Backcalculation: Basics and Beyond

1
Backcalculation Basics and Beyond

• Prof. L. H. Irwin, P.E., Ph.D.
• Cornell University
• FWD Users Group West Lafayette, IN 4
  October 2004

2
Basic Topics

• What is backcalculation?
• How did it evolve?
• How can you use it to the greatest advantage?
• Setting up the pavement model
• How do you assess the validity of the results
  that you get?
• Can you ever believe them?

3
Advanced Topics

• What is the surface modulus?
• How can you use it to estimate the depth to "hard
  bottom" (bedrock) beneath the pavement?
• How do we account for stress-dependency in
  unbound materials?
• Do we really need to ?
• What difference does it make if we don't?

4
Backcalculation

• The process of converting measured pavement
  deflections into layer moduli

5
How backcalculation works
1. Starting with a Seed Value for the modulus
calculate a deflection
2. Try a higher modulus
3. Use the measured deflection to estimate a
modulus for the layer
4. Work from the bottom layer to the top then
repeat
6
We do backcalculation today because

• Discovery of a relationship between pavement
  deflection and pavement strength (1935-1960)
• Development of mechanistic theories and computer
  programs (1940-1970)
• Development of deflection testing devices
  (1955-1980)
• Advent of desktop computers (1975 - )

7
Francis Frank Hveem

• California Dept. of Transportation Materials
  Research Laboratory
• 19301965
• Director 19511965
• Began measuring pavement deflections in 1938
• Had 400 sensors at 43 projects by 1955
• Used LVDTs and Benkelman beam

8
Hveems conclusion (1962)

• investigations over a variety of pavement
  structural sections will enable highway
  engineers to assign safe levels of deflection
  must take into account local materials, weather,
  mixture design and construction practices.

9
Allowable deflections (Hveem)
10
Problem

• It would be necessary to develop limiting
  deflection criteria for each different pavement
  structure, every materials type, and each
  environment.
• This would have been a formidable task.

11
Key equipment developments

• Benkelman beam (1950)
• Lacroix deflectograph
• Shell heavy vibrator
• WES 16-kip vibrator
• Dynaflect / Road Rater
• Falling weight deflectometer (1970)

12

• Benkelman beam

13
Isada, 1966
14
Dynatest, 2000
15
Carl Bro, 2002
16
Conclusion

• We have some fine tools available to measure
  pavement deflections
• The challenge now is to develop better analytical
  tools for deflection data analysis

17
Key developments in elastic layer theory

• Boussinesq 1885
• Westergaard 1925
• Burmister 1945
• Acum Fox 1951
• Schiffman 1962

18
Elastic layer computer programs

• Chevlay

• BISAR

• CIRCLY

• ELSYM 5

• WESLEA

• BISTRO

• JULEA

• NELAPAV

19
Basic assumptions of elastic layer theory

• Surface load - uniformly distributed over a
  circular area
• Vertical stress continuity, horizontal strain
  continuity at layer interfaces (no slip)
• Materials - homogenous, isotropic, and linearly
  elastic
• Layers extend horizontally to infinity
• Bottom layer is a semi-infinite half-space

20
Backcalculation computer programs

• MODCOMP

• PADAL

• ELMOD

• MODULUS

• EVERCALC

• WESDEF

21
Too many to name them all

• Published comparisons -
• Rada, et al (1992)
• COST 336, Task Group 1 (1999)
• What is the best backcalculation program?

22
Surface modulus

• The simplest form of backcalculation
• Given a measured deflection on the surface,
  assume a half-space and apply Boussinesqs
  equations to compute E0

23
Surface modulus concept(Boussinesq Equations)
24
Surface modulus for a half-space(a150 mm, E
60 MPa)
Calculated using BISAR at 1000 kPa plate pressure
25
Surface modulus for 3-layer system(E13600,
E2250, E360 MPa)
?z in microns, E0 in MPa
26
Surface modulus for half-space and 3-layer
pavement
27
Conclusion

• Boussinesq equations work fairly well for
  deflections on a half-space
• For a multi-layer system, E0 not accurate near
  the load
• A mismatch between the theoretical assumptions
  and the data will inevitably result in modulus
  errors

28
Another conclusion

• E0 is a good estimate of the subgrade modulus for
  3-layer system at r gt 6a
• Outer deflections can be used to determine the
  modulus of a deeper layer

29
Yet another conclusion

• Poissons ratio, ?, has relatively little
  influence in (1-?2)
• An increase of ? from 0.30 to 0.35 (17) results
  in a 5.4 decrease in (1-?2)
• Make a good estimate of ?, but if you are
  slightly off it is not a big problem

30
Assessing the validity of backcalculation

• Check the deflection basin fit using the
  root-mean-square (RMS) error
• When the RMS error is less than 1 to 2 percent,
  that is an encouraging outcome
• That does not assure that the backcalculated
  moduli are correct
• A large RMS error (gt3) indicates "something is
  not right"

31
Deflection basin fit
32
Assessing the validity of backcalculation

• Experience in doing backcalculation, and a good
  knowledge of the pavement materials will help in
  assessing the validity
• Use a large RMS error as an indicator that there
  are problems with the pavement model
• One never really knows whether the
  backcalculated moduli are correct

33
It helps to know what is there !
34
Detecting shallow bedrock

• According to Boussinesqs equations, deflection
  is proportional to 1/r
• At large radius deflection goes to zero for a
  half-space
• Plot ?Z versus 1/r, and if intercept is not zero,
  this is a measure of the depth to a hard bottom
  layer

35
Detecting shallow bedrock(4-layer system,
bedrock at 3.7 m)
36
Detecting shallow bedrock
37
Detecting shallow bedrock

• Calculated depth 4.6 m
• Actual depth 3.7 m
• Although the method is not perfect, it provides
  some information that might otherwise be unknown
• A negative calculated depth can be interpreted
  to mean that there is no bedrock present

38
Conclusion

• For bedrock (e.g., hard bottom) depth
  prediction to be practical, it needs to be built
  into the backcalculation program
• The calculated depth can be highly variable from
  station to station
• There must be some means for the program user to
  smooth out the variability

39
Stress-dependent materials

• A linear elastic material is one for which E
  constant
• Most pavement materials are stress dependent
• For many years we have believed
• E k1 Stress k2
• which is a log-log model

40
Stress parameters
41
Problem

• Pavement under load is in bending, thus stresses
  can be positive (compression) or negative
  (tension)
• Bulk stress is often negative at bottom of upper
  layers (surface and base courses)
• Solution Use semi-log model
• E k1 exp(Stress k2)

42
Comparison of models
43
Comparison of models

• Results of regression with the data

44
Conclusion

• Using statistics (r2) or visual evaluation, one
  cannot say which is the better model
• However, the semi-log model behaves more
  reasonably for negative bulk stresses
• There is a need to improve the state-of-the-art
  regarding constitutive models

45
The pavement model

• Thickness of each layer
• Seed modulus
• Poissons ratio
• Materials model (linear versus nonlinear)
• Depth to hard bottom (if present)
• Depth to water table (if known)

46
How do you model this?

• Consider a pavement that has
• 1.5 in asphalt concrete top course
• 6 in asphalt conc. binder course
• 10 in unbound gravel base (nonlinear)
• Silty sand subgrade (nonlinear)
• Water table at 12 ft below the surface
• Bedrock at 25 ft below the surface
• 5 layers?

47
Schematic not to scale
48
Modeling thin layers

• Backcalculation will not be able to give a
  modulus for the 1.5 in surface course
• The layer is too thin (insensitive)
• It must be combined with the 10 in binder layer
  of similar material that lies below it
• If the modulus of a layer does not influence the
  surface deflections, one cannot use deflections
  to determine the layer modulus

49
Modeling thin layers

• The term sensitivity is used to describe the
  effect of a layers modulus on the surface
  deflections
• An insensitive layer can have most any modulus
  and it will have little effect on the deflection
• The best approach to use with an insensitive
  layer is to give it a fixed modulus or combine it
  with an adjacent (similar) layer

50
Layer sensitivity
51
Modeling subgrades

• The upper portion of a subgrade is affected by
  weather
• It goes through seasonal cycles of freeze-thaw
  and/or wet-dry
• Thus its modulus changes over time
• Even if the depth is arbitrary, it is wise to
  model the upper subgrade as a separate layer

52
Modeling bedrock

• Shallow bedrock (less than 40 ft deep) must be
  included in the pavement model
• Use the 1/r method to check for shallow bedrock

53
The pavement model

• Combined asphalt surface and base layers (7.5 in)
• Unbound granular subbase layer (10 in)
• Upper, weather affected subgrade (3 ft)
• Middle subgrade (7.5 ft)
• Subgrade below water table (13 ft)
• Bedrock
• This model has 6 layers !

54
Problem

• Not very many backcalculation programs allow the
  pavement model to have six layers
• This will be illustrated here using a 20-layer
  stress-dependent pavement model generated with
  NELAPAV

55
The 20-layer system

• Asphalt
• 1.5 in surface course
• 6.0 in binder course
• Granular base
• 3 layers at 3.3 in each
• Upper subgrade
• 2 layers at 18 in each
• Middle subgrade
• 4 layers at 18 in each

• Lower subgrade
• 8 layers at 18 in each
• Below the water table
• Bedrock
• Base and subgrade are stress-dependent
• Forward calculated using NELAPAV to get the
  deflection basin

56
20-layer pavement modelforward calculated to
get deflections
57
Modeled as a 6-layer pavementbackcalculated
using MODCOMP
58
Modeled as a 4-layer pavementbackcalculated
using MODCOMP
59
Comparison of modelsbased on deflection basin fit

• 4-layer pavement model
• RMSE 15.5
• 6-layer pavement model
• RMSE 0.30
• The 4-layer model doesnt look very good

60
Comparison of modelsbased on calculated stresses
and strains
Model used for input to backcalculation
61
Conclusion

• Comparison of stresses and strains from 4-layer
  and 6-layer pavement models not as bad as the RMS
  errors would lead one to believe
• This is a simulation. One should not make too
  many conclusions from it.

62
Spatial variations

• Layer thicknesses, depth to water table and depth
  to bedrock all vary along the road
• Materials vary along the road
• Traffic usage may vary along the road
• There is no reason to expect pavement moduli to
  be constant over space

63
Homogeneous?
64
Dealing with spatial variations

• Do backcalculation at each individual test point
• Do pavement analysis or design at all test points
  
• Then take the 85th percentile result

65
Seasonal variations

• Temperature and moisture conditions in the
  pavement vary over time
• These conditions can vary within a single day
• There is no reason to expect pavement moduli to
  be constant over time

66
Seasonal?
67
Dealing with seasonal variations

• Backcalculated moduli are valid for the date and
  conditions of test, nothing more
• For important projects, test the pavement at two
  or more times in the year
• Use Miners hypothesis to account for seasonal
  variability

68
In conclusion

• Backcalculation, as we use it today, is the
  product of 65 (or more) years of development
• Mechanistic theories
• Equipment
• Computers
• It will be interesting to see what develops over
  the next few years

69
In conclusion

• Backcalculation is widely used
• Certain topics require further development
• The paper offers several specific suggestions
• Talented and knowledgeable people should be used
  to do it

70
In conclusion

• Even though the current state-of-the-art has
  problems, the combination of backcalculation and
  mechanistic pavement analysis seems to be fairly
  robust
• Use it !