Superstructure Behavior of a Stub-Type Integral Abutment Bridge
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Thevaneyan K. David1; John P. Forth2; and Jianqiao Ye3 Abstract: Records show that research leading to the successful introduction of integral-type structures such as continuous beams and frames actually began in the 1930s. Simple stub-type abutments have been found to perform well and are recommended for widespread use. The purpose of this analysis was to consider the behavior of the superstructure and substructure/backfill soil when they are subjected to thermally induced lateral movement and vertically imposed load at deck level. With the Oasys Safe finite-element analysis programs, finite-element models were developed to represent a typical stub-type integral abutment bridge configuration and backfill/foundation soil profile. It was found that the behavior of the superstructure of an integral bridge was predominantly influenced by the loading magnitude, irrespective of backfill soil properties. The results suggest that when designing the superstructure, the design requirements to resist the imposed loading may be sufficient to accommodate any effects attributable to the thermal load. DOI: 10.1061/(ASCE)BE.1943-5592.0000583. © 2014 American Society of Civil Engineers. Author keywords: Integral abutment bridge; Stub-type abutment; Soil model; Duncan-Chang model; Mohr-Coulomb model; Soil-structure interaction.
Introduction The term integral bridge usually refers to bridges with abutments that are connected rigidly to the bridge deck, i.e., without joints. This rigid connection allows the abutment and the superstructure to act as a single monolithic structural unit. The system exists as a single-span or multiple-span bridge with a movement system composed primarily of abutments supported on flexible piles. According to Burke (2009), the first integral bridge was built in the United States in 1938. By the mid-1960s, the adoption of continuous bridges with integral abutments had become a favorable construction practice in many states in the United States (Arsoy et al. 1999). The use of integral bridge construction has also expanded to Europe and Asia. Integral abutment bridges have proven themselves to be significantly superior compared with conventional bridges (Dicleli 2000; Arsoy 2000; Abendroth and Greimann 2005; Huang et al. 2008). Because there are no expansion joints and bearings in an integral bridge, the abutment, its characteristics, boundary conditions, design, and construction will potentially have a greater influence on the overall behavior of the integral bridge compared with any other components. Integral abutments are rigidly connected to the bridge beams and deck with no expansion joints. Cooke (2003) stated that the North American Study Tour Report had identified and recommended 1 Senior Lecturer, Division of Structure and Material, Faculty of Civil Engineering, Univ. Technology MARA (UiTM), Shah Alam, Selangor 40450, Malaysia (corresponding author). E-mail: thevaneyan@salam .uitm.edu.my 2 Senior Lecturer, School of Civil Engineering, Univ. of Leeds, LS2 9JT Leeds, U.K. E-mail:
[email protected] 3 Chair of Mechanical Engineering, Dept. of Engineering, Lancaster Univ., LA1 4YR Lancaster, U.K. E-mail:
[email protected] Note. This manuscript was submitted on May 28, 2013; approved on November 12, 2013; published online on January 14, 2014. Discussion period open until June 14, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Bridge Engineering, © ASCE, ISSN 1084-0702/04014012(12)/$25.00.
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eight types of abutments, namely, full-height frame, embedded-wall abutments, embedded wall with reinforced earth, spread footings on reinforced earth wall, stub-type at top of side slope, vertical wall with semi-integral, and stub-type abutment with semi-integral joint, stubtype abutment. An example of a stub-type abutment can be seen in Fig. 1. However, simple abutments, such as stub-type abutments, have been found to perform well (Faraji et al. 2001; Dicleli and Albhaisi 2004; Huang et al. 2008). Stub-type abutments supported by piling (Fig. 1) were recommended for widespread use by Cooke (2003). In this research, a stub-type abutment, supported by a circular concrete piling, which is commonly used in Malaysia, has been used.
Temperature Effects on the Behavior of Integral Abutment Bridges Temperature changes influence the movement of the bridge. Bridge decks expand and contract because of these changes. The response of an integral abutment bridge to these changes is critical compared with the case of a conventional bridge. Generally, conventional bridges are designed and built with an expansion joint and bearings that would accommodate the movements caused by temperature changes. However, in the case of an integral abutment bridge, because it does not have expansion joints or bearings, the structure restrains the temperature-induced movement, causing additional stresses in the bridge deck and abutments/piles. These restrained movements lead to thermally induced moments, which are recognized by designers as being potentially significant (Mistry 2005; Arsoy 2000), so it is important to have a good understanding of the temperature changes that the bridge will experience. Lawver et al. (2000) conducted a field test and found that the effects from environmental loading by solar radiation and changing ambient temperature were as large as or larger than the live-load effects. Paul et al. (2005) also found that thermally induced superstructure stresses and shear forces in integral abutment bridges were comparable to those caused by live loads. It has also been
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suggested that the behavior of integral abutments is not only influenced by the environmental conditions but also by the soil condition and type and that these effects are at least equivalent to the effects of its structural configuration (Huang et al. 2008). Thermally induced expansion of the superstructure causes the abutment and piles to push against the backfill soil, producing a passive backfill pressure. The nature of the backfill pressure is dictated by the movement of the structure toward and away from the soil media. Lateral earth pressure generally ranges from at-rest to active or at-rest to passive conditions, depending on the structural movement. Passive earth pressure develops when a structure moves against the soil; active earth pressure results from the structure moving away from the soil (Fig. 2). The stresses caused by temperature differentials can be described in terms of a uniform component over the entire section and a temperature gradient through the outer and inner faces of the bridges.
Uniform temperature rises only cause changes in the axial length of the superstructure, whereas temperature gradients or differentials through the entire section will cause bending deformation if restrained (Jaafar et al. 2003; Barr et al. 2005). These differences may alter the centroid of the stress action, affecting the bending moment when coupled with the vertical deflections. The effects of temperature differentials in a structure are often neglected in design, and a uniform temperature distribution is assumed for simplicity (Paul et al. 2005). Paul et al. (2005) evaluated the effects of a temperature differential versus uniform temperature change and found that the differential effect was not significant.
Numerical Analysis Over the years, field monitoring, numerical modeling, and design methods have been the focus of integral abutment analysis. The cost
Fig. 1. Stub-type integral abutment bridge
Fig. 2. Earth pressure condition versus structural movement: (a) structure in at-rest condition; (b) lateral translation movement; (c) rotational
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of field instrumentation and duration of fieldwork studies (Kim and Laman 2012; Huang et al. 2005) have led researchers to find alternative methods to further substantiate their findings. Developments in numerical analysis and the advancement of computer technology have meant that the investigation of the behavior of integral abutment bridges is now possible using numerical methods. With regards to numerical modeling of integral abutment structures, several modeling approaches (Ooi et al 2010b) have been developed over the last three decades to explore bridge behavior. The use of numerical analysis can be traced back to Jorgenson in 1983, who proposed a two-dimensional (2D) linear frame model (Arsoy 2000). The soil was then simulated as linear springs; the soil-structure interaction between the backfill and abutment was neglected. Greimann et al. (1987) improved the 2D frame model of Jorgenson by incorporating the geometric and material nonlinearities of the pile, nonlinear soil behavior, and soil-pile interaction. Arsoy (2000) later modeled an integral abutment bridge as a plane strain problem incorporating beam-bar elements, four-node quadrilateral elements, and three-node triangular elements. In 2001, Faraji built a three-dimensional (3D) computational model using beam-column and shell elements to model the girders, deck, abutments, and piles. Although extensive research has been carried out over the last 30 years, the effects of some key design variables (i.e., magnitude and distribution of backfill soil pressure; bridge length and depth; pile size, type, and orientation; and skew angles) are still not fully understood (Arockiasamy et al. 2004; Ooi et al. 2010a). Consequently, design rules for these variables vary significantly in engineering practice (Arsoy et al. 1999; Civjan et al 2007; Ooi et al. 2010b). To minimize these uncertainties, a deeper understanding of the bridge behavior is needed.
The bridge was modeled as a 2D plane strain problem with symmetry around the centerline of the bridge, because a similar behavior is anticipated at both ends.
Model Verification and Validation Finite-element analyses were performed to quantitatively validate the model used in this investigation. The objective of this validation was to assess and consolidate the capabilities of the Oasys Safe finite-element model used for this research. The results of field testing by Rollins and Cole (2006) and numerical analyses by Anoosh et al. (2007), who investigated the cyclic lateral load behavior of a pile, pile cap, and backfill, were used to develop a model using Oasys Safe. A verification model with a converging number of elements was chosen (Fig. 3). (This was based on preliminary studies performed by the authors.) The purpose of this model was to verify its competency and accuracy, hence confirming its further use in this study. The structural properties and backfill soil types considered in this model are shown in Tables 1 and 2. One of the pertinent issues when it comes to the modeling of the soil medium is the choice of the soil constitutive model. In general,
Scope and Objective
Fig. 3. Verification model
Although extensive studies through field instrumentations, laboratory experiments, and numerical analyses have been carried out, the lack of understanding in some areas of the behavior of integral abutment bridges is still a concern. Therefore, with respect to analysis, design, and behavior of integral bridges, it is apparent that there is still a great deal of research to be performed. Faraji et al. (2001) expresses the need for future research on these types of bridges to help streamline their design process and hence improve their performance. The following concerns are considered as pertinent to the design and analysis of integral abutment bridges: • Lack of standard design guidelines (Arsoy et al 1999; Dicleli 2000; Huang et al. 2004; Dicleli and Erhan 2010; Kim and Laman 2010); • No clear understanding of the soil-structure interaction behavior of integral abutment bridges in response to thermally induced lateral loading (Huang et al. 2004; Lawver et al. 2000; Dicleli and Albhaisi 2004; Comisu and Gheorghita 2010); and • No comprehensive computational model available to analyze the behavior of integral abutment bridges (Dicleli 2000; Jaafar et al. 2003; Arockiasamy and Sivakumar 2005; Kim and Laman 2010). These concerns have motivated this research work to consider the behavior of the superstructures and backfill/foundation soil when they were subjected to thermally induced lateral movement and vertically imposed loads at deck level. To achieve this objective, a numerical model using the Oasys Safe finite-element analysis programs was developed to represent a typical stub-type integral abutment bridge configuration and backfill/foundation soil profile. © ASCE
Table 1. Geometric Properties of Verification Model Parameter
Description
Pile height Pile size Pile cap height Pile cap width Soil type
12.2 m 1.1 m diameter 1.12 m 2m Clean sand, silt-sand, fine gravel, coarse gravel
Table 2. Material Properties of Integral Abutment Bridge Verification Model Properties Modulus of elasticity EðGN=m2 Þ
Element/material
Poisson ratio n
Superstructure Girder and slab: precast, prestressed concrete girders with cast in situ concrete
30
0.3
27 33
0.3 0.3
Substructure Abutments: cast in situ concrete Piles: prebored concrete
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the choice of the soil constitutive model should take into consideration the simplicity and the ability to realistically represent the real soil behavior (Thevaneyan and Forth 2011a, b). Therefore, as part of this study, to identify an appropriate soil model, the effects of different soil constitutive models (i.e., Duncan-Chang hyperbolic model, Mohr-Coulomb model, and linear model) were considered and compared with the field results obtained by Rollins and Cole (2006). The result of this preliminary study (Fig. 4) indicates that the Duncan-Chang hyperbolic soil model represented the soil behavior reasonably well. The validation study also suggests that the MohrCoulomb soil model represents the soil behavior reasonably well up to 8 mm of displacement. This suggests that, for any laterally induced movement less than 10 mm, the Mohr-Coulomb soil model can be used to reasonably represent the soil behavior. It is reasonable to use the nonlinear Duncan-Chang soil model for backfill and foundation soils in the numerical analyses, because it is known that soil is a nonlinear material. Analyses were done for four different types of backfill soil parameters as prescribed in Table 3, using Oasys Safe. As can be seen from Figs. 5–8, the numerical analyses agree reasonably well with the field test results for the first cycle of loading. It was observed that the variability was within 10%. These observed differences may have been caused by the simplification of the field test conditions in the numerical analyses. However, it is notable that the nature of the initial load-displacement relationships produced by the numerical models was typically linear.
Fig. 5. Load-displacement for clean sand
Fig. 6. Load-displacement for silt-sand
Fig. 4. Lateral load-displacement profile for clean sand Table 3. Set of Soil Properties for Verification Model [Data from Rollins and Cole (2006) and Anoosh et al. (2007)] Type
m g ðkN=m3 Þ (%)
c n ðkN=m2 Þ w Rf
n
nur
K Kur
Clean sand 18.4 13.4 0.3 3.83 39 0.98 0.81 0.81001 200 530 Silt sand 19.2 14.6 0.35 31.0 27 0.97 0.81 0.81001 100 500 Fine gravel 20.8 5.5 0.3 4.0 34 0.98 0.81 0.81001 200 550 Coarse 23.2 4.0 0.3 12.0 40 0.95 0.80 0.80001 200 550 gravel Note: g 5 bulk unit weight; m 5 moisture content; n 5 Poisson ratio; c 5 cohesion; w 5 friction angle; Rf 5 failure ratio; n 5 stress index of proportionality; nur 5 n for unload/reload; K 5 constant for proportionality; Kur 5 K for unload/reload. © ASCE
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Fig. 7. Load-displacement for fine gravel
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In addition to the load-displacement values of the numerical analyses being compared with the field test results, the behavior of the soil profiles was also compared. Rollins and Cole (2006) reported that lateral loading, especially cyclic lateral loading, caused slippage and separation between the bottom of the pile cap and the ground surfaces; these were also observed in the numerical analyses. A 27-mm-deep slippage (Fig. 9) was observed in the numerical analyses, which agreed well (i.e., at the same maximum loading intensity as in the numerical analyses) with the 25-mm-deep depression observed by Rollins and Cole (2006) in their fieldwork analyses. Basinlike depressions were observed in the numerical
Fig. 8. Load-displacement for coarse gravel
analyses, which is similar to the findings of Basack and Bhattacharya (2009) (Fig. 10).
Soil-Integral Abutment Bridge Model A typical 42-m-long and 11.5-m-wide integral abutment bridge was selected for the finite-element analysis. The bridge consists of I20 prestressed concrete girders, a 180-mm-thick concrete deck, and a 100-mm-thick asphalt concrete resting on 4-m-high, 2-m-thick abutments. The abutments are supported by six equally spaced 1,000-mm diameter bored piles. These dimensions and the geometry of the bridge were selected after examining several existing bridges and their construction drawings; there were some minor changes in dimensions to simplify the model and the analysis. To confirm, the bridge was known by the authors and provided an insight into the interactions between the superstructure, the abutment, the approach fill, the foundation piles, and the foundation soil, allowing an informal confirmation of some of the analysis performed and presented in this paper. Initially, models ranging from a frame/beam-element model to 2D plane strain elements were developed to identify a suitable and comprehensive model for the purpose of this study. This study used a 2D plane strain modeling approach in-line with the studies by Arsoy (2000) and Paul et al. (2005). As an extension to this 2D plane strain modeling approach, the nonlinearity of the soil-structure interaction between the bridge and backfill was accommodated by using nonlinear material constitutive models. In the structural models, the equivalent width of the abutment and slabs is set equal to the spacing of the girder and pile. Full composite behavior between the slab and girder was assumed (Fig. 11). The finite-element mesh used in the analyses is shown in Fig. 12.
Fig. 9. Basinlike depression formed at the bottom of the pile cap and the ground surface
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Material Properties The superstructure and substructures of the integral abutment bridge were modeled with elements possessing linear-elastic properties. It is known that the nonlinear behavior of soil is significant for the analyses of the soil-structure interaction (Arsoy 2000; Dicleli and Erhan 2010; Kok et al. 2009; Faraji et al. 2001; Sekhar and Roy 2001). Exclusion of the nonlinear nature of the soil in the analyses can mislead the soilstructure interaction computation. In this work, actual soil profiles from a Malaysian geotechnical consultant were modeled using the DuncanChang hyperbolic properties. Four types of soil were used for the purpose of this study. Table 4 summarizes the material properties of the soils used in the analyses. An important rheological aspect of cyclic soil loading is the accumulation of plastic (nonrecoverable) strains because of the inherent
Fig. 10. Illustration of basinlike depression/slippage (Basack and Bhattacharya 2009)
hysteretic behavior of soil (Noorzaei et al. 1993). The hyperbolic model only approximately replicates hysteretic behavior. However, studies by Noorzaei et al. (1993), Arsoy et al. (1999), and Thevaneyan (2005) showed that this would not detract from the overall qualitative and quantitative correctness of the results of this study.
Superstructure Lateral Displacement–Backfill Soil Interaction In this section, the effects of four types of backfill soil and their thermal expansion on the lateral displacement of the superstructure were studied. Under thermal expansion, the superstructure moves laterally toward the abutment; this movement is potentially resisted by the backfill soil. Resistance from the backfill soil combined with the abutment-pile resistance means that the lateral movement of the superstructure, between the top and bottom of the integral superstructure, is different. The observations also show that the difference between the top and bottom displacements increases with thermal expansion, similar to the behavior shown in Fig. 2. Fig. 13 shows the lateral displacement of the superstructure for various thermal expansion–induced loads applied linearly through the depth at deck level. Various types of backfill soil were used to investigate the influence of backfill soil types on the lateral displacement of the superstructure. The results suggest that the displacement of the superstructure is dependent on the different backfill soil types at lower expansion loads, with the displacements being greatest when silt-sand is considered. From Fig. 13, it can be seen that, as the expansion load increases, the differences between the backfill soil effects become smaller. For instance, at 6C the difference in superstructure displacements with silt-sand backfill soil compared to those with clay soil was 10.7%; this drops to 3% at 30C. This appears to indicate that, as the thermal expansion load increases, the backfill soil is less influential on the lateral displacement of the superstructure; this was noted by Duncan and Arsoy (2003). Fig. 14 compares the lateral displacement of the superstructure resulting from the expansion of the four types of backfill soil. (Thermal expansion loads were produced from three different temperature changes, i.e., 6, 18, and 30C.) As anticipated, the result
Fig. 11. Structural geometry of the modeled integral abutment bridge
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Fig. 12. Finite-element model of integral abutment bridge Table 4. Material Properties Used in This Study Material properties Linear property Element Girder Abutment Pile Soil
Material
EðkN=m2 Þ
Nonlinear property n
n
Concrete 27,000,000 0.35 — Concrete 27,000,000 0.35 — Concrete 27,000,000 0.35 — Clay 25,000 0.3 0.98 Silt 45,000 0.3 0.995 Silt 1 sand 50,000 0.35 0.9 Silt 1 gravel 65,000 0.35 0.81
Pam Et — — — 101 101 101 101
— — — 290 200 200 230
Rf — — — 0.846 0.88 0.875 0.885
C ∅ — — — 10 22 21 25
— — — 4 19 19 16
also indicated that the increase in lateral displacement of the superstructure was found to be proportionate to the increase in the thermal expansion load. This suggests that the lateral displacement is a function of the thermal strain, which is a product of the temperature differential and length. The relationship between the lateral displacement and thermal expansion was linear; i.e., an increase in lateral displacement of up to 200% was noted for an increase of an equally proportionate thermal expansion from 6 to 18C, and a 67% increase in the lateral displacement was noted for an increase of 67% in thermal expansion from 18 to 30C. Therefore, it was concluded that the thermal expansion of the backfill soil had a negligible effect on the lateral displacement of the superstructure. As such, it appears that the elastic shortening (and thus the force resulting from the soil pressure) is insignificant.
Superstructure Vertical Displacement–Backfill Soil Relation In this section, the effects of the thermal expansion of various types of backfill soil on the magnitude of the superstructure vertical displacement (i.e., span length from 31 to 70 m) and the behavior of the superstructure under serviceability limit state (SLS) imposed vertical load were investigated. Studies on the vertical behavior of the © ASCE
superstructure and superstructure backfill soil interaction are scarce. However, the backfill soil properties are anticipated to affect the magnitude of the vertical displacement resulting from thermally induced expansion/contraction and imposed vertical load. Thus, four types of backfill soils, as presented in Table 4, were used for the purpose of this study. As mentioned previously, the finite-element model represented 50% of the bridge cross section because of the symmetry of the bridge. However, for illustration purposes and for greater clarity and understanding, the figures that follow have been presented in terms of the full span length of the superstructure by super transposition at the centerline. Fig. 15 illustrates the vertical displacement of the superstructure resulting from the thermal expansion loads from the various backfill soils. Unlike the lateral displacement of the superstructure, the vertical displacements were not proportional to the thermal expansion load. The results suggest that the backfill soil properties have a significant effect on the vertical displacements of the superstructure when it is subjected to thermal expansion loads. However, the difference between the highest and lowest vertical displacements in terms of backfill type reduced as the thermalexpansion loads increased. For instance, a difference of 272% was observed for a thermal-expansion load corresponding to 6C between the highest and lowest vertical displacements; however, the difference was only 70% for the 30C thermal-expansion loads. Sagging was observed when thermally induced contraction loads were applied. As seen in the lateral displacement of the superstructure (Figs. 16–19), as the thermally induced loads increase the influence of backfill soil becomes insignificant on the vertical displacement of the superstructure. Fig. 16 shows the bending moment produced in the superstructure for the maximum thermal load (because of a 30C temperature change) for the various backfill soil properties. A similar flexural behavior was observed for all the various thermal loads. The maximum variation in moment for each soil type case was about 6%. This result further confirms that the backfill soil type may have an insignificant effect on the behavior of the superstructure. The effect of the various backfill soils on the shape and magnitude of the vertical displacement of the superstructure and the bending moment in the superstructure produced by the vertically
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Fig. 13. (a) Lateral displacement at 6C of superstructure at various thermal expansions for different types of soil using Safe Mohr-Coulomb (MC); (b) lateral displacement at 18C of superstructure at various thermal expansions for different types of soil using Safe MC; (c) lateral displacement at 30C of superstructure at various thermal expansions for different types of soil using Safe MC
imposed load was observed. The results indicated that the backfill soil properties have a noticeable effect on the shape and magnitude of vertical displacement and bending moment of the superstructure. Fig. 17 shows the vertical displacement shape and magnitude for the various backfill soils because of vertically imposed loads. The results suggest that the vertical displacement of the bridge superstructure because of a vertically imposed load is influenced by the stiffness of the backfill soil. However, the difference in displacement between the most and least stiff soil types was only about 12%. When compared with the variations in elastic modulus for the given backfill soils, i.e., the difference between the most and least stiff soil types was 300%, this difference of 12% in the vertical displacements does not appear to be significant. The shape of the bending moment for the various backfill soil properties is presented in Fig. 18. The results suggest that the © ASCE
magnitude of the bending moment will be similar irrespective of backfill soil properties. In other words, the shape and magnitude of the bending moments are not influenced by the properties or types of backfill soil. The combined effect of the thermally induced expansion load and the vertically imposed load may be beneficial because of the precamber effect. However, a comparison of the magnitude of the hogging vertical displacement resulting from the thermally induced expansion load to the sagging vertical displacement from the vertically imposed load reveals that the effect of precamber may not be significant. The vertical displacement of the superstructure indicates that the behavior of the superstructure is dominantly affected by the vertically imposed load rather than the thermally induced load. Fig. 19 compares the bending moment resulting from the thermal expansion loads, the vertically imposed loads, and their
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Fig. 14. Superstructure lateral displacement comparison between various types of backfill soil at three different thermal expansion loads
Fig. 15. (a) Vertical displacement of superstructure for various backfill soil properties at thermal expansion of 6C; (b) vertical displacement of superstructure for various backfill soil properties at thermal expansion of 18C; (c) vertical displacement of superstructure for various backfill soil properties at thermal expansion of 30C
combinations for silt-gravel and clay soil (representing the highest and lowest stiffness parameters, respectively). The results further confirm that the behavior of the superstructure for the given backfill properties and loading is more significantly affected by the vertically imposed load in comparison with the effect of the thermal load. © ASCE
Summary and Conclusions The present analyses demonstrate the integral superstructure behavior with regard to the given various backfill soil properties and different loading conditions. The following conclusions may be drawn from the analyses:
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Fig. 16. Bending moment from maximum expansion thermal load for various backfill soil properties
Fig. 17. (a) Vertical displacement of superstructure for various backfill soil properties at 50% of vertical imposed load; (b) vertical displacement of superstructure for various backfill soil properties at 100% of vertical imposed load
1. The behavior of the superstructure of an integral bridge is predominantly influenced by the loading magnitude, irrespective of backfill soil properties (within the investigated configurations and loading conditions considered in this paper). The results also indicate that the given backfill soils may have an insignificant effect on the behavior of the superstructure when subjected to high thermal expansion and contraction loads and for any given vertically imposed load. 2. The superstructure bending moments resulting from these applied thermal loads (within the investigated configurations and loading conditions considered in this paper) are not significant and may be ignored when evaluating the superstructure design. This is consistent with the findings of Duncan and Arsoy (2003). 3. The combined effect of the thermally induced expansion load and the vertically imposed load may be beneficial in design because of the precamber effect. However, the effect of the thermal contraction load may cause additional distress in the © ASCE
superstructure because of the sagging displacement it produces. As a result, this would increase the imposed load–induced displacement further. By comparing the magnitude of the upward vertical displacement attributable to the thermally induced expansion load with the sagging vertical displacement from the vertically imposed load, the effect of precamber may considered to be insignificant. 4. The results suggest that the conventional design requirements of the superstructures for a nonintegral abutment bridge to resist the imposed loading may be sufficient to accommodate any effects attributable to the thermal (expansion and contraction) loads in stub-type integral abutment bridges, especially when the range of thermal expansion and contraction is approximately 630C. The integral design approach presented in this paper is limited to some simple cases where the structure is assumed to be fully symmetrical and the soil pressures at both sides of the bridge are assumed to be in equilibrium. The correlation between the temperature
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Fig. 18. (a) Bending moment shape and magnitude for various backfill soils at 50% of vertical imposed load; (b) bending moment shape and magnitude for various backfill soils at 100% of vertical imposed load
Fig. 19. (a) Bending moment comparison in superstructure for silt-gravel; (b) bending moment comparison in superstructure for clay
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variation and the magnitude of earth pressure is pertinent as far as the analysis and design practice of integral abutment bridges is concerned. Therefore, further studies are needed to further establish and consolidate the correlation between these two influencing factors.
Acknowledgments The major part of this work was carried out during postgraduate study at University of Leeds, United Kingdom, by the first author.
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