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Publication Number: FHWA-HRT-05-150
Date: February 2006

Review of The Long-Term Pavement Performance (LTPP) Backcalculation Results

Chapter 6. LTPP Backcalculation Database Screening Results

This chapter gives a summary and discussion of the screening results of the LTPP backcalculation database. Backcalculation data at all LTPP record levels (A to E) were screened. Level E data versus other levels’ (A to D) backcalculation data are compared first. Screening results of the flexible pavement systems are then provided, followed by the screening results of the rigid pavement systems using various backcalculation procedures or models. Finally, screening results of the section average values are presented.

LEVEL E AND OTHER LEVELS OF DATA QUALITY

In the past, LTPP generally released only those data that had passed to level E in the database. In the case of FWD data, the status of level E was principally assigned when the LTPP data tables were complete in other regards, the quality or correctness of the FWD data notwithstanding. Figure 23 is an example of a level E data analysis for the subgrade layer(s) using a linear-elastic model from MODCOMP compared to the forwardcalculation approach using the Hogg model as delineated in the previous sections. Figure 24, meanwhile, is the same set of subgrade charts, but for all levels of subgrade data in the flexible pavement system database.

For all pie chart figures in this chapter, the slices are shown in clockwise order, starting with the “not assumed”/“acceptable”/“reasonable” slice, which always faces right.

Click for text description.

Figure 23. Charts. Screening results of the elastic moduli of the subgrade
for all flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based
on the linear elastic model (the level E records only).

Click for text description.

Figure 24. Charts. Screening results of elastic moduli of the subgrade
for all the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based
on the linear elastic model (contains both level E and nonlevel E records).

Comparing the pie charts in Figure 23 and Figure 24 shows no appreciable difference in the results. The level E data consist of about 442,000 records, of which 3 percent were assumed, or fixed. Of the remaining 97 percent, 86 percent of these were reasonable, meaning they were within the broad limits shown in Table 14 for subgrade materials (15–650 MPa (2,000–95,000 psi). By contrast, the entire data set consisted of some 580,000 records, with 96 percent not assumed, and 83 percent of these were reasonable—not much different from the level E data. Finally, in the case of the level E data, 39 percent will not be assigned any outlier flag, or a flag of “0.” For the entire data set, the corresponding percentage for a flag of “0” is 38 percent. (A flag of “0” means that the backcalculated modulus is within a factor of 1.5 times or divided by the forwardcalculated subgrade modulus value.)

In almost all other instances, the differences between level E data and all the data were negligible. Therefore, in the following sections, results of screening the entire database will be reported without breaking out the level E data as a separate subcategory of these data.

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION PARAMETERS—LINEAR ELASTIC MODEL

This section deals with the portion of the database that comprises asphalt (flexible) pavements where the MODCOMP backcalculation program was used to populate the current LTPP computed parameter data table, using a linear elastic model.(2)

The entire set of backcalculated asphalt surface course moduli consists of more than 200,000 records. Only 1 percent used an assumed value for backcalculation purposes (see Figure 25, left pie chart).

Click for text description.

Figure 25. Charts. Screening results of elastic moduli of the asphalt concrete
layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model.

Of the 99 percent of moduli that were not assumed, both backcalculated and forwardcalculated values were reasonable in 88 percent of the remaining records, meaning the estimated moduli were within a very broad range for asphalt-bound surface layers of 700–25,000 MPa (100,000–3,600,000 psi) in these records. The reason for such a broad range is that asphalt concrete surfaces are viscoelastic and influenced by seasonal temperatures, which in the case of LTPP ranged from well below freezing to over 50 °C (122 °F). Both values were outside of this broad range in only 2 percent of all nonassumed records (see Figure 25, middle pie chart).

Of the above 88 percent, the right-hand pie chart in Figure 25 shows that 71 percent were acceptable, again meaning that the forwardcalculated values were within a factor of 1.5 times or 2/3 of the backcalculated value (see Table 15). In addition, 14 percent of the backcalculated values were marginal, 8 percent were questionable, and 7 percent were unacceptable. Table 15 explains these terms in detail.

Figure 26 shows the subgrade charts for the flexible pavement, linear elastic set of data.

Click for text description.

Figure 26. Charts. Screening results of elastic moduli of the subgrade
for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model.

In this case, the number of records is about 2.5 times greater than for the surface course layer, because the MODCOMP program generally divides the subgrade into two or more layers. In addition, many records have a subgrade modulus listed but not a bound layer modulus, probably because of problems in the backcalculation process, which starts with the determination of the subgrade modulus based on one of the outermost sensors.

The Hogg model handles the subgrade as a single effective layer, under the load and to a finite depth (to hard bottom or the appearance of a hard bottom).

Because the Hogg forwardcalculation model, on average, calculates a subgrade modulus around half that of the linear elastic backcalculation model, the percentage of acceptable moduli is much lower than that associated with the asphalt surface course (38 percent versus 71 percent). This phenomenon is mainly because the backcalculation model uses the outer sensor deflections to calculate the subgrade response characteristics, while the Hogg model uses the center deflection and the shape of the entire deflection basin to arrive at an effective subgrade modulus under the load. For pavement performance and design applications, the Hogg model is the more conservative and realistic. This difference is one reason why the older AASHTO design guides recommend dividing the subgrade modulus by three for a more conservative pavement design.

Figure 27 shows plots of the intermediate or unbound base course moduli (linear model).

Click for text description.

Figure 27. Charts. Screening results of elastic moduli of the base layer
for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model.

The middle chart in Figure 27 indicates that only about 70 percent of the backcalculated base course moduli were within the rather broad limits set forth in Table 14. Furthermore, of the 66 percent of records where both values were reasonable, only 32 percent of the records involved were acceptable by Table 15 definitions. Also, 18 percent of the backcalculated intermediate layer data were unacceptable (i.e., different by more than a factor of 3). Clearly, the base course is the most difficult to backcalculate with any consistency.

SCREENING OF THE FLEXIBLE PAVEMENT BACKCALCULATION PARAMETERS—NONLINEAR ELASTIC MODEL

This section deals with the portion of the database that comprises asphalt (flexible) pavements and where the MODCOMP backcalculation program was used to populate the current LTPP-computed parameter data table using a nonlinear elastic model.

While the linear elastic dataset of backcalculated asphalt surface course moduli consists of some 200,000 records, the nonlinear elastic dataset only contains 37,000 records, covering essentially the same data for the same structural layer. Evidently, the nonlinear feature of the MODCOMP program was only used when beneficial to do so (see Figure 25 and Figure 28, left pie charts).

Click for text description.

Figure 28. Charts. Screening results of elastic moduli of the asphalt
concrete layer for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT
table based on the nonlinear elastic model.

There was not a great deal of difference between the linear elastic and nonlinear elastic model results. If anything, the correspondence between forwardcalculation and backcalculation is slightly poorer with the nonlinear model. For example, 57 percent of the AC modulus values were acceptable (see right pie chart in Figure 28), whereas 71 percent were acceptable using the linear elastic model (see Figure 25).

These counterintuitive results are not necessarily because the materials were truly linear elastic, but rather because the use of any backcalculation program is highly user-dependent, requiring engineering skill and knowledge to model the pavement to get reasonable results. Such results were not possible with the LTPP data because it was processed in batch mode, so attention to each individual test point (record) was not feasible.

Figure 29 shows plots of the intermediate (unbound) base course moduli using the nonlinear model.

Click for text description.

Figure 29. Charts. Screening results of elastic moduli of the base
layer for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT
table based on the nonlinear elastic model.

The three plots in Figure 29 once again don’t show a great deal of difference in their comparison to forwardcalculated values, between the base moduli derived though linear (Figure 27) and nonlinear (Figure 29) backcalculation. In spite of an attempt to improve the large variability associated with backcalculated base course moduli, the batch mode of nonlinear backcalculation did not help a great deal.

Figure 30 shows the subgrade charts for the nonlinear elastic flexible pavement set of data.

Click for text description.

Figure 30. Charts. Screening results of elastic moduli of the subgrade for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT table based on the nonlinear elastic model.

In the case of the subgrade, for all practical purposes, no difference exists between the linear and nonlinear elastic analysis methods (see Figure 26 and Figure 30). Evidently, in spite of using the nonlinear model on about 15 percent of available FWD load-deflection records, backcalculation still results in subgrade moduli that are much higher than the Hogg model calculations (or ELMOD, for example), because of the differences in how nonlinearity is handled by the three methods.

It is possible to use the MODCOMP program and model the nonlinearity of the subgrade (or the upper portion of the subgrade) in another manner, which can result in lower subgrade moduli in many cases. Once again, however, this technique was not possible because of the need for careful attention on a case-by-case basis to material properties, nonlinear models, and material coefficients in the various LTPP test sections.

ADAPTATION OF FORWARDCALCULATION TECHNIQUE FOR LTPP RIGID PAVEMENT SECTIONS

This section deals with the criteria used to adapt the forwardcalculation routines to the backcalculation database.

Since forwardcalculation is designed to calculate only two modulus values directly (the bound surface course and the subgrade), it is necessary to use relationships between one of these layers and the base course, whether bound or unbound. Additionally, since one of the methods used to generate the backcalculated tables in the LTPP database involved a choice between a 100 percent bonded and a 100 percent unbonded condition between the PCC slab and the base course, it was also necessary to develop a method for forwardcalculation that would consider these two different input assumptions.

As discussed previously, only the PCC surface course and the subgrade moduli are forwardcalculated, essentially ignoring the effect of the base layer. Therefore, the computed EPCC actually reflects the effect of both the upper PCC layer and the underlying base layer. In other words, EPCC is an apparent modulus of these two upper layers, and needs to be divided into two parts, especially when a bound base layer is involved: the actual modulus of the PCC layer and the calculated modulus of the base. In these cases, EPCC is called Epcc,app., which is the apparent modulus of the PCC layer alone as influenced by the base.

The method used to divide the calculated Epcc,app.-value is adopted from Khazanovich, et al.(1) The upper PCC surface layer and the base layer may be bonded or unbonded and are assumed to act as plates. Thus, no through-the-thickness compression is assumed. The details of this method are given below for an unbonded and bonded condition between the PCC slab and the base, respectively.

For the unbonded case, the PCC slab modulus is computed from the equation in Figure 31.

Click for text description.

Figure 31. Equation. PCC slab modulus—100 percent unbonded case.

For the bonded case, the PCC slab modulus is computed from the equation in Figure 32.

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Figure 32. Equation. PCC slab modulus—100 percent bonded case.

where:

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Figure 33. Equation. Layer thickness relationship—both cases.

and:

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Figure 34. Equation. Modular ratio Beta—both cases.

and:

Epcc,app. = Apparent modulus of the PCC layer, assuming no base course effect
E1 = Modulus of upper plate, i.e., the PCC layer
E2 = Modulus of lower plate, i.e., the base layer
h1 = Thickness of upper plate, i.e., the PCC slab
h2 = Thickness of lower plate, i.e., the base layer

The procedures presented above require the modular ratio as an input parameter. Engineering judgment should determine this ratio. It is assumed that if the ratio is assigned within reasonable limits, the PCC modulus results (= E1) are insensitive to the ratio. Table 16 presents the recommended modular ratios (Beta) of the calculated PCC and base moduli for each type of base layer. It should be noted thatfrom Figure 34 is defined as a ratio of base to PCC moduli. This equation creates stability for the case of a weak base (i.e., whenBetaapproaches 0). Therefore, the ratios from Table 16 should be inverted before using them in the procedure described above.

Given the values for Beta and for the actual plate thicknesses, h1 and h2, the equations in Figure 31 and Figure 32 may be used with the forwardcalculated Epcc,app.-value to yield E1 and E2 for the two upper layers.

Identify Interface Condition Between the PCC Slab and the Base Layer(s)

For the point-by-point forwardcalculated moduli, modulus values were calculated for both the unbonded and the bonded cases. These values can be used to screen the corresponding unbonded and bonded values in the backcalculation tables.

For the section mean modulus, the bond condition between the PCC slab and the base is given in the backcalculation table as a bond index, as estimated by Khazanovich, et al.(1) The same bond index was adopted for the forwardcalculation moduli to select either the unbonded or the bonded values for the section database.

 

Table 16. Back- and forwardcalculated modulus ratios for EPCC /EBase.
LTPP Code Base Type RatioBeta*=1/Beta
1 Hot-mixed, hot-laid AC, dense graded 10
2 Hot-mixed, hot-laid AC, open graded 15
3 Sand asphalt 50
4 Jointed plain concrete pavement (JPCP) 1
5 Jointed reinforced concrete pavement (JRCP) 1
6 Continuously reinforced concrete pavement (CRCP) 1
7 PCC (prestressed) 1
8 PCC (fiber reinforced) 1
9 Plant mix (emulsified asphalt) material, cold laid 20
10 Plant mix (cutback asphalt) material, cold laid 20
13 Recycled AC, hot laid, central plant mix 10
14 Recycled AC, cold laid, central plant mix 15
15 Recycled AC, cold laid, mixed in place 15
16 Recycled AC, heater scarification/recompaction 15
17 Recycled JPCP 100
18 Recycled JRCP 100
19 Recycled CRCP 100
181 Fine-grained soils: lime-treated soil 100
182 Fine-grained soils: cement-treated soil 50
183 Bituminous-treated subgrade soil 100
292 Crushed rock 150
302 Gravel, uncrushed 200
303 Crushed stone 150
304 Crushed gravel 175
305 Crushed slag 175
306 Sand 250
307 Soil-aggregate mixture (predominantly fine grained) 400
308 Soil-aggregate mixture (predominantly coarse grained) 250
319 Hot-mixed AC 15
320 Sand asphalt 50
321 Asphalt-treated mixture 50
322 Dense-graded, hot-laid, central plant mix AC 10
323 Dense-graded, cold-laid, central plant mix AC 15
324 Dense-graded, cold-laid, mixed-in-place AC 15
325 Open-graded, hot-laid, central plant mix AC 15
326 Open-graded, cold-laid, central plant mix AC 15
327 Open-graded, cold-laid, mixed-in-place AC 15
328 Recycled AC, plant mix, hot laid 10
329 Recycled AC, plant mix, cold laid 15
330 Recycled AC, mixed in place 15
331 Cement aggregate mixture 5
332 Econocrete 4
333 Cement-treated soil 50
334 Lean concrete 2
335 Recycled PCC 100
338 Lime-treated soil 100
339 Soil cement 10
340 Pozzolanic-aggregate mixture 100
341 Cracked and seated PCC layer 25
351 Treatment: lime, all classes of quick lime and hydrated lime 100
352 Treatment: lime fly ash 150
353 Treatment: lime and cement fly ash 150
354 Treated: PCC 50
355 Treatment: bitumen (includes all classes of bitumen and asphalt treatments) 100
700 AC 15
730 PCC 1

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—LINEAR ELASTIC MODEL

The same linear elastic backcalculation program (MODCOMP) used to populate the backcalculated flexible pavement system data was also used to backcalculate interior slab layered elastic moduli.

Since the forwardcalculation routines developed to screen the LTPP backcalculated database were designed to operate in two modes—one with and one without bond between the PCC and base layers—the summary charts shown in this section are divided into two parts. One of these compares the forwardcalculated values assuming 100 percent bond between layers and the other, assuming 100 percent slip between the concrete surface layer and the base.

Figure 35 summarizes the screening results for forwardcalculated PCC moduli based on 100 percent bond between the concrete slab and the base, while Figure 36 is based on forwardcalculated values based on 100 percent slip between the two upper layers.

Click for text description.

Figure 35. Charts. Screening results of elastic moduli of the interior
concrete slab for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model for backcalculation and a bonded
condition between the slab and base for forwardcalculation.

Click for text description.

Figure 36. Charts. Screening results of elastic moduli of the interior
concrete slab for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model for backcalculation and an unbonded
condition between the slab and base for forwardcalculation.

Similarly, Figure 37 depicts the screening results for forwardcalculated base course moduli based on 100 percent bond between the concrete surface and the base, while Figure 38 reflects the forwardcalculated moduli based on 100 percent slip between the two upper layers.

Click for text description.

Figure 37. Charts. Screening results of elastic moduli
of the base layer for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model for backcalculation and a bonded
condition between the concrete slab and base layer for forwardcalculation.

Click for text description.

Figure 38. Charts. Screening results of elastic moduli of the base layer
for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the
linear elastic model for backcalculation and an unbonded condition between the
concrete slab and base layer for forwardcalculation.

The four preceding figures do not show a great deal of difference in the charts comparing the forwardcalculated values with slip between the concrete and the base and the cases with no slip to backcalculated moduli. These values are not because there isn’t any difference in the two; rather, the acceptance and flagging criteria for the backcalculated tables is rather broad, as for example having to be more than a factor of 1.5 different before any flag (1, 2, or 3) is applied.

In the case of the backcalculated PCC modulus, the 100 percent slip criterion used in forwardcalculation resulted in a somewhat better comparison: 83 percent versus 61 percent of the remaining values (see right pie charts in Figure 36 and Figure 35, respectively). Conversely, in the case of the base course moduli, the use of the 100 percent bonded criterion results in a slightly better comparison: 35 percent versus 31 percent—see Figure 37 and Figure 38, respectively.

Figure 39 shows the comparison of the screening results for forwardcalculated subgrade moduli based on the Hogg model versus backcalculated subgrade moduli using MODCOMP. Since the Hogg model uses a direct (closed form) solution that is not dependent on the moduli of the overlying layers, no difference occurs whether there is 100 percent slip or 100 percent bond between the surface and the base course.

Click for text description.

Figure 39. Charts. Screening results of elastic moduli of the
subgrade for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear elastic model.

There is some improvement in the backcalculated table of subgrade moduli for rigid sections compared to the table for flexible sections. For the rigid sections, 50 percent of the sections were within a factor of 1.5 of the forwardcalculated subgrade moduli, while in the flexible case only 31 percent of the values were within the same factor of 1.5.

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—SLAB-ON-ELASTIC-SOLID ANALYSIS

Another method used to populate the table of backcalculated moduli in the LTPP database was the theory of a concrete slab on an elastic solid foundation. The method used was developed specifically for the LTPP FWD database and the rigid pavements within that database.(1) Using this approach, two different backcalculation methods can be employed: bonded and unbonded condition between the concrete slab and the base.

Figure 40 and Figure 41 show the screening results for this portion of the database, for the concrete layer with a bonded and unbound condition between the slab and the base. Figure 42 and Figure 43 show the corresponding base course charts for the elastic solid model set of data.

Click for text description.

Figure 40. Charts. Screening results of elastic moduli of the PCC slab
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic
solid model for backcalculation and assuming bonded condition
between the slab and the base for back- and forwardcalculation.

Click for text description.

Figure 41. Charts. Screening results of elastic moduli of the PCC slab
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic
solid model for backcalculation and assuming unbonded condition between the slab
and the base for back- and forwardcalculation.

Click for text description.

Figure 42. Charts. Screening results of elastic moduli of the base layer
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table
using the elastic solid model for backcalculation and assuming bonded
condition between the slab and the base for back- and forwardcalculation.

Click for text description.

Figure 43. Charts. Screening results of elastic moduli of the base layer
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic
solid model for backcalculation and assuming unbonded condition between
the slab and the base for back- and forwardcalculation.

As Figure 40 and Figure 41 show, the correspondence between the reasonable range forwardcalculated and backcalculated concrete modulus is excellent, both for the bonded and unbonded cases (97 and 99 percent, respectively). This correlation is mainly because the backcalculation method used, which was essentially a two-layer system with fixed ratios between the concrete surface and base courses, was also used in forwardcalculation of rigid pavement systems. In the forwardcalculation procedure, the same ratios, as a function of the base course type, were used to calculate the base course modulus. It is believed that this approach to both back- and forwardcalculation is much more tenable—and realistic.

Accordingly, the base course moduli comparison between back- and forwardcalculation was also very good. Of all reasonable values, at least 95 percent were within a factor 67 to 150 percent of the forwardcalculated modulus (see Figure 42 and Figure 43).

Figure 44 shows the subgrade modulus charts for the elastic solid backcalculation method.

Click for text description.

Figure 44. Charts. Screening results of elastic moduli of the subgrade
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table
using the elastic solid model for backcalculation.

Once again, the correspondence between back- and forwardcalculation of the subgrade was excellent (see Figure 44). In fact, the subgrade modulus relationship is the best of all, with close to 100 percent of the values in the backcalculated database (i.e., the elastic solid model) being in the reasonable range and 99 percent of these being within a factor of 1.5 of the forwardcalculated moduli from the Hogg model.

SCREENING OF THE RIGID PAVEMENT BACKCALCULATION PARAMETERS—SLAB-ON-DENSE-LIQUID ANALYSIS

The last approach used for backcalculating the moduli of rigid pavement layers is based on the theory of a slab on dense liquid, which also was originally developed by Westergaard. This approach is explained in full in the same reference as the slab-on-dense-liquid model.(1) Similar to the elastic solid model, two different backcalculation methods were used, a bonded and an unbonded condition between the concrete slab and the base layer.

Figure 45 and Figure 46 show the screening results for this portion of the database, for the concrete layer, for a bonded and unbonded condition between the slab and the base. Figure 47 and Figure 48 show the corresponding base course charts for the dense-liquid model set of data.

These four figures show that the correspondence between back- and forwardcalculation is also excellent for the dense liquid model of backcalculation, compared to forwardcalculation. Nevertheless, the percentages that were within of 67 to 150 percent (2/3 to 3/2) of the forwardcalculated values were lower than for the elastic solid model. Most of these values were around 90 percent with no flag identified, for both a bonded and an unbonded condition between the concrete slab and the base course.

The slightly better results associated with the elastic solid model are not surprising, since the forwardcalculation formulae for a concrete layer were developed using elastic layer theory, not Westergaard’s equations.

Click for text description.

Figure 45. Charts. Screening results of elastic moduli of the PCC slab
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the
dense liquid model for backcalculation and assuming bonded condition between
the slab and the base for back- and forwardcalculation.

Click for text description.

Figure 46. Charts. Screening results of elastic moduli of the PCC slab
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense
liquid model for backcalculation and assuming unbonded condition between
the slab and the base for back- and forwardcalculation.

Click for text description.

Figure 47. Charts. Screening results of elastic moduli of the base layer
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the
dense-liquid model for backcalculation and assuming bonded
condition between the slab and the base for back- and forwardcalculation.

Click for text description.

Figure 48. Charts. Screening results of elastic moduli of the base layer
for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the
dense-liquid model for backcalculation and assuming unbonded condition
between the slab and the base for back- and forwardcalculation.

When the dense-liquid model is used, the subgrade is not characterized by a modulus of elasticity, but rather by a k-value. Accordingly, the k-value in the case of forwardcalculation was derived using the same relationship developed when the dense-liquid and elastic-solid models were developed. Since this relationship is empirical and has inconsistent units, the E-value must be in MPa while the k-value is in kPa/mm.

Click for text description.

Figure 49. Equation. Subgrade k-value.

and:

k-value = Subgrade modulus of reaction, k-value, kPa/mm
Esubgrade = Subgrade modulus of elasticity, MPa

Figure 50 shows the subgrade k-value charts for the dense-liquid backcalculation method.

Click for text description.

Figure 50. Charts. Screening results of the subgrade k-values for
the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table
using the dense-liquid model for backcalculation.

Again, the correspondence between the two methods of calculating the k-value of the subgrade under a concrete slab is very good, although somewhat poorer than with the elastic solid model versus forwardcalculation. In this case, 92 percent of all reasonable values were within 67 to 150 percent of the forwardcalculated k-value.

SCREENING OF THE SECTION AVERAGE BACKCALCULATED DATABASE

In addition to the point tables, the LTPP database also consists of section backcalculated data tables, designed to represent LTPP pavement section average moduli rather than point-by-point moduli as were screened in the preceding subsections. Each LTPP section was typically 152 m (500 ft) in length.

The existing section average data in the LTPP database were derived by first calculating the arithmetic average and standard deviation of the moduli for a given layer for each pavement section. Next, all data lying outside of two standard deviations were eliminated, and a new average was calculated based on the remaining moduli after elimination of outliers. One of the problems with this approach is that the data typically are not normally distributed on an arithmetic scale, but rather much closer to a log normal distribution. Accordingly, more often than not—especially when more than two unknown structural layers were backcalculated—the two standard deviation approach did not eliminate the very low modulus values, since two standard deviations downwards on an arithmetic scale often resulted in negative moduli. Accordingly, many higher-than-reasonable values were (correctly) eliminated while the lower-than-reasonable values were (incorrectly) retained from the section average. Accordingly, this procedure often introduces a bias (on the low side) into the section averages.

To rectify this discrepancy, the forwardcalculated values were treated as follows: The logarithms of all point data from a given section and structural layer were tabulated. Next, the IQR was calculated on these data, as Moore and McCabe describe in chapter 5.(11) Outliers then were identified as those values outside the range of (Q1 - 1.5 * IQR, Q3 + 1.5 * IQR). Finally, the average of the remaining (unexcluded) moduli was calculated, which is the section average modulus for a given layer.

Figure 51 and Figure 52 show examples of a section data table from back- and forwardcalculation as compared to the equivalent example from the point data table. Figure 51 represents the results for screening of the base course layer(s) in the point data table from MODCOMP (linear elastic model) for the flexible pavement database. (This figure is the same as Figure 27.) Figure 52 shows the corresponding section data, screened using the same criteria as for the point data according to the above-outlined procedure. There is little percentage difference between the two figures, although a small improvement occurs from the point to the section level in the backcalculated tables.

Figure 53 and Figure 54 show another example of the difference between the point and section data tables for the subgrade k-value in the rigid section LTPP database, based on the dense-liquid model of backcalculation. In this example, a small improvement occurs in the correspondence between back- and forwardcalculation from the point level to the section level. This pattern was, in general, the case for other layers and backcalculation methods.

All charts associated with the section database are presented in appendix A.

Click for text description.

Figure 51. Charts. Screening results of elastic moduli of the point base layer
for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT
table based on the linear-elastic model.

Click for text description.

Figure 52. Charts. Screening results of elastic moduli of the section base layer
for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT
table based on the linear-elastic model.

Click for text description.

Figure 53. Charts. Screening results of the subgrade point k-value
table for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT
table using the dense-liquid model for backcalculation.

Click for text description.

Figure 54. Charts. Screening results of the subgrade section k-value
table for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT
table using the dense-liquid model for backcalculation.

 

FHWA-HRT-05-150

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
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