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Thermally induced soil structure interaction in the existing integral bridge
Engineering Structures 106 (2016) 484–494
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Thermally induced soil structure interaction in the existing integral bridge Dunja Peric´ a, Marta Miletic´ a,⇑, Bhavik R. Shah b, Asad Esmaeily a, Hongyu Wang c a
Department of Civil Engineering, Kansas State University, Manhattan, KS 66506-5000, United States Read Jones Christoffersen Ltd., Consulting Engineers, 144 Front Street West, Suite 500, Toronto, Ontario M5J 2L7, Canada c Department of Civil and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China b
a r t i c l e
i n f o
Article history: Received 31 December 2014 Revised 4 June 2015 Accepted 21 October 2015
Keywords: Integral abutment bridge Soil–structure interaction Thermal effects Finite element analysis
a b s t r a c t While Cross’ method enabled scientifically based structural design of integral bridges (IB) a similar progress in understanding and analyzing the relevant complex soil structure interaction has not been made yet. This hampers a wider adoption of IB systems, whose geo-structural system inherently brings multiple sustainability and performance benefits to transportation infrastructure. To this end, a full 3D finite element model of an existing three-span integral bridge was assembled and subjected to a combined thermal and gravity loads. The bridge superstructure consists of the two sets of concrete piers, two abutments, and fourteen HP steel piles (seven at each abutment), whose strong axis of bending is oriented parallel to the longitudinal direction of the bridge. Upon a successful validation and the verification of the computational model, several loading scenarios simulating different amounts of temperature increase in the presence of different soils adjacent to the abutment were simulated. Further analyses indicated that effects of the compaction level of the soil adjacent to the abutments, and of a magnitude of the thermal load on the substructure are opposite from the effects of these agents on the superstructure. Published by Elsevier Ltd.
1. Introduction According to Burke [1] integral bridges were implemented in practice shortly after Cross [2] had developed a simple method for the analysis of continuous beams and frames. This enabled the design and construction of bridges without deck joints, which are known as integral bridges (IB). In 1935 Kansas was among the first states in the U.S. that constructed an IB (Bakeer et al. [3]). Since then the construction of integral bridges has been pursued by many states in U.S. and provinces in Canada. At first IBs were built to eliminate the leakage of deicing chemicals and the resulting corrosion of primary structural members, which remains the main cause of limited service lives of jointed bridges. The additional benefits of IB, many of which turned out to increase their sustainability, are inherent to its geo-structural system. Economic benefits are accomplished through lowered whole life cycle costs including decreased construction and maintenance costs. Other benefits include elimination of noise associated with crossing of vehicular traffic over jointed bridges, and ⇑ Corresponding author. Tel.: +1 785 317 2283. E-mail addresses: [email protected] (D. Peric´), [email protected] (M. Miletic´), [email protected] (B.R. Shah), [email protected] (A. Esmaeily), why.nxts@163. com (H. Wang). http://dx.doi.org/10.1016/j.engstruct.2015.10.032 0141-0296/Published by Elsevier Ltd.
more pleasing aesthetics of a continuous superstructure. The social benefits comprise better connectedness for urban and rural environments, which is achieved through less maintenance caused traffic disruptions, and easier widening and future replacement of IBs. Furthermore, a vehicular ride quality is improved, and traffic safety is increased by elimination of joints. In addition, an IB is a continuous geo-structural system that results in more uniform distribution of internal forces than jointed bridges (Dicleli [4]). Consequently, IBs exhibit an increased redundancy and resilience. The important uncertainty related to the design and performance of IBs is stress in piles. Cyclic loading such as temperature variations and traffic loads, can cause significant horizontal displacements of a bridge. A long term cyclic loading generates rotations and horizontal displacements of abutments that cause a settlement of the abutment backfill. During this process a void gradually forms behind an abutment, thus causing the soil pressure to further increase upon the subsequent expansion of the bridge. Consequently, IBs have to deal with greater soil pressures acting on the abutments than jointed bridges. Settlement of the abutment fill and movement of the superstructure can lead to cracking of the wing-walls and opening of joints between a bridge and an approach slab. Furthermore, due to settlement, and thermal changes and gradients creep and shrinkage of concrete and additional secondary stresses can develop in the superstructure.
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Additional disadvantages include minor longitudinal and transverse cracking, poor drainage at abutments, and cracking and spalling in bearing areas (Bakeer et al. [3]). In spite of many advantages of IBs that outweigh their disadvantages there is still a need for knowledge discovery, which will help to further reduce the disadvantages of IBs.
2. Literature review Although many studies, including those addressing field instrumentation, laboratory experiments, and numerical modeling have been carried out the lack of understanding of the behavior of IBs is still a concern. A brief overview of the research addressing primarily a numerical modeling of IBs is presented next in the chronological order. Dicleli [4] had proposed a simplified structural model of an IB, on the basis of which a computer program was developed. The deck, abutment and piles were represented by structural elements having effective widths corresponding to the spacing between girders, which essentially extended into the abutment and piles, thus lumping the piles based on the tributary width. The program was capable of analyzing different loading scenarios separately and combining the corresponding results as needed, thus indicating that it was assumed that an IB remained in the elastic range. The proposed method produced more economic designs than the conventional analysis used previously. Dicleli and Albhaisi [5] focused on the abutment-backfill system while evaluating the performance of IBs built on clay. They used the SAP 2000 software to conduct static push-over analyses on a 2D model, thus simulating a thermal load. They concluded that maximum length limit of IBs is controlled by the flexural capacity of abutment under positive temperature changes for the abutments taller than 4 m. They suggested that piles should be oriented about their weak axis of bending to enhance the maximum length limits as determined by the flexural capacity of abutment. Furthermore, they also suggested that pinned connection between the abutment and the pile head may be used to reduce the flexural demand on the abutment. Dicleli and Albhaisi [6] conducted static pushover analyses of a pile–soil system by using a finite element-based software SAP 2000. Their model accounted for nonlinear responses of structure and soil. Dicleli and Albhaisi [6] found that the maximum length limits for IB with stub abutments decrease as the foundation soil becomes stiffer. They also found that the pinned abutment-pile connection significantly increases the displacement capacity of integral bridges with stub abutments based on the capacity of piles under cyclic loading. They concluded that maximum length limits of concrete and steel IB in moderate climates range from 180 to 320 m and from 125 m to 220 m respectively. Huang et al. [7] used a P beam numerical model to model the prestressed concrete IB with a total length of 66 m located in Rochester, Minnesota. They compared numerical predictions with the actual measurements that were reported by Lawver et al. [8]. Based on the prediction of their numerical model they concluded that the creep rate of the concrete girder could have increased due to the increased backfill soil pressure. They also detected steadily increasing pile curvatures over seven years. They concluded that creep and shrinkage significantly affect behavior of concrete IB. Civjan et al. [9] presented results of a 2D finite element analysis of an 82.3 m long three-span integral bridge located in Orange– Wendell, Massachusetts. The bridge has a concrete deck and steel girders. Two node elements with three degrees of freedom per node were used to model the bridge by using a GT STRUDL software. They modeled expansion and contraction of the bridge based
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on the comparison with the actual measurements. Civjan et al. [9] concluded that their computational model captured neither the transition from passive to active soil states, nor the peak active pressures. They also found that bending moments in piles were minimized by using a denser backfill. Huang et al. [10] performed a 3D finite element analysis of a 66 m long three-span prestressed concrete integral bridge located in Rochester, Minnesota. They used shell and beam–column elements and ANSYS software. They modeled expansion and contraction of the bridge combined with gravity loads, but assumed nocontact between the abutment and soil in the case of the bridge contraction by using Winkler’s springs with zero stiffness. Huang et al. [10] verified their computational model against the actual measurements and conducted a number of parametric studies assessing effects of several design variables. They concluded that the selection of the pile type and orientation should be based on balancing the stresses in piles and in superstructure for long span bridges or bridges surrounded by stiff soils. They recommended that the pile selection and orientation should be based on the specific bridge situation. Pugasap et al. [11] used an ANSYS software to predict a long term response of IBs. Verification and validation was performed by comparing the numerical results with the field measurements obtained on three IBs in Pennsylvania over several years. Numerically obtained and measured soil pressures were found to be in a good agreement. In addition, it was shown that predicted abutment displacements and corresponding design moments and forces at the end of the numerically simulated 100-year period have a significant influence on a long term behavior which should be considered in IB design. Kim and Laman [12] conducted a parametric study of a prestressed concrete IB by using a 2D numerical model. The imposed loads included a superstructure temperature loads including temperature gradients, and concrete time-dependent loads. Reponses of three different bridges with total lengths ranging from 18.3 m to 121.9 m were simulated in their study. They found that the magnitude of a thermal expansion coefficient significantly influences the axial force and bending moment in a girder, and lateral force and bending moment in the pile, as well as the pile/head displacement. They also found that the bridge length significantly influences axial forces in girders, lateral forces and the bending moments in piles, as well as the pile head displacement. Kalayci et al. [13] studied the effect of an in-plan curvature on the thermally induced response of an actual IB located in Vermont, USA. They selected a two-span curved IB and subjected it to the temperature increase and decrease, each of which was equal to 55.6 °C. The bridge is 67.7 m long, 11.3 m wide, and it has 11.25° curvature. It has steel girders and concrete deck. Kalayci et al. [13] assembled a finite element model of the IB whereby the soil was modeled by non-linear Winkler’s springs. They found that longitudinal displacements, earth pressures and weak axis bending moments in piles decreased with increasing curvature. Conversely, lateral displacements increased with increasing curvature. To investigate the long-term effect of temperature variations on the superstructure of an IB, William et al. [14] monitored a newly constructed three-span IB in West Virginia for four years. The total length of the bridge is 44.8 m. It has steel girders and concrete slab. William et al. [14] developed a detailed three dimensional finite element (FE) model of the bridge by using an ADINA software. Comparison of the measured data and numerically obtained results showed a very good agreement of longitudinal strains in the middle girder, and longitudinal and transverse deck strains. They found similarly to Kalayci et al. [13] that the lateral displacements at the ends of steel girders increase with increasing skew angle. Additionally, their results show that the backfill and supporting piles restrain movement of the integral abutment, thus inducing axial
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forces in the superstructure. These forces are not explicitly considered in the design of the IBs. Field measurements of the bridge movement due to temperature variation were carried out by Barr et al. [15] for twelve months on 400 South Street Bridge, Salt Lake City, Utah. The bridge is a three-span IB with a curved deck, while the girders beneath are in three separate, straight segments. First, the SAP2000 software was used to create a detailed model of the IB, which produced high stress concentrations in the abutment adjacent to the bottom girder flange. This confirmed the observed cracking at the same location. Furthermore, in order to better understand the cause of the observed spalling at the abutment of IB, a simplified model was created using the same software. A parametric study was performed on the effects of a skew angle, span length, and temperature gradient on the weak-axis bending moment of the abutment. The results of the parametric study showed that even a slight increase in skew angle (as little as a 5°) and the increase in span length can markedly increase the weak-axis bending moment of the bridge abutment. In addition, a large increase in the weak-axis bending moment was observed as the temperature gradient within the bridge increased. Barr et al. [15] concluded that the combination of the bridge parameters (skew angle, curvature of the bridge, span length, and detailing) is most likely the cause of the abutment cracking. Thevaneyan et al. [16] developed the Oasys Safe FE analysis program to simulate the behavior of a typical stub-type IB configuration and backfill-foundation soil profile subjected to a thermally induced lateral movement and vertically imposed load at deck level. They have shown that different properties of the backfill soil and loading conditions have a major influence on the behavior of the IB superstructure. It is noted, that the IB design recommended by Thevaneyan et al. [16] is limited to 2D plane strain problem with symmetry around the centerline of the bridge. Erhan and Dicleli [17] focused on modeling a seismically induced soil structure interaction in a two-span 82 long, and 16 m wide IB. To accomplish this goal they used five different levels of structural models ranging from the most complex to the simplest one. While the most complex model included free field effects, p–y curves and dashpots, and shear column simulating a local soil–pile interaction and radiation damping, the simplest model did not contain springs adjacent to piles. Erhan and Dicleli [17] found that difference between predictions of different models depended on the ground motion intensities and also on particular models compared. Although seven actual earthquake ground motions were selected for the analyses the predictions were not verified against the actual measurements. In summary the literature review indicates that there are at least two outstanding problems related to IBs that require a further inquiry. They include the effect of the soil structure interaction on the long term performance of IBs and a seismic behavior of IBs. It is very helpful to have a clear understanding of a short term static soil structure interaction before embarking on the research addressing these two outstanding problems. To this end, the present study was performed within the realm of IBs whose piers are hinge-connected to the superstructure.
comprising a computational modeling of an IB, whose results are presented herein. The main goal of the study was to investigate the effects of compaction levels of the soil adjacent to abutments on the behavior of a three-span IB whose piers are hingeconnected the superstructure. Consequently, a selected IB was subjected to a combined thermal and gravity loads. Moreover, three different magnitudes of thermal load were considered, thus representing IBs located in different climates. The additional objective was also to identify the loading scenarios that would likely lead to a formation of a plastic hinge between the abutment and the pile. 4. Computational model of the selected IB A detailed full 3D finite element model of the ‘‘Bemis Road Bridge: F-4-20” over the Nashua River in Fitchburg, Massachusetts (Ting and Faraji [18]), which was assembled in this study by using ABAQUS/Standard [19], is shown in Fig. 1. It is noted that this model is nearly a full replica of the actual bridge, the schematics of which are shown in Fig. 2. Only one half of the bridge is modeled due to the symmetry. The piles and piers/drilled shafts are fixed at their bottom (Fig. 1). The Winkler’s springs are attached to the abutment and piles. This bridge was selected because it represents a typical IB in Kansas. The main differences between the FE model used in this study, and the one used by Faraji et al. [20] can be grouped in four categories: (1) differences in the computational models, (2) differences in the material properties, (3) differences in the loads, and (4) differences in the modeling approaches. The main difference in the computational model is in that the piers in the present model are hinge-connected to the superstructure, while this connection is fixed in Faraji et al. [20]. This modification has been implemented upon a request of KDOT because it reflects the current design and construction of IBs in Kansas. It is also noted that Faraji et al. [20] used plate elements to model abutment, and beam elements to model the piles, while the present study uses eight node brick elements for the entire bridge (except the hinges) thus creating nearly the exact replica of the actual bridge. Differences in material properties include two different coefficients of thermal expansion for concrete and steel while Faraji et al. [20] used a single value for the entire bridge. It is because the primary focus of this study was on the effects of the compaction levels of the soil adjacent to the abutment that three different types of abutment backfill are modeled. Specifically, a design curve for dense sand specified by Canadian Geotechnical Society (CGS) [21] is added to design curves given by National Cooperative
3. Research significance A development of a deeper understanding of a complex soil structure interaction in IBs will facilitate a paradigm shift leading to more science based rather than experientially based design. This will ultimately enable a more extensive adoption of IB systems in practice, thus directly contributing to the increased sustainability and resilience of the transportation infrastructure. To this end, Kansas Department of Transportation (KDOT) funded a small study
Fig. 1. A detailed full 3D finite element model of the ‘‘Bemis Road Bridge”.
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Fig. 2. Schematics of the actual integral bridge (a) the longitudinal view and (b) cross-section.
Highway Research Program (Barker et al. [22]) to cover different shapes of the coefficient of lateral earth pressure versus normalized abutment displacement curves. Furthermore, according to (Faraji et al. [20] the level of soil compaction adjacent to piles does not significantly influence the deflections and moments in the superstructure. Additionally, the maximum moment in the piles occurred in the case when loose abutment backfill was used in combination with dense sand adjacent to piles. Consequently, three different abutment backfills are combined with dense sand adjacent to the piles in this study. It is noted that Faraji et al. [20] used two soil types behind the abutment and two soil types adjacent to the piles. The present study models a response of the IB to a simultaneous action of gravity and thermal loads unlike Faraji et al. [20] who modeled only thermal loading corresponding to a temperature increase of the composite deck of 44.4 °C. Furthermore, the present study includes three different temperature increases. The temperature is applied in a fashion shown in Fig. 3, thus imposing a thermal gradient within the abutment. It is believed that this temperature distribution is more realistic than the one applied by Faraji et al. [20] who heated solely the composite deck. The differences in the modeling approach are related to Winkler’s springs. These springs represent the action of soil on the abutment and piles. Non-linear springs attached to the abutment
Fig. 3. Nodal temperature increase for one of the loading scenarios (numbers in the legend denote the magnitude of a temperature increase in °C).
are modeled by using an equivalent iterative linear approach (Eq. (1)). Faraji et al. [20] used explicit non-linear springs instead. For the springs attached to the piles an empirical approach based on the actual field test data is adopted herein. Modeling of these non-linear springs also requires an iterative procedure, which is summarized in Eq. (4). Faraji et al. [20] used so called p–y curves instead (see Fig. 4).
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488
Longitudinal Displacement (m) -0.005 0
0.000
0.005
0.010
0.015
Depth from Abutment Top (m)
2
4
Shah - DD 44.4°C 6
Faraji et al. - DD 44.4°C
8
10
12 Fig. 4. Verification and validation of the present model: longitudinal substructure displacements at the intersection of the back of the abutment and the centerline.
The length of the central span is 18.3 m, while each of the two end spans is 13.7 m long. The width of the bridge is 16.5 m. The superstructure consists of a 0.22 m thick concrete slab, seven W920 201 steel girders, and five W920 201 transverse steel beams. The longitudinal view and cross-sectional area of the IB with all dimensions are illustrated on Fig. 2. A full composite action between the steel girders and beams with the concrete slab is enforced by invoking the merge option in ABAQUS. The superstructure shown in Fig. 1 consists of one set of concrete piers, a concrete slab, and transverse and longitudinal steel girders, whereby the latter are monolithically connected to the concrete abutment. A single row of steel HP310 110 piles, whose strong axes of bending are oriented parallel to the longitudinal direction of the bridge serves as the foundation for the abutment. The deck is additionally supported by two sets of concrete piers/ drilled shafts, which are hinge connected to the superstructure. The full 3D finite element model shown in Fig. 1 contains 191,894 eight-node coupled temperature-displacement elements (C3D8T), 277,530 nodes, 12 connector elements (CONN3D2) modeling the hinges, and 546 linear spring elements. A total of 140 springs were attached behind the abutment resulting in a 0.610 m 0.601 m tributary area for each spring. Additionally, a total of 58 springs were attached to each pile, each of them having a tributary area of 0.305 m 0.155 m. It is noted that the springs were attached to piles in pairs, thus resulting in two springs at a given elevation. 4.1. Structural materials Concrete and steel are modeled as isotropic linear elastic materials whose properties are listed in Table 1. 4.2. Soil behind abutments Design guidelines for the load–displacement response of the soils behind the abutment provided by National Cooperative Highway Research Program (Barker et al. [22]) and CGS [21] were used
Table 1 Properties of structural materials. Property
Concrete
Steel
Young’s Modulus, E (GPa) Poisson’s ratio, t Coefficient of thermal expansion, a (C1) Mass Density, q (kg/m3)
30 0.3 1 105 2402
206.84 0.3 1.17 105 7849
to determine the stiffness of the springs attached to the abutment. To investigate the effect of different compaction levels three different sands were modeled: (1) the dense sand described in Barker et al. [22], denoted by ‘‘D”, (2) the loose sand described in Barker et al. [22], denoted by ‘‘L”, and (3) the dense sand described by CGS [21], denoted as ‘‘Dc”. Dry unit weights of loose and dense sands are assumed to be equal to 17.8 kN/m3 and 18.9 kN/m3 respectively, while the maximum dry unit weight is 19.7 kN/m3. Thus, the loose and dense sands represent relative compaction levels of 90% and 96%, respectively, which correspond to relative densities of 50% and 80% respectively. Design guidelines given by Barker et al. [22] provide only the angles of internal friction, which are equal to 30° and 45° for loose and dense sands, respectively. Both sets of design curves provide the relationships between the lateral displacement at the top of an abutment, and the coefficient of lateral earth pressure. It should be noted that unit weights, relative densities, and relative compactions of both dense sands (‘‘D” and ‘‘Dc”) are equal in the present study. Based on the results presented by Faraji et al. [20] it is evident that the critical combinations of soil types, which produce maximum bending moments in the deck, and the piles are DD and LD respectively. The first letters in these abbreviations denote the type of sand behind the abutment while the second letters denote the type of sand adjacent to the piles. Since both critical combinations correspond to the presence of dense sand adjacent to the piles, the focus of this study is on the effect of the type of the abutment backfill. Thus, three types of sands are selected. Specifically, Dc sand is added to D and L sands because it is characterized by a different shape of curve relating the lateral displacement to the coefficient of lateral earth pressure. Fig. 5 depicts a rigid body motion of the abutment, which is associated with a thermal expansion of the bridge. Thus, a total lateral displacement (D) at the top of the abutment is decomposed into translational (DT) and rotational (DR) components. The piles experience maximum deflections at the pile heads (yt), hence leading to the maximum bending moments at the same location. The magnitude of stresses in piles due to these bending moments is a vital concern in design of integral bridges. An equivalent iterative linear approach used to determine the stiffness of the springs attached behind the abutment is described by Eq. (1) as follows:
kiþ1;j ðDi ; di;j Þ ¼
K i ðDi Þcd zA;j ðDAÞj di;j
ð1Þ
where index i is the iteration counter, while index j denotes the spring row number corresponding to its depth. The stiffness of an individual spring is denoted by ki+1,j whereby Ki is the coefficient of lateral earth pressure, cd is dry unit weight of soil, and zA,j is the depth of the spring with tributary area (DA)j. Global and local lateral displacements of the abutment are denoted by Di and di.j, respectively, whereby the later denotes the displacement at the location of the corresponding spring. According to the equivalent linear iterative approach the spring stiffness for the subsequent iteration (i + 1) is determined based on the global and local displacements from the previous iteration (i). A single iteration corresponds to a single ABAQUS run. For the very first run there were
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T
DECK
489
(2) the coefficient of the horizontal subgrade reaction at 1 m depth can be expressed as a function of the pile head displacement. The stiffness of the spring attached to a pile at this depth (k [kN/m]) can be obtained by multiplying the stiffness of the spring in terms of the pressure (Kh) by the tributary length (DL). Prakash and Kumar [23] assumed that Kh varies linearly with depth, thus giving the following expression for the spring stiffness (k [kN/m]):
R
b 1þt K h;max kiþ1 ðzP ; yt;i Þ ¼ a zP ðDLÞ yt;i 2:5B zR
H GIRDER
ð4Þ
where ‘‘i” is the iteration counter and zP is the depth from the pile head. The convergence is achieved when the relative error in the pile head displacement falls below 1% in two subsequent iterations. All cases herein exhibited an exponential rate of convergence, whereby the displacements in the very first iteration were the largest. It is noted that springs were attached to the model in the second iteration, and their stiffness was determined based on the displacement from the previous iteration. The selected value
ABUTMENT
yt PILES
Fig. 5. Rigid body motion of the abutment decomposed into translation and rotation, accompanied by bending of the piles.
no springs attached to the bridge. Global and local displacements of the abutment were then obtained from the output data. They were inserted into Eq. (1) to obtain the spring stiffness for the second run. It is noted that the coefficients of lateral earth pressure (K1) were determined from design charts (Barker et al. [22] and CGS [21]) based on the global abutment displacement from the first run. Iterations are continued until the relative error in the abutment displacements, based on the two subsequent iterations fell below 1%.
Fig. 6. Longitudinal normal stress (S11 in MPa) in the bridge for DD 55.6 (deformation scale factor 130).
-80
Prakash and Kumar [23] proposed a method alternative to p–y curves, which describes a non-linear load–displacement relationship for a single laterally loaded pile. It is an empirical method, which is based on the experimental observations that were collected from the fourteen full scale tests on different types of laterally loaded piles reported by Mwindo [24]. According to Prakash and Kumar [23] the coefficient of the horizontal subgrade reaction (Ks [kN/m3]) at a depth of 1 m below the pile head is given by:
K s ðcÞ ¼ K h =zR ¼ acb K h;max =zR
ð2Þ
where c is the shear strain in the sand behind the pile, zR is the reference depth of 1 m, Kh,max is the value of lateral pressure that produces unit displacement in the soil, at the shear strain of 0.2%. The values of the empirical coefficients a, and b of 0.05 and 0.5 respectively, were used in accordance with the recommendations found in Mwindo [24] for HP steel piles. Prakash and Kumar [23] expressed the average shear strain in the sand in terms of the pile head displacement (yt) as:
cðyt Þ ¼
1þt y 2:5B t
Maximum Compressive Axial Stress (MPa)
4.3. Soil behind piles -100
-120
-140
-160
-180
-200
-220
ð3Þ
where t is Poisson’s ratio of sand assumed to be equal to 0.3 in this study, and B is the width of the pile. By substituting Eq. (3) into Eq.
LD DD DcD
32
35
38
41
44
47
50
53
56
Fig. 7. Maximum compressive axial stress (S11) at the bottom flange of the central girder in the vicinity of the abutment.
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of Kh,max is 69,053 kPa, which is about 88% of the value suggested by Prakash and Kumar [23] for dense, medium to fine sands, and 3.05 to 4.6 m deep ground water table. The particular value used in this study was determined based on the best fit against the longitudinal displacements of the abutment and piles obtained by Faraji et al. [20] for the equal loading scenarios. 4.4. Loading scenarios To fulfill the main goal of this study, which was assessing the effects of the temperature change ranges and soil compaction
levels, nine different loading scenarios were considered. They reflect the presence of three different soils behind the abutment, one single soil behind the piles, and three different temperature increases corresponding to 33.3 °C, 44.4 °C and 55.6 °C. These temperature changes reflect different climatic conditions. The corresponding loading scenarios are named: DD 33.3, DD 44.4, DD 55.6, DcD 33.3, DcD 44.4, DcD 55.6, LD 33.3, LD 44.4, LD 55.6, whereby the first letter indicates the soil type behind the abutment, followed by the soil type behind the pile, and by the amount of the superstructure temperature increase. In each case the selfweight of the bridge is applied first by simply switching on the gravity acceleration. The superstructure of the bridge is subsequently subjected to the above temperature change ranges in the fashion indicated in Fig. 3. Only the steady state thermal loading is considered. 5. Results and discussion
Fig. 8. Composite bending moment of the bridge deck and girders for temperature increase of 55.6 °C.
The finite element model depicted in Fig. 1 was first successfully verified and validated against the corresponding result of Faraji et al. [20]. For this purpose the weightless analysis, without thermal gradient within the abutment, and with the same coefficient of thermal expansion for the concrete and steel was carried out (Shah [25]). In addition and in accordance with Faraji et al. [20] piers were rigidly connected to the superstructure. An excellent agreement between the predictions of the present analysis and the one presented by Faraji et al. [20] was obtained (Fig. 4), thus successfully validating and verifying the model used for this study. It is noted that Faraji et al. [20] have not validated their results against any actual measurements most probably because they were not available. The discontinuity in the displacement gradient that is exhibited by the prediction of Faraji et al. [20] was most likely caused by a connection of the abutment plate and pile beam elements. A smoother displacement that is exhibited in the present analysis is attributed to the use of full 3D elements in the entire bridge model. Fig. 6 depicts a deformed shape of the bridge with the superimposed color coded longitudinal stresses (S11) for the DD 55.6 loading scenario. Compressive normal stresses are negative. Fig. 6 indicates that the superstructure accommodates the temperature increase by a combined expansion and bending. The presence of
Fig. 9. Total axial force in the bridge deck and girders for temperature increase of 55.6 °C.
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On the contrary, the effect is more significant in the central span in the case of axial force. Fig. 11 shows longitudinal displacements of the substructure at the intersection of the abutment back face and the centerline of the bridge for six loading scenarios representing three different soils behind the abutment and the two extreme temperature changes. Soil conditions have little or no influence on the displacement of the abutment top. However, the mode of the abutment motion is significantly affected by the soil compaction level and temperature change range. Further information is provided in Fig. 12, in which
0
-2
Depth from Abutment Top (m)
the soil behind the abutment suppresses the expansion of the bridge, whereby this effect is increasing with the increase in depth below the soil surface, thus inducing the bending of girders and slab. This phenomenon is responsible for the buildup of compressive axial stresses in the bottom flanges of the longitudinal girders. Fig. 7 shows that these maximum compressive stresses at the bottom flange of the central girder decrease with decreasing soil density and decreasing temperature change. Additionally, the buildup of compressive stresses implies that girders should be secured against the possibility of a local buckling. Fig. 8 depicts the composite bending moments of the bridge slab and girders for the temperature increase of 55.6 °C in the presence of different soils. The composite bending moment was obtained by a direct numerical integration of the moment of axial stress about the elastic neutral axis of the superstructure. In the case when piers are connected to the deck by fixed connections Faraji et al. [20] showed that the effects of the compaction level of the abutment backfill extends only up to the bent. In other words, the bending moment in the central span is not affected by the abutment backfill type. In the present study piers are hinge connected to the deck, which causes a slight decrease in the magnitude of bending moments in the vicinity of the bent. It is because of this decrease that the magnitude of bending moment in for example dense sand becomes the smallest only in the vicinity of the bent. Although the effect of the abutment backfill type now extends all the way to the bridge centerline it is less pronounced in the central span. Fig. 9 shows the total axial force in the bridge superstructure for the temperature increase of 55.6 °C, which exhibits a significant sensitivity to the soil compaction level. The total axial force in superstructure appears to be very sensitive to the compaction level of the soil behind the abutment. For example, it is as much as 3.5 times larger in the presence of the dense sand as compared to loose sand. Fig. 10 shows the composite bending moment of the bridge slab and girders for three different temperature changes in the presence of dense soil adjacent to the abutment. Although both, the temperature change range and the soil compaction levels affect the composite bending moment, the effect of the soil compaction level is more pronounced and it extends further away toward the centerline of the bridge. However, both factors have a more significant effect on the end span with regard to the bending moment.
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-4
-6
-8
-10
-12 -0.005
0.000
0.005
0.010
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Longitudinal Displacement (m) Fig. 11. Longitudinal displacements of the substructure at the centerline of the bridge for six different loading scenarios.
Fig. 10. Composite bending moment of the bridge deck and girders when dense sands (DD) are adjacent to the bridge.
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Fig. 12. Translation and rotation of the abutment for all temperature changes.
-0.18 0
-0.13
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Fig. 13. Ratio of translation and rotation of the abutment for all temperature changes.
Depth from Pile Head (m)
-2
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-5 -6
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the displacement at the top of the abutment is decomposed into the translational and rotational components. In loose sand (L) the translational displacement is larger than the rotational displacement across all temperature increases. On the contrary, in dense (D) sand the rotational displacement is larger than translational for the two smaller temperature changes, with translation and rotation becoming nearly equal for DD 55.6 scenario. Dense sand (Dc) falls between these two extreme cases. This can also be seen from Fig. 13, in which the ratio between the translational and rational displacements at the top of the abutment is shown on yaxis. Thus, the larger the abutment translation, the larger the bending moment at the pile head, which can also be inferred from Fig. 11. Fig. 14 shows bending moment diagrams for the central pile and three different sand densities. The decrease in the relative compaction of the soil from 96% to 90% increases the maximum bending moment 2.12 times, which is significant. In this study only dense sand is adjacent to the piles, for which Kh,max is 69,053 kPa. Thus, according to Eq. (4) the stiffness of the springs attached to piles depends only on the pile head displacement. Specifically,
-8
-9
Bending Moment (MNm) Fig. 14. Bending moment diagram for the central pile for three different loading scenarios.
for a larger pile head displacement the spring stiffness is smaller. Conversely, for a smaller pile head displacement the spring stiffness is larger. Thus, at a depth of about 1.4 m the bending moments for all soil types are equal. This observation will still be valid for different temperature changes as long only dense sand is adjacent to piles. Fig. 15 presents a 3D deformed shape of the central pile with superimposed color coded axial stress (S22). This stress increases with decreasing density of the soil behind abutment and with the increasing temperature change. Assuming that the yield stress of structural steel is 340 MPa Fig. 15 indicates an onset of yielding
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Fig. 15. Axial stress (S22 in MPa) in the central pile for DD 55.6 (deformation scale factor 130).
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In summary, integral bridges experience a complex interaction with the surrounding soil. The compaction levels of the soil adjacent to the abutment and bridge temperature increases have significant effects on the internal forces in the substructure and superstructure. In particular, the presence of loose sand behind the abutments shifts critical locations from the bridge superstructure to the substructure, while the presence of dense sand behind the abutments shifts critical locations from the bridge substructure to the superstructure. In terms of magnitude of the effects, the soil compaction level adjacent to the abutment has the most pronounced effect on the maximum bending moment in piles, thus indicating that the compaction level might be optimized to give the best overall performance of the bridge substructure and superstructure. An onset of plastic yielding at the pile head was detected for the loading scenario DD 55.6 thus indicating a possible plastic hinge formation in this case. Acknowledgments
at the pile head and in its very small vicinity. Thus the loading scenario DD 55.6 °C might lead to the formation of plastic hinge at the pile head.
6. Conclusions Upon the successful verification and validation of the computational model of the existing three-span integral bridge against the equivalent loading scheme in Faraji et al. [20] its responses to nine different loading scenarios, were obtained. The loads included selfweight combined with different amounts of temperature increase in the presence of different soils adjacent to the abutment. It was found that the type of the abutment motion is significantly affected by the compaction level of the soil adjacent to the abutment and the magnitude of the temperature increase. The looser the sand and the larger the temperature increases, the more dominant the translation of the abutment is in comparison to its rotation. It is because integral bridges act as a single structural unit that the type of abutment motion is directly relevant for the maximum bending moments in piles, and the maximum negative composite bending moments of the superstructure. In particular, the loose sand adjacent to the abutments maximizes the maximum bending moment in piles, while minimizing the maximum negative composite bending moment of the superstructure and the maximum compressive stress in the girders, for any given temperature increase. On the contrary, the presence of the dense sand behind the abutment minimizes the maximum bending moment in piles, while maximizing the maximum negative composite bending moment of the superstructure and maximum compressive stresses in the composite deck for any given temperature increase. All maximum bending moments and maximum compressive stresses are further magnified by the larger temperature increases. For example, the maximum bending moment in the central pile increases by 211% when the relative compaction level of the sand adjacent to the abutment decreases from 96% to 90%, and the temperature increase is equal to 55.6 °C (Fig. 14). At the same time, the maximum negative composite bending moment of the superstructure experiences a decrease of 40% (Fig. 8), and the maximum compressive stress in the central girder also decreases by 40% (Fig. 7). The magnitude of temperature increase has only slightly smaller effects than the soil compaction level. For example, when dense sand is adjacent to abutments a decrease of 22.3 °C in the temperature change reduces the maximum negative composite moment of the deck by 30% (Fig. 10).
Funding for this study, which was provided by the Kansas Department of Transportation through the KTRAN program and by the University Transportation Center located at Kansas State University is gratefully acknowledged. In addition, the help with preparation of few figures for this manuscript provided by Vijaya K. Tadikamalla is also greatly appreciated. The fifth author would also like to acknowledge the support of China Scholarship Council. References [1] Burke MP. Integral bridges. Washington, DC: Transportation Research Record 1275, Transportation Research Board, National Academy of Science; 1990. p. 53–61. [2] Cross H. Analysis of continuous frames by distributing fix-end moments. Trans Am Soc Civil Eng 1932;96(1):1–10. [3] Bakeer RM, Mattei NJ, Almalik BK, Carr SP, Homes D. Evaluation of DOTD semiintegral bridge and abutment system. Final report FHWA/LA.05/397, Louisiana. New Orleans, Louisiana: Transportation Research Center, Tulane University; 2005. [4] Dicleli M. Simplified model for computer-aided analysis of integral bridges. J Bridge Eng 2000;5(3):240–8. [5] Dicleli M, Albhaisi SM. Performance of abutment–backfill system under thermal variations in integral bridges built on clay. Eng Struct 2004;26 (7):949–62. [6] Dicleli M, Albhaisi SM. Effect of cyclic thermal loading on the performance of steel H-piles in integral bridges with stub-abutments. J Constr Steel Res 2004;60(2):161–82. [7] Huang J, Shield CK, French CEW. Time-dependent behavior of a concrete integral abutment bridge. Washington, DC: Transportation Research Record 11S, Transportation Research Board, National Academy of Science; 2005. p. 299–309. [8] Lawver A, French CEW, Shield K. Field performance of integral abutment bridge. Washington, DC: Transportation Research Record 1740, Transportation Research Board, National Academy of Science; 2000. p. 108–17. [9] Civjan SA, Bonczar C, Brena SF, DeJong J, Crovo D. Integral abutment bridge behavior: parametric analysis of a massachusetts bridge. J Bridge Eng 2007;12 (1):64–71. [10] Huang J, Shield CK, French CEW. Parametric study of concrete integral abutment bridges. J Bridge Eng 2008;13(5):511–26. [11] Pugasap K, Kim W, Laman JA. Long-term response prediction of integral abutment bridges. J Bridge Eng 2009;14(2):129–39. [12] Kim W, Laman JA. Integral abutment bridge response under thermal loading. Eng Struct 2010;32(6):1495–508. [13] Kalayci E, Civjan SA, Breña SF. Parametric study on the thermal response of curved integral abutment bridges. Eng Struct 2012;43(10):129–38. [14] William GW, Shoukry SN, Riad MY. Study of thermal stresses in skewed integral abutment steel girder bridges. Struct Eng Int 2012;22(3):308–17. [15] Barr PJ, Halling MW, Huffaker C, Boyle H. Behavior and analysis of an integral abutment bridge. Bridges Transportation Research Board; 2013. [16] Thevaneyan KD, John PF, Jianqiao Y. Superstructure behavior of a stub-type integral abutment bridge. J Bridge Eng 2014;19(6):04014012-1–04014012-12. [17] Erhan S, Dicleli M. Effect of dynamic soil-bridge interaction modeling assumptions on the calculated seismic response of integral bridges. Soil Dynam Earthquake Eng 2014;66(11):42–55. [18] Ting JM, Faraji S. Streamlines analysis and design of integral abutment bridges. Report UMTC 97-13, Amherst, MA: University of Massachusetts Transportation Center; 1998. [19] ABAQUS. ABAQUS Analysis User’s Manual 6.5-1; 2004.
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[20] Faraji S, Ting JM, Crovo DS, Ernst H. Non-linear analysis of integral bridges: finite element model. J Geotech Geoenviron Eng 2001;127(5):454–61. [21] Canadian Geotechnical Society (CGS). Canadian foundation engineering manual. 3rd ed., Toronto, Ontario; 1992. [22] Barker RM, Duncan JM, Rojiani KB, Ooi PSK, Tan CK, Kim SG. Manuals for design of bridge foundations. National Cooperative Highway Research Program (NCHRP). Washington, D.C.: Transportation Research Board, National Academy of Science; 1991.
[23] Prakash S, Kumar S. Nonlinear lateral pile deflection prediction in sands. J Geotech Eng 1996;122(2):130–8. [24] Mwindo MJ. Strain dependent soil modulus of horizontal subgrade reaction. MS thesis, Rolla, MO: University of Missouri-Rolla; 1992. [25] Shah BR. 3D finite element analysis of integral abutment bridges subjected to thermal loading. MS thesis, Manhattan, KS: Department of Civil Engineering, KSU; 2007.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Thermally induced soil structure interaction in the existing integral bridge Dunja Peric´ a, Marta Miletic´ a,⇑, Bhavik R. Shah b, Asad Esmaeily a, Hongyu Wang c a
Department of Civil Engineering, Kansas State University, Manhattan, KS 66506-5000, United States Read Jones Christoffersen Ltd., Consulting Engineers, 144 Front Street West, Suite 500, Toronto, Ontario M5J 2L7, Canada c Department of Civil and Hydraulic Engineering, Ningxia University, Yinchuan 750021, China b
a r t i c l e
i n f o
Article history: Received 31 December 2014 Revised 4 June 2015 Accepted 21 October 2015
Keywords: Integral abutment bridge Soil–structure interaction Thermal effects Finite element analysis
a b s t r a c t While Cross’ method enabled scientifically based structural design of integral bridges (IB) a similar progress in understanding and analyzing the relevant complex soil structure interaction has not been made yet. This hampers a wider adoption of IB systems, whose geo-structural system inherently brings multiple sustainability and performance benefits to transportation infrastructure. To this end, a full 3D finite element model of an existing three-span integral bridge was assembled and subjected to a combined thermal and gravity loads. The bridge superstructure consists of the two sets of concrete piers, two abutments, and fourteen HP steel piles (seven at each abutment), whose strong axis of bending is oriented parallel to the longitudinal direction of the bridge. Upon a successful validation and the verification of the computational model, several loading scenarios simulating different amounts of temperature increase in the presence of different soils adjacent to the abutment were simulated. Further analyses indicated that effects of the compaction level of the soil adjacent to the abutments, and of a magnitude of the thermal load on the substructure are opposite from the effects of these agents on the superstructure. Published by Elsevier Ltd.
1. Introduction According to Burke [1] integral bridges were implemented in practice shortly after Cross [2] had developed a simple method for the analysis of continuous beams and frames. This enabled the design and construction of bridges without deck joints, which are known as integral bridges (IB). In 1935 Kansas was among the first states in the U.S. that constructed an IB (Bakeer et al. [3]). Since then the construction of integral bridges has been pursued by many states in U.S. and provinces in Canada. At first IBs were built to eliminate the leakage of deicing chemicals and the resulting corrosion of primary structural members, which remains the main cause of limited service lives of jointed bridges. The additional benefits of IB, many of which turned out to increase their sustainability, are inherent to its geo-structural system. Economic benefits are accomplished through lowered whole life cycle costs including decreased construction and maintenance costs. Other benefits include elimination of noise associated with crossing of vehicular traffic over jointed bridges, and ⇑ Corresponding author. Tel.: +1 785 317 2283. E-mail addresses: [email protected] (D. Peric´), [email protected] (M. Miletic´), [email protected] (B.R. Shah), [email protected] (A. Esmaeily), why.nxts@163. com (H. Wang). http://dx.doi.org/10.1016/j.engstruct.2015.10.032 0141-0296/Published by Elsevier Ltd.
more pleasing aesthetics of a continuous superstructure. The social benefits comprise better connectedness for urban and rural environments, which is achieved through less maintenance caused traffic disruptions, and easier widening and future replacement of IBs. Furthermore, a vehicular ride quality is improved, and traffic safety is increased by elimination of joints. In addition, an IB is a continuous geo-structural system that results in more uniform distribution of internal forces than jointed bridges (Dicleli [4]). Consequently, IBs exhibit an increased redundancy and resilience. The important uncertainty related to the design and performance of IBs is stress in piles. Cyclic loading such as temperature variations and traffic loads, can cause significant horizontal displacements of a bridge. A long term cyclic loading generates rotations and horizontal displacements of abutments that cause a settlement of the abutment backfill. During this process a void gradually forms behind an abutment, thus causing the soil pressure to further increase upon the subsequent expansion of the bridge. Consequently, IBs have to deal with greater soil pressures acting on the abutments than jointed bridges. Settlement of the abutment fill and movement of the superstructure can lead to cracking of the wing-walls and opening of joints between a bridge and an approach slab. Furthermore, due to settlement, and thermal changes and gradients creep and shrinkage of concrete and additional secondary stresses can develop in the superstructure.
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Additional disadvantages include minor longitudinal and transverse cracking, poor drainage at abutments, and cracking and spalling in bearing areas (Bakeer et al. [3]). In spite of many advantages of IBs that outweigh their disadvantages there is still a need for knowledge discovery, which will help to further reduce the disadvantages of IBs.
2. Literature review Although many studies, including those addressing field instrumentation, laboratory experiments, and numerical modeling have been carried out the lack of understanding of the behavior of IBs is still a concern. A brief overview of the research addressing primarily a numerical modeling of IBs is presented next in the chronological order. Dicleli [4] had proposed a simplified structural model of an IB, on the basis of which a computer program was developed. The deck, abutment and piles were represented by structural elements having effective widths corresponding to the spacing between girders, which essentially extended into the abutment and piles, thus lumping the piles based on the tributary width. The program was capable of analyzing different loading scenarios separately and combining the corresponding results as needed, thus indicating that it was assumed that an IB remained in the elastic range. The proposed method produced more economic designs than the conventional analysis used previously. Dicleli and Albhaisi [5] focused on the abutment-backfill system while evaluating the performance of IBs built on clay. They used the SAP 2000 software to conduct static push-over analyses on a 2D model, thus simulating a thermal load. They concluded that maximum length limit of IBs is controlled by the flexural capacity of abutment under positive temperature changes for the abutments taller than 4 m. They suggested that piles should be oriented about their weak axis of bending to enhance the maximum length limits as determined by the flexural capacity of abutment. Furthermore, they also suggested that pinned connection between the abutment and the pile head may be used to reduce the flexural demand on the abutment. Dicleli and Albhaisi [6] conducted static pushover analyses of a pile–soil system by using a finite element-based software SAP 2000. Their model accounted for nonlinear responses of structure and soil. Dicleli and Albhaisi [6] found that the maximum length limits for IB with stub abutments decrease as the foundation soil becomes stiffer. They also found that the pinned abutment-pile connection significantly increases the displacement capacity of integral bridges with stub abutments based on the capacity of piles under cyclic loading. They concluded that maximum length limits of concrete and steel IB in moderate climates range from 180 to 320 m and from 125 m to 220 m respectively. Huang et al. [7] used a P beam numerical model to model the prestressed concrete IB with a total length of 66 m located in Rochester, Minnesota. They compared numerical predictions with the actual measurements that were reported by Lawver et al. [8]. Based on the prediction of their numerical model they concluded that the creep rate of the concrete girder could have increased due to the increased backfill soil pressure. They also detected steadily increasing pile curvatures over seven years. They concluded that creep and shrinkage significantly affect behavior of concrete IB. Civjan et al. [9] presented results of a 2D finite element analysis of an 82.3 m long three-span integral bridge located in Orange– Wendell, Massachusetts. The bridge has a concrete deck and steel girders. Two node elements with three degrees of freedom per node were used to model the bridge by using a GT STRUDL software. They modeled expansion and contraction of the bridge based
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on the comparison with the actual measurements. Civjan et al. [9] concluded that their computational model captured neither the transition from passive to active soil states, nor the peak active pressures. They also found that bending moments in piles were minimized by using a denser backfill. Huang et al. [10] performed a 3D finite element analysis of a 66 m long three-span prestressed concrete integral bridge located in Rochester, Minnesota. They used shell and beam–column elements and ANSYS software. They modeled expansion and contraction of the bridge combined with gravity loads, but assumed nocontact between the abutment and soil in the case of the bridge contraction by using Winkler’s springs with zero stiffness. Huang et al. [10] verified their computational model against the actual measurements and conducted a number of parametric studies assessing effects of several design variables. They concluded that the selection of the pile type and orientation should be based on balancing the stresses in piles and in superstructure for long span bridges or bridges surrounded by stiff soils. They recommended that the pile selection and orientation should be based on the specific bridge situation. Pugasap et al. [11] used an ANSYS software to predict a long term response of IBs. Verification and validation was performed by comparing the numerical results with the field measurements obtained on three IBs in Pennsylvania over several years. Numerically obtained and measured soil pressures were found to be in a good agreement. In addition, it was shown that predicted abutment displacements and corresponding design moments and forces at the end of the numerically simulated 100-year period have a significant influence on a long term behavior which should be considered in IB design. Kim and Laman [12] conducted a parametric study of a prestressed concrete IB by using a 2D numerical model. The imposed loads included a superstructure temperature loads including temperature gradients, and concrete time-dependent loads. Reponses of three different bridges with total lengths ranging from 18.3 m to 121.9 m were simulated in their study. They found that the magnitude of a thermal expansion coefficient significantly influences the axial force and bending moment in a girder, and lateral force and bending moment in the pile, as well as the pile/head displacement. They also found that the bridge length significantly influences axial forces in girders, lateral forces and the bending moments in piles, as well as the pile head displacement. Kalayci et al. [13] studied the effect of an in-plan curvature on the thermally induced response of an actual IB located in Vermont, USA. They selected a two-span curved IB and subjected it to the temperature increase and decrease, each of which was equal to 55.6 °C. The bridge is 67.7 m long, 11.3 m wide, and it has 11.25° curvature. It has steel girders and concrete deck. Kalayci et al. [13] assembled a finite element model of the IB whereby the soil was modeled by non-linear Winkler’s springs. They found that longitudinal displacements, earth pressures and weak axis bending moments in piles decreased with increasing curvature. Conversely, lateral displacements increased with increasing curvature. To investigate the long-term effect of temperature variations on the superstructure of an IB, William et al. [14] monitored a newly constructed three-span IB in West Virginia for four years. The total length of the bridge is 44.8 m. It has steel girders and concrete slab. William et al. [14] developed a detailed three dimensional finite element (FE) model of the bridge by using an ADINA software. Comparison of the measured data and numerically obtained results showed a very good agreement of longitudinal strains in the middle girder, and longitudinal and transverse deck strains. They found similarly to Kalayci et al. [13] that the lateral displacements at the ends of steel girders increase with increasing skew angle. Additionally, their results show that the backfill and supporting piles restrain movement of the integral abutment, thus inducing axial
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forces in the superstructure. These forces are not explicitly considered in the design of the IBs. Field measurements of the bridge movement due to temperature variation were carried out by Barr et al. [15] for twelve months on 400 South Street Bridge, Salt Lake City, Utah. The bridge is a three-span IB with a curved deck, while the girders beneath are in three separate, straight segments. First, the SAP2000 software was used to create a detailed model of the IB, which produced high stress concentrations in the abutment adjacent to the bottom girder flange. This confirmed the observed cracking at the same location. Furthermore, in order to better understand the cause of the observed spalling at the abutment of IB, a simplified model was created using the same software. A parametric study was performed on the effects of a skew angle, span length, and temperature gradient on the weak-axis bending moment of the abutment. The results of the parametric study showed that even a slight increase in skew angle (as little as a 5°) and the increase in span length can markedly increase the weak-axis bending moment of the bridge abutment. In addition, a large increase in the weak-axis bending moment was observed as the temperature gradient within the bridge increased. Barr et al. [15] concluded that the combination of the bridge parameters (skew angle, curvature of the bridge, span length, and detailing) is most likely the cause of the abutment cracking. Thevaneyan et al. [16] developed the Oasys Safe FE analysis program to simulate the behavior of a typical stub-type IB configuration and backfill-foundation soil profile subjected to a thermally induced lateral movement and vertically imposed load at deck level. They have shown that different properties of the backfill soil and loading conditions have a major influence on the behavior of the IB superstructure. It is noted, that the IB design recommended by Thevaneyan et al. [16] is limited to 2D plane strain problem with symmetry around the centerline of the bridge. Erhan and Dicleli [17] focused on modeling a seismically induced soil structure interaction in a two-span 82 long, and 16 m wide IB. To accomplish this goal they used five different levels of structural models ranging from the most complex to the simplest one. While the most complex model included free field effects, p–y curves and dashpots, and shear column simulating a local soil–pile interaction and radiation damping, the simplest model did not contain springs adjacent to piles. Erhan and Dicleli [17] found that difference between predictions of different models depended on the ground motion intensities and also on particular models compared. Although seven actual earthquake ground motions were selected for the analyses the predictions were not verified against the actual measurements. In summary the literature review indicates that there are at least two outstanding problems related to IBs that require a further inquiry. They include the effect of the soil structure interaction on the long term performance of IBs and a seismic behavior of IBs. It is very helpful to have a clear understanding of a short term static soil structure interaction before embarking on the research addressing these two outstanding problems. To this end, the present study was performed within the realm of IBs whose piers are hinge-connected to the superstructure.
comprising a computational modeling of an IB, whose results are presented herein. The main goal of the study was to investigate the effects of compaction levels of the soil adjacent to abutments on the behavior of a three-span IB whose piers are hingeconnected the superstructure. Consequently, a selected IB was subjected to a combined thermal and gravity loads. Moreover, three different magnitudes of thermal load were considered, thus representing IBs located in different climates. The additional objective was also to identify the loading scenarios that would likely lead to a formation of a plastic hinge between the abutment and the pile. 4. Computational model of the selected IB A detailed full 3D finite element model of the ‘‘Bemis Road Bridge: F-4-20” over the Nashua River in Fitchburg, Massachusetts (Ting and Faraji [18]), which was assembled in this study by using ABAQUS/Standard [19], is shown in Fig. 1. It is noted that this model is nearly a full replica of the actual bridge, the schematics of which are shown in Fig. 2. Only one half of the bridge is modeled due to the symmetry. The piles and piers/drilled shafts are fixed at their bottom (Fig. 1). The Winkler’s springs are attached to the abutment and piles. This bridge was selected because it represents a typical IB in Kansas. The main differences between the FE model used in this study, and the one used by Faraji et al. [20] can be grouped in four categories: (1) differences in the computational models, (2) differences in the material properties, (3) differences in the loads, and (4) differences in the modeling approaches. The main difference in the computational model is in that the piers in the present model are hinge-connected to the superstructure, while this connection is fixed in Faraji et al. [20]. This modification has been implemented upon a request of KDOT because it reflects the current design and construction of IBs in Kansas. It is also noted that Faraji et al. [20] used plate elements to model abutment, and beam elements to model the piles, while the present study uses eight node brick elements for the entire bridge (except the hinges) thus creating nearly the exact replica of the actual bridge. Differences in material properties include two different coefficients of thermal expansion for concrete and steel while Faraji et al. [20] used a single value for the entire bridge. It is because the primary focus of this study was on the effects of the compaction levels of the soil adjacent to the abutment that three different types of abutment backfill are modeled. Specifically, a design curve for dense sand specified by Canadian Geotechnical Society (CGS) [21] is added to design curves given by National Cooperative
3. Research significance A development of a deeper understanding of a complex soil structure interaction in IBs will facilitate a paradigm shift leading to more science based rather than experientially based design. This will ultimately enable a more extensive adoption of IB systems in practice, thus directly contributing to the increased sustainability and resilience of the transportation infrastructure. To this end, Kansas Department of Transportation (KDOT) funded a small study
Fig. 1. A detailed full 3D finite element model of the ‘‘Bemis Road Bridge”.
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Fig. 2. Schematics of the actual integral bridge (a) the longitudinal view and (b) cross-section.
Highway Research Program (Barker et al. [22]) to cover different shapes of the coefficient of lateral earth pressure versus normalized abutment displacement curves. Furthermore, according to (Faraji et al. [20] the level of soil compaction adjacent to piles does not significantly influence the deflections and moments in the superstructure. Additionally, the maximum moment in the piles occurred in the case when loose abutment backfill was used in combination with dense sand adjacent to piles. Consequently, three different abutment backfills are combined with dense sand adjacent to the piles in this study. It is noted that Faraji et al. [20] used two soil types behind the abutment and two soil types adjacent to the piles. The present study models a response of the IB to a simultaneous action of gravity and thermal loads unlike Faraji et al. [20] who modeled only thermal loading corresponding to a temperature increase of the composite deck of 44.4 °C. Furthermore, the present study includes three different temperature increases. The temperature is applied in a fashion shown in Fig. 3, thus imposing a thermal gradient within the abutment. It is believed that this temperature distribution is more realistic than the one applied by Faraji et al. [20] who heated solely the composite deck. The differences in the modeling approach are related to Winkler’s springs. These springs represent the action of soil on the abutment and piles. Non-linear springs attached to the abutment
Fig. 3. Nodal temperature increase for one of the loading scenarios (numbers in the legend denote the magnitude of a temperature increase in °C).
are modeled by using an equivalent iterative linear approach (Eq. (1)). Faraji et al. [20] used explicit non-linear springs instead. For the springs attached to the piles an empirical approach based on the actual field test data is adopted herein. Modeling of these non-linear springs also requires an iterative procedure, which is summarized in Eq. (4). Faraji et al. [20] used so called p–y curves instead (see Fig. 4).
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Longitudinal Displacement (m) -0.005 0
0.000
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Depth from Abutment Top (m)
2
4
Shah - DD 44.4°C 6
Faraji et al. - DD 44.4°C
8
10
12 Fig. 4. Verification and validation of the present model: longitudinal substructure displacements at the intersection of the back of the abutment and the centerline.
The length of the central span is 18.3 m, while each of the two end spans is 13.7 m long. The width of the bridge is 16.5 m. The superstructure consists of a 0.22 m thick concrete slab, seven W920 201 steel girders, and five W920 201 transverse steel beams. The longitudinal view and cross-sectional area of the IB with all dimensions are illustrated on Fig. 2. A full composite action between the steel girders and beams with the concrete slab is enforced by invoking the merge option in ABAQUS. The superstructure shown in Fig. 1 consists of one set of concrete piers, a concrete slab, and transverse and longitudinal steel girders, whereby the latter are monolithically connected to the concrete abutment. A single row of steel HP310 110 piles, whose strong axes of bending are oriented parallel to the longitudinal direction of the bridge serves as the foundation for the abutment. The deck is additionally supported by two sets of concrete piers/ drilled shafts, which are hinge connected to the superstructure. The full 3D finite element model shown in Fig. 1 contains 191,894 eight-node coupled temperature-displacement elements (C3D8T), 277,530 nodes, 12 connector elements (CONN3D2) modeling the hinges, and 546 linear spring elements. A total of 140 springs were attached behind the abutment resulting in a 0.610 m 0.601 m tributary area for each spring. Additionally, a total of 58 springs were attached to each pile, each of them having a tributary area of 0.305 m 0.155 m. It is noted that the springs were attached to piles in pairs, thus resulting in two springs at a given elevation. 4.1. Structural materials Concrete and steel are modeled as isotropic linear elastic materials whose properties are listed in Table 1. 4.2. Soil behind abutments Design guidelines for the load–displacement response of the soils behind the abutment provided by National Cooperative Highway Research Program (Barker et al. [22]) and CGS [21] were used
Table 1 Properties of structural materials. Property
Concrete
Steel
Young’s Modulus, E (GPa) Poisson’s ratio, t Coefficient of thermal expansion, a (C1) Mass Density, q (kg/m3)
30 0.3 1 105 2402
206.84 0.3 1.17 105 7849
to determine the stiffness of the springs attached to the abutment. To investigate the effect of different compaction levels three different sands were modeled: (1) the dense sand described in Barker et al. [22], denoted by ‘‘D”, (2) the loose sand described in Barker et al. [22], denoted by ‘‘L”, and (3) the dense sand described by CGS [21], denoted as ‘‘Dc”. Dry unit weights of loose and dense sands are assumed to be equal to 17.8 kN/m3 and 18.9 kN/m3 respectively, while the maximum dry unit weight is 19.7 kN/m3. Thus, the loose and dense sands represent relative compaction levels of 90% and 96%, respectively, which correspond to relative densities of 50% and 80% respectively. Design guidelines given by Barker et al. [22] provide only the angles of internal friction, which are equal to 30° and 45° for loose and dense sands, respectively. Both sets of design curves provide the relationships between the lateral displacement at the top of an abutment, and the coefficient of lateral earth pressure. It should be noted that unit weights, relative densities, and relative compactions of both dense sands (‘‘D” and ‘‘Dc”) are equal in the present study. Based on the results presented by Faraji et al. [20] it is evident that the critical combinations of soil types, which produce maximum bending moments in the deck, and the piles are DD and LD respectively. The first letters in these abbreviations denote the type of sand behind the abutment while the second letters denote the type of sand adjacent to the piles. Since both critical combinations correspond to the presence of dense sand adjacent to the piles, the focus of this study is on the effect of the type of the abutment backfill. Thus, three types of sands are selected. Specifically, Dc sand is added to D and L sands because it is characterized by a different shape of curve relating the lateral displacement to the coefficient of lateral earth pressure. Fig. 5 depicts a rigid body motion of the abutment, which is associated with a thermal expansion of the bridge. Thus, a total lateral displacement (D) at the top of the abutment is decomposed into translational (DT) and rotational (DR) components. The piles experience maximum deflections at the pile heads (yt), hence leading to the maximum bending moments at the same location. The magnitude of stresses in piles due to these bending moments is a vital concern in design of integral bridges. An equivalent iterative linear approach used to determine the stiffness of the springs attached behind the abutment is described by Eq. (1) as follows:
kiþ1;j ðDi ; di;j Þ ¼
K i ðDi Þcd zA;j ðDAÞj di;j
ð1Þ
where index i is the iteration counter, while index j denotes the spring row number corresponding to its depth. The stiffness of an individual spring is denoted by ki+1,j whereby Ki is the coefficient of lateral earth pressure, cd is dry unit weight of soil, and zA,j is the depth of the spring with tributary area (DA)j. Global and local lateral displacements of the abutment are denoted by Di and di.j, respectively, whereby the later denotes the displacement at the location of the corresponding spring. According to the equivalent linear iterative approach the spring stiffness for the subsequent iteration (i + 1) is determined based on the global and local displacements from the previous iteration (i). A single iteration corresponds to a single ABAQUS run. For the very first run there were
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T
DECK
489
(2) the coefficient of the horizontal subgrade reaction at 1 m depth can be expressed as a function of the pile head displacement. The stiffness of the spring attached to a pile at this depth (k [kN/m]) can be obtained by multiplying the stiffness of the spring in terms of the pressure (Kh) by the tributary length (DL). Prakash and Kumar [23] assumed that Kh varies linearly with depth, thus giving the following expression for the spring stiffness (k [kN/m]):
R
b 1þt K h;max kiþ1 ðzP ; yt;i Þ ¼ a zP ðDLÞ yt;i 2:5B zR
H GIRDER
ð4Þ
where ‘‘i” is the iteration counter and zP is the depth from the pile head. The convergence is achieved when the relative error in the pile head displacement falls below 1% in two subsequent iterations. All cases herein exhibited an exponential rate of convergence, whereby the displacements in the very first iteration were the largest. It is noted that springs were attached to the model in the second iteration, and their stiffness was determined based on the displacement from the previous iteration. The selected value
ABUTMENT
yt PILES
Fig. 5. Rigid body motion of the abutment decomposed into translation and rotation, accompanied by bending of the piles.
no springs attached to the bridge. Global and local displacements of the abutment were then obtained from the output data. They were inserted into Eq. (1) to obtain the spring stiffness for the second run. It is noted that the coefficients of lateral earth pressure (K1) were determined from design charts (Barker et al. [22] and CGS [21]) based on the global abutment displacement from the first run. Iterations are continued until the relative error in the abutment displacements, based on the two subsequent iterations fell below 1%.
Fig. 6. Longitudinal normal stress (S11 in MPa) in the bridge for DD 55.6 (deformation scale factor 130).
-80
Prakash and Kumar [23] proposed a method alternative to p–y curves, which describes a non-linear load–displacement relationship for a single laterally loaded pile. It is an empirical method, which is based on the experimental observations that were collected from the fourteen full scale tests on different types of laterally loaded piles reported by Mwindo [24]. According to Prakash and Kumar [23] the coefficient of the horizontal subgrade reaction (Ks [kN/m3]) at a depth of 1 m below the pile head is given by:
K s ðcÞ ¼ K h =zR ¼ acb K h;max =zR
ð2Þ
where c is the shear strain in the sand behind the pile, zR is the reference depth of 1 m, Kh,max is the value of lateral pressure that produces unit displacement in the soil, at the shear strain of 0.2%. The values of the empirical coefficients a, and b of 0.05 and 0.5 respectively, were used in accordance with the recommendations found in Mwindo [24] for HP steel piles. Prakash and Kumar [23] expressed the average shear strain in the sand in terms of the pile head displacement (yt) as:
cðyt Þ ¼
1þt y 2:5B t
Maximum Compressive Axial Stress (MPa)
4.3. Soil behind piles -100
-120
-140
-160
-180
-200
-220
ð3Þ
where t is Poisson’s ratio of sand assumed to be equal to 0.3 in this study, and B is the width of the pile. By substituting Eq. (3) into Eq.
LD DD DcD
32
35
38
41
44
47
50
53
56
Fig. 7. Maximum compressive axial stress (S11) at the bottom flange of the central girder in the vicinity of the abutment.
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of Kh,max is 69,053 kPa, which is about 88% of the value suggested by Prakash and Kumar [23] for dense, medium to fine sands, and 3.05 to 4.6 m deep ground water table. The particular value used in this study was determined based on the best fit against the longitudinal displacements of the abutment and piles obtained by Faraji et al. [20] for the equal loading scenarios. 4.4. Loading scenarios To fulfill the main goal of this study, which was assessing the effects of the temperature change ranges and soil compaction
levels, nine different loading scenarios were considered. They reflect the presence of three different soils behind the abutment, one single soil behind the piles, and three different temperature increases corresponding to 33.3 °C, 44.4 °C and 55.6 °C. These temperature changes reflect different climatic conditions. The corresponding loading scenarios are named: DD 33.3, DD 44.4, DD 55.6, DcD 33.3, DcD 44.4, DcD 55.6, LD 33.3, LD 44.4, LD 55.6, whereby the first letter indicates the soil type behind the abutment, followed by the soil type behind the pile, and by the amount of the superstructure temperature increase. In each case the selfweight of the bridge is applied first by simply switching on the gravity acceleration. The superstructure of the bridge is subsequently subjected to the above temperature change ranges in the fashion indicated in Fig. 3. Only the steady state thermal loading is considered. 5. Results and discussion
Fig. 8. Composite bending moment of the bridge deck and girders for temperature increase of 55.6 °C.
The finite element model depicted in Fig. 1 was first successfully verified and validated against the corresponding result of Faraji et al. [20]. For this purpose the weightless analysis, without thermal gradient within the abutment, and with the same coefficient of thermal expansion for the concrete and steel was carried out (Shah [25]). In addition and in accordance with Faraji et al. [20] piers were rigidly connected to the superstructure. An excellent agreement between the predictions of the present analysis and the one presented by Faraji et al. [20] was obtained (Fig. 4), thus successfully validating and verifying the model used for this study. It is noted that Faraji et al. [20] have not validated their results against any actual measurements most probably because they were not available. The discontinuity in the displacement gradient that is exhibited by the prediction of Faraji et al. [20] was most likely caused by a connection of the abutment plate and pile beam elements. A smoother displacement that is exhibited in the present analysis is attributed to the use of full 3D elements in the entire bridge model. Fig. 6 depicts a deformed shape of the bridge with the superimposed color coded longitudinal stresses (S11) for the DD 55.6 loading scenario. Compressive normal stresses are negative. Fig. 6 indicates that the superstructure accommodates the temperature increase by a combined expansion and bending. The presence of
Fig. 9. Total axial force in the bridge deck and girders for temperature increase of 55.6 °C.
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On the contrary, the effect is more significant in the central span in the case of axial force. Fig. 11 shows longitudinal displacements of the substructure at the intersection of the abutment back face and the centerline of the bridge for six loading scenarios representing three different soils behind the abutment and the two extreme temperature changes. Soil conditions have little or no influence on the displacement of the abutment top. However, the mode of the abutment motion is significantly affected by the soil compaction level and temperature change range. Further information is provided in Fig. 12, in which
0
-2
Depth from Abutment Top (m)
the soil behind the abutment suppresses the expansion of the bridge, whereby this effect is increasing with the increase in depth below the soil surface, thus inducing the bending of girders and slab. This phenomenon is responsible for the buildup of compressive axial stresses in the bottom flanges of the longitudinal girders. Fig. 7 shows that these maximum compressive stresses at the bottom flange of the central girder decrease with decreasing soil density and decreasing temperature change. Additionally, the buildup of compressive stresses implies that girders should be secured against the possibility of a local buckling. Fig. 8 depicts the composite bending moments of the bridge slab and girders for the temperature increase of 55.6 °C in the presence of different soils. The composite bending moment was obtained by a direct numerical integration of the moment of axial stress about the elastic neutral axis of the superstructure. In the case when piers are connected to the deck by fixed connections Faraji et al. [20] showed that the effects of the compaction level of the abutment backfill extends only up to the bent. In other words, the bending moment in the central span is not affected by the abutment backfill type. In the present study piers are hinge connected to the deck, which causes a slight decrease in the magnitude of bending moments in the vicinity of the bent. It is because of this decrease that the magnitude of bending moment in for example dense sand becomes the smallest only in the vicinity of the bent. Although the effect of the abutment backfill type now extends all the way to the bridge centerline it is less pronounced in the central span. Fig. 9 shows the total axial force in the bridge superstructure for the temperature increase of 55.6 °C, which exhibits a significant sensitivity to the soil compaction level. The total axial force in superstructure appears to be very sensitive to the compaction level of the soil behind the abutment. For example, it is as much as 3.5 times larger in the presence of the dense sand as compared to loose sand. Fig. 10 shows the composite bending moment of the bridge slab and girders for three different temperature changes in the presence of dense soil adjacent to the abutment. Although both, the temperature change range and the soil compaction levels affect the composite bending moment, the effect of the soil compaction level is more pronounced and it extends further away toward the centerline of the bridge. However, both factors have a more significant effect on the end span with regard to the bending moment.
491
-4
-6
-8
-10
-12 -0.005
0.000
0.005
0.010
0.015
Longitudinal Displacement (m) Fig. 11. Longitudinal displacements of the substructure at the centerline of the bridge for six different loading scenarios.
Fig. 10. Composite bending moment of the bridge deck and girders when dense sands (DD) are adjacent to the bridge.
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Fig. 12. Translation and rotation of the abutment for all temperature changes.
-0.18 0
-0.13
-0.08
-0.03
0.02
0.07
-1
Fig. 13. Ratio of translation and rotation of the abutment for all temperature changes.
Depth from Pile Head (m)
-2
-3
-4
-5 -6
-7
the displacement at the top of the abutment is decomposed into the translational and rotational components. In loose sand (L) the translational displacement is larger than the rotational displacement across all temperature increases. On the contrary, in dense (D) sand the rotational displacement is larger than translational for the two smaller temperature changes, with translation and rotation becoming nearly equal for DD 55.6 scenario. Dense sand (Dc) falls between these two extreme cases. This can also be seen from Fig. 13, in which the ratio between the translational and rational displacements at the top of the abutment is shown on yaxis. Thus, the larger the abutment translation, the larger the bending moment at the pile head, which can also be inferred from Fig. 11. Fig. 14 shows bending moment diagrams for the central pile and three different sand densities. The decrease in the relative compaction of the soil from 96% to 90% increases the maximum bending moment 2.12 times, which is significant. In this study only dense sand is adjacent to the piles, for which Kh,max is 69,053 kPa. Thus, according to Eq. (4) the stiffness of the springs attached to piles depends only on the pile head displacement. Specifically,
-8
-9
Bending Moment (MNm) Fig. 14. Bending moment diagram for the central pile for three different loading scenarios.
for a larger pile head displacement the spring stiffness is smaller. Conversely, for a smaller pile head displacement the spring stiffness is larger. Thus, at a depth of about 1.4 m the bending moments for all soil types are equal. This observation will still be valid for different temperature changes as long only dense sand is adjacent to piles. Fig. 15 presents a 3D deformed shape of the central pile with superimposed color coded axial stress (S22). This stress increases with decreasing density of the soil behind abutment and with the increasing temperature change. Assuming that the yield stress of structural steel is 340 MPa Fig. 15 indicates an onset of yielding
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Fig. 15. Axial stress (S22 in MPa) in the central pile for DD 55.6 (deformation scale factor 130).
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In summary, integral bridges experience a complex interaction with the surrounding soil. The compaction levels of the soil adjacent to the abutment and bridge temperature increases have significant effects on the internal forces in the substructure and superstructure. In particular, the presence of loose sand behind the abutments shifts critical locations from the bridge superstructure to the substructure, while the presence of dense sand behind the abutments shifts critical locations from the bridge substructure to the superstructure. In terms of magnitude of the effects, the soil compaction level adjacent to the abutment has the most pronounced effect on the maximum bending moment in piles, thus indicating that the compaction level might be optimized to give the best overall performance of the bridge substructure and superstructure. An onset of plastic yielding at the pile head was detected for the loading scenario DD 55.6 thus indicating a possible plastic hinge formation in this case. Acknowledgments
at the pile head and in its very small vicinity. Thus the loading scenario DD 55.6 °C might lead to the formation of plastic hinge at the pile head.
6. Conclusions Upon the successful verification and validation of the computational model of the existing three-span integral bridge against the equivalent loading scheme in Faraji et al. [20] its responses to nine different loading scenarios, were obtained. The loads included selfweight combined with different amounts of temperature increase in the presence of different soils adjacent to the abutment. It was found that the type of the abutment motion is significantly affected by the compaction level of the soil adjacent to the abutment and the magnitude of the temperature increase. The looser the sand and the larger the temperature increases, the more dominant the translation of the abutment is in comparison to its rotation. It is because integral bridges act as a single structural unit that the type of abutment motion is directly relevant for the maximum bending moments in piles, and the maximum negative composite bending moments of the superstructure. In particular, the loose sand adjacent to the abutments maximizes the maximum bending moment in piles, while minimizing the maximum negative composite bending moment of the superstructure and the maximum compressive stress in the girders, for any given temperature increase. On the contrary, the presence of the dense sand behind the abutment minimizes the maximum bending moment in piles, while maximizing the maximum negative composite bending moment of the superstructure and maximum compressive stresses in the composite deck for any given temperature increase. All maximum bending moments and maximum compressive stresses are further magnified by the larger temperature increases. For example, the maximum bending moment in the central pile increases by 211% when the relative compaction level of the sand adjacent to the abutment decreases from 96% to 90%, and the temperature increase is equal to 55.6 °C (Fig. 14). At the same time, the maximum negative composite bending moment of the superstructure experiences a decrease of 40% (Fig. 8), and the maximum compressive stress in the central girder also decreases by 40% (Fig. 7). The magnitude of temperature increase has only slightly smaller effects than the soil compaction level. For example, when dense sand is adjacent to abutments a decrease of 22.3 °C in the temperature change reduces the maximum negative composite moment of the deck by 30% (Fig. 10).
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