Hybrid SPH and Experimental Modeling for Stability Evaluation of a Floating Portable Toilet in Flood-Prone Environments

Flooding is one of the most frequent hydrometeorological disasters in various regions of Indonesia, particularly in areas with high rainfall intensity, lowland topography, or inadequate drainage systems [1, 2]. The impacts of flooding extend beyond material losses, infrastructure damage, and disruption of community activities; they also pose significant public health risks due to deteriorating sanitation conditions.

In emergency flood situations, conventional sanitation systems such as permanent toilets become unusable due to inundation, structural damage, or loss of access [3]. This increases the risk of waterborne diseases such as diarrhea, leptospirosis, and skin infections [4-6]. Therefore, emergency sanitation solutions capable of operating effectively in flood-affected areas are urgently needed, one of which is the use of floating portable toilets (FPTs).

The concept of an FPT combines portability with buoyancy, enabling its use even when land-based infrastructure is non-functional. While this idea offers a practical solution, its primary challenge lies in ensuring structural stability under dynamic flood currents and wave conditions. Instability may compromise user comfort, increase the risk of capsizing, and pose safety hazards. Thus, stability assessment becomes a critical aspect prior to field implementation [7, 8].

Previous studies on floating structures have primarily focused on boats, pontoons, or floating platforms, emphasizing hydrostatic analysis and hydrodynamic behavior rather than sanitation-specific applications such as floating toilets. Research on hydrostatic stability of pontoons and floating structures often employs classical hydrostatic analysis and GZ curve evaluation for initial stability assessment [9].

Additionally, experimental and numerical investigations into dynamic motion and hydrodynamic responses of pontoons under wave, wake, and current conditions are essential for determining hydro-elastic coupling in floating structures [10]. Alternatively, particle-based or mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) have gained attention for their ability to simulate highly nonlinear free-surface flows, breaking waves, and strong fluid structure interactions (FSIs). SPH has been validated through numerical and experimental studies for semi-submersible and pontoon applications [11].

Important studies have also been conducted in Japan on operational safety and comfort limits [12]. On the numerical side, grid-based Computational Fluid Dynamics (CFD) and FSI methods are widely used to model FSIs in floaters and offshore platforms, particularly in the context of floating offshore wind turbines (FOWTs). Recent reviews highlight the critical role of CFD/FSI in addressing flow complexity, nonlinear wave behavior, and highlighting sanitation challenges in post-disaster evacuation centers, where damage to basic infrastructure, such as water supply, drainage, and waste treatment, hinders survival and recovery.

One innovation developed is a mobile flush toilet that provides sanitation services equivalent to permanent toilets without relying on existing infrastructure. This technology has been deployed in three flood response operations in Japan and installed on islands and public areas as a sustainable solution to daily sanitation challenges. The implementation of mobile flush toilets has proven effective in enhancing disaster-resilient infrastructure while preserving user dignity, health, and safety in emergencies [13].

A highly relevant study in Indonesia focused on estimating clean water requirements and wastewater treatment systems for FTP in flood-prone areas. The study employed qualitative analysis of water and waste systems along with analytical calculations to determine water demand. It demonstrated that FTP could serve as an environmentally friendly sanitation solution in inundated regions, while also promoting sustainable technology development. Although the study shares the same object of interest, its focus was on water and waste system design rather than structural stability under flood conditions [8].

The novelty of the present study lies in the integration of numerical SPH methods with laboratory-scale experimental testing to evaluate the stability of FTP under flood conditions. The SPH method, as implemented in the DualSPHysics software, enables simulation of free-surface fluid phenomena with complex geometries and strong fluid–structure interactions [14]. Unlike grid-based CFD, which faces limitations in modeling extreme free-surface deformations, SPH is mesh-free and capable of realistically representing irregular waves and multiphase interactions [15].

This approach offers advantages over previous methods that relied solely on hydrostatic analysis or single-mode numerical simulations. By combining SPH simulation with experimental testing, direct validation can be achieved, resulting in more reliable outcomes.

Furthermore, testing under flood conditions with varying wave heights, wave periods, and current velocities will generate a comprehensive dataset for developing safer and more user-friendly designs. The objective of this study is to verify and compare simulation results through physical testing in a hydraulic laboratory against numerical modeling outcomes. The findings will likely contribute to the development of effective, safe, and widely applicable emergency sanitation solutions for disaster-affected regions.

3.1 Physical model testing

Prior to conducting the physical model tests, several preparations were required. To generate waves within the flume, appropriate amplitude and frequency configurations were needed for the wave generator setup. Preliminary trials were conducted to determine the configuration that matched the target wave conditions for testing. The final wave configuration obtained from instrument calibration is presented in Table 4.

Table 4. Instrument test results for wave generator settings

The next stage involved the installation of the model and loading system. During the installation process, the model nearly capsized several times due to stiffness in the connecting rope. At this stage, testing of the effective rope length was carried out. The first trial used a connecting rope with a length of 90 cm (Figure 2(a)). Under 5 cm wave conditions, the rope stiffness remained within a normal and safe range. However, when tested under 10 cm wave conditions, the rope became rigid and caused the model to overturn. A second trial was conducted using a 110 cm connecting rope (Figure 2(b)). The results of the second trial showed that the 110 cm rope was effective in maintaining model stability without significant stiffness, thereby allowing unobstructed movement of the model during analysis.

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(b)

Figure 2. Testing of effective connecting rope length for the model: (a) rope length 90 cm, (b) rope length 110 cm

3.2 Model stability simulation

Model stability simulations were conducted using four scenarios: HKG, HPG, VKG, and VPG, as described in Table 3. The simulation results provided values for surge (translational movement), pitch (rotational movement), and heave (vertical movement) under two wave directions: horizontal (HKG and HPG) and vertical (VKG and VPG). The simulation outcomes for both directions are presented in Table 5. Based on the comparative results, both numerical and experimental tests consistently indicate that the portable floating toilet remains stable and safe, even when subjected to wave conditions ranging from mild to extreme, under both minimum and maximum loading scenarios.

Table 5. Comparison of numerical and experimental simulation results

3.3 Response Amplitude Operator (RAO)

The RAO analysis was conducted to normalize the data, enabling a clearer comparison of the dynamic behavior between the two sets of results. The RAO analysis results are tabulated in Table 6. These results are further illustrated as comparative curves shown in Figure 3. Figure 3 presents the RAO curve comparisons for heave (Figure 3(a)), pitch (Figure 3(b)), and surge (Figure 3(c)) between experimental testing and numerical simulation based on SPH.

Table 6. Analysis of the RAO

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Figure 3. RAO analysis, (a) heave, (b) pitch, and (c) surge

In the heave mode, the quantitative discrepancy indicates a tendency for underprediction in the SPH model, where the numerically computed vertical response is lower than the actual response measured in the laboratory. This condition may be attributed to several factors, including relatively high numerical damping due to artificial viscosity settings, insufficient particle resolution to capture fluid–structure interactions accurately, or minor differences in boundary representation and model geometry between the simulation and physical testing.

Nevertheless, the numerical curve still exhibits a response amplification pattern at mid-range frequencies that resembles the experimental trend. This suggests that the SPH model has captured part of the dynamic characteristics of the structure under wave loading. Similar findings have been reported in studies involving SPH modeling of floating structures such as FOWTs, where validation against experimental data showed good consistency—but only after careful calibration of parameters such as mooring and numerical viscosity [35].

In the pitch response, a relative discrepancy is also observed, with the experimental RAO exhibiting a sharp peak, while the numerical simulation produces a broader and more flattened curve. This likely reflects the sensitivity to moment of inertia and the influence of hydrostatic restoring forces, which the numerical model may not fully capture. A parametric approach combined with mooring coefficient tuning has proven effective in reproducing pitch RAO trends in spar-type floating structures, where such calibration helps compensate for inaccuracies in inertia estimation and flow assumptions within potential theory [36, 37].

Unlike the other two modes, the surge response shows the largest amplitude deviation between experimental and numerical results, particularly at mid to high frequencies. Nevertheless, the fluctuation pattern at low frequencies still exhibits a similar shape, indicating that the SPH model has limitations in accurately representing horizontal translational dynamics across the full frequency range. This significant discrepancy may be attributed to the surge mode's sensitivity to boundary conditions, viscous drag representation, and more complex wave–body interactions in the lateral direction [38, 39].

Overall, the consistent quantitative differences, especially the tendency for amplitude underprediction, are likely caused by SPH parameter settings such as artificial viscosity, particle spatial resolution, and suboptimal boundary condition representation. However, the similarity in RAO curve trends suggests that the core model adequately captures the structure's dynamic characteristics. As illustrated in the aforementioned FOWT study, a more accurate representation of mooring dynamics and surrogate parameters such as moment of inertia is crucial for reducing numerical discrepancies in RAO predictions [35].

Therefore, further calibration efforts on the SPH model are strongly recommended, including adjustments to numerical viscosity, enhancement of particle resolution, and refinement of boundary conditions, to achieve better quantitative agreement with experimental data. With sufficient validation and calibration, the SPH model holds significant potential as a reliable predictive tool for studying equilibrium and dynamic responses of floating structures even under more complex wave conditions and supports practical applications in advanced marine engineering.

3.4 Percentage difference in amplitude (ΔA%)

The amplitude difference (ΔA%) was calculated to quantify the relative error between numerical simulation and experimental results. The computed values are presented in Table 7. The comparison results indicate that ΔA% for heave is predominantly negative across all test scenarios, suggesting that the numerical response (SPH) tends to underpredict the experimental data. This pattern is consistent with previous SPH validation studies for floating structures, where artificial viscosity often contributes to increased effective damping, resulting in lower computed vertical motion amplitudes compared to physical measurements unless dissipation parameters and particle resolution are carefully calibrated. Recent literature highlights that dissipation scheme settings in SPH directly affect wave energy attenuation and response peaks, making RAO curves and derived metrics such as ΔA% highly sensitive to these parameter choices [39].

Table 7. Percentage difference in amplitude (ΔA%)

For pitch, ΔA% exhibits wider variation, with instances of overprediction (positive ΔA%) at lower amplitudes, shifting toward underprediction at higher amplitudes. This behavior is common when the effective moment of inertia, hydrostatic restoring stiffness, and wave structure coupling are not fully represented in the numerical model. Comparative studies on modern floating structures report that reproducing sharp RAO pitch peaks near resonance frequencies typically requires calibration of stiffness and mooring components, or hybrid modeling approaches to prevent numerical amplitude flattening. This trend aligns with the observed ΔA% sign shifts across excitation levels, indicating high sensitivity of rotational modes to model parameters [40, 41].

Unlike the heave mode, which shows the most consistent pattern, surge yields the largest ΔA% values across most frequency ranges, indicating significant amplitude discrepancies relative to experimental results. Nevertheless, at low frequencies, the surge still displays a replicable trend in SPH simulations, consistent with the nature of longitudinal translation being more directly influenced by linear wave forces.

These quantitative differences are likely affected by damping representation and boundary condition settings in the numerical model. Several experimental–numerical studies on floating platforms have found that surge and heave responses can achieve good agreement after tuning damping and mooring characteristics, which is reflected in a systematic reduction of ΔA% values relative to experimental data [38, 39].

Methodologically, ΔA% calculations should be performed for both test types. According to ITTC documentation [23], quantifying test uncertainty and ensuring transparent numerical–experimental validation practices, including reporting relative errors or percent differences per test condition, is essential. Based on these guidelines, small and consistent ΔA% values across conditions are more meaningful than coincidental matches at isolated points; conversely, large and systematic ΔA% values (e.g., consistently negative across all levels) indicate model bias that should be addressed through calibration of dissipation parameters, particle resolution, and boundary condition alignment [42].

The practical implications of ΔA% observations are as follows: the dominance of negative ΔA% in heave and surge suggests a conservative bias, where the numerical model tends to underestimate responses. While this may be acceptable for preliminary studies, it risks obscuring peak loads in limit-state design applications.

Meanwhile, the variability of ΔA% in pitch underscores the need for multi-level calibration: (i) adjusting numerical viscosity and particle spacing to reduce over-damping, (ii) refining mooring representation and inertia properties to preserve RAO peak sharpness, and (iii) re-verifying wave condition equivalence between test facilities and numerical domains. Previous studies on wave energy devices and floating wind platforms have shown that after implementing these steps, amplitude agreement assessed via RAO and derived metrics improves significantly relative to experimental data [35, 43].

To put the relative amplitude differences (ΔA%) obtained in this study into context, it is important to consider typical error levels reported in the literature on motion response predictions. Experimental uncertainty analyses in seakeeping tests have demonstrated that, under controlled laboratory conditions, expanded uncertainty in RAO measurements for heave and pitch motions can be quite small: heave RAO measurements often exhibit uncertainties below 3% and pitch RAO uncertainties below 1% at a 95% confidence level when standardized procedures are applied.

These narrow uncertainty bounds reflect the precision achievable in high-quality experimental facilities and provide a benchmark for understanding the measurement error inherent in physical tests [44].

Comparatively, the ΔA% values obtained in the present work span a wider range: for heave, ΔA% varies between 72.64% and -39.25%; for pitch, ΔA% ranges from -69.81% to 55.44%; and for surge, ΔA% ranges from -92.59% to 35.75%.

The magnitudes of these differences exceed typical experimental measurement uncertainty and are comparable to, or larger than, motion prediction errors reported in comprehensive validation studies for seakeeping and motion response modelling, where average errors in motion amplitudes relative to experimental data have been reported on the order of tens of percent across different methods and conditions.

This comparison highlights a common characteristic of numerical predictions of motion in complex fluid–structure interaction problems: while numerical methods can capture overall trends in motion response, quantitative discrepancies with experimental results often arise from limitations in modelling damping, viscous effects, and boundary conditions. Within this context, the ΔA% values for heave and pitch indicate areas where the current SPH model may benefit from further refinement, whereas the relatively narrower ΔA% observed in some surge conditions suggests that longitudinal motion predictions may be less sensitive to certain aspects of model configuration under specific test conditions. Collectively, these comparisons provide a meaningful assessment of the current model’s performance and clearly identify specific motion modes for targeted improvement in future work.

3.5 Applicable scope of the model

The applicability of the proposed SPH model is currently confined to the range of working conditions investigated in this study. The model has been validated under regular wave excitation at laboratory scale, with fixed geometric configuration and mooring arrangement. Within this scope, the SPH model demonstrates consistent capability to reproduce the heave response of the FTP, as indicated by the similarity in RAO trends across the tested frequency range.

For the pitch motion, the model captures the general response pattern; however, noticeable amplitude discrepancies are observed at certain frequencies, suggesting sensitivity to rotational dynamics and to the damping representation. The surge response shows the largest deviation from experimental results, particularly at medium to high frequencies, suggesting that the current SPH configuration is less reliable for accurately predicting longitudinal motion under these conditions.

Accordingly, the current model is most applicable for preliminary stability and motion assessments of FTP subjected to regular waves with small to moderate amplitudes. Its application to irregular wave conditions, extreme wave environments, or full-scale scenarios should be approached with caution, as these conditions have not been explicitly validated in the present study. Further model refinement and additional validation are required before extending the model to broader operational conditions.