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Chapter 7 - Establishing an empirical formula
7.1 Introduction
This chapter presents the search for an empirical formula allowing the determination of the maximum
scour depth. Based on the analysis of existing scour formulae and the parameters used by
the different authors, several approaches were explored.
• In a first step a dimensional analysis was performed (§ 7.2) indicating the essential parameters
influencing the scour process.
• In a second stage a large number of different approaches were explored to establish a new
scour formula. They include the optimization of existing scour formulae, new approaches,
based on the s-shaped cross-section profile, the pi-theorem as well as an approach with a
dimensionally aware genetic algorithm.
• Finally the influence of the macro-roughness on the scour process is discussed and a formula
determined to estimate the scour depth with vertical ribs on the outer side wall.
In this study, the square of the Pearson product moment correlation coefficient R was used
defined as:
n ⋅ ΣXY – ΣX ⋅ ΣY
R = ------------------------------------------------------------------------------------------------
(7.1)
( n ⋅ ΣX 2 – ( ΣX) 2 ) ⋅ ( n ⋅ ΣY 2 – ( ΣY) 2 )
R 2 ranges from 0 to 1 and reflects the extent of a linear relationship between two data sets.
NB: The square of Pearson’s correlation factor R 2 quantifies the extent of a linear relationship
between two data sets and not the error between measured and computed data!
page 150 / November 9, 2002
Wall roughness effects on flow and scouring