The designed discharge in this study was derived from hydrological analysis of rainfall data over the past 10 years from 2013 to 2022. The data analyzed included the maximum daily intensity of rainfall data from six rainfall stations in the Konaweha Watershed, namely Lasusua, Latoma Tua, Abuki, Meluhu, Motaha, and Lambuya rainfall stations.

The use of rainfall data for hydrological analysis generally prefers records more than 10 years. However, according to the Indonesian National Standard (SNI 6728.1:2015), the minimum required data length for analysis is 10 years.

There are some approach could be used to estimate the precipitation averages over the catchment area. Each approach has its own advantages and disadvantages. The Thiessen polygons is one of the approach that commonly wide used to estimate specially for the large areas since it was proposed by bib14. However, bib15 simulated five approach of precipitation distribution based on recent development in information technology, particularly in GIS and concluded that this approach had the lowest accuracy since the polygons did not represent the actual pattern of precipitation. bib16 Examined Thiessen Linier Weighting, a new approach of thiessen polygon by adding liner line on the polygon as the weighting and concluded that this approach could improve the accuracy. Nevertheless, Thiessen polygons remain the popular method due to its practicality compared to others, especially for Indonesian hydrologists.

Figure 2 illustrates the map of the Konaweha Watershed, the positions of the rainfall stations, and the distribution of the influence areas of the rain stations based on Thiessen polygons. The maximum daily rainfall data, after being proportionally weighted with Thiessen coefficients, is presented in table 1.

The maximum daily rainfall data was analyzed for its distribution using four methods: Normal distribution, Log-Normal distribution, Log Pearson Type III distribution, and Gumbel distribution. Flood frequency analysis was conducted on these four distribution methods to predict the probability of designed rainfall based on return periods (T) of 2, 5, 10, 25, 50, and 100 years as shown in table 2.

The designed rainfall according to these four distributions was subsequently examined using the Chi-Square and Kolmogorov-Smirnov tests to assess the compatibility between the data distribution and the theoretical distribution. According to bib28, the most powerful tests for hydrological statistics are the Kolmogorov-Smirnov, Chi-Square, and Anderson-Darling tests, respectively. The test outcomes indicated that the Gumbel distribution emerged as the most suitable distribution, in line with the theoretical data trend. Then, the Gumbel distribution was analyzed to determine the designed discharge

bib17 And bib18 analysed design flood discharge by comparing several methods of Synthetic Unit Hydrograph (SUH), including Nakayasu, Snyder, SCS, Gama-1, and ITB-1, and concluded that the Nakayasu method was the most suitable method for watershed characteristics in Indonesia. Therefore, the design discharge in this study was calculated using the Nakayasu Synthetic Unit Hydrograph. The multiplication coefficient (C) used was 0.5 (hilly forest), and the effective rainfall distribution employed the Mononobe formula. Figure 3 illustrates the designed flood discharge hydrograph for return periods of 10 years, 25 years, and 50 years.

The designed discharge data used for groyne design is 3638.29 m3/s, a maximum discharge of a 50-year return period. This data also serves as the initial condition on the downstream side of the mathematical modeling.

The design of permeable pile groyne in this study adheres to the Indonesian National Standard (SNI), which outlines the standards for designing concrete pile groyne in rivers. According to this standard, groyne must be both structurally and hydraulically stable and safe. Hydraulically, it must withstand scouring, collisions with floating objects, hydrodynamic pressure, and the pressure of transported material. Structurally, it must resist overturning, strain, and stress from lateral forces such as velocity and deposition load. This standard advises the distance between each pile should be 2 to 5 times the diameter or dimension of the pile, with the distance decreasing nearer to the riverbank. The groyne's top elevation is set to be the same as the water level during flood conditions. Additionally, it recommends that one row on each pile group be connected with a beam, and one additional pile be installed perpendicular to the last pile to support the stability of the structure.The designed discharge data used for groyne design is 3638.29 m3/s, a maximum discharge of a 50 year return period. This data also serves as the initial condition on the downstream side of the mathematical modelling.

Several primary data were obtained through surveying and investigation by the author and team, including soil conditions examined using the boring log process, topography and bathymetry data. The proposed pile groyne in this study is square-shaped with the following dimensions as shown in table 3.

The groyne design is illustrated in the following figure 4

A two-dimensional mathematical flow model was conducted numerically using the NAYS-2D module of the IRIC (International River Interface Cooperative) Application developed by Professor Yasuyuki Shimizu (Hokkaido University) and Dr. Jonathan Nelson (USGS) in 2007. The IRIC Application is a numerical modelling tool that employs finite difference methods and uses boundary-fitted coordinates within general curvilinear coordinates. The governing equation used in this model are:

- Continuity equation

- Momentum equation

in which,

Where,h is water depth, t is time, u ; v are depth averaged velocities in x and y directions, g is gravitational accelerations, H is water depth, ; are components of shear stress in river bed in x and y directions, Fx ; Fy are components of drag force by vegetation in x and y directions, is drag coefficient of the bed shear stress, is eddy viscosity coefficient, is drag coefficient of vegetation, is area of interception by vegetation per unit volume, and is minimum value of water depth and height of vegetation.

Figure 5 illustrates the grid that serves as the domain for modeling. The y-direction grid is denoted by j, and the x-direction grid is denoted by i. The grid size in the y-direction is represented by dj, and the grid size in the x-direction is represented by di. The average width of the river is 75 meters, however to accommodate erosion locations in the river bend, the domain width for simulation was set to 100 meters, with a total of 150 grid cells in the y-direction, resulting in dj being 0.667 meters. Meanwhile, for the x-direction, the number of grid cells was set to 500, with di being 0.989 meters, resulting in a domain length of 494.828 meters in the x-direction.

To analyse the flow patterns, observation positions are applied along the length of the river at grid j24 (cutting through the middle of the groyne), j49 (at the end of the groyne), and j86 (in the mainstream of the river). Meanwhile, observations on the cross section of the river are made at grid i208 (before the groyne), i302, i338 and i400 (between the groyne).

In this study, flow stratification due to sediment concentration was not considered in the numerical simulations. The flow was assumed to be well-mixed and vertically homogeneous. However, in rivers with high flow magnitude and greater depth, vertical variations in sediment concentration may lead to flow stratification. Under such conditions, the assumption of a fully mixed flow may not accurately represent real hydraulic behavior, and this aspect should be further examined in future studies. Moreover, a rigid (fixed) bed condition was assumed, and local scour around the groyne piles was not modeled. This assumption was applied to focus on the hydrodynamic response and flow patterns induced by the permeable groyne

Before applying the mathematical model, it was necessary to ensure the validity of the results. Since the experimental case is not yet available for this study, the results were verified and evaluated by comparing them to recorded empirical result and previous similar study. Figure 6 show simulation result of depth and water surface elevation before the groyne was installed.

The water surface elevation averages 59.547 meters above mean sea level (MSL) for a discharge of 3638.29 m³/s, as shown in figure 8. This elevation is identified as the flood elevation. A measured data survey was set up for comparison. Figure 7 shows a photo taken during the flood conditions recorded in 2018, with the measured surface elevation at about 58.758 meters (1.322 meters below the existing road elevation of 60.081 meters). The comparison between the simulation results and the measured data survey from 2020 shows an accuracy of 98%. It can be confirmed that the flood that occurred in 2020 had a 50-year return period. A similar study conducted by bib19 on the same location of the Konaweha River found a flood water surface elevation of about 58.38 meters above mean sea level for a 25-year return period.

Figure 9 illustrates the longitudinal profile of the river showing the simulated water surface elevation at positions j24 (near the riverbank/cutting through the groyne), j49 (at the end of the groyne), and j86 (in the mainstream).

One of the phenomena that occur at river bends is the tilting of the water surface elevation in the transverse direction of the river, commonly known as superelevation. In this phenomenon, the water surface rises on the outer side of the bend while it decreases on the inner side. The main causes are the centrifugal force that deflects water particles and the distribution of vertical velocity within the channel. bib20 Stated that the primary cause of the spiral flow phenomenon is friction on the channel walls, which results in higher velocity near the center compared to near the walls. The centrifugal force around the bend produces a unique effect, causing the water level to rise on the outer part of the bend while it lowers on the inner part (superelevation). Simulations in this study indicate the occurrence of superelevation at the river bend. Figure 10 illustrates the difference in water surface elevation at the curved positions.

Based on the simulation results, it is known that under existing conditions, with an average flow velocity of 6 m/s (designed flood discharge with a 50 year return period), there is a change in elevation (superelevation) of the water surface in the transverse direction of the river. The elevation on the outer side of the river increases by an average of 0.50 m, while the elevation on the inner side decreases by an average of 1.5 m under existing conditions. However, the installed groyne could reduce the superelevation effect. The increase in water surface elevation on the outer edge averages only about 0.20 m, and the elevation on the inner side decreases by an average of 1 m. This is due to the reduced flow velocity on the outer edge caused by the presence of groyne.

The installation of the groyne alters the local flow field, which leads to changes in hydraulic gradients and the energy grade line (EGL) along the channel. The groyne increases flow resistance near the structure, resulting in a localized rise in water surface elevation upstream and a steeper hydraulic gradient in the vicinity of the groyne. Downstream of the structure, a gradual recovery toward the original gradient occurs. The energy line follows a similar pattern, reflecting the increased head loss induced by flow contraction and turbulence around the groyne. These results illustrate the influence of the groyne on channel hydraulics and highlight the importance of considering energy dissipation and slope adjustments in river training works. Moreover, another issue that needs to be evaluated in the next study is the bed variation along the bend and local scour around the groyne.

Groyne failures, particularly due to local scour, have been extensively studied. Laboratory tests conducted by bib21 examined local scour around groyne with both fixed and movable beds, revealing that the scour area was greater for impermeable groyne compared to permeable ones. Increased permeability generally resulted in a decrease in the scour area. bib22 Investigated numerically bed deformation around groyne. According to bib23 groyne failure due to local scour is influenced by temporal and maximum erosion depths, flow patterns, and other parameters such as groyne geometry including size, shape, and angle with respect to approach flow.

The erosion of riverbanks generally occurs as a result of the riverbank being eroded by the forces caused by the river flow. This most commonly occurs at bends in the river because the centrifugal force at the bend will cause the emergence of cross-stream currents, which together with the main flow will form helical flow, namely the spiral movement of river water and creating secondary velocity, causing erosion of the outer bank of the river and deposition on the inner bank. According to bib24, the magnitude of this cross-stream velocity ranges from 10% to 15% of the velocity of the main flow. bib25 Conducted physical modelling of river bend scour, changes in riverbed topography occur where there is shallowing on the inner side of the bend and scouring on the outer side.

The simulation results in figure 11. Show a secondary velocity occurred in the form of vortices at the outer edge of the river bend. This is what causes erosion at that location. The flow velocity reaches 4 m/s during maximum discharge (50-year return period flood conditions) at the bank. bib26 Stated that the velocity distribution at river bends is significantly influenced by the bend radius. The higher the flow velocity, the more gradual the formation of river bends (erosion process). This secondary velocity decreases as the bend radius increases.

The width of the groyne used in this study is 0.4 m and the spacing between the piles are 1.5 m, resulting in a groyne permeability of 75%. bib27 Investigated experimentally the effects of permeability and length of groynes on riverbank erosion. The froude number and percentage of permeability have the highest impact on relative changes in the riverbank. With an increase in the froude number, the relative bank retreat increases. Similarly, increasing permeability leads to an increase in relative riverbank retreat.

The installation of groyne can reduce the flow velocity at the outer bend of the river. Simulation results shows that the flow velocity at the edge of the river bend can be reduced. However, secondary velocities still occur at a relatively slower magnitude due to the presence of the groyne. Figure 12 illustrates the simulation results of flow vector in existing condition and after the groyne were installed.

Figure 13 shows that during the flood discharge (50-year return period), the averaged flow velocity of the river in the mainstream is about 6 m/s. The installation of groynes on the outer bend of the river can reduce the flow velocity in this area. Simulation results indicate that the flow velocity at cross-section i302 (between groyne no.2 and no.3) can be reduced by 73% from an initial average velocity of 2.5 m/s to an average of 0.68 m/s. The flow velocity at cross-section i338 (in the middle of the river bend, between groyne no.3 and no.4) can be reduced by 74% from an initial average velocity of 2.8 m/s to an average of 0.95 m/s. The flow velocity at cross-section i400 (between groyne no.6 and no.7) can be reduced by 50% from an initial average velocity of 2.2 m/s to an average of 0.94 m/s.

Permeable groynes are designed to allow partial flow and sediment passage; however, gradual sediment deposition between pile gaps may occur over time. Sediment accumulation can reduce the groyne's permeability and alter local flow patterns, potentially shifting hydraulic performance closer to that of impermeable structures. Routine monitoring and periodic removal of deposited sediment or debris are therefore recommended to maintain hydraulic efficiency.Permeable groynes also represent a practical and economical riverbank protection solution, particularly suited for rural and developing regions with limitations budget. Unlike impermeable groynes, permeable groynes rely on simple installation techniques, require minimal heavy construction equipment, and can utilize locally sourced materials such as timber piles, logs, bamboo, etc. This not only reduces material and transportation costs but also promotes community participation in construction and maintenance activities. Despite their cost-efficiency, permeable groynes can effectively reduce flow energy, redirect near-bank currents, and reduce local scour, thereby stabilizing the riverbank and supporting long-term channel morphology improvements. Consequently, permeable groynes provide an accessible and scalable solution for flood-prone and erosion-vulnerable regions, contributing to sustainable and community-driven river management and infrastructure development initiatives.

Permeable groynes also present broader prospects as a technically and environmentally sustainable alternative for river training applications. Their ability to allow water and sediment to pass through the structure prevents sharp flow concentration and avoids major hydraulic disturbances that can occur with impermeable-type groynes. This characteristic reduces flow velocity near the bank while minimizing excessive deflection toward the main channel, thus lowering the risk of bed degradation, secondary circulation, and unwanted erosion on the opposite bank. In addition to reduced construction costs, permeable groynes often require lower maintenance budget. Their open structure supports aquatic habitat connectivity, preserves sediment continuity, and encourages natural deposition patterns that gradually enhance riverbank stability. Given these hydraulic, economic, and ecological benefits, permeable groynes are particularly advantageous for rivers with diverse hydrodynamic characteristics and in developing regions seeking robust yet affordable river training solutions. By aligning structural performance with environmental functionality, permeable groynes contribute to a more integrated and nature-based river engineering approach.

In addition to the technical feasibility, the implementation of permeable pile groynes demonstrates a favorable Budget–Cost Ratio when compared to the potential economic losses caused by riverbank erosion and flood-related disasters. In many rural and developing regions, the economic impact of riverbank failure—including damage to local infrastructure, disruption of transportation routes, reduction in property value, and community displacement often exceeds the available budget for structural mitigation. When evaluated against avoided economic losses and long-term benefits, the cost-effectiveness of permeable groynes becomes evident. As a result, this approach provides a rational and economically viable strategy for risk reduction, optimizing limited public investment while safeguarding livelihoods and minimizing long-term socio-economic impacts in hazard-prone river corridors.