Fatigue Behaviour of Cement Concrete Pavement under Single and Tandem Axle Load Using F.E.M

IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 08, 2015 | ISSN (online): 2321-0613

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M Shri S.S Goliya1 Dr. K.K Pathak2 Dr. Y.P. Joshi3 Miss Tanu Chaturvedi4 1 Assistant Professor 2Professor 3Professor 4Lecturer 1,2,3,4 Department of Civil Engineering 1,3,4 S.A.T.I, Vidisha (M.P) 2N.I.T.T.T.R, Bhopal (M.P) Abstract— Fatigue is the important aspect in the rigid pavement design. Due to applications of the heavy loads fatigue occurs in the pavement in the form of micro cracks. fatigue concepts which is an important parameter in cement concrete pavement and mainly failure occurs due to fatigue failure. Therefore study has been done in order to study the fatigue concepts. In this paper fatigue behaviour of CC pavement has been assessed using finite element method.

Stress analysis for single and tandem axles have been carried out. Based on the IRC recommendation, allowable repetitions are calculated.

Key words: Fatigue, F.E.M I. INTRODUCTION Like conventional concrete and other engineering materials, CC pavement is subject to effects of fatigue. A fatigue failure occurs when a material ruptures under continued repetitions of loads that cause stresses less than the strength of material. The load applied by single as well as tandem axles cause maximum flexural stresses when tyre imprint touches the longitudinal edges of the pavement as shown in Figure-1

Fig. 1(d): Double Axle –Interior Loading Fig. 1: Tyre Imprints Touch the Longitudinal Edges in Single and Tandem Axle Arrangement In this study, fatigue behaviour of CC pavement has been assessed using finite element method. Stress analysis for single and tandem axles have been carried out.

Based on the IRC recommendation, allowable repetitions are calculated.

II. MATERIAL PROPERTIES Boundary Box Length X Length Y Length Z 350 cm 350 cm 25 cm Model 1 350 cm 350 cm 30 cm Model 2 350 cm 350 cm 35 cm Model 3 Table 1: Material Properties Following values in Table 1 are possessed as isotropic constants of concrete.

III. GEOMETRY

Fig. 1(a): Single Axle –Edge Loading

A model as shown in Figure 2, having same width and length but three different thicknesses (Table 2), has been analysed using ANSYS Workbench 15.0.

Boundary Box Length X Length Y Length Z 350 cm 350 cm 25 cm Model 1 350 cm 350 cm 30 cm Model 2 350 cm 350 cm 35 cm Model 3 Table 2: Geometry Details

Fig. 2(b) Single Axle –Interior Loading

Fig. 1(c): Double Axle – Edge Loading

Fig 2: Model in the Coordinate Plane

All rights reserved by www.ijsrd.com

355

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

IV. LOADING PATTERN Each of above three stated model (varying thickness 25/30/35 cm) is subjected to four kinds of loading patterns, as shown in Figure-3 those are  Single Axle Edge Loading  Single Axle Interior Loading  Tandem Axle Edge Loading  Tandem Axle Interior Loading So, in total twelve models have been analysed based on thickness and Loading.

The average spacing of tandem axle is taken to be 130 cm; effective spacing from the corner in the case of centre loading is 70 cm in X direction. All the models are square shaped.

Tandem axle is carrying the load of 19 Tons and that for Single Axle is 10.2 Tons.

Fig. 3(d): Double Axle –Edge Loading Fig 3: Models – Loading Patterns with Dimensions All Loadings are generated by using Named Selection method in ANSYS R15.0; Loads are Nodal loads, lies in Z – Plane and acting on Plate (Pavement) which is in X-Y plane.

Load value is equally distributed to all nodes in each case.

V. SUPPORT CONDITION All models are taken to be fixed in X-Y plane by their lower Face only, a static structural fixed support is shown in Figure 4; it resembles the concrete pavement on sub-base layer.

Fig. 3(a): Single Axle – Interior Loading

Fig 4: Static Structural Fixed Support In X-Y Plane VI. FINITE ELEMENT MODELLING Fig. 3(b): Single Axle –Edge Loading

Fig. 3(c): Double Axle –Interior Loading

Default preference is mechanical and Relevance as 40, Fine relevance centre, medium smoothing and fast transition are used for meshing, in all models, element size is 5 cm.

In Table 3, total numbers of element and node formed after meshing is given for all varying thickness of the model. A typical FE model is shown in Figure 5, FE analyses has been carried out using ANSYS15.0

Fig 5: Finite Element Meshing Of Model

All rights reserved by www.ijsrd.com

356

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

Thickness 25 cm 30 cm 35 cm 24500 29400 34300 Elements 115091 135113 155135 Nodes SIZE OF THE ELEMENT 5 Cm Element Type - Hexahedron Table 3: Element Specifications VII. RESULTS Using Finite element Simulation a comparative study of models with varying thickness, have been performed for following parameters. Results are stated in tabular as well as in the form of Bar charts. Results are discussed under following heads –  Maximum Equivalent Stress (Von Mises Stress)  Maximum Shear Stress  Maximum Principle Stress  Maximum Total Deformation  Maximum Deformation in Z- axis  Maximum Shear Elastic Deformation A. Maximum Equivalent Stress (von Mises Stress) A contour of maximum equivalent stress or von Mises stress formed for single axle, interior loading to the model having 25 cm thickness, is shown in Figure 6. For the different thickness and loading type, comparative results are shown through bar charts, in Figure 7 and Figure 8.

Two different bar charts have been prepared for two different kind of loading positions, interiorloading and edge loading. This can be seen in the results that maximum equivalent stress in the case of corner loading is 0.55 % more than that in centre loading case for both single axle as well as tandem axle.

Fig. 6: Contour of Maximum Equivalent Stress For Single Axle Interior Loading

Fig 7: Maximum Equivalent Stress in Single Axle Loading For Different Thicknesses Models

Fig 8: Maximum Equivalent Stress In Tandem Axle Loading For Different Thicknesses Models B. Maximum Shear Stress A contour of maximum shear stress formed for single axle, centre loading to the model having 25 cm thickness, is shown in Figure 9.

For the different thickness and loading type, comparative results are shown through bar charts, in Figure 10 and Figure 11.

Two different bar charts have been prepared for two different kind of loading positions, centre loading and corner loading.

It can be seen in the results that maximum shear stress in the case of corner loading is 1.26 % more than that in centre loading case for both single axle as well as tandem axle.

Fig 9: Contour of Maximum Shear Stress for Single Axle Centre Loading

Fig 10: Maximum Shear Stress in Single Axle Loading For Different Thicknesses Models

All rights reserved by www.ijsrd.com

357

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

Fig 11: Maximum Shear Stress In Tandem Axle Loading For Different Thicknesses Models C. Maximum Principle Stress A contour for maximum principle stress formed for single axle, centre loading to the model having 25 cm thickness, is shown in Figure 12.

For the different thickness and loading type, comparative results are shown through bar charts, in Figure 13 and Figure 14.

Two different bar charts have been prepared for two different kind of loading positions, centre loading and corner loading.

Maximum principle stress in the case of corner loading is 4.61 % more than that in centre loading case for both single axle as well as tandem axle.

Fig 12: Contour Of Maximum Principle Stress For Single Axle Interior Loading

Fig 13: Maximum Principle Stress In Single Axle Loading For Different Thickness Models

Fig 14: Maximum Principle Stress In Tandem Axle Loading For Different Thickness Models D. Maximum Total Deformation Contour of maximum total deformation formed for single axle, centre loading to the model having 25 cm thickness, is shown in Figure 15 For the different thickness and loading type, comparative results are shown through bar charts, in Figure 16 and Figure 17 Two different bar charts have been prepared for two different kind of loading positions, centre loading and corner loading.

Maximum total deformation in the case of corner loading is 1.25 % more than that in centre loading case for both single axle as well as tandem axle.

Fig 15: Contour Of Maximum Total Deformation For Single Axle Interior Loading

Fig 16: Maximum Total Deformation In Single Axle Loading For Different Thickness Models

All rights reserved by www.ijsrd.com

358

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

Fig 17: Maximum Total Deformation in Tandem Axle Loading For Different Thickness Models

Fig 20: Maximum Deformation in Z-Axis for Tandem Axle Loading For Different Thickness Models

E. Maximum Deformation in Z- Axis Contour for maximum deformation in Z-Axis for single axle, centre loading to the model having 25 cm thickness, is shown in Figure 18 For the different thickness and loading type, comparative results are shown through bar charts, in Figure 19 and Figure 20 Two different bar charts have been prepared for two different kind of loading positions, centre loading and corner loading.

Maximum deformation in z-axis in the case of corner loading is 1.24 % more than that in centre loading case for both single axle as well as tandem axle.

F. Maximum Shear Elastic Deformation Contour for maximum shear deformation formed for single axle, centre loading to the model having 25 cm thickness, is shown in Figure 21.

For the different thickness and loading type, comparative results are shown through bar charts, in Figure 22 and Figure 23.

Two different bar charts have been prepared for two different kind of loading positions, centre loading and corner loading.

Maximum shear elastic deformation in the case of corner loading is 1.26 % more than that in centre loading case for both single axle as well as tandem axle.

Fig 18: Contour Of Maximum Deformation In Z-Axis For Single Axle Interior Loading

Fig 21: Contour Of Maximum Shear Elastic Deformation For Single Axle Interior Loading

Fig 19: Contour Of Maximum Deformation In Z-Axis For Single Axle Loading For Different Thickness Models

Fig 22: Maximum Shear Elastic Deformation In Single Axle Loading For Different Thickness Models

All rights reserved by www.ijsrd.com

359

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

Different values of stress ratio are provided in Table 4 which is taken from the Table 6 of IRC: 58 – 2002.

It is based on Miner’s Hypothesis.

TABLE STRESS RATIO AND ALLOWABLE REPETITION IN CEMENT CONCRETE, IRC:58-2002 Stress Allowable Stress Allowable Ratio Repetitions Ratio Repetitions 0.45 6.28E+07 0.66 5.83E+03 0.46 1.43E+07 0.67 4.41E+03

Fig 23: Maximum Shear Elastic Deformation In Single Axle Loading For Different Thickness Models VIII. DESIGN FOR FATIGUE Due to repeated application of flexural stresses by the traffic loads, progressive fatigue damage takes place in the concrete slab in the form of gradual development of microcracks especially when the applied stress in the terms of flexural strength of concrete is high.

Traffic loadings cause Flexural stress and the ratio of flexural stress to the flexural strength of concrete is termed as Stress Ratio (SR).

As stated in IRC: 58-2002, if Stress Ratio is less than 0.45, infinite numbers of repetitions are allowed.

With increase in Stress Ratio, the number of repetitions required to cause cracking decreases. Relations are also given in IRC: 58-2002, between Fatigue Life (N) and stress ratio, those are,

0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55

5.20E+06 2.40E+06 1.29E+06 7.62E+05 4.85E+05 3.26E+05 2.29E+05 1.66E+05 1.24E+05

0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76

3.34E+03 2.53E+03 1.97E+03 1.45E+03 1.10E+03 8.32E+02 6.30E+02 4.77E+02 3.61E+02

0.56

9.41E+04

0.77

2.74E+02

0.57

7.21E+04

0.78

2.07E+02

0.58

5.40E+04

0.79

1.57E+02

0.59

4.08E+04

0.8

1.19E+02

0.6

3.09E+04

0.81

9.00E+01

0.61

2.34E+04

0.82

6.80E+01

0.62 0.63 0.64 0.65

1.77E+04 0.83 5.20E+01 1.34E+04 0.84 3.90E+01 1.02E+04 0.85 3.00E+01 7.70E+03 Table 4: Codal Provision Further in Table 5 stress ratio is calculated as ratio of maximum equivalent stress or von Mises stress to the characteristic strength of concrete. Table 5 has the interpolated values by using the Table 4, Grade of the concrete, M30 is taken in account.

Equivalent Stress Ratio Allowable Repetitions M30 Grade of Concrete 25 30 35 25 30 35 25 30 35 19.963 19.9 19.9 0.665 0.665 0.665 5058.5 5134 5186 Single Axle Centre Loading 20.071 20.1 20 0.669 0.669 0.668 4547.3 4618 4666 Single Axle Corner Loading Tandem Axle Centre Loading 18.593 18.6 18.6 0.62 0.619 0.619 17833 18118 18308 Tandem Axle Corner Loading 18.693 18.7 18.7 0.623 0.623 0.622 16367 16553 16697 Table 5: Interpolated Values of Allowable Repetitions Table 6: Percentage Increment in Parameters While Moving IX. CONCLUSIONS From Interior Loading To Edge Loading A clear result can be acquired from the all above On the basis of loading pattern, loading position and contours and bar charts that effects in the case of tandem thickness in total twelve different models have been axle loading are more adverse than in single axle loading analysed for six parameters, maximum equivalent stress, case. maximum shear stress, maximum principle stress, maximum Furthermore, on changing the loading positions total deformation, maximum directional deformation and from interior loading to edge loading in both above stated maximum shear elastic deformation. cases, all six parameters get increased by some amount of Percentage Increment Parameters percentage, provided in Table 6.

0.55 Max Equivalent Stress Allowable repetitions are calculated for M30 1.26 Max Shear Stress grade of concrete by using the ratio of maximum 4.61 Max Principle Stress equivalent stress and characteristic strength of concrete, by 1.25 Max Total Deformation using the same procedure, allowable repetitions for different 1.24 Max Directional Deformation 1.26 Max Shear Elastic Deformation

All rights reserved by www.ijsrd.com

360

Fatigue Behavior of Cement Concrete Pavement under Single and Tandem Axle Load using F.E.M (IJSRD/Vol. 3/Issue 08/2015/090)

grade of concrete can be calculated and can be used in various field design problems directly.

REFERENCES [1] Indian Road Congress 2002, “Guidelines for the Design of Plain Jointed Rigid Pavements for Highways”. IRC: 58 – 2002, Second Revision.

[2] ANSYS® Academic Research, Release 15.0, WorkBench, Help System, Design Modeler User's Guide, ANSYS, Inc. [3] Timoshenko, SM. and Gere, J.M., Theory of Elastic Stability, McGraw-Hill Book Co., New York, 1961 [4] Weaver, Jr., W. And Johnson, P.R. (1984).

Finite Elements for Structural Analysis, PrenticeHall, Englewood Cliffs, New Jersey [5] Zienkiewicz, O. C., and Y. K. Cheung, “Finite Element Solution of Field Problems”, The Engineer, pp. 507510, September 1965.

[6] S.S. Bhavikatti, Finite Element Analysis, New Age International (P) Limited , 200 [7] S.M.A. Kazimi, Solid Mechanics. Pp. 450, Tata McGraw-Hill Publishing Co. Ltd., New Delhi, 1976

All rights reserved by www.ijsrd.com

361