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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


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%.


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.


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)


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


Med

/ M

wk

3Æ0.60m

3Æ1.00m


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


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


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


Med

/ M

wk

0 40 80 120 160 200

1

0

0,2

0,4

0,6

0,8


Med

/ M

wk

0 40 80 120 160 200

1

0

0,2

0,4

0,6

0,8


Med

/ M

wk


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


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


Med

/ M

wk

60 100 140 180 220

1

0

0,2

0,4

0,6

0,8


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


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.

creep, shrinkage p temperature - fenix.tecnico.ulisboa.pt · d. gama: prestressed concrete integral...

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