Roads and Bridges - Drogi i Mosty
13, 1, 2014, 33-48

New analytical solution of flow and heat refraction problem in multilayer pavement

Mirosław Graczyk Mail
Road and Bridge Research Institute, Warsaw
Józef Rafa Mail
Military University of Technology, Warsaw
Leszek Rafalski Mail
Road and Bridge Research Institute, Warsaw
Adam Zofka Mail
Road and Bridge Research Institute, Warsaw


The paper covers a new analytical solution of a flow and refraction problem in a multilayer pavement. The solution includes conditions of internal and external exchange as well as cyclic temperature and heat flux changes. Solution of a problem of heat conduction in a multilayer system showed a significant influence of coefficients introduced by the authors on the temperature and thermal stresses field in structure of a multilayer pavement. The coefficients were: diffusivity, thermal matching of layers and thermal refraction of layers. It was found that solar radiation is very important climatic factor acting directly on the upper layer of pavement, causing an increase in temperatures and creation of an additional temperature gradient in a multilayer pavement. It is shown that temperature field in a multilayer pavement depends significantly on geometry of layers structure, thermal characteristics of upper and lower layers expressed by Biot and Fourier numbers, colour of a surface course, humidity, velocity of wind etc., which are expressed by value of an external heat transfer coefficient. Moreover, an original example of analysis of an influence of pavement layer and subgrade parameters as well as climatic conditions on the temperature field in three different pavement structures, is shown. Results of the presented analysis can be directly applied in roads and airstrips pavements design.


Biot number, Fourier number, heat flow and refraction, multilayer pavement; refraction coefficient, thermal matching

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New analytical solution of flow and heat refraction problem in multilayer pavement

Graczyk, Mirosław et al. New analytical solution of flow and heat refraction problem in multilayer pavement. Roads and Bridges - Drogi i Mosty, [S.l.], v. 13, n. 1, p. 33-48 , feb. 2014. ISSN 2449-769X. Available at: <>. Date accessed: 03 Jul. 2020. doi: