M A S T E R ' S T H E S I S
Optimized Design of Integral Abutments for a Three Span Composite Bridge
Gabriela Tlustochowicz
Luleå University of Technology MSc Programmes in Engineering
Department of Civil and Environmental Engineering
Division of Steel Structures
for a 3 span composite bridge.
Gabriela T ustochowicz
List of contents:
Preface … … … .. I Abstract … … … ... III Summary … … … . IV .
I. Part
1.0 Introduction … … … 1
1.1 What are integral bridges … … … .… … … 1
1.2 Advantages of integral abutment bridges … … … 2
1.3 Problems and uncertainties … … … .. 3
2.0 Literature review … … … ... 5
2.1 Types of piles … … … . 5
2.2 Piles configuration … … … . 5
2.3 Pile orientation … … … ... 6
2.4 Pile-abutment connection … … … ... 8
2.5 Length limits for integral bridges … … … .. 9
2.6 Behaviour of piles supporting abutments … … … .. 9
3.0 Practice … … … . 11
3.1 USA experience … … … . 11
3.2 Swedish experience from a new solution … … … .. 13
3.3 Poland … … … 15
3.4 United Kingdom … … … .16
3.5 Germany … … … 17
3.6 Canada … … … ... 18
4.0 Design models and methods … … … . 19
4.1 General issue … … … .. 19
4.2 Calculation methods … … … .. 19
4.2.1 Equivalent cantilever method … … … 19
4.2.2 Finite Element Method … … … .. 20
4.2.3 The method of p-y curves … … … . 20
5.0 Theoretical background: Subgrade reaction modulus … … … .. 21
5.1 Winkler soil model … … … 21
5.2 Subgrade modulus concept … … … 24
5.3 Horizontal subgrade reaction modulus … … … .. 25
6.0 Simplified (hand) calculation of piles … … … .. 29
6.1 Global analysis … … … .. 29
6.2 Ultimate limit state … … … 29
6.3 Calculation of the steel piles supporting integral abutment … … … . 31
6.3.1 Data … … … ... 31
6.3.2 Ultimate limit capacity … … … . 32
6.3.3 Serviceability Limit State … … … . 34
6.3.4 Conclusions … … … ... 36
II Part 1.0 Genaral data … … … .. 37
1.1 Location … … … . 37
1.2 Soil conditions … … … ..… … … . 38
1.3 Material properties … … … ...… … .… … … . 38
1.4 General characteristics of the bridge … … … . 38
2.0 Initial assumptions and calculations comments… … … . 41
2.1 Design assuptions and calculation comments ..… … … . 41
2.1.1 Bridge model … … … . 41
2.1.2 Pile model … … … ...… … … ... 41
2.1.3 Earth pressure … ..… … … ...… … … ... 42
2.2 Calculations of forces acting on piles … … … 42
2.3 Calculations of initial imperfections of the piles … … … ... 44
2.4 Calculations of stresses … … … .. 46
2.4.1 Piles cross-sections … … … .... 47
2.4.2 Calculations … … … ... 48
2.5 Calculations of stresses with the use of simplified method ..… … … ... 56
2.5.1 Ultimate Limit Capacity … … … ... 57
2.5.2 Serviceability Limit State … … .… … … ... 61
2.6 Comparison of stresses … … … ...… … … … 65
3.0 Actions to lower the stresses in the piles … … … .. … … … … ... 67
3.1 Elimination of horizontal displacements induced during casting … … … ... 67
3.2 Lower the height of abutment … … … .. … … … ... 67
3.3 Use softer material at the pile top … … .… … … . 67
3.4 Construction of a hinge … … … .… … … . 70
4.0 Analysis with program SOFiSTiK … … … ..… … … .. 73
4.1 Numerical model… … … … .… … … ... 73
4.1.1 Types of elements… … … .… … … .. 73
4.1.2 Elements not included and simplifications … … … 73
4.2 Calculations… … .… … … … .… … … .. 73
4.2.1 Design assumptions… … .… … … ... 73
4.2.2 Calculations … … … ..… … … . 73
5.0 Summary and conclusions … … … .… … … ... 83
References … … … .. 83
Appendixes A. Appendix Calculations of forces and displacements ..… … … 85
B. Appendix: Geometry of the bridge... 117
C. Appendix: Calculation of pile and soil stiffnes... 121
D. Appendix: Loads ... 133
E. Appendix: In-data files for caculations of inner forces in bridge members and forces acting on the abutment ... 139
F. Appendix: In-data files for piles calculations ... 143
G. Appendix: Explanation of commends used in program CONTRAM ... 149
P REFACE
The thesis is performed for a company Ramböll Sverige AB in Luleå as a part of reasearch on development of integral abutment bridges and their wider application in Sweden.
I would like thank company Ramböll Sverige AB on Luleå for giving me the opportunity to carry out my thesis work at the company and for making me feel so welcome.
Especially I would like to thank my supervisor Professor Peter Collin for his great help, support and good will. I would also like to thank very much Hans Pétursson for his guidance during my work and for helping me with all the difficulties.
I would like to thank very much my family and friends for their support, help and belief in me.
Luleå, 2005-09-21
Gabriela T ustochowicz
A BSTRACT
The aim of the thesis is to analyse the foundation piles supporting the bridge over Dalälven River in the middle-east Sweden, which is designed as an integral abutment bridge. The analytical part of the work includes the checking of stresses in piles supporting integral abutments. The piles that are considered are steel piles with three different cross-sections: pipe pile with outer diameter equals 219.1 mm and 12.5 mm thick and two different cross-sections of X piles (200x30mm and 180x24 mm), which are the Swedish innovation in the field of integral abutments bridges. The piles analysed are loaded with vertical force and subjected to horizontal displacement caused by contracting and expanding under influence of temperature changes, but also by breaking and accelerating of vehicles on the bridge and shrinking and creeping of a concrete bridge deck. The particular attention is paid to the influence of displacements perpendicular to the longitudinal axis of the pile for the pile’ s behaviour. In this analysis the behaviour of pile depends a lot on soil surrounding the pile. In connection with this fact the author paid also attention to modelling behaviour of different types of soil in the process of analysing and designing. In the thesis the possible solutions enabling reduce the stresses in piles are also considered.
The analysis of the structure is done with the help of two computer programs using Finite Element Method and with the help of simplified method. In the Swedish program named CONTRAM considered structure is analysed as a flat frame (two-dimensional model), in the program SOFiSTiK the bridge is modelled as a three-dimensional structure, however the simplified analysis concerned only the vertical piles loaded with a vertical axial force and subjected to lateral and rotational displacements at the pile top. The methods and models used are described and compared.
Furthermore, rather an extensive review of available literature related to designing of integral bridges is included in the thesis. In the thesis technological solutions applied in integral abutment bridges and advantages (especially from economical point of view) and disadvantages of these structures are discussed. Examples of application of the integral abutment concept in a few countries, where the widest experience belongs to United States of America, are presented. Information about particular objects is at times rather poor with regard to not bad availability in the literature concerning the subject.
The problems and uncertainties applied for designing integral bridges and the attempts of
solving them are discussed. The methods and models available in the literature used for analysis of
foundation piles subjected to mentioned influences were described. One of the models, beam on elastic
foundation (or on Winkler’ s foundation) is discussed more in detail because of the widespread usage
of this model. Also in connection with this model, researches and analyses that had been carried out to
define elasticity of different types of soil, which created the theoretical base concerning the considered
subject are also presented.
S UMMARY
Part I
Chapter 1 Introduction introduces integral and semi-integral bridges as structures offering numerous advantages comparing to traditional bridges, especially from economical point of view.
However this type of structure has also disadvantages limiting its applications and those are also discussed.
Chapter 2 Literature review has been done to recognise the current state of knowledge concerning integral abutment bridges around the world with a special interest in following areas: types of piles, pile orientation, pile-abutment connection, length limits for integral bridges and behaviour of piles supporting abutments.
Chapter 3 Practice presents the gained information about a few countries and their experience in designing and building integral bridges.
Chapter 4 Design models and methods describes problems and uncertainties connected with designing integral bridges and the attempts to solve them. Different methods available in the literature are presented with their advantages and disadvantages.
Chapter 5 Theoretical background includes a theoretical basis for the methods of analysing piles under lateral loads. This chapter is focused on the soil response, soil modelling and research considering this subject.
Chapter 6 Simplified calculations of piles presents the simplified calculations for the vertical piles subjected to vertical force, horizontal displacement and rotation at the pile top. There is also included a theoretical basis for the calculations.
Part II
Chapter 1 General data includes all the data and information necessary for designing bridge over Dalälven.
Chapter 2 Initial calculations and stresses analysis includes the analysis of the whole bridge and the foundation piles. The bridge is considered as supported on the piled integral abutments. This chapter also compares behaviour of piles with three different cross-sections used for integral abutments. There are made calculations of forces and displacements acting on piles caused by applied loads. Stresses in piles are calculated in two states according to Swedish norm.
Chapter 3 Actions to lower stresses presents calculations of stresses in piles for different options possible to decrease stresses in piles.
Chapter 4 Analysis in program SOFiSTiK presents modelling and analysing bridge over Dalälven as a three dimensional structure.
Chapter 5 Summary and conclusions presents final results and compares all the methods used in
the thesis.
PART I
1.0 Introduction
1.1 W HAT ARE INTEGRAL BRIDGES ?
Development of traffic, which happens nowadays in many countries, results in building and modernization roads and highways. This requires building a great number of small and medium span bridges. In many countries as Great Britain, Canada and USA these objects are very often built as integral bridges.
Integral bridges are bridges where the deck is continuous and connected monolithically with the abutment with a moment-resisting connection. As an effect we obtain a structure acting as one unit.
The terminology varies in different sources, so sometimes the bridges which just do not have dilatations are called joint-less bridges. These structures still have bearings, so the structure still can move in the horizontal plane (but these movements are limited).In polish literature, there are many definitions used with regard to discussed structures: bridges with spans connected with supports with no-hinged connection (with regard to the way of supporting spans on supports), frame bridges (with regard to static scheme of construction), bridges supported on piles (with regard to the type of foundation), etc. However, there is no definition which describes all the features of integral structures (a material, foundation type, static scheme and cooperation with surrounding soil).
There exists also a design variant called the semi-integral abutment bridge, which is a combination of conventional and integral abutment bridge. The semi-integral abutment is similar to the fully integral abutment, except for a lateral joint forming a rotational hinge above the top of the piles. To prevent shear displacements between the top and bottom sections of the abutment, a dowel passes through this joint [1].
The use of semi-integral abutments is recommended to eliminate passive pressure below bridge seats and also for longer bridges to inhibit foundation restraint to longitudinal movement.
Abutment
Pile Girder
Dowel Joint filler Pile cap
Pile Abutment Girder
Figure 1
Enlarged details of fully integral bridge and semi-integral bridge.
The advantage of using semi-integral abutments is that the superstructure behaviour is independent of the foundation type. Therefore, large spread footings or stiff pile groups can be used.
As the superstructure of the bridge expands and contracts under cyclic movements induced by
temperature variations and traffic (influences from second order effects: creep, shrinkage, thermal
gradients, differential settlements, differential deflections and earth pressure also should be
considered), a series of interactions takes place. We can observe interactions between the abutment
and the approach fill, between the approach fill and the foundation soil, between the abutment and the
piles supporting it, and between the piles and the foundation soil. Understanding those interactions is important for effective design and satisfactory performance of integral bridges.
The concept of integral abutment bridges is based on the theory that the flexibility of the piling allows transferring thermal stresses to the substructure by the way of a rigid connection between the superstructure and substructure. Assumptions are made that concrete abutment contains sufficient bulk to be considered as a rigid mass. The positive moment connection with the ends of the beams or girders is provided by rigidly connecting the beams or girders and by encasing them in reinforced concrete. This provides for full transfer to temperature variations and live load rotational displacement to the abutment piling. The crucial problem concerning piles supporting integral bridges is their behaviour under cyclic lateral pile movements induced by temperature variations and traffic (traffic acceleration, breaking and turning) and also by rotations of the superstructue. These bridges do not have expansion joints so the structure has to withstand moves back and forth when subjected to repeated cyclic loading. However, the possibility of deflections is limited by structural integrity and it causes formation of additional inner forces that structure has to withstand. This problem is also essential for development and wider application of integral bridges and to find out which pile type performs in best way. There is a necessity of finding a reasonably good estimation of the forces generated in the abutments for design purposes to ensure satisfactory performance of the integral bridges through their life service.
The integral abutment bridges are usually built as one, two or three span structures. The simplified geometry of one span integral abutment bridge is shown on the Fig. 2.
Foundation Foundation
Abutment Abutment
Superstructure
Bridge system
Approach system
Pevement Approach slab Approach slab Pavement
Sleeper slab Backfill
Backfill Sleeper
slab
Approach slabs and sleeper slabs are optional elements
Figure 2
Simplified geometry of an integral abutment bridge.
Integral abutment bridges have numerous attributes and few limitations. Detailed discussion of those is presented below.
1.2 A DVANTAGES OF INTEGRAL BRIDGES
Primarily, integral bridges eliminate the problem associated with movement joints and
bearings. The reduction of initial cost is associated with elimination of expensive deck joints, anchor
bolts, bearings and their time and money consuming assembling. We can also observe reduction of
long term maintenance costs. The maintenance costs reduction appears due to reduced corrosion (no
leakage onto critical structural elements) and reduced material degradation. For this reason integrated
bridges are becoming attractive options in cold climates such as northern United States, Canada and
northern Europe. The integrated structures can eliminate joint-related damage caused by the use of
deicing chemicals and restrained growth of rigid movement. In conventional bridges, much of the cost
of maintenance is related to repair of damage of joints. Even waterproof joints will leak over time,
allowing water (salt-leaden or otherwise) to pour through the join accelerating corrosion damage to
girder ends, bearings and supporting reinforced concrete substructures. The dirt, rocks and trash are
accumulating in the elastomeric glands and leading to failure.
The absence of deck joints has also advantage for bridge users, which should be quite important factor. The smooth structure without joints provides improved vehicular riding quantity and diminishes vehicular impact stress level.
Bearings are especially expensive to replace. Over time, steel bearings may tip over and/or seize up due to loss of lubrication or build up of corrosion. Elastomeric bearing can split due to unanticipated movements, or ratchet out of position. Avoiding joints and bearing we can eliminate a major source of bridges maintenance problems [2].
Integral bridges are also more favourable with a structural point of view. They have increased reserve load capacity and load distribution, resulting in higher resistance to damaging effects of illegal overloads. There is also observed reduction of number of foundation piles.
The use of integral abutments allows also avoiding the risk of abutments instability and provides substantial reserve capacity to resist potentially damaging overloads, by distributing loads along the continuous and full-depth diaphragm at bridge ends.
Structural integrity has additional advantage, which is simplicity of design. An integral bridge may, for analysis and design purposes, be considered as a continuous frame with a single horizontal member and two or more vertical members. This eliminates separate design process for superstructure and foundations. On the other hand, integral bridges present a challenge for load distribution calculations because the bridge deck, piers, abutments, embankments and soil must all be considered as a single compliant system. There are also some more complicated interactions which are difficult to model in design process.
The article [3] presents that the concept of integral abutment bridges can be applied successfully for new designed and built bridges, also with skewed alignments, as well as for strengthening existing bridges. In addition, since the simple design of the integral abutments lends itself to simple structural modifications, future widening or bridge replacement becomes easier.
1.3 P ROBLEMS AND UNCERTAINTIES
Despite the significant advantages of integral abutment bridges, there are some problems and uncertainties associated with them.
The article written by John S. Horvath [4] suggests that integral abutment bridges problems are fundamentally geotechnical in the nature and they can manifest themselves both structurally and geotechnically any time in the life of an integral abutment bridge.
Many articles, however mention, that the main problem connected with integral abutment bridges are consequences of temperature variations and traffic loads, which cause horizontal bridge movements. Horizontal movements and rotations of the abutment cause settlement of the approach fill, resulting in a void near abutment if the bridge has approach slabs.
Effects of lateral movements of integral abutments under cyclic loadings are obvious problem which demands solving, but positive aspect in this case is that temperature induced displacements in the traditional bridge is over twice bigger than displacement at the end of (considering objects with the same span length) integrated structure because of symmetrical nature of the thermal effects as illustrated on the Fig. 3 [5].
(a) fre ely su p p o rted (b ) c o n tin u o u s
T T
< /2 < /2
Figure 3
Thermal displacements of the load carrying structure
For the reason of temperature-induced displacements, concrete bridges are regarded as more suited for integral bridge constructions as they are less sensitive to temperature variations and recommended especially in cold climates.
The other uncertainties connected with designing and performance of integral abutment bridges are:
The elimination of intermediate joints in multiple spans results in a structural continuity that may induce secondary stresses in the superstructure. These forces due to shrinkage, creep, thermal gradients, differential settlement, differential deflections, and earth pressure) can cause cracks in concrete bridge abutments. Wing-walls can crack due to rotation and contraction of the superstructure.
Some sources recommend integral abutments for skewed bridges, but the design process for this type of structure should be careful and approximate methods should not be used. Most of these methods do not include the influence of torsional moments arising in integral skewed bridges. The behaviour of skewed integral bridges differs from straight bridges. Under the influence of cyclic changes in earth pressures on the abutment, the skewed integral bridges tend to rotate [6]. In USA the design guideline recommends that the skew angles for integral bridges should be less than 20 degrees.
Bridge abutment can be undermined due to water entering into the approach fills at the bridge ends.
The piles that support the abutments may be subjected to high stresses as a result of cyclic elongation and contraction of the bridge structure. These stresses can cause formation of plastic hinges in the piles and may reduce their axial load capacities.
The application of integral bridge concept has few other limitations. Integral bridges can not
be used with weak embankments or subsoil, and they can only be used for limited lengths, although
the maximum length is still somewhat unclear. Integral bridges are suitable if the expected
temperature induced moment at each abutment is certain value specified by suitable authorities in
every country, and somewhat larger moments can be tolerable.
2.0 Literature review
The objectives of literature review are:
1) to recognize the current state of knowledge concerning integral bridges around the world,
2) to review available pile types and solutions used in steel and composite bridges with integral abutments,
3) to synthesize the information available on the general behaviour of integral bridges.
The results of literature review and obtained information were organized according to following areas of interest:
§ Types of piles
§ Pile configuration
§ Pile orientation
§ Pile-abutment connection
§ Length limits for integral bridges
§ Behaviour of piles supporting the abutment 2.1 T YPES OF PILES ( AND PILES SIZE )
Literature review made in [6] revealed that there was found limited number of published papers in the subject area. These publications concerned behaviour of integral bridges (survey of five existing bridges: The Cass Country Bridge, The Boone River Bridge, The Maple River Bridge, a bridge in Rochester (Minnesota), Route 257 overpass on I-81 . All these bridges were supported by H- piles, which were able to withstand the loads, including those induced by temperature variations. No sign of damage was reported. Author suggests that steel H-piles can withstand cyclic loading as long as the maximum stresses remain equal to or less than the nominal yield stress of the pile material.
After testing three types of piles, which were steel H-pile, steel pipe pile and concrete pre-stressed pile the author of [6] drew following conclusions and recommendations.
For a given pile width pipe piles have significantly higher flexural stiffness than steel H-piles is weak axis bending. This is why for a given displacement in an abutment supported by pipe piles the stresses will be higher then in an abutment supported by steel H-piles oriented in weak axis bending.
In other words, the abutment will be more severely loaded if stiff pipe piles are used. Therefore, stiff pipe piles are not recommended for support of integral bridges.
Concrete piles are not recommended for integral bridge support, because under lateral loads tension cracks progressively worsen and significantly reduce the vertical load carrying capacity of these piles.
It is also worth mentioning that the strongly recommended abutment type is stub abutment (abutments with a length ~1.0 m below the deck soffit), because the use of this type of abutment reduces the detrimental effects of thermal-induced movements on the components of the bridge.
2.2 P ILE CONFIGURATION
The only recommendation given by Tennessee Department of Transportation in [7], but also by Departments of Transportation in many states, is to use one row of piles driven vertically. Orienting piles vertically causes that the abutment can move in the longitudinal direction and greater amount of flexibility is achieved to accommodate cyclic movements.
The Swedish innovation in integral abutment bridges is the use of X-shaped piles. Piles are
supposed to be located in one row vertically. The piles are rotated 45 degrees from the line of support
in order to minimise the bending stresses from traffic load (Fig. 4). [8]’
1
1
45°
900 900 900 1500
Figure 4
Pile configuration in bridge over Fjällån.
2.3 P ILE ORIENTATION
A survey taken in 1983 [9] demonstrated that states in USA differ in opinion and practice with regard to pile orientation. Fifteen states orient piling so that the direction of thermal movement causes bending about the strong axis of the pile. Thirteen others orient the piling so that the direction of movement causes bending about the weak axis of the pile. Both methods have proven to be satisfactory to the respective agencies. Orienting the piling for weak-axis bending offers the least resistance and facilitates pile-head bending for fixed head conditions. However, due to the potential for flange buckling, the total lateral displacement that can be accommodated is more limited than when the piling is oriented for strong-axis bending. However the most often recommendation is to facilitate the bending about weak axis of the pile, which means that the web of the H piles should be perpendicular to centreline of the beams regardless of the skew.
From the comparative analysis of two sizes of H-piles (HP 310x125 and HP 250x85) presented in [10] it was concluded that the axis of bending has only a negligible effect of the displacement capacity of integral bridges with stub abutments. This may not be true for bridges with larger abutment height.
According to [11] it is observed that at small abutment displacements where the backfill and the foundation soil remains within elastic limits, the size and orientation of the piles do not have a remarkable effect on the magnitude of the bending moment and shear forces in the abutment.
However, at larger displacements, as the size of pile increases, the maximum bending moment and the shear force in the abutment increases as well.
2.4 P ILE - ABUTMENT CONNECTION
The abutment-pile connection detail is believed to have a significant influence on the pile stresses [12].
Anchorage of beams to pile cap
Steel beams according to [13] should be connected to the pile caps with anchor bolts prior to making integral connections.
There are two solutions of pile – abutment connection proposed in [2]:
− Placing beams on ¼ in. plain elastomeric pads, anchor bolts pass from the abutment pile cap
through both the pad and the bottom flange of the beam or girder ( Fig. 5);
21
ELASTOMERIC PAD
4'' minimum 6'' typical
ELASTOMERIC PAD
4'' minimum 6'' typical
21
APPROACH SLAB
typical deck reinforcement
Figure 5
− Usage of taller projecting anchor bolts equipped with double nuts, one above and one below the flange; this method provides better control over the grade of the beam and requires less precision in preparing the bridge seats of the pile cap (Fig. 6).
21
4'' minimum 6'' typical ANCHOR BOLT
W/ DOUBLE NUTS
typical deck reinforcement APPROACH SLAB
21
4'' minimum 6'' typical RF BAR
ANCHOR BOLT W/ DOUBLE NUTS
Figure 6
The connection between the abutments and the superstructure shall be assumed to be pinned for the superstructure’ s design and analysis. The superstructure design shall include a check for the adverse effects of fixity. [14]
The typical detail used in Scotch Road Bridge over Route I-95, showed on Fig. 7, is the
other possible solution for pile – abutment connection detail, which insures full moment transfer .
Figure 7
The detail of pile-abutment connection used in Scotch Road, I-95 Integral Abutment Bridge
The alternate joint-less bridge detail is proposed in the article [15] and showed on the Fig. 8 In this option the beams are rigidly connected to pear caps and abutments, and a continuous reinforced concrete or asphalt wearing surface is provided. When steel sections are used, for example, shear connectors are welded to beam ends and encased in reinforced concrete pier caps and abutments.
Shear connectors are also welded to the top flanges to develop the composite action with a reinforced concrete deck slab.
These methods have been extensively used in New Zealand and Australia in lengths up to 160 feet.
Figure 8
Alternate joint less bridge detail for steel beam bridge.
2.5 L ENGTH LIMITS
Reasons for length limitations for integral bridges:
As the length of integral bridges increases, the temperature-induced lateral cyclic displacements in steel piles supporting construction become larger as well. As a result, the piles may experience cyclic plastic deformations. This may result in the reduction of their service life due to low-cycle fatigue effects. Thus, the lengths of integral bridges should be limited to minimize such determine effects.
The ability of piles to accommodate lateral displacements is a significant factor in determining the
maximum possible length bridges, because temperature induced displacements are proportional to
bridge length. The way to build the longer bridges is to keep the stresses in piles low [16].
Maximum length for steel integral bridges recommended in United States range between 80 and 145 m in cold climates, and between 125 to 220 m in moderate climates [17]. Sometimes the limitations are not in force and there are built longer bridges. For example Tennessee Department of Transportation recommends maximal length for steel bridges with integral abutments – 120 m and for concrete bridges 240 m. The newer data available in article [17] considering length limits for integral abutment bridges from various state departments of transportation for comparison purposes are presented in Table 2.1. The longest bridges with integral abutments are: steel bridge – 152m and concrete bridge – 352 m. In Sweden and Great Britain the recommended length for integral abutment bridges is 60 – 70 m [18].
Despite some recommendations, universal guidelines to determine the maximum length of integral bridges do not exist. Generally, bridge designers, especially in USA, depend on the performance of previously constructed integral bridges to specify the maximum lengths for their new designs.
According to [19] the most of the problems connected with temperature induced movements does not have substantial influence on the work of construction with the total length shorter than 60m. In the case of longer bridge there must be carried out researches to estimate approach fill movements, but this kind of necessity do not exist very often, because in most of countries the percentage of new built long bridges is very small.
Table 2.1: Maximum length limits for integral bridges.
Department of Transportation
Steel bridges length [m]
Concrete bridges length [m]
Colorado 195 240
Illinois 95 125
New Jersey 140 140
Ontario, Canada 100 100
Tennessee 152 244
Washington 91 107
It is noteworthy that concrete bridges are more recommended than steel bridges as integral structures. Assuming the same length and localization, the seasonal thermal-induced displacements in steel integral bridge are about 20% bigger than displacements induced in concrete bridge. The daily temperature induced displacements for steel bridge can be around three times bigger than for concrete bridge [19].
2.6 B EHAVIOUR OF PILES SUPPORTING THE ABUTMENTS
While designing integral bridges, designers have to pay special attention on piles supporting abutments. One of the not finally solved problems is their behaviour under influence of climatic, meteorological and topographic factors. In integral bridges the thermal deformations are considered as three-dimensional and their scale and directions depend on: geometry of the bridge, length of spans, height of the supports, type of cross-section, deck/supports stiffness ratio and the material, that the structure is made of.
The number and magnitude of factors cause that this is not possible to accurately estimate values of thermal displacements and deformations, so also we can observe not expected behaviour of the bridge.
This is why there are limitations in application of integral bridges [19].
The ability of foundation piles to carry the vertical load may be reduced when piles are
subjected to lateral displacements. Piles can fail when the induced lateral loads are higher than the
elastic buckling load. The effective designing of piles should assure the low level of stresses in
designed piles. However this may be difficult, because of a big number of parameters that influence
the magnitude of strains in the piles, e.g. changes of temperature, number of the trucks that pass the
bridge and their weight, span length, stiffness of soil surrounding the pile, stiffness of the bridge deck
and the height of the abutment wall.
One of used methods to decrease stresses in piles is using predrilled oversized holes filled with loose sand after pile drilling, but this is a good practice when the stiffness of removed soil is higher than that of the loose sand, this mean for very stiff soil [16].
The Figure 9 shows the installation of the sleeved HP piles within crushed stoned backfill. The gap between the sleeving is filled with sand to facilitate the movement of the piles as subjected to lateral displacements transferred from the superstructure (applied for The Scotch Road Bridge, located in Trenton, New Jersey). In USA there are similar recommendations to use pre-bored holes filled with granular material as one of the solutions to make the abutment more compatible with longitudinal movements [20].
Figure 9
Installation of the sleeved HP piles within crushed stoned backfill.
The opinions about behaviour of piles under vertical loads and influences of lateral movements differ. But most probable opinion scenario is that although a section in steel pile may reach yield stresses, this does not imply that the ultimate load is reached. The further load increase is possible, because the bending moment along the pile can be re-distributed. The more advanced tools at present allow for analysis based on plastic design. If the elastic theory is used to design the piles, the moment re-distribution and effects of plastic behaviour of the pile can not be taken into account [21].
The behaviour of piles supporting integral abutments depends, between others, on stiffness of soil which is adjacent to the piles. The research described in [22] revealed that piles driven in stiffer soils will experience moment magnitudes greater than those experienced by piles driven in softer soil.
The models with less stiff soil are capable to withstand a larger axial load than those in stiffer soil.
However it should be noticed that to big reduction of soil stiffness may result buckling of piles because of lack of lateral support.
As described above, there are many factors that have an influence on behaviour of piles supporting
integral abutment bridges and this is the reason why it is very difficult to suggest design rules that are
valid for all bridges with integral abutment.
3.0 Practice
Integral abutment bridges are not commonly used in Europe but the researches and observations are going on in many countries. Lack of experience in designing bridges with integral abutments makes it time consuming. Also people from roads administration have a little experience and knowledge in this field and therefore demand vary detailed analysis. The increased demand of very detailed analysis makes the design process very expensive. The costs saved in construction stage may be consumed in designing stage to make the offer satisfactory for everyone. Despite these problems, we can observe progress in this field in many countries .
3.1 U NITED S TATES OF A MERICA
In the USA integral abutment bridges have been built since the 1960’ s and are increasingly being used for replacement structures. The concept of integral abutment bridges has been proved to be competitive in this country and it is believed to be so in most countries, if only given the chance by contractors and authorities. Tennessee with more than 2 400 bridges with integral abutment is probably the state with the widest experience in this field.
The example of attempts to improve the integral abutment idea can be built in Tennessee State Bridge carrying Route 50 over Happy Hollow Creek (Fig. 10) at a total length of 1,175 ft. (358 m), which is the longest joint-less integral abutment bridge in the country .
Figure 10
Happy Hollow Creek
The other examples of integral abutment bridges built in USA are:
v Big East River Bridge, 63.4m long and 13.96m wide.
Figure 11
Big East River Bridge.
v Highway 518 Parry Sound - one span bridge with the length of 47.4 m supported on piles HP310x310.
Figure 12
Highway 518 Parry Sound
v Duffin Creek Bridge
Figure 13 Duffin Creek Bridge
For bridges presented above there has been found no data about their performance. However in USA there is a big number of bridges with integral abutments. For example authors of article [1]
present results of studies on behaviour of integral abutment bridges. Investigated bridges were:
v The Cass Country Bridge in Fargo, in Dakota, which is six spans concrete bridge. Total length of the bridge is 137 m and width 9.7 m. The bridge consists of six spans, 22.9 m each. The Boone River Bridge, in central Iowa, which is also concrete bridge with pre-stressed concrete girders. The bridge is 98.9m long with four continuous spans and 12.2 m, with a skew of 45º.
v The Maple River Bridge located in northwest Iowa and consists of a composite concrete deck and steel girders. Total bridge has three spans and is 97.5 m long. The bridge is 9.75 m wide, with a skew of 30º.
v The unnamed concrete bridge located in Rochester, Minnesota, built in 1996. The bridge is 66 m long with 3 equal spans, 22m each and 12 m wide.
All of those bridges are supported on H piles oriented in weak-axis bending under abutments. The
first of mentioned bridges has also integral piers but supported on H piles oriented in strong-axis
bending. For three out of four examined bridges, the foundation piles were installed in predrilled boreholes. Even though the departments of transportation in many states recommend for integral abutments one row of vertical piles, the Boone River Bridge and the Maple River Bridge have foundation piles battered in the movement direction of the bridge. During the monitoring period of the Cass Country Bridge, the strain gauges failed. However with analytical methods it was found that the maximal stresses in piles were around the yield stress. For two other bridges monitoring period revealed that stresses in piles are around 60-75% of the nominal yield stress. For the last mentioned bridge the highest stresses in piles were slightly above the nominal yield stress of the piles. In all of those bridges the foundation piles were able to tolerate the expansion-contraction cycle without damage.
3.2 S WEDEN
In Sweden the concept of integral abutment bridges becomes more popular, but there is a need to adapt wide American experience in this field to Swedish conditions. To develop the technology and solutions used in designing and building integral bridges the Division of Steel Structures at Luleå University of Technology realised a post-graduate project – the licentiate thesis of Hans Pètursson [23].
The thesis included static testing of X-piles, Swedish innovation in integral abutment bridges technology. The piles tests simulated forces, to which piles are subjected in real conditions: normal forces and lateral displacements corresponding to displacements induced by temperature movements at the ends of the bridge. Of course, as it was said before, not only temperature induced expansion and contraction, but also by changes of air moisture, traffic, second order effects, etc. The effects of mentioned influences were also analysed with help of computer simulations.
v Bridge over Fjällån
The new technology was put into practice while building the bridge crossing over the Fjällån River [8].
Bridge is located in the Swedish province Västerbotten. This is a single span composite bridge with a span of length of 37.15 m. The bridge is supported by eight X piles (180x24 mm) for each abutment. The piles were rotated 45 degrees from the line of support in order to minimise the bending stresses.
Figure 14
Bridge over Fjällån after completion
v Bridge over Hökvik River
The bridge is located in the central part of Sweden. This is an arch bridge with the span length 42m.
The idea of integral abutment bridge was used in this case to replace the old concrete bridge.
The construction works were completed in September 2004. The advantage of using integral abutment bridge technology for the new bridge was that the foundation of the old bridge was left in place and the piles of the integral abutments were driven just behind the old abutment (visible on the Fig. 15).
The choice of integral abutments had time saving benefit, because the old abutment did not have to be removed.
Figure 15
Bridge W1299 over Hökviksån in Linghed.
There was also used technology which allows decrease the stresses in piles caused by lateral movements. The steel tubes were placed over the piles and the loose sand was filled around the piles.
This action should minimise the pressure against the piles, when they deform due to translation and rotation.
The piles supporting abutments are steel cross shaped piles (Fig.16) with width (b) equals 200mm and thickness (t) equals 30 mm. Under each abutment was placed one row of eight piles. Six of them were driven vertically and two the outermost are inclined (4:1) to take counteract transverse horizontal loads, which are wind and transverse component of vehicle brake force .
h
t
b a
Figure 16
Cross section of X pile.
v One span, concrete, monolithic flyover showed on the Fig. 17 can be described as an example of the simplest integral flyover.
The type of integral bridge shown on the Fig.17 has been one of the most common types of bridges in Sweden for over 70 years. In this country at least 8 000 out of 14 000 bridges owned by The Swedish Road Administration are of the type shown above [24].
.
Figure 17
The example of integral structure - monolithic concrete frame flyover .Integral slab frame bridge
One of the main reasons why integral abutment bridges have not become common in Sweden is the difficulty with analysing them.
3.3 P OLAND
In Poland there is also visible interest in integrated load carrying system and so-called small and medium bridges are built as integral bridges. Unfortunately many designers did not include in the design process interactions between structure and surrounding soil while temperature induced movements. Many solutions did not appear favourably because proper draining devices were not applied. These facts brought about that many solutions did not function properly [5].
According to Wojciech Trochymiak [6], the integral structures supported on piles are not, by no means, a novelty. They were built already before the II World War, but then called bridges on Ferro concrete piles.
There were for example built:
v In 1930’s the bridge over Tarczynka River in Tarczyn,
Figure 18
v The bridge over the Srebrna River in Mi sk Mazowiecki,
Figure 19
v The one span composite integral fly over in Wyszogród
Figure 20
The built ring road of Ostrowia Mazowiecka crosses the single-track railway line, so there was a need to design two similar flyovers with a big angle of skew (130.29 between the longitudinal axis of the road and the longitudinal axis of the railway line). The integral abutment solution was chosen for these purposes because of few reasons. The main reasons are: less expected maintenance costs compared to a traditional solution and the big skew of the flyovers that would cause the necessity of very complicated bearings and dilatations.
Figure 21
One of the flyovers on the Ostrowia Mazowiecka ring road.
Even though the interest in integral abutment bridges arises, nowadays in Poland there are neither length limitations nor recommendations for integral bridges. This is why designers almost never choose integral structures [19].
3.4 U NITED K INGDOM
The one of the first integral bridges in UK was The North Shotton overbridge (Fig. 22) on the
A1 Trunk Road in Numberland. The bridge was designed by Northumberland County Council
Technical Services Consultancy on behalf of the Highways Agency using recommendations contained
in a draft version of the design standard which was later issued as BA & BD 57 and with the help of
LUSAS Bridge analysis. The bridge is two spans continuous bridge with four steel plate girders and a
reinforced concrete deck. The abutments are supported on steel H piles oriented in weak axis bending .
Figure 22
The North Shotton over bridge.
In this country, the Highways Agency Departmental Standard, BD57, "Design for Durability", requires designers to consider designing all bridges with lengths of up to 60 metres and skew angles of less than 30 degrees as integral bridges. This advice is intended to prevent all the maintenance problems connected with transition joints .
3.5 G ERMANY v Berching South Bridge v Nesselgrund Bridge v Schwabachtal Bridge v Rednitztal Bridge
(These bridges were built for the Deutsche Bahn AG) 3.6 C ANADA
The examples of steel integral bridges supported on piled foundation type:
v Browns River Bridge
The bridge has steel I-girders and the span of length 15+60+15=90m. The bridge is 22.4 m wide.
v Forbidden Plateau Underpass
The bridge is one span with the length of 42 m and 22.4 m wide. Bridge has steel box girder.
4.0 Design models and methods.
Integral abutments have been successfully used for over 50 years, but their implementation (especially in USA) has been anything but an exact science, but rather a matter of intuition, experimentation and observation. Despite the lack of proper analytical tools, engineers have been pushing the envelope by constructing longer and longer integral bridges, thus building on the lessons learned. Since the age of the computer started, the tools have been developing and nowadays there is a big number of possible methods. The design process demands prediction of behaviour of the whole structure, but especially problematic for integral abutment bridges is the behaviour of the piles supporting abutments. The problems and uncertainties connected with designing integral bridges have been discussed in point 1.0. Here are presented chosen methods to analyse the piles under lateral loads and also the whole structure, suggested in the literature as the most widely used.
4.1 G ENERAL ISSUE
As we consider case when the soil along the pile length is not changing and the soil stiffness is constant, the calculation of foundation piles is not complicated. In point 6.0 there is the example of calculating the ultimate limit capacity and the plastic stresses in three types of piles. In more real cases, when the soil along the pile length varies, the common practice is to model the soil by specifying a series of spring supports along a pile. In this way we can approximate the soil behaviour, when the structural load effects are the main item of interest. When the soil movement is of interest continuum models are used instead [21].
In designing steel piles supporting integral abutments there is no need to consider lateral-torsional buckling or global buckling instability, because piles are laterally supported by the surrounding soil.
However, the width to thickness ratios of the flanges and the web for steel H piles (the mostly recommended piles in most of states in USA) must be limited to allow for large plastic deformations without local buckling.
4.2 C ALCULATION METHODS
The literature review in [7] presents various methods to calculate laterally loaded piles such as the Method of p-y Curves Differential Equation, Closed Form Formula, Approximate Solution Methods, Empirical Methods and Equivalent Cantilever Method. These methods for solving laterally loaded pile problems are mostly empirical since the soil modulus is not a unique soil property. Numerical methods such as finite difference and finite element methods provide very accurate results if the soil pressure is appropriately represented.
4.2.1 Equivalent cantilever method.
The equivalent cantilever method is a quite commonly used method and this is a simplified model
offered by Abendorth. The soil-pile system is modelled as an equivalent length of horizontally
unsupported cantilever beam-column (the model showed on Fig. 23). The method is based on
analytical and finite element studies and introduces an equivalent cantilever column to replace the
actual pile. In other words, the soil-pile system is reduced to an equivalent cantilever column. The
method provides two alternatives involving both elastic and plastic behaviour. Finite element
simulations indicated that both alternatives are conservative. Both alternatives are concerned with the
vertical load carrying capacity of piles under lateral displacements induced by temperature changes,
traffic and secondary forces. This method does not consider the effects of the abutment-approach fill
interactions [16] .
A b u tm e n t
P ile
Le
M o m en t d ia g ra m
Figure 23
Equivalent cantilever concept.
4.2.2 Finite Element Method
Finite Element Method nowadays is probably the most often used method to analyse constructions. There is a great number of computer programmes, which allow defining the structure, creating model and apply the loads. Proper analysis is mostly a matter of defining a model as near to real conditions as possible.
There are researches going on the proper integral bridge mode. Khodair and Hassiotis present in their report [13] that there is a possibility to model integral abutment bridges with the use of finite element method model and obtain results very similar to experimental data (results were measured by data acquisition system connected to fully instrumented bridge).
For FEM analysis the most usual case is laterally loaded piles modelled as elastic beam-column and the soil as a series of uncoupled “Winkler” springs (more about the Winkler soil model in point 5.0) . The most proper representation of laterally loaded pile seems to be the 3D-model. The problem is three-dimensional, because apart from vertical force acting on the pile, lateral loading causes lateral displacements on planes perpendicular to the vertical axis of the pile.
4.2.3 The Method of p-y Curves
The p-y curve method is a widely used empirical method in the subject area and it considers the fact that the soil pressure (p) and the pile deflection (y) are non-linear. The essential of the method is to introduce a series of p-y curves to represent the true behaviour of soils by considering the non- linearity of the soil modulus. The main purpose of the method is to obtain a representative value of k
h– modulus of horizontal subgrade reaction for the desired depth and deflection values. This is accomplished through an iterative process by assuming a deflection and calculating the value of k
h. The iterations are continued until the assumed and calculated deflections are the same within a tolerance limit. When representative p-y curves are used, the method is capable of reflecting the real deflection behaviour of the pile and the moment distribution along the pile. The challenge is to obtain a representative set of p-y curves for each site .
The most crucial point of the solution is the proper representation of the soil modulus through
p(x). If p(x) is assumed to be linear, then a system of linear equations is obtained. The solution
becomes trivial with matrix solvers. It is a well known fact that p(x) is a function of the lateral
deflection, which leads to a set of non-linear equations. For nonlinear p(x), the solution is obtained by
iterative procedures by assuming deflections for each node and thereby calculating p(x) and solving
for qj (nodal unknowns) until the assumed and the calculated nodal unknowns are the same within a
tolerance range. The Newton and the Modified Newton methods are mostly used for iteration.
The p-y curve method is related to Subgrade Reaction Approach, which is also one of the most often used methods to analyse the behaviour of piles loaded laterally. In this work piles are analysed with the use of Subgrade Reaction Approach and this method and its assumptions will be discussed more detailed in Chapter 4: Theoretical background.
Most of methods to solve laterally loaded pile problems are empirical, since the soil modulus is
not a unique soil property. According to Arsoy Sami [7] numerical methods such as finite difference
and finite element methods provide very accurate results if the soil pressure is appropriately
represented. The equivalent cantilever method does not consider the effects of the abutment/approach
fill interactions.
5.0 Theoretical background: Horizontal Subgrade Reaction Modulus.
The aim of this part is introduce theoretical basis used in designing foundations, in considered in this work case: piles subjected to vertical loads and lateral displacements.
5.1 T HE W INKLER SOIL MODEL
The Winkler soil model (1867) treats foundation as a beam on the elastic foundation (Fig. 24 - above), but the elastic medium is replaced by a series of infinitely closely spaced independent and elastic springs. The model for this soil idealization is showed below on Fig. 24 [25].
W
b eam of E I
reaction depend ent on deflection of in divid ual springs only
b eam of E I
Figure 24
Beam on the elastic foundation (above), Winkler’s idealization (below)
For vertical piles there can be made similar idealization and the predicted behaviour of the laterally loaded piles according to Winkler’s idealization is showed on Fig. 25. Unfortunately, the real soil-reaction deflection relationship is nonlinear and the Winkler’s idealization would require modification.
P
y
x
p=k
xy
xPile, EI Pile before
loading
Pile before loading
M Q
ground surface
x
ground surface
M
Elastic springs k
h=p/y
Q y
P
Figure 25
Laterally loaded pile in soil (on the left), laterally loaded pile on springs (right).
In the Winkler’s soil idealization the soil is represented by springs. For the design purpose there is a need to determine the soil stiffness – spring constants. The stiffness of those springs can be expressed with the use of modulus of horizontal subgrade reaction:
=
2length force y
k
hp
where
p – the soil reaction at a point on the pile per unit of the length along the pile, y – the pile deflection at this point .
In some sources [25] it is claimed that the determination of deflections and moments of piles subjected to lateral loads and moments based on the theory of subgrade reaction is unsatisfactory, because the continuity of the soil mass is not taken into account.
5.2 S UBGRADE MODULUS CONCEPT
The analysis of laterally loaded piles can be done generally in two ways. The first way is to find the allowable lateral load by dividing the ultimate load by an adequate factor of safety. The other method consists in finding the allowable lateral load that is corresponding to an acceptable lateral deflection. Those two ways determine two groups of methods of analysing piles subjected to lateral loads.
In the analysis done in this work, there is used programme CONTRAM in which the soil is assumed to act as series of independent linearly elastic springs (Winkler’s soil idealization). For this reason, the discussion in this chapter will be limited to method called in [25] Modulus of Subgrade Reaction Approach (Reese and Matlock, 1956), which also treats a laterally loaded pile as a beam on elastic foundation.
In 1961 Vesic extended Biot’s work concerning a flexible beam supported on an elastic half space.
He assumed piles as a long relatively flexible member and showed that the error in computations of bending moments based on the subgrade reaction modulus is no more than few percent comparing to the solution based on the theory of plasticity.
Therefore, the subgrade modulus concept has a reasonable theoretical foundation and has been used in practice for a long time. This is quite commonly used method for computing response of piles under lateral loads. The advantage of this method is a relative simplicity and this method can incorporate factors such as nonlinearity, variation of subgrade reaction with depth and layered systems. On the other hand this method has also disadvantages such as: not considering continuity of the soil and the use of modulus of subgrade reaction, which is not a unique soil property but depends on the foundation size and deflection.
The behaviour of a laterally loaded pile can be analysed by using the equation of a beam on the elastic foundation. For the case, when the modulus of subgrade reaction (k
h) varies with depth and can be expressed as a function of deflection (y) k
h= f(y), the equation for the beam is following:
) 0 (
4
4
+ =
EI y y f dx
y d
For the more simple case, when the subgrade reaction modulus (k
h) is assumed as constant with the depth, the equation for the beam on the elastic foundation can be rewritten:
4
0
4
+ =
EI y k dx
y
d
h5.3 H ORIZONTAL SUBGRADE REACTION MODULUS
In point 4.0 there has been described the p-y curve method, which is connected with the subgrade
reaction modulus concept. Fig. 26 shows a typical soil reaction versus deflection curve (p-y curve) for
soil surrounding laterally loaded piles.
Deflection, y
S oi l r ea cti on, p
Secant modulus
p vs y Tangent
modulus
Figure 26
Soil reaction versus deflection for soil surrounding a pile.
For soil reactions less than one third to one half of the ultimate soil reaction, the p-y relationship can be expressed adequately by a tangent modulus. The slope of the line is the coefficient of horizontal subgrade reaction for the pile, k
h.
For soil reactions exceeding approximately one third to one half of the ultimate soil reaction, the secant modulus should be considered. The horizontal subgrade modulus becomes a function of the deflection.
Many researchers tried to find the actual variation of the subgrade modulus with depth and the results of some of those can be found in [25].
The investigations considered different types of soil and the example results are as follows:
Uniform preloaded cohesive soils
Terzaghi (1955) [25] recommended that for this type of soil the k
hcan be assumed as constant with depth (k = const) as shown on the Fig. 27 with the dashed line. However, because of deformations of the soil at the ground surface, there is more realistic variation of the subgrade reaction modulus showed at the same figure by the solid line.
h
