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Federal Highway Administration Research and Technology
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Publication Number: FHWA-RD-98-085
Basin shape factors are used to quickly and easily extract meaningful information out of measured deflection basins. This information is typically related to relative stiffness of the surface to the base, the entire pavement to the subgrade, or the base to the subgrade.
Basin shape factors were developed as empirical relationships that were related to the more rigorous elastic layer or finite element analysis results that could only be run on mainframe computers. Since it was not practical to analyze each deflection basin with the computing equipment available at the time of their development, basin shape factors were looked at as the computationally expedient way of extracting information about the structural characteristics of a pavement.
Even though computational capabilities have improved tremendously from the days when basin shape factors were first developed, they can still provide valuable information about the structural behavior of a pavement section, particularly when circumstances are unfavorable to backcalculation. Some such circumstances are heavily deteriorated pavements or lack of layer thickness information. In addition, a plot of an appropriate basin shape factor versus station can be quickly performed in the field to delineate where changes in pavement condition or thickness occur. Such a delineation is useful in choosing locations for taking cores, for example.
All of the basin shape factors included here respond in some manner or another, to the ratio of stiffness of the upper layer to a lower layer. The AREA factor is sensitive to the composite stiffness of the overall pavement section compared to the stiffness of the underlying subgrade support. The F-1 basin factor is sensitive to the relative stiffness of the upper layers and less so to the lower subgrade layers. The Delta and Ratio factors respond primarily to the stiffness of the asphalt layer for the factors calculated from deflections close to the load plate. Delta and Ratio factors that are based on deflections further away from the load plate respond to the ratio of the composite pavement stiffness to the subgrade stiffness.
To illustrate the general magnitude and shape of deflection basins, CHEVRON2, a layered elastic analysis program, was used to calculate a series of deflection basins for a pavement structure consisting of six inches of asphalt over 12 inches of aggregate base on a subgrade layer of 222 inches which is resting on a stiff infinite half space that simulates a "hard bottom." Three moduli were used for each of the layers, as shown in Figure 7.
Figure 7. Pavement Structure Used to Illustrate Basin Shape Factors
The asphalt moduli represent asphalt stiffness at a high, medium, and low temperature, and were selected to provide simple round numbers. To relate these moduli in temperature terms, they would represent 46.5, 18.5, and 6.5 degrees Celsius (115.6, 65.3, 43.6 degrees Fahrenheit) if using a slope of -0.025 in the Log(E) = intercept + slope*temperature relationship.
The base moduli were selected to bracket typical values. The 15,000 psi represents the stiffness of a poorly compacted natural sand or gravel, 30,000 psi is typical of a well compacted natural gravel, and 50,000 psi is typical of a well compacted crushed stone.
The subgrade moduli span a range of soft to medium soils. The 4,000 psi moduli is typical of many fine grained soils such as fat clay or poorly compacted silt, 8,000 psi is typical of lean clay or a loose sand, and 12,000 psi is typical of compacted glacial till or a silty sand.
The stiffness of unbound materials is highly variable and dependent on many factors, such as grain size and shape, moisture content, density, stress state, and other characteristics are less commonly evaluated such as the mineralogy of the particles. The stiffness of unbound materials can be measured in the laboratory, or backcalculated from deflection data.
All the combinations of moduli shown in Figure 7 result in 27 calculated deflection basins, or three asphalt stiffnesses for nine combinations of base and subgrade moduli as shown in Table 1. The impact of the temperature is seen by looking at the results of each of these nine sets.
|Key||Layer Moduli, psi
|Layer Moduli, psi
|Layer Moduli, psi
Deflection basins were calculated for each of the rows in Table 1 and graphed in Figures 8, 9 and 10 to illustrate how the asphalt, base, and subgrade affect the magnitude and shape of the basin. From these figures, it is apparent that the deflections furthest away from the center of the load are nearly the same, regardless of the stiffness of the asphalt and base. The deflections measured by the outer sensors are sensitive only to the stiffness of the subgrade soil.
Figure 8. Asphalt and Base Stiffness Combinations on a High Stiffness Subgrade
Figure 9. Asphalt and Base Stiffness Combinations on a Medium Stiffness Subgrade
Figure 10. Asphalt and Base Stiffness Combinations on a Low Stiffness Subgrade
Many of the basin shape factors covered here involve some sort of normalization of the basins. The next set of figures uses the same basins as the previous set, but each basin was normalized by dividing each measured deflection by the deflection at the center of the load plate. Therefore, each normalized basin has a magnitude of 1.0 at the center of the load plate and the offset deflections are less than 1.0. Figure 11, Figure 12, and Figure 13 indicate the shape of the normalized basin near the load plate is dependent primarily on the stiffness of the asphalt, not on the stiffness of the base and subgrade. The influence of the base on the normalized basin shapes is most noticeable in relative magnitude, or curvature, of the basin as defined by the sensors at intermediate offset.
Figure 11. Normalized Basins on High Stiffness Subgrade
Figure 12. Normalized Basins on Medium Stiffness Subgrade
Figure 13. Normalized Basins on Low Stiffness Subgrade
The behavior of the deflection as a function of layer stiffness exhibits two obvious characteristics that can be used in analysis:
Given these two very basic basin behaviors, the stiffness of the subgrade and asphalt can be estimated; leaving only the base stiffness to be determined. Backcalculation techniques that use basin closure routines based on these two concepts can quickly close in on a solution.
Keep in mind that the basins shown here are calculated basins, based on elastic layer theory and a very simple three-layer model on a stiff layer. Real deflection basins are almost never quite that simple. The asphalt stiffness usually varies from top to bottom due to both temperature gradient and the different mixes used for the wear and non-wear courses. The base layer might also have a stiffness gradient with depth due to moisture, density, or confinement changes. The subgrade might also have moisture and density gradients, changes in the soil itself with depth, and hard bottom at various depths. In addition, the unbound materials, both base and subgrade, tend to have horizontal stiffness gradients that are dependent on the load because of what is commonly termed as non-linear characteristics. None of these conditions are reflected in these idealized plots (nor are they reflected in many backcalculation routines). Nevertheless, these plots are based on the output of the linear elastic layer models that are used for most backcalculation deflection analysis.
Temperature of the asphalt not only affects the stiffness or modulus of the asphalt and magnitude of the deflection, but the shape of the deflection basin itself as shown in Figure 14.
Figure 14. Basin Shape as a Function of Temperature
Figure 14 shows the shape of the deflection basin at the same point measured at three different times during a single day. The mid-depth temperature increased from 18 °C at 9:42 am to 32.1°C at 2:14 pm. The warmer asphalt results in higher deflections under the load plate, and greater bending in the deflection basin.
Pavement engineers have developed a variety of Basin Shape Factors that reduce some characteristic of the deflection basin to a single value. These Basin Shape Factors often are more sensitive to a single component of the pavement, such as the bound surface layers or the subgrade.
Basin shape factors that describe the bending of the pavement surface, or shape of the deflection basin, near the load are sensitive to the stiffness of the upper pavement layer. In the case of asphalt pavements, the stiffness of the upper layer is a function of the asphalt temperature. Basin shape factors that describe the bending away from the load are less sensitive to temperature.
The following basin shape factors are sensitive to the temperature of asphalt pavement layers, and will be dealt with in greater detail: