Accuracy of the Two Common Semi- Analytical Equations in Predicting Asphalt Permeability

Transcription

1 Accuracy of the Two Common Semi- Analytical Equations in Predicting Asphalt Permeability M. Emin Kutay * Ahmet H. Aydilek** * Research Engineer, Turner-Fairbank Highway Research Center (TFHRC) 6300 Georgetown Pike, McLean, Virginia 220, USA. mkutay@fhwa.dot.gov ** Assistant Professor, Civil and Environmental Engineering 63 Glenn Martin Hall, University of Maryland College Park, Maryland 20742, USA aydilek@eng.umd.edu ABSTRACT: Three-dimensional internal pore structures of various asphalt specimens with varying mix-designs and compaction levels were generated using X-ray Computed Tomography (CT) technique. Pore structure parameters were computed using image processing algorithms and estimated permeabilities using two semi-analytical equations were compared to laboratory-based vertical permeability. Furthermore, an analysis method was proposed to improve the accuracy of the equations. KEY WORDS: asphalt, permeability, X-ray CT, Kozeny-Carman, image processing. Introduction Permeability is an important characteristic that influences the long term field performance of asphalt pavements. Permeability has been increasingly included in the design of the asphalt pavements in the form of "pessimum permeability" where the pavement's susceptibility to moisture induced damage is maximum (Lytton et al. 2005). Laboratory or field measured unidirectional permeability is usually assumed to be constant in all directions. However, since asphalt pavements usually have an anisotropic and heterogeneous internal pore structure, measured unidirectional permeability does not accurately provide the three-dimensional fluid flow characteristics in the field. Alternatively, several semi-analytical equations (Kozeny 927, Carman 956, Walsh and Brace 984) have been used for the estimation of permeability (k) of asphalt pavements (Al-Omari et al. 2002). Table

2 2 GeoX 2006, 2 nd International Workshop on X-Ray CT for Geomaterials provides two common equations. Derivations of these equations are based on the approximation of pore structure with simple geometries, such as tubes and cones, and most importantly they assume an isotropic pore structure. Therefore, these equations do not fully represent anisotropic pore structures of asphalt pavements. Furthermore, previous studies indicated that asphalt pore structure has a sandglass shape in the vertical direction, in which constrictions in the mid-depth controls the vertical permeability (Kutay et al. 2006). As a result, most of semi-analytical equations that utilize the entire pore structure often overestimate the vertical permeability. Therefore, there is a need for determination of limits of applicability of these semi-analytical equations to different asphalt pavement types. To respond to this need, three-dimensional internal pore structures of various asphalt specimens with varying mix-designs and compaction levels were generated using X-ray Computed Tomography (CT) technique. Pore structure parameters required as inputs in these equations were computed using image processing algorithms and estimated permeabilities were compared to laboratory-based ones. Furthermore, an analysis method was proposed to improve the accuracy of the equations. Table. Semi-analytical permeability equations. Kozeny-Carman (KC) Walsh & Brace (WB) k KC = µ γ Cn 3 e 2 2 ( ne ) S a k WB γ = µ Note: C =shape factor (= /80 for spherical particles), S a =specific surface area, n e =effective porosity, γ = unit weight of the fluid (water at 20 o C), µ =fluid viscosity, T=tortuosity, b=2 for perfectly circular pore structure or b=3 for rough pore space. n bt 3 e 2 S 2 a 2. Materials and Methods A set of laboratory specimens and field cores were utilized in this study. Of the 36 laboratory specimens, 24 were Superpave mixtures and 2 were SMA (Stone Matrix Asphalt) mixtures. For the Superpave mixtures, two different gradations (i.e., fine and coarse) from NMASs of 9.5 mm, 2.5 mm, 9 mm and 25 mm were selected. SMA gradations were selected from three different NMASs: 9.5 mm, 2.5 mm and 9 mm. In addition, seven 50-mm diameter field cores were obtained from the test sections of the Accelerated Loading Facility (ALF) located at the Federal Highway Administration (FHWA) Turner-Fairbank Highway Research Center (TFHRC). Vertical permeabilities (k zz ) of the specimens were determined using a flexible wall permeameter (so-called Bubble Tube Constant Head Permeameter ) that was specifically developed for measuring the permeability of 50-mm diameter asphalt specimens. Detailed information on the mix design, geometrical properties of the asphalt specimens and the permeameter are provided in Kutay et al. (2006). Three-dimensional internal structures of the asphalt specimens were generated from the X-ray CT images, which were acquired at the radiography laboratory of TFHRC. The X-ray CT device included a 420 kev continuous X-ray source and a linear array

3 Semi-analytical Equations for Asphalt Permeability 3 detector of 52 channels. The resolutions of the images were approximately 0.3 mm/pixel in horizontal and 0.8 mm/pixel in the vertical direction. Figure presents a three-dimensional image of one of the asphalt specimens generated using the X- Ray CT technique. 3. Image Processing and Analysis Grayscale X-ray CT images were first converted to a binary form (black and white), where black areas (pixel values of 0) represent solid and white areas (pixel values of ) represent air voids. After obtaining the three-dimensional pore geometry defined by the white voxels (3D equivalent of a pixel), isolated pores were eliminated and a 3D image of the interconnected pore structure was generated using an algorithm developed in Matlab. The algorithm, named PORECON, first labeled the interconnected white pixels by using a build-in-connected-component function that grouped the connected pixels based on a neighborhood criterion. The neighborhood criteria can be 4 or 8 in 2D and can be 6, 8 or 26 in a 3D image, and the 8-connected neighborhood criterion was selected for labeling in the current study. For example, a neighborhood criterion of 4 (also called four-connected neighborhood) suggests that only four neighboring pixels which are above, below, right and left of a pixel should be considered connected. An example of grouping pixels using a four-connected neighborhood criterion is illustrated in Figure 2. After the labeling was complete, the labeled groups that were not connected to both ends of specimen (top and bottom) were eliminated. This produced a pore channel that was connected to both ends of the specimen. The pore volume of each specimen was calculated in units of voxels by simply counting the number of white pixels and was converted to the world units as V p =V' p x y z. V p and V' p are pore volume in world units (mm 3 ) and lattice units (voxels), respectively, and x, y and z are the resolutions (in mm/pixel) in x, y and z directions respectively. The porosity was then calculated by dividing V p by the total volume of the specimen. Specific surface area (SSA) is another pore geometry characteristic that is defined as the ratio of the surface area of the pores to the total volume of the specimen (Walsh and Brace 984). The surface area of the pores was calculated by first calculating the perimeter of pores in each image slice. The surface area (A i ) of the i th slice was determined as: A i = P' i x z, where P' i is the perimeter in pixels, x and z are horizontal and vertical resolutions, respectively. Cumulative summation of A i over all slices of the specimen yields the total surface area of the pores. Tortuosity (T) is defined as the ratio of the longest path traveled by the fluid particles (L e ) to the shortest distance between two ends of a specimen (L). Figure 3a illustrates the concept of tortuosity in a simplistic manner, however, it is usually very difficult to calculate the tortuosity of a pore geometry without conducting a tracer test (Walsh and Brace 984). An algorithm named TORT3D was developed to calculate the tortuosity using the interconnected pore structure of the specimens. First, isolated pore cross sections were grouped in each image slice and centroid of each group was connected to the centroid of the closest pore cross

4 4 GeoX 2006, 2 nd International Workshop on X-Ray CT for Geomaterials sectional area in the next image slice. For each line connecting two pore cross sections, a tortuosity was then calculated by dividing the length of the connecting line to the vertical distance between two slices. The lines that illustrate various possible flow paths estimated by the TORT3D algorithm in the pore structure of an asphalt specimen are provided in Figure 3b. After obtaining a set of tortuosity values for each consecutive image slice, an average tortuosity was calculated for the entire specimen. Figure. 3D reconstructed image of an asphalt specimen. (a) Figure 2. Labeling of white pixels based on the four-connected neighborhood criterion (b) L L e Figure 3. (a) Illustration of the longest flow path and shortest distance for tortuosity calculation, (b) various flow paths estimated by the TORT3D algorithm in the pore structure of an asphalt specimen. 4. PREDICTED VERSUS LABORATORY MEASURED PERMEABILITIES The pore connectivity analyses revealed that eighteen of the tested specimens did not have interconnected macro pores (i.e. minimum size greater than 0.3 mm) between their two opposite faces. The laboratory based permeabilities of those specimens were one to three orders of magnitude lower as compared to the specimens that had interconnected pores. The low permeabilities measured in the laboratory were attributed to the flow occurring in micro pores that had sizes less than 0.3 mm. It should be noted that the highest resolution level that was obtained for a 50-mm diameter specimen by using the X-ray CT device was 0.3 mm/pixel. Therefore, X-ray CT technique was not able to capture the micro pores in the specimens. For the specimens with interconnected macro pores, the permeabilities were generally higher. Figure 4a shows the predictions of two different analytical

5 Semi-analytical Equations for Asphalt Permeability 5 equations and corresponding laboratory measurements. Estimations of analytical equations were relatively accurate at high permeabilities (i.e., k zz > mm/s), whereas, at low permeabilities (i.e., k zz < mm/s), their estimations were up to two orders of magnitude higher than ones measured in the laboratory. In general, predictions of the KC equation were closer to lab-measurements as compared to the WB equation. In addition, relatively good predictions were observed for the permeable SMA specimens, whereas, the predictions for the coarse and fine graded Superpave and field cores were up to several orders of magnitude higher than the labmeasurements. This was attributed to the relatively uniform and isotropic structure of the SMA specimens when the pore size variation in different directions was analyzed. On the other hand, pore size distribution of the Superpave and field specimens exhibited large variation in different directions. More detailed discussion of the pore size distribution of the specimens could be found elsewhere (Kutay 2006). It should be noted that the constants C and b seen in Table can have a significant affect on the estimation of permeability. Using the reported values of these constants (i.e. C=/80 and b=3) revealed a biased estimation at low permeabilities. These empirical constants can be adjusted to for a better estimation; however, the new constants may not represent all asphalt pavements. On the other hand, these equations may provide good qualitative comparison between different asphalt specimens. Predicted k zz (mm/s) (a) Line of equality WB-Coarse KC-Coarse WB-Fine KC-Fine WB-SMA KC-SMA WB-Field KC-Field Laboratory k zz (mm/s) Predicted k zz (mm/s) (b) Line of equality WB-Coarse KC-Coarse WB-Fine KC-Fine WB-SMA KC-SMA WB-Field KC-Field Laboratory k (mm/s) zz Figure 4. Comparison of laboratory-based permeability with those produced by the analytical equations: (a) Pore parameters calculated for the entire specimen and (b) pore parameters computed for the mid part of the specimen. Permeability anisotropy of the asphalt pavements has been widely discussed in previous studies where vertical (i.e., k zz ) permeability is usually one to two orders of magnitude lower than the horizontal permeabilities (i.e., k xx and k yy ) (Kutay et al. 2006). This phenomenon is primarily due to the anisotropic pore structure of the pavements in which the porosity is typically lower in the mid-depth of an asphalt pavement layer and higher at the top and bottom, and the vertical permeability is controlled by the constrictions in the middle. In order to illustrate this effect, the specimens were divided into three equal layers and the pore structure

6 6 GeoX 2006, 2 nd International Workshop on X-Ray CT for Geomaterials parameters needed in Table were calculated for the middle layer. Resulting permeability predictions versus laboratory-based permeabilities are shown in Figure 4b. The KC and WB predictions based on pore parameters of the middle layer are closer to the line of equality and less scattered indicating that the vertical permeability is probably controlled by the constrictions in the middle. 5. SUMMARY AND CONCLUSIONS Asphalt specimens with varying mix design, and compaction levels were tested to study the applicability of two simple semi-analytical equations in estimating the permeability of asphalt pavements. Three-dimensional internal microstructures of the specimens were generated using the X-ray CT technique. Several image processing algorithms were developed to calculate pore structure parameters that are needed for the semi-analytical equations. The predictions of the equations were compared to the laboratory-measured permeabilities. The results revealed that the estimations of the two analytical equations were relatively accurate at high permeabilities (i.e., k zz > mm/s), whereas, at low permeabilities (i.e., k zz < mm/s), their estimations were up to two orders of magnitude higher than the laboratory measurements. In general the Kozeny-Carman (KC) equation performed better than the Walsh & Brace (WB) s equation. Furthermore, The KC and WB predictions based on pore parameters of the middle layer are closer to the line of equality and less scattered which indicated that the vertical permeability is most probably controlled by the constrictions in the mid-section of the specimen. The observations made in the current study suggest that physically dividing asphalt specimens into three layers and using the pore parameters of the mid layer may lead to a better estimation of vertical permeability as the constrictions are very likely to be located in the mid-section. 6. REFERENCES Al-Omari, A., Tashman, L., Masad, E., Cooley, A., and Harman, T., (2002). Proposed Methodology for Predicting HMA Permeability, Journal of Association of Asphalt Paving Tech., V. 7, pp Carman, P. C. (956). Flow of Gases through Porous Media, Academic Press, NY. Kozeny, J. (927) Ueber Kapillare Leitung des Wassers im Boden, Wien, Akad. Wiss., 36 (2A), 27. Kutay, M.E., Aydilek, A.H., Masad, E., and Harman, T. (2006) Computational and Experimental Evaluation of Hydraulic Conductivity Anisotropy in Hot-Mix Asphalt, International Journal of Pavement Engineering, in press. Lytton, R. L., Masad, E. A., Zollinger, C., Bulut, R. and Little, D. (2005) Measurements of Surface Energy and its Relationship to Moisture Damage,FHWA/TX-05/ Walsh, J. B. and Brace, W. F., (984). The Effect of Pressure in Porosity and the Transport Properties of Rock, Journal of Geophysical Research, Vol. 89, No. B, pp