On the numerical computation of earthworks in road and railway projects

Selecting an appropriate method to estimate the earthwork volumes in road and railway projects is essential for automatic searching of optimal designs. In this paper, the most widely used techniques for conducting this task (surface-to-surface and cross-section-based methods) are studied and analyzed in terms of accuracy and efficiency (computation time). Specifically, starting from a completely general scenario, and only using classical techniques of vector calculus and numerical integration, we develop two algorithms: one for a surface-to-surface method based on a Delaunay triangulation, and another for the average-end-area (AEA) method and its correction, the average-volume (AV) method. The performance of these algorithms is shown on an academic test and on a real case study, where a design commercial software (ISTRAM®) and a surface-to-surface method provided by a QGIS 3.40 plugin are also used to assess their behavior. The results obtained show that the algorithm proposed to implement the AV method can provide results as accurate as needed with significantly low computation times, concluding that it is the most suitable for automatic road and railway design. • A comprehensive analysis of the main techniques for earthworks computation is provided. • Simple and efficient implementations of different methods for estimating earthwork volumes are proposed. • The most appropriate method for earthworks computation in automatic design of roads and railways is identified.