Pore Pressure and Viscous Shear Stress Distribution Due to Water Flow within Asphalt Pore Structure

Transcription

1 Computer-Aided Civil and Infrastructure Engineering 24 (2009) Pore Pressure and Viscous Shear Stress Distribution Due to Water Flow within Asphalt Pore Structure M. Emin Kutay Assistant Professor, Department of Civil and Environmental Engineering, Michigan State University, 3554 Engineering Building, East Lansing, MI , USA & Ahmet H. Aydilek Associate Professor, Department of Civil and Environmental Engineering, 163 Glenn L. Martin Hall, University of Maryland, College Park, MD 20742, USA Abstract: There has been a concentrated effort in modeling fluid flow in asphalt pavements, and most of the existing work has been limited to evaluation of directional permeabilities. The effects of other phenomena, such as development of flow-induced pore pressure and viscous shear stress distributions at the pore solid interfaces, on moisture damage in an asphalt pore structure have not been fully understood. A three-dimensional (3D) numerical fluid flow model was developed using the lattice Boltzmann (LB) method to simulate water flow within the pore structures of various hot mix asphalt (HMA) pavements. In this article, an in-depth analysis of variations of pore pressures and viscous shear stresses caused by water flow within the 3D pore structure of different HMA specimens is provided. The relationship between the pore geometry and the pore water pressure and viscous shear stresses were studied. Pore pressures and viscous shear stresses were computed after 3D fluid flow simulations conducted within the real pore structures of numerous HMA specimens. X-ray computed tomography (CT) was used to acquire 3D pore structures of HMA specimens, and the obtained images were input into the LB model. The results indicated that the pore water pressure gradient is highly nonlinear within the To whom correspondence should be addressed. kutay@ msu.edu. pore structure of HMA pavements, as opposed to a linear gradient commonly observed in homogeneous pore structures (e.g., granular soils). The viscous shear stresses were observed to be the largest at the constrictions located at the mid-depth of the specimens. Furthermore, a one-toone relationship was observed between the reduction in the pore area and viscous shear stresses developed during the water flow. 1 INTRODUCTION One of the major factors that cause frequent pavement maintenance is moisture damage. The moisture damage can destruct the cohesive bond within the asphalt binder or the adhesive bond between the aggregate and the binder. McCann et al. (2005) and Castelblanco et al. (2005) report cracks and excessive deflections due to stripping of the binder as a result of moisture damage. One way to quantify the moisture damage and characterize fluid transport properties in asphalt concrete is the measurement or modeling of permeability (hydraulic conductivity). Laboratory- or field-measured permeability of asphalt pavements was assumed to be constant in all directions in the early work (Gogula et al., 2003; Hunter and Airey, 2005). Recent studies, on the other hand, indicated that a majority of asphalt C 2009 Computer-Aided Civil and Infrastructure Engineering. DOI:.1111/j x

2 Pore pressure and viscous shear stresses in HMA 213 pavements have an anisotropic and heterogeneous internal pore structure, which directly influences the magnitude of permeabilities in different directions (Masad et al., 1999, 2003; Al-Omari and Masad, 2004; Hunter and Airey, 2005; Kutay et al., 2007). In spite of the fact that there has been a concentrated effort in modeling fluid flow in asphalt pavements, most of the existing work has been limited to evaluation of directional permeabilities. The effects of other phenomena, such as development of flow-induced pore pressure and viscous shear stress distributions at the pore solid interfaces, on moisture damage in an asphalt pore structure have not been fully understood. Critical values of these shear stresses and pore pressures can be important and need to be explored to accurately estimate the flow patterns in asphalt pavements. They can especially be important for use as part of numerical simulations of moisture damage at the microstructural level (e.g., analysis of raveling). For example, Kringos and Scarpas (2005) introduced a modeling technique to understand the physical processes and mechanics causing debonding of the mastic from the aggregates due to the fluid flow in asphalt pavements. The main objective of the current study was to investigate the effect of directional flow on moisture transport through pavements. The first phase of the study focused on experimental and computational evaluation of directional permeabilities in hot mix asphalt (HMA) and analysis of factors affecting these permeabilities (Kutay et al., 2006, 2007). This article summarizes the findings of the second phase of the study and discusses the variations of pore pressures and pore solid interface shear stresses within HMA. To evaluate these variations, a three-dimensional (3D) pore scale-based fluid flow model was developed by utilizing the lattice Boltzmann (LB) approach. X-ray computed tomography (CT) was used to acquire real 3D pore structures of HMA specimens, and the images were input into the model. The effects of pore structure on the measured quantities were studied. 2 SPECIMEN PREPARATION AND IMAGE ACQUISITION The analysis of fluid flow in HMA included field cores and laboratory-prepared specimens. The laboratory specimens were fabricated as per American Association of State Highway and Transportation Officials (AASHTO) PP28 procedure to study a number of mixture variables that are likely to affect the pore structure distribution and hydraulic conductivity. The selected variables included nominal maximum aggregate size (NMAS), compaction energy (number of gyrations in the gyratory compactor), and aggregate size distribution or gradation. Of the 35 laboratory specimens prepared for this study, 23 were Superpave (National Academy of Sciences, Washington, D.C.) dense graded mixtures and 12 were relatively permeable stone matrix asphalt (SMA) mixtures. For the Superpave mixtures, NMASs of 9.5 mm, 12.5 mm, 19 mm, and 25 mm were selected. SMA gradations were selected from three different NMASs: 9.5 mm, 12.5 mm, and 19 mm. The number of gyrations was varied from 25 to 75 to cover a range of compaction energies. Seven 150-mm-diameter field cores were obtained from the test sections of the Accelerated Loading Facility (ALF) located at the Turner- Fairbank Highway Research Center (TFHRC) of the Federal Highway Administration (FHWA). Table 1 presents the mix design properties of all the specimens used in this study. The 3D internal structures of the specimens were obtained using the nondestructive X-ray CT imaging technique. The X-ray CT is a powerful nondestructive 3D imaging technique that captures the interior structure of materials using their X-ray attenuation characteristics (primarily based on density differences within the sample). Two-dimensional image slices of the specimens are captured using the X-ray CT device and are stacked to reconstruct the 3D structure. An example of a reconstructed image of an asphalt specimen is shown in Figure 1a. From the reconstructed image, regions with similar densities (e.g., air voids and aggregates) can be segmented to compute samples characteristics such as the air void distribution and connectivity. In this study, grayscale 3D images of the specimens were converted to binary 3D images by morphological thresholding, where black voxels represent solid, and white voxels represent air voids. Then, the 3D binary (black and white) image was input to the LB numerical fluid flow model. More detailed discussion on the X-ray CT technique, specifications of the device utilized in this study, and the methods followed for processing the captured images are provided by Kutay et al. (2007). 3 THREE-DIMENSIONAL NUMERICAL MODELING OF FLUID FLOW 3.1 Lattice Boltzmann method Among the various techniques in numerical fluid flow modeling, the LB method was chosen in the current study due to its ease of implementation of boundary conditions at the solid fluid interface and its numerical stability in a wide variety of flow conditions with various Reynolds numbers. The LB method has emerged as a versatile alternative to traditional finite element and finite difference Navier Stokes solvers as it has proven to be very accurate in modeling isothermal, incompressible flow, especially in the case of flow

3 214 Kutay & Aydilek Table 1 Properties of the asphalt specimens tested Specimen ID NMAS (mm) N.Gyr. Gradation P b (%) G mm (g/cm 3 ) G mb (g/cm 3 ) n(%) 9.5F Fine C25 Coarse F50 50 Fine C50 Coarse F75 75 Fine C75 Coarse F Fine C25 Coarse F50 50 Fine C50 Coarse F75 75 Fine C75 Coarse C Coarse F50 50 Fine C50 Coarse F75 75 Fine C75 Coarse F Fine C25 Coarse F50 50 Fine C50 Coarse F75 75 Fine C75 Coarse SMA-A SMA SMA-A2 SMA SMA-B1 25 SMA SMA-B2 SMA SMA-A SMA SMA-A2 SMA SMA-B1 50 SMA SMA-B2 SMA SMA-A SMA SMA-A2 SMA SMA-B1 75 SMA SMA-B2 SMA L NA Field-B L2 Field-A L3 Field-A L4 Field-A L5 Field-A L6 Field-A L7 Field-A Notes: G mb = bulk specific gravity of the mix; G mm = maximum specific gravity of the mix; n = porosity; NA = not applicable; N.Gyr. = number of gyrations; NMAS = nominal maximum aggregate size; P b = optimum binder content. through porous media (Succi, 2001). The LB method approximates the continuous Boltzmann equation by discretizing physical space with lattice nodes and velocity space by a set of microscopic velocity vectors (Maier et al., 1997). The time- and space-averaged microscopic movements of fluid particles are modeled using molecular populations called distribution function. The distribution function defines the density and velocity of fluid molecules at each lattice node at each time step. Fluid particles travel on the lattice nodes based on the magnitude and direction of the distribution function components. Specific particle interaction rules are set so that the Navier Stokes equations are satisfied. The governing equations and detailed explanation of the LB method can be found in Succi (2001). The D3Q19 (3D 19 velocity) LB model was used in this study. The set

4 Pore pressure and viscous shear stresses in HMA 215 e 9 =[-1,-1,0] z e 2 =[-1,0,0] e 14 =[-1,0,1] e 13 =[-1,0,-1] y x e 18 =[0,-1,1] e 8 =[-1,1,0] e 4 =[0,-1,0] e 17 =[0,-1,-1] (a) e 5 =[0,0,1] e 19 =[0,0,0] e 6 =[0,0,-1] (b) e 15 =[0,1,1] e 3 =[0,1,0] e =[1,-1,0] e 16 =[0,1,-1] e 11 =[1,0,1] e 1 =[1,0,0] e 7 =[1,1,0] e 12 =[1,0,-1] Fig. 1. (a) Three-dimensional reconstructed image of an asphalt specimen using the X-ray. (b) D3Q19 lattice microscopic velocity directions generated at the center of each pixel. of microscopic velocity vectors for the D3Q19 model is shown in Figure 1b. A more detailed explanation of the method can be found in Kutay et al. (2006). 3.2 Fluid flow simulations within asphalt specimens The binary 3D images of the asphalt specimens were utilized to generate the lattice nodes used in the LB model. Before generation of the lattice nodes, an additional task was performed to increase the speed of the simulations. The isolated pores that had no connection to any of the outside boundaries (i.e., surface) of the specimen were eliminated. This was accomplished using a so-called connected components algorithm developed in Matlab (The MathWorks, Inc., Natick, MA) (Kutay and Aydilek, 2005). Then the lattice nodes were generated at the centers of each white voxel in the binary image representing the interconnected pore structure. It is important to mention that this step was not required for the LB simulations; however, the isolated pores were eliminated solely to speed up the simulation at each time step. Including the isolated pores would lead to propagation and collision operations of the LB method at those pores, which results in zero velocity as there is nowhere for the water to flow. Decreasing the number of nodes by eliminating the isolated pores helps in reducing the amount of time that is required for the completion of each time step, requiring less computer memory and reducing the total number of time steps to reach the steady-state flow condition. Fluid flow simulations were performed by specifying constant inlet and outlet pressures such that the difference would yield a steady-state water flow from the inlet toward the outlet. Figure 2a shows a portion of the 3D structure of the specimen 19SMA-B2 together with a surface plot (shown in blue) of the water flow pathway. This pathway shows the interconnected pore space where the absolute value of the water velocity is greater than the threshold value. For example, the pores that are included in the blue surface plot are the ones where the velocity is greater than 1% of the overall average velocity. It should be observed from the surface plot that only a portion of the interconnected pore space is utilized by water. This is due to the presence of dead-end pores that do not contribute to fluid flow, as illustrated in Figure 2b. This indicates that computation of the interconnected pore structure may not be sufficient to accurately predict water flow pattern. Due to the same reason, a significant variability is observed when the permeability of the asphalt specimens are predicted using modified versions of the Kozeny Carman equations that utilize effective porosity, that is, the porosity computed using the interconnected pore space (Kutay and Aydilek, 2006). 3.3 Analysis of pore pressure distribution The results of the LB simulations indicated that the pore water pressure gradient is highly nonlinear within the pore structure of asphalt specimens, as opposed to a linear gradient commonly observed in homogeneous pore structures (e.g., granular soils). To illustrate the

5 216 Kutay & Aydilek (a) (b) Dead end pore (no flow) Fig. 2. (a) Flow pathway within the specimen 19SMA-B2 computed by the LB fluid flow simulation. (b) Conceptual illustration of a dead-end pore that does not contribute to fluid flow. observed phenomenon, the trends for 9.5C50 are given in Figure 3a as an example. In Figure 3a, the pressure at each depth is the average of the pressures computed at all lattices at the given depth. It was observed that the pore water pressure stayed relatively constant within the upper 45-mm portion of the specimen, and a sharp decrease in the pressure was observed between 45 and 65 mm. Then the pressure was approximately constant for the remaining depths. The dashed line in Figure 3a shows the linear decrease in pressure (i.e., constant pressure gradient throughout the depth) for a homogeneous pore structure, such as the pore structure of a uniformly graded granular soil. However, asphalt specimens exhibited a quite different behavior, primarily due to the heterogeneous pore structure evident in Figure 3c. To quantify the decrease in the pressure throughout the depth, a local pressure gradient (slope of the pressure decrease line) was computed as follows: P i = P i+1 P i 1 2 l (1)

6 Pore pressure and viscous shear stresses in HMA Pore Water Pressure (Pa) P z-in (pressure at inlet) Pressure Gradient (g/mm 2 -s 2 ) max. pressure gradient P = 2.25x -4 g/mm 2 -s 2 max Pore Cross Sectional Area (mm 2 ) min. pore area = 32.3 mm 2 Depth (mm) observed pressure distribution in 9.5C50 linear decrease in pressure (for an ideal homogeneous and isotropic pore structure) Depth (mm) mean pressure gradient P = 0.2x -4 g/mm 2 -s 2 ave Depth (mm) A min mean pore area A = mm 2 ave 120 P z-out (pressure at outlet) (a) 120 (b) 120 (c) Fig. 3. Variation of (a) pore water pressure, (b) pressure gradient, and (c) pore cross-sectional area with depth for specimen 9.5C50. where P i is the local pressure gradient within the ith slice, l is the slice thickness, and P i 1 and P i+1 are the average pressure values for the previous and next slices, respectively. Figure 3b shows the local pressure gradient variation within 9.5C50. It is clear that the pore constrictions (the location of minimum pore areas) are the zones where the nearly maximum pore water pressures and local pressure gradients are located. The variation of pore cross-sectional area in specimen 9.5C50 is shown in Figure 3c, where the constriction zone (minimum pore cross-sectional area) is located at about 60 mm. At this depth, the local pressure gradient is much higher than the gradient at other depths as well as the overall average pressure gradient within the entire specimen (Figure 3b). Considering the principles of conservation of mass, the presence of high pressure gradients at the constrictions is meaningful. When fluid particles are forced to pass through a constriction where the area available for moving fluid particles decreases significantly, the velocities must be very high to conserve the momentum between the inlet and the outlet of the constriction. These high velocities can only be created by large pressure gradients at this zone. A summary of maximum pressure gradients and pore water pressures at the constrictions is provided in Table 2. The maximum pressure gradients observed within the pore structure are two to six times larger than the overall average pressure gradient. This is possibly caused by the constrictions that exist along the flow path, and it is an important indicator of highly nonuniform pore structure of asphalt mixtures, regardless of mixture type. Table 2 also shows that most of the fine-graded gyratory samples did not have an interconnected (macro) pore structure, whereas all of the SMA mixtures have interconnected pores. It should be noted that the minimum pore size that the X-ray CT could measure for the given specimen size was 0.3 mm. Therefore, pores smaller than 0.3 mm were considered as micropores and were ignored in this analysis. A comparison of the data presented in Tables 1 and 2 indicate that effective porosities (n eff ) were about 20 to 90% of the total porosities (n), further justifying this assumption. To investigate the relation between the constriction zone and local pressure gradient, two ratios were defined: pressure gradient ratio ( P r ) and area ratio (A r )as P r = P max (2) P ave A r = A ave A min (3) where A ave and A min are the average and minimum pore cross-sectional areas, respectively, and P max and P ave are the maximum and average pressure gradients, respectively (see Figures 3b and c). It can be seen from Figure 4 that the pressure gradient ratio increases with increasing area ratio for the asphalt specimens tested. Such a trend was

7 218 Kutay & Aydilek Table 2 Pore pressures, maximum pressure gradients, and minimum pore areas for the HMA specimens tested Minimum Maximum Average Pore water pore cross- pressure pressure pressure at the sectional area gradient gradient constriction Sample no. ID Specimen ID n eff (%) ( 8 mm 2 ) ( 8 g/mm 2 -s 2 ) (x 8 g/mm 2 -s 2 ) ( 3 Pa) 1 Coarse-graded 9.5C gyratory 9.5C50 NA NC NC NC NC 3 specimens 9.5C75 NA NC NC NC NC C C50 NA NC NC NC NC C75 NA NC NC NC NC 7 19C C C C C C Fine-graded 9.5F25 NA NC NC NC NC 14 gyratory 9.5F50 NA NC NC NC NC 15 specimens 9.5F75 NA NC NC NC NC F25 NA NC NC NC NC F50 NA NC NC NC NC F75 NA NC NC NC NC 19 19F NC NC NC NC 20 19F50 NA NC NC NC NC 21 19F75 NA NC NC NC NC 22 25F F50 NA NC NC NC NC 24 25F75 NA NC NC NC NC 25 SMA mixtures 9.5SMA-A SMA-A SMA-B SMA-B SMA-A SMA-A SMA-B SMA-B SMA-A SMA-A SMA-B SMA-B Field cores L1 NA NC NC NC NC 38 L L3 NA NC NC NC NC 40 L L L6 NA NC NC NC NC 43 L7 NA NC NC NC NC Note: NA = effective porosity was not available due to lack of interconnected pore structure; NC refers to the specimens with no interconnected macropores (i.e., minimum size greater than 0.3 mm) between two opposite faces of a specimen; n eff = effective porosity. expected because the area ratio increases when the gap between the average and the minimum pore crosssectional area increases. This large gap can cause high differences in pressure, thus high local pressure gradients. The data presented in Table 2 also indicate that the maximum pressure gradients were 1.6 to 6 times higher than the average pressure gradient for the tested specimens.

8 Pore pressure and viscous shear stresses in HMA (b) the pore solid interface. The following equation defines the fluid force acting on a surface (Panton, 1996): A r 5 y = x R 2 = P r Fig. 4. Pressure gradient ratio versus area ratio relationship for the specimens tested. 3.4 Analysis of viscous shear stresses at the pore solid interfaces High velocities at the constriction zones generated due to the presence of large local pressure gradients directly affect the magnitude of the viscous shear force acting on R i = η i T ij (4) where R i is the surface force per unit area, η i is the unit normal vector of the surface, and T ij is the stress tensor. The physical meaning of the stress tensor is that a component of the stress tensor T ij is equal to the stress in direction j on a plane with a unit normal vector in direction i. Equation (4) is given in index notation and a more explicit form can be written as follows: R x T xx T xy T xz R y = [ η x η y η z ] T yx T yy T yz (5) R z T zx T zy T zz Equation (5) implies that the force acting on a surface can simply be calculated by multiplying the stress tensor with the unit normal vector of a surface. In the current study, the unit normal vectors of each voxel surface in 3D images of asphalt specimens were orthogonal to each other, which facilitated the computations. For example, for a given plane with unit normal η i = [1, 0, 0] (Figure 5), the components of the surface force can be calculated using R j = 1T xj + 0T yj + 0T zj. Accordingly, the surface force components become R x = T xx R y = T xy R z = T xz (6) Fig. 5. Components of a surface force acting on different faces of a cubical voxel.

9 220 Kutay & Aydilek Figure 5 also presents the surface force components acting on different faces of a cubical voxel. It can clearly be seen that the surface force components acting in shear are actually the shear components of the stress tensor (i.e., T ij with i j), which indicates that these components can directly be used for computing shear stresses. The interfacial forces can be decomposed into two parts in a tensor form: pressure term and viscous term (Panton, 1996) as T ij = Pδ ij + τ ij (7) where T ij is stress tensor, P is the pore water pressure, and τ ij is viscous stress tensor. δ ij is called the Kronecker delta and is defined as follows: δ ij = 1 if i = j (8) δ ij = 0 if i j The matrix form of Equation (7) can then be written as T xx T xy T xz τ xx τ xy τ xz T yx T yy T yz = P τ yx τ yy τ yz T zx T zy T zz τ zx τ zy τ zz (9) The pressure term Pδ ij in Equation (7) is directly linked to the pore water pressure, whereas, the viscous term (τ ij ) is caused by the viscous fluid movement. The pressure term does not have a direct influence on the shear components of the stress tensor. Therefore T ij = τ ij when i j () The viscous stress tensor components were computed using the following formula (Panton, 1996): ( ux τ xy = τ yx = μ y + u ) y (11) x ( uy τ yz = τ zy = μ z + u ) z (12) y ( uz τ zx = τ xz = μ x + u ) x (13) z where μ is the kinematic viscosity of the fluid. The partial differentiations in Equations (11) (13) were computed numerically at the end of the LB simulations. Figures 6a 6c show the shear stress components (τ xy, τ yz, and τ zx ) computed at the lattice nodes of the specimen 19SMA-B2. The color level (red = higher shear stresses, blue = lower shear stresses) represents the magnitude, whereas, the x, y, and z axes indicate the spatial location of the pore. In general, high shear stresses were observed at the mid-depth of the specimens, as shown in Figures 6a 6c. Those locations could be ideal candidates for binder stripping (i.e., the debonding of the binder from the aggregate). The likelihood of penetration of water to the aggregate binder interface, and thus weakening of the bond strength, is higher at those locations due to the large viscous shear stresses applied by the water. Table 3 provides a summary of maximum shear stresses observed for different HMA specimens. To study the variation of the shear stresses throughout the specimen, the mean value of shear stress tensor components at each depth (i.e., in z direction) were computed. An example plot for 9.5C50 is given in Figure 6, where all three components of shear stress tensor exhibited a sharp increase at a depth of about 60 mm. It was evident from Figure 3c that the pore cross-sectional area is the lowest at the same zone. This is meaningful because the pressure gradient is the highest at this zone (Figure 3b), leading to high velocities, and thus shear stresses. Similar observations were made during the analysis of all the asphalt specimens utilized in this study. Similar to the ratio defined for the pressure gradient, shear stress ratios were defined to investigate the effect of minimum pore area on shear stress components as Txy r = Tmax xy Txy ave Tyz r = Tmax yz Tyz ave Tzx r = Tmax zx Tzx ave (14) where T r ij is the shear stress ratio, and Tmax ij and T ave ij are the maximum and average values of shear stress components, respectively (see Figure 6). The shear stress ratios were plotted against the area ratio (A r )infigure7.a direct relationship exists between the shear stress ratios and the area ratio. This indicates that the ratio of the cross-sectional area of the constrictions to the overall average pore cross-sectional area of the entire specimen directly affects the maximum viscous shear stresses occurring at the constriction zones. 4 SUMMARY AND CONCLUSIONS A numerical study was undertaken to analyze the variation of pore water pressures and pore solid shear stresses throughout asphalt concrete. Real pore structures of 35 laboratory-prepared HMA specimens and 7 field cores were acquired using an X-ray CT. A 3D pore scale-based fluid flow model was developed by utilizing the LB approach. The LB simulations revealed that a linear decrease in the pressure was not observed when a constant pressure difference was applied between the inlet and the outlet of the asphalt specimens. The pressure gradient varied greatly in different specimens depending on the existence of a pore constriction. The local pressure gradients at constrictions were up to six times higher than the average pressure gradient, which created very high

10 Pore pressure and viscous shear stresses in HMA 221 Fig. 6. Viscous stress tensor components (a) τ xy = τ yx,(b)τ yz = τ zy,and(c)τ zx = τ xz for specimen 9.5C50. Dimensions on axes are in pixels, and pixel resolution is 0.8 mm/pixel. Shear stress tensor components for T xy, T yz,andt zx.

11 222 Kutay & Aydilek Table 3 Maximum solid water interfacial shear stresses for the HMA specimens tested Minimum pore crossmax T xy max T yz max T zx Sample no. ID Specimen ID sectional area (mm 2 ) ( 11 Pa) ( 11 Pa) ( 11 Pa) 1 Coarse-graded 9.5C gyratory 9.5C50 NC NC NC NC 3 specimens 9.5C75 NC NC NC NC C C50 NC NC NC NC C75 NC NC NC NC 7 19C C C C C C Fine-graded 9.5F25 NC NC NC NC 14 gyratory 9.5F50 NC NC NC NC 15 specimens 9.5F75 NC NC NC NC F25 NC NC NC NC F50 NC NC NC NC F75 NC NC NC NC 19 19F50 NC NC NC NC 20 19F75 NC NC NC NC 21 25F F50 NC NC NC NC 23 25F75 NC NC NC NC 24 SMA mixtures 9.5SMA-A SMA-A SMA-B SMA-B SMA-A SMA-A SMA-B SMA-B SMA-A SMA-A SMA-B SMA-B Field cores L1 NC NC NC NC 37 L L3 NC NC NC NC 39 L L L6 NC NC NC NC 42 L7 NC NC NC NC Note: NC refers to the specimens with no interconnected macropores (i.e., minimum size greater than 0.3 mm) between two opposite faces of a specimen. velocities at these locations. Two newly defined ratios, pressure gradient ratio ( P r ) and area ratio (A r ), correlated well with each other. The simulations suggested that the maximum shear stresses caused by the viscous fluid movement were generated at the pore constrictions. The ratios of the maximum shear stresses observed at the constrictions to the overall average shear stress ranged from 1 to 13. This indicates that the viscous shear stresses can be extremely high if pore constrictions exist and water is forced to go through these locations (i.e., there is no other water pathway). These large shear stresses

12 Pore pressure and viscous shear stresses in HMA 223 T xy r 1 1 Line of equality (y=x) (a) a specimen is its permeability. A specimen with high permeability probably will not have constrictions. On the other hand, if the permeability is extremely low, water may be flowing through the micropores within the mastic, and there may not be interconnected macropores. The constrictions probably exist at a range of permeabilities that are neither too high nor too low. This supports the findings of Castelblanco (2004) who defined the concept of pessimum permeability range and showed that the moisture damage is maximized at intermediate permeabilities, which in general correspond to total air void levels between 7 and 13%. T yz r A r ACKNOWLEDGMENTS The funding for this project was provided by U.S. Department of Transportation, Federal Highway Administration (FHWA) through contract no. 03-X This support is gratefully acknowledged. The opinions expressed in this article are solely those of the authors and do not necessarily reflect the opinions of the FHWA. 1 1 T zx r 1 1 Line of equality (y=x) A r A r (c) (b) Line of equality (y=x) Fig. 7. Shear stress ratios (a) T r xy,(b)tr yz,and(c)tr zx versus area ratio relationship. may cause the asphalt binder to separate from the aggregate surface. Once binder separation from the aggregate starts, water can easily penetrate between the binder and the aggregate. This can potentially further accelerate the debonding of the binder from the aggregate. An indication of the existence of constrictions in REFERENCES Al-Omari, A. & Masad, E. (2004), Three dimensional simulation of fluid flow in X-ray CT images of porous media, International Journal of Numerical and Analytical Methods in Geomechanics, 28, Castelblanco, A. (2004), Probabilistic analysis of air void structure and its relationship to permeability and moisture damage of hot mix asphalt. MS thesis, Texas A&M University. Castelblanco, A., Masad, E. & Birgisson, B. (2005), HMA moisture damage as a function of air void size distribution, pore pressure and bond energy, in Proceedings of the 82nd Transportation Research Board Annual Meeting, Washington, DC; (CD-ROM). Gogula, A., Hossain, M., Romanoschi, S. & Fager, G. (2003), Correlation between the laboratory and field permeability values for the Superpave pavements, in Proceedings of the 2003 Mid-Continent Transportation Research Symposium, Ames, IO. Hunter, A. E. & Airey, G. D. (2005), Numerical modeling of asphalt mixture site permeability, in Proceedings of the 84th Transportation Research Board Annual Meeting, Washington, DC; (CD-ROM). Kringos, N. & Scarpas, A. (2005), Raveling of asphaltic mixes due to water damage: computational identification of controlling parameters, in Proceedings of the 84th Transportation Research Board Annual Meeting, Washington, DC; (CD-ROM). Kutay, M. E. & Aydilek, A. H. (2005), Lattice Boltzmann method in modeling fluid flow through asphalt concrete, Environmental Geotechnics Report 05-2, University of Maryland, College Park, MD, 284. Kutay, M. E. & Aydilek, A. H. (2006), Accuracy of the two common semi-analytical equations in predicting asphalt permeability, in 2nd International Workshop on X-ray CT

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