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Parameter sensitive analysis of flexible pavement
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ScienceDirect International Journal of Pavement Research and Technology xxx (2016) xxx–xxx www.elsevier.com/locate/IJPRT
Parameter sensitive analysis of flexible pavement M.S. Ranadive, Anand B. Tapase ⇑ Department of Civil Engineering, College of Engineering, Pune, Maharashtra, India Received 21 March 2016; received in revised form 17 October 2016; accepted 2 December 2016
Abstract This paper describes the usefulness of FEM for exploring the parameter sensitive analysis. Using 2D axisymmetric analysis, the critical performance parameters are examined by varying the thickness and material properties of different layers of flexible pavement. Hypothetical pavement sections are also analyzed with a view to check the sensitivity of horizontal axisymmetric extent and refinement of mesh. The developed computer program after validation is used to calculate the horizontal tensile strain at the bottom of the bituminous layer (BL) and the vertical compressive strain at the top of the subgrade. These computed strains are incorporated in the fatigue and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions. Tensile strain at the bottom of BL and compressive strain on top of the subgrade decreases with an increase in the thickness of BL, which results in increase of fatigue and rutting lives. An increase in thickness of the base layer and the increase in its elastic modulus reduces the damage due to rutting, while it has less effect on damage due to fatigue. Such type of analysis proves beneficial for designing a pavement, keeping equilibrium between fatigue and rutting lives. Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Flexible pavement; Parametric study; Finite element method
1. Introduction The application of direct or indirect empirical approach in the current design procedures, results either in premature failure of the pavement or building up of uneconomical pavement sections. The relationship between design inputs and pavement failure is applied through experience, experimentation or a combination of both, which is limited to a certain set of environmental and material conditions [1,2]. A good pavement design is one that provides the expected performance with appropriate economic consideration, so, here the need arises to find an economical alternative in the
⇑ Corresponding author.
E-mail addresses: [email protected] (M.S. Ranadive), [email protected] (A.B. Tapase). Peer review under responsibility of Chinese Society of Pavement Engineering.
form of analytical tool which can accommodate the details of the complex pavement system [3]. Application of such enhanced analytical tool can prove to be beneficial to predict the performance of pavement without actual construction or even by surpassing the expensive and time consuming laboratory or in situ tests, for various thicknesses and material properties of different component layers instead of relying on CBR values. In this connection, the application of the versatile finite element method (FEM) towards the design of flexible pavement holds a perfect assurance. As FEM is not constrained to two dimensional axisymmetric conditions, if required FEA can be easily used for two-dimensional plane stress/ strain as well as more rigorous three dimensional finite element analysis for further extension of work [4]. Axisymmetric modeling predicts pavement behavior using a 2D mesh revolving around a symmetric axis by assuming identical stress states exist in every radial direction; therefore, loading is circular [5].
http://dx.doi.org/10.1016/j.ijprt.2016.12.001 1996-6814/Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
Figs. 1 and 2 summarizes many of the finite element parameters and should be referenced throughout the paper. Fatigue and rutting are generally assumed as two independent modes of distresses which can be analytically evaluated [6]. If the horizontal tensile strain at the bottom of the bituminous layer (Point P as shown in Fig. 1) is excessive, cracking of the surface layer will occur, and the pavement distresses due to fatigue. If the vertical compressive
Fig. 1. Flexible pavement composition showing critical line and its material properties.
strain on top of the subgrade (Point Q as shown in Fig. 1) is excessive, permanent deformation occurs on the surface in the pavement structure, and the pavement distresses due to rutting. Present analysis is performed considering the tyre pavement interaction as an axisymmetric solid to mechanistically solve the layered pavement response to variation in material properties of different component layers, variation in thickness, considering any point on the critical line as a center[7]. The obtained results are then incorporated as input to estimate the pavement life in terms of rutting and fatigue lives in number of standard axles. The major objective of the paper is to illustrate the usefulness of finite element analysis for examining the effect of variation in thickness and material properties of critical parameters, especially on rutting and fatigue lives, with a view to develop a design chart for particular condition which correlates with actual field condition. If such type of analysis is validated, it will prove to be beneficial to derive useful design charts for any combinations of thicknesses, material properties and field conditions without relying on theoretical/empirical design procedures. The hypothetical thicknesses and material properties which are considered for analysis are generally used in practice as per IRC: 37-2012 [8]; hence it is an attempt to correlate the present study with actual field conditions. An equilibrium between fatigue and rutting lives can be achieved from such type of analysis.
Fig. 2. Pavement section showing critical line and hypothetical idealization. Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
2. Literature review Number of literatures have reported the use of an axisymmetric configuration like Abdhesh et al. [9], Issac et al. [5], Helwany et al. [10], Tutumluer et al. [11], Ranadive et al. [12]. Cho et al. [13] favored axisymmetric analysis for simulating pavement from a comparative study of 3 dimensional, plane-strain, and axisymmetric modeling structure and traffic loading interaction. Immanuel and Timm (2006) [14] used layered elastic analysis to compare predicted vertical stress in the base and subgrade layers to field measured vertical pressures obtained from the National Center for Asphalt Technology (NCAT) Test Track. The authors found that the predicted pressure was only a reasonable approximation up to vertical pressures of 82 kPa in the base and 48 kPa in the subgrade. The IRC: 37-2012 [8] Guidelines for the design of flexible pavement recommends using the IITPAVE, which is a modified version of FPAVE developed under the research scheme R-56 for layered system analysis. Sam Helwany et al. [10], illustrates the usefulness of finite element method by discretising a three layer pavement system with the right boundary at a distance of about 8 times the loaded radius subjected to different types of loading. The author carried out two dimensional and three dimensional analyses. In this analysis three layers were assigned the same elastic moduli, transforming the three systems into a simpler one layer system. Ranadive et al. [15] illustrates that axisymmetric analysis of flexible pavement is carried out by a computer program (ANSYS), and different performance parameters of pavement were studied for varying conditions of thickness. Increase in thickness of the base course and sub-base course layer does not help to reduce stress and deflection as compared to asphalt concrete layer in which it is observed that there is a substantial reduction in stress as there is an increase in thickness of asphalt concrete. Abdhesh K. Sinha et al. [9] Illustrates the usefulness of finite element method to study the performance of a flexible pavement with different types of local materials in its subbase. Three types of naturally occurring materials, namely; coarse sand, conventional subbase material, stone dust and four types of industrial waste materials; Blast furnace slag, granulated blast furnace slag, Linz-Donawitz slag and fly ash were used. In this work multilinear elasto-plastic hardening model in Ansys was used and the effect of the type of subbase on life of the pavement is evaluated. In the study, right boundary was placed at 1100 mm from the outer edge of loaded area, which is more than 7 times the radius 150 mm of the applied load. A uniform pressure of 0.575 MPa (575 kPa) was applied to a circular contact area having a radius of 150 mm causing a single axle load of 40.80 KN. Tapase and Ranadive [16], reported the usefulness of two dimensional finite element analysis to study the effect of variation in thickness of different component layers on
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the critical parameters. They noted that the tensile strain at the bottom of the bituminous layer (BL) and compressive strain on top of the subgrade decreases with an increase in the thickness of BL, which ultimately results in increase of fatigue and rutting lives. In continuation with the investigation related to varying the thickness and material properties of different layers reported in Tapase and Ranadive [16], this paper reports the usefulness of finite element analysis for exploring the parameter sensitive analysis of flexible pavement. A part of the analysis is to check the sensitivity of horizontal axisymmetric extent for the hypothetical trials. Also, the mesh refinement study of the selected thicknesses and material properties of different layers is conducted. 3. Model geometry and material characteristics Depending on different material constituents of individual layers, the layers posses varied strength characteristics, and this information is used as the input for analysis. The function of granular base and sub base (many times considered as a single granular layer for analysis) is to reduce traffic induced stresses in the pavement structure and to minimize the intensities of rutting. In the present study, a conventional pavement section as per IRC:37-2012 consisting of bituminous layer and single granular layer which together are constructed over the subgrade soil as shown in Fig. 1 are considered for analysis. To study the effect of varying thickness of the bituminous layer (h1) and the base layer (h2) on critical parameters, in all four trial thicknesses of the bituminous layer as explained in Fig. 1 and three trials of granular base layer thicknesses starting from 300 mm with an increment of 150 mm for each trial is considered for analysis. Similarly, to study the effect of variation in material property of base layer on the rutting and fatigue lives, three naturally occurring materials like natural gravel, E2 = 100 MPa, 300 MPa and high quality graded crushed rock, E2 = 450 MPa are considered in base layer for analysis keeping Poisson’s ratio l2 = 0.35 constant for each trial. In the present study, a uniform pressure of 0.575 MPa (575 kPa) caused by a single axle wheel load of 40.80 KN [8,9] is applied on a circular contact area having a radius of 150 mm as shown in Figs. 1 and 2. All the above trials are checked for their suitability in the pavement section for selected bituminous layer material (modulus of bituminous mix is taken as E1 = 1700 MPa and Poisson’s ratio (l1 = 0.35) and subgrade condition E3 = 80 MPa [17]. 4. Finite element modeling In general the finite element solution technique is adopted through three basic stages of the analysis; those are idealization of the system being investigated, formulation and solution of equations governing the phenomenon and evaluation of the structural response required for
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
undertaking the design process as reported by Tapase and Ranadive [16]. Basically, constitutive laws in the present development are confined towards consideration to only modulus of elasticity and the Poisson’s ratio of the materials used in the pavement system being analyzed is presented in Fig. 1.
5. Finite element idealization Wherever examination is necessary about soil structure interaction problem, the required structure in modeled. It is well known fact that the area away from the load intensity is not affected much. However, the question arises about exactly upto what extent the parameters are sensitive to the intensity of loading. Sam Helwany et al. [10], discretized a three layer pavement system with the right boundary at a distance of about 8 times the loaded radius. Abdhesh K. Sinha et al. [9] located the right boundary of which is more than 7 times the radius 150 mm of the applied load. One way of evaluating the effect of loading is, to start with certain assumed extent and determine the critical parameters. Then increase or decrease the extent, analyse and compare the obtained results with an earlier one. This type of preliminary sensitive study helps in identifying the more accurate area for analysis. In respect to this, a trial horizontal axisymmetric extent of finite element idealization is considered for analysis from 5 times the radius to 8 times the radius. On the other hand, accuracy of calculation increases if higher order elements or more number of elements is used during analysis. There was a time when limitation on the use of a number of elements comes from the total degrees of freedom the computer can handle and the cost of computation time required. However, the cost of the calculation is coming down so much that such limitations are not relevant today. Accuracy is the only criteria left due to the modern high speed techniques used today. In the present study, the finite element idealization for the pave-
ment system being analyzed is developed by means of the four noded quadrilateral elements. A very fine mesh near the load that becomes progressively coarser with distance from the load is commonly observed in the literature, the same phenomenon is used during the analysis also the aspect ratio is maintained as close as possible to the specified limits. In order to study the effect of refinement of mesh, few hypothetical separate meshes are developed and analyzed for a typical pavement structure as shown in Figs. 1 and 2, consisting of 200 mm of the bituminous layer (E = 1700 MPa, l = 0.35) over 450 mm of granular base (E = 3000 MPa, l = 0.35) over a subgrade (E = 1000 MPa, l = 0.3). A single wheel load was modeled as a uniform pressure of 0.575 MPa (575 kPa) over a circular area of 150 mm radius. A very coarse refinement mesh consisting of 12 elements, with a smallest element size of 150 mm by 200 mm. Four elements spanned the thickness of the bituminous layer, four elements spanned the thickness of the base layer and four elements spanned the thickness of the sub grade layer. A medium refinement mesh consisting of a 96 elements, with a smallest element size of 75 mm by 50 mm. A very fine refinement mesh consisting of 210 elements, with a smallest element size of 50 mm by 25 mm (Fig. 3). Intermediately numbers of hypothetical meshes are studied during analysis. In the present work, the total thickness of the pavement is taken as 1300 mm to 1750 mm as per the trials described in Figs. 1 and 2 with constant thickness of 900 mm for the subgrade. 6. Boundary conditions The nodes over the base of the subgrade i.e., at depth of more than eight times the radius of circular contact area are restrained in both radial (r) and axial (z) directions. The nodes over the axis of symmetry are restrained in radial direction. Considering preliminary sensitive study to identify how much horizontal axisymmetric extent should be used for analysis, four trial extents of finite element idealization are considered starting from assuming
Fig. 3. Comparison of vertical stresses of finite element analysis with Ansys results. Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
5 times the radius to 8 times the radius. Also, it is assumed that, due to the indefinite lateral extent of the pavement section, the nodes over the extreme vertical face of the pavement from the centerline of the wheel loading [2,9]; do not suffer radial displacements. Hence those nodes are treated as restrained in the radial (r) direction for each trail [18]. By employing the interpolation characteristics of the elements, the modulus of elasticity and the Poisson’s ratio at the element nodes are extrapolated by using their respective values at the Gauss integration points. Finally after employing direct averaging technique, the strains and stresses at the nodes of the idealized system are established. The nodal displacements provide information regarding the deflection suffered, which in turn helps in analyzing the phenomenon of rutting.
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the allowable limit 178 10 06 and the computed vertical compressive strain on subgrade is 127 10 06 which is also found well within the allowable limits which is 370 10 06. From the obtained results, it is observed that the pavement composition is safe for the selected trial ultimately validating the current analytical process. A sensitivity analysis conducted to find the influence of the horizontal extent on the model geometry suggests that a length of seven times the radius (Fig. 6) is appropriate and hence is adopted in present study. Also, the surface displacements (Fig. 4) and stress (Fig. 5) for the fine and very fine refinement meshes appears to be coinciding and seems to be virtually identical, so fine mesh is selected for analysis. Effect of variation in thickness of the base layer, BL and use of different materials in base layer on conventionally critical parameters like the horizontal tensile strains at
7. Results and discussion A preliminary analysis is conducted to verify the correctness of the FEA. For the same, the three layers are assigned the same elastic moduli, transforming the three layer system into simpler one layer system. The obtained results of the FEA are checked against the Boussinesq close form solution which is readily available for uniform circular pressure and also compared with the results obtained through the general purpose software Ansys as presented in Fig. 3. The obtained results are coinciding with the results of Boussinesq’s close form solution, which is validating the developed program. Secondly, validation of present finite element analysis is done against IRC: 37-2012 pavement design plate/chart. Available data from IRC: 37-2012 for plate 8 (CBR 15%) with 150 msa is analysed with the program used in present analysis and results are compared with the allowable limits set by the guidelines for the design charts. The computed horizontal tensile strain in bituminous layer is 161 10 06 which is less than
Fig. 4. Surface displacements computed at different mesh refinement.
Fig. 5. Horizontal stresses along centreline at different mesh refinement.
Fig. 6. Surface displacements computed for different hypothetical horizontal extent.
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
the bottom of BL and the vertical compressive strain at the top of the subgrade is observed and interpreted. For the selected subgrade condition, the values of horizontal tensile strain at the bottom of BL for E2 = 100 MPa, l = 0.35 as a hypothetical base material, is exceeding the allowable limit at all trial thicknesses. At every base thickness, it is observed that E2 = 300 MPa, l = 0.35 and E2 = 450 MPa, l = 0.35 as a trial base material, show values of all critical parameters well within the allowable limit as per IRC: 37-2012. When a material property of base course varies from E2 = 100 MPa, l = 0.35 to E2 = 300 MPa, l = 0.35 more than 20 percent reduction in vertical displacement is noticed, wherein from E2 = 300 MPa, l = 0.35 to E2 = 450 MPa, l = 0.35 not even a 2 percent reduction in vertical displacement is observed. At every trial increase in the thickness of the base layer and its elastic modulus, a gradual decrease in vertical compressive strain is noticed at the top of selected subgrade. For the selected subgrade condition and constant base thickness (450 mm), variation in thickness of BL for three trial base layer material properties is analyzed. From Fig. 6, it is observed that the value of horizontal tensile strain for E2 = 300 MPa, l = 0.35 and for E2 = 450 MPa, 0.35 is safe at 200 mm and 250 mm thickness of bituminous layer. Also, it is obvious from the Fig. 7, that 100 mm and 150 mm thickness of BL are not safe for the selected trials. At every base thickness, it is observed that E2 = 450 MPa, l = 0.35 shows the values of horizontal tensile strain within the allowable limit, also vertical compressive strain is within the safe limit for all trials except at base E2 = 100 MPa and 100 mm BL thickness. The computed strains are taken as input and are incorporated in the fatigue and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions.
Fig. 7. Effect of BL thickness on horizontal tensile strain at bottom of BL.
7.1. Fatigue criterion As per the guidelines for the design of flexible pavements (IRC: 37-2012), Fatigue criterion for 80 percent reliability level is considered for analysis. The obtained results for horizontal tensile strain at bottom of bituminous layer is incorporated in fatigue criteria to calculate the fatigue life in terms of number of standard axles. The fatigue cracking of flexible pavements is based on the horizontal tensile strain at the bottom of BL. On this criterion, the allowable number of load repetitions that causes fatigue cracking is related to the tensile strain at the bottom of BL. Fig. 8 gives a graphical presentation of fatigue life in a number of standard axles on y-axis versus the thickness of the bituminous layer on x-axis for all trail base material. 7.2. Rutting criterion As per the guidelines for the design of flexible pavements (IRC: 37-2012), rutting criterion for controlling rutting in the subgrade and granular layers is considered for analysis. The obtained results for vertical compressive strain at top of subgrade is incorporated in rutting criteria as inputs to calculate the ruttin life in terms of number of cumulative standard axles. Fig. 9 gives a graphical presentation of a number of cumulative standard axles on y-axis versus the thickness of the bituminous layer on x-axis for all trail base material. 8. Conclusions and recommendations It is observed that number of rutting cycles increase by 4.48% with change in thickness of base layer from 300 mm to 450 mm. However, the same increase is only 2.47% when the change in thickness is from 450 mm to
Fig. 8. Fatigue life in number of standard axles Vs thickness of bituminous layer.
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
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References
Fig. 9. Number of cumulative standard axles Vs thickness of bituminous layer.
600 mm. From the observations, it is concluded that the increase in thickness of the base layer and increase in its elastic modulus reduces the damage due to rutting, while it has less effect on damage due to fatigue. Also, the number of fatigue cycles increase by 5.13% due to variation of elastic modulus of base layer from 100 MPa to 300 MPa. However, beyond 300 MPa, its effect is least. Hence, the increase in the elastic modulus of base layer reduces damage due to fatigue. From the selected trials for base materials and base thicknesses, use of 300 MPa material and 450 mm thickness of the base layer is suitable at the selected subgrade condition. Here it is clear that 100 mm and 150 mm thickness of bituminous layer is not safe for the selected trials. The value of tensile strain at the bottom of BL for E2 = 300 MPa, l = 0.35 and E2 = 450 MPa, l = 0.35 is under the allowable limit at 200 mm and 250 mm thickness of bituminous layer for the selected subgrade condition. At every base thickness, it is noticed that high quality graded crushed rock (E2 = 450 MPa, l = 0.35) shows the values of tensile strain at the bottom of BL within the allowable limit, also the value of vertical compressive strain is within the safe limit for all trials except at base E2 = 100 MPa and 100 mm bituminous layer thickness. Horizontal tensile strain at bottom of bituminous layer and vertical compressive strain at top of subgrade is decreased with increase in the thickness of bituminous layer. Increase in bituminous layer thickness reduces the damage due to both rutting and fatigue.
[1] American Association of State Highway and Transportation Officials AASHTO, 1993. AASHTO guide for design of pavement structures, AASHTO, Washington, D.C. [2] Huang H. Yang (Pavement Analysis and Design), second ed., Pearson Education Inc, and Dorling Kindersley Publishing Inc, 2008. [3] M.S. Ranadive, A.B. Tapase, Investigation of Behavioral Aspects of Flexible Pavement Under Various Conditions by Finite Element Method, Constitutive modeling of geomaterials, Springer-Verlag, Berlin, 2013, pp. 765–770, http://dx.doi.org/10.1007/978-3-64232814-5_100. [4] O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, vol. 2, McGraw Hill, New York, 1991. [5] Issac L. Howard, Kimberly A. Warren, Finite element modeling of Instrumented flexible pavements under stationary transient loading, J. Transp. Eng., ASCE 135 (2) (2009) 53–61, http://dx.doi.org/10.1061/ (ASCE)0733-947X(2009) 135:2(53). [6] Ripunjoy Gogoi, Animesh Das, Partha Chakroborty, Are fatigue and rutting distress modes related?, IJPRT 6 (4) (2013) 269–273 [7] Partha Chakroborty, Animesh Das (Principles of Transportation Engineering), Prentice Hall of India private limited, 2003. [8] IRC: 37-2012. Guidelines for the design of flexible pavements, Indian Roads Congress, New Delhi. [9] Abdhesh K. Sinha, Satish Chandra, Praveen Kumar, Finite element analysis of flexible pavement with different subbase materials, Indian Highways, New Delhi 42 (2) (2014) 53–63. [10] Sam Helwany, John Dyer, Joe leidy (Finite element analysis of flexible pavement), J. Transp. Eng., ASCE 124 (5) (1998) 491–499, http://dx.doi.org/10.1061/(ASCE)0733-947X(1998)124:5(491). [11] E. Tutumluer, D.N. Little, S. Kim, Validated model for predicting field performance of aggregate base courses, Transp. Res. Rec. 1837 (2003) 41–49, Transportation Research Board, Wash-ington, D.C.. [12] M.S. Ranadive, A. Tapase, Pavement Performance Evaluation for Different Combinations of Temperature Conditions and Bituminous Mixes, Innov. Infrastruct. Solut, Springer International Publishing, Switzerland, 2016, http://dx.doi.org/10.1007/s41062-016-0040-9, 1: 40. [13] Y. Cho, B.F. McCullough, J. Weissmann, Considerations on finiteelement method application in pavement structural analysis, Transp. Res. Rec. 1539 (1996) 96–101, Transportation Research Board, Washington, D.C.. [14] S. Immanuel, D.H. Timm, 2006, Measured and theoretical pressures in base and subgrade layers under dynamic truck loading, in: Proc., 2006 Airfield and Highway Pavement Specialty Conference, American Society of Civil Engineers, pp. 155–166. [15] M.S. Ranadive, A.B. Katkar, Finite element analysis of flexible pavements, Indian Highways 38 (6) (2010). [16] Anand Tapase, M.S. Dr. Ranadive, 2016, Performance evaluation of flexible pavement using finite element method, ASCE GSP series 266, Geo-China 2016: Material, Design, Construction, Maintenance and Testing of Pavement, pp. 9–17, http://dx.doi.org/10.1061/ 9780784480090.002. [17] Zeevaert Leonardo (Foundation Engineering for Difficult Subsoil Conditions), second ed., Van Nostrand Reinhold comPany Inc, 1982. [18] NCHRP, Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures, National Cooperative Highway Research Program (NCHRP), Project 1-37A, Washington DC, 2004.
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
ScienceDirect International Journal of Pavement Research and Technology xxx (2016) xxx–xxx www.elsevier.com/locate/IJPRT
Parameter sensitive analysis of flexible pavement M.S. Ranadive, Anand B. Tapase ⇑ Department of Civil Engineering, College of Engineering, Pune, Maharashtra, India Received 21 March 2016; received in revised form 17 October 2016; accepted 2 December 2016
Abstract This paper describes the usefulness of FEM for exploring the parameter sensitive analysis. Using 2D axisymmetric analysis, the critical performance parameters are examined by varying the thickness and material properties of different layers of flexible pavement. Hypothetical pavement sections are also analyzed with a view to check the sensitivity of horizontal axisymmetric extent and refinement of mesh. The developed computer program after validation is used to calculate the horizontal tensile strain at the bottom of the bituminous layer (BL) and the vertical compressive strain at the top of the subgrade. These computed strains are incorporated in the fatigue and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions. Tensile strain at the bottom of BL and compressive strain on top of the subgrade decreases with an increase in the thickness of BL, which results in increase of fatigue and rutting lives. An increase in thickness of the base layer and the increase in its elastic modulus reduces the damage due to rutting, while it has less effect on damage due to fatigue. Such type of analysis proves beneficial for designing a pavement, keeping equilibrium between fatigue and rutting lives. Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Flexible pavement; Parametric study; Finite element method
1. Introduction The application of direct or indirect empirical approach in the current design procedures, results either in premature failure of the pavement or building up of uneconomical pavement sections. The relationship between design inputs and pavement failure is applied through experience, experimentation or a combination of both, which is limited to a certain set of environmental and material conditions [1,2]. A good pavement design is one that provides the expected performance with appropriate economic consideration, so, here the need arises to find an economical alternative in the
⇑ Corresponding author.
E-mail addresses: [email protected] (M.S. Ranadive), [email protected] (A.B. Tapase). Peer review under responsibility of Chinese Society of Pavement Engineering.
form of analytical tool which can accommodate the details of the complex pavement system [3]. Application of such enhanced analytical tool can prove to be beneficial to predict the performance of pavement without actual construction or even by surpassing the expensive and time consuming laboratory or in situ tests, for various thicknesses and material properties of different component layers instead of relying on CBR values. In this connection, the application of the versatile finite element method (FEM) towards the design of flexible pavement holds a perfect assurance. As FEM is not constrained to two dimensional axisymmetric conditions, if required FEA can be easily used for two-dimensional plane stress/ strain as well as more rigorous three dimensional finite element analysis for further extension of work [4]. Axisymmetric modeling predicts pavement behavior using a 2D mesh revolving around a symmetric axis by assuming identical stress states exist in every radial direction; therefore, loading is circular [5].
http://dx.doi.org/10.1016/j.ijprt.2016.12.001 1996-6814/Ó 2016 Chinese Society of Pavement Engineering. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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M.S. Ranadive, A.B. Tapase / International Journal of Pavement Research and Technology xxx (2016) xxx–xxx
Figs. 1 and 2 summarizes many of the finite element parameters and should be referenced throughout the paper. Fatigue and rutting are generally assumed as two independent modes of distresses which can be analytically evaluated [6]. If the horizontal tensile strain at the bottom of the bituminous layer (Point P as shown in Fig. 1) is excessive, cracking of the surface layer will occur, and the pavement distresses due to fatigue. If the vertical compressive
Fig. 1. Flexible pavement composition showing critical line and its material properties.
strain on top of the subgrade (Point Q as shown in Fig. 1) is excessive, permanent deformation occurs on the surface in the pavement structure, and the pavement distresses due to rutting. Present analysis is performed considering the tyre pavement interaction as an axisymmetric solid to mechanistically solve the layered pavement response to variation in material properties of different component layers, variation in thickness, considering any point on the critical line as a center[7]. The obtained results are then incorporated as input to estimate the pavement life in terms of rutting and fatigue lives in number of standard axles. The major objective of the paper is to illustrate the usefulness of finite element analysis for examining the effect of variation in thickness and material properties of critical parameters, especially on rutting and fatigue lives, with a view to develop a design chart for particular condition which correlates with actual field condition. If such type of analysis is validated, it will prove to be beneficial to derive useful design charts for any combinations of thicknesses, material properties and field conditions without relying on theoretical/empirical design procedures. The hypothetical thicknesses and material properties which are considered for analysis are generally used in practice as per IRC: 37-2012 [8]; hence it is an attempt to correlate the present study with actual field conditions. An equilibrium between fatigue and rutting lives can be achieved from such type of analysis.
Fig. 2. Pavement section showing critical line and hypothetical idealization. Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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2. Literature review Number of literatures have reported the use of an axisymmetric configuration like Abdhesh et al. [9], Issac et al. [5], Helwany et al. [10], Tutumluer et al. [11], Ranadive et al. [12]. Cho et al. [13] favored axisymmetric analysis for simulating pavement from a comparative study of 3 dimensional, plane-strain, and axisymmetric modeling structure and traffic loading interaction. Immanuel and Timm (2006) [14] used layered elastic analysis to compare predicted vertical stress in the base and subgrade layers to field measured vertical pressures obtained from the National Center for Asphalt Technology (NCAT) Test Track. The authors found that the predicted pressure was only a reasonable approximation up to vertical pressures of 82 kPa in the base and 48 kPa in the subgrade. The IRC: 37-2012 [8] Guidelines for the design of flexible pavement recommends using the IITPAVE, which is a modified version of FPAVE developed under the research scheme R-56 for layered system analysis. Sam Helwany et al. [10], illustrates the usefulness of finite element method by discretising a three layer pavement system with the right boundary at a distance of about 8 times the loaded radius subjected to different types of loading. The author carried out two dimensional and three dimensional analyses. In this analysis three layers were assigned the same elastic moduli, transforming the three systems into a simpler one layer system. Ranadive et al. [15] illustrates that axisymmetric analysis of flexible pavement is carried out by a computer program (ANSYS), and different performance parameters of pavement were studied for varying conditions of thickness. Increase in thickness of the base course and sub-base course layer does not help to reduce stress and deflection as compared to asphalt concrete layer in which it is observed that there is a substantial reduction in stress as there is an increase in thickness of asphalt concrete. Abdhesh K. Sinha et al. [9] Illustrates the usefulness of finite element method to study the performance of a flexible pavement with different types of local materials in its subbase. Three types of naturally occurring materials, namely; coarse sand, conventional subbase material, stone dust and four types of industrial waste materials; Blast furnace slag, granulated blast furnace slag, Linz-Donawitz slag and fly ash were used. In this work multilinear elasto-plastic hardening model in Ansys was used and the effect of the type of subbase on life of the pavement is evaluated. In the study, right boundary was placed at 1100 mm from the outer edge of loaded area, which is more than 7 times the radius 150 mm of the applied load. A uniform pressure of 0.575 MPa (575 kPa) was applied to a circular contact area having a radius of 150 mm causing a single axle load of 40.80 KN. Tapase and Ranadive [16], reported the usefulness of two dimensional finite element analysis to study the effect of variation in thickness of different component layers on
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the critical parameters. They noted that the tensile strain at the bottom of the bituminous layer (BL) and compressive strain on top of the subgrade decreases with an increase in the thickness of BL, which ultimately results in increase of fatigue and rutting lives. In continuation with the investigation related to varying the thickness and material properties of different layers reported in Tapase and Ranadive [16], this paper reports the usefulness of finite element analysis for exploring the parameter sensitive analysis of flexible pavement. A part of the analysis is to check the sensitivity of horizontal axisymmetric extent for the hypothetical trials. Also, the mesh refinement study of the selected thicknesses and material properties of different layers is conducted. 3. Model geometry and material characteristics Depending on different material constituents of individual layers, the layers posses varied strength characteristics, and this information is used as the input for analysis. The function of granular base and sub base (many times considered as a single granular layer for analysis) is to reduce traffic induced stresses in the pavement structure and to minimize the intensities of rutting. In the present study, a conventional pavement section as per IRC:37-2012 consisting of bituminous layer and single granular layer which together are constructed over the subgrade soil as shown in Fig. 1 are considered for analysis. To study the effect of varying thickness of the bituminous layer (h1) and the base layer (h2) on critical parameters, in all four trial thicknesses of the bituminous layer as explained in Fig. 1 and three trials of granular base layer thicknesses starting from 300 mm with an increment of 150 mm for each trial is considered for analysis. Similarly, to study the effect of variation in material property of base layer on the rutting and fatigue lives, three naturally occurring materials like natural gravel, E2 = 100 MPa, 300 MPa and high quality graded crushed rock, E2 = 450 MPa are considered in base layer for analysis keeping Poisson’s ratio l2 = 0.35 constant for each trial. In the present study, a uniform pressure of 0.575 MPa (575 kPa) caused by a single axle wheel load of 40.80 KN [8,9] is applied on a circular contact area having a radius of 150 mm as shown in Figs. 1 and 2. All the above trials are checked for their suitability in the pavement section for selected bituminous layer material (modulus of bituminous mix is taken as E1 = 1700 MPa and Poisson’s ratio (l1 = 0.35) and subgrade condition E3 = 80 MPa [17]. 4. Finite element modeling In general the finite element solution technique is adopted through three basic stages of the analysis; those are idealization of the system being investigated, formulation and solution of equations governing the phenomenon and evaluation of the structural response required for
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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undertaking the design process as reported by Tapase and Ranadive [16]. Basically, constitutive laws in the present development are confined towards consideration to only modulus of elasticity and the Poisson’s ratio of the materials used in the pavement system being analyzed is presented in Fig. 1.
5. Finite element idealization Wherever examination is necessary about soil structure interaction problem, the required structure in modeled. It is well known fact that the area away from the load intensity is not affected much. However, the question arises about exactly upto what extent the parameters are sensitive to the intensity of loading. Sam Helwany et al. [10], discretized a three layer pavement system with the right boundary at a distance of about 8 times the loaded radius. Abdhesh K. Sinha et al. [9] located the right boundary of which is more than 7 times the radius 150 mm of the applied load. One way of evaluating the effect of loading is, to start with certain assumed extent and determine the critical parameters. Then increase or decrease the extent, analyse and compare the obtained results with an earlier one. This type of preliminary sensitive study helps in identifying the more accurate area for analysis. In respect to this, a trial horizontal axisymmetric extent of finite element idealization is considered for analysis from 5 times the radius to 8 times the radius. On the other hand, accuracy of calculation increases if higher order elements or more number of elements is used during analysis. There was a time when limitation on the use of a number of elements comes from the total degrees of freedom the computer can handle and the cost of computation time required. However, the cost of the calculation is coming down so much that such limitations are not relevant today. Accuracy is the only criteria left due to the modern high speed techniques used today. In the present study, the finite element idealization for the pave-
ment system being analyzed is developed by means of the four noded quadrilateral elements. A very fine mesh near the load that becomes progressively coarser with distance from the load is commonly observed in the literature, the same phenomenon is used during the analysis also the aspect ratio is maintained as close as possible to the specified limits. In order to study the effect of refinement of mesh, few hypothetical separate meshes are developed and analyzed for a typical pavement structure as shown in Figs. 1 and 2, consisting of 200 mm of the bituminous layer (E = 1700 MPa, l = 0.35) over 450 mm of granular base (E = 3000 MPa, l = 0.35) over a subgrade (E = 1000 MPa, l = 0.3). A single wheel load was modeled as a uniform pressure of 0.575 MPa (575 kPa) over a circular area of 150 mm radius. A very coarse refinement mesh consisting of 12 elements, with a smallest element size of 150 mm by 200 mm. Four elements spanned the thickness of the bituminous layer, four elements spanned the thickness of the base layer and four elements spanned the thickness of the sub grade layer. A medium refinement mesh consisting of a 96 elements, with a smallest element size of 75 mm by 50 mm. A very fine refinement mesh consisting of 210 elements, with a smallest element size of 50 mm by 25 mm (Fig. 3). Intermediately numbers of hypothetical meshes are studied during analysis. In the present work, the total thickness of the pavement is taken as 1300 mm to 1750 mm as per the trials described in Figs. 1 and 2 with constant thickness of 900 mm for the subgrade. 6. Boundary conditions The nodes over the base of the subgrade i.e., at depth of more than eight times the radius of circular contact area are restrained in both radial (r) and axial (z) directions. The nodes over the axis of symmetry are restrained in radial direction. Considering preliminary sensitive study to identify how much horizontal axisymmetric extent should be used for analysis, four trial extents of finite element idealization are considered starting from assuming
Fig. 3. Comparison of vertical stresses of finite element analysis with Ansys results. Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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5 times the radius to 8 times the radius. Also, it is assumed that, due to the indefinite lateral extent of the pavement section, the nodes over the extreme vertical face of the pavement from the centerline of the wheel loading [2,9]; do not suffer radial displacements. Hence those nodes are treated as restrained in the radial (r) direction for each trail [18]. By employing the interpolation characteristics of the elements, the modulus of elasticity and the Poisson’s ratio at the element nodes are extrapolated by using their respective values at the Gauss integration points. Finally after employing direct averaging technique, the strains and stresses at the nodes of the idealized system are established. The nodal displacements provide information regarding the deflection suffered, which in turn helps in analyzing the phenomenon of rutting.
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the allowable limit 178 10 06 and the computed vertical compressive strain on subgrade is 127 10 06 which is also found well within the allowable limits which is 370 10 06. From the obtained results, it is observed that the pavement composition is safe for the selected trial ultimately validating the current analytical process. A sensitivity analysis conducted to find the influence of the horizontal extent on the model geometry suggests that a length of seven times the radius (Fig. 6) is appropriate and hence is adopted in present study. Also, the surface displacements (Fig. 4) and stress (Fig. 5) for the fine and very fine refinement meshes appears to be coinciding and seems to be virtually identical, so fine mesh is selected for analysis. Effect of variation in thickness of the base layer, BL and use of different materials in base layer on conventionally critical parameters like the horizontal tensile strains at
7. Results and discussion A preliminary analysis is conducted to verify the correctness of the FEA. For the same, the three layers are assigned the same elastic moduli, transforming the three layer system into simpler one layer system. The obtained results of the FEA are checked against the Boussinesq close form solution which is readily available for uniform circular pressure and also compared with the results obtained through the general purpose software Ansys as presented in Fig. 3. The obtained results are coinciding with the results of Boussinesq’s close form solution, which is validating the developed program. Secondly, validation of present finite element analysis is done against IRC: 37-2012 pavement design plate/chart. Available data from IRC: 37-2012 for plate 8 (CBR 15%) with 150 msa is analysed with the program used in present analysis and results are compared with the allowable limits set by the guidelines for the design charts. The computed horizontal tensile strain in bituminous layer is 161 10 06 which is less than
Fig. 4. Surface displacements computed at different mesh refinement.
Fig. 5. Horizontal stresses along centreline at different mesh refinement.
Fig. 6. Surface displacements computed for different hypothetical horizontal extent.
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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the bottom of BL and the vertical compressive strain at the top of the subgrade is observed and interpreted. For the selected subgrade condition, the values of horizontal tensile strain at the bottom of BL for E2 = 100 MPa, l = 0.35 as a hypothetical base material, is exceeding the allowable limit at all trial thicknesses. At every base thickness, it is observed that E2 = 300 MPa, l = 0.35 and E2 = 450 MPa, l = 0.35 as a trial base material, show values of all critical parameters well within the allowable limit as per IRC: 37-2012. When a material property of base course varies from E2 = 100 MPa, l = 0.35 to E2 = 300 MPa, l = 0.35 more than 20 percent reduction in vertical displacement is noticed, wherein from E2 = 300 MPa, l = 0.35 to E2 = 450 MPa, l = 0.35 not even a 2 percent reduction in vertical displacement is observed. At every trial increase in the thickness of the base layer and its elastic modulus, a gradual decrease in vertical compressive strain is noticed at the top of selected subgrade. For the selected subgrade condition and constant base thickness (450 mm), variation in thickness of BL for three trial base layer material properties is analyzed. From Fig. 6, it is observed that the value of horizontal tensile strain for E2 = 300 MPa, l = 0.35 and for E2 = 450 MPa, 0.35 is safe at 200 mm and 250 mm thickness of bituminous layer. Also, it is obvious from the Fig. 7, that 100 mm and 150 mm thickness of BL are not safe for the selected trials. At every base thickness, it is observed that E2 = 450 MPa, l = 0.35 shows the values of horizontal tensile strain within the allowable limit, also vertical compressive strain is within the safe limit for all trials except at base E2 = 100 MPa and 100 mm BL thickness. The computed strains are taken as input and are incorporated in the fatigue and rutting criteria recommended in Indian Road Congress (IRC: 37-2012) to estimate the pavement life for various hypothetical conditions.
Fig. 7. Effect of BL thickness on horizontal tensile strain at bottom of BL.
7.1. Fatigue criterion As per the guidelines for the design of flexible pavements (IRC: 37-2012), Fatigue criterion for 80 percent reliability level is considered for analysis. The obtained results for horizontal tensile strain at bottom of bituminous layer is incorporated in fatigue criteria to calculate the fatigue life in terms of number of standard axles. The fatigue cracking of flexible pavements is based on the horizontal tensile strain at the bottom of BL. On this criterion, the allowable number of load repetitions that causes fatigue cracking is related to the tensile strain at the bottom of BL. Fig. 8 gives a graphical presentation of fatigue life in a number of standard axles on y-axis versus the thickness of the bituminous layer on x-axis for all trail base material. 7.2. Rutting criterion As per the guidelines for the design of flexible pavements (IRC: 37-2012), rutting criterion for controlling rutting in the subgrade and granular layers is considered for analysis. The obtained results for vertical compressive strain at top of subgrade is incorporated in rutting criteria as inputs to calculate the ruttin life in terms of number of cumulative standard axles. Fig. 9 gives a graphical presentation of a number of cumulative standard axles on y-axis versus the thickness of the bituminous layer on x-axis for all trail base material. 8. Conclusions and recommendations It is observed that number of rutting cycles increase by 4.48% with change in thickness of base layer from 300 mm to 450 mm. However, the same increase is only 2.47% when the change in thickness is from 450 mm to
Fig. 8. Fatigue life in number of standard axles Vs thickness of bituminous layer.
Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001
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References
Fig. 9. Number of cumulative standard axles Vs thickness of bituminous layer.
600 mm. From the observations, it is concluded that the increase in thickness of the base layer and increase in its elastic modulus reduces the damage due to rutting, while it has less effect on damage due to fatigue. Also, the number of fatigue cycles increase by 5.13% due to variation of elastic modulus of base layer from 100 MPa to 300 MPa. However, beyond 300 MPa, its effect is least. Hence, the increase in the elastic modulus of base layer reduces damage due to fatigue. From the selected trials for base materials and base thicknesses, use of 300 MPa material and 450 mm thickness of the base layer is suitable at the selected subgrade condition. Here it is clear that 100 mm and 150 mm thickness of bituminous layer is not safe for the selected trials. The value of tensile strain at the bottom of BL for E2 = 300 MPa, l = 0.35 and E2 = 450 MPa, l = 0.35 is under the allowable limit at 200 mm and 250 mm thickness of bituminous layer for the selected subgrade condition. At every base thickness, it is noticed that high quality graded crushed rock (E2 = 450 MPa, l = 0.35) shows the values of tensile strain at the bottom of BL within the allowable limit, also the value of vertical compressive strain is within the safe limit for all trials except at base E2 = 100 MPa and 100 mm bituminous layer thickness. Horizontal tensile strain at bottom of bituminous layer and vertical compressive strain at top of subgrade is decreased with increase in the thickness of bituminous layer. Increase in bituminous layer thickness reduces the damage due to both rutting and fatigue.
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Please cite this article in press as: M.S. Ranadive, A.B. Tapase, Parameter sensitive analysis of flexible pavement, Int. J. Pavement Res. Technol. (2016), http://dx.doi.org/10.1016/j.ijprt.2016.12.001