Calculation of temperature differences between the sunny slopes and the shady slopes along railways in permafrost regions on Qinghai–Tibet Plateau

The change in temperature is the main source of all frozen soil mechanics problems. After an embankment has been built in a permafrost region, there will be different thermal regime on the slopes because of different embankment orientation. This leads to distinct thawing morphologies under the embankment and complicates the embankment thermal stability. In view of the specific natural environment on Qinghai–Tibet Plateau, field monitored ground temperatures and meteorological data are difficult to obtain. This paper sets up a regression equation, using statistical methods, between the temperature difference of shallow ground (0.5 m) and solar radiation difference on slopes. When the slope gradient of the sunny slope is equal to the slope gradient of the shady slope, the temperature difference on slopes of shallow ground (0.5 m) along different embankment orientations is obtained by:ΔT=f(ΔQ)=2aRctgh*sina|cos(β−η)|+bΔT=f(ΔQ)=2aRctgh*sina|cos(β−η)|+bwhere, ΔT — the temperature difference on the slopes of shallow ground (0.5 m)(°C), ΔQ — solar radiation difference on slopes (Wm− 2), R — solar radiation absorbed by horizontal ground surface per square meter, h — sun altitude, a — slope gradient of the embankment slope, β — sun azimuth, η — embankment orientation, a, b — are constants, and equal to 0.01428 and 0.34756, respectively.Moreover, the equation is validated feasible, by which the mean annual temperature difference on slopes of railway embankment with different orientations can be better calculated in Beiluhe. The equation may provide a dependable scientific basis for numerical calculations of the thermal boundary conditions of embankment and for road construction and maintenance in permafrost regions on Qinghai–Tibet Plateau.