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Keywords: pavement analysis, flexible pavement, finite element, cyclic loading, nonlinear, ABAQUS, permanent strain, rut depth, design chart.

Summary

Presently used mechanistic methods in the analysis of layered pavement systems employ either multi-layer elastic theory or finite element theory. Various computer programs have been developed as tools for those methods. In most mechanistic methods, the pavement layers are considered as homogeneous, isotropic and linear elastic, and the loading is considered as static. However, few programs have been developed to incorporate nonlinear, and/or anisotropic materials, dynamic or cyclic loading and the particulate structure of granular materials. These computer programs are very useful for pavement engineers who design pavements for complex loading situations with modified materials, whereas those who design pavements for standard loading conditions with specified materials would not necessarily use such complex methods. To make the design procedure easier, a research is being undertaken to develop a design chart for the design of flexible pavements. In developing this design chart, output results from a finite element computer code ABAQUS/Standard [1] is used, while the pavement structure is modelled as a finite element model, materials are modelled as linear elastic and nonlinear and the loading is considered as cyclic loading in the input data to the computer code.

A pavement structure with a thin bituminous surfacing, a granular base and a subgrade is modelled as a finite element model. Half of standard axle is considered in the current analysis. The pavement structure is assumed to be a three metre cube. Due to symmetry of the pavement structure only quarter of the cube is considered. The 40 kN load in half of standard axle is transferred to the road pavement through dual wheels inflated to a pressure of 750 kPa [2]. The contact area between tyre and pavement surface is assumed as a rectangle as suggested by Huang [3], having an area of 0.5227L² and a width of 0.6L. $\left[ L=\sqrt{20/(750\times0.5227)}=0.225m \right]$ . This area is subjected to a cyclic step loading having a cycle time of 0.5 secs and an amplitude equal to 750 kPa during the finite element analysis. The asphalt and granular base layers are modelled as linear elastic. In estimating the linear elastic properties of pavement materials road guides AASHTO [4] and Austroads [2] are used. The subgrade is modelled as a nonlinear inelastic material. The Mohr-Coulomb failure criterion is used in modelling the nonlinearity of subgrade. The angle of friction $\phi$ , the angle of dilation $\psi$ and an isotropic hardening curve are required when modelling a material with Mohr-Coulomb criterion. The angles of $\phi$ and $\psi$ are assumed as for a normal clayey soil. In the absence of an isotropic hardening curve the available literature is applied to develop a typical curve suitable for subgrade material. The curves given in [5], showing the relationships of stresses and strains for typical clays, greatly helped in developing the hardening curve. The finite element analysis is carried out stage by stage, increasing the initial stresses given to subgrade elements before submitting the problem for analysis. The displacements at critical points are calculated from each analysis. The initial stresses given to subgrade elements are related to strains by the developed hardening curve. The relationships between strains (permanent strain) and the number of stress cycles given in [6] are used in selecting a suitable relationship between strain and number of load applications, for the subgrade material. The maximum displacement at a point on the surface directly under the load is calculated from each analysis. The maximum displacement (rut depth) versus number of load applications is plotted in log scale. A curve is drawn to establish the relationship between rut depth and number of load applications. Similar curves are drawn changing the thickness of granular base layer. The number of load applications required to produce a 25mm rut depth are estimated from theses curves, and are used in preparing the design chart.

The developed isotropic hardening curve, and the relationships used between strain and number of load applications are verified by carrying out the analysis for a pavement structure where ALF (Accelerated Loading Facility) trials have been carried out [7]. The displacements (rut depths) versus number of load applications plotted with calculated values and field values are found to be in agreement.

References

1: "ABAQUS Version 6.2, User's Manual", Hibbit, Karlson, Sorenson, Inc., Pawtucket, USA, 2001.
2: "Pavement Design - A guide to the structural design of road pavements", Austroads, Sydney, 1992.
3: H.Y. Huang, "Pavement Analysis and Design", Prentice-Hall Inc., 1993.
4: "AASHTO Guide to Design of Pavement Structures", American Association of State Highway and Transportation Officials, Washington D.C., 1993.
5: K. Terzaghi and R.B. Peck, "Soil Mechanics in Engineering Practice", John Wiley and Sons Inc., USA, 1967.
6: S.F. Brown, "Repeated Load Testing of a granular material", Journal of the Geotechnical Engineering Division, ASCE July publications, 825-841, 1974. doi:10.1016/0148-9062(74)90618-4
7: P. Kadar, "The Performance of Overlay Treatments and Modified Binders Under Accelerated Full-Scale Loading - The Callington ALF trial", Research Report ARR198, Australian Road Research Board, Victoria, Australia, 1991.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 77 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping Paper 26 A Design Chart for the Design of Flexible Pavements Based on Finite Elements B.C. Bodhinayake and M.N.S. Hadi Faculty of Engineering, University of Wollongong, Australia doi:10.4203/ccp.77.26 purchase the full-text of this paper Full Bibliographic Reference for this paper B.C. Bodhinayake, M.N.S. Hadi, "A Design Chart for the Design of Flexible Pavements Based on Finite Elements", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 26, 2003. doi:10.4203/ccp.77.26 Keywords: pavement analysis, flexible pavement, finite element, cyclic loading, nonlinear, ABAQUS, permanent strain, rut depth, design chart. Summary Presently used mechanistic methods in the analysis of layered pavement systems employ either multi-layer elastic theory or finite element theory. Various computer programs have been developed as tools for those methods. In most mechanistic methods, the pavement layers are considered as homogeneous, isotropic and linear elastic, and the loading is considered as static. However, few programs have been developed to incorporate nonlinear, and/or anisotropic materials, dynamic or cyclic loading and the particulate structure of granular materials. These computer programs are very useful for pavement engineers who design pavements for complex loading situations with modified materials, whereas those who design pavements for standard loading conditions with specified materials would not necessarily use such complex methods. To make the design procedure easier, a research is being undertaken to develop a design chart for the design of flexible pavements. In developing this design chart, output results from a finite element computer code ABAQUS/Standard [1] is used, while the pavement structure is modelled as a finite element model, materials are modelled as linear elastic and nonlinear and the loading is considered as cyclic loading in the input data to the computer code. A pavement structure with a thin bituminous surfacing, a granular base and a subgrade is modelled as a finite element model. Half of standard axle is considered in the current analysis. The pavement structure is assumed to be a three metre cube. Due to symmetry of the pavement structure only quarter of the cube is considered. The 40 kN load in half of standard axle is transferred to the road pavement through dual wheels inflated to a pressure of 750 kPa [2]. The contact area between tyre and pavement surface is assumed as a rectangle as suggested by Huang [3], having an area of 0.5227L² and a width of 0.6L. $\left[ L=\sqrt{20/(750\times0.5227)}=0.225m \right]$ . This area is subjected to a cyclic step loading having a cycle time of 0.5 secs and an amplitude equal to 750 kPa during the finite element analysis. The asphalt and granular base layers are modelled as linear elastic. In estimating the linear elastic properties of pavement materials road guides AASHTO [4] and Austroads [2] are used. The subgrade is modelled as a nonlinear inelastic material. The Mohr-Coulomb failure criterion is used in modelling the nonlinearity of subgrade. The angle of friction $\phi$ , the angle of dilation $\psi$ and an isotropic hardening curve are required when modelling a material with Mohr-Coulomb criterion. The angles of $\phi$ and $\psi$ are assumed as for a normal clayey soil. In the absence of an isotropic hardening curve the available literature is applied to develop a typical curve suitable for subgrade material. The curves given in [5], showing the relationships of stresses and strains for typical clays, greatly helped in developing the hardening curve. The finite element analysis is carried out stage by stage, increasing the initial stresses given to subgrade elements before submitting the problem for analysis. The displacements at critical points are calculated from each analysis. The initial stresses given to subgrade elements are related to strains by the developed hardening curve. The relationships between strains (permanent strain) and the number of stress cycles given in [6] are used in selecting a suitable relationship between strain and number of load applications, for the subgrade material. The maximum displacement at a point on the surface directly under the load is calculated from each analysis. The maximum displacement (rut depth) versus number of load applications is plotted in log scale. A curve is drawn to establish the relationship between rut depth and number of load applications. Similar curves are drawn changing the thickness of granular base layer. The number of load applications required to produce a 25mm rut depth are estimated from theses curves, and are used in preparing the design chart. The developed isotropic hardening curve, and the relationships used between strain and number of load applications are verified by carrying out the analysis for a pavement structure where ALF (Accelerated Loading Facility) trials have been carried out [7]. The displacements (rut depths) versus number of load applications plotted with calculated values and field values are found to be in agreement. References 1 "ABAQUS Version 6.2, User's Manual", Hibbit, Karlson, Sorenson, Inc., Pawtucket, USA, 2001. 2 "Pavement Design - A guide to the structural design of road pavements", Austroads, Sydney, 1992. 3 H.Y. Huang, "Pavement Analysis and Design", Prentice-Hall Inc., 1993. 4 "AASHTO Guide to Design of Pavement Structures", American Association of State Highway and Transportation Officials, Washington D.C., 1993. 5 K. Terzaghi and R.B. Peck, "Soil Mechanics in Engineering Practice", John Wiley and Sons Inc., USA, 1967. 6 S.F. Brown, "Repeated Load Testing of a granular material", Journal of the Geotechnical Engineering Division, ASCE July publications, 825-841, 1974. doi:10.1016/0148-9062(74)90618-4 7 P. Kadar, "The Performance of Overlay Treatments and Modified Binders Under Accelerated Full-Scale Loading - The Callington ALF trial", Research Report ARR198, Australian Road Research Board, Victoria, Australia, 1991. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £123 +P&P)
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