Mostafa M. Arnaout, Ashraf Mohamed Ahmed Heniegal and Adel M. El-Kelesh published a paper on forecasting the penetration rate (PR) in horizontal directional drilling in the International Journal of Construction Management. The work is titled "Modeling the prediction of penetration rate of horizontal directional drilling" and carries DOI 10.1080/15623599.2026.2736296. It was published online on 28 September 2026.

The problem: progress depends on judgement

According to the authors, predicting PR in current practice is difficult and relies heavily on the experience of practitioners. A progress forecast is needed for planning and cost management of HDD works, yet engineers have no model that would let them determine it reliably. The result is schedule slippage and cost overruns.

How the model was built

The basis was structured interviews with HDD experts together with the analytic hierarchy process (AHP). On that basis the authors assessed the relative importance of ten factors that significantly affect PR. They also present a method for scoring PR for each of these factors.

The model combines the PR scores obtained for the conditions of a given project with the factor weights and, on that basis, predicts progress. The forecasts were compared with actual PR records from seven HDD projects.

The result

The comparison produced consistent results and implies a correction relationship with an R2 of 0.893 and an RMSE of 0.066 m/min. The authors performed leave-one-out cross-validation (LOOCV) to examine the robustness of the model, as well as a sensitivity analysis of changes in factor weights and scoring thresholds.

According to the authors, the model lets engineers assess how changing important factors, such as the type of drilling equipment or the type of drilling tools, affects drilling performance. This is meant to give better work performance and reduce uncertainty in scheduling and cost estimation.

The authors do not state what the correction relationship consists of, nor give its form - it is absent from the abstract and we do not give it. All figures and conclusions come from the paper's abstract. The full text is available from the publisher for a fee; the abstract was verified via OpenAlex and the metadata (authors, journal, publication date) confirmed in the Crossref registry.