MODELING OF SLAB-FOUNDATION FRICTION IN JOINTED CONCRETE ...docs.trb.org/prp/13-3147.pdf · 1...

Zokaei, Tirado, Carrasco, Nazarian and Bendaña 1

MODELING OF SLAB-FOUNDATION FRICTION IN JOINTED CONCRETE 1 PAVEMENTS UNDER NON-LINEAR THERMAL GRADIENT OR TRAFFIC LOADS 2 3

Mohammad-Ali Zokaei-Ashtiani, MSCE (corresponding author) 4 Research Assistant 5 Center for Transportation Infrastructure Systems 6 The University of Texas at El Paso 7 500 W. University Ave., El Paso, Texas 79968 8 Tel: (915)-747-8407, Email: [email protected] 9 10

Cesar Tirado, PhD 11 Research Engineer 12 Center for Transportation Infrastructure Systems 13 The University of Texas at El Paso 14 500 W. University Ave., El Paso, Texas 79968 15 Tel.: (915)-747-6925, E-mail: [email protected] 16 17

Cesar Carrasco, PhD 18 Associate Professor and Chair 19 Department of Civil Engineering 20 The University of Texas at El Paso 21 500 W. University Ave., Engineering Bldg., Room A-225 22 El Paso, TX 79968 23 Tel.: (915)-747-6919, Fax: 915-747 8037, E-mail: [email protected] 24 25

Soheil Nazarian, PhD, PE 26 Professor and Director of 27 Center for Transportation Infrastructure Systems 28 The University of Texas at El Paso 29 500 W. University Ave., El Paso, Texas 79968 30 Tel: (915)-747-6911, Email: [email protected] 31

32

Julian Bendaña, PhD, PE 33 Engineering Consultant, Albany, NY 12203 34 Tel.: (518)-466-1468, E-mail: [email protected] 35 36

37 Total words: 3976(Text) + 3250(12 Figures+1 Table) + 203(Abstract) = 7429 38

39

Revised Paper: November 2012 40

41

42

43

TRB 2013 Annual Meeting Paper revised from original submittal.


ABSTRACT 1 The accurate modeling of the thermo-mechanical response of jointed concrete pavements is of 2

primary importance in the design of pavement sections. From the initial development of 3 pavement analysis software in the early 1970’s, it was recognized that the Finite Element 4

Method was the most appropriate modeling tool due to its potential ability to capture all the 5 pavement response features. A series of software development efforts have culminated in the 6

production of NYSLAB, a jointed pavement analysis tool that has the capability to predict the 7 complete thermo-mechanical response including pavement curling and the interactions that occur 8

between the slabs and the foundation. This paper presents a series of studies developed in 9 NYSLAB looking specifically into the slab-foundation friction generated by nonlinear thermal 10

gradients and traffic loads. Nonlinear temperature gradients can produce slab expansion and 11 contraction that lead to the generation of frictional tractions between slabs and foundation. The 12

prediction of these friction tractions is complicated by the curling of the slabs that cause some 13 portions of the slabs to lose contact with the foundation. The results presented here highlight the 14

importance of considering these frictional tractions in the analysis of jointed concrete pavements 15 since they have a significant impact on PCC slabs bending stresses. 16

Key Words: Rigid Pavement, Jointed Plain Concrete Pavement, Finite Element Modeling, 17

Thermal loads, Friction. 18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34



INTRODUCTION 1 Jointed plain concrete pavements (JPCP) are the most commonly used type of rigid pavement 2

systems and the accurate prediction of their thermo-mechanical responses due to the combined 3 effect of environmental and traffic loads are of primary importance for rigid pavement designers 4

in a mechanistic-empirical pavement design procedure. The temperature gradient and resulting 5 slab shape play a crucial role in the magnitude of stresses and deflections caused by the 6

superimposed traffic loads. Field measurements reveal that the actual temperature gradient 7 through the depth of pavement slabs is nonlinear (1). This nonlinear thermal gradient can not 8

only produce curling and expansion or contraction in slabs but actually leads to stresses that are 9 higher than those produced by a linear gradient with the same top to bottom temperature 10

difference. While the thermal curling tends to produce bending stresses in slabs, the uniform 11 thermal expansion or contraction tends to produce additional compressive or tensile stresses 12

within pavement slabs due to slab-foundation friction. In JPCP, which technically cannot be 13 considered as a semi-infinite slab, the contact conditions along the slab-foundation interface 14

significantly impact the mechanical behavior of pavements. Temperature induced curling 15 significantly impacts slab-foundation contact conditions and interface friction further 16

complicates JPCP analysis because it introduces some nonlinearity to the problem. For this 17 reason, a sophisticated modeling method such as finite element (FE) modeling is required to 18

more accurately consider the nonlinearity of the problem and take all the possible loads and 19 environmental condition into consideration (2). 20

The first FE-based tool for the analysis of rigid pavements was developed in 1979 under 21 the ILLI-SLAB software package (3). In ILLI-SLAB, thermal loads could only be considered for 22

one slab with fully bonded or completely unbonded slab-base interface conditions. Also, only a 23 linear temperature distribution within the slab depth was allowed (3). 24

Tayabji and Colley (4) developed JSLAB based on the initial ILLI-SLAB formulation in 25 1986 to incorporate partial contact in the slab-foundation interface and to calculate the thermal 26

and principal stresses (5). The next generation of this software, JSLAB2004, could analyze JPCP 27 responses under the combined effect of traffic and thermal loads with linear temperature gradient 28

for a two-layer pavement system (6). That program was able to model the separation between 29 slabs and foundation as a consequence of positive and negative temperature gradient. However, 30

modeling the horizontal interaction of slab-foundation was not possible. 31 EverFE is a rigid pavement 3D FE analysis tool which was developed to overcome the 32

limitation of the 2D programs (7). Linear or non-linear temperature gradient can be considered in 33 that program. EverFE allows for specifying up to three either bonded or unbounded elastic base 34

layers. For unbonded slab-base interface, shear transfer can be captured via a bilinear elastic –35 plastic curve that defines the shear-stresses to relative-displacement constitutive relation. This 36

relation can be obtained from an experimental push test for each type of base material to define 37 the relative displacement for which slip occurs and to determine the frictional or shear stresses at 38

the slip state (8). In this method the frictional or shear stresses are independent of the normal 39 stresses. 40

To overcome the limitations of JSLAB2004, researchers at the University of Texas at El 41 Paso completely redesigned this tool and developed a new JPCP analysis tool named NYSLAB 42

that significantly improved the capabilities of JSLAB2004 (2, 6). NYSLAB does not have a 43 limitation in the number of Portland cement concrete (PCC) slabs and foundation layers and all 44

the layers are modeled independently. Debonded slab layers as well as the interface of bottom 45



slab and top foundation layer are connected through interface elements to better model the slabs 1 curling response as well as the interactions between slabs and foundation (6). 2

This paper presents the results of a series of studies that highlight NYSLAB’s capabilities 3 to predict pavement response under nonlinear temperature gradient and the frictional tractions 4

generated by thermal and traffic loads and their impact on the PCC slabs bending stresses and 5 deflections. 6

MODELING OF SLAB-FOUNDATION FRICTION 7 Slab elements in the initial development of NYSLAB had only three degrees of freedom (vertical 8

deflection and two rotations about longitudinal and transverse axes) per node just as JSLAB2004 9 did. This meant that only the pure bending in PCC slabs as a consequence of thermal curling, self 10

weight and traffic loads could be captured. Since the slab elements did not account for in-plane 11 deformations, the effects of thermal expansion and contraction in PCC slabs could not be 12

considered. A thorough explanation of the finite element formulation and underlying theory in 13 this initial version of NYSLAB can be found in Carrasco et al. (2). 14

In the new formulation of NYSLAB the “first order shear deformation laminated plate 15 theory” or “Mindlin laminated plate theory” has supplanted the Mindlin plate theory to model 16

multiple bonded slab layers with different material property and thickness more accurately. In 17 the modified formulation, slab elements are enhanced to consider two additional in-plane degrees 18

of freedom in longitudinal and transverse directions. Nine-node isoparametric elements are used 19 to discretize the pavement slabs based on the formulation proposed by Reddy (9). 20

Debonded layers within the composite slab are connected to one another through 21 interface elements. The same interface elements are used to model the interface between the 22

bottom slab layer and the top foundation layer. Interface elements have the characteristic of 23 being active in each node when in compression and inactive when in tension to model the 24

interface separation produced during curling. Also, each node of the interface elements has the 25 ability to define the state of contact during sliding as a consequence of thermal expansion and 26

contraction; whether in slip mode or stick mode (10). The active/inactive and slip/stick states are 27 determined through an iterative process. The use of interface elements facilitates the modeling of 28

the loss of contact between layers when thermal curling occurs and when voids between the PCC 29 slabs and the foundation are present. Also, calculating the frictional or shear stress at the 30

interface between layers and determining the state of contact is possible by using these elements 31 and by applying an appropriate constitutive friction law (11-14). For each node in contact, 32

normal and shear stresses are related through the following isotropic Mohr-Coulomb friction 33 law, 34

35

(1) 36

37

Where, is the tangential or shear stress, is the normal stress, and is the coefficient of 38

friction. Shear stress at each node of interface element is calculated based on the normal stress at 39

that point, which can be affected by temperature curling and traffic loads. The interface element 40 and the constitutive relation in the tangential direction are shown in Figure 1. Parameters k1 and 41

k2 in this figure are the penalty parameters which are used to impose displacement constraints in 42 the equilibrium equations (11, 15). 43

Nine-node interface elements consistent with the elements used to discretize the slabs and 44 foundation layers are used in the interface (see Figure 1). These elements have the capability to 45

capture relative displacements between two surfaces in contact in two orthogonal tangential 46



(horizontal) directions and normal (vertical) direction. A thorough explanation of the finite 1 element formulation and underlying theory can be found in Zokaei et al. (16) and is not repeated 2

here for the sake of brevity. The mathematical model of the entire pavement section in the 3 formulation of NYSLAB is shown in Figure 2. 4

5

FIGURE 1 Interface element and tangential constitutive relation (11, 16). 6

7 8

9

FIGURE 2 Jointed pavement section as modeled in NYSLAB (16). 10

11

PARAMETRIC STUDIES 12 A series of parametric studies were carried out to evaluate the performance of the new 13

improvements implemented in NYSLAB and to better understand the impact of the most 14

relevant parameters that affect the behavior of JPCP. For this purpose, a three by two jointed 15 PCC slab in longitudinal and transverse direction, respectively, resting on a Winkler foundation 16

with modulus of subgrade reaction of 200 psi/in (5.43 10 a ) was modeled (see Figure 3). 17

Each slab was 15 ft (4.6 m) long, 14 ft (4.3 m) wide and 10 in. (254 mm) thick. The modulus of 18

elasticity of the PCC was set to 4,000 ksi ( 7 10 a) with a oisson’s ratio of 0 1 , 19

coefficient of thermal expansion of and a unit weight of 150 pcf (2432 kg/m3). The 20

space between the adjacent slabs was set to 0.25 in. in both directions. The slabs were connected 21



by dowels (1.5 in. (38mm) )and tie bars (0.75 in. (20mm)) in the transverse and longitudinal 1 joints, respectively. The modulus of elasticity of the steel dowels and tie bars was set to 29,000 2

ksi ( 00 10 a) and the oisson’s ratio to 0 3 3

When applicable, the pavement was loaded with a standard truck with a single steering 4 axle, and two sets of tandem axles (see Figure 3). Each tire had dimensions of 8 in. (203 mm) by 5

6 in. (152 mm), with a contact pressure of 90 psi (620 kPa). The last axle of the trailing tandem 6 axle was placed outside of the three-slab system. For the other parametric studies presented 7

below, only thermal loads are considered together with the self weight of the slab. 8 9

10

FIGURE 3 Pavement structure and placement of truck. 11 12

Effect of Non-linear Temperature Gradient 13

NYSLAB is capable of simulating thermal effects with a nonlinear temperature profile. This 14

allows for a more realistic modeling of temperature variation through the thickness of the PCC 15 slabs since several field studies confirm that the temperature gradient within the slab is not linear 16

(17). For this reason, the temperature profile through the thickness of the slab is modeled as a 17 cubic function (Eq. 2) that can be fitted by considering the temperature at four different points 18

through the depth, 19

(2) 20

The constant term a0 produces expansion and contraction in PCC slabs. The linear term 21

a1 produces pure bending in the PCC slab due to the temperature difference between its top and 22

bottom. The higher-order terms of temperature profile in Eq. 2 produce internal stresses in the 23

PCC slab regardless of its external constraints (18). 24

The effect of a non-linear temperature profile was studied by evaluating the stresses and 25

displacements along a longitudinal section that passes through the center of the slabs as shown in 26

Figure 3 (Line 1). Four temperature profiles with different level of deviation from the linear 27

profile were selected (see Figure 4). The coefficients ai (in Eq. 2) for the four case studies are 28

shown in Table 1. In all cases, the temperatures at the top and bottom of slabs were maintained at 29

45 F and 65 F respectively, while the set temperature was set at 80 F. This means that thermal 30

contraction occurred throughout the depth of the PCC slab while the decrease in temperature at 31



the top was greater than that at the bottom of the slab (night-time negative temperature-1

variation). The coefficient of friction between the PCC slab and foundation was set to 0.3 in this 2

case study. 3

4

5

Figure 4 Temperature-change profile for the four cases studied. 6 7

8

Table 1 Coefficients for Temperature-Change Profiles 9 Case a0 a1 a2 a3

1 -15 -2 0.0 0.0

2 -15 -1.2 -0.08 0.0

3 -15 0.0833 -0.2679 0.006

4 -15 0.6587 -0.3056 0.004

10

Figure 5 shows the bending stresses in the longitudinal direction at the top and bottom of 11

the PCC slabs along Line 1 described above. With a linear temperature profile (Case 1), the 12

stresses at the top and bottom of the slab are equal in magnitude (top in tension and bottom in 13

compression). However, as the temperature profile becomes more nonlinear, the stresses, both at 14

the top and bottom, shift in the positive (tensile) sense about 120 psi (827 kPa). These results 15

indicate that even though in all four cases the temperature-change at the top and bottom of the 16

slabs are the same, the nonlinear thermal terms produce significant additional stresses. This 17

shows that assuming a linear temperature gradient would tend to under-estimate the stresses 18

within the pavement slabs and may lead to their significant under-design. Figure 6 shows the 19

longitudinal displacement at the mid-depth of the PCC slabs. As expected, longitudinal 20

contraction occurs in all cases as a consequence of the decrease in temperature from the set 21

temperature throughout the slab thickness. However, for all four temperature profiles, the 22

increasing non-linearity decreases the average temperature change leading to a decrease in the 23

thermal contraction of the slabs (see Figure 4). It is important to note that general conclusion 24

cannot be drawn about the thermal contraction pattern since it greatly depends on the shape of 25

the temperature profile. However, these results show NYSLAB’s capability to calculate the 26

maximum in-plane displacements for any type of temperature variation in order to predict the 27

amount of joint opening or closing. 28



1

2

3

a) Top of PCC slab 4

5

6

7

b) Bottom of PCC slab 8 9

Figure 5 Bending stress at the top and bottom of PCC slabs in longitudinal direction (σxx) 10 through Line 1 for various temperature gradients. 11

(NOTE: Tension is positive and Compression is negative) 12 13

1 in. = 25.4 mm

1 in. = 25.4 mm



1

2

Figure 6 Longitudinal displacement (Ux) of mid-depth of PCC slabs through Line 1 for 3 various temperature gradients. 4

5

Effect of Friction between Slab and Foundation 6

Thermal expansion or contraction of a PCC slab generates frictional tractions between the slab 7 and foundation that can significantly affect the bending stresses. The addition of the in-plane 8

degrees of freedom and the interface elements in the enhanced version of NYSLAB allow 9 capturing the constraining effects that frictional tractions have on the PCC slabs and their 10

corresponding impact on longitudinal bending stresses. 11 12

Linear Thermal Gradient with Mid-Plane Contraction 13 To demonstrate the effect of slab-foundation contact friction on PCC slabs stresses and 14

deformations, a series of simulations were performed using the Case 1 temperature gradient 15

described above. This case includes a uniform temperature change of -25 F that tends to produce 16

a contraction of the mid-plane of the PCC slabs and in fact, causes the entire cross section of the 17 slabs to contract. The coefficient of friction was varied between 0.0 for the case with no friction 18

to 1.5. The longitudinal bending stresses are compared with the frictionless case in Figure 7. As 19 expected, the linear temperature profile in Case 1 produces tensile stresses at the top and 20

compressive stresses at the bottom of the PCC slabs. However, the uniform negative temperature 21 change produces additional stresses in the PCC slabs because of the presence of friction. When 22

the PCC slabs contract, the frictional resistance of the foundation layer produces a uniform 23 tensile traction on the PCC slabs. In this case, the moments induced by the frictional resistance 24 reduces the tensile stresses at the top and compressive stresses at the bottom of the PCC slabs. As 25

is apparent in Figure 7, increasing the coefficient of friction caused a decrease in the magnitude 26 of the longitudinal stresses, especially in the central area of each slab, by as much as 40% for a 27

coefficient of frictions of 1.5. This is because due to the negative temperature gradient curling, 28



only the central areas of slabs maintain contact with the foundation while the areas close to the 1 edges lose their contact and thus the frictional resistance has no impact on those areas. 2

3

4

5 6 7

a) Top of PCC slabs 8

9

10 b) Bottom of PCC slabs 11

Figure 7 Bending stress at the top and bottom of PCC slabs in longitudinal direction (σxx) 12 through Line 1 for different coefficients of friction due to temp. gradient Case 1. 13

(NOTE: Tension is positive and Compression is negative) 14 15

1 in. = 25.4 mm

1 in. = 25.4 mm



It is important to note that the effects of these frictional tractions are larger at the bottom 1 of the slabs because of their constraining effect and lead to a non-symmetric longitudinal 2

bending stress profile about the mid-plane of the slabs. Figure 8 shows the effect of the frictional 3 tractions on the vertical deflection of the PCC slabs. By increasing the coefficient of friction, the 4

vertical deflection increases slightly because of the resulting positive moment produced by the 5 frictional tractions at the bottom of the PCC slabs. 6

7

8

Figure 8 Vertical deflections (Uz) of PCC slabs through Line 1 for different coefficients of 9

friction due to temp. gradient Case 1. 10 11

Linear Thermal Gradient without Mid-Plane Contraction 12

In this case study the effect of friction between PCC slabs and foundation was examined when 13 the linear thermal gradient is such that the mid-plane of the slabs has zero change in temperature. 14

For this purpose, the difference between temperature at the top and bottom of slabs was set to 15

10 F (in Eq. 2, a0=5, a1=-1, a2=a3=0). This negative temperature gradient causes the bottom of 16 the slabs to expand. Therefore, although the horizontal displacements at the mid-depth of slabs 17

are zero, the horizontal displacements at the bottom surface of PCC slabs can produce frictional 18 tractions. Figure 9 shows the longitudinal stress at the top and bottom of PCC slabs for different 19

coefficients of friction. As expected, a negative temperature gradient produces tensile stresses at 20 the top and compressive stress at the bottom of the PCC slabs. As the bottom surface of slabs 21

expand, the compressive frictional tractions produce an additional negative moment in the PCC 22 slabs. By increasing the coefficient of friction and consequently the frictional tractions, the 23

additional moment produces additional tensile and compressive stresses at the top and the bottom 24 of PCC slabs by as much as 30% for a coefficient of friction of 1.5. These results are the 25



opposite of those obtained in the case study described before where the top and bottom stresses 1 actually decreased in magnitude. This is because while both case studies imposed a negative 2

thermal gradient, in the first case study the bottom of the slabs is actually contracting while in the 3 present case it is expanding. This translates into frictional tractions that actually have opposite 4

senses and thus lead to opposing effects on the longitudinal bending stresses. 5

6

7

a) Top of PCC slabs 8 9

10

11 b) Bottom of PCC slabs 12

Figure 9 Bending stress at the top and bottom of PCC slabs in longitudinal direction (σxx) 13 through Line 1 for different coefficients of friction. 14

(NOTE: Tension is positive and Compression is negative) 15

16

1 in. = 25.4 mm

1 in. = 25.4 mm



Also, the vertical deflection in this case decreases as the coefficient of friction increases 1 (see Figure 10). This is because the moments caused by the frictional tractions reduce the curling 2

effect of the negative thermal gradient and consequently decrease the vertical deflections. 3

4

5

Figure 10 Vertical deflections (Uz) of PCC Slabs through Line 1 for different coefficients of 6 friction. 7

8

Case with Only Traffic Load 9

In this case, the pavement section was loaded with a standard truck (as shown in Figure 3) and 10

zero thermal gradient. While in this case there is no thermal expansion, it is the deformation of 11 the bottom of the slabs caused by the truck induced bending moments that produce frictional 12

tractions in the interface between slabs and foundation. Figure 11 shows a typical contour plot of 13 the longitudinal bending stress at the bottom of PCC slabs. The longitudinal bending stress at the 14

bottom of PCC slabs along Line 2 that passes through the right tires of the truck (see Figure 3) is 15 shown in Figure12 for different coefficients of friction. As expected, the effect of frictional 16

tractions between PCC slabs and foundation in this case is not as significant as in the cases with 17 the thermal gradient described above and it is actually away from the tire loads that the largest 18

differences are observed. 19 20



1

Figure 11 Bending stress at the bottom of PCC slabs in longitudinal direction (σxx) 2 in frictionless case due to truck load. 3

4

5

Figure 12 Bending stress at the bottom of PCC slabs in longitudinal direction (σxx) 6

through Line 2 for different coefficients of friction due to truck load. 7 (NOTE: Tension is positive and Compression is negative) 8

9

10

1 in. = 25.4 mm



SUMMARY AND CONCLUSIONS 1 Pavement responses due to nonlinear temperature gradient within a PCC slab and frictional 2

contact between the PCC slab and foundation were examined in this paper. The study employed 3 improved finite element models that were incorporated in NYSLAB to calculate pavement 4

stresses and deflections Recent enhancements to NYSLAB’s slab and interface elements were 5 summarized highlighting their capabilities in capturing the horizontal or shear interaction in the 6

slab-foundation interface. A series of parametric studies were conducted that considered various 7 coefficients of friction and temperature gradient. From the results presented here, the following 8

conclusions can be drawn: 9 10

a) The nonlinear terms in the temperature gradient can produce additional internal stresses 11 at the top and bottom of PCC slabs. This demonstrates that assuming a linear temperature 12

gradient tends to under-estimate the stresses within the pavement slabs and may lead to 13 their significant under-design. 14

b) Friction between pavement layers significantly affects the bending stresses in the PCC 15 slab, and should be included in their analysis. The effect of friction is especially 16

significant when the PCC slabs are subjected to thermal loads. The magnitude of stresses 17 due to friction in the PCC slabs depends on the relative movements of the bottom surface 18

of the slab and the top surface of the underlying foundation layer during thermal 19 expansions and contractions. This translates into frictional tractions that act in the 20

opposite direction of the relative displacement of the bottom of the slab and produces 21 tensile or compressive stresses. 22

c) In cases when truck loads are considered, the stresses due to frictional tractions between 23 the PCC slabs and foundation may not be as significant as the stresses with the thermal 24

loads. 25 26

ASSUMPTIONS AND LIMITATIONS 27 NYSLAB was developed to eliminate some of the existing analysis tools limitations in order to 28 obtain a reliable prediction of thermo-mechanical behavior of jointed concrete pavements. 29

Although NYSLAB has reached a top level of maturity, it still has some limitations: 30

1- The initial curvature of PCC slabs due to built-in curling was not taken into account in 31 the analysis. 32

2- In the case of stabilized bases, a linear constitutive friction law to calculate the frictional 33 traction at the PCC slab /base interface needs to be improved. In the case of stabilized 34

bases the cohesion between two surfaces would tend to change frictional characteristics 35 as compared to the unstabilized bases. Thus, shear tractions cannot be correlated linearly 36

to normal tractions. An experimental Push-off test is required to obtain frictional 37 characteristic for each type of stabilized bases. 38

3- The effects of creep and relative humidity have not been implemented in NYSLAB. The 39 results from field studies (19) and finite element modeling (20) can be utilized to model 40

such environmental effects. 41 42

The development to NYSLAB is still continuing with the objective of overcoming the mentioned 43

limitations. 44



REFERENCES 1

1 Thompson, M. R., B. J. Dempsey, H. Hill, and J. Vogel. Characterizing Temperature Effects 2

for Pavement Analysis and Design. In Transportation Research Record: Journal of the 3 Transportation Research Board, No. 1121, Transportation Research Board of the National 4

Academies, Washington, D.C., 1987, pp. 14-22. 5 2 Carrasco, C., M. Limouee, M. Celaya, I. Abdallah, and S. Nazarian. NYSLAB: A Software for 6

Analysis of Jointed Pavements. Publication FHWA-RD-07-1008-01. FHWA, U.S. 7 Department of Transportation, 2010. 8

3 Ioannides, A. M. Analysis of Slabs-On-Grade, for a Variety of Loading and Support 9 Conditions. PH.D. Thesis, University of Illinois Urbana, 1984. 10

4 Tayabji, S. D., and B. E. Colley. Analysis of Jointed Concrete Pavements. Publication 11 FHWA-RD-86-041. FHWA, U.S. Department of Transportation, 1986. 12

5 Heinrichs, K. W., M. J. Liu, M. I. Darter, and A. M. Ioannides. Rigid Pavement Analysis and 13 Design. Publication FHWA-RD-88-068. FHWA, U.S. Department of Transportation, 1989. 14

6 Carrasco, C., M. Limouee, S. Nazarian, and J. Bendana. Development of NYSLAB 15 Improved Analysis Tool for Jointed Pavement. In Transportation Research Record: Journal 16

of the Transportation Research Board, No. 2227, Transportation Research Board of the 17 National Academies, Washington, D.C., 2011, pp. 107-115. 18

7 Davids, W. G., G. M. Turkiyyah, and J. P. Mahoney. EVERFE: Rigid Pavement Three-19 Dimensional Finite Element Analysis Tool. In Transportation Research Record: Journal of 20

the Transportation Research Board, No. 1629, Transportation Research Board of the 21 National Academies, Washington, D.C., 1998, pp. 41-49. 22

8 Davids, W. G., and Z. Wang. 3D Finite Element Analysis of Jointed Plain Concrete 23 Pavement with EverFE2.2. In Transportation Research Record: Journal of the 24

Transportation Research Board, No. 1853, Transportation Research Board of the National 25 Academies, Washington, D.C., 2003, pp. 92-99. 26

9 Reddy, J. N. Mechanics of Laminated Composite Plates and Shells Theory and Analysis. 27

CRC Press LLC, Second edition, 2004. 28 10 Urzua, J. L., D. A. Pecknold, L. A. Lopez, and W. H. Munse. Analysis Procedure for 29

frictional contact problem using interface finite elements. Civil Engineering Studies, 30 Structural research series NO. 438. Department of Civil Engineering University of Illinois at 31

Urbana-Champaign, March 1977. 32 11 Barbero, E. J., R. Lucianof, and E. Sacco. Three-Dimensional Plate and Contact/Friction 33

Elements for Laminated Composite joints. Computers & Structures, Vol. 54, No. 4, 1995, pp. 34 689-703. 35

12 Gens, A., I. Carol, and E .E. Elonso. An interface element formulation for the analysis of 36 soil-reinforcement interaction. Computers and Geotechnics, Vol. 7, No. 1–2, 1989, pp. 133–37

151. 38 13 Ghaboussi, J., E. L. Wilson, and J. Isenberg. Finite Element for Rock Joints and Interfaces. 39

Journal of the Soil Mechanics and Foundations, Vol. 99, No. 10, 1973, pp. 849-862. 40 14 Day, R. A., and D. M. Potts. Zero Thickness Interface Elements-Numerical Stability and 41

Application. International Journal for Numerical and Analytical Methods in Geomechanics, 42 Vol. 18, 1994, pp. 689-708. 43

15 Pantano, A., and R. C. Averill. A penalty-based finite element interface technology. 44 Computers & Structures, Vol. 80, 2002, pp. 1725–1748. 45



16 Zokaei, M. A., C. Tirado, C. Carrasco, and S. Nazarian. Development and Improvement of 1 Computer Software NYPAS. Publication FHWA-RD-07-1008-03. FHWA, U.S. Department 2

of Transportation, 2011. 3 17 Mohamed, A. R., and W. Hansen. Prediction of Stresses in Concrete Pavements subjected to 4

Non-Linear Gradients. Cement and Concrete Composites, Vol. I8, 1996, pp. 381-387. 5 18 Ioannides, M., and L. Khazanovich. Nonlinear Temperature Effects on Multilayered 6

Concrete Pavements. Journal of Transportation Engineering, Vol. 124, No. 2, 1998. 7 19 Ye, D. et al. Literature Review of Curling in Portland Cement Concrete Pavement. 8

Publication FHWA/TX06/0-5106-1. FHWA, U.S. Department of Transportation, 2006. 9 20 Kim, S., M. Won, and B. McCullough. Numerical Modeling of Continuously Reinforced 10

Concrete Pavement Subjected to Environmental Loads. In Transportation Research Record: 11 Journal of the Transportation Research Board, No. 1629, Transportation Research Board of 12

the National Academies, Washington, D.C., 2007, pp. 76-89. 13 14

15

16


Date post:	01-Feb-2018
Category:	Documents
Upload:	phamtuyen
View:	221 times
Download:	0 times

MODELING OF SLAB-FOUNDATION FRICTION IN JOINTED CONCRETE ...docs.trb.org/prp/13-3147.pdf · 1...

Documents