Adaptation of Selected Formulas for Local Scour Maximum Depth at Bridge Piers Region in Laboratory Conditions

The study aimed to adapt selected formulas for the estimation of the maximum depth of local scour in the area of the bridge pillar model: Begam formula, Laursen and Toch equation and the equation included in the Regulation of the Polish Minister of Transport and Marine Economy of 30 May 2000 on technical requirements for road engineering structures and location of these structures. The results of own laboratory tests were used for the adaptation. A total of 19 series of measurements with different durations, water flow rates and water depths were performed. The tests were carried out on a model of a washable flume model with a sandy bed, with a single cylindrical bridge pier. The formulas were optimized using the Monte Carlo sampling method. The best match among the original formulas was obtained for Laursen and Toch’s formula (mean relative error 15.3%). For Begam’s formula, an average relative error of 21.6% was received, and for calculations using the Regulation equation, a relative error of 30.1% was obtained. Optimization of formulas using the Monte Carlo sampling method resulted in a formula that describes laboratory data with a mean relative error of 8.8% based on the Begam equation, a mean relative error of 13.8% based on the Laursen–Toch equation, and 28.5% for the formula based on equation included in the Regulation.