Parameter Estimation in Layered Media Using Dispersion-Constrained Inversion
Publication: Journal of Engineering Mechanics
Volume 144, Issue 11
Abstract
The need to estimate the properties of layered elastic or viscoelastic media arises commonly in various engineering applications, including geotechnical site characterization and pavement condition assessment. The layered medium is usually probed with small-amplitude waves, and the medium’s response is used to drive an inverse medium problem leading to the identification of the properties. The property estimation problem is solved by a new methodology that seeks to minimize the misfit between measured and computed responses, constrained by the dispersion relation of the layered medium, the latter expressed in terms of the forward eigenvalue problem and the associated orthonormality condition. The medium’s properties are recovered upon satisfaction of the first-order optimality conditions of the system’s Lagrangian. The reported numerical results are based on synthetic records illustrating the methodology in the frequency domain, and demonstrating reconstruction of the medium’s material properties and geometric characteristics.
Get full access to this article
View all available purchase options and get full access to this article.
References
Akçelik, V., G. Biros, O. Ghattas, J. Hill, D. Keyes, and B. van Bloemen Waanders. 2006. “Parallel algorithms for PDE-constrained optimization.” In Parallel processing for scientific computing, edited by M. Heroux, P. Raghavan, and H. Simon, 291–322. Philadelphia: SIAM.
Akçelik, V., G. Biros, O. Ghattas, D. Keyes, K. Ko, L. Lee, and E. Ng. 2005. “Adjoint methods for electromagnetic shape optimization of the low-loss cavity for the international linear collider.” J. Phys.: Conf. Ser. 16 (1): 435–445.
Ali, N., and N. Khosla. 1987. “Determination of layer moduli using a falling weight deflectometer.” Transp. Res. Rec. 1117: 1–10.
Al-Khoury, R., C. Kasbergen, A. Scarpas, and J. Blaauwendraad. 2001. “Spectral element technique for efficient parameter identification of layered media.” Int. J. Solids Struct. 38 (48): 8753–8772. https://doi.org/10.1016/S0020-7683(01)00109-3.
Anderson, M. 1989. “A data base method for backcalculation of composite pavement layer moduli.” In Vol. 1026 of Nondestructive testing of pavements and backcalculation of moduli, 201–216. West Conshohocken, PA: ASTM.
Astaneh, A., and M. Guddati. 2016. “Improved inversion algorithms for near-surface characterization.” Geophys. J. Int. 206 (2): 1410–1423. https://doi.org/10.1093/gji/ggw192.
Bui-Thanh, T., and O. Ghattas. 2014. “A PDE-constrained optimization approach to the discontinuous Petrov-Galerkin method with a trust region inexact Newton-CG solver.” Comput. Methods Appl. Mech. Eng. 278: 20–40. https://doi.org/10.1016/j.cma.2014.04.018.
Bush, A., and D. Alexander. 1985. “Pavement evaluation using deflection basin movement and layered theory.” Transp. Res. Rec. 1022: 16–29.
Chou, Y., and R. Lytton. 1991. “Accuracy and consistency of backcalculated pavement layer moduli.” Transp. Res. Rec. 1293: 72–85.
Doyle, J. F. 1997. Wave propagation in structures: Spectral analysis using fast discrete Fourier transforms. 2nd ed. New York: Springer.
Fathi, A., L. F. Kallivokas, and B. Poursartip. 2015. “Full-waveform inversion in three-dimensional PML-truncated elastic media.” Comput. Methods Appl. Mech. Eng. 296: 39–72. https://doi.org/10.1016/j.cma.2015.07.008.
Fileccia Scimemi, G., T. Turetta, and C. Celauro. 2016. “Backcalculation of airport pavement moduli and thickness using the Lévy Ant Colony optimization algorithm.” Constr. Build. Mater. 119: 288–295. https://doi.org/10.1016/j.conbuildmat.2016.05.072.
Foinquinos, R. 1995. “Dynamic nondestructive testing of pavements.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Texas at Austin.
Foinquinos, R., J. Roësset, and K. Stokoe. 1995. “Response of pavement systems to dynamic loads imposed by nondestructive tests.” Transp. Res. Rec. 1504: 57–67.
Grenier, S., and J. Konrad. 2009. “Dynamic interpretation of falling weight deflectometer tests on flexible pavements using the spectral element method: backcalculation.” Can. J. Civ. Eng. 36 (6): 957–968. https://doi.org/10.1139/L09-010.
Hadidi, R., and N. Gucunski. 2010. “Comparative study of static and dynamic falling weight deflectometer back-calculations using probabilistic approach.” J. Transp. Eng. 136 (3): 196–204. https://doi.org/10.1061/(ASCE)0733-947X(2010)136:3(196).
Hall, K., and A. Mohseni. 1991. “Backcalculation of asphalt concrete-overlaid portland cement concrete pavement layer moduli.” Transp. Res. Rec. 1293: 112–123.
Harichandran, R., T. Mahmood, A. Raab, and G. Baladi. 1993. “Modified Newton algorithm for backcalculation of pavement layer properties.” Transp. Res. Rec. 1384: 15–22.
Haskell, N. A. 1953. “The dispersion of surface waves on multilayered media.” Bull. Seismol. Soc. Am. 43 (1): 17–34. https://doi.org/10.1029/SP030p0086.
Kallivokas, L. F., A. Fathi, S. Kucukcoban, K. Stokoe, J. Bielak, and O. Ghattas. 2013. “Site characterization using full waveform inversion.” Soil Dyn. Earthquake Eng. 47: 62–82. https://doi.org/10.1016/j.soildyn.2012.12.012.
Kang, J., and L. Kallivokas. 2011. “The inverse medium problem in heterogeneous PML-truncated domains using scalar probing waves.” Comput. Methods Appl. Mech. Eng. 200 (1–4): 265–283. https://doi.org/10.1016/j.cma.2010.08.010.
Kausel, E. 1981. An explicit solution for the green functions for dynamic loads in layered media. Cambridge, MA: Massachusetts Institute of Technology.
Kausel, E., and J. Roësset. 1981. “Stiffness matrices for layered soils.” Bull. Seismol. Soc. Am. 71 (6): 1743–1761. https://doi.org/10.1016/0148-9062(83)91665-0.
Lions, J. L. 1971. Vol. Bd. 170 of Optimal control of systems governed by partial differential equations. New York: Springer.
Liu, M., H. Liao, and J. Chuang. 2007. “Dynamic time domain backcalculation of LTPP test sites.” J. Eastern Asia Soc. Transp. Stud. 7: 2017–2029.
Loizos, A., and J. Scarpas. 2005. “Verification of falling weight deflectometer backanalysis using a dynamic finite elements simulation.” Int. J. Pavement Eng. 6 (2): 115–123. https://doi.org/10.1080/10298430500141030.
Mahoney, J., B. Winters, N. Jackson, and L. Pierce. 1993. “Some observations about backcalculation and use of a stiff layer condition.” Transp. Res. Rec. 1384: 8–14.
Maina, J., W. Steyn, E. van Wyk, and F. le Roux. 2013. “Static and dynamic backcalculation analyses of an inverted pavement structure.” Vol. 723 of Innovation and sustainable technology in road and airfield pavement: Advanced materials research, 196–203. Portland, OR: Trans Tech Publications.
Mamlouk, M. S. 1987. “Dynamic analysis of multilayered pavement structures—Theory, significance and verification.” In Proc., 6th Int. Conf. on Structural Design of Asphalt Pavements, 466–473. Ann Arbor, MI: Cushing-Malloy, Inc.
Meier, R., and G. Rix. 1994. “Backcalculation of flexible pavement moduli using artificial neural networks.” Transp. Res. Rec. 1448: 75–82.
Meier, R., and G. Rix. 1995. “Backcalculation of flexible pavement moduli from dynamic deflection basins using artificial neural networks.” Transp. Res. Rec. 1473: 72–81.
Mora, P. 1987. “Nonlinear two-dimensional elastic inversion of multioffset seismic data.” Geophysics 52 (9): 1211–1228. https://doi.org/10.1190/1.1442384.
Na, S.-W., and L. F. Kallivokas. 2008. “Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering.” Comput. Mech. 41 (4): 579–594. https://doi.org/10.1007/s00466-007-0216-4.
Nocedal, J., and S. J. Wright. 2006. Numerical optimization. 2nd ed. New York: Springer.
Rakesh, N., A. K. Jain, M. A. Reddy, and K. S. Reddy. 2006. “Artificial neural networks-genetic algorithm based model for backcalculation of pavement layer moduli.” Int. J. Pavement Eng. 7 (3): 221–230. https://doi.org/10.1080/10298430500495113.
Roque, R., B. Ruth, and S. Sedwick. 1998. “Limitations of backcalculation and improved methods for pavement layer moduli predictions.” In Proc., 5th Int. Conf. on the Bearing Capacity of Roads and Airfields. Trondheim, Norway: Tapir Publishing.
Saltan, M., V. Uz, and B. Aktas. 2013. “Artificial neural networks-based backcalculation of the structural properties of a typical flexible pavement.” Neural Comput. Appl. 23 (6): 1703–1710. https://doi.org/10.1007/s00521-012-1131-y.
Scrivner, F., C. Michalak, and W. Moore. 1973. “Calculation of the elastic moduli of a two-layer pavement system from measured surface deflections.” Highway Res. Rec. 431: 12–24.
Sharma, S., and A. Das. 2008. “Backcalculation of pavement layer moduli from falling weight deflectometer data using an artificial neural network.” Can. J. Civ. Eng. 35 (1): 57–66. https://doi.org/10.1139/L07-083.
Sivaneswaran, N., S. Kramer, and J. Mahoney. 1991. “Advanced backcalculation using a nonlinear least squares optimization technique.” Transp. Res. Rec. 1293: 93–102.
Thomson, W. T. 1950. “Transmission of elastic waves through a stratified solid medium.” J. Appl. Phys. 21 (2): 89–93. https://doi.org/10.1063/1.1699629.
US Federal Aviation Administration. 2004. Use of nondestructive testing in the evaluation of airport pavements. Washington, DC: US Dept. of Transportation, Federal Aviation Administration.
Uzan, J. 1994. “Advanced backcalculation techniques.” In Vol. 1198 of Nondestructive testing of pavement and backcalculation of moduli. 3–37. West Conshohocken, PA: ASTM.
Waas, G. 1972. “Linear two-dimensional analysis of soil dynamics problems in semi-infinite layered media.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of California, Berkeley.
Yi, J., and S. Mun. 2009. “Backcalculating pavement structural properties using a Nelder-Mead simplex search.” Int. J. Numer. Anal. Methods Geomech. 33 (11): 1389–1406. https://doi.org/10.1002/nag.769.
Zhao, Y., D. Cao, and P. Chen. 2015. “Dynamic backcalculation of asphalt pavement layer properties using spectral element method.” Road Mater. Pavement Des. 16 (4): 870–888. https://doi.org/10.1080/14680629.2015.1056214.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 144 • Issue 11 • November 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 16, 2017
Accepted: May 16, 2018
Published online: Aug 25, 2018
Published in print: Nov 1, 2018
Discussion open until: Jan 25, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.