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《China Journal of Highway and Transport》 2003-01
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Backcalculation of modulus for pavements based on homotopy method

ZHA Xu dong 1, WANG Bing gang 2 (1. Department of Road and Traffic Engineering, Changsha Communications University, Changsha 410076, China; 2. School of Highway, Chang′an University, Xi′an 710064, China)  
Firstly, the backcalculation of modulus is transferred into finding zero points of nonlinear maps according to extreme conditions of optimization problems. A mathematical model for backcalculation of pavement layer modulus based on the homotopy method is established with partial derivatives of the l st and 2nd order for deflections to modulus computed by numerical derivative methods. Secondly, partial differential equations are solved with LI YORKE algorithms to follow homotopy paths, and backcalculated results are obtained. A program for backcalculation of modulus is written. Thirdly,3 measured deflection basins of 3 kinds of pavements from falling weight deflectometers(FWD) are backcalculated. Modulus results of homotopy method are compared to ones of other programs. Accuracy and reliability of the results are validated. Lastly,convergency of wide range and stability of backcalculated results for homotopy method are checked through selecting different initial values. It shows that the problems of initial values and partial convergences for conventional optimum algorithms are solved efficiently by using homotopy method to backcalculate layer modulus of pavements.Therefore,using homotopy method to backcalculate layer modulus of pavements is great in accuracy, fast in speed,high in efficiency,stable in result and wide in convergency.
【Fund】: 国家自然科学基金青年基金项目 ( 5 0 2 0 80 0 4)
【CateGory Index】: U416.2
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