Mathematical processing of geodetic measurements in the planning and management of mountain roads by means of GIS (on the example of the R-24 motor road)

Source abstract

Most mountain roads in the Ukrainian Carpathians were designed in the past century, and their subsequent operation is generally limited to renewing the pavement surface without re-checking the geometric parameters of the alignment, in particular the horizontal curvature radius. This paper considers the mathematical apparatus for processing geodetic relief measurements to determine the horizontal curvature radius of a road by means of geographic information systems. A geometric derivation of the circumscribed-circle radius formula from three points is presented, based on the law of sines, and the algorithm for applying it to a sequence of points along the road’s longitudinal axis, obtained from a digital elevation model, is described in two variants: local (three adjacent points) and smoothed (a five-point sliding window). The algorithm’s numerical stability for near-collinear points is analysed separately, together with its consistency with regulatory provisions on limiting radii. A comparative analysis of the accuracy, cost and speed of determining the curvature radius by the proposed method versus traditional geodetic methods (total-station surveying, GNSS-RTK) is carried out. The methodology is tested on the R-24 motor road (Bukovetsky Pass, Ukrainian Carpathians): the road axis was segmented into 1672 elementary sections, for which curvature radius values were computed and compared against the requirements of DBN V.2.3-4:2015. The proposed approach is shown to allow rapid, field-survey-free identification of mountain-road sections whose geometric parameters do not meet current standards, providing a basis for well-founded planning and prioritisation of road-network reconstruction works.