Abstract
Labyrinth weirs are a class of hydraulic structures that increase the effective crest length of a spillway by folding the weir wall into a repeating geometric pattern — typically triangular, trapezoidal, or W-shaped in plan view. This increased crest length allows significantly higher discharge capacity for a given channel width, making labyrinth weirs an attractive option for dam spillways, irrigation diversion structures, and flood control systems where space is constrained.
The design challenge lies in accurately predicting the discharge coefficient. Unlike a simple straight-crested weir, the discharge through a labyrinth weir depends on a complex interplay of geometric variables — cycle width, wall angle, crest shape, number of cycles — and the upstream head ratio. Traditional empirical formulae, while useful, are calibrated to specific geometries and can produce significant errors when extrapolated to non-standard configurations.
This study experimentally investigated the discharge performance of two labyrinth weir plan forms: the multi-cycle W-form and the circular arc configuration, both with sharp-crested profiles. Experiments were conducted in a rectangular flume under free-flow conditions.
To predict discharge performance, the authors employed machine learning techniques — comparing Artificial Neural Networks (ANN), Multiple Linear Regression (MLR), and Support Vector Machines (SVM). The input parameters included geometric ratios (cycle width, wall height, crest length ratio) and the head-to-wall-height ratio. The output was the discharge coefficient.
The results demonstrated that the SVM regression model provided the most accurate predictions, outperforming both ANN and MLR in terms of root-mean-square error and coefficient of determination. The circular arc labyrinth weir configuration showed favourable hydraulic efficiency characteristics compared to the W-form under certain head ratios.
For hydraulic structure design in India — where thousands of dams, barrages, and irrigation diversions operate with limited spillway capacity — this research offers a practical, data-driven tool for rapid discharge estimation. Rather than conducting extensive physical model tests for every design variant, engineers can leverage trained ML models to explore the design space quickly and identify optimal geometries.
Key Findings
- SVM regression provides the most accurate discharge coefficient predictions, outperforming ANN and MLR.
- Multi-cycle W-form and circular arc labyrinth weir configurations were experimentally tested under free-flow conditions.
- Machine learning models enable rapid design-space exploration without extensive physical model testing.
Methodological Approach
Experimental flume testing of W-form and circular arc labyrinth weirs under free-flow conditions, with discharge prediction via ANN, MLR, and SVM regression models. Inputs: geometric ratios and head-to-wall-height ratio. Output: discharge coefficient.
Implications for Hydraulic Practice
Provides dam and spillway designers with a rapid, ML-driven tool for discharge estimation, reducing reliance on physical model tests and enabling efficient exploration of labyrinth weir geometries.
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