A comparative study on equilibrium scour volume around circular cylinders in clay–sand mixed cohesive beds, at near threshold velocity of sand – an experimental approach Open Access

C_p

clay percentage [M⁰ L⁰T⁰];

S1

fine sand (d₅₀ = 0.182 mm);

S2

medium fine sand (d₅₀ = 0.44 mm);

d

sediment particle diameter [L];

d₁₆

16% finer particle diameter [L];

d₅₀

50% finer particle diameter [L];

d₈₄

84% finer particle diameter [L];

d_s

equilibrium scour depth [L];

d_st

scour depth at time t [L];

d_m

scour hole diameter [L];

D

pier diameter [L];

[M⁰ L⁰T⁰];

[M⁰ L⁰T⁰];

g

acceleration due to gravity [LT⁻²];

PI

plasticity index [M⁰ L⁰T⁰];

t

time [T];

critical shear velocity for sand used in clay–sand mixture [LT⁻¹];

V

depth-averaged velocity [LT⁻¹];

V_cs

critical threshold velocity for sand used in clay–sand mixture [LT⁻¹];

[M⁰ L⁰T⁰];

volume of scour hole in the equilibrium phase [L³];

[M⁰ L⁰T⁰];

W_c

water content by weight of dry mix [M⁰ L⁰T⁰];

W_L

liquid limit [M⁰ L⁰T⁰];

W_P

plastic limit [M⁰ L⁰T⁰];

y

approach flow depth [L];

[M⁰ L⁰T⁰];

Z

slope of scour hole;

bulk density of sediment [ML⁻³];

dry density of sediment [ML⁻³];

maximum dry unit weight [ML⁻³];

[M⁰ L⁰T⁰];

bed shear stress [ML⁻¹T⁻²];

threshold bed shear stress for particle movement [ML⁻¹T⁻²];

maximum bed shear stress around pier [ML⁻¹T⁻²];

bed shear strength [ML⁻¹T⁻²];

[M⁰ L⁰T⁰].

Local scour around bridge piers is a problem of special interest to hydraulic engineers. This is a complex phenomenon resulting from the interaction of the three-dimensional turbulent flow field around hydraulic structures such as bridge piers, abutments, spurs etc. One of the leading concerns of the stability of bridges founded in river-beds is the local lowering of the bed level (commonly known as ‘local scour’) caused by the flows around bridge piers (Kothyari et al. 2007, 2014; Sheppard et al. 2014; Muzzammil et al. 2015; Garfield & Ettema 2021; Jain et al. 2021; Karkheiran et al. 2021; Nou et al. 2021; Pandey & Azamathulla 2021). The perturbation of the flow field caused by a cylindrical obstruction (e.g., bridge pier) in rivers and streams introduces a complex flow field marked by turbulent structures such as a horseshoe vortex, surface rollers, and wake vortices (Ettema et al. 2006; Garfield & Ettema 2021; Jain et al. 2021; Pandey et al. 2021, 2022). The combination of these structures leads to removal of bed sediments from around the bridge pier, which ultimately results in the development of a scour hole around the base of the bridge pier. An accurate estimation of scour depth below the stream-bed is important during design since it determines the foundation levels and expansion of the bridge foundation structures such as pier, abutment, guide bank, spur, etc. Under-prediction of scour profile, including not only the depth but also its peripheral extension, can lead to costly bridge failures, while over-prediction can result in unnecessary expenditure in terms of construction costs.

For last few decades a number of field and flume studies have been carried out by researchers to estimate the equilibrium scour depth, proposing empirical equations and a reasonable understanding and quantification of scour depth around bridge piers (Shen et al. 1969; Breusers et al. 1977; Raudkivi & Ettema 1983; Yanmaz & Altinbilek 1991; Kothyari et al. 1992, 2007; Dey et al. 1995; Melville 1997; Raudkivi 1998; Melville & Chiew 1999; Oliveto & Hager 2002, 2005; Sheppard et al. 2004, 2014; Chavan & Kumar 2017; Das et al. 2020; Singh et al. 2020; Singh et al. 2022; Garfield & Ettema 2021). Most of the available studies on pier scour deal with non-cohesive sediment beds. By contrast, a comparatively limited number of studies have been reported on local scour around bridge piers on cohesive (muddy) sediment beds. This is probably because the mechanics of cohesive sediment transport processes itself is not yet properly understood due to the complexity of the problem that arises from interplay between various parameters required to characterize these sediments (Berlamont et al. 1993; Houwing & van Rijn 1998; Molinas & Hosny 1999; Ravens & Gschwend 1999; Debnath et al. 2007a, 2014; Debnath & Chaudhuri 2012; Kothyari et al. 2014; Najafzadeh & Barani 2014; Muzzammil et al. 2015; Chaudhuri et al. 2018; Pandey et al. 2019; Singh et al. 2019; Singh et al. 2020; Singh et al. 2022; Das et al. 2020; Jain et al. 2021). Further, flume experiments using cohesive sediment are challenging to conduct because of difficulties with preparing and handling cohesive sediment due to its sticky nature and the large number of physical parameters involved. The physics of transport of cohesive sediment is entirely different from that of sand and larger-sized particles (Debnath et al. 2007a, 2007b). Cohesion of individual grains, arising from molecular-scale physicochemical attractive forces, causes colliding grains to bond and form aggregates and is a major controlling factor in fine sediment transport, deposition, and erosion. Erosional properties of combined mud and sand are a direct function of the relative proportions of sand and mud (Debnath et al. 2007a). It was found that adding sand to mud or vice versa increases erosion resistance and reduces erosion rate. Also, the mode of erosion changes from cohesionless to cohesive at a low proportion of mud added to sand. This transition occurs in the range of 3%–15% mud by weight, depending on different compaction levels of the mixture and clay mineral type (Mitchener & Torfs 1996). Here, mud is defined as particles less than 63 μm in size, i.e., clay and silt. However, throughout the paper, clay will refer to particles less than 63 μm as has been done by others (Ting et al. 2001; Debnath & Chaudhuri 2012). This clay fraction or percentage clay (i.e. d ≤ 63 μm) by weight of clay–sand mix will be denoted by C_p, where d = size of sediment particle.

Huber (1991) stated that since 1950 about 500 bridges had failed in the USA and that a majority of them were the result of hydraulic conditions primarily due to the scour of foundation material. Therefore, it is essential to quantify both the depth and total volume of material dislodged from the base of hydraulic structures by the flow. To date, investigations on scour volume, that is, the total volume of the eroded bed material from the base of the structures, especially for cohesive sediments, is of the utmost rarity.

In this paper, we present 52 experimental data on scour volume around circular bridge piers in clay–sand sediment mixture that comprise clay–sand mixtures using two different sand sizes (S1 & S2). This allowed us to address whether sand size has any effect on equilibrium scour volume and depth in clay–sand mixtures. Regression based models are developed from 56 experimental runs to develop a relation between scour volume and slope with increasing clay content and maximum equilibrium scour depth. Detailed comparison has been made between present experimental data with those of one of the pioneering experimental works of Molinas & Hosny (1999) on bridge pier scour in clay–sand mixed cohesive sediment, for an overall understanding of the mentioned relations.

Experiments were conducted in a straight tilting flume (kept at constant slope = 0.001 m/m) 18.3 m long, 0.9 m wide, and 0.9 m deep, located in the Fluid Mechanics and Hydraulics Laboratory of the Indian Institute of Engineering Science and Technology, Shibpur, India (Figure 1). The test section of the flume was 2.5 m long and 0.25 m deep and was located 10 m downstream of the flume entrance. Water was recirculated into the flume by one vertical turbine pump of 0.3 m³ s⁻¹ capacity from a sump 57 m long, 3 m wide and 2 m deep. Water from the pump was first delivered into a stilling basin and thereafter passed through a series of wire mesh and baffle to break large-scale turbulence and waves. Water depth in the flume was controlled by a tail gate located at the downstream end of the flume.

A point gauge was used to measure the scour hole profile. The discharge into the flume was controlled with a flow control valve. The depth-averaged mean velocity, V, was approximated by measuring the mean velocities with Micro ADV at 0.2y and 0.8y – with y flow depth and averaging them (similar to Ting et al. 2001; Debnath & Chaudhuri 2012). The values of V for the different runs are given in Tables 2 and 3 and are referred as approach flow velocity. The circular cylinder models of pier were made of (transparent) Perspex having diameter (D) = 6, 9 and 12 cm with vertical graduated tapes glued inside of the pier model at 0° (front), 90° (left side), 180° (behind), and 270° (right side). An NB Pro-Logitech camera was inserted inside the pier model from a carriage unit (camera holder) with vertical and rotational degrees of freedom, and was used for recording the temporal progression of scour depth (d_st) at regular time intervals against the 0°, 90°, 180° and 270° scales and to confirm the (eventual) occurrence of the equilibrium state of scouring. Figure 1 shows the photograph of the experimental setup just before the experimental run.

Each experimental run was stopped when no changes in scour depths were observed for five successive hours in any of the four planes at 0°, 90°, 180° and 270°. Considering this as an equilibrium state of the scouring process (Dey & Westrich 2003), the flow was gradually reduced, before it was stopped by controlling the flow control valve, and the tail gate was carefully adjusted to avoid any disturbance to the final scour profile. The water from the scour hole was drained out by siphoning. Then, detailed readings of the scour hole geometry were taken with a point gauge with graduated traverse arrangement in all three coordinate directions. In order to measure the final equilibrium volume of the scour hole, a thin plastic sheet was carefully placed so that it could cover the entire scour hole and water was slowly poured into the lined scour hole from a calibrated measuring tube until the water level in the scour hole reached the (initial) undisturbed bed surface, as shown in Figure 2. The total volume of the water poured into the scour hole from the measuring tubes was assumed to be the volume of the equilibrium scour hole (⁠⁠). Tables 2 and 3 reveal the ranges of experimental conditions and obtained results, with the observed equilibrium scour depths and estimated scour volumes.

For both sand sediments (i.e., S1 and S2), it was observed that the increment in clay percentage, C_p, led to a noticeable reduction in scour volume while the other flow parameters were fixed. Figure 3 shows photographs of the scour hole morphologies at the equilibrium stage for the runs no. 8 (C_p = 5%), no. 9 (C_p = 10%), no. 10 (C_p = 20%), and no. 11 (C_p = 25%), which reveal a significant reduction of the scour hole volume with increasing C_p.

To confirm what it has been just said, Figure 4 shows the longitudinal and lateral cross-sectional views of the scour hole profiles at the equilibrium stage for the runs from no. 8 to no. 11 It is immediately observed that there is a significant decrease of the scour volume as C_p increases, but the slopes of the scour hole do not show a specific trend.

The average slope (i.e., tan θ) of the equilibrium scour hole was estimated by averaging the slope of the equilibrium scour hole profiles collected at all four sides of the pier (i.e., 0°, 90°, 180°, 270°). It was calculated by determining the slope of the best-fit straight line along each of the four sides. However, the plotting of data against C_p, and still considering the same intervals for the threshold dimensionless velocity, did not give any specific trend as can be seen in Figure 5. In contrast, Molinas & Hosny (1999) highlighted a rapid increase in slope as C_p increases. This discrepancy may be due to the difference between our study and that by Molinas & Hosny (1999) mainly in regard to the bed characteristics in terms of clay mineralogy. In this study, the slope of the scour hole would exhibit some tendency to increase only for a restricted range of C_p (5%–25%). The scouring process in a clay–sand mixture is very complex due to interaction of the clay–sand network structure and bed shear stresses. The flow-induced shear stresses tend to decline inside the scour hole as the scour volume increases, but scouring processes develop differently depending on the characteristics of the clay–sand mixtures, which are the most governing factors for the final shape and volume of the scour hole.

Equations from (8) to (10), as well as the previous ones from (5) to (7), were obtained considering only the experimental data collected in this study.

For this equation the coefficient of determination R² is equal to 0.88, which is reasonably good taking into account the complexity of the problem. To validate the proposed equation, the data from Molinas & Hosny (1999) were considered and compared with Equation (11), as shown in Figure 8. The fitting can be considered as satisfactory, especially if divergences between the experimental work by Molinas & Hosny (1999) and the present one are taken into account.

The new experimental data set from the present study along with literature data reported in Molinas & Hosny (1999) for clay–sand mixed beds reveal that the presence of clay can significantly reduce the scour volume around a bridge pier.

• With the rise of C_p, the reduction of the equilibrium scour hole volume is much less in fine sand (S1) than in medium sand (S2). This is probably because for fine sand particles more specific surface area is available to clay particles for agglomeration contact, which results in formation of larger sediment flocs that require more energy to be dislodged or to get eroded out initially as bed load.

• Molinas & Hosny (1999) reported that with the increasing of the clay percentage C_p the slope of the scour hole increases. However, present experiments do not show any significant change in the slope of the scour hole in relation to C_p; instead, the scour holes observed in this study resembled more or less cones of reducing size with the increase in C_p.

• In this study the slope of the scour hole would exhibit some tendency to increase only for a restricted range of C_p (5%–25%). The scouring process in a clay–sand mixture is very complex due to interaction of the clay–sand network structure and bed shear stresses. However, scouring processes develop differently depending on the characteristics of the clay–sand mixtures, which are the most governing factors for the final shape and volume of the scour hole.

• The effect of the clay content C_p on the dimensionless scour volume was satisfactorily presented by best-fit exponential curves depending on three ranges for the threshold dimensionless velocity constant (i.e., = 0.99–1.1, = 0.87–0.92, and = 0.78–0.85).

• Finally, a single exponential equation for the dimensionless scour volume as a function of the equilibrium scour depth was found by regression analysis with a coefficient of determination R² equal to 0.88, which is reasonably good taking into account the complexity of the problem.

• The proposed equations were validated by the data set of Molinas & Hosny (1999) and they have shown a satisfactory agreement with the experimental data.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.