Linear genetic programming for prediction of circular pile scour

Abstract

Genetic programming (GP) has nowadays attracted the attention of researchers in the prediction of hydraulic data. This study presents linear genetic programming (LGP), which is an extension to GP, as an alternative tool in the prediction of scour depth around a circular pile due to waves in medium dense silt and sand bed. Field measurements were used to develop LGP models. The proposed LGP models were compared with adaptive neuro-fuzzy inference system (ANFIS) model results. The predictions of LGP models were observed to be in good agreement with measured data, and quite better than ANFIS and regression-based equation of scour depth at circular piles. The results were tabulated in terms of statistical error measures and illustrated via scatter plots.

Introduction

When a pile is embedded vertically in a loose sedimentary bed, scour takes place in the vicinity of the pile under the action of ocean and lake waves or currents. Scour phenomenon is of high practical importance from the point of view of the stability of marine and river structures, such as offshore platforms, subsea templates, bridges, etc., as excessive scour at piles is detrimental to the structures (Dey et al., 2006). When a pile is located on the sea floor, because of mutual actions between pile and wave or current, the bed around a pile will undergo a significant change in capacity of sediment transport or scour. Scour around a pile can lead to the structure instability, damage or failure in marine and coastal environments. Therefore, an accurate estimation of the pile scour for a safe design of a marine structure has to be considered.

Many investigations about pile scour, frequently in laboratory, have been reported. Sumer et al. (1992) carried out experimental studies about scour due to waves around a pile. They presented scour depths as the function of the Keulegan–Carpenter number, KC, by regression approach, in the dimensionless form of empirical expression:

$$S/D=1.3(1-e^{-0.03(\mathit{KC}-6)})\mathrm{for}\mathit{KC}\ge 6$$

where S is the scour depth, D is pile diameter (m).

$$\mathit{KC}=\frac{U_{m}T}{D}$$

where U_m is the mean flow velocity, T the wave period and D is the pile diameter.

The effects of pile cross section (square pile with 90° and 45° orientation) have been reported by Sumer et al. (1993). Kobayashi and Oda (1994) showed the KC number as the main parameter governing scour process and then scour depth. Also, Sumer and Fredsoe (2001) studied scour around piles due to combined wave and current. The study based on controlling the scour around a circular pile due to wave and current have been done by Dey et al. (2006). They found that the scour depth can decrease about 62% by adding addendums (splitter plate and spiral cable) to the pile. Furthermore, Sumer et al. (2007) studied scour around a pile in sand (with relative density Dr=0.23), medium dense silt (Dr=0.38) and dense silt (Dr=0.74) bed and showed the scour depth can increase in dense silt by a factor of 1.2–2.

Because of nonlinearity and complexity, more robust tools are required to model scour processes around piles due to wave action. Most commonly regression relations are used to predict pile scour due to waves; however, regression analysis can have large uncertainties, which own major drawbacks pertaining idealization of complex scour process, approximation and averaging widely varying prototype conditions. Thus, the computed scour depths can be far from the actual ones. Another important issue, apart from the complexity of the scour phenomenon involved, is due to the limitation of the regression analysis. In regression analysis, whatever the nature of corresponding problem is, it is tired to model by a predefined equation, either linear or nonlinear. Another major constraint in application of regression analysis is the assumption of normality of residuals.

Recently, artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and genetic programming (GP) are being used to model these processes. These soft computing tools, which can approximate nonlinear behavior and simplicity of computations, are widely used to outline input-output data sets in engineering problems. These models have been used to estimate scour around piles (Kambekar and Deo, 2003), below spillways (Azamathulla et al., 2008a), downstream of ski-jump bucket (Azamathulla et al., 2005, Azamathulla et al., 2008b), and downstream of grade-control structures (Guven and Gunal, 2008a, Guven and Gunal, 2008b). GP and ANNs were successfully applied in maritime engineering by Kalra and Deo (2007), Singh et al., 2008, Singh et al., 2007, Gaur and Deo (2008), Ustoorikar and Deo (2008). Also, combinations of Fuzzy Inference System (FIS) with ANN (ANFIS) have been employed to predict wave characteristics (Kazeminezkad et al., 2005a, Kazeminezkad et al., 2005b; Mahjoobi et al., 2008), sediment concentration (Kisi, 2005), water level in reservoir (Chang and Chang, 2005) and pile group scour (Bateni and Jeng, 2007).

This study investigates LGP and ANFIS methods in prediction of scour depth due to ocean/lake waves around a pile/pier in medium dense silt and sand bed, and evaluates the relative importance of input parameters on scour process. The results are tabulated in terms of statistical measures and also illustrated in scatter plots.