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Federal Highway Administration > Publications > Public Roads > Vol. 57· No. 3 > Modeling of Geotextiles and Other Membranes in the Prevention of Reflection Cracking in Asphaltic Resurfacing 
Summer 1994 

Modeling of Geotextiles and Other Membranes in the Prevention of Reflection Cracking in Asphaltic Resurfacingby Luis F. DaSilva and Juan A. ConfréAbstractAn analytic study on the use of membranes in asphaltic resurfacing of fractured pavements is presented in this article. Based on general laws such as Hooke's Law, Paris' Law, and the energy conservation law plus some reasonable hypotheses, the Fabric Effectiveness Factor (FEF) has been determined. This factor indicates the increment in the service life of an asphaltic overlay. According to the results obtained, it is possible to conclude that geotextiles are physically the best membranes, followed by the wire mesh and some other alternatives. The results are general and provide a framework for future research (both theoretical and in the laboratory) on road service life related to thermal and traffic loading distresses. IntroductionAsphaltic resurfacing is a way of rehabilitating deteriorated and fractured roads, providing a partial solution based mainly on economic considerations. Nevertheless, this solution is restrained, among other secondary factors, by the premature emergence of cracks on the new layer surface, as a consequence of reflection cracking from the original pavement. Many different methods have been tried in order to prevent or delay this reflection. An attempt to delay the emergence of these cracks has also been made by incorporating such elements as geotextiles between the old pavement and the new layer. Whether the geotextile delays crack propagation or not has been a matter of divided opinion. Nevertheless, our interest in doing research on it was originally based upon some successful experimentation developed in Chile (more specifically on the "El Cobre" Road), where excellent results have been obtained. Although its application is not that extensive yet in the country, new research on the subject is currently being conducted. (1) Some successful experiences in the United States also influenced our interest. This theoretical study on the use of membranes for the prevention of reflection cracking in asphaltic resurfacing, provides a theoretical framework for future research, and gives credence to current empirical recommendations. Although approximate, its results are considered fairly acceptable; their interpretations will be given general treatment, focusing the analysis on the tendencies found. Geotextiles in PavementsA geotextile is defined as a synthetic permeable membrane, especially built for different uses related to soil engineering and whose materials belong to the great diversity of products manufactured by the polymer industry. Geotextile influence on longterm behavior of asphaltic overlays, along with the asphalt reinforcement effect, constitute a complex mechanism that depends on the "geotextileasphaltimpregnationpavement structuremanufacturing" system. This mechanism should by no means be related only to the tensile strength of the geotextile. In time, asphalt concrete roads will be exposed to cracking caused by temperature, asphalt aging, rutting, and flexural fatigue. In the resurfacing case, reflection cracking is also to be considered. This reflection is reduced and delayed by the seal and reinforcement properties of the geotextile considered. First, when saturated with asphaltic impregnation material, it forms an impermeable barrier that prevents water from reaching lower levels of the road; then, it dissipates stresses at each point. Requirements with which nonwoven geotextiles must comply are indicated in Table 1. Table 1  Geotextile Requirements
Theoretical Analysis of Traffic LoadsIn order to elaborate the best possible theoretical model that simulates vertical crack propagation to an asphaltic overlay, the analysis is based upon two principles: crack propagation due to the transmission of traffic loads and crack propagation due to temperature variations. Consideration is also given to concepts and hypotheses leading to acceptable results when compared to those obtained through experimentation. Pavement strength depends not only on maximum loads, but also on their frequency of occurrence. As for the effects due to traffic, this is a key aspect when it comes to loading trucks; it is under this point that the analysis of pavement design is conducted. Fatigue law relates stress levels to the number of cycles required to produce an asphaltic overlay failure, assuming the rest of the variables are constant. This law can be expressed in the form: where N is the number of times the load is repeated, is the maximum loading stress, and a, b are experimental parameters. (2) Nevertheless, the system to be analyzed includes an asphaltic overlay on an even sealed fractured pavement. In addition, the analysis should rest mainly upon the crack propagation itself from the rigid pavement to the surface. Therefore, under this concept of fatigue of the material, it is necessary to introduce the parameter f of propagation of the crack to the surface, whose equation is: the socalled Paris' law, indicating how much a fracture propagates per repeated load to produce such an increment. Analogously, C and m are parameters. (3) This criterion of resurfacing break will be defined at the time the crack reaches the surface. Due to the fact that this analysis deals essentially with the reflection phenomenon, it is necessary to say that it only considers upwards reflection cracking coming from a fractured concrete pavement. The duration of the acting load caused by a moving vehicle at a point in the fractured zone is indeed very short, just fractions of a second; besides, the load suffers a dispersion as it moves downwards in the material. The resulting deflection could be considered "elastic." For preventing crack propagation, some reinforcement elements (e.g., a geotextile) are incorporated into the system before applying the new layer. Avoiding reflection cracking is actually not possible, but an attempt can be made to delay such propagation. Thereby, a longer service life can be attained. The membrane stuffs the small space between the two concrete blocks and spreads the motion in the zone through a wide enough section of the upper layer so the deformation can be absorbed, thus reducing fatigue. (See Figure 1.) (4) If a load P is applied, a normal distribution of stresses S_{Z}(x,z) is verified at a given point of the membrane incorporated into the system, with: this relationship makes a normal distribution of P, and the standard deviation is given by zv, with v representing Poisson's coefficient. P is the load produced by the wheel, and its dimensions are force per unit width. (See Figure 2.)
Assuming that materials behave as an isotropic homogenous mean, and also that trafficloading distress produces small deformations within elastic limits, the following system of forces can be written with a general equation (according to Figure 3): (1) where: T(x) = T_{1}(x) + T_{2}(x), T1(x) = F_{1} [S_{z}(x,z) + Z ], superior tangential stress; T_{2}(x) = F_{2} [K_{s} w(x,z) + Z], inferior tangential stress; where is the specific weight of the asphaltic mix; Z is the thickness of the asphaltic overlay; and F_{1}, F_{2} are friction factors. The third term in equation (1) corresponds to an equation given by Winkler's modulus, where w(x) is the deflection at each point and K_{s} represents the reaction. The solution to this differential equation must comply with the condition of deformation compatibility. In general, and as a consequence of vertical displacements suffered by the concrete pavement, this layer will derive the flexure produced by traffic loading to the overlay pavement, thus propagating the crack to the surface. Through energetic considerations, it is possible to state the following differential equation: where, by definition, G df equals the work done by the splitting force G of a crack in a structure for a small propagation df (see Figure 4); V is the work done by the external forces; and, U is the internal energy of the structure. (3) According to Paris' law, mentioned above, it is possible to associate the increment in the differential df to the passing of a wheel by a fractured zone. The equation takes the form: rearranging this equation we get: Thus, evaluating and regrouping constant terms in C, we obtain the equation: (2) Study with MembraneWhen considering an overlay with the incorporation of such a membrane that leads to a prolongation of the service life, we would expect a greater loading frequency in order to reach the failure, that is, N (w/memb.) > N (wo/memb.). This could be possible through a reduction of the propagation force G, produced because of the work exerted by the external forces. The incorporation of a membrane such as a geotextile or a similar fabric ensures that the asphaltic overlay will be less loaded, owing to a greater elasticity supplied by the membrane. Analogously, as done with equation (2), we get an equation that includes the membrane through its thickness h_{g}, and presents an expected maximum stress T_{0} of smaller magnitude. Using N_{2} and T_{02} for the new situation with membrane, we have: (3) Assigning N_{1} to the original system without membrane, and considering h_{g}=0 for case 1, from (2) and (3) we get the quotient: (4) N_{1}/N_{2} represents how much the service life of an asphaltic resurface is prolonged by the incorporation of a membrane as a reinforcement element in order to control crack propagation produced by truck loadings. This quotient is actually the fabric effectiveness factor (FEF), supplied by manufacturers. (5) Nevertheless, the determination of FEF varies according to geometrical and loading conditions, presenting geotextiledifferent responses. It is necessary to say that the above equations are theoretical; parameters C and m are experimentally obtained by means of correlations between several loading tests that measure their corresponding cycles and loads. We assume that for both cases, coefficients C is of a similar order of magnitude. Likewise, it is possible to regroup exponents m, obtaining a much more sensitive parameter in equation (4), which implicitly depends upon the characteristics of the material for the respective loading state. (3) Distress produced by significant thermal variations is another important factor that affects pavements. These variations are cyclical, depending upon the maximum and minimum daily temperatures. The purpose of this analysis is to make it more convenient to consider daily, rather than yearly, temperature variations. This is the cycle that reduces service life of the pavement, having greater influence on crack propagation. Since we are studying an asphaltic overlay on the tip of an existing rigid pavement, consideration must be given to the fact that the response of each of these materials to thermal distress will be different. That is, when a pavement layer is subjected to these stresses, it tends to expand and contract at high and low temperatures, respectively. Therefore, an incompatibility between the deformation of the old pavement and the asphaltic overlay movement will occur. For the effect of modeling the propagation, cracks in solids may be taken as discrete surfaces under a displacement field. In the case of flat cracks, potential displacements of these surfaces are given by three independent fracturing modes. (See Figure 5.) When analyzing upward vertical crack propagations, as in this study, the most suitable fracturing mode is Mode I, opening. (6) More explicitly, when the concrete layer contracts  producing cracks  a slipping plane that stresses the asphaltic mix is generated in the interface of the two layers, inducing the reflection. One of the equations proposed for Mode I to relate displacements to stresses, outlined according to the reference system shown in Figure 6, is given by the analytic equation: (5) where K is the parameter that depends on loading (tensile intensity factor); e is the displacement normal to the direction of the crack (width of the transversal crack); G_{0} is the tensile modulus (G_{0} = E/2(1 + V)); E is the elasticity modulus: V is Poisson's Coefficient; f, are the ratio and the angle in polar coordinates, respectively; and k = 3  4v, is the flat deformation state. (3) Pavement temperature is depthdependent: the deeper, the lower (Thomlinson's criterion). This characteristic is represented by: (6) where T_{s} is the temperature at the surface level; _{d} is the coefficient dependent on thermal diffusiveness; and z is the depth at which temperature is T(z). (See Figure 7.) The tensile intensity factor is calculated from equation (5), where propagation occurs vertically, that is, when = (propagation angle is measured in relation to the propagation ratio). The general equation for this particular case takes the form: (7) The space e does not depend on the height of the crack. Nevertheless, it is proportional to the temperature variation on the plane at depth z. Rearranging, from (6) and (7) we get: Using Paris' law for the case of a thermal distress, we have: Under the boundary conditions stated above, we can obtain: (8) where From this equation, it is possible to conclude that the time to reach failure is proportional to two terms, both depending on thickness Z, from which the exponential term exp(m_{d}z) represents the gravitation of the thermal protection. A composed configuration that can be modeled by the following equation is shown in Figure 8: (9) where e_{q} represents the opening of the crack the propagation will develop when trespassing a membraneoverlay system whose thickness is determined by a multilayer system; Z_{t} is the overall thickness of this multilayer system; A_{q} is the equivalent proportionality coefficient; _{dq} is a factor that depends on the thermal diffusiveness of both materials; and T is the temperature difference that for all subsequent calculations will be considered constant and equal to 40 ^{0}C. Considering a multilayer model, we have: (10) where h_{g} is the thickness of the membrane, _{dg} is the thermal diffusiveness of the membrane, and A_{g} is the proportionality coefficient for the corresponding membrane. If we want N to increase in equation (8) with the incorporation of the geotextile, then we must have: (11) i.e., A_{g}A, which is true if e_{q}f, with:
According to the proposed hypotheses, the condition proportionality that coefficient A must comply with to prolong the service life is valid. Using equations (8) and (10) for the cases with and without membrane, the following quotient is obtained: (12) Equation (12) allows quantification of the increment in the number of loading cycleshence, of the service life  needed by the reflective crack coming from the concrete pavement in order to reach the surface of the asphaltic overlay. This equation gives the prolongation of the service life as a function of the thermal diffusiveness of the membrane; the thickness of the membrane; the thickness of the asphaltic overlay; exponent m and experimental parameter characteristics of bituminous materials; and coefficient A, obtained for each material. In addition, this quotient defines parameter FEF for the case of thermal distress, and is composed by three terms, the first two presenting a greater gravitation on the value of FEF: first, a relationship between coefficient A; second, an exponential term that is a function of parameter _{d} (depending on the thermal diffusiveness of the membrane constitutive material); and third, a term whose components are comparable in magnitude, having thus a lesser gravitation. Equivalent MembraneThe porous nature of a nonwoven membrane allows its elastic properties to be affected by the retention of asphaltic mix, forming an asphaltmembrane system that generates an equivalent membrane. At depth Z from the surface, there is a plane whose elastic properties are affected by the presence of a polymer fabric or some other material. Hence, an elasticity modulus o wing either to the incorporation of a membrane impregnated with asphalt or to the intrusion of asphaltic mix, depending on the case, is to be considered when modeling. This effect leads to an equivalent elasticity modulus, given by the equation: where E_{q} represents the term corresponding to the equivalent elasticity modulus; E_{a} corresponds to the stiffness of the asphalt in the mix, depending on loading frequency, temperature of application, penetration index, and temperature at penetration 800 (Van der Poel); and E_{m} corresponds to the value of the membrane elasticity modulus that shows a linear behavior and is determined by the tensile fatigue and the corresponding strain. The equivalent membrane is indeed a membrane that suffers less stress under the same deformation. and ß are interpreted as the ratio between the volume of the material and the total volume; their determination is obtained from the percentage of asphalt retention in the membrane, given that the areas are directly proportional to the part of the volume occupied by the material. From the equations obtained in the previous chapters, it is possible to implement a model where both events interact, under equal initial conditions, in a cracked concrete layer covered by an asphaltic overlay. The methodology to be followed consists of the determination of FEF, i.e., the increment in the number of loading and temperature distresses that will affect an asphaltic overlay. The final results are expressed in terms of the increment produced by the incorporation of a membrane in the loading cycle necessary to reach the failure; for this, we have to compare the systems with and without membrane, respectively. The model simulates a fake membrane whose material is an asphaltic mix; its thickness is the same as that of the equivalent membrane for the woven type, with which it will be compared by means of quotients. ParametersTo operate, the model requires all the data related to properties of materials and to the geometry of the system under consideration. To this end, we use the data contained in the different catalogs available for membranes like geotextiles, and other materials like iron or polyesterwoven structures. Nevertheless, in the case of burlap, and due to the lack of information on its properties, data on geotextiles of lowtensile strength and smaller thickness are used.
Table 2 indicates the parameters used in the model, where A_{g} is the proportionality constant between the width of the base of the crack and the temperature on the plane containing the vent of the crack, and gamma is the parameter that depends on thermal diffusiveness. Table 2  Membranes Physical and mechanical Property
Discussion and ConclusionsIn drawing the conclusions, we must stress the fact that the methodology used is based upon an analytic formulation, whose hypotheses are associated with the widely accepted elasticity theory and the fatigue laws. First of all, the simulation established that the deflection produced by temporary loads generates similar results to those obtained through the use of a deflectometer in a currently active highway. This fact allows the attainment of good approximations in the calculation of real stresses. It is possible to prove that the stresses under the asphaltic layer decrease as a consequence of a larger loading action area. Hence, the normal distribution used represents a good approximation. The incorporation of a membrane, such as a geotextile, provides a greater elasticity on the plane of stress located under the asphaltic overlay. This fact should be interpreted as an element that arrests distresses by modifying the elasticity modulus of the asphaltic material. A geotextile does not provide a greater strength to the system, but rather a greater flexibility in the cracked zone by reducing the stresses, generating a smaller vertical propagation force. Geotextiles do not allow control over deflections, but their smaller elasticity modulus lets them work at a smaller stress. Figure 9 of stress v/s thickness shows that for thicknesses greater than 3.94 in (10 cm), the incorporation of a geotextile has no gravitation. The effectiveness of these elements in reducing stresses becomes apparent in overlays whose thicknesses are between 1.57 and 2.76 in (4 and 7 cm). It is also possible to prove that the thicker the overlay, the greater the prolongation of the service life. To obtain a mixed material formed by bitumen and polymer, supplied by a geotextile, a concept of equivalent membrane was defined, corresponding to a membrane with retained bituminous material, which in the case of geotextiles is determined by the absorption parameter. The fabric absorption parameter is associated with the retention capacity, conforming an impermeable membrane whose elastic property allows a greater flexibility under a reduction of stresses. The compatibility between absorption and elasticity properties must be in equilibrium with the amount of bitumen contained in the membrane. Figure 10 tells that the elasticity supplied by the model increases the fabric effectiveness factor (FEF) of the resurfacing, and it is a function of the amount of bitumen; the membrane is saturated, reducing its effectiveness. Nevertheless, there is the limitation represented by the retention of bitumen; the effectiveness factor grows as the retention capacity increases. (9) For smaller absorption percentages, FEF goes down due to a low irrigation. The result of this analysis confirms an optimum absorption value of about 30 percent, implying a saturation amount of 1.3 x 10^{4} gal/in^{2} (0.9 L/m^{2}) for a geotextiletype membrane, according to recommendations by Task Force 25. It is important to state that only a good manufacturing process will allow an optimum outcome, since the goal of attaining an impregnated membrane that complies with the mentioned specifications requires a proper execution. One technique consists of using a roadroller when the tack coat is applied, allowing saturation of the membrane. On the other hand, from Figures 11 and 12, we can infer that for the same distresses, the greater the thickness of the asphaltic overlay, the smaller the value of FEF; this fact restresses the importance of membranes for thinner layers. We must take into account that for more elastic materials, that is, polyester screens (polyester woven) and geotextiles, the value found for FEF is a consequence of the greater flexibility developed in the interlayer, which is indicated in Figure 13. In contrast, for a wire mesh whose elasticity modulus is high, the FEF obtained is associated with the greater strength produced by a greater stiffness supplied to the system by the iron material. According to the general results obtained, it is possible to conclude that the geotextile is physically the best membrane, reaching the greater increment in the service life due to traffic loading, followed by the wire mesh, the woven structure, and, finally, the sackcloth. It is important to state that the prolongation of the service life through the incorporation of a geotextile would theoretically indicate a global amplification of four times. Nevertheless, precisely because of the theoretical approach of the analysis, only the trends in the results of the simulation are to be interpreted; these trends corroborate the excellent outcomes obtained in constructions that followed proper manufacturing processes. Due to the complex nature of the problem, it must be stressed that the parameters used were only those directly weighing on the propagation phenomenon. With this in mind, the asphalt aging process was not incorporated into the analysis, as well as the organic distresses the geotextile suffers; the goal sought is welldefined by the variables considered most important in the analysis. Consideration must be given to the fact that this research is based upon an analytic study done with little data provided by actual experiences, and with information supplied by catalogs. No laboratory experimentation was done; if it had been, certainly more precise results would have been reached through equation adjustment. In conclusion, we have to point out that the use of different sorts of materials leads to different theoretical behaviors, not necessarily reflecting reality, thus serving only as a reference framework. The importance of geotextiles derives from this fact, without denying possible advantages in the use of other materials. References(1) D. Cabrera and L. Serra. Experiencias con geotextiles en repavimentación asfáltica en pavimentos flexibles 3er. Congresso Iberoamericano del asfalto. Cartagena, Colombia, 1985. (2) Hugo Garcia. Ley de fatiga de mezcla asfáltica mediante ensayos de flexión. Boletín Técnico LNV No. 2. Laboratorio Nacional de Vialidad, MOP, Santiago, Chile, 1989. (3) H. Goagolou and J. P. Marchand. La méthode des éléments finis application à la fissuration des chaussées et au calcul des temps de remontee des fisures. Laboratoires des Ponts et Chaussées. Bulletin de Liaison 125. (4) P. R. Rankilor. Membranes in Ground Engineering. John Wiley & Son, Chichester, England, 1981. (5) K. Majidzadeh, M. S. Luther, and H. Sklyut. A Mechanistic Design Procedure for FabricReinforced Pavement Systems. Second International Conference on Geotextiles, 1992, Vol. II. Las Vegas, Nevada, U.S.A. (6) F. Erdogan. The Mechanism of Fracture. ASME Winter Annual Meeting, 1976. New York, N.Y., U.S.A. (7) Bidim. Catálogo de aplicaciones en obras públicas y de ingeniería civil. 3rd. ed. Edit. Rhodia S. A., Sao Paulo, Brasil, 1982. (8) Rehau. Rehau ARMAPAL. Reflection Cracking Beam Testing. SWK Pavement Engineering Highfields Science Park. Nottingham, Germany, 1987. (9) Amoco Fabrics Company. Boletines Técnicos. Atlanta, Georgia, U.S.A. Prof. Luis F. Da Silva is a researcher and faculty member in the Physics Department of the Universidad Técnica Federico Santa María in Valparaíso, Chile. He has done extensive research on experimental solid physics, with more than 40 publications in international journals and conference proceedings. Juan A. Confré is a civil engineer currently assigned as a project engineer at a Chilean government agency. He has done theoretical research on road rehabilitation. His dissertation at the Universidad Santa María in Valparaíso, Chile, dealt with the use of membranes in asphaltic resurfacing. 
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