Three-dimensional finite element analysis of treated sediment base cracked flexible pavement Abdellatif Selmi Abstract 3D-finite element method is used to predict the stresses, strains and displacements cracked and un-cracked pavement structures in which base layer is made of treated sediment. Using sediment in pavement base layer is a recent and important application. First, a parametric study is carried out in order to determine the cell dimensions to avoid the boundary effect. The impact of surface layer crack on the pavement and the prediction of the crack propagation are investigated. Then a study for comparison between the pavement structures is done. Results demonstrate that a 6-mm width transverse crack in the surface layer can lead to displacements and strains that can exceed the bearing capacity of the pavement layers and can induce damage in the base and sub-base layers. There are stresses, displacements and stains that are not influenced by the surface layer crack but the stresses and strains which are used for designing the pavement are spectacularly affected. The role of the roadway is to distribute the pressure of the tyre to bring it to a level consistent with what can be supported by the subgrade [5]. A schematic representation of a flexible composite pavement is shown in figure 1. Keywords Crack; Finite element; Pavement; Strains; Stresses. I. INTRODUCTION The choice of the sector of destination of dredged material must meet both regulatory compliance; environmental conditions, the best available technology and an economically acceptable cost [1]. Currently, sediment management is moving towards recovery rather than disposal and deposit [2]. The valuation may include several fields such as civil engineering, agriculture through soil amendment and rehabilitation of natural sites [3]. In French, 96% of aggregate consumption in civil engineering is of natural origin [4]. The aggregate reserves (alluvial or massive) are almost unlimited, but many of them remain unusable for various reasons: inaccessible, integrated into urban areas, sites classified or protected, operating too costly and environmental sensitivity [1]. Managing a career aggregate is expensive [1]. In this context, recycling sediments for use in public works is an interesting solution. Abdellatif Selmi is with the Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Rue Amor Ben El Khatab - 6029 Gabès, Tunisia (corresponding author s phone: (00216)21509049 ; e-mail: selmifr2000@yahoo.fr ). Fig. 1 Pavement structure: un-cracked pavement(left), Cracked pavement (right) First, the subgrade is usually surmounted by a sub-base. Then, the base layer and finally, the surface layer. From top to bottom, distribution of the load is less and less important. This permits the use of materials having mechanical properties varied depending on their position in the pavement structure. In this study, we seek to enhance the marine and river sediments for use in pavement base layer. To be recycled in road construction, sediment must meet several criteria [1]. In France, in terms of mechanics, immediate bearing index (IPI), the modulus of elasticity (E) and tensile strength (Rt) are the main parameters that determine the suitability of the material for use in seat pavement. By their physical characteristics, studied sediment belongs to the class of clay loam materials which are high in organic material [1]. To enable the use of fine sediments in sub-base and base layers of pavement, the mechanical characteristics of sediment; water sensitivity, compressibility and immediate bearing index are improved by the addition of granular markers (sands and sand dredging Boulonnais) followed by treatment with hydraulic binders and / or air (cement and / or lime) [3]. The environmental impact of mixtures is verified through the leaching test [6]. The obtained results allow assimilating the mixtures to inert waste [1]. The obtained results on 115
samples crushed marine sediments also indicate that mixtures exceed the level of inert waste to enter the category of nonhazardous waste [7]. According to the French circular relating to the valuation of incineration bottom ash waste, these mixtures can be used in the road sector [3]. In his work, Dubois concluded that the fine fraction (% of particles having a diameter less than 63 microns) in the mixture is critical to ensure adequate bearing capacities more than the coefficients of uniformity or of curvature. The fine fraction was limited to 20% of these mixtures [8]. Thus, in the material formulations based on east harbor sediments and based on river sediments, the limitation of fine fraction was preferred over the particle size distribution of the mixture. From the experimentation results, it appears that all studied formulations show adequate mechanical performance for use pavement base [1], [9]. Two pavement structures were considered, the type pavement structure is composed of a layer of asphalt concrete, a base layer of sand cement and a sub-base in untreated gravel. In the second structure, the sand-cement base layer is substituted with the treated sediment. All layers are assumed to consist of isotropic elastic materials and therefore a stiffness modulus (E) and the Poisson s ratio (v) are used to represent their behavior. Data traffic for the design is based on the data of the technical guide for the design and sizing of pavement structures [10]. In their work, the French method of design of these types of road is used [11]. The comparison between the two structures shows that the use of treated sediment can reduce with 11 cm the body pavement thickness (over 30%) [1]. This saves sand - cement. In addition, a layer of reduced thickness can decrease the number of compaction to achieve desirable compactness. All this can substantially reduce the construction cost. Investigations have demonstrated that cracks generally initiate at the surface and propagate downwards [12]. Cracked pavement calculations by finite elements are increasingly developed with the growth of computing processors. These models are made from a multilayer structure based on a deep and wide massive. In this work, a 3D-finite element (FE) based numerical approach is used, which allows to model cracked and uncracked pavement structures. Then, comparison in terms of stresses, displacements and strains between the two structures is investigated. The main contribution of the paper is the prediction of the stresses, displacements, strains in surface layer transversally cracked pavement made of treated sediment base layer. The paper has the following outline. In Section 2, the Pavement structure is presented. The un-cracked and cracked pavements are modeled in Section 3 and 4. In Section 5, several numerical predictions are presented. Conclusions are discussed in Section 6. II. PRESENTATION OF THE PAVEMENT STRUCTURE 3D modeling will be performed on two flexible pavement structures formed of the same layers and the same materials. The base layer of the two structures is consisted of treated sediment (see Fig. 1). The elastic properties Used of different layers are reported in Table 1 [1]. In the second structure, the surface layer is transversely cracked (see Fig. 1). The objective of this work is to compare the stresses, displacements and strains at the pavement/pavement and pavement /subgrade interfaces between the cracked and uncracked structures. TABLE I ELASTIC CONSTANTS AND THICKNESS OF PAVEMENT LAYERS Young modulus Poisson s ratio Thickness E (MPa) (m) Bituminous Concrete 5400 0.35 0.06 Sand-Cement 7040 0.25 0.21 Untreated Gravel 150 0.35 0.25 Subgrade 50 0.35 6.00 A. Description of the load applied to the pavement The design of a road is made so that it can support the cumulative traffic of trucks throughout its life. This traffic is the combination of different types of vehicles with different loads and axle geometries. The French design method has used a reference axle as a single axle with dual wheels carrying a total load of 130KN. Sizing is usually done by taking into account a half axle, that is to say a combination of two wheels of 65KN. The burden of these two wheels is then transmitted to the road through two circular area loads of radius r = 0.125 m, center distance 3r = 0.375 m and uniformly distributed pressure q = 0.662 MPa. In fact, experimental measurements on seven different types of tyre and loading [13] have shown that truck tyre loading does not apply on a circular surface but rather rectangular. The average pressure of the tyre on the road varies from 0.42MPa to 0.72MPa depending on the type and loading of the tyre (which varies from 80 KN to 20 KN). The size of the filler is about 0.22m in width and 0.3m in length. In our following calculations and applications a rectangular load of 0.22x0.3m size and 0.662MPa pressure is taken, a total load of 85KN for a half-axle (21.25 KN per tyre). B. Criteria to check in the design of pavement To design a pavement, the criteria to check are: - The tensile stress, σ t,at the base of the sandcement layer must be less than the allowable stress - The vertical deformation, ε z, at the base of the treated sediment layer and at the subgrade surface must be below a permissible value. This is why the stress and strain fields created by the reference load are determined at the base of each layer. The 116
values obtained are then compared with those eligible for pavement materials. In order to compare the behavior of the structure in pavement which is cracked on the surface layer with the uncracked one, the two structures are modeled by general computer code ANSYS. The hypothesis of perfect interface is allowed for the calculation with the Ansys program. Discussion of the boundary conditions of the problem will be presented in sections 3. III. MODELING OF THE UN-CRACKED PAVEMENT STRUCTURE In this first case, we consider the structure shown in figure 1 which is considered made of three layers of square surface pavement resting on a high depth soil. The load of a truck wheel is taken as a rectangular load q = 0.662 MPa of dimension = 2ax2b =0.3x0.22m. The finite element modeling was carried out in three stages. The first involved generating the finite element mesh and defining the load and boundary conditions and material properties. The second involved computing displacements, stresses and strains and in the final stage these results will be converted into graphical outputs for ease of understanding. C. Structure dimensions For many calculations, we found that with the transverse size of the quarter of the structure equal to 3m (20 times the length of the load) and the soil depth of 6m, the fields of stresses, displacements and strains are converging. That is to say if these dimensions are increased, the results do not change much. The final mesh of the finite element method therefore includes 72879 solid elements 20 nodes, SOLID186. The total number of nodes is 314971. The computation time on a P.intel 2.2 Ghz is 4h 15 minutes. IV. NUMERICAL MODELING OF CRACK IN THE PAVEMENT The crack in the road is taken into account as a narrow gap of 6mm size. In the modeling of cracks, we consider that the lips of the crack are two free edges, and have no contact with each other under the truck loads. The crack is assumed to exist transversely across the thickness of the wearing layer (Fig. 1). A. Mesh structure Due to the symmetry of the problem, The FE mesh is done only for a quarter of the structure. Horizontally, the size of the elements increases in a geometric progression from the surface. Vertically, we define two different areas. The first part is under the load. The stress gradient is strong in this area, the mesh is tighter. The second is the rest of the field, the stress gradient is less important, the mesh is less tighter. B. Boundary conditions For these calculations, the materials layers are assumed perfectly bonded together. This amounts to consider the continuity of vertical and shear stresses and horizontal and vertical displacements. For the chosen structure, we assume that the edge of the pavement tends to infinity in the transverse direction. With the cited assumption and load applied vertically, boundary conditions of blocked edges are the best approximation. The appropriate boundary conditions are summarized in Table II. TABLE II DISPLACEMENT BOUNDARY CONDITIONS FOR CRACKED AND UN- CRACKED PAVEMENT STRUCTURE. Un-cracked pavement Cracked pavement x=0 u x = 0 u x = 0 (except for the surface layer edge which is free) x=3 u x = 0 u x = 0 y=0 u y = 0 u y = 0 y=3 u y = 0 u y = 0 z=6.52 u x = u y = u z = 0 u x = u y = u z = 0 Fig. 2: 3D view of FE mesh corresponding to cracked pavement The truck wheel load is assumed to be a pressure of q = 0.662 MPa over a rectangular area of a length a = 0.3m (in the direction of movement) and a width b = 0.22 m. The rectangular area is supposed symmetrical with respect to the crack. The material density is not taken into account, which leads to neglect of initial stresses in pavement layers. The road is assumed to be infinite in the plane; we consider that the edges of the road are blocked at a great distance. The pavement structure is studied on a parallelepiped rectangle, which consists of three layers of the road layers and the soil mass (figure 1). We use boundary conditions such as nil transverse displacements at the transverse limits and no vertical displacement at the bottom of the soil mass. Due to the symmetry, we study only a quarter of the structure. For many calculations, we found that with the transverse size of the quarter of the structure equal to 3m (20 times the length of 117
the load) and the soil depth of 6m, the fields of stresses and displacements are converging. The mesh of the quarter of the mass is similar to that of the non-cracked structure and the final (figure 2) is done with 73528 solid elements 20 nodes, SOLID186. The total number of nodes is 316629 nodes. The computation time is 5h 20minutes on a P. intel 2.2 GHz. V. RESULTATS Figures 3 and 4 show respectively the evolution of the vertical displacement, U z, at the base layer/sub-base layer (y=0.27mm) interface and the shear stress, s xz, at the surface layer/base layer (y=0.06mm) interface for cracked and uncracked pavements. Interpretation:For the interval [0; 0.5m], the crack leads to an increase of the vertical displacement. Out of this interval, no crack effect is seen. The increased factor is 1.0301. As illustrated in figure 4, the difference between cracked and un-cracked pavement shear stress is only throughout the first 0.5m. The increased factors are about 1.4451. Figure 5 shows the variation of the horizontal stress, σ xx, at the base layer/ sub-base layer interface (y=0.27mm) for cracked and un-cracked pavements. Fig. 5 Horizontal stress comparison at the base layer/ sub-base layer interface, y=0.27mm, for cracked and un-cracked pavements. Fig. 3 Vertical displacement comparison at the base layer/sub-base layer interface, y=0.27mm, for cracked and un-cracked pavements. Interpretation: From the figure 5, it is seen that the difference between stresses in cracked and cracked pavements is important for sections nearer to the zone where load is applied and is clearly visible for the origin x =y= 0.The increased factor is about 1.1797 and the maximum shear stress is 0.40287 MPa. Figure 6 compares the cracked and un-cracked pavement in terms of vertical strain,ε zz, at the sub-base layer/subgrade interfaces (y=0.52mm). Fig. 4 Shear stress comparison at the surface layer/base layer interface, y=0.06mm, for cracked and un-cracked pavements. 118
Fig. 6 Vertical strain at the sub-base layer/ subgrade interface, y=0.52mm, for cracked and un-cracked pavements. [7] JOCE, Décision du conseil du 19 décembre 2002 établissant des critères et des procédures d admission des déchets dans les décharges, conformément à l article 16 et `a l annexe II de la directive 1999/31/CE. Journal officiel des Communautés européennes, 2003. [8] V. Dubois, Caractérisation physico-mécanique et environnementale des sédiments marins, Application en technique routière. Ph.D. Thesis, Ecole des Mines of Douai, Université d artois, French, 2006. [9] S. Kamali, F. Bernard, V. Dubois, and N. E. Abriak, Beneficial use of marine dredged sand and sediment in road construction. First International Conference on Engineering for Waste Treatement: Beneficial Use of Waste and By Products, Albi, France, 2005. [10] SETRA, Conception et Dimensionnement des structures de chaussées. Guide technique, 1994. [11] GDR. Assises de chaussées Guide dapplication des normes pour le réseau routier national, LCPC-SETRA, ISBN : 2-11-085849-4, 1998. [12] M. E. Nunn, An investigation into reflection cracking in composite pavements. RILEM International Conference on reflection Cracking. Liege, Belgium, 1989. [13] M. De Beer, C. Fisher, and F. Jooste. Determination of pneumatic /pavement interface contact stresses under moving loads and some effects on pavements with thin asphalt surfacing layers. The eighth International Conference on Asphalt Design. 1997. Interpretation: It is shown that near to the area where the load is applied, the crack leads to an increase of the vertical strain. The increased factor is about 1.1682. The maximum vertical strain is 0.18838E-03. VI. CONCLUSIONS The crack propagation for pavement in which base layer is made of treated sediment was predicted using a 3D finite element method. This helps filling a gap in the literature where almost the only available results are about the possibility of using dredged sediment in pavement. After the choice of the volume dimensions, the 3-D FE method were used to predict the elastic stresses, strains and displacements of flexible pavement. The FE data of cracked pavement are compared against those of un-cracked one. Results demonstrate that the stresses, displacements, strains and the crack development are strongly dependent on the surface layer transverse crack. Hence, it is proved that a 6 mm surface layer crack can induce a serious rupture in the base and consequently the sub-base layers. REFERENCES [1] N. T. TRAN, Valorisation de sédiments marins et fluviaux en technique routière. Ph.D. Thesis, Ecole des Mines of Douai, Université d'artois, French, 2009. [2] AIPCN, La gestion des sédiments pollués en rivière, source AIPCN. www.cetmef.equipement.gouv.fr/aipcn/fichiers/sediments.doc, 2006. [3] D. Colin, Valorisation de sédiments fins de dragage en technique routière. Ph.D. Thesis, Université de CAEN, French, Octobre 2003. [4] V. Nicolas, L exploitation des granulats marins. UNICEM, 2005. [5] D. T. Quang, Modèle simplifié pour les chaussées fissurées multicouches. Ph.D. Thesis, Ecole Nationale des Ponts et Chaussees, French, 2004. [6] R. Zentar, V. Dubois, and N. E. Abriak, Mechanical behaviour and environmental impacts of a test road built with marine dredged sediments. Resources Conservation and Recycling. 52(6), 947-954, 2008. 119