Introduction. Roads constitute the backbone of the transport infrastructure, and their technical condition directly affects logistics stability, traffic safety, and economic efficiency. A significant portion of Ukraine’s road network has flexible pavements, for which the condition of the subgrade soil plays a decisive role.
Problem statement. Enhancing the reliability of road structures remains a pressing issue in the sector. Since the strength and deformation parameters of flexible pavements depend on the physical and mechanical characteristics of the subgrade soil—and consequently on its moisture content — there is a need to account for all influencing factors and to develop accurate computational relationships.
Objective. To develop an engineering-applicable mathematical modeling approach to assess the impact of atmospheric precipitation on the hydro-thermal regime of the working layer of the road embankment.
Materials and methods. The proposed approach is based on a hydro-thermal model that employs differential equations of heat and moisture transfer in partial derivatives.
Results. To compute the moisture field W(z, t) in the soil layer along depth z, the authors propose, instead of the commonly used function f(t) — a time-dependent but depth-uniform source of moisture inflow — to introduce a function f(z, t) = q(t) p(z). This formulation more accurately represents the moisture ingress from rainfall into the pavement structure.
Conclusions. The proposed formulation, based on a diffusion equation with a spatial-temporal source, provides a balanced compromise between computational complexity and accuracy for engineering applications. It enables the use of actual rainfall data, accounts for realistic moisture variation with depth, and considers the type of soil involved.
