Andrew J. Wimsatt, Ph.D., P.E.

Fort Worth District Pavement Engineer

Texas Department of Transportation

P.O. Box 6868

Fort Worth, TX 76115

Phone 817-370-6702

Fax 817-370-6848

email: awimsat@mailgw.dot.state.tx.us

This paper presents two direct methods of analyzing Falling Weight Deflectometer deflection data. One method, which involves dividing the deflection 1828.8 mm (72 inches) away from the load plate by the deflection underneath the load plate, relates directly to the ratio between the pavement modulus and subgrade modulus for a two layer system. Another method described in the paper gives a qualitative evaluation of the stiffness of the base material as it relates to the pavement surface. Examples of using these methods are described and compared to results from the Modulus Version 5.0 computer program developed by the Texas Transportation Institute.

Keywords: Falling Weight Deflectometer, Deflection, Analysis, Index

The author thanks Dr. B. Frank McCullough, Dr. Mike Murphy, Mr. Scott Lambert, Mr. Gary Graham, Mr. Mohan Yeggoni, and Mr. Mark McDaniel of the Texas DOT and Mr. Tom Scullion of the Texas Transportation Institute for their advice and support in presenting this concept.

Many of the Texas Department of Transportation (TxDOT) District Pavement Engineers have expressed interest in a more direct method of analyzing pavement deflection data obtained from the Falling Weight Deflectometer (FWD). Currently, the Department uses the Texas Transportation Institute's Modulus version 5.0 computer program to determine layer moduli for flexible pavement design (Reference 1). The program, although very reliable and useful, is not suited to analyze literally thousands of FWD deflection basins obtained for the TxDOT Pavement Management Information System's (PMIS) network level needs estimates, especially since pavement layer information is not currently available in the TxDOT PMIS. In addition, several District Pavement Engineers expressed interest in analyzing project level deflection data on a spreadsheet before running the Modulus program. Finally, simpler FWD analysis methods can be incorporated into pavement management system analysis programs. The results do not have to be as precise as those generated by the Modulus program, but the methods can be used to determine the relative structural conditions of pavements.

For purposes of this paper, the following variables are defined as follows:

W1=Deflection measured directly under a FWD load plate

W2=Deflection measured 304.8 mm (12 inches) away from the center of the load plate

W3=Deflection measured 609.6 mm (24 inches) away from the center of the load plate

W4=Deflection measured 914.4 mm (36 inches) away from the center of the load plate

W5=Deflection measured 1219.2 mm (48 inches) away from the center of the load plate

W6=Deflection measured 1524.0 mm (60 inches) away from the center of the load plate

W7=Deflection measured 1828.8 mm (72 inches) away from the center of the load plate

The author developed two direct methods for analyzing FWD deflection data. The first method is dividing W7 by W1 (W7/W1), which corresponds to the ratio between the pavement modulus and the subgrade modulus (Pavement Modulus/Subgrade Modulus). The W7/W1 term is effective since W1 represents the stiffness properties of the pavement and the subgrade, while W7 represents the properties of the subgrade only.

The second method is finding the minimum value of W2/W1, W3/W2, W4/W3, W5/W4, W6/W5, or W7/W6. If the minimum ratio value does not occur at W2/W1, it is very likely that the base layer is much weaker than the surface layer.

This paper mainly describes the use of these methods in analyzing asphalt surfaced, or flexible, pavements. The W2/W1 ratio has been used in portland cement concrete pavement joint analysis. The author did search the available literature for use of these ratios for flexible pavements, but no references have been found.

The W7/W1 term and the location of the minimum ratio value was developed in order to take advantage of these properties in the deflection equations described above.

To determine the sensitivity of W7/W1 to various pavement and subgrade moduli values, the author conducted an extensive study using the WESLEA linear elastic layer program developed by the U.S. Army Corps of Engineers (Reference 3). Subroutines of this program are used in the latest version of the Modulus Version 5.0 computer program developed by the Texas Transportation Institute (Reference 1). The loading used in the WESLEA program modeled the FWD at a 40 kN (9,000 pound) load level and a 150 mm (5.91 inch) radius load plate, except as noted in Table 1.

Table 1 also shows the results of modeling an 80 kN (18,000 pound) load on a thin pavement structure. As shown in the Table, the W7/W1 values did not change from the 40 kN (9,000 pound) load level.

In addition, Table 1 shows the estimated subgrade modulus using the following equation found in the 1993 AASHTO Guide for Design of Pavement Structures (Reference 4):

Subgrade Modulus, MPa = 0.24 * FWD Load Level, N / (W7 deflection, mm * 1828.8 mm)

As shown in Table 1, the ratio between this estimated subgrade modulus and the actual modulus used in the WES5 program stayed relatively constant ( between 1.24 and 1.32). As a result of this finding, the estimated subgrade moduli using this equation are divided by 1.25 for the analyses found later in this paper.

As stated earlier, W7/W1 relates directly to the Pavement to Subgrade Modular Ratio (Pavement Modulus/Subgrade Modulus). As a result, the set of regression equations shown in Table 3 was developed from the WESLEA computer program results using the input values in Table 2. Table 4 shows the resulting Pavement to Subgrade Modular ratios versus W7/W1. Figure 1 is a plot of the data in Table 4. As shown in Table 4, when W7/W1 is less than 0.028, the regression equations indicate that the pavement modulus is less than the subgrade modulus.

As stated earlier, the location of the minimum value of W2/W1, W3/W2, W4/W3, W5/W4, W6/W5, or W7/W6 changes depending on the pavement layer moduli. Generally, weaker base moduli result in the minimum ratio value not occurring at W2/W1. Table 5 shows the results of an analysis using output from the WESLEA computer program for a three layer system consisting of an ACP surface layer ranging from 51 mm to 203 mm (two to eight inches) thick; a 305 mm (12 inch) thick base layer, and a 7,620 mm (300 inch) thick subgrade layer overlying a semi-infinite rigid layer. The actual ratio between the surface modulus and the base modulus cannot be determined from the minimum ratio value; only the minimum possible surface to base modular ratio can be indicated.

In addition, when the minimum ratio occurred at W7/W6 for 51 deflection basins in Table 5, the overall pavement modulus was much larger than the subgrade modulus (i.e., the ACP modulus was greater than 4,000,000 kPa or the base modulus was greater than 300,000 kPa, and the subgrade modulus was 34,723 kPa for 47 basins and 68,946 kPa for 4 basins). When this situation occurs, it would not be possible to determine the relative stiffness of the base at it relates to the surface.

Table 6, which was also generated from the WESLEA computer program output, shows when the subgrade depth is 3,302 mm, 32 percent of the minimum ratio values occur at W7/W6. In addition, when the subgrade depth is 1,524 mm (60 inches), all of the minimum ratio values occur at W7/W6. These results indicate that when the minimum ratio occurs at W7/W6, a stiff or rigid layer may be present as part of the overall pavement structure.

The regression equations were used in analyzing the following pavement structures with the following procedure:

The tables in the following examples include results from the Modulus Version 5.0 computer program developed by the Texas Transportation Institute (Reference 1). All of the examples showed that the pavement moduli values determined from W7/W1 compared favorably with the values generated from the Modulus program.

This section of US 79 had just been constructed when TxDOT personnel conducted FWD testing. According to the construction plans, the pavement structure consisted of 127 mm (five inches) of a coarse matrix high binder ACP, 254 mm (ten inches) of a flexible base, and 203.2 mm (eight inches) of a lime treated subgrade. The pavement structure was exhibiting no distress whatsoever. The air temperature at the time of FWD testing ranged from 28.8 degrees Celsius (84 degrees Fahrenheit) to 30.6 degrees Celsius (87 degrees Fahrenheit).

Table 7 show the results of the FWD analysis. Approximately 33 percent of the calculated pavement moduli are below the specified design pavement modulus for this roadway. However, on the whole, these data points did not drop significantly below the design pavement modulus. In addition, almost all of the minimum ratio values occurred at W2/W1, indicating that the base materials are in good condition from a stiffness standpoint.

This section of US 77 showed substantial alligator cracking and some pumping and rutting when TxDOT personnel conducted FWD testing. According to the construction plans, the pavement structure consisted of 177.8 mm (seven inches) of asphaltic concrete pavement, 330.2 mm (thirteen inches) of a flexible or granular base, and 152.4 mm (six inches) of lime treated subgrade. The air temperature at the time of FWD testing was around 22.2 degrees Celsius (72 degrees Fahrenheit).

TxDOT personnel trenched the pavement structure at one location and found that the base material, consisting of caliche, was saturated and very weak. However, personnel also observed that the lime treated subgrade (LTS) was very stiff. During trenching operations, the LTS broke apart in large slabs.

Table 8 shows the results of the FWD analysis. All of the calculated pavement moduli are below the specified design pavement modulus for this roadway, indicating a uniformly weak pavement structure. In addition, all of the minimum ratio values did not occur at W2/W1, indicating that the base was considerably weaker than the surface.

In May, 1995, TxDOT personnel conducted a forensics analysis of Ranch to Market Road 2222 in Austin. According to the construction plans, the pavement structure consisted of 63.5 mm (two and a half inches) of an asphaltic concrete pavement and 393.7 mm (15 1/2 inches) of a flexible or granular base. However, the actual ACP surface thickness ranged from 57.2 mm (2.25 inches) to 96.5 mm (3.8 inches), based on core measurements. The pavement structure rested essentially on natural clay material interspersed with fractured limestone (i.e., the depth to the stiff layer was less than 1,524 mm or five feet). The project was approximately 3.22 km (two miles) in length.

The pavement structure was open to traffic in the summer of 1994. By January, 1995, alligator cracking and pumping of base fines appeared on the surface in several isolated areas. By May, 1995, the alligator cracking had progressed extensively. Tests on the ACP cores extracted from the roadway found that the ACP surface was especially porous. This condition allowed water into the base material, thus weakening the base and leading to the alligator cracking.

TxDOT personnel obtained falling weight deflectometer (FWD) data (around 100 basins) at approximately 61 m (200 foot) intervals in May, 1995. TxDOT Personnel obtained the FWD deflection data in the morning on a partly cloudy day. The air temperature ranged from 25.6 degrees Celsius (78 degrees Fahrenheit) to 28.9 degrees Celsius (84 degrees Fahrenheit).

Results of the FWD data analysis for the eastbound lanes are shown in Table 9. The deflection data was uniformly low in magnitude.

Analysis of the data using showed that most of the frequently occuring minimum values did not occur at W2/W1, which indicates loss of stiffness in the base layers. Eighty three percent of the calculated pavement moduli are below the specified design pavement modulus for this roadway.

It would make sense that pavements exhibiting load associated distress would have lower W7/W1 values. Analysis of data from the TxDOT Pavement Management Information System (PMIS) tested this hypothesis. The TxDOT PMIS contains extensive FWD deflection and corresponding visual distress data from highways all over the state of Texas.

Figures 2 and 3 show the results of comparing W7/W1 to Fiscal Year 1994 TxDOT PMIS data for pavements with projected 80 kN (18,000 pound) loadings of more than 1,000,000 over twenty years (7,583 data points). As shown in Figure 2, the majority of the minimum ratios came from W2/W1 and W3/W2. The W3/W2 ratio was the most frequently occurring minimum ratio, which indicates that the base layers are considerably weaker than the surface layers.

Also, Figure 3 shows that 339 deflection basins (4.5 percent of the total) had W7/W1 values between 0 and 0.028, which indicates that the pavement moduli are less than or equal to the subgrade moduli in those areas. Out of those 339 deflection basins, 205 deflection basins (or 2.7 percent of the total) indicated that the estimated subgrade modulus from the W7 sensor for each basin was greater than 206,839 kPa (30,000 psi), which indicates that those pavement structures are placed over stiff subgrade layers.

The most frequently occurring W7/W1 values are in the 0.028 to 0.056 range, which indicates that the pavement moduli in those areas are between one and three times times the subgrade moduli.

The direct analysis procedures described in this paper seem to have some promise in FWD deflection analysis. It appears to be a reasonable indicator of distress manifestation in pavement structures and should be a good predictor.

Of course, the ratio between the pavement modulus and the subgrade modulus can also be determined by dividing W6 by W1 (W6/W1), W5 by W1 (W5/W1), or even W4 by W1 (W4/W1), and calculating the subgrade modulus using the W6, W5, or W4 sensor. Other agencies or researchers may want to use these sensors in such calculations. However, this paper showed that the W7/W1 value can generate meaningful results for network and project deflection analysis purposes.

[1] Michalak, Chester H. and Tom Scullion, "Modulus 5.0: User's Manual," Research Report 1987-1, Texas Transportation Institute, The Texas A & M University System, November, 1995, 104 pp.

[2] Ullidtz, Per, "Pavement Analysis," Developments in Civil Engineering, Elsevier, 1987.

[3] WES5 (or WESLEA), available from Don Alexander, Pavements Systems Division, U.S. Army Corps of Engineers Waterways Experiment Station, 3909 Halls Ferry Road, Vicksburg, Mississippi, 39180-6199

[4] American Association of State Highway and Transportation Officials, 1993 AASHTO Guide for Design of Pavement Structures, AASHTO, Washington, D.C., 1993

-1693.4*(SQRT(W7/W1))^5+3035.9*(SQRT(W7/W1))^4

-756.71*(SQRT(W7/W1))^3+100.68*(SQRT(W7/W1))^2-2.5058*(SQRT(W7/W1))

847.37*(SQRT(W7/W1))^5-167.85*(SQRT(W7/W1))^4+251.45*(SQRT(W7/W1))^3

-24.01*(SQRT(W7/W1))^2+3.081*(SQRT(W7/W1))

672.02*(SQRT(W7/W1))^5-245.62*(SQRT(W7/W1))^4+207.83*(SQRT(W7/W1))^3

-5.9825*(SQRT(W7/W1))^2+1.7989*(SQRT(W7/W1))

516.94*(SQRT(W7/W1))^5-214.46*(SQRT(W7/W1))^4+159.56*(SQRT(W7/W1))^3

+6.143*(SQRT(W7/W1))^2+1.0826*(SQRT(W7/W1))

421.55*(SQRT(W7/W1))^5-192.16*(SQRT(W7/W1))^4+131.78*(SQRT(W7/W1))^3

+12.33*(SQRT(W7/W1))^2+0.7697*(SQRT(W7/W1))

356.26*(SQRT(W7/W1))^5-172.52*(SQRT(W7/W1))^4+112.71*(SQRT(W7/W1))^3

+16.095*(SQRT(W7/W1))^2+0.6075*(SQRT(W7/W1))

311.37*(SQRT(W7/W1))^5-158.63*(SQRT(W7/W1))^4+100.05*(SQRT(W7/W1))^3

+18.393*(SQRT(W7/W1))^2+0.5278*(SQRT(W7/W1))