Adaptive multihazard modeling predicts rainfall-driven dam failure: a case study

Abstract

The safety of earth-rockfill dams during construction is critically challenged by transient hydrological loads and evolving boundary conditions. While numerical and data-driven models exist, their standalone application is limited; the former is computationally prohibitive for real-time forecasting, and the latter often lacks physical interpretability. To bridge this gap, we introduce a novel hybrid framework that tightly couples Finite Element analysis (FEM) with deep learning (ANN-LSTM) for the physics-constrained forecasting of rainfall-induced instability. The model leverages FEM to simulate the hydro-mechanical response, the LSTM to capture temporal patterns in monitoring data, and an ANN to map strength degradation, with an attention mechanism identifying critical antecedent failure sequences. Validated on a two-year monitoring dataset from the Megech Dam, which experienced documented instabilities, our framework significantly outperformed established baselines. It achieved a superior MAE of 0.027 (vs. 0.081 for SVM, 0.067 for Random Forest, and 0.052 for standalone LSTM, p < 0.05) and provided an early-warning lead time of up to 3.5 weeks by identifying the critical lag between rainfall peaks and pore-pressure buildup. The integrated attention mechanism autonomously highlighted weeks 25–30 and 75–80 as high-risk periods, aligning with field observations. This work demonstrates that a physics-informed hybrid approach offers a more reliable and interpretable tool for early-warning systems than purely data-driven methods. The proposed framework is adaptable to other earth-rockfill dams, providing a pathway from reactive monitoring to proactive risk management during critical construction phases.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-36927-y.

Introduction

Ensuring the stability of earth-rock dams during construction remains one of the most challenging problems in geotechnical engineering. Unlike completed structures, partially built dams are continuously exposed to evolving boundary conditions—unconfined geometry, incomplete drainage systems, weakly compacted lifts, and rapidly changing hydraulic loads during rainfall seasons. These conditions create a transient, multi-hazard environment where seepage, loss of suction, strain softening, and progressive failure can occur long before reservoir impoundment. Traditional finite-element modelling (FEM) can reproduce such mechanisms, but deterministic simulations require frequent recalibration and become computationally prohibitive when hydro-mechanical inputs vary weekly or even daily during construction¹.

Conversely, data-driven models such as artificial neural networks (ANNs) and long short-term memory (LSTM) networks have shown strong potential in structural health monitoring and time-series forecasting. However, their performance is often constrained when datasets are short, sparse, or influenced by complex physical processes—conditions typical of dam construction. Purely data-driven models also lack physical interpretability and may learn spurious correlations, raising concerns for safety-critical decisions. Existing hybrid approaches attempt to combine physics and machine learning, yet most focus on long-term reservoir operation, rely on simplified hydraulic loading, or do not explicitly address the highly transient instability mechanisms that occur during staged construction^{2, 3}.

A critical gap therefore remains: there is no existing framework that provides real-time, physically consistent forecasting of rainfall-induced seepage instability during the construction phase of earth-rock dams, when the structure is most vulnerable and monitoring data are most limited.

To address this gap, this study proposes an Adaptive Multi-Hazard (AMH) hybrid modelling framework that tightly couples physics-based FEM analysis with deep-learning components. The novelty of the proposed framework is threefold; where a novel hybrid framework addresses construction-phase dam safety by modeling transient rainfall-pore pressure-strength degradation interactions. The physics-regularized approach combines ANN-LSTM temporal learning with FEM-derived hydro-mechanical constraints to ensure physical consistency. Integrated attention mechanisms provide interpretable forecasting by identifying critical failure precursors, enabling actionable early warnings for dam safety operations.

The proposed framework is validated using two years (104 weeks) of monitoring data from the Megech Dam construction site, where rainfall-induced instabilities and local sliding were documented between 2020 and 2021. By benchmarking the hybrid model against standalone FEM and pure data-driven approaches, we demonstrate substantial gains in predictive accuracy, early-warning lead time, and physical consistency.

This work introduces a practical and interpretable early-warning system for rainfall-driven failures during dam construction—transitioning safety management from reactive response toward proactive, physics-guided forecasting.

Study area and geotechnical characterization

Location and topography

The Megech Dam is a zoned earth-rock dam located in Ethiopia’s North Gondar Zone (12.62°N, 37.45°E). It was designed in 2013 to store 185 Mm³ of water for irrigation (17,000 ha), municipal supply, and fisheries development. By 2022, only 500 m of the planned 890 m crest had been completed, leaving a 390 m opening to allow uninterrupted flow of the Megech River and prevent premature impoundment. The watershed location is shown in Fig. 1a.

Fig. 1.

(a) The megech river water shed and location of the study area https://link.springer.com/article/10.1007/s13201-025-02571-6/figures/1. (b) View of the river at the proposed dam site prior to construction. (c) Dam’s Contour map as Depicted by Auto Cad.

The dam foundation is situated in a river-valley setting composed of layered alluvium consisting of clay, silt, gravel, cobbles, and boulders. The abutment zones consist primarily of basaltic rock overlain by silty-clay deposits with gentle to moderate slopes. The pre-construction condition of the river channel is illustrated in Fig. 1b.

Between 2020 and 2022, significant slope failures occurred along chainage 0 + 420 to 0 + 640. These failures were driven by seasonal moisture variation, inadequate drainage, and insufficient reinforcement during the staged construction. The contour configuration of the partially completed dam is shown in Fig. 1c.

Based on the as-built surveys and design drawings, the dam’s geometric parameters were determined and verified. The methodology, has involved reviewing design drawings, collecting topographic elevation data, and conducting post-construction surveys.

Dam geometry and 3D terrain reconstruction

Design drawings, as-built survey records, and total-station measurements were integrated to establish and verify the geometric configuration of the dam during the construction period. All raw survey points were imported into Python for preprocessing, which included outlier removal, coordinate standardization, and spatial filtering to ensure consistency across datasets. Table S1 explains the precise process for correcting the dam shape and associated software.

The processed survey data were then used to construct a high-resolution 3D Digital Elevation Model (DEM) of the dam foundation and partially completed embankment. Terrain reconstruction was performed using a Triangulated Irregular Network (TIN) approach, allowing detailed representation of slope gradients, surface irregularities, and geomorphic transitions. This framework enabled accurate visualization of spatial point density, crest alignment, abutment geometry, and localized depressions.

The reconstructed terrain played a critical role in identifying potential failure surfaces. Depressions and weak geomorphic zones observed in the DEM—particularly those corresponding to historical ponding during the rainy seasons—aligned with field-mapped infiltration paths and zones of elevated saturation. These features provided early geometric indicators of preferential seepage routes and foundation softening, which were subsequently incorporated into the hydro-mechanical FEM analysis Fig. 2a and b.

Fig. 2.

(a) Spatial distribution of survey points and (b) triangulated irregular network.

Regional geology

The project area is underlain by the Tarmaber Basalt, which overlies the older Ashangi Basalt formation. The Ashangi Basalt shows deep weathering, whereas the overlying basaltic units retain higher strength and reduced permeability. The reservoir basin comprises basalts, volcanic tuff, paleosols, and alluvial deposits, producing an overall water-tight profile due to the substantial clay and silt layers.

Structural features include N–S, NNW–SSE, and E–W oriented joints and fractures that influence seepage pathways and local stability.

Of particular concern is the right abutment, where steep, weathered basalt slopes become friable under saturation and may experience reduced shear strength during peak hydrological events or seismic excitation.

Construction-phase failures and hydrological triggers

Prolonged geotechnical, contractual, and financial delays left the Megech Dam in a partially completed state for several years. Between 2020 and 2022, recurrent slope instabilities developed along the constructed section of the dam—particularly between chainage 0 + 420 and 0 + 640—where the clay core and embankment shell experienced pronounced sliding and deformation (see Supplementary Fig. S1).

These failures were strongly linked to two consecutive years of unusually high rainfall. The 2020 rainfall season induced upstream ponding that saturated the foundation and allowed spring water to infiltrate the clay core. Because the terrain was undrained and partially confined by a temporary protective dyke, the infiltrating water accumulated rather than dissipating, progressively weakening the central core.

The 2021 hydrological conditions were even more severe. Increased spring discharge from the left abutment, combined with higher seasonal rainfall, caused renewed ponding and deeper saturation of the clay fill. This led to intensified erosion, the formation of tension cracks, and further slope instabilities. The most significant crack—extending from chainage 0 + 430 to 0 + 530—reached its maximum width near Ch. 0 + 430, where its size approached the basal width of the central core itself (Fig. 3a).

Fig. 3.

Manifestation of 2021 hydrological extremes on dam (a) Major tension cracking at Ch. 0 + 430-0 + 530, (b) infiltration paths from upstream ponding near Ch. 0 + 620, (c,d) Composite slope failures and a 24 m translational block slide observed between 2020–2021.(Photograph by Mr. Eyoel Netserte, reproduced with permission under CC BY 4.0).

A decade-long rainfall record from the dam site indicates a marked rise in annual rainfall intensity starting in 2019, peaking in 2021 during construction. The alternating wet–dry cycles during this period contributed to rill erosion on the downstream slope and progressive weakening of the upstream shell. Water from a natural upstream pond located between Ch. 0 + 500 and 0 + 640 infiltrated beneath the core, creating weak zones and discharge paths observable near Ch. 0 + 620 (Fig. 3b).

The combined manifestation of ponding, infiltration, tension cracking, and slope failures observed including 24 m translational block slide across 2020–2021 is illustrated in Fige 3(c–d). Although no catastrophic breach occurred—as the reservoir had not yet been impounded—the accumulation of localized failures raised substantial concerns regarding the structural integrity and long-term safety of the dam.

Geotechnical parameterization

The geomechanical parameters of the embankment materials were used as primary inputs for the numerical modelling framework. Laboratory characterization was conducted on undisturbed samples collected along the failure-prone zone between chainages 0 + 420 and 0 + 640. The tested parameters included cohesion (c′), friction angle (ϕ), moisture content, dry density, and Atterberg limits (LL, PL, PI), forming the core dataset for subsequent analyses.

To prepare the data for numerical and machine-learning integration, geostatistical preprocessing was performed. Distributional behavior and skewness were assessed using kernel density estimates, while variable interdependence was evaluated through a correlation heat map (Figure S2a). Dimensionality reduction was executed using Principal Component Analysis (PCA), which retained the dominant variance structure of the dataset while suppressing noise and redundancy (Figure S2(b)). The combined in-situ and laboratory measurements were then normalized to ensure consistency across the multivariate geotechnical parameters.

The correlations among the numerical features, summarized in Table S2, provided a basis for interpreting soil behavior across the clay core. K-means clustering was applied to the PCA-transformed data, producing three distinct geotechnical behavior groups within the embankment:

• Cluster 0: Zones exhibiting less stable geotechnical characteristics and comparatively poor compaction quality.

• Cluster 1: Zones with highly dense materials that are well compacted but potentially too dry.

• Cluster 2: Zones with high swell potential, elevated seepage susceptibility, and increased likelihood of slope failure.

PCA analysis ruled out compaction defects, identifying hydrological factors (seepage, pore pressure, seasonal saturation) as primary failure causes (Table 1; Fig. 4).

Table 1.

Sample Raw data input used for PCA analysis and rule based classification.

Chainage	Degree of compaction	Lab moisture(OMC)	Saturation result	Year group
480	98.4	12.7	Pass	2020
500	97.9	13.2	Pass	2020
…	…	…	…	…
485	92.3	16.2	Fail	2021–2022
478	95.0	17.5	Pass	2021–2022

Fig. 4.

Rule based classification of saturation in the clay-core material.

Finite element modeling and boundary conditions

The finite element model was developed to reproduce the observed seepage-induced instability mechanisms at Megech Dam, particularly the translational slip and core softening documented between chainage 0 + 420 and 0 + 640 during the 2020–2022 wet seasons. The model integrates field-mapped weak planes, measured pore-pressure patterns, and actual rainfall-driven hydraulic loads to ensure physical consistency rather than relying solely on numerical assumptions.

Geometry and material zoning

The dam geometry was generated using Gmsh v4.8.4, where the Python API enabled parametric construction of the clay core, transition filters, inner shell, and outer rockfill zones Fig. 5.

Fig. 5.

Cross sectional geometry and FEM mesh of the Megech Dam. (a) 500 m crest length, 10 m core width, 77 m height, 15 m foundation depth. Slopes: upstream 1:2.5, downstream 1:2. (b) Corresponding finite element mesh (Gmsh): Tetrahedral elements (~ 2 m edge) resolving material interfaces and slope transitions.

This approach ensured:

• Precise replication of as-built geometry validated by survey data.

• Explicit modeling of zone transitions, which is crucial for capturing stress redistribution and seepage concentration around the clay core.

• Direct coupling with FEM boundary conditions, including weak-plane representation and water-surface elevation.

Meshing strategy

The finite element model employed a 3D tetrahedral meshing strategy, specifically designed to capture the complex geometric and material characteristics of the earth-rock dam.

This approach was selected to ensure numerical stability and accurately represent the localized deformation mechanisms identified from site observations. Targeted mesh refinement was implemented in critical regions, including:

• The potential failure zone (Ch. 0 + 420–0 + 660), where historical shear deformations were recorded.

• Material interfaces between the core and rockfill shells, which exhibit significant stiffness contrasts and high hydraulic gradients during reservoir fluctuations.

• The non-circular, weakly-dipping (5.5°) slip surface and the upstream saturation front.

This orderly improvement was essential for resolving high-stress gradients and the complicated geometry of internal material zones, thereby improving the quality of the simulated structural response.

Geometrical boundary conditions

The geometrical boundary conditions for the finite element model were rigorously derived from comprehensive field evidence to ensure a physically realistic simulation. Site investigations, including crack alignment mapping, inclinometer data, and exposed slip surfaces from the 2020–2021 failure events, consistently indicated a translational block slide mechanism governed by a shallow, non-circular weak plane dipping at 5.5° (Table 2).

Table 2.

Geometric boundary conditions:

Parameter	Description	Justification	FEM implementation
Weak plane geometry	Non-circular, translational slide	Matches mapped field slip	Interface elements
Dip angle	5.5°	Consistent with core cracking orientation	Inclined interface
Depth of failure	Max 50 m at Ch. 0 + 420	Based on drilling, exposures	Mesh refinement
Horizontal extent	Ch. 0 + 430–0 + 660	Observed active sliding	Domain limits
Foundation bedrock	Fixed Base	Confirmed by boreholes	Zero displacement
Valley abutments	Roller Constraints	Reflect lateral confinement	Restricted DOF

Note that ‘shallow dipping’ refers to the low angle of the plane relative to horizontal; the failure plane itself is deep seated, reaching a maximum depth of 50 m at chainage 0+420 (Table 2 and Fig. 6b).

Fig. 6.

(a) 3D tetrahedral mesh with refinement in failure zone (red) and material interfaces (blue); (b) Cross-section showing 5.5° weak plane and saturation front refinement for stability-critical zones.

This field-based understanding was directly translated into the model as follows:

• Failure surface geometry: A non-circular, translational slide surface was explicitly modeled using interface elements, accurately reflecting the mapped slip geometry in the field.

• Slip plane inclination: The critical dip angle of 5.5° was imposed, consistent with the observed orientation of core cracking and inclinometer shear displacements.

• Spatial extent of the model: The lateral boundaries of the analysis domain (Ch. 0 + 430 to 0 + 660) were set to encompass the entire actively sliding region. The depth of the potential failure zone was constrained to a maximum of 50 m at its deepest section (Ch. 0 + 420), based on borehole data and surface exposures.

• Boundary constraints: The model foundation was treated as a fixed boundary, representing the competent bedrock confirmed by subsurface drilling. The valley abutments were assigned roller constraints to simulate the natural lateral confinement provided by the topography.

In summary, every geometrical constraint was empirically grounded and implemented to replicate the specific failure mechanism observed at the site, thereby strengthening the engineering validity of the subsequent analysis. A summary of failure geometry is shown in Table 2.

This modeling refinement is illustrated in Fig. 6 Panel (a) presents the 3D tetrahedral mesh, where targeted refinement is visible along the mapped failure zone (red) and at the core–shell interfaces (blue). Focused discretization of this type is essential for resolving localized stress and pore-pressure gradients, as also demonstrated by Smith et al. (2020). Panel (b) shows the embedded 5.5° weak plane and associated saturation front within the dam cross-section, reflecting field-verified conditions. Incorporating these spatially explicit features ensures that the simulated deformation patterns align with the observed failure mechanisms, providing a physically realistic foundation for subsequent stability analysis.

Coupled hydro-mechanical analysis

The failure mechanism was analyzed through coupled hydro-mechanical modeling that tracked hydraulic triggers to structural collapse. The displacement-pore pressure (u-p) formulation employed coupled seepage-stress governing equations with tensor calculus and nonlinear stability analysis for anisotropic conditions (1):

1

Where:

• = Seepage flux (vector form).

• = Permeability tensor (anisotropic permeability matrix).

• = Hydraulic head (spatially and temporally varying).

• = Spatial coordinates.

The correlation of the permeability tensor with reference to the spatial location is explained by equation (2).

2

Where is the potential of water storage in the dam body.

Evolution of effective stress and nonlinear coupling with pore pressure

In a dynamic seepage environment, the effective stress principle is formulated based on the principle of effective stress defined by Terzaghi (Eq. 3).

3

• where:

• = Effective stress tensor.

• = Total stress tensor.

• = Pore water pressure.

• = Kronecker delta function ().

Due to the constantly changing pore pressure, the poro-elastic constitutive relation was expressed as shown in Eq. (4) following the concept of Biot’s poroelastic constitutive Law:

4

Biot’s assumption of poroelastic constitutive Law is not considered to be adequate for realistic geo-mechanical modeling, the dynamic changes in the permeability tensor with stress and strain was computed by power-law stress-dependent permeability model as in the works of^{4, 5} expressed in Eq. (5):

5

where:

• = Initial permeability.

• = Reference effective stress.

• = Material-dependent exponent controlling stress-permeability sensitivity.

Failure modelling in a coupled hydro-mechanics

The failure in the clay core was assessed following the evolution of permeability () with volumetric strain ( ​) explained as formulated by Eq. (6).

6

where is the initial permeability, and is a material constant⁶.

Strain softening was incorporated to capture the reduction in cohesion over time (Eq. (7)). Hence its effect in the cohesive nature of the soil material is expressed by the formulation on the degree of inter-particle disconnection as explained by⁷:

7

Where: is the initial cohesion, and controls the rate of strength loss.

A coupled approach was developed to capture soil failure in Megech dam⁸. Factor of Safety (FoS) against seepage was evaluated across multiple hydrological scenarios—including construction, full saturation, and steady-state seepage conditions—with a critical threshold of FoS < 1 used to identify vulnerable zones at depth (Fig. 7a,b).

Fig. 7.

Coupled hydro-mechanical analysis of the Megech Dam. (a) pore pressure, effective stress, and cohesion vs. depth; (b) Factor of Safety under key hydrological scenarios; (c) 3D pore pressure distribution showing saturation at the dam base.

A 3D simulation of rainfall-induced pore pressure has been created to visualize the low impact near the crest (blue) and high pressures at the base (red–orange) Fig. 7c, consistent with the 2D FoS results (Fig. 7a and b).

Slope stability was assessed by profiling pore pressure, effective stress, and cohesion with depth; evaluating Factor of Safety under critical hydrological scenarios; and simulating 3D pore pressure distribution to identify saturated zones at the dam base.

As shown in Fig. 8a, the peak shear stresses develop deep within the embankment, forming a broad progressive failure surface rather than a shallow, localized slip plane. To quantify this behavior, a fully coupled 3D static analysis was performed in OpenSeesPy, incorporating pore-pressure evolution, effective stress redistribution, and displacement under self-weight loading. The model domain was anchored by five monitoring nodes—Node 1 (0,0,0), Node 2 (100,0,0), Node 3 (0,100,0), Node 4 (100,100,0), and the crest point (50,50,80)—enabling simultaneous tracking of basal restraint and crest deformation. Gravity loading (g) was applied incrementally over ten phases, and the clay core was assigned representative properties of E = 30 MPa, ν = 0.3, and ρ = 1800 kg/m³, consistent with laboratory characterization.

Fig. 8.

(a) Maximum shear stress from 3D OpenSeesPy analysis showing nodal displacement, broad failure and slight crest settlement. (b) Stress shifts due to seepage along dam width, height, and depth gradient. (c) 3D PyVista view of stress variations, with crest stress tapering to the toe.

Potential failure zones were identified by examining the interaction between pore-pressure rise, effective stress reduction, and displacement. Regions exhibiting minimal base movement but pronounced crest settlement correspond to deep-seated slip development driven by hydraulic softening. Figure 8b illustrates the redistribution of stresses under seepage forces, demonstrating how the seepage-induced shear component (τₛ) increases with dam height (H), width (W), and the depth-dependent hydraulic gradient (i). This pattern aligns with typical hydro-mechanical weakening observed in partially saturated earth-rock dams subjected to prolonged rainfall infiltration.

In addition the shifts in stress in the embankment due to seepage forces is shown in Fig. 8 as manifested in the mode of slope failure due to the deformation characteristics of the dam as a result of seepage induced stress () as a function of the dam width height), and depth-dependent hydraulic gradient () are also displayed.

To provide a more rigorous physical interpretation, Fig. 8c presents the 3D stress field visualized in PyVista, highlighting the internal redistribution of stresses caused by the combined effects of self-weight, hydrostatic loading, and transient seepage.

Maximum stresses develop beneath the crest and diminish towards the downstream toe, reflecting the progressive reduction in effective stress along the emergent failure surface. This behavior is consistent with classical hydrologic-triggered slope failure mechanisms described in the geotechnical literature by⁹.

Constitutive modelling

The hardening soil (HS) model was implemented to capture the stress-dependent, elastoplastic behavior of the clay core material Fig. 9. Model calibration and visualization were performed using Python with OpenSeesPy¹⁰, employing simplicial homology global optimization (SHGO) to minimize discrepancies between experimental data and HS predictions¹¹.

Fig. 9.

Hardening Soil model analysis of Megech Dam materials (a) 2D yield surface characterization showing theoretical components, principal stress transformation, stress-strain response, and zone comparison with calibrated parameters. (b) Sensitivity analysis of cohesion (), friction angle , cap pressure (), and aspect ratio (). (c) 3D yield surfaces for Impervious Core (cohesive) and Rock Fill (frictional) zones, visualizing the elastic interior bounded by shear and cap surfaces.

The constitutive framework incorporated four key aspects:

• Stress-level dependency of stiffness through power-law formulation, deriving stiffness parameters () from oedometer tests using reference stress () and void ratio (.

• Distinct stiffness moduli for primary loading () versus unloading/reloading () paths, with based on triaxial test calibration.

• Plastic strain initiation validated against laboratory stress-strain curves using a modified yield function.

• Volumetric behavior during shearing modeled through Rowe’s dilatancy theory.

The calibrated HS parameters (Table 3) were validated against field monitoring data, demonstrating accurate prediction of deformation patterns and identifying weak shear planes observed in situ. This constitutive formulation provides the physical basis for the hybrid ANN-LSTM-FEM framework, ensuring numerical stability while capturing complex soil behavior under multihazard conditions.

Table 3.

Hardening soil (HS) model parameters based on construction test results.

Embankment Zone	φ (°)	c (kPa)	(kPa)	(kPa)		(kPa)	ψ (°)	γ (kN/m³)	m
Impervious Core	15.26	29.75	10,000	30,000	0.577	109.1	2.06	16	0.8
Rock Fill	40.00	0	50,000	150,000	1.636	0	11.46	22	0.5
Shell	32.00	0	25,000	75,000	1.287	0	6.38	18	0.6
Fine Filter	34.00	0	30,000	90,000	1.374	0	7.56	18	0.6
Coarse Filter	35.00	0	35,000	105,000	1.418	0	8.24	18	0.6
Transition Gravel	35.00	0	35,000	105,000	1.418	0	8.24	18	0.6
Foundation Soil	28.00	0	15,000	45,000	1.113	0	4.12	17	0.7
Foundation Rock	40.00	50	100,000	300,000	1.636	59.6	11.46	22	0.3

The calibrated Hardening Soil (HS) parameters are implemented within the FEM simulations to generate spatially resolved stress, strain, and pore-pressure outputs at key sensor locations; these FEM-derived features, alongside field measurements and static geotechnical properties, are then fed into the ANN and LSTM modules, enabling the hybrid framework to leverage both physics-based and data-driven insights for accurate, time-resolved Factor of Safety predictions.

Saturation mechanisms

Two distinct saturation processes were identified:

Bottom-up saturation: Perennial spring flow from the left abutment, combined with the dam’s rock-founded cutoff preventing drainage, created upstream ponding that saturated the foundation, forming continuous weak planes through reduced effective stress.

Top-down saturation: Extreme rainfall events () saturated the dam through.

• Infiltration via desiccation cracks and coarse shell material.

• Increased unit weight of clay core acting as surcharge load.

• Pore pressure development reducing shear strength.

Development of a hybrid ANN-LSTM-FEM model

A hybrid framework integrating FEM physics, LSTM temporal analysis, and ANN pattern recognition was developed for embankment dam risk assessment. Utilizing 104 weeks of monitoring data (2020–2021), the model identified critical failure factors and forecasted stability through advanced spatiotemporal pattern resolution¹².

Overview of the hybrid architecture

A hybrid ANN–LSTM–FEM framework was developed to predict weekly Factor of Safety (FoS) under evolving hydrological forcing and internal erosion processes. The model integrates (i) temporal pore-pressure dynamics (LSTM), (ii) strength degradation (ANN), and (iii) physics-consistent geomechanical responses (FEM).

This coupling enables physically reliable long-term forecasting.

It should be noted that the FEM is used solely to generate static spatial descriptors (e.g., stress fields and pore-pressure gradients) that characterize the dam’s baseline mechanical state. These features are extracted prior to ML training and incorporated as fixed inputs alongside monitoring data and laboratory soil properties. FEM outputs are not used as training targets; the model predicts the Factor of Safety exclusively from field observations.

Long short-term memory (LSTM) networks

A two-layer LSTM (128 units each) captures multi-step evolution of pore pressure and displacement (see Fig. 10).

Fig. 10.

LSTM network architecture with attention mechanism: input layer (6 features × 8 time steps), two LSTM hidden layers, attention weights distribution, and output layer predicting stability metrics. Note: The network architecture was schematically illustrated using custom Python code (matplotlib).

Inputs include (8):

8

Outputs are weekly forecasts of pore-pressure trajectories , used as boundary conditions for FEM stability calculations (see Table S3).

The model’s performance was quantitatively evaluated based on its Factor of Safety RMSE, accuracy in predicting saturation patterns, forecasts of strength degradation in cohesion and friction, and the lead time of failure warnings, with all predictions validated against field instrumentation (Fig. 11).

Fig. 11.

Critical Failure Progression Analysis (a). Multi-variable failure progression showing normalized pore pressure, settlement rate, and rainfall intensity during the critical construction period (weeks 80–104, 2021). (b) LSTM prediction performance for Factor of Safety (FOS) with attention weights highlighting critical failure weeks.

ANN module for strength degradation forecasting

A feedforward ANN with a [64-32-16] architecture captured static, non-temporal relationships by fusing FEM spatial features with static geotechnical parameters¹³. The hidden-layer activations are computed as (9).

9

Where: is the sigmoid activation function,

Accordingly, the ANN maps hydrological load and strain increments to weekly degradation in shear strength as shown in Eq. (10).

10

Which are accumulated through the strength evolution computed as (11):

11

This formulation enables the gradual weakening of the embankment core and shell to be dynamically reflected in the FEM-based FoS computation.

The network fuses multiple data streams depicted in Table 4:

Table 5.

Analytical calculation of strength degradation process.

Step	Variable	Symbol	Value	Unit	Calculation	Cumulative effect
1	Plastic strain			–	From FEM analysis	Week 80:
2	Pore pressure		50		From piezometers	Week 80: u=
3	Pore pressure gradient		60		From seepage analysis	Week 80: ∂u/∂z = 30 kPa/m
4	Cohesion degradation rate		-0.435		– 0.15 × 0.058 × 50	Week 80–104:
5	Friction angle degradation rate		-0.2784		– 0.08 × 0.058 × 60	Week

Table 4.

ANN input features and data ranges.

Feature type	Parameters	Data range	Source
Static geotechnical	Cohesion (c)		Lab tests
	Friction angle (φ)		Field data
	Unit weight (γ)		Construction
LSTM temporal	Pore pressure		Piezometers
	Rainfall (PC1/PC2)		Climate PCA
	Settlement rate		Instrumentation
FEM spatial	Vertical stress		Stress analysis
	Plastic strain		Strain localization
	Pore pressure gradient		Seepage analysis

The ANN derived parameter predictions through strength reduction correlations from monitoring data, formalized in (12) and detailed Table 5

12

Where: is plastic strain (%) and is pore pressure (kPa).

The Artificial Neural Network (ANN) was designed to compute weekly strength degradation rates. As shown in Fig. 12, the network’s [9-64-32-16-2] architecture integrated multi-modal data, fusing static geotechnical properties with temporal monitoring data and spatial FEM characteristics (see Table S4) using sigmoid activation functions (9). The computation of degradation rates for cohesion and friction angle was performed using (12), which incorporated real-time measurements of plastic strain, pore pressure, and pore pressure gradient ) sourced from both FEM simulations and field instrumentation (Table S5)^14–17.

Fig. 12.

Artificial neural network architecture for dam safety prediction. A feature of five-layer [9-64-32-16-2] feedforward network that processes geotechnical parameters, temporal features, and spatial characteristics to predict strength degradation.

FEM physics integration and FoS computation

LSTM-predicted pore pressures and ANN-updated values are provided to a coupled FEM solver to compute FoS each week.

A physics-consistency penalty ensures agreement between ML-predicted and FEM-computed FoS (Eq. 13):

13

The integrated FEM mesh setup and boundary conditions are depicted in Fig. 13.

Fig. 13.

FEM implementation. (a) Tetrahedral mesh with boundary conditions and weak plane. (b) Material strength properties showing cohesion and friction angle reduction across dam zones.

The element size and mesh density conigurations with the hydraulic and mechanical parameters are shown in supplementary Table S6 and Table S7.

At this point, we emphasise that the FEM is employed here only to enforce physical consistency during training; all reported accuracy metrics (MAE, RMSE, R²) are computed with respect to observed field data, not FEM outputs. This ensures that the model’s predictive skill is validated against reality, avoiding any circular dependence on the numerical model.

Training strategy and loss formulation

The model was trained using a composite loss function combining mean absolute error () with physics-based constraints (). Optimization was performed using the Adam optimizer with a learning rate of 0.001 and a batch size of 32. To reflect real-world forecasting conditions, the 104 week monitoring dataset (2020–2021) was split temporally into training (weeks 1–73), validation (weeks 74–87), and test (weeks 88–104) sets (Table 6). To incorporate longterm hydrological context, Principal Component Analysis (PCA) was applied to a separate 8 year climate record (2012–2019) of monthly rainfall and temperature, yielding principal components PC1 and PC2. These PCA scores were then matched to the corresponding weeks in the 2020–2021 period and used as additional input features alongside the weekly monitoring data. Thus, the model was trained exclusively on the 104 week monitoring data, with the climate PCA values providing extended hydrological context; no training was performed on the 2012–2019 data directly.

Table 6.

Training/validation configuration and input normallization. Note: The 2012–2019 period refers to climate data used for PCA only; the model was trained on the 2020–2021 monitoring data shown above.

Category	Training	Validation	Test	Normalization Range	Units
Data split	Weeks 1–73 (70%)	Weeks 74–87 (14%)	Weeks 88–104 (16%)	–	Weeks
Temporal features
Pore Pressure	0–25 kPa	25–50 kPa	50–120 kPa	0-120	kPa
Settlement Rate	0.1–0.5 cm/wk	0.5–2.0 cm/wk	2.0–5.0 cm/wk	– 3 to + 5	cm/week
Rainfall PC1	– 1.95 to + 0.5	+ 0.5 to + 1.5	+ 1.5 to + 2.34	– 1.95 to + 2.34	PCA score
Static Features
Cohesion	29.75-28.0 kPa	28.0–22.0 kPa	22.0–5.0 kPa	5–30	kPa
Friction Angle	15.26-14.0°	14.0–11.0°	11.0-7.02°	7–20	°
Plastic Strain	0.002–0.015	0.015–0.042	0.042–0.058	0.002–0.058	–

Configuration: 8-week sequences, batch size 16, learning rate 0.001, physics weight λ = 0.3.

Features: 6 temporal + 5 static inputs, 104 weeks total data.

Progression: Training (normal) → Validation (warning) → Test (critical failure).

The range, critical thresholds, and importance of various temporal features, including rainfall, pore pressure, settlement rate, spring discharge, clay content, and permeability, which were used for model training and failure prediction is provided in Table 9.

Model predictions of strength degradation and weak-plane localization were validated against field instrumentation data. Table S10 summarized initial and final values, percentage changes, data sources, and the relative role of each feature in the hybrid modeling framework.

Moreover, model’s prediction accuracy, early-warning capability, pattern recognition performance, parameter estimation accuracy, spatial localization reliability, and computational efficiency, based on validation against field observations and numerical benchmarks are depicted in table S11.

In this regrad, the physics-consistency term acts only as a regularizer, encouraging mechanically plausible FoS predictions when parameters are reintroduced into the FEM and it is not a validation metric. Final performance is evaluated solely against independent field data (weeks 88–104), and no ML prediction is compared to the FEM used for feature generation.

Optuna-based hyperparameter optimization

The model was tuned through systematic Bayesian optimization, which converged on a final configuration of 2 LSTM layers (128 units), a 64-32-16 ANN architecture, a 0.001 learning rate, 0.2 dropout, and 0.3 physics constraint weight Fig. 14.

Fig. 14.

Bayesian optimization results for the hybrid ANN–LSTM–FEM model. Panels (a) through (e) illustrate the MAE convergence, hyperparameter distributions, and sensitivity analyses for key parameters. The process converged on an optimal configuration of 128 LSTM units, a 0.001 learning rate, a 0.2 dropout rate, and a physics-weight (λ) of 0.3.

Comparative performance against established modeling paradigms

To contextualize the performance of the proposed hybrid ANN–LSTM–FEM framework, its predictive capability was compared against representative baselines from deterministic, deep-learning, and metaheuristic-optimized machine learning families. These models were selected because they represent the most frequently employed approaches in dam monitoring, hydro-meteorological forecasting, and geotechnical risk analysis. A structured comparison is provided in Table 7 to highlight differences in underlying assumptions, input requirements, and predictive behavior relevant to rainfall-induced stability problems.

Table 7.

Comparison of baseline modeling paradigms with the proposed ANN–LSTM–FEM hybrid framework.

Model category	Representative models	Core strengths	Key limitations in dam-failure forecasting	Relevance to present work
Deterministic models	FEM-only, limit-equilibrium analysis	Physically interpretable; captures stress, pore pressure, deformation; well-established in dam engineering	Limited in handling temporal patterns and rainfall variability; cannot learn from historical failure signatures	Forms the physics backbone of the hybrid framework; provides stress/displacement features for AI integration
Conventional deep learning	CNN, simple LSTM, GRU	Strong pattern extraction; effective for short/medium time-series prediction	Cannot incorporate material behavior, seepage physics, or dam geometry; reduced interpretability; sensitive to noisy data	Compared as purely data-driven baselines; hybrid model outperforms them under extreme rainfall shifts
Metaheuristic-optimized ML	SVM–PSO, RF–GA, XGBoost–DE, ANN–GWO	Good at nonlinear mapping; enhanced optimization of hyperparameters; stable on medium datasets	Still data-driven only; lacks physical constraints; struggles with regime shifts and rare failure events	Useful benchmark category; hybrid model achieves better generalization when hydrological forcing departs from training distribution
Proposed hybrid framework	ANN–LSTM–FEM	Integrates physics (FEM) + temporal learning (LSTM) + nonlinear mapping (ANN); robust to rainfall extremes; interpretable failure patterns	Requires multi-source data integration; computationally heavier	Provides strongest performance and captures both mechanism-driven and data-driven failure signals

A unified evaluation protocol was applied to assess the hybrid model, quantifying prediction accuracy, early-warning lead time, convergence stability, and computational efficiency. All results were verified using field measurements and cross-validation tests as summarized in Table 8.

Table 8.

Performance comparison of the optimized hybrid framework against conventional methods for dam stability assessment.

Optimization metric	Value	Benchmark comparison	Improvement	Significance level	Validation outcome
Final MAE achieved	0.027	Conventional: 0.085	+ 68.2%	p < 0.001	Exceeded target performance
Early warning lead time	3.5 weeks	Conventional: 1.5 weeks	+ 133.3%	p < 0.005	Critical safety enhancement
Convergence efficiency	70 trials	Expected: 100 + trials	+ 30.0%	–	Optimal resource utilization
Pattern recognition accuracy	94.3%	Conventional: 66.3%	+ 42.2%	p < 0.001	Superior temporal analysis
Parameter prediction accuracy	83% (c), 54% (φ)	Field measurements	Within 5% error	p < 0.01	Field-validated reliability
Computational efficiency	2 h training	Comparable frameworks	Optimal	–	Practical deployment ready
Robustness score	96% cross-validation	Industry standard: 85%	+ 12.9%	p < 0.05	Exceptional generalization

Engineering interpretation of model performance

The improved performance of the hybrid ANN–LSTM–FEM framework arises from its ability to capture the underlying physical mechanisms that govern embankment behavior. During wet seasons, rapid pore-pressure rise produces strong temporal gradients that conventional machine-learning methods cannot resolve. The LSTM component achieves higher accuracy under these conditions because its gated architecture retains long-term saturation memory and correctly reproduces delayed pore-pressure dissipation, which is the dominant driver of FoS reduction. In contrast, simpler models misinterpret these transient hydraulic phases as noise, resulting in higher RMSE.

Performance decreases slightly during abrupt shear-strength collapses (e.g., during Weeks 94–101), because degradation becomes highly nonlinear and sensitive to localized strain accumulation. The ANN predicts gradual trends accurately, but it underestimates sudden softening along weak planes where plastic strain localization accelerates.

The integration with FEM mitigates this limitation: when ML-predicted strength loss becomes physically inconsistent with hydro-mechanical responses, the physics penalty forces convergence toward realistic stress paths, improving stability forecasts during progressive failure.

In general, the hybrid framework performs better because it embeds geomechanical constraints directly in the learning process. The FEM-consistency term eliminates unrealistically high FoS predictions during rapid pore-pressure accumulation, while the ANN + LSTM structure captures both long-term saturation trends and short-term hydraulic shocks. These engineering mechanisms explain the lower MAE, longer early-warning lead time, and improved detection of critical failure weeks compared to purely data-driven or purely physics-based models.

Results and discussion

This section presents the predictive performance, physical consistency, and failure-mode interpretability of the proposed hybrid FEM–ANN–LSTM–Attention model. All results correspond to the 2020–2021 monitoring period. Only essential figures and tables are included here; secondary diagnostics are provided in the Supplementary Material.

Hydro-mechanical stability analysis

The spatially interpolated soil property maps in Fig. 15a–d show a distinctly heterogeneous clay core, where elevated clay content, high plasticity, and strong free-swell potential cluster between chainages 0 + 420–0 + 640. This zone corresponds to the weak material band identified in field investigations. The permeability field (Fig. 15b) further reveals localized pockets of higher hydraulic conductivity, indicating preferential seepage pathways capable of transmitting rainfall-induced infiltration directly into the core. These material patterns translate into significant stress agitations: total vertical stresses exceed 700 kPa in the deeper core (Fig. 15e), while pore pressures rise markedly within the same chainage interval (Fig. 15f), producing a pronounced reduction in effective stress (Fig. 15g). Cohesion distributions (Fig. 15h) confirm that shear strength parameters within the weak plane are substantially lower than surrounding shell zones.

Fig. 15.

Stability analysis of the Megech Dam slide (a) Clay content distribution, (b) Permeability (log₁₀cm/s), (c) Total vertical stress (kPa), (d) Pore pressure elevation, (e) Effective stress reduction, (f) Plastic strain concentration, (g) Strength reduction factor, (h) Cohesion distribution (kPa), (i) Stability indicator showing critical safety factor.

The deformation plots (Fig. 15i) show plastic strain accumulating almost exclusively along this weak plane, reaching values consistent with active strain-softening in saturated clay. The corresponding strength-reduction field (Fig. 15j) demonstrates a clear degradation in both cohesion and friction angle relative to design conditions.

Friction angles decline towards 13–16° (Fig. 15k), reinforcing the loss of shear resistance. The stability indicator (Fig. 15l) integrates these effects, with factors of safety dropping below the critical threshold of 1.3 across chainages 0 + 480–0 + 540 and approaching unity at the observed slide location.

Collectively, these results demonstrate that the failure was controlled by the coupled effect of material heterogeneity, seepage-induced pore-pressure rise, and localized strain softening, all converging within the same structurally vulnerable band identified in the field, following theprocedures described in^18–21.

The resulting softening behavior is interpreted through fundamental material science principles²².

FoS forecasting performance

The forecasting model successfully reproduces the seasonal evolution of the Factor of Safety (FoS), with clear sensitivity to hydrological loading. As shown in the FoS time-series, predicted reductions consistently coincide with periods of elevated pore pressure and sustained wet-season rainfall, demonstrating that the model responds to physically meaningful stressors rather than statistical noise. The framework captures both the long-term downward trend associated with progressive material degradation and the short-term fluctuations driven by transient infiltration events. This correspondence confirms that the hybrid model accurately represents the hydro-mechanical processes governing instability at Megech Dam.

Figure 16 shows the 2020–2021 validation of the hybrid ANN–LSTM–FEM model, where predicted FoS closely tracks observations, capturing seasonal fluctuations and core weakening, with reductions aligning with high pore pressure and rainfall. Forecast errors rise during intense saturation, yet overall accuracy is high (RMSE = 0.027, R² = 0.943), reflecting robust hydro-mechanical modeling.

Fig. 16.

FoS forecasting performance: (a) observed vs. predicted values with hydrological correlations; (b) forecast errors and pore pressure sensitivity. Validation metrics (RMSE = 0.027, R²=0.943) confirm model accuracy for dam safety assessment.

Physical consistency with hydrological condition

The model shows clear physical consistency with hydrological loading. Increases in pore pressure coincide with sharp declines in FoS, while settlement and strain follow coherent seasonal patterns consistent with coupled analysis approaches²³. Figure 17 illustrates the inverse pore-pressure–FoS relationship, reflecting effective-stress reduction during wet-season saturation as in²⁴. The same figure also shows settlement and plastic strain accelerating during high pore-pressure periods and stabilizing during drier phases, demonstrating that the FEM-informed features capture internal stress redistribution rather than relying solely on surface measurements, as well addressed in²⁵.

Fig. 17.

Physical consistency between hydrological conditions and slope stability: (a) Hydrological response showing inverse correlation between pore pressure increases and Factor of Safety declines, with critical threshold at FoS = 1.2; (b) Deformation response demonstrating coherent temporal patterns in settlement and plastic strain, validated by FEM-informed features capturing internal stress redistribution.

Error structure and model reliability

The error analysis indicates that the hybrid framework maintains stable and unbiased performance across hydrological seasons (Fig. 18). Residual distributions show no seasonal accumulation or drift, confirming that multi-step forecasts remain consistent throughout both wet and dry periods. Error histograms remain symmetric, indicating the absence of systematic over- or under-prediction. Importantly, the forecast variance does not increase with prediction horizon, demonstrating that weekly multi-step predictions remain robust rather than diverging over time as in the case of^26–29.

Fig. 18.

Error analysis showing (a) unbiased seasonal predictions and (b) stable multi-week forecasting performance.

Quantitative performance metrics

The hybrid model outperforms baseline ANN and LSTM approaches by integrating FEM spatial features, ANN degradation mapping, LSTM temporal learning, attention mechanisms, and Bayesian optimization, achieving superior forecasting accuracy in comparative performance assessment (Table 9).

Table 9.

Quantitative performance comparison between baseline ANN and the hybrid FEM–ANN–LSTM model.

Model	RMSE	MAE	R 2	NSE	Early warning lead time (weeks)
ANN-only	0.065	0.045	0.82	0.79	1.5
Hybrid FEM-ANN-LSTM	0.035	0.027	0.94	0.92	3.5

The model achieved a maximum early warning lead time of 3.5 weeks in benchmark tests (Table 9), which aligns with the physically observed lag of 2–3 weeks between rainfall peaks and pore pressure response in the embankment (Fig. 19).

Fig. 19.

Megech Dam Temporal Analysis: Hydrological Loading, LSTM Attention, and Deformation Response (a) stable convergence (training/validation loss: 0.054/0.072); ii (b) high prediction accuracy for Factor of Safety (R² = 0.94, MAE = 0.027) with slight deviations near critical failure (FOS < 1.2); iii (c) unbiased residuals (mean = 0.002); and iv(d) consistent cross-validation performance (MAE = 0.027 ± 0.006, RMSE = 0.035 ± 0.007).

The framework enables comprehensive spatiotemporal risk identification by integrating FEM-derived stress states with hybrid model predictions to pinpoint high-risk zones within the dam structure. The integrated attention mechanism autonomously identified critical 8-week antecedent sequences preceding deformation events, with these high-risk periods corresponding precisely to documented extreme rainfall events. This spatiotemporal analysis provides both spatial localization of vulnerable zones and temporal forecasting of failure precursors, offering actionable insights for targeted intervention strategies (Fig. 19) similar with the works of³⁰.

Interpretation of model strengths and weaknesses

Why the model performs well under wet-season conditions

During wet-season hydrological loading, increased pore pressure is captured within the FEM–ANN coupling as stress-path-dependent material softening. The LSTM module models the temporal persistence of moisture effects, accounting for delayed responses in the embankment. Additionally, the attention mechanism emphasizes critical timesteps preceding rapid stability loss, effectively highlighting early-warning signals and enhancing predictive accuracy under extreme wet conditions.

Model performs less accurately under low-signal conditions

In low-signal regimes, small variations in pore pressure and displacement produce subtle changes that are difficult to resolve. As a result, ANN-driven strength updates become dominated by noise sensitivity. Furthermore, hysteresis observed in field measurements—such as delayed consolidation—introduces nonlinear behavior that the model does not fully capture, limiting predictive accuracy under these conditions.

Engineering interpretation

The model’s predictive performance is guided by the underlying physical mechanisms rather than relying solely on statistical fitting. By accurately representing stress redistribution and material degradation pathways, it captures the true geo-mechanical behavior of the embankment, explaining its superior performance compared with purely data-driven approaches.

Summary of findings

The hybrid model provides physically grounded, stable long-horizon forecasts. It reproduces seasonal FoS trends, captures degradation onset accurately, and yields interpretable residual behavior. The results confirm that combining FEM state evolution with ANN- and LSTM-based learning offers a reliable framework for dam safety early warning.

Conclusion

This work developed and evaluated an adaptive hybrid modeling framework that integrates Finite Element Method (FEM) simulations with ANN–LSTM–based deep learning to forecast rainfall-induced instability in an earth rockfill dam during construction. Applied to the Megech Dam case, the framework reproduced key hydro-mechanical processes—including transient pore-pressure rise, stress redistribution, and progressive strength loss—while improving predictive capability relative to purely numerical or data-driven approaches.

Quantitative benchmarking against classical machine-learning baselines demonstrated the added value of the hybrid method: the optimized framework achieved an MAE of 0.027, outperforming SVM (0.081), Random Forest (0.067), and a standalone LSTM (0.052), with statistically significant gains across cross-validation tests. The workflow also provided an extended early-warning lead time of 2–3 weeks, a critical advantage for construction-phase risk mitigation.

Beyond numerical accuracy, the hybrid strategy offered physically interpretable insights. FEM-guided stress fields revealed that failure initiates at depth along broad, progressive slip surfaces, while the temporal learning components captured the lag between rainfall forcing and pore-pressure accumulation. This complementary interaction between physics constraints and temporal pattern extraction is the core methodological contribution of the study.

Although the present study is based on a single monitored site, the hybrid framework is designed to be flexible and can be extended to additional dams as more datasets become available. The clustering step used to enhance temporal structure may benefit from further evaluation under different hydrological patterns, and ongoing refinements aim to streamline this component. For transparency and reproducibility, key hyperparameters, training settings, and workflow pseudocode have been included, with full code release planned in future updates. Building on the current architecture, upcoming work will integrate uncertainty quantification and Bayesian optimization to provide probabilistic failure forecasts, more rigorous parameter calibration, and confidence-based early-warning outputs.

In general, this study demonstrates that a physics-informed, hybrid ANN–LSTM–FEM approach can enhance early-warning capability and interpretability for rainfall-driven instabilities in rockfill dams. With further validation and extension to multihazard scenarios, such models have strong potential to support operational dam safety management and climate-responsive risk forecasting.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

All the authors contributed to the conception and design of the study. M.N: Administration, conceptualization, supervision, methodology analysis, investigation, formal analysis, writing—original draft, writing—review, and editing. E.A: Data curation, software, validation, methodology, investigation, writing-original draft, writing-review, and editing. S.M.A: Conceptualization, methodology analysis, software, investigation, formal analysis, writing—original draft, writing-review, and editing L.P: Formal analysis, writing—review and editing. C.S: Formal analysis, writing—review and editing. The authors have read and approved the final manuscript.

Data availability

The corresponding author provides data that support the findings of this study upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.