EVALUATION OF BEARING CAPACITY OF LOW …docs.trb.org/prp/14-2146.pdf · 1 EVALUATION OF BEARING...

EVALUATION OF BEARING CAPACITY OF LOW-VOLUME ROADS IN 1

MINNESOTA 2

3

Lev Khazanovich (corresponding)

Associate Professor

University of Minnesota

Department of Civil Engineering

500 Pillsbury Drive S.E.

Minneapolis, MN 55455

Phone: 612-624-4764

E-mail: [email protected]

Derek Tompkins

Research Associate

University of Minnesota

Department of Civil Engineering

500 Pillsbury Drive S.E.

Minneapolis, MN 55455

Phone: 612-626-4098

E-mail: [email protected]

Erland Lukanen 4

Consultant 5

251 Reid Lane 6

South St Paul, MN 55075 7

Phone: 651-455-4970 8

E-mail: [email protected] 9

10

11

12

13

Paper submitted 31 July 2013 for 14

Transportation Research Board 93rd Annual Meeting, 15

12-16 January 2014 16

17

Words: 4937 18

Figures: 3 19

Tables: 5 20

Photographs: 0 21

Total Word Count: 6937 22

23

TRB 2014 Annual Meeting Paper revised from original submittal.

Khazanovich, Tompkins, and Lukanen 1

EVALUATION OF BEARING CAPACITY OF LOW-VOLUME ROADS IN 1

MINNESOTA 2

3

ABSTRACT 4 Deflection testing and analysis is routinely used to evaluate the spring load capacity of 5

pavements and to design structural overlays. The current Falling Weight Deflectometer (FWD) 6

deflection analysis process used by the Minnesota Department of Transportation was found to be 7

unreliable. Traditionally, the process used to interpret FWD deflection measurements converted 8

the measured maximum FWD deflection to an equivalent Benkelman Beam deflection and 9

compared it to the allowable deflection for a pavement with given asphalt surface thickness and 10

anticipated traffic. Since the maximum FWD deflection is greatly affected by the subgrade 11

stiffness, the TONN program may underestimate the allowable axle load for subgrades 12

depending on the subgrade material. As a result, it was determined that the allowable axle load 13

rating procedure should be revised. This paper details those revisions and the development of a 14

new low-volume road rating procedure. 15

16

17

18

19



INTRODUCTION 1 While state and local transportation agencies have become more and more adept at managing 2

large road networks, one continuing challenge is estimating the remaining service life for low-3

volume roads. The pavement designs for these roads vary due to many factors, including the era 4

in which the pavement was constructed, rehabilitation efforts, or natural changes in or 5

availability of local materials. An important aspect of understanding a road network from a 6

pavement engineering perspective is determining the traffic (in terms of both axle load and 7

volume) that those different roads can tolerate. 8

There are two major issues for the agency in determining the axle load and traffic 9

tolerance of its road network. The first issue is assessing the structural adequacy of the roadway 10

to carry traffic. This assessment includes the use of non-destructive tests (NDT) to approximate 11

the pavement response to controlled load applications. The second issue is determining the need 12

for axle load restrictions, which includes the consideration of seasonal loads. Load restrictions 13

may also consider detours, haul roads, development, and new industries; they may also include 14

overloads, which are an important issue for low-volume roads but are not discussed in this paper. 15

State agencies have historically used NDT to assess pavements for decades, and as a 16

result the developed testing apparatuses (such as the falling-weight deflectometer) are very 17

sophisticated and precise devices capable of easy, repeated testing. Furthermore, the procedures 18

that accompany these devices are often equally sophisticated, and in many cases the collection of 19

pavement response data has been automated so that the responsibilities of the test operator are 20

further simplified. However, the analysis tools for the collected field test data have lagged 21

considerably behind both the test devices and procedures in terms of sophistication. 22

This paper presents one such analysis tool: the FWD deflection analysis procedure used 23

by the Minnesota Department of Transportation (MNDOT) in its computer program TONN. 24

After decades of use, MNDOT determined that the previous TONN procedure overestimated 25

axle load capacity for stiffer soils and underestimated load capacity for softer soils. As a result, 26

researchers at the University of Minnesota assisted MNDOT in revising and updating both the 27

analysis procedure and TONN program. The paper also describes the updated procedure, called 28

TONN2010, for the benefit of readers, especially those at other state and local agencies. 29

30

31

HISTORY OF THE USE OF BEARING CAPACITY EVALUATION OF LOW-32

VOLUME ROADS IN MINNESOTA 33 Deflection testing has been used by pavement engineers for decades to assess roadways. The 34

basic principle of deflection testing is that the amount of deflection under a loaded axle is a good 35

predictor of a pavement’s ability to sustain heavy loads. For instance, the Minnesota Department 36

of Transportation (MNDOT) has a long history with deflection testing, which includes the plate 37

bearing test in the 1940s and 1950s, the Benkelman beam in the 1960s to the late 1970s, the 38

Road Rater in the late 1970s and early 1980s, and the falling-weight deflectometer (FWD) since 39

then. Nearly every mile of flexible pavement on the Minnesota Trunk Highway system has been 40

tested using deflection-based assessments at some point in time (1). 41

Both the FWD apparatus and test procedure are simple and direct. The final result of 42

FWD testing is data that is ready to be used for analysis. This analysis will ultimately determine 43

the bearing capacity of a pavement. The previous version of MNDOT’s FWD analysis program, 44

TONN, used the deflection under the FWD load plate, D1, for its analysis (2). TONN first 45



converted the deflection, D1, to an equivalent Benkelman Beam deflection, BB. For flexible 1

pavements this conversion was 2

3

𝐵𝐵 = 5.15 + 1.05𝐷1 (1)

4

where BB and D1 are given in mils. The TONN procedure then accounted for thermal effects 5

through the pavement system by adjusting BB accordingly. For pavement surface temperatures 6

larger than or equal to 80°F, no adjustment was made to BB. For surface temperatures, T, less 7

than 80°F, one of three different adjustments to BB would be made, based on the magnitude of 8

BB. 9

10

𝐵𝐵𝑇 = 𝐵𝐵 + ∆𝐵𝐵𝑇 (2)

∆𝐵𝐵𝑇 = (16 − 0.2𝑇)(0.375 + 0.025𝐵𝐵), for 𝐵𝐵 < 25 (3)

∆𝐵𝐵𝑇 = (16 − 0.2𝑇), for 25 ≤ 𝐵𝐵 ≤ 35 (4)

∆𝐵𝐵𝑇 = (16 − 0.2𝑇)(0.125 + 0.025𝐵𝐵), for 𝐵𝐵 > 35 (5)

11

The adjusted BBT is then converted to a “Spring Deflection” (for when the pavement system is 12

most vulnerable, after spring thaw) Benkelman Beam deflection, BBS, using a pre-determined 13

value from TONN (3). In addition, for a given pavement (of asphalt surface thickness and traffic 14

volume), a table of allowable spring deflection values, AD, is provided with TONN. Given both 15

AD from the corresponding table and BBS from the FWD testing and TONN analysis, TONN 16

estimates the allowable axle load, L, as: 17

18

𝐿 = 10 ×𝐴𝐷

𝐵𝐵𝑆

(6)

19

While the previous TONN procedure served MnDOT well for many years, one limitation of the 20

procedure was that, as noted in the description of TONN, it did not use the full deflection basin 21

in assessing the structural capacity of a given pavement. The use of the deflection at the center 22

of the load plate only led to inaccurate estimation of allowable axle loads for different pavement 23

systems. As the FWD maximum deflection is greatly affected by the subgrade stiffness, the 24

TONN procedure could underestimate the allowable axle load for soft clay subgrades, yet 25

overestimate the allowable axle load for stiff sand or granular subgrades. 26

Thus, under the previous version of TONN, the structural contribution of the constructed 27

layers in the pavement system was not fully accounted for. The following sections detail the 28

revision of TONN to better account for the structural contribution of all layers of the pavement 29

system. 30

31

32

DEVELOPMENT OF NEW PROCEDURE 33 MNDOT’s first objective in revising TONN was to keep the procedure based on FWD data. A 34

second but equally important objective was to prioritize the usability of the procedure for state 35

and local engineers. The final objective was to expand the original TONN, which only 36

considered one criterion (for bearing capacity), to include criteria for asphalt concrete (AC) 37

fatigue cracking, subgrade rutting, and base shear failure based on models from MnPAVE, 38



MNDOT’s local mechanistic-empirical design procedure for flexible pavements, and the 1

Mechanistic-Empirical Pavement Design Guide (MEPDG) models (4, 5). 2

While the incorporation of new evaluation criteria was important, it was not a major 3

concern given that it used existing models. The biggest concern was both updating the bearing 4

capacity procedure and maintaining a simple, direct process for state and local engineers. One 5

way to address usability was to make every effort to minimize the number of inputs required 6

from the user while still maintaining a robust procedure. For any FWD test of a given pavement 7

section, the revised procedure therefore only requires: 8

9

AC layer thicknesses, 10

air temperature and pavement surface temperature at the time of testing, 11

pavement location, 12

anticipated traffic, and 13

the deflection basin. 14

15

Using this data, the procedure first backcalculates layer moduli using the backcalculation 16

procedure developed specifically for this project. The procedure then adjusts the backcalculated 17

moduli using temperature and seasonal adjustment factors taken from the MNDOT flexible 18

pavement design program MnPAVE. Finally, the procedure estimates pavement axle load 19

capacity using mechanistic-empirical analysis. All the inputs required for the tasks in the 20

procedure are outlined above, and all of those inputs can be easily obtained by the user. More 21

details are provided in the subsections below. 22

23

Simplified backcalculation 24

The bearing capacity evaluation procedure begins with FWD backcalculation, which involves the 25

determination of the elastic properties of the pavement system given deflection basins. MNDOT 26

identified the following needs for the backcalculation process to be incorporated into the revised 27

procedure: 28

29

The backcalulation model should be based on layered elastic theory. 30

The layered system considered should include four layers: the AC surface layer, a 31

base layer, a subgrade, and a very stiff layer. The first three layers can be of various 32

thicknesses and the last layer is semi-infinite. 33

The backcalculation process should not require user-defined seed values. 34

The apparent depth to the semi-infinite layer should be either an input parameter 35

provided by the user or should be determined in the process of backcalculation. 36

The procedure should be integrated seamlessly with the rest of the revised TONN 37

procedure. 38

39

Although several publicly available backcalculation procedures were evaluated, none were found 40

to satisfy all of the above criteria. Therefore, a simple backcalculation procedure was developed 41

specifically for the revised TONN. 42

The backcalculation procedure utilizes a database of thousands of pre-calculated 43

deflection basins to interpolate and estimate a deflection basin for an arbitrary pavement. This 44

process is thus a neural network, whose use in pavement analysis is well documented (6, 7). To 45

develop the original database of deflection basins, the layered elastic analysis program 46



MnLAYER was used to calculate vertical deflections at the top of the AC surface layer, at lateral 1

positions of 0, 8, 12, 18, 24, and 36 inches away from a 10,960-lb load uniformly distributed 2

over a circular area with a radius of 5.9 in (8). Structural systems were developed in which layer 3

properties were assumed to have one of the following values: 4

5

Top layer (representing the AC surface layer) 6

Modulus of elasticity, E1: 100, 200, 300, 400, 600, 800, 1200, 1500, 2000, 7

3000, and 4000 ksi 8

Thickness, h1: 2, 3, 4, 5, 6, 8, 10, and 12 in 9

Second layer (representing the granular base) 10

Modulus of elasticity, E2: 10, 20, 30, 40, 50, 60, 80, 100, and 999 ksi 11


Third layer 13

Modulus of elasticity, E3: 10 ksi 14


Fourth layer 16

Modulus of elasticity, E4: 1,000 ksi 17

Thickness: Semi-infinite 18

19

The developed backcalculation procedure has a few limitations regarding the properties of the 20

pavement system. First, the AC surface layer thickness must be greater than 2 inches and less 21

than 12 inches, the base layer must be between 3 and 48 inches in thickness, and the subgrade 22

must be between 12 and 240 inches in thickness. The layer moduli E1 and E2 must be such that 23

24

400𝐸2 > 𝐸1 >𝐸2

10

(7)

100𝐸3 > 𝐸2 > 𝐸3 (8)

25

These requirements for layer thickness and stiffness properties do not generally limit the analysis 26

of the majority of pavements to be assessed using the revised TONN procedure. 27

The database of pre-computed deflections was used to backcalculate elastic moduli of the 28

three-layered pavement system (AC layer, base, and subgrade) from measured FWD deflections. 29

The thicknesses of the AC and base layer should be provided by the user. The user should also 30

either specify the thickness of the subgrade layer (i.e. depth to bedrock) or allow the program to 31

determine this value as a part of the backcalculation process. The following steps define this 32

process. 33

34

Step one. Using on-grid optimization, find elastic moduli E1 and E2 that minimizes the following 35

error between non-dimensional measured and computed deflections 36

37

𝐸𝑅𝑅 = ∑ (𝐷𝑚𝑒𝑎𝑠(𝑟𝑖)

𝐷0𝑚𝑒𝑎𝑠−

𝐷𝑐𝑎𝑙𝑐(𝑟𝑖)

𝐷0𝑐𝑎𝑙𝑐)

26

1

(9)

38



where Dmeas and Dcalc are FWD measured and FWD calculated deflections at lateral distances ri 1

(0, 8, 12, 18, 24, or 36 in) away from the center of the load, respectively, and D0meas and D0calc 2

are measured and calculated deflections under the center of the load, respectively. 3

4

Step two. Determine the subgrade modulus of elasticity that minimizes the error function ERR2, 5

where 6

7

𝐸𝑅𝑅2 = ∑ (𝐷𝑚𝑒𝑎𝑠(𝑟𝑖) −𝑃

𝑃0

𝐸3

𝐸𝑠𝑢𝑏𝑔𝑟𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖))

26

1

(10)

8

and where P is the load magnitude and P0 is a FWD load of 10,960 lb. To minimize ERR2, the 9

subgrade modulus should satisfy the condition 10

11 𝜕(𝐸𝑅𝑅2)

𝜕𝐸𝑠𝑢𝑏𝑔𝑟= 0

(11)

12

which leads to an expression for the subgrade layer modulus of elasticity Esubgr 13

14

𝐸𝑠𝑢𝑏𝑔𝑟 =𝑃

𝑃0𝐸3

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖))26

1

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖)𝐷𝑚𝑒𝑎𝑠(𝑟𝑖))61

(12)

15

Step three. Determine base and AC moduli. The AC and base modulus can be found from the 16

equations 17

18

𝐸𝐴𝐶 =𝑃

𝑃0𝐸1

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖))26

1

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖)𝐷𝑚𝑒𝑎𝑠(𝑟𝑖))61

(13)

𝐸𝑏𝑎𝑠𝑒 =𝑃

𝑃0𝐸2

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖))26

1

∑ (𝐷(𝐸1, 𝐸2, 𝐸3, 𝑃0, 𝑟𝑖)𝐷𝑚𝑒𝑎𝑠(𝑟𝑖))61

(14)

19

Step four. The use of MnLAYER determines the degree of discrepancy between the measured 20

and generated deflection basins – that is, the relationship described in Equation (9) above. 21

22

Climate adjustment 23

Prior to the estimation of the actual structural response of the pavement, the revised TONN 24

procedure accounts for climatic effects. The FWD backcalculation procedure described above 25

determines the layer moduli for the environmental conditions at the time of testing. Given that 26

the asphalt modulus is temperature dependent, the backcalculated moduli should be adjusted. To 27

do so, the AC temperature at a depth of one-third of the AC surface layer thickness at the time of 28

FWD testing is determined using the BELLS3 procedure (9). BELLS3 uses the pavement 29

surface temperature measured by the FWD device, the previous day’s average air temperature, 30

the thickness of the asphalt, and the time of the test to estimate the temperature at one-third of 31

the depth of the AC surface layer. The BELLS3 model takes the form 32



𝑇(𝑧) = 2.78 + 0.912𝑇𝑠 + 0.027𝑇𝑠 sin(ℎ𝑟18 − 13.5)

+ [−0.448𝑇𝑎𝑖𝑟,1−𝑑𝑎𝑦 + 0.553𝑇𝑠 + 2.63 sin(ℎ𝑟18 − 15.5)] log(𝑧

3− 1.25)

(15)

1

where 2

T(z) = pavement temperature at depth z, oC

z = depth at which material temperature is to be predicted, mm

Ts = infrared surface temperature, oC

Tair,1-day = average air temperature the day before testing, oC

hr18 = Time of day, in a 24-hr clock system, but calculated using an 18-hr AC

temperature rise-and-fall time cycle

3

Given the results of the BELLS3 analysis, the AC modulus for a reference temperature of 22 deg 4

C (~72°F) is computed using analysis developed by Lukanen et al (1998), which was developed 5

using Long Term Pavement Performance (LTPP) Seasonal Monitoring Program (SMP) data. 6

Once E1 is estimated for the AC surface reference temperature, the seasonal AC modulus of 7

elasticity values are developed using the procedure adopted for MnPAVE to determine average 8

seasonal pavement temperatures. Here the seasonal pavement temperature for the upper-third is 9

estimated according to 10

11

𝑇𝑝𝑖= 𝑇𝑎𝑖

(1 +1

𝑧 + 4) −

34

𝑧 + 4+ 6

(16)

12

where 13

Tpi = average seasonal pavement temperature at depth z for ith season (deg F)

Tai = average seasonal air temperature for ith season (deg F)

z = depth at which material temperature is to be predicted, inches

14

Given the seasonal pavement temperatures, the corresponding AC seasonal moduli can be 15

determined using the procedure developed by Lukanen et al (2000) and alluded to above. 16

Finally, as the elastic behavior of unbound materials is moisture dependent and thus varies 17

season to season, the backcalculated base and subgrade moduli are adjusted given 18

19

𝐸2,𝑖 = 𝐸2 ∙𝑏𝑠𝑖

𝑏𝑑𝑎𝑦

(17)

𝐸3,𝑖 = 𝐸3 ∙𝑠𝑠𝑖

𝑠𝑑𝑎𝑦 (18)

20

where 21

E2 = backcalculated base modulus

E2,i = average base modulus for season i

bsi = base modulus season adjustment factor for season i

bday = base modulus adjustment factor accounting for a difference in the

moisture conditions for the test day; by default it is equal to 1

E3 = backcalculated subgrade modulus



E3,i = average subgrade modulus for season i

ssi = subgrade modulus season adjustment factor for season i

sday = subgrade modulus adjustment factor accounting for a difference in

the moisture conditions for the test day; by default it is equal to 1.

1

Structural modeling 2

After the backcalculated layer moduli are adjusted to account for the seasonal effects, the critical 3

pavement responses (strains and deflections) are computed using a layered elastic program. For 4

the TONN procedure, the layered elastic program MNLAYER was incorporated into the final 5

program to enable the critical response calculation. The pavement responses are computed for 6

five seasons to mirror MnPAVE. The pavement is assumed to be loaded by an 18,000 lbs single 7

axle load. Only half of an axle (two wheels) is considered. Each tire footprint is assumed to 8

have a radius of 3.8 in and the tire pressure is assumed to be equal to 100 psi. The wheels are 9

assumed to be placed 13.5 in apart. 10

Pavement responses in terms of displacements, strains, and stresses are calculated using 11

MnLAYER. Responses are evaluated at either six or eight points, depending on the thickness of 12

the base layer. The distribution of evaluation points for the two cases is illustrated in Figure 1, 13

where points are allocated directly under the wheel load or at the mid-point of the wheel paths. 14

15

Figure 1. Evaluation points for pavement system with base layer h2 ≤ 12 in (at left) or h2 > 16

12 in (at right) 17 18

The maximum principal horizontal strain computed at point A, at the bottom of the AC surface 19

layer, is used in the AC damage calculation. For cases where h2 ≤ 12 in, the maximum vertical 20

strains computed at points C and G, 12 inches below the top of the base layer, are used for the 21

rutting damage analysis. For cases where h2 > 12 in, the maximum vertical strains computed at 22

points D and H, at the top of the subgrade, are used for the rutting damage analysis. Stresses 23

computed at the mid-depth of the base layer at points B and F are used to compute the principal 24

and critical stresses as defined by the base shear failure criteria from MnPAVE, which is stated 25

as 26

27

𝜎1 < 𝜎1,𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = 𝜎3 ∙ tan2 (45 +𝜑

2) + 2𝐶 tan (45 +

𝜑

2) (19)

28

where 29

φ = Internal friction angle (in degrees)

C = Cohesion coefficient

σ1 = Maximum allowable major principal stress



σ3 = Minor principal stress or confining pressure for the triaxial test.

1

It should be noted that the MNDOT flexible pavement design program MnPAVE contains 2

default values of internal friction angle and cohesion coefficient for typical Minnesota base 3

materials. 4

5

The stresses at points B and F are used to compute the strength-to-stress ratios, where strength-6

to-stress ratio, SRc, is 7

8

𝑆𝑅𝑐 = max (𝜎𝐵,1

𝜎𝐵,𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙,

𝜎𝐹,1

𝜎𝐹,𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙)

(20)

9

and σB,1 and σF,1 are first principal stresses at points B and F and σB,critical and σF,critical are critical 10

stresses computed for points B and F. MEPDG uses a comprehensive procedure for the 11

estimation of rutting in the base/subbase layer which requires detailed characterization of the 12

base and subbase. In this case, a simpler approach was used. 13

Finally, the vertical displacement at point C, 12 inches below the top of the base layer, is 14

subtracted from the vertical displacement at point A at the bottom of the AC surface layer. 15

Similarly, for points at the mid-distance between the wheel loads, the vertical displacement at 16

point G is subtracted from the vertical displacement at point E. The maximum of these two 17

differences, DW, is used in the subsequent analysis. 18

19

𝐷𝑊 = max(𝑤𝐴 − 𝑤𝐶, 𝑤𝐸 − 𝑤𝐺) (21)

20

Damage Analysis 21

After the critical responses are determined for each season, the damage analysis is performed to 22

account for AC fatigue cracking damage, subgrade rutting damage, base shear failure, and base 23

deformation. The anticipated AC fatigue damage, DAMAC, over the design life is determined 24

using 25

26

𝐷𝐴𝑀𝐴𝐶 =BESAL

365∑

𝐷𝐴𝑌𝑆𝑖

0.314𝜀𝐴,𝑖−3.291𝐸𝐴𝐶𝑖

−0.854

5

𝑖=1

(22)

27

where 28

BESAL = anticipated cumulative number of ESALs over the pavement design

life

DAYSi = duration of season i in days.

εA,i = principal horizontal strain at point A for season i combinations of

elastic properties

EACi = AC elastic modulus for season i.

29

The anticipated subgrade rutting damage, DAMrut, over the design life is determined using 30

31



𝐷𝐴𝑀𝑟𝑢𝑡 =BESAL

365∑

𝐷𝐴𝑌𝑆𝑖

0.0261𝜀𝐵,𝑖−2.35

5

𝑖=1

(23)

1

where εB,i is the vertical strain at point B for season i combinations of elastic properties. 2

Analysis of equations (22 and (23 suggests that for a given structure, an increase in anticipated 3

traffic leads to an increase in anticipated damage. Also, if the anticipated damage exceeds that of 4

the critical fatigue and cracking damage values, then the pavement structure should be 5

considered inadequate in fatigue or rutting, respectively. In the MnPAVE analysis these critical 6

values are equal to 1. However, since the backcalculated FWD values are not necessarily equal 7

to the elastic properties used in the MnPAVE calibration, these critical damage values can be 8

different and should be determined through calibration, which will be presented below. 9

If the anticipated damage is equal to or less than the critical damage at the end of the 10

design life, then the pavement should be rated as a 10-ton pavement. If the anticipated damage is 11

greater than this critical damage, then one of two scenarios should be considered: 12

13

the pavement should require rehabilitation before the end of the design period or 14

axle load limits should be imposed on the pavement, especially during the seasons 15

when the damage is the greatest. 16

17

The following relationships were used to translate the anticipated damage of pavements into 18

TONN indices 19

20

𝑇𝑂𝑁𝑁𝐴𝐶 = 𝐶𝐴𝐶𝐷𝐴𝑀𝐴𝐶−0.25 (24)

𝑇𝑂𝑁𝑁𝑟𝑢𝑡 = 𝐶𝑟𝑢𝑡𝐷𝐴𝑀𝑟𝑢𝑡−0.25 (25)

21

where 22

TONNAC = TONN index based on AC damage

TONNrut = TONN index based on subgrade rutting

CAC = calibration coefficients for AC damage index

Crut = calibration coefficients for rutting index.

23

If the stresses computed from an 18 kip single axle load result in a strength-to-stress ratio equal 24

to 1, then the road should be classified as 9 TONN with respect to base shear failure (SF). 25

Similarly for other strength-to-stress ratios, the TONN index can be defined as 26

27

𝑇𝑂𝑁𝑁𝑆𝐹 = 9 max𝑗(𝑆𝑅𝑗) (26)

28

where 29

TONNSF = shear failure TONN index based on the strength to stress ratio

SRj = Strength-to-stress ratio computed for point j and as defined in

Equation (20

j = point (C or D) in the structural system.

30



Finally, a higher difference in deflections at the base indicates a higher probability that the 1

pavement will fail prematurely in compression. The following expression for the TONN base 2

deformation (BD) index was developed for the deflection differences. 3

4

𝑇𝑂𝑁𝑁𝐵𝐷 =𝐶𝐵𝐷

max𝑘(𝐷𝑊𝑘)

(27)

5

where 6

TONNBD = TONN index based on differential deflections in the base layer

DWk = difference in the vertical deflections computed for point pair k and as

defined in Equation (21

k = a pair of points (either A + E or F + G) in the structural model

CBD = calibration parameter relating allowable axle load to difference in

vertical base deflections.

7

The overall TONN2010 rating for the road is determined as the minimum of the four individual 8

TONN ratings 9

10

𝑇𝑂𝑁𝑁2010 = min (𝑇𝑂𝑁𝑁𝐴𝐶, 𝑇𝑂𝑁𝑁𝑟𝑢𝑡, 𝑇𝑂𝑁𝑁𝑆𝐹, 𝑇𝑂𝑁𝑁𝐵𝐷) (28)

11

The TONN2010 procedure was encoded into a FORTRAN program that is executed with a user 12

created input file containing information about the pavement system, climatic data, and the FWD 13

deflection basin. 14

15

16

MODEL CALIBRATION 17 To finalize the TONN2010 procedure it is necessary to assign values to the calibration constants 18

CAC, CRUT, and CBD. This section provides a brief example of how these coefficients can be 19

calibrated using data from the Minnesota Road Research facility (MnROAD). This calibration 20

uses data from two flexible, low-volume test sections, Cells 83 and 84 (10). 21

Cell 84 was designed to represent a 10-ton road. It has a 5.5-in AC layer placed on a 9-in 22

thick granular (MNDOT Class 5) base. The pavement has an AC shoulder. Cell 83 was 23

designed to represent a 7-tonn road. It has a 3.5-in thick AC layer, an 8-in thick granular base, 24

and a gravel shoulder. Both pavement sections have two lanes. The cells were constructed in 25

October 2007. Since then they were subjected to heavy traffic two weeks per year: one week in 26

March and another week in August. The traffic consisted of two MnROAD trucks (one 80-kip, 27

the other 102-kip) and heavy farm equipment. After three years of testing, Cell 84 did not show 28

any appreciable signs of distresses. The westbound lane of Cell 83 failed in the spring of 2009 29

and the eastbound lane of Cell 83 failed in the summer of 2010. The distresses in both lanes 30

included base and subgrade permanent deformation and AC cracking. 31

The performance data for Cells 83 and 84 indicate that they can be adequately classified 32

as 7-tonn and 10-tonn pavements, respectively. However, since they were subjected to an 33

atypical mix of traffic, which included a relatively small number of heavily overloaded vehicles, 34

the design ESAL traffic for these sections was determined through simulation of performance of 35

these sections using MnPAVE. MnPAVE analysis indicated that Cell 83 could sustain 160,000 36

ESALs over 20 years and Cell 84 could sustain 600,000 ESALs over 20 years. Rutting damage 37



was found to be critical for both test cells. The expected performance for both pavements in AC 1

fatigue damage was 48 years. 2

FWD deflection data was collected for both cells in August 2008. The testing was 3

conducted for four load levels (6, 7.5, 9.5, and 12.5 kips). 172 deflection basins were collected 4

for Cell 83 and 168 deflection basins were collected for Cell 84. In addition to the deflection 5

data, the AC surface temperature measured by the FWD infrared sensor was recorded. 6

Backcalculation of the FWD deflection basins was performed using the procedure described 7

above, wherein the depth to the apparent stiff layer was assumed to be equal to 240 in. Table 1 8

summarizes the results of backcalculation. 9

10

Table 1. Backcalculation summary for MnROAD Cells 83 and 84 11

Cell 83 Cell 84

EAC, ksi Ebase, ksi Esubgr, ksi EAC, ksi Ebase, ksi Esubgr, ksi

Mean 188 12.2 11.7 184 17.3 15.6

Minimum 91 7.5 7.5 139 13.0 12.4

Maximum 520 25.9 15.3 302 32.9 19.9

12

The backcalculation for Cells 83 and 84 resulted in a remarkably close mean AC moduli. At the 13

same time, the backcalculated AC modulus for Cell 84 exhibited lower variability than the 14

backcalculated AC modulus for Cell 83. A likely explanation of this phenomenon is that the 15

actual AC layer thickness deviated from the as-designed thickness. (The as-designed thickness 16

was assumed in the backcalculation.) Since Cell 83 is thinner, thickness variation has a greater 17

relative effect on the results than the thicker section. In addition, in Table 1 it can be observed 18

that the backcalculated base and subgrade moduli for Cell 83 are lower than the corresponding 19

backcalcuated moduli for Cell 84. This can be explained by: 20

21

poorer compaction of the base and subgrade in Cell 83; 22

the effect of damage inflicted in the base and subgrade on Cell 83 during Spring 2008 23

testing; or 24

the surface layer itself being thinner for Cell 83 consequently allowed a greater 25

response in the subgrade. 26

27

Using the results of backcalculation, damage analysis was performed using the procedure 28

detailed above. The seasonal parameters used in the analysis are provided in Table 2. Table 3 29

summarizes the mean values for the computed damage parameters for Cells 83 and 84. As 30

expected, Cell 83 exhibited greater fatigue and rutting damage as well as greater base deflection 31

differences, but a lower stress ratio, SR. 32

33

Table 2. Seasonal parameters used in calibration example using MnROAD test cells 34

Winter Early

Spring

Late

Spring

Summer Fall

Duration, days 100 15 55 105 90

Mean air temperature, oF 18 50 50 70 41

Base stiffness adjustment factor, bs 10 0.35 0.85 1 1

Subgrade stiffness adjustment factor, ss 10 10 0.7 0.85 1

35



Table 3. Mean damage values for calibration example using MnROAD test cells 1

CELL 83 CELL 84

Rutting Damage 0.214 0.102

Fatigue Damage 0.133 0.053

Stress Ratio 1.017 1.243

Base Deformation (in mils) 18.14 11.47

2

The selection of appropriate calibration coefficients is an iterative process, in which initial values 3

– based on preliminary damage analysis similar to this section – are selected and used for the 4

procedure. Based on Table 3, initial values of CAC = 5.6, Crut = 5.6, and CBD = 0.115 are selected, 5

where all coefficients were indicated explicitly in Equations (24, (25, and (27. Given the first 6

attempt at calibration coefficients, the TONN2010 procedure can be applied to the MnROAD 7

cells. Table 7 present the mean values of the TONN2010 analysis for Cells 83 and 84. Based on 8

this analysis, TONN2010 evaluates Cell 83 as a 6.65-tonn road and Cell 84 as a 10-tonn road. 9

10

Table 4. Mean damage values for MnROAD Cells 83 and 84 as part of the calibration 11

process 12

CELL 83 CELL 84

TONNRUT 8.5 10.0

TONNAC 9.6 11.3

TONNSF 9.2 11.2

TONNDW 6.65 10.1

TONN2010 6.65 10.0

13

If these results were deemed unacceptable, the calibration coefficients could be adjusted and the 14

procedure repeated until appropriate ratings were recovered. 15

Finally, as part of this brief calibration, the MnROAD test cells were also analyzed using 16

other currently available bearing capacity procedures: the current MnDOT Investigation 603 17

TONN method, the MnDOT Investigation 183 (INV183) method, and the Soil Factor (SF) 18

method (11-13). In addition the bearing capacity was estimated using the TONN method, but 19

with the allowable deflection table replaced with deflections that would result from a design 20

using the AASHTO 1993 method (14). Table 8 compares the TONN2010 ratings with these 21

other methods. 22

23

Table 5. Mean ratings for MnROAD test cells according to TONN2010 and four other 24

bearing capacity rating methods 25

CELL 83 CELL 84

TONN2010 6.65 10.0

TONN 7.7 11.4

TONNinv183 6.8 8.1

TONNSF 9.1 10.5

TONNAASHTO 8.2 10.0

26

TONN2010 agrees with the most conservative estimate, the INV183-based TONN index for Cell 27

83. Considering that Cell 83 failed during both spring and fall testing, these indexes appear to be 28

reasonable, while other procedures do not provide sufficiently conservative estimates. On the 29



other hand, for Cell 84, the INV183-based TONN index appears to be overly conservative, as the 1

pavement exhibited no damage under heavy axle loading. The AASHTO-based procedure leads 2

to a more reasonable assessment of Cell 84 as a 10-tonn road. TONN2010 matches this 3

evaluation. 4

5

6

COMPARISON WITH CURRENT PROCEDURES 7 The TONN2010 procedure was utilized for the analysis of almost 8400 deflection basins 8

collected from pavements in nine Minnesota counties (Benton, Clay, Dakota, Houston, Lake, 9

Meeker, Nicollet, Nobles, and Polk). The pavement sections had varied profiles, with an AC 10

layer thickness that varied from 2.6 to 13.4 inches. The expected traffic for these sections ranged 11

from 30,000 to 5,700,000 ESALs (15). 12

Figure 2 presents results of the TONN2010 analysis for a stretch of Benton County State 13

Aid Highway (CSAH) 2 (from CSAH 1 to West Lake). One can observe that the individual 14

TONN ratings show a wide spread for individual locations. Subgrade rutting and shear strength 15

ratings range from 8.8 to 16.5, whereas deflection difference and asphalt fatigue ratings were as 16

high as 62 and 33, respectively. For some locations, the deflection difference rating was as low 17

as 11 and controlled the overall rating, but for other locations either subgrade rutting or Strength-18

to-stress ratio criteria will be the limiting factor. 19

20

21 Figure 2. TONN2010 analysis for CSAH 2 in Benton County, Minnesota 22

23

Figure 3 compares the TONN2010 results with 1) other TONN rating procedures for the Benton 24

County CSAH 2 basins (at left) and 2) the previous TONN procedure for all the FWD basins 25

evaluated in this study (at right). While TONN2010 agrees with other ratings for a majority of 26

cases, a perfect correspondence between TONN2010 and other ratings was not expected. Each 27



of the other ratings uses only one criterion for pavement evaluation, whereas TONN2010 1

evaluates four different criteria prior to making an assessment. In Figure 3 (at left), one can 2

observe that TONN2010 generally agrees with the other ratings. While it is not as conservative 3

as the INV 183-based rating, it is more conservative than the current TONN procedure, which 4

overestimates the pavement bearing capacity compared to other rating systems. Figure 3 (at 5

right) illustrates the general observation that TONN2010 is more conservative than the current 6

TONN for the majority of FWD basins. 7

8

Figure 3. Visual comparison of TONN2010 ratings with other low-volume road ratings for 9

CSAH 2 in Benton County (at right) and all FWD basins from Minnesota counties with 10

available FWD data (at right) 11 12

CONCLUSIONS 13 Unlike the old TONN procedure which utilizes only one criterion to evaluate the pavement, the 14

revised TONN procedure (a.k.a. TONN2010) uses four criteria: AC damage, subgrade rutting, 15

base shear failure, and base deformation. Furthermore, TONN2010 uses a limited set of data that 16

can be collected easily by any FWD operator. The procedure has been calibrated extensively 17

using the deflection information from MnROAD pavement sections, and TONN2010 has also 18

been validated against alternative procedures for the structural capacity evaluation of pavements. 19

Overall, TONN2010 is an attractive alternative to those other procedures. 20

The TONN2010 procedure has been encoded into a Fortran program that can be run in a 21

MS-DOS or Windows computing environment. This program allows users to easily conduct 22

analysis given an FWD dataset. As it stands, the program requires that the user is able to execute 23

and feed input files to the program from an MS-DOS command line. Future work involving the 24

TONN2010 program would possibly benefit from the creation of a graphical user interface to 25

further improve its user-friendliness. 26

27

28

ACKNOWLEDGEMENTS 29 The research described in this paper was supported by the Minnesota Department of 30

Transportation and the Minnesota Local Road Research Board under the research project 31

“Allowable Axle Loads on Pavements.” The authors thank the members of the project technical 32

panel, in particular the project technical liason, Jerry Geib of the MnDOT Office of Materials 33

and Road Research. 34

35



1

REFERENCES 2 1. Lukanen, E.O., Personal communication with Mr. Shongtao Dai of Minnesota 3

Department of Transportation, June 2013. 4

2. Pavement Design Documents. Minnesota Department of Transportation. 5

www.dot.state.mn.us/materials/pvmtdesign/docs/SpringLoadCapacityTONNMethod.pdf. 6

Accessed July 21, 2013. 7

3. Kruse, C.G., and E.L. Skok, Jr.. Flexible Pavement Evaluation with the Benkelman 8

Beam. Revision to Summary Report, Investigation No. 603. Office of Materials, 9

Minnesota Department of Highways, Saint Paul, MN, 1983. 10

4. Tanquist, B. Local Road Material Properties and Calibration for MnPAVE Summary 11

Report. Report No. MN/RC 2008-56, Minnesota Department of Transportation, Saint 12

Paul, MN, 2008. 13

5. American Association of State Highway and Transportation Officials. Mechanistic-14

Empirical Pavement Design Guide, Interim Edition: A Manual of Practice. Washington, 15

D.C. 2008. 16

6. Khazanovich, L. and J. Roesler. DIPLOBACK: Neural-Network-Based Backcalculation 17

Program for Composite Pavements. Transportation Research Record 1570, pp. 143-150, 18

Washington D.C., 1997. 19

7. Khazanovich L., Selezneva O. I., Yu H. T., and Darter M. I. Development of Rapid 20

Solutions for Prediction of Critical Continuously Reinforced Concrete Pavement Stresses. 21

Transportation Research Record 1778, pp. 64-72, Washington D.C., 2001. 22

8. Khazanovich, L. and Wang, X. MnLayer: High-Performance Layered Elastic Analysis 23

Program. Transportation Research Record 2037, pp. 63-75. Washington, D.C., 2007. 24

9. Lukanen, E.O., Stubstad, R.N., and R. Briggs. Temperature Predictions and Adjustment 25

Factors for Asphalt Pavement. Report No. FHWA-RD-98-085, Federal Highway 26

Administration, United States Department of Transportation, Washington, D.C., 2000. 27

10. Khazanovich, L., Lim, J., Azary, A., Wang, S., Kim, S., Ceylan, H., and K. 28

Gopalakrishnan. Effects of Implements of Husbandry (Farm Equipment) on Pavement 29

Performance. Report No. MN/RC 2012-08, Minnesota Department of Transportation, 30

Saint Paul, MN, 2012. 31

11. Kruse, C.G., and E.L. Skok, Jr.. Flexible Pavement Evaluation with the Benkelman 32

Beam. Summary Report, Investigation No. 603. Office of Materials, Minnesota 33

Department of Highways, Saint Paul, MN, 1968. 34

12. Lukanen, E.O.. Application of AASHO Road Test Results to Design of Flexible 35

Pavement in Minnesota. Final Report, Investigation No. 183, Office of Research and 36

Development, Minnesota Department of Transportation, Saint Paul, MN, 1980. 37

13. Wolfe, R. E. Load Carrying Capacity of Minnesota Secondary Flexible Pavements. 38

Progress Report, Investigation No. 603. Materials and Research Section, Minnesota 39

Department of Highways, Saint Paul, MN, 1964. 40

14. Skok, E.L., Dai, S., Westover, T., Labuz, J., and Lukanen, E.O.. Pavement Rehabilitation 41

Selection. Report No. MN/RC 2008-06, Minnesota Department of Transportation, Saint 42

Paul, MN, 2008. 43

15. Khazanovich, L, and E.O., Lukanen, Personal communications with Mr. Neil Lund and 44

Mr. Chunhua Han of Braun Intertec, Inc., 2012. 45

46


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