Experimental investigation of the efficiency of stone revetment for different temporal variations with the static water condition

The hazards of riverbank failure and land loss present a global concern. West Bengal witnesses significant distress among riverside residents annually, leading to substantial expenditures on protection efforts, amounting to hundreds of crores (Thakur et al. 2012; Mondal & Patel 2020). Unfortunately, many of these protective measures fail to endure beyond the subsequent monsoon seasons (Deng et al. 2022), because most of the protection has been done without a proper understanding of the causes of failure. Bank stability analysis is a complex problem in comparison with a normal slope stability problem (Khatun et al. 2019). Under submergence, a soil mass effective stress decreases, lowering its shear strength (Li & Aubertin 2010). As a result, the mechanical and physical characteristics of the soil vary as the water-level varies (Parker et al. 2008). The pace and direction of seepage flow are regulated by changes in the water level of a submerged riverbank (Okeke et al. 2020). When the external water-level changes without giving the water on the bank enough time to drain, it is known as a sudden or rapid drawdown (Berilgen 2007). It is widely acknowledged that seepage into the bank, as opposed to seepage in the opposite direction, increases the stability of the bank due to matric suction, and that seepage from the bank towards the river decreases the shear strength of the bank material (Semmad et al. 2022), thereby reducing its stability due to an increase in positive pore water pressure that also leads to bank failure (Dapporto et al. 2003; Rinaldi et al. 2004; Nardi et al. 2011).

For the protection of riverbanks, several methods and materials, such as vanes, bank pitching, spurs, groynes, guide vanes, jack-jetty systems, board fencing, tetrahedral frames, natural geotextiles such as jute geotextile (JGT), vetiver grass, soil nailing, grouting, geotextile, and geogrid, have been used in the field. Stone revetment is also one of the methods to protect the riverbank. The effect of turbulence intensity on riprap stability was studied experimentally by Amirshahi et al. (2022). The stable riprap size was increased by 2.5 times when turbulence was increased from 10% to 25%. Myagmar et al. (2023) did the cost–benefit analysis of bioengineering and mechanical methods for bank protection. Zhou et al. (2024) explored the field and conducted a numerical study on bank failure, considering the direct action of flow and the application of river stage change to bank revetment.

Depending on the nature of riverbank failure with respect to geotechnical properties and hydraulic loading, specific measures for protecting the banks have been made (Duong Thi & Do Minh 2019). Stone revetment is one of the popular methods among others to protect against the failure of the riverbank (Craig & Zale 2001; Schmetterling et al. 2001; Reid & Church 2015). Depending on the construction method adopted, ripraps can be classified as either dumped or placed (Ravindra et al. 2020). Dumped riprap comprises stones that are haphazardly deposited, whereas placed riprap involves arranging stones in an interlocking pattern (Hiller et al. 2018). Stone revetment offers flexible protection with self-healing capacity, low construction costs, long-lasting performance, and easy repair (Jafarnejad et al. 2017; Jafarnejad et al. 2019).

For designing riprap (stone revetment), several methods and codes are available such as IRC:89-1997 (1997), IS:14262 (1995), Hydraulic Engineering Circular No. 11 (Brown & Clyde 1989), Escarameia & May (1992), Pilarczyk (1990), Maynord et al. (1989), Maynord (1992), and Isbash (1935). All these methods considered mean flow velocity as the most important factor in determining the rock size for the protection of riverbanks. Water-level depletion, also called sudden drawdown, is also one of the causes of the failure of the riverbank (Kim et al. 2023; Zhou et al. 2023). Jamal et al. (2024) showed the importance of the drawdown and time on bank failure. Despite these valuable observations, a notable research gap remains. Specifically, there is a need to investigate the optimal size of stone revetment, the impact of drawdown, improvements in the vertical settlement of protected bank, the potential for shifts in failure locations, and the duration of protected bank exposure against the water level.

An attempt has been made to find out the optimal effective size of stone for different water exposure times and sudden drawdown. A total of 45 design experiments have been performed in the fabricated model. The percentage loss of the cross-sectional area of the most damaged section of the model bank and the percentage loss of stone revetment for different sizes and different periods were considered in this study.

Physical model tests of a riverbank were conducted in this study to examine the impact of the time and size of stone for effective protection under drawdown. The model bank was prepared with soil collected from Parlalpur ferry ghat on the river Ganga, Kaliachak, Malda district, West Bengal State, India. Gravity is a dominating factor in the modelling of riverbanks. Froude (F) similitude is suitable for the physical modelling of the riverbank. In their experimental study on the stability of riverbanks, Khatun et al. (2019) took a scale of 1:25. Jafarnejad et al. (2019) and Aziz & Islam (2023) took a scale range of 1:20 to 1:30, respectively. Considering these studies, a distorted scale of (linear) Lr = 1/200 and a (depth) of Hr = 1/20 were taken for the preparation of the bank model. The height of the bank at the selected site was 3.2 m. A bank height of 16 cm was kept in the model to simulate the 3.2 m height in the field. Other parameters of the model and prototype are mentioned in Table 1.

The soil was collected from the Parlalpur ferry ghat of river Ganga, Kaliachak, Malda district, West Bengal, India, for the preparation of the model bank. The soil collected from the riverbank site was air-dried and pulverized. The collected soil sample was characterized for index and engineering properties according to the procedure mentioned in different Indian Standards. All tests were conducted in the Geotechnical Engineering Laboratory of Aliah University, Kolkata, India.

Soil investigation reveals that the soil was silty clay. The index and engineering properties of the soil are tabulated (Table 2) (IS:2720-Part-1, 2, 3, 4, 5, 12, 17).

The aggregate was collected from the quarry. The detailed properties of the aggregate are tabulated in Table 3 (ASTM 1993, 2007; IS:2386 (1963)).

The data obtained by the series of experiments have been examined to find the influence of the size of the stone, drawdown, and water standing time on the model bank.

The study results provide valuable insights into the influence of stone size on the vertical settlement of the model riverbank. Notably, there is a clear relationship between stone size and the extent of vertical settlement, as shown in Figure 3. As the stone size increases, the vertical settlement of the bank decreases significantly, with settlements ranging from 32.3 mm for smaller stone sizes to 15.3 mm for larger stone sizes. This decrease represents a substantial reduction in vertical settlement, amounting to a 52.6% decrease. Additionally, an interesting pattern emerges in the data. There exists an optimal stone size of around 6.33 mm, at which the vertical settlement is minimized. Beyond this optimal size, further increases in stone size increase settlement. This pattern underscores the notion that simply using larger stone sizes does not guarantee optimal protection for the model bank. These findings highlight the importance of tailoring the choice of stone size to the specific characteristics of the soil and the intended purpose of the bank protection. It is not a one-size-fits-all solution, and an optimum stone size should be determined based on factors such as the type of soil and the environmental conditions. This insight is invaluable for engineering and design considerations in riverbank protection as it emphasizes the need for a customized approach in selecting the most effective stone revetment size to ensure the stability and protection of riverbanks.

With extended observation times of 30 and 45 min, the location of maximum vertical settlement shifted further from the toe, reaching 192.3 and 193.8 mm, respectively. These distances represented 33.3% and 32.8% of the total bank length. These results suggest that as water standing time increases, the point of maximum vertical settlement tends to move away from the bank's toe, with a relatively stable pattern emerging after the 30-min mark. Furthermore, the size of the stone influenced the shifting of the maximum settlement location from the bank's toe. As the stone size increased from 2.33 to 3.22, 4.58, 6.31, and 8.84 mm, the shifting of the failure location was observed at 120.1, 48, 72.1, and 96.1 mm, respectively. These findings highlight that a stone size of 4.58 mm appeared to be most effective in preventing the shifting of the failure location along the bank. In summary, Figure 5 illustrates how the maximum vertical settlement location changes relative to time and stone size. The results emphasize the influence of these factors on the stability and protection of the riverbank, with important implications for the design of revetment and strategies to prevent the shifting of failure locations.

Figure 6 illustrates the variation in the model bank's area loss across different water standing durations and stone sizes. The analysis reveals that employing solely large stone sizes does not effectively mitigate the model bank's failure. Therefore, determining the effective size and weight per unit area of the deployed stone is crucial before implementing bank protection measures. The graphical representation demonstrates a trend wherein increasing effective stone sizes corresponds to improved bank protection. Specifically, a 6.31 mm stone size consistently exhibits optimal performance across all standing times. Beyond this size, a decrease in effectiveness is observed, resulting in greater area loss for the bank and stone revetment. Initially, the bank possessed a cross-sectional area of 192 cm² and a surface area of 2,595.6 cm².

Using 2.33 mm stone initially resulted in a required weight of 2,413 g. Subsequent observations at 15-, 30-, and 45-min standing times revealed declining cross-sectional areas of 145.73, 127.20, and 123.61 cm², indicating area losses of 24.1%, 33.75%, and 35.62%, respectively. Correspondingly, stone losses were noted at 38.6%, 45.2%, and 46.2% for the 2.33 mm size and 15-, 30-, and 45-min durations. However, employing a 6.31 mm stone revetment demonstrated area losses of 7.2%, 7.9%, and 8.3%, with revetment losses of 12.2%, 14.3%, and 14.7% for the same time intervals. This optimal size notably safeguarded the bank area by 91%–93%, with minimal impact from varying water standing durations. Overall, the data underscore the significance of the 6.31 mm stone size, emphasizing its efficacy in protecting bank areas while exhibiting lower susceptibility to the effects of differing water standing durations.

The different profiles of the model bank before and after the experiment are shown in Figure 7. The bank profile of the model bank was measured with the help of a measuring gauge. Initially, the vertical rod of the measuring gauge was lowered down to determine the initial model bank profile. After the drawdown, the most damaged section of the model bank was located, and the measuring rod was lowered down to measure the deformation. The difference between the initial reading of the rod and the reading after the test gave the profile of the bank. It has been observed that the effective size (D10) of 2.33 mm shows failure from the crest of the model bank for time durations of 15, 30, and 45 min. The percentage area loss of the bank for a particular location was 24.10%, 33.75%, and 35.62%, respectively. The difference in area loss between 30 and 45 min of water exposure is not significant. The same pattern is observed for other sizes of the stone. As the size increases, the location of failure also shows a significant improvement in shifting towards the toe of the model bank (Jafarnejad et al. 2017, 2019). The effective size of 6.33 mm shows the maximum protection of the model bank in terms of area loss and stone revetment loss. The area and revetment losses for the size of 6.33 mm were less than 10% and 15%, respectively. Losses increase above the 6.33 mm size of stone in area and riprap.

In the present study, the stability of a stone revetment-protected model bank and the response against the different temporal variations were analysed. The outcome of this study may be recommended in field applications for the stable revetment for silt-dominated clay riverbanks or small pond banks. The principal findings are outlined below:

• (1)

  The study identifies 6.31 mm as the optimal stone revetment size for model bank protection in a laboratory-developed boundary condition. This size shows the minimum loss of revetment (12.2%–14.7%) and cross-sectional area loss (7.2%–8.3%). This finding indicates the critical role of precise stone-sizing in optimizing riverbank protection.

• (2)

  The study challenges the common fact that larger stones give good protection. Stones with an 8.84 mm diameter, compared with the optimal 6.31 mm size, exhibited reduced benefits, increased area losses, and more revetment dislodgment. This underscores the importance of careful stone selection, considering soil characteristics.

• (3)

  The maximum vertical bank settlement during various water exposure times reveals that after achieving full saturation, the substantial settlement variations cease. These findings offer valuable insights into the temporal dynamics of bank stability under real-world hydrological conditions, benefitting engineers.

• (4)

  During the drawdown, the dissipation of pore water pressure emerged as a key mechanism leading to bank failure. So, for designing any protection work, the synergetic impact of drawdown and velocity has to be considered.

All authors have read, understood, and have complied as applicable with the statement on ‘Ethical responsibilities of Authors’, as found in the Instructions for Authors.

This research received no external funding.

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

The authors declare there is no conflict.