COMPARISON OF FORMULAE FOR THE PREDICTION OF SCOUR DEPTH AT PIERS

Local scour at bridge piers was extensively studied in the literature and several empirical formulae were proposed to assess the maximum scour depth at equilibrium. Since the equations were derived in small scale conditions, the application to practical cases is uncertain. Recently, formulae were tested by using field datasets, but in few cases only. In this paper, six design formulae for the estimation of the equilibrium maximum scour depth at a circular pier were compared by using synthetic and original field data. In the former case, random input variables were generated with the Monte Carlo simulation technique in realistic ranges typical of many natural watercourses, in both clear-water and livebed scour conditions, in order to achieve useful results for field applications. The results show that different formulae produce significantly different predictions. The selected formulae were also tested on a field dataset in the case of uniform bed sediments, confirming that their ability to assess the maximum scour depth at equilibrium is not satisfactory. INTRODUCTION Over the past 50 years, numerous equations have been developed to predict local scour depth at bridge piers. Most formulae are based on laboratory experiments, and only some of them have already been tested using field data. The limited use of field datasets leads to some uncertainty in the application of pier-scour formulae to predict scour in real cases. Based on a brief consideration of the literature, Johnson (1995) used field data to consider the accuracy and limitations of seven pier-scour formulae in various field conditions. An extensive analysis and comparison of field data with predictions of five selected formulae by Landers and Mueller (1996) showed that none of the selected formulae accurately estimates the depth of scour in all the measured conditions. Their results also clarified that some of the equations performed well as conservative design formula; however they overestimated many observed scour depths by large amounts. The results of a more recent study by Mohamed et al. (2006) showed that the CSU formula, which was later improved and published as FHWA (HEC-18) formula (Richardson and Davis, 2001), is more accurate in comparison to other three selected pier-scour formulae. A review of previous studies shows that a large number of empirical formulae was proposed to estimate pier scour depth. All proposed equations can be classified in two groups: 1) formulae developed through a correlation among effective parameters and scour depth; 2) formulae based on envelope curves, in order to estimate the maximum scour depth for safe design purposes. In this study, six well-known pier scour formulae were selected for comparison. All of the selected formulae were recommended in literature for design procedure. Owing to the general lack of field datasets, a comparison between formulae (two by two) can be carried out using large synthetic datasets, which can be generated in various hydraulic and sediment conditions. The main purpose of the present work is to compare the performance of six bridge pier scour equations using both randomly generated and field data. SELECTED FORMULAE The selected formulae are presented below. a) Breusers et al. (1977) formula (hereinafter BR) for clear-water and live-bed scour conditions: θ K K b h U U b d s c se ⋅ ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = tanh 1 2 2 (1) where dse is the maximum scour depth in equilibrium condition, b the pier width, U the approaching flow velocity, Uc the critical velocity for sediment motion – computed with the Neill (1973) equation in SI units ( 3 / 1 50 6 / 1 2 / 1 08 . 31 d h Uc θ = ), where the Shields mobility parameter, θ, can be computed based on sediment size (see Mueller and Wagner 2005, p. 20) – h the approaching flow depth, Ks the pier shape factor and Kθ the pier alignment factor (see details in Breusers et al., 1977). b) Jain and Fischer (1979) formula (hereinafter JF) for clear-water and live-bed scour conditions: 25 . 0 3 . 0 84 . 1 c se Fr b h b d ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = , valid for Fr-Frc<0 in clear-water conditions; (2a)