Semisequicentennial Transportation Conference Proceedings
May 1996, Iowa State University, Ames, Iowa

Nonlinear Finite Element Based Model for Simulation of Performance of Concrete Pavements

M. Asghar Bhatti, Idelin Molinas-Vega, and James W. Stoner

M. Bhatti and J.W. Stoner,
Department of Civil and Environmental Engineering,
University of Iowa,
Iowa City, Iowa 52242.

I. Molinas-Vegas,
Department of Civil Engineering,
Catholic University of Asuncion, Paraguay.

This paper presents a finite element model for jointed concrete pavements. The model allows for nonlinear representation of the properties of concrete, both in compression and in tension. It also accounts for the behavior under cyclic loading. Pavement slabs are connected through dowels that are modeled to allow relative deformation between the bars and the concrete slabs and accounts for the effect of repetitive loading on the load transfer efficiency of dowels. The subgrade model is capable of representing pumping of the fine material with repetitive loading. A numerical simulation of the effects of an eighteen-wheel tractor-trailer on the concrete pavement damage is presented. Key words: concrete pavements, finite element analysis, pavement damage, subgrade pumping.

Numerous studies have been conducted to determine strains and deflections in pavements caused by the passage of heavy vehicles. Instrumented pavements have been used to gather experimental data and a variety of computational models have been used to represent both rigid and flexible pavements. A number of references describe traditional thickness design procedures and the analysis of strains, temperature differentials, deformation, and consequent damage to pavements. This paper is concerned with the simulation of the performance of rigid concrete pavements, of the type typically found in the US Interstate Highway system, using finite elements. Several computer programs have been developed to model the response of concrete pavements (1). Recently, Nasim et al. (2) compared the strains obtained with a finite element model with those measured in the field for dynamic moving loads. A close agreement was found between the measured strains and those predicted by the finite element model, thus validating the response predicted with the finite element model. This work has also given support to the finding of Markow et al. (3) and Stoner et al. (4), where the dynamic loads were calculated not by direct measurements but by numerical simulation.

Section 2 briefly describes the finite element model of the pavement. Section 3 describes pavement distress measures and clarifies overall solution procedure. Section 4 describes the effects of certain vehicle characteristics on the pavement damage. It should be pointed out that the results in this section are meant to show the feasibility of such damage indices from simulation of vehicle response and finite element analysis. No attempt is made in the paper to relate these indices to actual pavement damage. In order for the results to be of practical significance the indices must be calibrated using actual pavement damage data. This work is currently underway.

Finite Element Model

The complete finite element model for analysis of pavement response consists of the following three separate models: (a) concrete slab model, (b) subgrade model, and (c) dowel bar model.

The concrete slab is modeled using 9-node quadrilateral elements. The basic element development is described by Yang and Bhatti (5). The element is further extended to handle layers with different material properties through the thickness. This layered discretization allows for better monitoring of crack and fatigue propagation. The element considers yielding and crushing type failures for concrete layers in compression, cracking of concrete layers in tension and fatigue for concrete in tension. Fatigue for concrete in compression is not included in the model because the compressive stresses in typical pavements are so low that no significant fatigue effects are anticipated.

The subgrade model assumes that the subgrade behaves as a Winkler foundation. The constant of proportionality between the slab deflection and the reaction, known as the modulus of subgrade reaction k, is defined as the pressure necessary to produce a unit deformation of the subgrade determined through plate loading with a standard plate radius of 15 inches. The subgrade model also considers pumping that is defined as decay in the subgrade support due to the ejection of fine material, with water, as traffic loads are applied. After severe pumping, voids are created with consequent loss of subgrade support. The amount of material pumped depends on factors such as structural properties of the pavement, magnitude and number of load applications, climatic conditions, and type of material used in the subgrade. The pumping model is defined in terms of the total energy of deformation imposed on the pavement and is described in detail by Bhatti et al.(6).

The basic representation of the dowel bars is that of a beam, allowing for shear deformation of the beam. The effects of different variables such as joint width, dowel diameter, dowel length, and number of load repetitions are included (4).

Pavement Distress Measures

A typical pavement slab is depicted in Figure 1 showing its dimensions and the finite element discretization. Vehicle is assumed to travel with its outermost wheel along the travel path A-A. To fully accomodate a typical truck usually eight slabs are required. The four central slabs are selected for analyzing the damage caused by the different vehicle configurations. The position of the vehicle causing the maximum deflection on the two central slabs is

selected. This position is chosen based on the axle forces calculated during the dynamic simulation and assuming a linear behavior of the slabs as the vehicle travels along a selected path. Details of this procedure can be found in the report by Stoner and Bhatti (4).

A numerical simulation is performed to study the effects of different characteristics of an eighteen-wheel tractor-trailer on the concrete pavement damage. Different cases are compared based on various damage indices as a function of number of load repetitions. The following indices are defined (4):

(i) Cracked Volume. It is possible to monitor crack propagation through the thickness of the slab. The cracked volume index reflects the severity of cracking on the pavement slabs.

(ii) Volume of Subgrade Material Pumped from Underneath the Slabs.

(iii) Area Over which Pumping Damage has Occurred. It is presented as percentage of the area of the four central slabs and represents the extent of the pavement over which there is no support to pavement.

(iv) Decay in Concrete Slab Stiffness. This index is associated with the fatigue behavior of concrete.


In this section a parametric study on the damage caused by the repetitive passing of an eighteen wheel tractor trailer over a selected jointed concrete pavement section is discussed. The parametric study is done by varying certain characteristics of the vehicle and computing the forces on the axles as it travels along the pavement section. The dynamic simulation of the vehicle takes into account the geometrical and nonlinear characteristics of a multibody dynamic system. Details of the dynamic simulation procedure are reported in reference (4). The base vehicle configuration is shown in Figure 2. The vehicle is assumed to travel on a road profile that is obtained from actual field data for a pavement considered to be near the end of its useful life. The characteristics considered for the parametric study are travel speed, payload carried by the trailer, tire stiffness, and leaf spring stiffness.

Figure 3 shows the evolution of pavement damage indices for the case of nominal configuration for two different speeds: 45 mph and 65 mph. It can be seen that the spread of cracking is faster at 65 mph in the initial stages. However, once the crack propagation, associated with 45 mph, starts it develops very rapidly. After one million load applications the volume of concrete cracked at 45 mph is almost five times greater than that at 65 mph. The fatigue index plot indicates that fatigue damage initiates sooner at 65 mph than at 45 mph, but that once damage begins at 45 mph it does so at a higher rate than at 65 mph. Similar plots for volume of material pumped show that after 750,000 load repetitions the rate of pumping at 45 mph is almost double that at 65 mph. However from the beginning the area covered by pumping is higher at 45 mph than at 65 mph and this difference increases with increasing number of load applications.

Plots of the evolution of the damage indices with the number of load repetitions were generated for a variety of vehicle configurations. For brevity the complete set of plots is not included in the paper. Since the comparison of these indices after a large number of load applications is of most interest, Figure 4 presents the values of two of these indices after one million load applications. It can be seen that the changes in the stiffness of tires or leaf springs have a more acute effect at lower speeds. At 45 mph small changes in these parameters produce substantial changes in the damage indices. Fortunately, both these changes actually reduce damage in most part.


A comprehensive finite element model for the analysis of jointed concrete pavement is presented. This model allows for the representation of non-linear properties of concrete, as well as changes in the material properties and subgrade conditions as function of the number of load applications. A parametric study is carried out by analyzing the effect of changing characteristics of the heavy vehicles on the damage caused to the concrete pavements. Different damage indices are obtained which characterize the state of the pavement after specified number of load repetitions. From this study it can be observed that the effects of lower speeds are more detrimental than those of higher speeds for typical rough road profiles with about 20 feet joint spacing. Specifically in the cases of cracking and material pumped, the indices at lower speeds can be substantially higher than at higher speeds.

  1. S.D. Tayabji and B.E. Colley. Analysis of Jointed Concrete Pavements. Report No. FHWA-RD-86-041. Federal Highway Administration, U.S. Department of Transportation, Washington, D.C., 1984.
  2. M.A. Nasim, et al. The Behavior of Rigid Pavement Under Moving Dynamic Loads, Paper for Transportation Research Board Annual Meeting. Held at Washington, D.C., 1991.
  3. M.J. Markow, J.K. Hedrick, B.D. Brademeyer, and E. Abbo. Analyzing the Interactions between Dynamic Vehicle Loads and Highway Pavements. Transportation Research Record 1196, TRB, National Research Council, Washington, D.C., 1988, pp. 161–169.
  4. J.W. Stoner and M.A. Bhatti. Estimating Pavement Damage from Longer and Heavier Combination Vehicles. Report prepared for the Midwest Transportation Center, Public Policy Center, University of Iowa, Iowa City, Iowa, 1994.
  5. R.J. Yang and M.A. Bhatti. Nonlinear Static and Dynamic Analysis of Plates. ASCE Journal of Engineering Mechanics, Vol. 111, No. 2, 1985, pp. 175–187.
  6. M.A. Bhatti, J.A. Barlow, and J.W. Stoner. Modeling Damage to Rigid Pavements Caused by Subgrade Pumping. ASCE Journal of Transportation Engineering, Vol. 122, No. 1, Jan/Feb. 1996, pp. 12–21.

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