To whom it may concern

The falling weight deflectometers are sold around the world, however, they have not offered any dynamic analytical method or softwares that could be used for the interpretation the deflection data of the FWD. The currently used methods are all based on static analysis. This limits the use of the FWD machine greatly. I’m writing this because I've developed an accurate and fast algorithm which could calculate the dynamic deflections of the pavement under FWD pulse load. It will help the use of FWD.
I’ve made a presentation at the TRB annual meeting about this method. The paper was included in the CD of the meeting.
This paper provides a feasible algorithm which can compute the dynamic response of pavement structure under resilient load pulse. It is an accurate and fast program and can also deal with viscoelastic materials as well such as AC layer. This program will have a lot of applications in the engineering practice, such as FWD simulation, structure response calculation under vehicle load, dynamic modulus test simulation, et al. You know the currently used calculation methods for FWD are based on static analysis, which completely ignored the impact nature of the load. And I think in the future the dynamic analysis method will definitely be used in the pavement design, pavement detection and laboratory tests.
If you are interested in this program, you can contact me at any time through this email: greatchengsheng@gmail.com.

Simulation of FWD

The process of FWD can be simulated perfectly by DynaPav. The advantage of Dynapave encompasses in its moderate input and computational robustness.

The load impulse:

The input file:

/* START */

Pulse Properties :
Amplitude/MPa Pluse Duration/s Calculation Range/n*T radius/m layers points
0.7E6 0.025 20 0.15 4 9

Points Distance/cm :
0 20 30 45 60 90 120 150 180

Pavement Structure :
E-Modulus/Pa Poison ratio Density/g/cm3 Thickness/m friction E1 E2 eta1 eta2 BK visco-flag
4000E6 0.25 2300 18E-2 1 8000E6 4000E6 200E6 150E6 8000E6 1
8000E6 0.15 2000 36E-2 1
3000E6 0.15 2000 20E-2 1
80E6 0.35 1500 0 0

/* END */

Pavement surface oscillations:

For the situation of viscoelastic asphalt surface:

TeFC

TFC is a Temperature field calculator based on finite differential method. For calculating the transient temperature field in the structure, the energy flow on the surface of the pavement are analyzed.

Details of the algorithm will be added later.

StaticFWD

StaticFWD was modified from StaticPave.

StaticFWD uses a static algorithm to calculate the pavement deflection response under falling weight deflectometer(FWD) load. Unlike Bisar3, it can handle a lot of input datas once and calculate together. The results are written to one output file.

sample input file:

/*   START   */

2
4
 2000,0.35,18
 8000,0.15,36
 3000,0.15,20
 50,0.35
 0.7, 15

4
 2000, 0.35, 18
 8000,0.15,36
 3000,0.15,20
 50,0.35
 0.7, 15

/*   END   */

sample output:

 1
  1 0.0246
  2 0.0201
  3 0.0192
  4 0.0187
  5 0.0182
  6 0.0172
  7 0.0160
  8 0.0149
  9 0.0138
 2
  1 0.0246
  2 0.0201
  3 0.0192
  4 0.0187
  5 0.0182
  6 0.0172
  7 0.0160
  8 0.0149
  9 0.0138

Contact the author(greatchengsheng@gmail.com) for more details about the program.

StaticPave

StaticPave can calculate the pavement response under static load, such as stress, strain, and displacement. It can deal with any number of load at any form, and compute the response at any point of the struture. It can be used in the pavement design and detection.

This program takes a text file as input data source, and outputs the calculating results to another text file. The file names are assigned by the user.

It is coded in fortran and is OS independent. 

Sample input:

/*   START   */

1
3
20000,0.25,16,0.5
17000,0.25,30,0.5
410,0.35
2,0
7.07,10.65,0,0
7.07,10.65,0,31.95
4
1,0,0,0
1,0,15.975,0
1,0,0,16
2,0,0,46

/*   END   */

Sample output:

  SYSTEM NUMBER 1
  LAYER CALCULATION YOUNG'S POISSONS THICKNESS INTERFACE
  NUMBER METHOD MODULUS RATIO SPRINGCOMPL
  1 ROUGH .2000E+05 .2500E+00 .1600E+02 .0000E+00
  2 ROUGH .1000E+06 .1500E+00 .3800E+02 .0000E+00
  3 ROUGH .8000E+05 .1500E+00 .2000E+02 .0000E+00
  4 .5000E+03 .3500E+00
  LOAD NORMAL RADIUS OF LOAD - POSITION
  NUMBER STRESS LOADED AREA X Y
  1 7.0700 10.6500 .0000 .0000
  NUMBER LAYER X Y Z  
  1 1 .0000 .0000 .0000
  2 2 .0000 .0000 16.0000
  3 2 5.0000 .0000 16.0000

  TOTAL STRESS(R T Z YZ XZ XY) AND DISPLACEMENT(X Y Z )
  1 -4.5903 -4.5903 -7.0700 .0000 .0000 .0000 : .0000 .0000 .0131
  2 -.7901 -.7901 -3.7328 .0000 .0000 .0000 : .0000 .0000 .0091
  3 -.8427 -.7753 -3.3172 .0000 -.6062 .0000 : .0000 .0000 .0091

  TOTAL STRAIN(R T Z YZ XZ XY)
  1 -.8376E-04 -.8376E-04 -.2387E-03 .0000E+00 .0000E+00 .0000E+00
  2 -.1117E-05 -.1117E-05 -.3496E-04 .0000E+00 .0000E+00 .0000E+00
  3 -.2288E-05 -.1514E-05 -.3075E-04 .0000E+00 -.6971E-05 .0000E+00

  PRINCIPLE STRESS(R T Z) AND PRINCIPLE STRAIN(R T Z)
  1 -4.5903 -4.5903 -7.0700 : -.8376E-04 -.8376E-04 -.2387E-03
  2 -.7901 -.7901 -3.7328 : -.1117E-05 -.1117E-05 -.3496E-04
  3 -.7022 -.7753 -3.4577 : -.6720E-06 -.1514E-05 -.3236E-04

Contace the author(greatchengsheng@gmail.com) for more details of the program.

DynaPave

DynaPave can calculate the dynamic response of pavement structures. The algorithm of DynaPave is based on spectral element method(SEM). The program is coded in C++ and OS independent.

SEM combines the exact solution of wave motion with the finite element formulation of multi-layered systems. A spectral element is capable of describing the wave propagation, reflection and refraction in a layer in a closed form. Consequently, the size of the mesh of a pavement structure is as large as the number of the layers involved. This reduces the computational requirements substantially.

The transformation between time-space domain and frequency-wavenumber domain was achieved by using Kreyszig solution and FFT, instead of the hankel transform and fourier transform, so infinite integration can be avoided and the problems are more convenient for numerical solutions.

The process of falling weight deflectometer(FWD) test and portable falling weight deflectometer(PFWD) test have been simulated successfully in this project.

SEM computes system response in frequency-wavenumber domain. This approach allows for adjustment of frequency dependent properties. This is especially useful in the description of the AC layer, where properties exhibit strong frequency dependence. By substituting the rheological model into SEM formulation, the dynamic response of viscoelastic material could also be computed.

The algorithm can compute the dynamic response of layered media exactly, such as stress, strain, displacement et al. It can be applied in the process of pavement design and pavement detection.

Contact the author(greatchengsheng@gmail.com) for more details of this project.

About the Author

PERSONAL DATA

Name: Sheng Cheng
E-mail: greatchengsheng@gmail.com

EDUCATION

2005-2008 Southeast University(Nanjing, China), Master of Highway and railway engineering.

2000-2005 Tongji University(Shanghai, China), Bachelor of Civil engineering.

RESEARCH

A dynamic deflection calculation program based on the SEM(spectral element method). It was used for the computing of FWD pavement detection.	2008
A DEM(discrete element method) simulating program, for the research of cement-treated aggregate mixture.	2007
The temperature field model in the pavement structure. A theory model was firstly developed based on the heat conduction equations. Then it was corrected from the measured temperature data.	2006

Sheng Cheng, 2008, Performance Research and Construction Control of Cement-Treated Aggregate Mixture, Master’s Degree Thesis of Southeast University.

Sheng Cheng, 2005, Calculation of Rut Effective Temperature for Asphalt Pavement. Bachelor’s Degree Thesis of Tongji University.