An experimental investigation for the determination of the optimum ratio of nano clay for reducing local scour around a cylindrical bridge pier Open Access

Numerous scholars employed laboratory experimental prototyping to study the scour mechanism and its primary factors, which were classified as hydraulic, geotechnical, and structural. Hydraulic variables include shear velocity, mean velocity, Reynold number, and Froude number. Geotechnical factors include sediment density, coarseness, size, homogeneity, and sediment motion. Finally, the structural aspect consists of the pier's shape and diameter (Raudkivi & Ettema 1977, 1985; Baker 1980; Chiew 1984; Melville & Sutherland 1988; Dargahi 1989; Salim & Jones 1996; Ettema et al. 1998; Melville & Coleman 2000; Roulund et al. 2005; Zhao et al. 2010; Baykal et al. 2015; Liang et al. 2020).

In the past few decades, comprehensive investigations have been carried out on the occurrence of local scour with varying types of sediment beds, such as sand beds (non-cohesive sediment), clay or silt beds (cohesive sediment), and mixed beds (sand-clay beds).

In terms of the sand beds (non-cohesive sediment), the studies reached a deep comprehension of the behavior and mechanisms of the local scour within non-cohesive beds, and several equations have been developed to calculate the local scour depth in sand beds (non-cohesive sediment). Furthermore, researchers have developed several experimental methodologies to simulate local scour as well as developed artificial intelligence models for predicting this phenomenon (Raudkivi & Ettema 1977, 1985; Baker 1980; Chiew 1984; Melville & Sutherland 1988; Dargahi 1989; Salim & Jones 1996; Ettema et al. 1998; Melville & Coleman 2000; Roulund et al. 2005; Moncada-M et al. 2009; Zhao et al. 2010; Baykal et al. 2015; Ismael et al. 2015; Wang et al. 2017; Liang et al. 2020).

On the other hand, numerous inquiries have been conducted to examine the phenomenon of local scour in clay and silt (cohesive beds). Scholarly investigations have provided valuable insights into the fundamental features of fine-grained (cohesive sediment). Cohesive sediments are influenced by electromagnetic and electrostatic inter-particle forces, which lead to the formation of tightly bonded particles. Therefore, the duration of the equilibrium stage of the local scour in cohesive sediments is longer than in sand (non-cohesive sediment). Moreover, erosion in cohesive sediments can happen either through individual particles or clusters of particles. In contrast, non-cohesive sediments can erode particle by particle, causing a rapid increase in the depth of local scour (Rambabu et al. 2003; Sumer et al. 2007; Debnath & Chaudhuri 2010; Abou-Seida et al. 2012; Najafzadeh & Barani 2014; Zhang et al. 2022).

In recent times, researchers have shown a growing interest in studying the impact of fine particles mixed with sand on the behavior of local scour (Mitchener & Torfs 1996; Van Ledden et al. 2004; Debnath & Chaudhuri 2010, 2011; Chaudhuri et al. 2022). The researchers utilized fine particles, known as cohesive sediment, consisting of clay and silt with particle sizes smaller than 36 μm (Debnath & Chaudhuri 2010). Studies have shown that mixing the fine particles with sand can change the sediment transport mode from cohesionless to cohesive, decreasing the depth of local scour due to the increasing inner friction between sand particles. The resistance to erosion of the sand and fine particle mixture is most noticeable when the fraction of fine particles is low (Mitchener & Torfs 1996; Van Ledden et al. 2004; Debnath & Chaudhuri 2010, 2011). According to Debnath & Chaudhuri (2010), the scour depth was found to be higher when finer sand was used in clay-sand mixtures compared to coarser sand. Chaudhuri & Debnath (2013) stated that the local scour decreases as the clay ratio increases. However, after reaching a clay ratio of 0.5, the local scour increases with a further increase in the clay ratio. Chaudhuri et al. (2022) found that mixing clay with medium sand particles was more effective in reducing the local scour hole size than mixing clay with fine sand.

Previous studies have primarily focused on using clay particles that are micro-sized. However, no research has been carried out to examine the impact of nanomaterials on local scour. The objective of this study was to enhance the current understanding of how a mixture of nano clay and sand affects the depth of local scour around a cylindrical pier. The main goal was to examine how various pier diameters and flow depths affect the nano clay-sand bed. In addition, the study aimed to determine the optimal ratio of nano clay. Furthermore, a predictive model was developed to estimate the potential for local scour in the nano clay-sand bed.

Nano clay (Montmorillonite) was utilized in this investigation, which exhibits various unique characteristics that make it a highly appropriate substrate for engineering applications based on nanotechnology. Norhasri et al. (2017) identified various significant characteristics of nano clay, such as stability, interlayer spacing, high hydration, swelling capacity, and strong chemical reactivity. Table 1 presents a comprehensive overview of the parameters associated with both the sand and nano clay.

A single cylindrical pier with three different diameters (3, 5, and 7.5 cm) was used in this study. According to Chiew & Melville (1987), the ratio between the flume width and the pier diameters should be B/D > 10. Therefore, the pier diameters were carefully selected to ensure that the channel wall does not have a significant impact on scouring. The experimental methodology entailed utilizing one flow rate and three different flow depths, as listed in Table 2.

In order to examine the impact of nano clay on the mitigation of scour depth around cylindrical bridge piers, a series of experiments were conducted. The experimental procedure was as follows: A sediment bed was prepared for the test area, measuring 150 cm in length, 20 cm in depth, and 80 cm in width. In the middle of this area, a pier was installed and its verticality was checked to prevent any slope influence on the vortex. Subsequently, the section was filled with sediment and leveled using a scraper. A laser range finder was utilized to measure the bed's dimensions.

The experiments started with a slow flow rate to gradually achieve the required flow depth and ensure any air bubbles were expelled from the sediments, guaranteeing full saturation. The flow depth was regulated using a tailgate. Afterward, the necessary discharge rate was pumped, and an electromagnetic flowmeter monitored the flow, controlled via a valve. During the final phase of the experiments, once the local scour equilibrium was reached, the water was drained slowly to prevent any alterations in the bed's topography. The contours of the bed were then measured using a laser range finder.

When M_s, M_n, and M_w are the mass of the sand, nano clay, and water, respectively, and G_s and G_n are the specific gravity of the sand and nano clay, respectively. The mixing ratios were 0.25, 0.5, 0.75, and 1%.

The process of mixing the nano clay into the sand involved several steps. First, the quantities of sand, nano clay, and water were determined using Equation (2). Next, a solution of nano clay was prepared by adding it to water and using a high-speed mixing machine. The resulting solution was then added to the sand, and both components were mixed together using a steel trowel for a duration of 30 min until a uniform color was observed. Afterward, the mixture was left for 24 h to ensure proper distribution and prevent additional water absorption, as Debnath et al. (2007) recommended. Finally, the mixture was applied to the test section in layers, with each layer being 5 cm deep. The layers were mixed using a steel trowel without compaction. This systematic approach ensured a controlled and precise methodology for mixing the nano clay into the sand.

Rearranging Equation (3) by substitute Froude number Fr = V/(gh)^0.5, pier Reynolds number Re = DVρ/μ, S_S is the specific gravity of sediment = (ρ_s)/ρ. By combining some terms, we can obtain that, firstly, the mass of sand with the mass of nano clay (⁠⁠) and it can be written as the proportions of the mixture Mr = Second, by recombining and rearranging of the specific gravity of sediment S_S, and the flow Froude number Fr, it can be expressed as sediment densimetric Froude number ⁠.

This study included a series of 45 experiments. The experimental setup consisted of control tests involving a sand bed, as well as a second phase involving a nano clay-sand bed. The findings of these experiments, including specific details, can be found in Table 3.

The results of the control tests were analyzed by comparing them with four equations obtained from relevant literature, which are listed in Table 4. The purpose of this comparison was to assess the calibration of the experimental measurements. Careful consideration was given to the selection of these equations to ensure that all parameters being investigated were appropriately addressed. Figure 4 presents a comparison between the calculated and measured data, along with an error band of approximately ±30%. Based on this analysis, it can be concluded that the control test data are deemed acceptable and has been validated through the comparison with data obtained from the equations.

Table 4

Scour equations

Reference .	Equations .
Equation (3) of Raeisi & Ghomeshi (2020)
Equation (8) of Raeisi & Ghomeshi (2020)
HEC-18/Jones equation (Richardson & Davis 2001b)
HEC-18/Mueller equation (Mueller 1996)	with modified K4

Reference .	Equations .
Equation (3) of Raeisi & Ghomeshi (2020)
Equation (8) of Raeisi & Ghomeshi (2020)
HEC-18/Jones equation (Richardson & Davis 2001b)
HEC-18/Mueller equation (Mueller 1996)	with modified K4

K₁ is the pier shape's correction factor, K₂ is the flow direction's correction factor, K₃ is the bed's correction factor, and K₄ is the armoring of the coarse bed's correction factor (Mueller 1996; Richardson & Davis 2001b).

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Figure 5 demonstrates that the minimum scour depth was observed for a 3 cm pier diameter when utilizing 0.25% nano clay across all flow depths. The reduction in scour depth reached up to 68, 66, and 64% for flow depths of 9.1, 7.55, and 5.7 cm, respectively, compared to the control test with 0% nano clay. However, it was observed that increasing the ratio of nano clay beyond the optimal proportion resulted in an increase in scour depth. Similar trends were observed when the pier diameter was increased to 5 cm, with the minimum scour depth observed at 0.25% nano clay. The highest reduction values were 48, 43, and 41% for flow depths of 9.1, 7.55, and 5.7 cm, respectively. Overall, the addition of nano clay had a significant impact on reducing the depth of scour, with the optimal reduction achieved at a concentration of 0.25% nano clay. However, as the concentration increased to 1% nano clay, the effectiveness decreased, resulting in a reduction of 25–20% in scour depth.

However, the utilization of nano clay–non-uniform sand bed has demonstrated a significant ability to mitigate erodibility and enhance the performance of sand in resisting local scour due to various factors, including enhanced molecular-scale physicochemical attractive forces, increased particle cohesion, higher inner sand fraction, formation of aggregates through particle collisions, and the role of fine sediment in controlling transport, deposition, and erosion, which was also indicated by Debnath & Chaudhuri (2011). Al-Shayea (2001) found that adding a small proportion of clay to sand decreases the mixture's permeability, while a higher percentage of clay significantly increases permeability. Due to the high permeability ratio, it was also found that once the optimal nano clay content is reached, the resistance of the sediment to local scour decreases.

Overall, according to the experimental results, it can be stated that the optimum ratio of nano clay in the non-uniform sand is between 0.25 and 0.5%. This range closely aligns with the proportion of fine sediments (d₁₆) in the used sand (coarse sand), (d₁₆) is 0.5% of the total used sand volume. The mix of nano clay and coarse sand has proven to be highly effective. This observation aligns with the findings presented by Debnath & Chaudhuri (2010) and Chaudhuri et al. (2022). Both studies also demonstrated the effectiveness of the clay-coarse sand bed.

Additionally, the coarseness of the sediments D/d₅₀ is the third factor that directly affects the local scour depth. It can be defined as the ratio between the diameter of the pier to the median size of the particles d₅₀. The D/d₅₀ values are 21.74, 35.71, and 53.2 for the pier diameters 3, 5, and 7.5 cm, respectively. Based on Ettema (1980), for the values of the coarseness of the sediments D/d₅₀ < 50, the sediments can be considered coarse, which will increase in the dissipation of energy of the downflow along with the depth of the pier and porous between the particles resist the erosion force, and for D/d₅₀ close to 50, the local scour depth will be in high value and that was observed in the case of 7.5 cm pier diameter.

The present experimental study sought to investigate the effectiveness of nano clay particles in mitigating local scour around cylindrical bridge piers and study the behavior of the nano clay-sand bed. Hence, various factors were considered, such as pier diameters, flow depths, and different mixture ratios ranging from 0.25 to 1%. The findings of this study have significant implications for managing bridge pier scour. The use of nano clay was found to significantly affect the local scour mechanism and the depth of local scour is influenced by the proportion of nano clay used. One of the main findings is that a lower proportion of nano clay decreased local scour depth, whereas a higher proportion led to an increase. This suggests that considering an optimal mixing ratio of nano clay and sand could be an alternative solution for reducing the depth of pier scour.

Furthermore, the research findings indicated that a nano clay concentration of 0.25% is an optimal proportion for narrow piers having a flow shallowness (h/D) less than 1.4. This specific ratio led to a significant reduction in scour depth, with the maximum reduction in local scour depth being 68% for a pier diameter of 3 cm and 48% for a pier diameter of 5 cm. It is noteworthy that this optimal mixing ratio remained consistent for narrow piers. In contrast, for wide piers with a flow shallowness greater than 1.4 (h/D > 1.4), it was observed that the optimal mixing ratio of nano clay increased to 0.5%. This higher proportion led to a maximum reduction in local scour depth of 28% for a pier diameter of 7.5 cm.

Using nano clay for reducing scour depth around bridge piers offers several advantages. First, nano clay is a safe and environmentally friendly substance, with no observed negative side effects during the study. Second, it is a cost-effective solution that can be applied during the initial construction phase or as a remedial measure for existing structures using techniques such as jet grouting, permeation grouting, or deep soil mixing.

In conclusion, this study represents a significant step toward a sustainable and cost-effective solution for mitigating bridge pier scour. Further research in this field is expected to yield additional advancements and insights.

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

The authors declare there is no conflict.