Analysis of periodic cracks in surface layer of pavement structures

2010 Accepted 24 September 2010 Available online 29 September 2010 Keywords: Periodic cracks Pavement structures the FEM method. The formation mechanism of the periodic cracks is analyzed and the the cracking of asphalt surfacing on long-spanned steel bridges. According to their long-term observation, longitudinal crack was also the main crack style and these short longitudinal cracks formed earlier would soon propagate parallel cracks if there were not properly sealed. These short longitudinal cracks occurred at/near the ribs or the girders, as shown in Fig. 3. Another type of longitudinal cracks of asphalt surfacing which occurs in between the trough of ribs is also mentioned, as shown in 1350-6307/$ - see front matter Crown Copyright � 2010 Published by Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: [email protected] (C. Xu). Engineering Failure Analysis 18 (2011) 411–420 Contents lists available at ScienceDirect Engineering Failure Analysis doi:10.1016/j.engfailanal.2010.09.023 Surface cracking in pavements has long been regarded as a main cause of deterioration in roadways because surface water penetration can reduce the strength of the sub-base layers and result in broader cracks and potholes. Thus, surface cracking has a direct bearing on pavement’s quality and service life, which attracts more and more attention in recent years [1–5]. There are many different types of pavement crack shapes, with occasionally complex morphologies. Nonetheless, crack pat- terns existing on pavements are generally classified into the following four categories: (1) longitudinal cracks, (2) transverse cracks, (3) block cracks and (4) alligator cracks. Among these crack patterns, an interesting phenomenon can be found at some pavements that cracks are periodically distributed and spaced equally, as shown in Fig. 1. These periodic cracks can also be observed at surface of bridge pavement structures. Xu and Zhang have surveyed the cracks of steel orthotropic bridge deck pavement [6]. They found that the lon- gitudinal crack is the main crack style, as indicated in Fig. 2. Chen et al. [6] reported the characteristics and propagations of Stress state transition Evolving process 1. Introduction evolving process is simulated. A parametric study, including effects of the layer thickness, tensile strength of surface layer and layer elastic modulus on the crack spacing is carried out. The numerical results indicate that the horizontal stress between two adjacent cracks decreases gradually as the crack spacing decreases. The horizontal stress transits from ten- sile to compressive when the crack spacing decreases to a certain value. Such a stress state transition leads to the periodic array of the surface cracks. The evolving process of the peri- odic cracks indicates that new cracks infill in sequence between two earlier formed adja- cent cracks and the crack spacing decreases in half simultaneously. No more new crack can infill when the crack spacing reaches to a certain value even with the increasing of external load. Numerical simulations also show that the crack spacing is strongly depen- dent on the surface layer thickness, tensile strength of the surface layer and elastic modu- lus of the surface layer. Crown Copyright � 2010 Published by Elsevier Ltd. All rights reserved. Analysis of periodic cracks in surface layer of pavement structures Chang Xu a,⇑, Yan Anzhi a, Mingcheng Liao a, Tang Chunan b aCollege of Civil Engineering, Henan Polytechnic University, Jiaozuo City, Henan Province 454000, People’s Republic of China b The State Key Lab of Coastal and Offshore Engineering, Dalian University of Technology, Dalian City, Liaoning Province 116024, People’s Republic of China a r t i c l e i n f o Article history: Received 6 June 2010 Received in revised form 24 September a b s t r a c t As a critical issue for the pavement’s quality service life, surface cracking of the pavement structure is an ongoing research topic which attracts many researchers. This paper presents a numerical study of the periodic cracks in surface layer of pavement structures based on journal homepage: www.elsevier .com/locate /engfai lanal Fig. 1. Periodic cracks in surfaces of pavement structures. Fig. 2. Periodic cracks in steel orthotropic bridge deck pavement []. Fig. 3. Periodic cracks in concrete pavement. 412 C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 the pavement. For example, the bridge deck pavement could be under conditions because of the external loads and rids/gird- C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 413 ers, as shown in Fig. 5a. For other pavement structures, bending zone can also form duo to the non-uniform foundation sub- sidence, as shown in Fig. 5b. Significant efforts have been devoted to investigation of the surface cracking of pavement structure. Most of the existing studies focus on describing the cracking patterns or analyzing the mechanism of a single crack on the pavements [7–9]. Little work has been carried out on these periodic surfacing cracks of layered pavement structures. Better understanding and mod- eling of the periodic cracking can help not only improve the prediction of the service life of pavement structure, but also optimize appropriate materials for improved the performance of pavement structure. In this contribution, attention is fo- cused on the formation mechanism and the evolving process of the periodic crack arrays in pavements. The paper is orga- nized as follows. Firstly, the numerical model is described briefly. Subsequently, the formation mechanism and the ongoing cracking process are discussed in details. Finally, a parametric study, including the thicknesses and elastic modulus of dif- ferent layers, etc., is also carried out. 2. Numerical simulation on formation mechanism of periodic cracks Fig. 4. According to the description mentioned above, we note that these periodic cracks always occur in the bending zone of Fig. 4. Periodic cracks of asphalt surfacing which occur between the trough of ribs of the bridge []. 2.1. Numerical code In this paper, a two-dimensional finite element code named Realistic Failure Process Analysis code (RFPA2D) is employed to investigate the periodic cracks of the pavement structure. RFPA2D is a Microsoft Windows package that can perform non- linear deformation analysis, which includes the initiation and growth of cracks and fractures. A user-friendly pre-processor is integrated to generate a finite element mesh and prepare the input data, and a graphic post-processor with an animation External load External load Pavement structure U-shape ribs External load External load Subsidence zone Subsidence zone Pavement structure (a) Bridge surfacing (b) Foundation subsidence Fig. 5. Sketch of the pavement structure under bending conditions. option for the presentation of results is available to assist the understanding of the failure mechanism. In the numerical code, the finite element method is employed as the basic stress analysis tool and the Mohr–Coulomb criterion with tension cut-off is utilized as damage threshold. The simulation of the crack initiation and propagation in this investigation is just as the method used in the smeared crack model, the crack is smeared over the whole element, which has the advantage of leaving the mesh topology untouched. No special singular element is adopted. The detailed descriptions about RFPA2D code could be found in Refs. [10–12]. 2.2. Transition of stress state as function of crack spacing/surface layer thickness ratio In this section, an analysis of stress is carried out to explain the formation mechanism of periodic cracks. To simplify the numerical model, a four-point bending beam model with four layers is established. The geometrical parameters for different layers are indicated in Fig. 6. Four pre-assigned cracks perpendicular to the long axis are equally-spaced along the surface Surface layer Base Subbase Subgrade 20 cm 20 cm 80 cm 360 cm T S Load Load Fig. 6. Numerical model of the pavement structure with four pre-assigned periodic cracks. Table 1 Material parameters used in numerical model. Items E (MPa) v Surface layer 2000 0.25 Base layer 1000 0.35 Sub-base layer 500 0.25 Subgrade layer 50 0.35 E, Elastic modulus; v, Poisson’s ratio. y S T 414 C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 Two central cracks x cc Fig. 7. Details of the zone between two central cracks and the coordinate system. aa bb layer. The two central cracks are used to represent any two adjacent cracks in a row composed of many members. The spac- ing between adjacent cracks and the thickness of the surface layer are denoted as S and T, respectively. Selection of the bond- ing coefficient is difficult because there is no standard test procedure to determine it. Thus, our numerical model assumes that the layers are fully bonded to each other to ease the modeling of the structure and the computation process. -0.2 0.2 0.6 1.0 0.0 0.5 1.0 line a-a line b-b line c-c Normalized position along the lines σ x /σ x m ax Fig. 8. The horizontal stress distribution between two central cracks for different y-coordinates. Normalized position along the line a-a σ x /σ x m ax -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 S=10T S=8T S=6T S=5T S=3T S=T Fig. 9. Stress state between two central cracks changes from tensile to compressive with the decreasing of crack spacing. Surface layer Base Subbase Subgrade 16 cm 20 cm 20 cm 80 cm LoadLoad C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 415 360 cm Fig. 10. Sketch of pavement structure without pre-assigned cracks under four-point bending. The four-node isoparametric quadrilateral element is used for these four layers. The model mesh is composed of 500 � 150 = 75,000 elements. Loading is applied through imposed displacement at the load points of the beam on the top edge. The model is numerically simulated as a plane stress problem. The material parameters used in the model are sum- marized in Table 1. (a) 1 2 (b) 1 2 3 (c) 1 2 3 4 (d) 1 2 3 4 5 (e) 1 2 3 4 5 6 1 2 3 4 5 6 7 (g) 1 2 3 4 5 6 7 8 (h) 1 2 3 4 5 6 7 8 9 (i) 1 2 3 4 5 6 7 8 9 (j) 416 C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 (f) Fig. 11. Evolving process of the periodic cracks. With this defined geometry, the evolution of the stress distribution is examined as a function of the crack spacing. In or- der to give quantitative analysis, we use the stress along the some lines between the two central cracks to represent the stress state between adjacent cracks, as shown in Fig. 7. Fig. 8 gives a clear understanding of the distribution of the horizontal stress (rx) corresponding to different y-coordinates. The horizontal stress decreases with the increase of the distance apart from the top of surface layer. At a given y-coordinate, the horizontal stress reaches a peak value at the mid-point between adjacent cracks. This indicates that the new crack may nucleate at mid-point of top surface between adjacent cracks. The line a–a is along the top of the surface layer between the two central cracks. The horizontal stresses along the line a–a decrease with the decreasing of crack spacing, as shown in Fig. 9. The horizontal stresses acting perpendicular to the cracks along the line a–a change from tensile to compressive when the crack spacing decreases to a certain value. This stress state transition would preclude new cracks between these two adjacent cracks. 2.3. Evolving process of periodic cracks In this section, a simply supported beam without pre-assigned cracks subjected to four-point bending is considered to investigate evolving process of the periodic crack arrays. The model also consists of four components, surface layer, base, sub-base and subgrade layer. No more interface element is used. The element type and the material parameters are the same as those mentioned above. The model, its boundaries, loading conditions are shown in Fig. 10. Also, a plane stress problem is considered in this section. Fig. 11 illustrates the numerically obtained formation process of the periodic cracks. According to the order of the crack C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 417 In this section, the numerical approach is implemented and a comprehensive parametric study is conducted to determine the effects of pavement structures on the crack spacing. In the following calculation, all the data are the same as those in the above section if not specified. 3.1. Effect of the layer thickness In order to explore effect of the thickness of surface layer on the crack spacing, we set six different thickness values. They are 70, 90, 110, 130, 150 and 200 mm. The computed crack spacing is 210, 271, 336, 401, 450 and 610 mm, respectively. By plotting the crack spacing versus the thickness of surface layer, we obtain the unique relation shown in Fig. 12. It is apparent Cr ac k sp ac in g/ m m 0 200 400 600 800 Surface layer thickness/mm 0 100 200 300 Fig. 12. Effect of surface layer thickness on crack spacing. formation, the whole process can be divided into three stages. In the first stage (Fig. 11a–b), two cracks initiate near the sup- port points of the top surface when the tensile stress reaches its tensile strength. It is easy to find from Fig. 10 that the cross sections at locations of two support points are weaker than others due to the sudden change of shear forces and the locations of maximummoments. Therefore, the earlier formed cracks always distribute at locations of these two support points. In the following stage, new cracks nucleate and infill in the earlier formed cracks sequentially as the external load increasing (Fig. 11c–i). An infilling crack always initiates at the middle point of top surface between two earlier formed adjacent cracks. This is because that the horizontal stress reaches the peak values at middle point between two adjacent cracks, as mentioned above. The crack spacing reduces by half as the crack infilling. Finally, no more crack initiates when the crack spacing reduces to a certain value and these formed cracks become more open with the increasing of external load (Fig. 11j). 3. Parametric study m m 0 100 200 300 400 418 C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 Base layer thickness/mm Fig. 13. Effect of base layer thickness on crack spacing. 600 Cr ac k sp ac in g/ 0 100 200 300 400 500 that the crack spacing strongly influences by the thickness of surface layer. The crack spacing (S) increases linearly with increasing thickness of surface layer (T) and the S/T ratio is about 3.0. For the pavement structures, the base layer is bond directly to the surface layer. Thus, the effect of base layer thickness on the crack spacing is also investigated. The base layer thickness values are set to be 200, 250, 300 and 350 mm while the sur- face layer thickness is kept 150 mm. Fig. 13 shows the numerical results that the crack spacing increases by increasing the base layer thickness when other parameters are kept constant. Thickness of the base layer plays a more slightly role in crack spacing compared with the thickness of surface layer. 3.2. Effect of layer elastic modulus In this part, pavement models with different layer elastic modulus are analyzed. Fig. 14 shows how the crack spacing var- ies with elastic modulus of the surface layer. It is indicated that crack spacing decreases inversely with increasing modulus of surface layer. When conducting the analysis of base layer modulus, we set the base layer modulus to be 1000, 2000, 3000, and 4000 MPa. The numerical results plotted in Fig. 15 indicate that crack spacing increases slightly when the elastic modulus of base layer increases. 3.3. Effects of tensile strength of surface layer In order to study the influence of the tensile strength of surface layer, we chose six different values of the tensile strength, 3, 5, 7, 9 and 10 MPa for the surface layer to setup models, while keeping other parameters constant. Cr ac k sp ac in g/ m m Elastic modulus of surface layer/MPa 0 200 400 0 2000 4000 6000 Fig. 14. Effect of elastic modulus of surface layer on crack spacing. C. Xu et al. / Engineering Failure Analysis 18 (2011) 411–420 419 0 2000 4000 6000 Cr ac k sp ac in g/ m m Elastic modulus of base layer/MPa 400 450 500 Fig. 15. Effect of elastic modulus of base layer on crack spacing. ac in g/ m m 450 600 By plotting the tensile strength of the surface layer versus crack spacing, we obtain the curve shown in Fig. 16 which indi- cates that higher tensile strength of the surface layer leads to increasing crack spacing. 4. Conclusion A numerical study on periodic cracks in surface layer of the pavement structures is carried out in this contribution. The following observations are reached based on the numerical approach: (1) The horizontal stress between two adjacent cracks changes from tensile to compressive when the crack spacing reaches to a certain value. The stress state transition precludes cracks infilling between two adjacent cracks. (2) The evolving process of the periodic cracks can be generally divided into three stages. Firstly, two cracks form at the weaker points when the horizontal stress reaches its tensile strength. In the following stage, new cracks infill between the earlier formed cracks sequentially and the crack spacing decreases. Finally, no more crack initiates when the crack spacing decreases to a certain value even with the increasing of the external load. (3) Parametric studies indicate that surface layer thickness has significant influence on the crack spacing while the effect of thickness of the base layer on the crack spacing is slight. The crack spacing increases linearly with increasing thick- ness of surface layer. Both the tensile strength and elastic modulus of the surface layer have significant influence on the crack spacing as well as the elastic modulus of base layer. Acknowledgments The research reported in this paper is supported by the Key Subject Foundation of Henan Province (No. 504906) and the Doctor Foundation of Henan Polytechnic University (B2009-2). The financial support is highly appreciated. 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