This article was downloaded by: [University of Connecticut] On: 09 July 2014, At: 06:20 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/nsie20
Finite element simulation of pile behaviour under thermo-mechanical loading in integral abutment bridges a
b
Jafar Razmi , Leila Ladani & Sherif M. Aggour
a
a
Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA b
Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL, USA Published online: 16 Jan 2013.
To cite this article: Jafar Razmi, Leila Ladani & Sherif M. Aggour (2014) Finite element simulation of pile behaviour under thermo-mechanical loading in integral abutment bridges, Structure and Infrastructure Engineering: Maintenance, Management, Life-Cycle Design and Performance, 10:5, 643-653, DOI: 10.1080/15732479.2012.757794 To link to this article: http://dx.doi.org/10.1080/15732479.2012.757794
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions
Structure and Infrastructure Engineering, 2014 Vol. 10, No. 5, 643–653, http://dx.doi.org/10.1080/15732479.2012.757794
Finite element simulation of pile behaviour under thermo-mechanical loading in integral abutment bridges Jafar Razmia1, Leila Ladanib* and Sherif M. Aggoura2 a
Department of Civil and Environmental Engineering, University of Maryland, College Park, MD, USA; bDepartment of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL, USA
Downloaded by [University of Connecticut] at 06:20 09 July 2014
(Received 20 April 2013; final version received 14 October 2012; accepted 16 November 2012; published online 16 January 2013) To study the behaviour of piles in integral abutment bridges, under seasonal and daily thermal loading, a three-dimensional, nonlinear finite element model was constructed for a bridge. The model was parametrically run for five different bridge lengths that varied from 122 to 549 m. A sinusoidal model was used to represent the daily and seasonal temperature variations. The results showed that maximum lateral displacement of the piles occurs during the winter when the thermal contraction and the dead and live loads on the bridge produce displacements in the same direction. Maximum stress occurred in the pile furthest from the centre of the bridge and was found to be in the flange of the pile immediately below the concrete abutment. Plastic deformation was observed in all of the piles for all bridge lengths. The lateral displacement and maximum plastic deformation in piles increased as the length of the bridge increased. A linear relationship was found between the length of the bridge and the lateral displacements for both seasonal and daily temperature variations. Keywords: bridge foundations; piles; integral abutment bridge; finite element analysis; lateral displacement; temperature effects
1. Introduction Integral abutment bridges (IABs) are bridges without expansion joints between the abutment and the superstructure. Because expansion joints are not included in IABs, the length of the bridge increases and decreases cyclically for many daily and seasonal cycles as the temperature changes daily and seasonally. The difference between the mean temperatures, also called effective bridge temperature, and the construction temperature is the primary factor that causes the expansion and contraction of a bridge (Black & Emerson, 1977; Emerson, 1977). Other factors such as creep, shrinkage effects and prestressing also cause the contraction of the deck and can be accounted for by considering an equivalent thermal contraction (Kalayci, Civjan, & Bren˜a, 2012). Large stresses generated during the expansion and contraction of the bridge deck can induce a large bending moment on the foundation due to eccentricity of the loads. The displacement of the piles depends on the temperature difference, length, type of bridge and the restraints provided by the abutment, the pile and the backfill soil. Large lateral displacements could result in plastic deformation in the piles. Cyclic elastic deformation of piles results in high-cycle fatigue, whereas cyclic plastic deformation could result in low-cycle fatigue and early
*Corresponding author. Email:
[email protected] q 2013 Taylor & Francis
failure of the piles. Therefore, it is crucial to determine the extent of the lateral displacement of the piles and their mode of deformation (elastic vs. plastic). In fact, many recorded measurements (Girton, Hawkinson, & Greimann, 1991; Jorgensen, 1983; Lawver, French, & Shield, 2000) of displacement and strains in piles have shown that stresses are very likely to exceed the yield strength of the piles in IABs; therefore, plastic deformation is expected. Jorgensen (1983) made measurements on an abutment bridge for a 1-year period and found that stresses at the top of the pile were sufficient to initiate yielding in the steel. Girton et al. (1991) studied two skewed bridges in Iowa experimentally. In their study, the authors found that the stress level may reach 60% to 75% of the yield stress, based on the amount of strain that they measured on the bridge over a one-year period. Lawver et al. (2000) monitored a bridge near Rochester, Minnesota, for several years of service using an extensive instrumentation. They found that piles appeared to deform in a double curvature, with the pile strains on the approach panel sides of the piles indicating the start of yielding. Alizadeh and Davisson (1970) conducted a study as part of a comprehensive pile testing programme initiated by the U.S. Army Engineers District, Little Rock, Corps of Engineers, in connection with the Arkansas River Navigation Project. They found that in an
644
J. Razmi et al.
Downloaded by [University of Connecticut] at 06:20 09 July 2014
ordinary bridge the maximum stresses in piles could reach 80% of nominal yield stress. Since piles are three-dimensional (3D) structures, it is expected that 3D stresses develop in them. As a result, determining the elastic or plastic deformation of piles requires utilisation of plasticity theory. The 3D states of stress require utilisation of one of the yield criteria, such as Tresca or von Mises criteria. Generally, von Mises criterion is believed to be more accurate because it is based on deviatoric energy, which is the driving energy for shear stresses. Shear stresses (von Mises, 1913) are stresses that cause dislocation motion, and thus cause plastic deformation and yielding in polycrystalline metallic materials. The von Mises yield criterion can be formulated in terms of the von Mises stress or equivalent tensile stress, seq, which is a scalar stress value that can be computed from the stress tensor 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi seq ¼ pffiffiffi ðsxx 2 syy Þ2 þ ðsyy 2 szz Þ2 þ ðsxx 2 szz Þ2 þ 6ðt2yz þ t2xz þ t2xy Þ; 2 ð1Þ
where sxx, syy and szz are normal stress components and tyz, txz and txy are the shear stress components. In this case, a material is believed to start yielding when its von Mises stress (seq) reaches a critical value of yield strength (sy). Numerical simulations were utilised in this study to determine the components of the stress tensor, and hence, the mode of deformation (elastic and plastic) in piles. In many of the reported simulations available for IABs, the steel is modelled elastically (Amde, Chini, & Mafi, 1997; Ellis & Springman, 2001; Hallmark, 2006; Kalayci, Civjan, Bren˜a, & Allen, 2011; Pe´tursson, Collin, Veljkovic, & Andersson, 2011). In some cases, the models are simplified to 2D models (Amde et al., 1997, Ellis & Springman, 2011; Hallmark, 2006; Kalayci et al., 2011; Pe´tursson et al., 2011). Elastoplastic behaviour of steel piles has not been modelled in conjunction with thermal cycling loading of bridge and bridge – soil interactions. The objectives of this study were to provide numerical verification of experimental measurements that were available in the literature related to the development of plastic strain in the piles of IABs. The mode of deformation of the piles of an IAB was determined using a nonlinear 3D FEM model. Material nonlinearity was included in the model for the soil and steel materials. Soil –pile interactions were modelled using the extended Drucker – Prager (DP) model to take into consideration the nonlinear behaviour of soil in plastic region. The seasonal and daily temperature loads were modelled using sinusoidal models. The bridge was assumed to be located in the harsh environment of the Rocky Mountains, where temperature variations between day and night and through different seasons are very significant. Symmetry was utilised to reduce the model size to a quarter of the bridge. Appropriate boundary conditions and dead and live loads were then applied to the model.
A parametric study was conducted for the bridge modelled with lengths varying from 122 to 549 m and pile displacements were determined. The stresses in the pile and the mode of deformation (elastic vs. plastic) when the bridge was subjected to daily and seasonal temperature variations were determined. The location of the maximum plastic deformation was determined. The location will thus indicate the onset of cyclic thermal fatigue crack if the daily and seasonal temperature cycles are continued for many cycles.
2.
Bridge modelled
An IAB designed and described by Thanasattayawibul (2006) was used as a case study in this paper. The bridge length was varied for five different cases with lengths of 122, 183, 244, 366 and 549 m. The span of the bridge was held constant at 15.25 m. A cross section of the bridge is shown in Figure 1. The bridge has a 0.178 m-thick concrete slab that was supported by six girders. The girders are supported at the piers by roller bearings and are rigidly connected to the abutments. The bridge deck has a 0.61-m overhang on each side and each abutment was supported by 11 piles. The piles were designed according to the Load and Resistance Factor Design (LRFD) requirement. Girders, cross bracings and piles are the structural members of standard shapes W30X132, L6X6X1 and HP10X42, respectively. The cross section and dimensions of these beams are shown in Figure 2. The piles are placed such that the bending occurs about their strong axis. The states of the USA do not agree on the directional orientation of the piles. In fact, a survey conducted by Maruri and Petro (2005) indicated that 33% of states orient the piles with the strong axis parallel to the centreline of the bearing, 46% of states orient the piles with the weak axis parallel to the centreline of the bearing, 8% of states (three states) leave it to the discretion of the engineer and the remaining 13% of states do not provide a comment or noted that the question was not applicable because of their use of symmetric piles. It was shown that the fatigue life is longer in piles oriented with the strong axis parallel to the centreline of bearing (Dicleli & Albhaisi, 2009). Therefore, if the orientation of a pile changes to the weak axis, the fatigue life is expected to be shorter. Figure 3(a) illustrates the layout of piles at one abutment, and Figure 3(b) illustrates their 3D finite 10.36 m 0.18 m 0.77 m Slab 1.83 m Cross bracing
Figure 1. bracings.
Cross section of the bridge slab, girders and cross
Structure and Infrastructure Engineering
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Figure 2.
645
The dimensions of the steel section used in the bridge.
element model (FEM). Each pile has a full length of 12.50 m, with 1.525 m embedded in the abutment. The total width of the abutment is equal to the width of the bridge, 10.36 m. Due to symmetry, this figure only shows half of the abutment. The soil for all bridges was the same, stiff clay, and extends to the bottom of the piles. The soils around the piles extend 1.22 m and 3.05 m in back and front of the piles, respectively. Figure 4 shows the girder – abutment – pile system.
3. Mathematical modelling of the temperature variations Both daily and seasonal temperature variations affect displacement in IABs. The greatest expansion takes place
during summer days, whereas the greatest contraction occurs during winter nights. In order to be able to model the bridge behaviour, these temperature variations were mathematically modelled and entered into the simulation. To model the temperature, historical temperature data were needed. These historical data can typically be obtained from climate centres in each geographical region. For this case study, the historical data were obtained from the Utah State Climate Center at Logan, Utah, for the period from 1998 to 2009 (Utah State University, 2009). In that region, the temperature declines to tens of degrees below freezing during the winter. Daily and seasonal temperature variations can be modelled based on sinusoidal or polynomial models (Hallmark, 2006). In this study, sinusoidal models were used as they can easily be adjusted to fit the historical data and can be used to represent many cycles of daily and seasonal variations. For the daily temperature variation, the model is (Hallmark 2006):
HR £ 2p T ¼ T d;amp sin þ t0 24
Cross bracings Girders
Abutment Piles
Figure 3. (a) View of half of the abutment from the top showing the piles and their location and (b) Image of 3D piles and abutment.
Figure 4. Girder – abutment – pile system.
þ T d;m ;
ð2Þ
646
J. Razmi et al. 35 Temperature (C)
Model prediction (C)
30
Temperature (°C)
25 20 15 10 5
–5 Days
Figure 5. The model of daily temperature in comparison with historical data of the month of September 2005. Only 7 days are shown in this figure.
2005) was selected as the temperature amplitude for this model. As a result, this model covers all daily temperature cycles and the results are thus conservative. The seasonal temperature variation is also modelled using a similar sinusoidal model (Hallmark, 2006): t d T s ¼ T s;amp sin 2p þ t0 þ T s;m ; ð3Þ 365
where Td,amp is the daily temperature amplitude and Td,m is the average daily temperature. HR varies between 0 and 24 (indicative of the 24 h of a day). A comparison of the historical data and the model is presented in Figure 5. In the model, the daily maximum is 27.88C and daily minimum is 2 2.88C, thus Td,amp is 15.38C and Td,m is 12.58C. The adjustment factor t0 (moves the model on the x-axis to the right or left) is 0 in this model. The expansion and contraction of the deck depend on the change in temperature and not the absolute value of temperature. Therefore, the largest daily temperature amplitude observed during 10 years of data (1 day in September
where Ts,amp is the seasonal temperature amplitude, Ts,m is the seasonal mean temperature and td represents the number of days for which the temperature is calculated. It varies between 1 day and 365 days and t0 is an adjustment
40 30 20 Temperature (˚C)
Downloaded by [University of Connecticut] at 06:20 09 July 2014
0
10 0 –10 –20 –30 Model prediction
Medium daily temperature.
–40 0
1000
2000
3000
4000
Days
Figure 6.
The model of the maximum seasonal temperature amplitude in comparison with the historical data obtained over 10 years.
4.
(a)
Symmetry surface 1 Symmetry surface 2
y
142.3 KN
142.3 KN
1.93 m
35.5 KN
(b)
4.27 m 4.27 m
15.25 m Pile
2.3 m
Girder
Modelling of the bridge
4.1 Finite element modelling The 3D, nonlinear FEM of the bridge was created using ANSYS 13 (ANSYS, Inc., 2011). To reduce the computation time, a quarter of the bridge was modelled because of the symmetry of the bridge. The entire model utilised a mapped mesh option with hexahedral elements. The concrete slabs, piles and girders were meshed using a 2D shell element (SHELL181) with thicknesses that correspond to thicknesses of concrete slabs, flanges, and webs. Each cross bracing was modelled using a 1D beam element (BEAM188). The concrete abutment and soil were modelled using 3D 20-node solid elements of SOLID185. The geometry and the boundary conditions are shown in Figure 7(a). Since only a quarter of the bridge was modelled, symmetry boundary conditions were applied on the symmetry planes: z ¼ 0 on symmetry surface 1 and x ¼ 0 on symmetry surface 2. The bottom of the soil was fixed in the y- and z-directions to simulate an end-bearing type pile. Gravity was applied in the 2ydirection. The soil thickness in the positive z-direction is 1.22 m and its thickness in the negative z-direction is 3.05 m as shown in Figure 7(b). Since all of the elements are either 4node, 8-node or 20-node elements, they are all compatible and intermediate elements between different parts of the bridge were not needed. The connection of the deck to the
x
z
Abutment
factor that can be varied to match the model to the historical data. For the data, the seasonal maximum temperature is 33.98C and the seasonal minimum temperature is 2 27.28C, thus Ts,amp is 30.558C and Ts,m is 3.358C. The adjustment factor t0 is 1.87 for the seasonal temperature cycle. This seasonal temperature cycle was used with the largest temperature amplitude in this study. Figure 6 presents a comparison between the model and the historical data collected for 10 years (Utah State University, 2009). Figures 5 and 6 show a conservative prediction of daily and seasonal temperature cycles. As seen in these figures, the amplitude of the historical data never exceeds the model, indicating that the model represents the most extreme values. These temperature models were used in FEM as thermal loads and were applied uniformly to the structure. The temperature of the entire structure was varied according to these models. The coefficient of thermal expansion used in this study was 11.7E 2 6/8C for steel and 10.8E 2 6/8C for the concrete (Thanasattayawibul, 2006). However, soil temperature was assumed not to vary. The model was run for three consecutive daily cycles, as well as three consecutive seasonal cycles to reach stabilisation (Ladani & Dasgupta, 2007, 2008). The models for daily and seasonal cycles were conducted separately.
647
10.9 m
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Structure and Infrastructure Engineering
1.22 m
3.05 m
Figure 7. (a) Geometry of the quarter of the bridge and the boundary conditions and (b) cross section of the bridge and substructure.
pier was considered to be a moveable bearing type that induces a small load in the z-direction (Amde & Klinger, 1987; Amde, Greimannan, & Johnson, 1983; Amde, Klinger, & White, 1988; Burke, 1993; Chini, Amde, & Aggour, 1993; Oesterle, Refai, Volz, Scanlon, & Weiss, 2002). Therefore, constraints were not placed on the deck in the x-direction. These piers only support the vertical load of the bridge. Therefore, displacement in the ydirection was assigned a value of zero at these supports.
4.2
Design load
According to AASHTO LRFD code (AASHTO, 2010), the design vehicle live loading, designated as HL-93 shall consist of a combination of a design truck or design tandem and design lane load. A design truck and design lane load were used in this analysis. To maximise the
648
J. Razmi et al.
effect of the live load, the design truck was placed in the middle of the first span of the bridge (Huang, Shield, & French, 2008). Figure 7(b) shows the location of the truck on the first span.
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Material properties
The primary materials used in this bridge are concrete and steel. Concrete is assumed to respond only elastically. Steel, however, is assumed to behave elastoplastic. Elastic properties of concrete and steel are shown in Table 1. An elastoplastic model (Mirambell & Real, 2000) was employed to represent the constitutive relationship of the steel material used in piles, girders and cross bracings, as shown in Figure 8. The elastic region can simply be represented by Hooke’s law and the nonlinear rateindependent inelastic region can be represented using a power law function as follows:
s ¼ 104901
0:2127
;
ð4Þ
where 1 is the summation of elastic (1e) and rateindependent inelastic strain (1p).
4.4
Soil – structure interaction modelling
The 3D, soil –structure interaction analysis in IABs includes both the soil –pile and the abutment backfill interaction. This interaction can be modelled as a mechanical model where springs are used to represent the soil or the use of the finite element. As an example, Krizek (2011) solved the problem of the soil – structure interaction by using soil springs. The stiffness of the spring is expressed by the modulus of subgrade reaction. Baptiste, Kim, and Laman (2011) used nonlinear springs with spring stiffness displacement defined on the basis of p –y curves. Kalayci et al. (2011) modelled the backfill soil and the in situ soil around the piles with nonlinear springs defined by using a force – deformation curve for the different soil layers used. In this study, the finite element method that can accommodate various complex features was used to simulate the soil – structure interaction. The extended DP model was used to represent the soil. Soil and other powder materials behave differently than conventional solids. For metal plasticity (assuming von Mises or a similar yield surface), only the deviatoric stress is
600 500 Stress (MPa)
4.3
700
400 300 200 100 0 0
0.005
0.01 Strain
0.015
0.02
Figure 8. Elastic – plastic constitutive behaviour of steel used in the simulation.
assumed to cause yielding. If the yield surface is plotted in principal stress space, this results in a cylinder whose axis is the hydrostatic pressure line, indicating that yielding is independent of the hydrostatic stress state. For the von Mises yield surface, theoretically, one could have infinite hydrostatic compression, and yielding would not occur. However, soil and other powder materials cannot resist tension and can only support compressive forces. Another characteristic is that the strength of these materials depends on the amount of compressive pressure. In other words, their strength and yield are pressure dependent. For example, as the depth increases in soils, the amount of shear strain needed to shear the soil increases because the compressive pressure due to soil weight increases. The DP model is able to show the plastic behaviour of the soil. The DP plasticity model is different from typical metal plasticity models since it contains a dependence on hydrostatic pressure. However, the DP model assumes elastic-perfect plastic behaviour, which is not accurate. In reality, as the soil pressure increases, the yield strength increases. The extended DP (ANSYS, Inc., 2011) is meant to address some shortcomings of the basic DP model – namely, the use of perfectly plastic behaviour and the requirement of a linear yield surface. Soil is modelled as stiff clay using the extended DP model. The same soil properties, shown in Table 2, were used for the foundation and backfill. Table 2. Soil properties used in finite element analysis.
Table 1.
Material
Elastic properties of concrete and steel. Elastic modulus (MPa)
Steel 200 £ 103 Concrete 25 £ 103
Coefficient of thermal expansion (ppm/8C) 11.7E-6 10.8E-6
Density Poisson’s (kg/m3) ratio 7840 2322
0.29 0.2
Soil parameter
Values
Modulus of elasticity (MPa) Density (kg/m3) Yield strength (MPa) Poisson’s ratio Internal friction angle Undrained cohesion of clay (MPa)
107 2002 0.055 0.27 258 0.007
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Structure and Infrastructure Engineering In this analysis, contact elements were used to model soil –pile and abutment – soil interactions. Use of contact pairs have shown to be beneficial in other studies (Baptiste et al., 2011). Contact pairs were created between the piles and soil surfaces that are in contact. They have also been created between the concrete and soil interfaces (to take abutment – soil interaction into account). Several different options are available in ANSYS for modelling contacts. In this particular case, a surface-to-surface contact was used. The rigid – flexible option was used where two areas in contact are the so-called target and contact areas. In this type of contact pairs, rigid areas are typically designated as ‘target’ areas and flexible areas are designated as ‘contact’ areas. Therefore, the pile areas that are steel material and abutment areas that are concrete material, which are much stiffer than soil, are considered to be ‘target’ areas in this case. Soil surfaces that are in contact with a pile or concrete are considered to be more flexible than steel and concrete and, therefore, are designated as ‘contact’ areas. Using the contact wizard, these contact pairs have been created using element types TARGET170 and CONTACT174, which are contact pairs that are used to represent 3D contact areas. The normal to target and contact elements must always be oriented towards each other. This may require reversing the normal to the elements in some areas of shell elements used in steel piles. Contact stiffness is defined automatically by the software using the material properties of contact and target surfaces. Such interface elements only provide compression without tension in modelling the soil – structure interaction. Sliding at the interface was permitted
Figure 9.
649
in the model, and the friction coefficient was set equal to the tangent of the friction angle of the soil.
5. 5.1
Pile behaviour Stresses and strains in the pile
A parametric study was conducted in which the bridge lengths were 122, 183, 244, 366 and 549 m. Finite element analysis results for all the bridge lengths for both seasonal and daily temperature variations show that the maximum stress in the piles occurs in the flange of the piles immediately below the concrete abutment. Figure 9 depicts both deformed and undeformed piles and the contour plot of the von Mises stress for the case of the 366m bridge. The stress is at a maximum in the pile that is farthest from the centre of the bridge (pile 6 in Figure 3(a)). Plastic deformation was also observed in this pile, indicating that yield stress occurred in the pile. It was also observed in all the other piles, but its magnitude in pile 6 was the largest. Plastic deformation occurred as well in the piles of the 122-m length bridge. The plastic deformation occurred in the flange of the pile due to yielding of the material at this point. Figure 10 shows contour plots of equivalent plastic strain (determined from the three principal strains and Poisson’s ratio, i.e. von Mises strain) for the case of the 366-m bridge. The plastic strains were determined in the flange of pile 6 below the abutment at the maximum daily temperature from the finite element analysis for all of the cases and are listed in Table 3 and are plotted in Figure 11. The figure shows that plastic strain
Contour plots of von Mises stress at maximum daily temperature.
650
J. Razmi et al.
270 260 Stress (MPa)
Pile 6
Pile 5
Pile 4
Pile 2
Pile 3
280
Max ep = 0.001
250 240 230
Seasonal stress
220
Daily stress
210
No thermal expansion
200 0
5
10
15
20
25
30
35
40
Time step
Figure 12. von Mises stress for one cycle of daily, seasonal and no temperature variation (the units of time step for the daily cycle is one hour and seasonal cycle is 10 days).
Table 3. Equivalent plastic strain observed in flange of pile 6 underneath the abutment. 1
Bridge length (m)
0.881E 2 3 0.914E 2 3 0.945E 2 3 1.005E 2 3 1.09E 2 3
122 183 244 366 549
increases approximately linearly as the length of the bridge increases. The stress analysis in the pile showed that during one cycle of loading, elements experience only compression – compression. This indicates that the stresses are not completely reversed during one load cycle (tension – compression). This is mainly because the dead and live loads on the bridge provide a large constant pressure that prevents these elements from exiting the compression side and transitioning to the tension side of the stress – strain 1.20E–03 1.15E–03 Equivalent plastic strain
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Figure 10. Contour plot of equivalent plastic strain at maximum daily temperature.
1.10E–03 1.05E–03 1.00E–03
region. The von Mises stress on one node in the vicinity of the maximum stress position is plotted as a function of time steps for daily and seasonal temperature variations for the case of the 366-m bridge (see Figure 12). Figure 12 also shows a case without thermal expansion where the FEM was conducted only for dead and live loads. The cyclic nature of the stress variation can be seen in both daily and seasonal temperature cycles. Although all cases start with roughly the same value of stress, the stress increases slightly in both daily and seasonal cases. The figure shows that the amplitude of stress is larger in the case of seasonal temperature variations than daily variation. However, one seasonal cycle occurs over 1 year. Therefore, the number of seasonal cycles is much smaller than daily cycles. Although the stress in the case without thermal expansion is comparable with the maximum stress observed in both daily and seasonal cases, since the case without thermal expansion does not produce cyclical behaviour, it will not cause fatigue. Cyclical stress is the main factor affecting fatigue life. As the amplitude of the cyclical stress increases, the fatigue life decreases. For example, Koh and Stevens (1991) showed that as the stress increases, the strain increases and the number of cycles to failure decreases. That is, both daily and seasonal temperature variations can cause fatigue in the piles.
9.50E–04 9.00E–04 8.50E–04 8.00E–04 100
200
300
400
500
600
Bridge length (m)
Figure 11. abutment.
Equivalent plastic strain in pile 6 right below the
5.2 Displacement of the pile Maximum lateral displacements in the piles at maximum and minimum daily and seasonal temperatures were obtained from the finite element analysis for all of the bridges. The results are listed in Table 4. The peak lateral displacements of pile 6 are plotted as a function of bridge length in Figure 13. It is evident that the deformation linearly increases with the length of the bridge.
Structure and Infrastructure Engineering
651
Table 4. Displacements due to thermal load in pile 6 in bridges with lengths varied from 122 to 549 m.
Bridge length (m)
Max daily
Min daily
Max seasonal
Min seasonal
122 183 244 366 549
0.88 0.95 1.03 1.17 1.39
22.00 22.91 23.80 25.05 27.98
1.15 1.35 1.56 1.96 2.53
23.57 25.24 26.86 29.85 214.56
Figure 15. Lateral displacement of the pile at maximum daily temperature: (a) displacement profile of middle nodes on the pile and (b) FEM illustration of displacement in the pile.
Figure 13. Lateral displacement of pile 6 as a function of bridge length for seasonal and daily temperature variations.
Lateral displacement of pile 6 for the case of the 366-m bridge due to the dead and live loads is shown in Figure 14.
(a)
Pile displacement (cm) 0 0.5 1
(b)
Figures 15 – 18 show the lateral displacement of pile 6 of the 366-m bridge for different temperature conditions. The displacement at maximum daily and seasonal temperatures is non-monotonic (see Figures 15 and 17). This is consistent with the results reported in the related literature (Huang, French, & Shield, 2004; Huang, Shield, & French,
0.56 cm
–100 –300 Pile depth (cm)
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Displacement (m £ 1022) in FEA
–500 –700 –900 –1100 –1300
Figure 14. loads.
Displacement of pile 6 due to live loads and dead
Figure 16. Lateral displacement of the pile at minimum daily temperature: (a) displacement profile of middle nodes on the pile and (b) FEM illustration of displacement in the pile.
652
J. Razmi et al. (a)
Pile displacement (cm) 0 2 4
(b) 1.96 cm
–100
cycle, which indicates a larger amount of plastic deformation and a lower number of cycles to failure for the seasonal temperature cycle. However, a bridge experiences many more daily temperature cycles, which may result in failure of the piles in a shorter time span.
Pile depth (cm)
–300
6. Conclusions Nonlinear, 3D finite element analysis of the IAB superstructure and substructure under cyclical thermal loading, due to seasonal and daily temperature variations, provided a qualitative verification of experimental measurements available in the literature regarding the development of plastic strain in the piles as well as the piles behaviour in these structures. In addition, the study showed the following:
–500 –700 –900
–1300
. Plastic strain is observed immediately underneath of
Figure 17. Lateral displacement of the pile at maximum seasonal temperature: (a) displacement profile of middle nodes on the pile and (b) FEM illustration of displacement in the pile.
the concrete abutment in the flange of the pile in both daily and seasonal temperature cycles for bridges with a length of 122 m and longer. The maximum stress occurred in the pile furthest from the centre of the bridge. This plastic strain indicates the possibility of yielding and low cycle fatigue failure of the pile. . Lateral displacement and maximum plastic deformation in piles increase as the length of the bridge increases. A linear relationship has been found between the length of the bridge and lateral displacements for both seasonal and daily temperature variations. . Pile displacement in summer and during the high temperature time of the day behaves non-monotonically with respect to the depth. Pile displacement in winter and during the low temperature time of the night is mostly monotonic. This occurs mainly because the deformation due to dead and live loads and temperature variations are in the same direction.
2005; Huang et al., 2008). The top of the pile is pulled in due to the bending moment caused by the vertical dead and live loads on the bridge. At the same time, it is pushed out due to thermal expansion. At minimum daily and seasonal temperatures, the behaviour of the pile is monotonic (see Figures 16 and 18). In these cases, the direction of displacements due to thermal contraction and the dead and live loads on the bridge are the same. Therefore, these deformations are added together to create the total displacement of the piles. The lateral displacement due to the seasonal temperature cycles was larger than that due to the daily temperature (b) –9.85 cm
(a) Pile displacement (cm) –10
–5
0 –100 –300
Notes –500 –700
Pile depth (cm)
Downloaded by [University of Connecticut] at 06:20 09 July 2014
–1100
–900 –1100 –1300
Figure 18. Lateral displacement of the pile at minimum seasonal temperature: (a) displacement profile of middle nodes on the pile and (b) FEM illustration of displacement in the pile.
1. 2.
Email:
[email protected] Email:
[email protected]
References AASHTO (2010). AASHTO LRFD bridge design specifications (5th ed.). Washington, DC: American Association of State Highway and Transportation Officials (AASHTO). Alizadeh, M., & Davisson, M.T. (1970). Lateral load tests on piles Arkansas river project. Journal of the Soil Mechanics and Foundations Division, 96, 1583– 1603. Amde, A.M., Chini, S.A., & Mafi, M. (1997). Model study of h-piles combined loading. Geotechnical and Geological Engineering, 15, 343– 355.
Downloaded by [University of Connecticut] at 06:20 09 July 2014
Structure and Infrastructure Engineering Amde, A.M., & Klinger, J.E. (1987). The State of- the-art in integral abutment bridge design and construction., AW087313-046, FHWA/MD-87/04. Amde, A.M., Greimannan, L.F., & Johnson, B. (1983). Performance of integral abutment bridges. Proceedings of International Association for Bridge and Structural Engineering, IABSE, Zurich, Switzerland (pp. 17 – 34). Amde, A.M., Klinger, J.E., & White, E.J. (1988). Performance of jointless bridges. ASCE Journal of Performance of Construction Facilities, 2(2), 111– 125. ANSYS (2011). Material data tables. Version 13, ANSYS, Inc, Canonsburg, PA. Baptiste, K.T., Kim, W.S., & Laman, J.A. (2011). Parametric study and length limitations for prestressed concrete girder integral abutment bridges. International Journal of Structural Engineering, 21(2), 151– 156. Black, W., & Emerson, M. (1977). Bridge temperatures derived from the measurement of movements. TRRL Laboratory Report, 748, 1 – 33. Burke, M.P. Jr (1993). Integral bridges: Attributes and limitations. Transportation Research Board, Transportation Research Record, 1393, 1 – 8. Chini, S.A., Amde, A.M., & Aggour, M.S. (1993). Drainage and backfill provisions for approaches to bridges. Transportation Research Board, Transportation Research Record, 1425, 45 – 53. Dicleli, M., & Albhaisi, S.M. (2009). Maximum length of integral bridges supported on steel h-piles driven in sand. Engineering Structures, 25, 1491 –1504. Ellis, E.A., & Springman, S.M. (2001). Modeling of soil structure interaction for a piled bridge abutment in plane strain fem analyses. Computers and Geotechnics, 28, 79 – 98. Emerson, M. (1977). Temperature differences in bridges: Basis of design requirements. TRRL Laboratory Report, 765, 1 – 39. Girton, D.D., Hawkinson, T.R., & Greimann, L.F. (1991). Validation of design recommendations for integral abutment piles. ASCE Journal of Structural Engineering, 117, 2117– 2134. Hallmark, R. (2006). Low-cycle fatigue of steel piles in integral abutment bridges., Master’s Thesis, Lulea˚ University of Technology, Switzerland. Huang, J., French, C., & Shield, C. (2004). Behavior of concrete integral abutment bridges., Final Report. Minnesota Department of Transportation, Research Service Section. Huang, J., Shield, C., & French, C. (2005). Time-dependent behavior of a concrete integral abutment bridge. Transportation Research Record: Journal of the Transportation Research Board, 11, 299– 309. Huang, J., Shield, C., & French, C. (2008). Parametric study of concrete integral abutment bridges. ASCE Journal of Bridge Engineering, 13, 511– 526.
653
Jorgensen, J.L. (1983). Behavior of abutment piles in an integral abutment in response to bridge movements. Transportation Research Board, 903, 72 – 79. Kalayci, E., Civjan, S.A., Bren˜a, S.F., & Allen, C.A. (2011). Load testing and modeling of two integral abutment bridges in Vermont, US. Structural Engineering International, 21, 181– 188. Kalayci, E., Civjan, S.A., & Bren˜a, S.F. (2012). Parametric study on the thermal response of curved integral abutment bridges. Engineering Structures, 43, 129– 138. Koh, S.K., & Stephens, R.I. (1991). Mean stress effects on low cycle fatigue for a high strength steel. Fatigue Fracture of Engineering Materials and Structures, 14(4), 413– 428. Krizek, J. (2011). Soil-structure interactions of integral bridges. International Journal of Structural Engineering, 21(2), 169– 174. Ladani, L., & Dasgupta, A. (2007). Effect of voids on thermomechanical durability of pb-free BGA solder joints: Modeling and simulation. ASME Journal of Electronic Packaging, 129, 273– 277. Ladani, L., & Dasgupta, A. (2008). Damage initiation and propagation in voided joints: Modeling and experiment. ASME Journal of Electronic Packaging, 130. 011008 (11 pages), doi: http://dx.doi.org/10.1115/1.2837562. Lawver, A., French, C., & Shield, C.K. (2000). Field performance of integral abutment bridge. Transportation Research Record: Journal of the Transportation Research Board, 1740, 108– 117. Maruri, R.F., & Petro, S.H. (2005). Integral abutments and jointless bridges (IAJB) survey summary. Proceedings of FHWA Conference on Integral Abutments and Jointless Bridges, Baltimore, MD (pp. 12 – 29). Mirambell, E., & Real, E. (2000). On the calculation of deflections in structural stainless steel beams: An experimental and numerical investigation. Journal of Constructional Steel Research, 54, 109– 133. Oesterle, R.G., Refai, T.M., Volz, J.S., Scanlon, A., & Weiss, W. J. (2002). Jointless and Integral Abutment Bridges: Analytical Research and Proposed Design Procedures. Washington, DC: Final Report to FHWA. Pe´tursson, H., Collin, P., Veljkovic, M., & Andersson, J. (2011). Monitoring of a Swedish integral abutment bridge. Structural Engineering International, 21, 175– 180. Thanasattayawibul, N. (2006). Curved integral abutment bridges. PhD Dissertation, Civil and Environmental Engineering Department, University of Maryland, MD. Utah State University (2009). Utah state climate center. Available from: http://www.climate.usurf.usu.edu/ [Reviewed 2009]. von Mises, R. (1913). Mechanik der festen Ko¨rperim plastisch deformablen Zustand. Nachrichten von der Gesellschaft der Wissenschaten zu Go¨ttingen, Mathematisch-Physikalische Klasse, 1, 582– 592.
