defines, in
practice, which is the sign (positive or negative) of the maximum bending
moment in piles, and consequently, which parameters will be influential.
For expansion, an increase of H will be associated to an increase of
passive earth pressures. Again, relies little on H. However
,
depending on H: (i) either results from the reaction of the soil (Fig. 8 a))
or (ii) from the passive earth pressures (Fig. 8 b)). In the first case, the
0
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Bending moment [kN.n]
z -
dep
th [
m]
Mmax-(z,Mhp=H)Head of the piles
Mhp
Mmax+
Figure 7. Effect of H (contraction)
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
6
bending moment diagram would be very similar to the one resulting from imposed deformations due to
contraction, contrarily to the second case in which is greater and static equilibrium needs to be satisfied.
a) H=2.0m b) H=4.00m
Figure 8. Effect of H (expansion)
The cases in which, due to H, the expansion movement is a limitation to serviceability design, must be analysed
with care, as there is not yet a completely established model that would permit to predict the influence of the
cyclic nature of actions in IABs on the quantification of earth pressures. Nevertheless, should the contraction
movement be more disadvantageous, an increase of H brings some benefits, as it allows for the equilibrium of
the negative bending moments on the abutment instead of on the piles. This is relevant when adopting pile
designs with a low EI, as shown in §2.5.3. There is another advantage, related to the design of the prestressing
force. As bridge contraction is less restricted by the soil, the state of coercion in the deck is lesser: it was found
that, in average, the need for prestress was near to 10% less for H=4.00m, compared to H=2.00m.
2.5.3 B5 - Pile bending stiffness
The variation in piles EI, impacts principally on the
bending moment at the heads of the piles (if negative),
as the negative bending moments are due to restriction
to head rotation resulting from a monolithic connection
of abutment and deck. Therefore, an increase of EI, and
so of the ratio EIpiles/EIdeck, is corresponded by minor
bending moments at the head of the piles, as shown in
Fig. 9. Nevertheless it is important to emphasize, that
the bending moments in pile heads are only of negative
sign when above the inflexion point of the bending
moment diagram. This depends on the height of the
abutment, as seen in §2.5.2.
Still looking at Fig. 9, it can be found that piles with
greater EI permit constructions with greater extensions.
However, EI cannot be increased freely, as
demonstrated in Fig. 10, because an increase in the ratio
EIpiles/EIdeck is associated to an increase in (there is
an increase in deck curvatures) and, eventually,
could become a limitation to serviceability design. On
the other hand, increasing EI will lead to the need for
more prestressing force (in average, an estimate
increase of about 10% for the cases tested and bridges
with 200m), as piles with a greater diameter are more
restrictive to deck movement.
7000-5000 -3000 -1000 1000 3000 5000
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Bending moment [kN.m]
z -
dep
th [
m]
Passive earth
Reaction ofMmax+
Mmax-
pressures
soil
Figure 9. Effect of pile bending stiffness in and
( =
)
Figure 10. Effect of pile bending stiffness in
( = )
0 40 80 120 160 200
6
0
1
2
3
4
5
L - Bridge lenght [m]
Med
/ M
wk
M,ed=M,wk
Æ0.60m; Mhp
Æ0.60m; Mmax+
Æ1.00m; Mmax+
Æ1.00m; Mhp
0 40 80 120 160 200
1,5
0
0,5
1
L - Bridge lenght [m]
Med
/ M
wk
3Æ0.60m
3Æ1.00m
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
7
2.5.4 A3 - Stiffness of the foundation soil
Fig. 11 illustrates the evolution of the ratio /Mwk
with the length of the bridge, for piles of 0.6m and
1.0m and for the considered soil types. An increase of
Ksoil is always corresponded by an increase of ,
however, although there is some sensitivity to the
variation of Ksoil in the results, in practice wil
only become a limitation to design when pile diameter
is very significant, as shown in §2.5.3.
Fig. 12 shows the evolution of the ratio /Mwk with
the length of the bridge, for piles with 0.6m and
1.0m and for the type of soils considered. The results
show that variations in Ksoil gain some relevance,
especially in piles with lesser stiffness EI. Fig. 12 also
shows the substantial difference between sands and
clays, in particular for greater imposed deformations, as
in cases of important soil deformations, a greater
deterioration in clay soils stiffness is observed.
The sensitivity of to Ksoil variations depends on the
depth at which the head of the pile is (i.e. the height of
the abutment). If is negative, the trend may not be
the same as the one described for (where to stiffer
soils corresponds a greater bending moment). This can be observed on the
Fig. 13 bending moment diagrams, where, on pile heads, to a less dense
soil corresponds a greater bending moment, because the variation rate of
curvatures is greater for the stiffer soil. Although this observation, shown
in Fig. 13, is not to be generalized ( is dependant on various factors),
it is important to mention this aspect, as any sensitivity analysis carried
out in design, should take this matter into account. This situation should
be considered especially if: (i) the maximum bending moment in piles is
equal to and (ii) in cases where a linear-elastic model is adopted for
the soil, as it is an approximation where the stiffness assumed is much
greater than the actual one, and so can lead to unsafely results for the
situation described herein.
In terms of the prestressing force, the variation between MDSand and
DSand corresponds, in average terms, to a maximum addition of 7%
(L=210m), and between MDSand and OClay to a difference of a
maximum 15% (L=210m).
2.6. Limits of use for prestressed concrete IABs with reinforced concrete piles
In the type of IAB design studied, the main limitation to design is crack control, associated to the maximum in-
service bending moment in the abutment foundation piles ( ), because, as shown in Gama study [9], the
ductility warrant is not a limitation factor. can result from: (i) contraction – in which case the active earth
pressures do not affect , thus depending on the magnitude of imposed deformations, or (and the design
variables affecting its quantification); or (ii) expansion – only when passive earth pressures are significant (as
>
), a load depending principally on the height of the abutments (see §2.5.2) and on the geotechnical
characteristics of the approach embankments and less on . Therefore, based on the ratio / in the
piles, the charts presented on Fig. 14 (for contraction) and Fig. 15 (for expansion) intend to provide a general
view of the limits to the use of the IAB type of design under study, according to: (i) bridge length; (ii) design
variables relevant in each situation – contraction or expansion – and (iii) LoA used in the structural analysis.
Figure 12. Effect of Ksoil in ( =
)
Figure 13. Effect of Ksoil in
)
Figure 11. Effect of Ksoil in ( =
)
18 000 -2000 2000 6000 10 000 14 0000
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Bending moment [kN.m]
z -
dep
th [
m]
Ksoil 1 > Ksoil 2
Mhp soil 1 < Mhp soil 2
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
8
Bridge contraction
The charts in Fig. 14 represent the evolution of the ratio / with bridge length, for the established LoAs.
Each chart shows minimum ( ) and maximum (
) limits for the limits of use of IABs – for sand or
clay soils -, while Table 3 shows the combination of design variables that originated each of the mentioned
limits, as well as the relative weight that each has in the variation between them. It is to be noted also that: (i) the
charts were made for structures with H=2.0m and 1.0m piles (the diameter permitting wider bridge extensions
– see §2.5.3) with 2% of reinforcement ratio and (ii) the variations shown on Table 3 are considered in average
terms, as in certain cases the evolution is not linear.
As observed on Table 3, both design options and project constraints have the same influence on the
quantification of loads. As such, in most cases, if the necessary LoA (as observed on the Fig. 13 Charts) is used,
it should be possible to design IABs up to 200m, when using adequate design options.
a) LoA I b) LoA II
a) LoA III b) LoA IV
Figure 14. Limits of use of prestressed concrete IABs with reinforced concrete piles (bridge contraction)
Table 3. Increase of MEd/Mwk in relation to its minimum value for the alteration of design variables from
minimum limit -> maximum limit
Design variable Minimum ( ) Maximum (
)
Weight in variation between
limits
Sand Curves Clay Curves
Geotechnical (foundations) A3 OClay OClay - -
MDSand DSand 17% -
Bridge location A1
=
- 10ºC 15% 18%
RH=75% RH=50% 23% 28%
Type of construction B1 concrete slab concrete beam 16% 20%
B2 Precast Cast-in-place 13% 15%
Concrete composition B4 CEM N CEM R 14% 17%
Age of concrete at prestressing C1 =30 days =15 dias 2% 3%
Bridge Expansion
The charts in Fig. 15 represent the evolution of the ratio / with bridge length, for the established LoAs
and depending on abutment height and geotechnical characteristics of the approach embankments. The charts
were created for designs based on 1.0m piles with 2% of reinforcement ratio and a secondary load of
0 40 80 120 160 200
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
OClay / Teq,min
DSand / Teq,max
OClay / Teq,maxMDSand / Teq,min
0 40 80 120 160 200
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
0 40 80 120 160 200
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
0 40 80 120 160 200
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
9
=+30ºC. It can be noted in Fig. 15, that for H=2.00m the soil characteristics do not influence the results, as a
consequence of the insensitivity of the maximum bending moment in piles to the passive earth pressures, as per
the description in §2.5.2. An increase of H, however, leads to a significant influence of the passive earth
pressures on the stresses in the piles, giving relevance to the geotechnical characteristics of the approach
embankments. Such cases must be given special attention, because the passive earth pressure coefficient, Kp,
increases almost exponentially with the rise of ´ (see, for example, Kérisel and Absi [11]). Nevertheless, as in
the case of contraction, it will be possible to design bridges with extensions up to 200m, for the type of IABs
studied, using adequate design options (in this case the height of the abutments) and/or the LoA necessary for
structural analyses.
a) LoA I b) LoA II
a) LoA III b) LoA IV
Figure 15. Limits of use of prestressed concrete IABs with reinforced concrete piles (bridge expansion)
2.7. Design of the prestressing force
On the charts in Fig. 16 (that must be observed together with Table 3, like the charts from Fig. 14) are given
indications of the expected additional percentage of prestressing force when adopting an integral design. The
charts were created for abutments with H=2.0m supported by 1.0m piles with 2% of reinforcement ratio. The
non-linear behaviour of concrete does not have an impacting effect in this case [9]. Given that LoA I, II, III show
the same results, contrary to LoA IV, where the non-linear behaviour of the soils was introduced. As such, the
non-linear behaviour of the soils is the main aspect to take into account, regarding the prestressing force
calculations, as an average additional prestressing force of up to 30%, for bridges of 200m, is to be expected, but
can rise to 60% in cases where a LoA IV is not considered.
a) LoA I, II, III b) LoA IV
Figure. 16 Additional prestress
60 100 140 180 220
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
H=4m / Æ´=43º
H=4m / Æ´=38º
H=2m / Æ´=38º and Æ´=43º
60 100 140 180 220
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]M
ed
/ M
wk
60 100 140 180 220
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
60 100 140 180 220
1
0
0,2
0,4
0,6
0,8
L - Bridge lenght [m]
Med
/ M
wk
60 100 140 180 220
100
0
20
40
60
80
L - Bridge lenght [m]Ad
dit
ion
al
pre
stre
ss
(%)
60 100 140 180 220
100
0
20
40
60
80
L - Bridge lenght [m]Ad
dit
ion
al
pre
stre
ss
(%)
OClay / Teq,min
DSand / Teq,max
OClay / Teq,max
MDSand / Teq,min
D. Gama: Prestressed concrete integral abutment bridges with reinforced concrete piles
10
3. CONCLUSIONS
The principal characteristics of IABs are the effects of time-dependent deformations on the concrete of the deck.
These deformations: (i) are restricted by the vertical elements and, because of this, axial tensile stresses and
bending stresses could appear on the deck – the first can be avoided with additional prestress, compared to the
need of a non-integral bridge and the latter with an adequate detailing of reinforcement and (ii) imposed
deformations on the vertical elements, which result in the main limitation to the design of an IAB, the crack
control on the piles supporting the abutments. This will be, in general, for stresses resultant from contraction, due
to the greater amplitude of these movements, compared to those of expansion. This bridge movement only leads
to limiting loads when abutment height is important and the approach embankments sufficiently dense to
mobilize greater passive earth pressures.
The results obtained from the parametric study indicate that, in most cases, the design of prestressed concrete
IABs, with reinforced concrete piles, will be possible in lenghts up to 200 meters, if: (i) a structural conception is
made, that takes into account the behavioural characteristics of this type of bridges – to convey both an adequate
structural response and prevent greater secondary loads (to mitigate their effects) – and (ii) adequate levels of
approximation are used in structural analysis. In average terms, the adoption of linear-elastic relations will be
possible: (i) in structures with extensions up to 100 meters, considering the modelling of concrete behaviour and
(ii) up to 150 meters, considering the modelling of foundation soils. However, the stiffness of the foundation soil
is the parameter most influent in the prestressing force calculations; not taking in consideration the non-linear
behaviour of the soil will be detrimental to the initial costs of the design. Concerning the earth pressures
quantification models, the use of the Caquot-Kérisel theory will only be possible when abutments have a limited
height, about 2.00m. For higher abutments, IAB dimensioning will only be possible with the adoption of models
taking into account the cyclic nature of loads in IABs. In such cases, the most adequate level of approximation
will depend on bridge length and on the geotechnical characteristics of the approach embankments.
Finally, it is emphasized that the analysis and results in this study are presented in a strictly structural
perspective, not allowing for their dissociation from the questions concerning approach embankment and
transition slab behaviour.
REFERENCES
[1] Kerokoski, O. (2006). "Soil-Structure Interaction of Long Jointless Bridges with Integral Abutments".
Tampere University of Technology, PhD Thesis.
[2] Maruri, R.; Petro, S. (2005). "Integral Abutment and Jointless Bridges 2004 Survey Summary". Proc. of the
2005 Federal Highway Administration Conference, Baltimore.
[3] Harry White 2nd (2007). "Integral Abutment Bridges: Comparison of Current Practice Between European
Countries and the United States of America". New York: New York State Department of Transportation,
Transportation Research and Development Bureau.
[4] EN1992-2 (2005), "Eurocode 2 - Design of Concrete Structures - Concrete Bridges, Part 2: General Rules
and Rules for Buildings". Brussels: CEN.
[5] NP EN1991-1-5 (2009), "Eurocode 1 - Actions on Structures, Part 1-5: General Actions - Thermal Actions".
Brussels: CEN.
[6] EN1992-1-1 (2010). "Eurocode 2 - Design of Concrete Structures, Part 1-1: Design and Detailing Rules".
Brussels: CEN.
[7] Computer and Structures, Inc. (2010), SAP2000 (vrs. 14.2.2)
[8] Fenema, J.L.; Laman, J. A.; Linzel, D. G. (2005). "Predicted and Measured Response of an Integral
Abutment Bridge". Journal of Bridge Engineering. American Society of Civil Engineers
[9] Gama, D. (2012). "Pontes Integrais de Betão". IST, Technical University of Lisbon. MSc Thesis.
[10] Reese, L; Van Impe, W. (2001). "Single Piles and Pile Groups Under Lateral Loading". London: Taylor &
Francis / Balkema, ISBN 90 5809 340 9.
[11] MC1990 (1993). "CEB-FIP Model Code 1990". London: CEB.
[10] J. Kerisel, J.; Absi, E. (1990). "Active and Passive Earth Pressure Tables". Taylor & Francis.