Stochastic Method for Calculating Lockage Capacity under Staggered Operation: A Case Study of the Gezhouba Lock Expansion Project

Abstract Because of constraints in space and budget, lock capacity expansion projects often adopt a layout in which multiple locks share a common approach channel. To prevent excessive water-level fluctuations and ensure navigation safety, a staggered operation mechanism must be implemented. Traditional lock capacity calculation methods rely on a fixed average lockage duration, disregarding the randomness of lock operations and the forced waiting delays caused by staggered operation. Consequently, such methods systematically overestimate the number of lockages under staggered operation. To address this gap, this paper presents a stochastic simulation method for calculating the number of lockages that incorporates the randomness of lockage durations. Based on the cumulative distribution function of lockage durations, the inverse transform sampling method is employed to generate a random sequence of lockage durations. During simulation, if the time difference between the current emptying moment and the previous one is less than the preset staggered time (denoted as TC), the operation is delayed accordingly, and the delay time is accumulated. The proposed method is demonstrated through a case study of the three locks sharing a common approach channel in the Gezhouba lock capacity expansion project. For this case, the reduction in lockages (NRL) and cumulative delay time (TCD) are quantified under varying TC and number of operational days ( N ). The key findings for this specific site are: For TC = 6 and 15 min, the average daily reduction in lockages is approximately 0.3 and 1.8, respectively, with corresponding average daily cumulative delays of approximately 25 and 145 min. TCD exhibits an almost linear relationship with NRL, with a slope of 79 min, very close to the theoretical lockage duration. While the quantitative results are derived from this single-site case study, the proposed stochastic simulation framework is transferable to other multilock systems with appropriate site-specific input data.