Numerical Modeling of Levee Failure Mechanisms by Integrating Seepage and Stability Processes

Abstract

Levee failures caused by prolonged flooding and elevated upstream water levels pose a significant risk to floodplain communities, especially as the number of extreme hydrological events increases under climate change. Understanding seepage-induced weakening and failure mechanisms is essential for improving levee design and resilience. This study develops a numerical framework that integrates unsaturated and saturated seepage analysis with slope stability evaluation to simulate seepage front progression and predict failure initiation. The model employs van Genuchten-based soil water retention properties and experimentally derived hydraulic conductivities, with results validated against five experimental cases with varying hydraulic conductivity contrasts between the levee body and foundation soils. The simulations reproduced seepage front evolution and slope deformation patterns with good agreement with experimental observations. In cases with high permeability contrasts, the model captured foundation-dominant seepage behavior, while moderate- and low-contrast scenarios showed close alignment with observed phreatic line development. Slight deviations were noted in failure timing, but the framework demonstrated potential for reproducing seepage-induced instability in levees. The findings contribute to understanding how the internal soil composition governs levee performance under flooding and provide a basis for developing seepage countermeasures and early warning tools. This approach offers practical value for risk-informed levee design and flood management.

1. Introduction

Levees are among the most critical components of flood risk reduction infrastructure. These elongated earth structures are constructed along rivers, canals, and coastlines to contain high water levels and protect residential, agricultural, and industrial areas from flooding. However, as the frequency and intensity of hydrological events continue to rise due to climate change and rapid urban development, levee failures have become increasingly common and more devastating. Therefore, a thorough understanding of levee failure mechanisms is required to create robust flood protection systems that can withstand extreme conditions and minimize the likelihood of disasters. The catastrophic impacts of Typhoon Hagibis on Japan in 2019 exemplify how even well-maintained levees can be breached, leading to extensive flooding in many regions. The event caused 139 confirmed deaths and resulted in estimated economic losses of approximately JPY 1.88 trillion, highlighting the urgent need for improved levee resilience. It also underscored the limitations of existing safety standards for levees and highlighted the urgent need for advancing numerical modeling techniques to enhance levee design, monitoring, and maintenance [1,2,3,4,5].

Levee failures can occur through multiple mechanisms, including overtopping, internal erosion, and slope instability. Among these, seepage-induced failure is particularly insidious, as it often progresses without visible warning signs until a critical state is reached. As water infiltrates the levee body and foundation, pore water pressures increase while matric suction decreases, reducing the effective shear strength of the soil. This process weakens the levee from within, potentially triggering slope failure or even complete structural collapse [6,7]. Unlike overtopping, which occurs during short peak flows, seepage failures can arise under prolonged high-water conditions, such as sustained rainfall or long flood events [8].

Despite their significance, seepage-induced failure mechanisms have received comparatively less attention in numerical modeling efforts, especially regarding their integration with slope stability analysis. Many existing models address seepage, slope stability, and erosion as isolated or loosely connected processes. This approach limits their ability to simulate the progressive nature of failure accurately, particularly in scenarios where pore pressure buildup, loss of matric suction, and gradual shear strength reduction interact dynamically. Furthermore, numerous models rely on overly simplified soil profiles and assume homogeneity, ignoring the natural variability of levee materials [3,6,7]. Seepage and infiltration are key mechanisms contributing to slope failure in earthen levees, particularly during intensive rain fall and flooding. These processes increase pore water pressure within the levee body and reduce matric suction, leading to a progressive reduction in shear strength. The conventional Richards equation, combined with van Genuchten-based soil water retention curves (SWRCs), has been applied in the current model, which assumes instantaneous hydraulic equilibrium between the suction and water content. This approach is widely used and effective for simulating gradual seepage behavior; however, it does not incorporate dynamic nonequilibrium suction effects that can arise under highly transient conditions such as intense rainfall or rapid infiltration [9,10]. The impact of such dynamic SWRC responses remains an important consideration for future model development. Figure 1 illustrates the critical processes associated with seepage-induced failure. It shows the infiltration of water from the upstream side, the development of a curved phreatic line within the levee body, and the eventual formation of a slip surface as stability conditions degrade. The infiltration process, primarily governed by hydraulic gradients between the river and the internal soil layers, leads to the gradual saturation of the levee body material. This saturation weakens the soil’s resistance to shear stress and can trigger deep-seated or surface slip failures. The current study focuses on seepage-induced instability under rising flood levels, and slope failure due to rapid drawdown is another critical mechanism in levee safety. Rapid water level reduction can trigger instability due to delayed pore pressure dissipation and reduced effective stress [11,12]. Although not included in the present model, the framework could be extended to evaluate such conditions in future work. Understanding the interaction between infiltration flow and slope instability is essential for predicting levee performance and designing effective countermeasures under extreme hydraulic loading.

One of the most critical oversights is the inadequate representation of hydraulic conductivity contrasts between the levee body and foundation layers. These contrasts can significantly influence the development and shape of the phreatic surface, leading to preferential seepage pathways or the formation of high-pore-pressure zones at the interface of different materials. If not accurately modeled, these factors can result in the underestimation of failure risks or the misidentification of critical slip surfaces. To address these challenges, it is essential to adopt a coupled modeling framework that captures the interaction between unsaturated and saturated seepage processes and slope stability in heterogeneous soil systems. This integration is key to improving the reliability of failure predictions, especially under transient boundary conditions such as fluctuating river stages or rapid drawdown scenarios [13,14,15].

In real-world levee systems, heterogeneity in the soil composition is the norm rather than the exception. A common configuration involves a levee body composed of finer, less permeable fill material placed over coarser, more permeable foundation soils. This arrangement creates a permeability contrast that may form a capillary barrier at the interface, delaying vertical saturation while allowing lateral seepage to progress. Such permeability contrasts have a significant effect on pore pressure distribution and can lead to unexpected seepage behavior. Specifically, water may accumulate above the fine layers, increasing pore water pressure in localized zones and potentially initiating instability along those interfaces. These effects are particularly pronounced during long-duration flood events or rapid water level changes, where the time-dependent development of the phreatic surface can strongly influence failure modes. Neglecting these stratification effects in numerical models can lead to an underestimation of seepage-induced failure risks. Simplified models that assume homogenous soil profiles may misrepresent critical seepage pathways, delay points of saturation, or fail to capture shear strength reductions accurately [16,17]. Moreover, without validation across diverse material combinations and real experimental cases, such models cannot be reliably used for design safety assessments, failure prediction, or emergency response planning. Therefore, incorporating detailed soil layering and permeability contrasts into seepage and stability simulations is essential for capturing the complex interactions that govern levee performance under flood conditions.

In recent years, the importance of a fully coupled modeling approach integrating unsaturated and saturated seepage behavior with slope stability analysis has been increasingly recognized as essential for understanding seepage-induced slope failures. Zhang et al. [18] developed a multifield coupled numerical model, showing that unsaturated flow dynamics significantly influence levee body dam slope safety values. Similarly, internal erosion and slope instability driven solely by seepage were investigated using two-phase flow and strength degradation models in levee body dam slopes, emphasizing the role of internal pore pressure in destabilizing slopes [19]. Furthermore, Al-Janabi et al. [20] demonstrated the value of coupling seepage and deformation in unsaturated river levee bodies using advanced constitutive models. Despite these advances, many models still treat seepage and slope failure as sequential steps, rather than a continuous coupled process. To improve the predictive modeling of seepage-induced failure, it is essential to integrate unsaturated seepage behavior, pore pressure evolution, and slope stability into a coupled framework. The Richards equation by Richards, (1931) [21], when paired with appropriate soil water retention functions such as the van Genuchten model [22], can simulate both saturated and unsaturated flow behavior in porous media. When combined with a physically meaningful slope stability method such as Janbu’s simplified limit equilibrium approach, this framework enables the simulation of how advancing seepage fronts reduce the factor of safety, ultimately leading to slope collapse [7,23,24,25]. The accurate representation of time-dependent infiltration and internal pore pressure development is particularly important in levees constructed with heterogeneous materials.

Despite recent advances, several critical research gaps persist in seepage stability modeling. Firstly, many numerical tools fail to model seepage stability interactions in a fully time-dependent and coupled manner, instead solving each component separately and missing the progressive weakening phase that precedes failure. Secondly, most validation efforts rely on simplified laboratory setups or hypothetical levee profiles, with few studies comparing simulated and observed failure surfaces under varying soil conditions. Third, the influence of hydraulic conductivity contrasts on the levee body and foundation layers has not been systematically explored, despite field and experimental evidence that such contrasts significantly alter failure patterns. Lastly, very few models assess whether seepage alone without overtopping can trigger block-type failures, a phenomenon often observed in experimental studies but underrepresented in practical modeling applications.

To address these gaps, this study adopts a validated numerical framework based on the CSBDSP (hereafter, CADMAS-SURF with Bed Deformation and Seepage Process) model. The Fortran-based simulation tool integrates seepage flow modeling using the Richards equation with van Genuchten parameters, slope stability analysis via Janbu’s method, incorporating suction-dependent strength reduction, and failure surface tracking based on changes in the factors of the safety and saturation profiles. While the original version of the model included overtopping erosion, the present study excludes overtopping effects and focuses exclusively on seepage-induced instability. Validation is conducted using the pre-overtopping phases of five previously published experimental test cases, each involving different levee body foundation combinations and exhibiting failure prior to overflow [26,27]. The objectives of this study include simulating time-dependent seepage front propagation, dynamically evaluating slope stability under evolving pore pressures, assessing the role of hydraulic conductivity contrasts, and validating failure predictions against experimental observations. By doing so, the study aims to improve modeling reliability for levees exposed to prolonged hydraulic loading.

2. Numerical Modeling Framework

This section presents the numerical modeling framework for simulating levee behavior during seepage conditions. The model combines seepage flow analysis and stability assessment to represent various levee failure mechanisms. To ensure accuracy and relevance in real-world scenarios, the computational approach is validated against results of five experimental cases, as summarized in Table 1.

2.1. Seepage Flow Analysis

Seepage is crucial for levee stability and integrity, serving as an important early warning of potential failure by gradually weakening the levee body and foundation. Water infiltration decreases shear strength, increases pore water pressure, and can eventually lead to internal erosion or slope failures. This study employs a numerical model to simulate unsaturated and saturated seepage flow by solving the Richards equation (Equation (1)), which thoroughly describes water movement in porous and transient media. This method considers hydraulic conductivity, moisture retention, and soil–water interactions under various conditions. The Richards equation by Richards, (1931) [21] is fundamental for modeling seepage flow in unsaturated soils, accounting for spatial and temporal variations in water movement. It is expressed as follows:

$$C\left(\psi \right){\displaystyle \frac{\partial \psi }{\partial t}}={\displaystyle \frac{\partial }{\partial x}}\left(K_x{\displaystyle \frac{\partial \psi }{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_z{\displaystyle \frac{\partial \psi }{\partial z}}+1\right)$$

(1)

where $C\left(\psi \right)$ represents the specific water capacity, which is a function of the pressure head and soil properties. The $K_x$ and $K_z$ denote hydraulic conductivities in horizontal and vertical directions, respectively, and x and z are the spatial coordinates.

The Richards equation links the unsaturated and saturated zones, facilitating accurate seepage front advancement predictions and the levee body’s pressure head distribution. To properly represent unsaturated soil behavior, the van Genuchten model in Equation (2) is utilized, which defines the relationship between the soil moisture content and pressure head [22]. The model is expressed as follows:

$$\theta ={\theta }_r+{\displaystyle \frac{{\theta }_s-{\theta }_r}{{{(1+(\alpha \left|\psi \right|)}^n)}^{1-\frac{1}{n}}}}$$

(2)

where $\theta$ denotes the volumetric water content and ${\theta }_r$ and ${\theta }_s$ correspond to the residual and saturated moisture contents, respectively. The van Genuchten parameters α, n, and m are soil-specific curve fitting parameters that define the moisture retention characteristics of the material, as listed in Table 2. These parameters were primarily derived by previous researchers following empirical relationships [28,29]. The saturated hydraulic conductivity k_s (m/s) was adopted from values previously calculated [26,27] based on an empirical relationship and chart originally proposed by Craeger et al. [30] and later referenced by Komiya et al. [31]. The formula used to estimate hydraulic conductivity is $K_s=0.359{D_{20}}^{2.327}$, where $D_{20}$ is the particle diameter corresponding to the 20% finer fraction, typically retained on Sieve No. 20. This approach allowed for the consistent estimation of permeability values aligned with the observed grain size distributions for the tested soils. Boundary conditions play a crucial role in determining seepage behavior and the movement of the saturation front, as shown in Figure 2a and Figure 3.

Experimental Cases for Model Validation:

Five experimental cases were used to validate the numerical framework, each representing different hydraulic conductivity contrasts between the levee body and foundation soils, as shown in Table 1. The nomenclature of the cases (e.g., SE-S74 and IO-E8-F4) follows the original physical model studies [26,27], where SE denotes seepage erosion, IO denotes infiltration followed by overflow, and the subsequent codes represent the levee body and foundation soil types. This consistency preserves direct comparability with prior research data. The cases span a range of hydraulic conductivity ratios to evaluate seepage front progression and, in one case, slope failure under varying soil configurations. In the present study, only the seepage phase of each case is modeled, with overtopping excluded from the simulations. These labels are retained to ensure consistency with previous datasets and to facilitate direct comparison between the numerical and experimental results.

Table 1. Validated experimental cases.

Exp/Validated Cases [26,27]	Levee Body (MSS)	Levee Foundation (Mikawa Silica Sand)	Failure Condition
SE-S74	Sand No. 7 (MSS7)	Sand No. 4 (MSS4)	Seepage Erosion (SE)
IO-E8-F4	MSS8	MSS4	Infiltration + overflow (IO)
IO-E7-F5	MSS7	MSS5	Infiltration + overflow (IO)
SE-S85	MSS8	MSS5	Seepage Erosion (SE)
SE-S87	MSS8	MSS7	Seepage Erosion (SE)

Note: SE-S74 seepage erosion failure condition with Mikawa Silica Sand (MSS) No. 7 in levee (embankment) body (E) and No. 4 in levee foundation (F), IO-E7-F5 infiltration and overflow condition with levee body (E) MSS7 and foundation (F) MSS5 in previous studies.

Table 1. Validated experimental cases.

Exp/Validated Cases [26,27]	Levee Body (MSS)	Levee Foundation (Mikawa Silica Sand)	Failure Condition
SE-S74	Sand No. 7 (MSS7)	Sand No. 4 (MSS4)	Seepage Erosion (SE)
IO-E8-F4	MSS8	MSS4	Infiltration + overflow (IO)
IO-E7-F5	MSS7	MSS5	Infiltration + overflow (IO)
SE-S85	MSS8	MSS5	Seepage Erosion (SE)
SE-S87	MSS8	MSS7	Seepage Erosion (SE)

Note: SE-S74 seepage erosion failure condition with Mikawa Silica Sand (MSS) No. 7 in levee (embankment) body (E) and No. 4 in levee foundation (F), IO-E7-F5 infiltration and overflow condition with levee body (E) MSS7 and foundation (F) MSS5 in previous studies.

Table 2. Soil parameters related to seepage flow.

Soil Type	Saturated Volumetric Water Content (${\mathit{\theta }}_{\mathit{s}}$)	Residual Volumetric Water Content (${\mathit{\theta }}_{\mathit{r}}$)	$\mathit{\alpha }$	$\mathit{n}$	${\mathit{K}}_{\mathit{s}}$  $\left(\frac{\mathit{m}}{\mathit{s}}\right)$
MSS4	0.38	0.022	0.082	4.872	$1.6\times {10}^{-3}$
MSS5	0.329	0.10	0.283	2.944	$3.2\times {10}^{-4}$
MSS7	0.351	0.095	2.552	4.148	$2.6\times {10}^{-5}$
MSS8	0.40	0.025	1.043	1.701	$5.5\times {10}^{-6}$

Note:${\theta }_s$ and ${\theta }_r$ correspond to the saturated and residual moisture contents, respectively. $\alpha$ and $n$ are van Genuchten parameters describing the soil–water retention curve. $K_s$ is the saturated hydraulic conductivity.

Table 2. Soil parameters related to seepage flow.

Soil Type	Saturated Volumetric Water Content (${\mathit{\theta }}_{\mathit{s}}$)	Residual Volumetric Water Content (${\mathit{\theta }}_{\mathit{r}}$)	$\mathit{\alpha }$	$\mathit{n}$	${\mathit{K}}_{\mathit{s}}$  $\left(\frac{\mathit{m}}{\mathit{s}}\right)$
MSS4	0.38	0.022	0.082	4.872	$1.6\times {10}^{-3}$
MSS5	0.329	0.10	0.283	2.944	$3.2\times {10}^{-4}$
MSS7	0.351	0.095	2.552	4.148	$2.6\times {10}^{-5}$
MSS8	0.40	0.025	1.043	1.701	$5.5\times {10}^{-6}$

Note:${\theta }_s$ and ${\theta }_r$ correspond to the saturated and residual moisture contents, respectively. $\alpha$ and $n$ are van Genuchten parameters describing the soil–water retention curve. $K_s$ is the saturated hydraulic conductivity.

The numerical simulation process follows a structured workflow, which outlines the key computational steps involved in seepage modeling. This process includes setting pressure head boundary conditions, obtaining soil parameters, discretizing the domain using finite difference methods, and solving the Richards equation iteratively. The numerical model effectively captures the progression of the seepage front, validating its ability to predict water infiltration under various hydraulic conditions.

2.2. Stability Analysis

Stability analysis evaluates the risk of failure due to seepage-induced weakening and erosion, which significantly contributes to levee failures. As water infiltrates the levee body, it reduces shear strength, increases pore water pressure, and weakens the internal structure, ultimately triggering slip failures. The numerical model developed in this study integrates two complementary approaches: the simplified Janbu method [32,33], which accounts for seepage-induced strength reduction, and the limit equilibrium method (LEM) for assessing slope stability [23]. These approaches comprehensively help to understand levee stability under various hydraulic and geotechnical conditions.

2.2.1. Slip Failure Analysis

The simplified Janbu method introduced in this study integrates the effects of suction on shear strength, which is crucial for assessing the stability of levees under seepage conditions. The method calculates the factor of safety (Fs) by incorporating the increment in suction-induced shear strength, considering soil properties and hydraulic conditions (Equation (3)) [34,35].

$$F_s={\displaystyle \frac{\sum _{i=1}^n\left\{\left({c_i}^{\prime }{l}_i+\left(N_i-u_{wi}{l}_i\right)\mathit{tan}\varphi +{\tau }_{suci}{l}_i\right)\right\}}{\sum _{i=1}^n{W}_i\mathit{sin}{\alpha }_i}}$$

(3)

This analysis considers the cohesion $\left({c_i}^{\prime }\right)$, normal stress ${(N}_i)$, pore water pressure ($u_{wi})$, suction-induced shear strength (${\tau }_{suci}),$ and internal friction angle ($\varphi )$, as well as the length of the potential failure surface ${(l}_i)$, weight of each segment $\left(W_i\right)$ and the inclination angle of each segment $\left({\alpha }_i\right)$ to evaluate the levee’s resistance to failure. The numerical findings were closely aligned with experimental data, effectively predicting areas of slip failure. Figure 2 depicts a schematic of the slip failure model, emphasizing key failure zones and mechanisms of block failure. The study centers on modeling failure progression as infiltration reaches critical thresholds, showing that numerical simulations identify failure initiation sooner than experimental observations. The seepage stability interaction is fundamentally governed by the redistribution of effective stress, influenced by pore water pressure and suction. The use of the Richards equation combined with the van Genuchten soil water retention function allows for an accurate representation of unsaturated flow behavior. Simultaneously, the limit equilibrium analysis accounts for strength reductions due to saturation. The theoretical framework aligns with Terzaghi’s effective stress principle, extended for unsaturated soils, and allows for the dynamic prediction of failure conditions as the water content evolves temporally.

2.2.2. Block Failure Analysis

As seepage progresses, the upper portion of the levee stays unsaturated, enhancing soil strength due to interparticle forces. However, ongoing infiltration results in saturation and the eventual collapse of soil blocks (Equation (4)) [36]. The moment equilibrium equation assesses block failure:

$$\begin{array}{c}f\left(W_f\right)=P_1{d}_{P1}+P_2{d}_{P2}+P_3{d}_{P3}+P_4{d}_{P4}\\ -2F_{c,f}{d}_{F_{c,f}}+G_1{d}_{G1}+G_2{d}_{G2}-N{d}_N\#\end{array}$$

(4)

This analysis considers the weight of the soil block ($W_f)$, the forces acting on different points ($P_1,P_2,P_3,P_4)$ with their respective lever arms ($d_{P1},d_{P2},d_{P3},d_{P4})$, the resisting force due to cohesion ($F_{c,f})$ with its lever arm ${(d}_{F_{c,f}})$, the gravitational forces $(G_1,G_2)$ with their respective lever arms ${(d}_{G1},d_{G2})$, and the normal force $\left(N\right)$ with its lever arm ${(d}_N)$ to comprehensively evaluate block failure due to seepage-induced weakening. Figure 2c illustrates the observed block failure patterns in experimental and numerical simulation.

The numerical model offers a thorough stability assessment by incorporating slip and block failure mechanisms, capturing slope instability and localized soil detachment events. Slope stability analysis was conducted under non-overtopping conditions. Therefore, external water pressure on the levee crest was not applied in stability calculations. Specifically, the boundary forces $P_1,P_2$ in Equation (4) and Figure 2c, which represent external hydrostatic pressure or surface water loading, were set to zero. Instability was evaluated based solely on internal pore water pressures arising from seepage through the levee body and foundation layers. This dual approach aligns with experimental findings and improves the model’s predictive capability in assessing levee failure risks during extreme hydraulic conditions.

2.3. Modeling Approach and Boundary Conditions

This section describes the numerical modeling framework used to simulate levee behavior under seepage conditions, emphasizing the levee’s structural composition and the boundary conditions applied to mimic real-world scenarios.

2.3.1. Levee Composition and Material Properties

This study examines a levee structure comprising two central regions with different material properties, the levee body and foundation layers. Each layer plays a crucial role in seepage dynamics and overall stability under varying hydraulic conditions, as shown in Figure 3. To confirm the accuracy of the calculation results, the same conditions were kept as in the seepage experiments conducted [26,27]. The levee body layer acts as the main structural element and is the first line of defense against flooding. It is made from Mikawa Silica Sand No. 8 and 7, a fine material chosen for its superior compaction and moisture retention capabilities. Its low permeability minimizes water infiltration, thus lowering the risk of internal erosion. Structurally, this layer withstands hydrostatic pressures from floodwaters, preserving the levee’s integrity by limiting seepage and preventing erosion. Below the levee body, the foundation layer offers vital support and enables controlled seepage. Composed of coarser sands, this layer has higher permeability, allowing for swift drainage and the relief of pore water pressures. The differing permeabilities of the two layers create significant hydraulic gradients that affect seepage patterns and overall stability. The foundation layer helps to reduce uplift pressures and alleviate structural instability risks by facilitating efficient seepage discharge. The hydraulic behavior of these layers is modeled using the van Genuchten approach, which enables accurate numerical simulations of seepage processes [22,28,29].

2.3.2. Boundary Conditions and Their Role in Seepage Analysis

Boundary conditions define the interaction between the levee and its surrounding hydraulic environment as shown in Figure 3. In this study, the following boundary conditions have been applied:

Upstream Boundary (Initial Water Level):

The upstream face of the levee is subjected to a constant water head to simulate flooding conditions, represented by the red arrows in Figure 3. This boundary allows for water infiltration under an applied hydraulic gradient, simulating real-world flood scenarios.

Downstream Boundary (Free Drainage):

The downstream side is modeled as a free drainage condition, facilitating the natural outflow of water without resistance and preventing pressure buildup.

Bottom Boundary (Impermeable Layer):

The levee’s base is treated as an impermeable boundary red line in Figure 3, preventing downward water movement and ensuring lateral seepage within the foundation layer.

Side Boundaries:

The side boundaries are assumed to be impermeable to prevent water escape, and the analysis is focused on vertical and horizontal seepage patterns.

It is recognized that soil saturation variation near hydraulic boundaries may involve transient nonequilibrium effects. In this study, an equilibrium-based SWRC was applied, but future work could consider dynamic formulations to better capture highly transient seepage behavior [9,10].

2.4. Seepage Flow Behavior and Failure Mechanisms

The interaction between the levee body and foundation layers generates complex seepage patterns that significantly affect levee stability. Water infiltrates the levee body layer slower due to its low permeability. In contrast, the foundation layer allows for faster water movement, creating a seepage front that advances toward the downstream side. This differential movement can cause the development of critical failure zones, including the following:

Internal Erosion: Triggered by the migration of fine particles from the levee body layer into the foundation layer, leading to structural weakening.

Slip Failure: The saturation of the levee body layer reduces shear strength, potentially initiating slip failure along critical failure surfaces.

Piping Effects: Uncontrolled seepage through the foundation layer may result in backward erosion piping, ultimately leading to levee breaching.

Understanding the interaction between the levee body and foundation layers and precisely defining boundary conditions is crucial for evaluating levee stability under seepage conditions. The numerical model used in this study considers these factors comprehensively, offering insights into seepage-driven failure mechanisms and facilitating the development of more resilient flood protection strategies.

2.5. Validation of Numerical Model Through Experimental Studies

The current numerical study was validated against experimental studies conducted [26,27] in a controlled flume environment. The model was calibrated and verified using experimental data for various levee configurations, including the levee body and foundation materials.

2.5.1. Validation Metrics and Observations

The numerical model was validated using key metrics to compare the simulation results with experimental data. These metrics comprehensively assess the model’s accuracy in capturing the essential seepage, erosion, and stability processes within the levee system.

Seepage Front Progression

The seepage front refers to the advancing boundary between saturated and unsaturated zones within the levee. The model’s capability to accurately simulate seepage behavior was assessed by comparing the predicted and observed seepage front advancement at different time intervals. The boundary between saturated and unsaturated zones, commonly referred to as the seepage front, is fundamentally critical in understanding structural instability because it directly governs the evolution of pore water pressure and matric suction, which in turn control the effective stress and shear strength of the soil. As the seepage front migrates, it transforms unsaturated soil into saturated zones, rapidly reducing matric suction and increasing pore pressure. This transition reduces the soil’s ability to resist deformation and creates potential slip surfaces. The dynamic position of the seepage front thus acts as a precursor to failure and defines the onset and progression of internal instability, especially in heterogeneous levee systems. Understanding this interface allows for a more accurate prediction of when and where failures may occur, particularly under prolonged or fluctuating hydraulic loading [18,34].

Failure Surface Geometry

The failure surface represents the slip plane where shear stresses exceed the resisting forces, leading to structural instability. Validation involved comparing the model’s predicted failure surface geometry with experimentally observed failure planes to evaluate its accuracy in capturing failure mechanisms.

3. Results and Discussion

The numerical simulations were validated against the five experimental cases summarized in Section 2.1. These include varying hydraulic conductivity contrasts between the levee body and foundation soils, providing a comprehensive basis for evaluating seepage front behavior and, in one case (IO-E8-F4), slope stability analysis. The numerical results are thoroughly compared to experimental findings to evaluate the model’s predictive strength, emphasize key similarities, and pinpoint areas needing improvement.

3.1. Seepage Front Progression

The seepage front, defined as the boundary between the saturated and unsaturated zones within a levee, plays a critical role in determining structural stability during seepage erosion conditions. Numerical simulations captured the dynamic progression of the seepage front under varied soil configurations and were validated against experimental data based on upstream water level heights. Results were validated using upstream water levels (half and full height of 0.375 m). The simulations employed saturation ratio (S_r) contours to represent moisture conditions, where red zones indicate fully saturated regions (S_r > 90%), green and blue shades depict transitional and unsaturated zones, respectively, and the experimental seepage front was tracked using a blue reference line. Overall seepage fronts were validated well with minor discrepancies. Nonetheless, these differences did not significantly impact the overall accuracy of seepage front predictions.

3.1.1. Seepage Behavior Comparison for SE-S74 and IO-E8-F4

Figure 4 illustrates the comparison of seepage behavior in SE-S74 and IO-E8-F4 cases at two different upstream water levels of half the height of 0.375 and the full water level at 0.375 m upstream. Figure 4a,c correspond to SE-S74, while Figure 4b,d correspond to IO-E8-F4.

In SE-S74, where the hydraulic conductivity contrast was moderate, i.e., the hydraulic conductivity of the foundation is 60 times higher than that of the levee body (k_F/L_L, ratio of hydraulic conductivity of levee foundation to body material = 60), the simulation showed a well-distributed seepage front moving progressively from the upstream face through the levee body. At the half height (Figure 4a), saturation started to penetrate the levee body and foundation, with visible red zones expanding. By the time the upstream water level reached 0.375 m (Figure 4c), the seepage front had extended to the downstream toe, forming a continuous red zone beneath the crest and slopes, indicating full saturation and substantial infiltration. The simulation aligns well with the experimental blue phreatic line, although minor discrepancies near the crest region suggest some underestimation of lateral infiltration.

In contrast, IO-E8-F4 exhibited a significant hydraulic conductivity contrast, i.e., the hydraulic conductivity of the foundation material was 300 times higher than that of the levee body material (k_F/k_L = 300). At the half water level (Figure 4b), the seepage front was minimal in the levee body but had already developed considerably in the foundation, with clear red bands forming horizontally. This indicates preferential flow through the foundation due to its higher permeability. When the upstream level reached 0.375 m (Figure 4d), saturation spread aggressively through the foundation while the levee body remained mostly unsaturated, supporting the capillary barrier effect. This delayed infiltration into the levee body reflects the capillary barrier phenomenon, a theoretical outcome of unsaturated flow mechanics where water entry into finer soil is resisted until a threshold matric potential is overcome. This is consistent with the van Genuchten model behavior for soils with low α values, where increased suction is required to initiate saturation. The result is a horizontal migration of water through the foundation, leading to a lateral seepage front. The blue phreatic line in experiments matched this trend, although the simulation showed slightly delayed levee body infiltration.

3.1.2. Seepage Behavior Comparison for SE-S85 and IO-E7-F5

Figure 5a,c compare seepage front development in IO-E7-F5, and Figure 5b,d show the same for SE-S85 at half and full upstream water levels. In SE-S85, red zones were prominent under the downstream toe at both half (Figure 5d) and full water levels (Figure 5b), highlighting foundation-dominant infiltration. The levee body showed modest saturation, confirming a permeability contrast like SE-S74. The infiltration transitions are from moderate to intense as the water level rises. Despite a similar hydraulic contrast to SE-S74, the hydraulic conductivity of the foundation is slightly lower, which reduces contact erosion risks. The failure mechanism is piping along the interface rather than contact erosion. Experimental results indicate a 100% downstream slope and 35% crest failure, which nearly matches the erosion in SE-S74. The numerical results correlated strongly with experimental front shapes, and the simulation accurately captured the transition from moderate to intense infiltration with increasing water levels.

SE-S75, characterized by a finer levee body material, displayed delayed seepage propagation. At the half level (Figure 5c), red zones were minimal, and infiltration remained shallow. At full height (Figure 5a), seepage extended more noticeably into the foundation but remained constrained in the levee body. This behavior confirmed the influence of lower hydraulic conductivity values. The comparison to experimental seepage fronts showed general agreement, though some differences in levee body depth suggest local heterogeneity not reflected in the model.

3.1.3. SE-S87 (Low Permeability Contrast and Stability)

Figure 6a shows the SE-S87 case at the full upstream water level, while Figure 6b illustrates the case at the half upstream water level. As this case had the lowest hydraulic conductivity contrast, i.e., the hydraulic conductivity of the foundation material was only eight times higher than that of the levee body material (k_F/k_L = 8), seepage progression was very slow. In both figures, red zones are largely confined to the upstream toe. Minimal water infiltration occurred, with blue and green zones dominating the levee body and foundation.

The numerical simulation shows excellent agreement with experimental seepage front progression, indicating a stable seepage pattern and confirming minimal erosion potential. The absence of a significant downstream red zone in both images emphasizes the uniform low permeability of the materials, which restricts rapid saturation even under higher hydraulic heads.

3.1.4. Numerical Vs. Experimental Agreement and Interpretation

Table 3. Summary of all experimental cases of seepage erosion tests.

Experimental Cases	SE-S74	IO-E8-F4	IO-E7-F5	SE-S85	SE-S87
kF/kL	60	300	12	60	8
Initiation (Water appears)	−2 min 0 sec	0 min 5 sec	10 min 0 sec	5 min 0 sec	Nil
Early erosion	(0–10) minutes 60% D/s slope	(0–10) minutes A big shear crack 25% D/s slope	(0–20) minutes 30% D/s slope	(0–20) minutes 10% D/s slope	Nil
Intermediate erosion	(10–20) minutes 100% D/s slope 15% crest	(10–20) minutes 100% D/s slope Crest 15%	(20–70) minutes 55% D/s slope	(20–60) minutes 100% D/s slope	Nil
Continued erosion	(20–90) minutes	20 min	(70–90) minutes	(60–90) minutes	Nil
Stabilization (relative stability)	After 90 min	After 90 min	After 90 min	After 150 min	Stable
D/S slope failure time	20 min Rapid failure	20 min Rapid failure	No d/s slope failure	60 min Slower failure	Nil
Percentage of D/s slope erosion	100%	100%	65%	100%	Nil
Percentage of crest erosion	30%	70%	0%	35%	Nil

Note: k_F/k_L (ratio of hydraulic conductivity of levee foundation to body material, min = minutes.

summarizes the experimental observations, including water appearance, erosion onset, and crest failure for each test case. In SE-S74, numerical and experimental data showed strong alignment in seepage progression and slope failure onset. IO-E8-F4 simulations accurately represented foundation-dominant flow but slightly lagged in levee body infiltration, likely due to simplifications in soil stratification.

In SE-S85, the simulated saturation under the downstream toe and foundation matched the expected behavior from its high conductivity contrast. SE-S75’s restricted levee body infiltration and moderate foundation flow were well-captured, though the onset of saturation appeared slightly delayed in the model.

SE-S87 showed near-perfect agreement between the simulation and experiment. Minimal seepage development, the absence of erosion, and balanced infiltration across the levee body and foundation were all confirmed by both visual and modeled outputs.

These results validate the model’s ability to replicate seepage progression under various hydraulic conductivity contrasts. The clear correlations between red saturation zones in simulations and experimental blue phreatic lines support the model’s accuracy. Furthermore, discrepancies noted in some cases, such as delayed levee body infiltration in IO-E8-F4 and SE-S75, underscore the importance of refining parameter estimation and considering soil heterogeneity in future modeling efforts. Overall, the numerical model successfully captured the complex dynamics of seepage propagation, reinforcing its value in predicting erosion-prone scenarios in levee systems.

3.2. Failure Surface Geometry

The accurate prediction of failure surfaces is crucial for assessing the stability of levees under seepage conditions. The numerical model employed in this study identified potential slip surfaces by minimizing the factor of safety (Fs) using dynamic programming and limit equilibrium methods. To evaluate model accuracy, the simulated failure surfaces were compared with experimentally observed failure planes, which were determined through visual inspection and displacement measurements. The results highlight key similarities and discrepancies between numerical predictions and experimental observations, offering insights into levee failure mechanisms under different hydraulic conditions. Among the five validation cases, IO-E8-F4 was the only scenario in which full slope failure occurred during the simulated seepage phase, enabling direct comparison of failure surface geometry.

3.2.1. Comparison of Experimental and Numerical Failure Surfaces

Figure 7 presents a comparative analysis of the failure surface obtained from numerical analysis (red line) and the initial slip failure observed in the experiment. Experimental results indicate that the first visible failure occurred approximately 120 s (2 min) after seepage initiation, whereas the numerical model predicted a significant slip failure earlier, at around 80 s. This discrepancy suggests that the numerical approach, which focuses on identifying the most critical failure mode, may have overestimated the rate of strength reduction, leading to an earlier failure prediction than observed in the experiment. However, despite this difference in timing, the shape of the numerically predicted failure surface closely resembles the experimentally observed failure plane, particularly at later stages (around 14 min). This similarity reinforces the model’s ability to capture the dominant failure mechanisms but also highlights the need to refine progressive erosion effects that contribute to small-scale deformations before large-scale collapse.

The red line in Figure 7 represents the computed slip surface, delineating the zone of mass movement where soil displacement occurs due to seepage-induced weakening. As observed in experimental and numerical results, the failure surface initiates from the downstream slope. It extends toward the crest, indicating a deep-seated slip mechanism driven by increasing pore water pressure and reduced shear strength. Notably, the final numerically predicted failure plane aligns well with the experimentally observed slip surface at 14 min, further validating the model’s ability to replicate large-scale mass movement. The onset of slope failure in IO-E8-F4 corresponds to a reduction in the factor of safety as pore pressures rise and matric suction is lost. According to unsaturated soil mechanics, the contribution of suction to shear strength is critical in maintaining stability [34]. The transition from unsaturated to saturated conditions under high-seepage gradients reduces this strength, promoting instability along interfaces where pore pressure exceeds resisting stresses.

3.2.2. Post-Failure Levee Profile and Sediment Deposition

Figure 8 further supports this comparison by illustrating the post-failure levee profile after sediment deposition. The black line represents the initial levee height, while the green dashed and blue dotted lines correspond to experimental observations at different time intervals (14 min and 18 min, respectively). The red line represents the numerically simulated post-failure profile, which follows the experimental data closely, demonstrating the model’s ability to predict the final deformed shape of the levee after mass movement. The development of a steep scarp and sediment buildup at the downstream toe, seen in both numerical and experimental profiles, confirms the similarity in failure mechanisms across the two methods.

Although the failure shapes align closely, differences in timing arise from multiple factors. First, variations in soil heterogeneity and permeability on a small scale in the experimental setup may have delayed failure compared to the more uniform conditions assumed in the numerical model. Second, boundary effects and initial saturation states in the experiment could have caused the slower progression of instability. At the same time, the numerical model focuses on the most critical failure scenario, often resulting in earlier collapse predictions. Moreover, the numerical approach did not completely capture the progressive erosion and minor slip events in the experiment during the early failure stages.

3.2.3. Model Limitations in Predicting Seepage-Induced Failure and Future Improvements

The combined analysis of Figure 7 and Figure 8 demonstrates that the numerical model can effectively simulate failure surface geometry and post-failure deformation for the IO-E8-F4 case, where failure occurred during the seepage phase. However, this is the only case among the five test scenarios in which the simulated hydraulic conditions triggered visible slope failure within the modeled time frame. In the remaining cases, including SE-S75 and SE-S85, failure was observed experimentally only after the upstream water level was maintained at its peak for extended periods, a condition not replicated in the current simulations. Consequently, stability analysis and slip surface validation were limited to IO-E8-F4. This case exhibited a particularly high contrast in hydraulic conductivity (k_F/k_L = 300), which led to foundation-dominated seepage, rapid lateral flow, and early pore pressure build up beneath the downstream slope. This made it uniquely suitable for capturing full slope failure during the simulation. In contrast, other cases with lower permeability contrast developed seepage fronts more gradually and did not reach the failure threshold within the rising water stage.

To generalize the model’s applicability for failure prediction across various soil conditions, future studies should consider extending the simulation time, allowing the upstream water level to remain constant, or even simulate fluctuating hydraulic loading. These adjustments may enable the observation and modeling of delayed or progressive failures in the remaining experimental cases. Additionally, incorporating small-scale erosion mechanisms and partial slip deformation will further enhance the model’s realism and predictive power.

3.2.4. Coupled Seepage Stability Response in IO-E8-F4

Among the five validation cases analyzed, only IO-E8-F4 exhibited slope failure during the modeled seepage phase. This case featured an exceptionally high hydraulic conductivity contrast between the levee body and the foundation layer, which created a pronounced capillary barrier effect. As a result, vertical infiltration into the levee body was delayed, while lateral seepage through the foundation accelerated. This led to rapid pore pressure build up beneath the downstream slope, reducing effective stress and ultimately initiating slip failure as the factor of safety dropped below 1.0. In this study, failure initiation was identified when the factor of safety approached unity (Fs = 1.0), which is common in research contexts for capturing the onset of instability. However, in engineering design practice, higher Fs thresholds are typically required to ensure safety under uncertainty. For example, Fs ≥ 1.3 -1.5 is often adopted for static levee stability, and values up to 2.0 are recommended under seismic or long-term serviceability conditions [37,38]. In current study, the Fs was computed using the Janbu simplified method, applied along potential slip surfaces extracted from transient pore pressure distributions obtained from the seepage model. While this approach effectively tracks the temporal evolution of slope stability at critical sections, it does not generate full spatial contour plots of Fs across the domain. The absence of Fs distribution maps is a current limitation, and future model development could integrate this functionality to allow for the broader spatial interpretation of failure risk zones. Such contour plots would provide enhanced visual diagnostics and allow for comparison with localized deformation patterns observed in physical tests or field monitoring. The model successfully captured the location and shape of the failure surface for this scenario, closely aligning with the experimental observations. This confirms the model’s ability to simulate seepage-induced slope failure under certain conditions where instability develops rapidly and is dominated by foundation flow. However, in the other four test cases, the simulated seepage phase did not extend far enough in time to trigger failure, even though these cases eventually exhibited failures as evident experimentally. This limitation primarily stems from the model simulating only the rising phase of the water level. In contrast, experimental tests often involved holding the upstream water level constant or introducing fluctuations, which allowed failure to develop at a later stage. Therefore, while the coupled seepage stability approach effectively reproduced failure in IO-E8-F4, its application in predicting failure geometry for other cases remains constrained by temporal and boundary condition limitations in the current modeling setup. Future work should aim to incorporate longer simulation durations, variable hydraulic loading, and more realistic saturation cycles to evaluate failure onset under a broader range of conditions.

3.2.5. Model Limitations Regarding Material Movement

While the model successfully simulates slope failure initiation, geometry deformation, and the location of critical slip surfaces, it does not include a post-failure sediment transport or deposition component. As a result, the model shows slope deformation and mass displacement along the failure surface but does not simulate the movement and accumulation of failed soil mass at the downstream toe, as observed in physical experiments. This limitation results in an apparent volume loss near the slope toe in the analysis output (e.g., the red profile in Figure 8), where experimental results show visible accumulation. The soil mass that fails is displaced and settles at the toe. However, the current model only adjusts the slope geometry to reflect failure progression; it does not physically transport the displaced mass beyond the slip surface. To accurately simulate this post-failure behavior and ensure mass conservation, future model improvements should consider coupling with a sediment transport module or a particle-tracking algorithm that can represent the dynamic relocation of failed materials.

4. Conclusions

This study implemented and calibrated a validated numerical model to investigate seepage front progression and failure mechanisms in levees under seepage flow conditions, focusing on varying hydraulic conductivity contrasts between the levee body and foundation materials. Numerical simulations were performed using van Genuchten-based soil water retention parameters and experimentally derived hydraulic conductivities, with results compared against a series of controlled physical model tests.

• The model effectively reproduced the infiltration dynamics and seepage front movement observed in the experiments across five test scenarios. In cases with moderate permeability contrast, such as SE-S74 and SE-S85, the simulations showed consistent seepage propagation through the levee body, aligning closely with experimental phreatic lines. For high-contrast cases like IO-E8-F4, the model successfully captured foundation-dominant flow and delayed levee body infiltration due to capillary barrier effects, although slight timing discrepancies were noted. In SE-S75, the finer levee body material led to vertical infiltration patterns with slower propagation, which the model replicated with minor deviations. In the low-contrast SE-S87 case, seepage progression was minimal, and the model achieved near-perfect agreement with experimental data.
• The validation of the failure surface geometry was performed only for the IO-E8-F4 case, where slope failure occurred during the modeled seepage phase. In this case, the model accurately captured the shape and extent of the slip surface, demonstrating strong alignment with experimental observations. However, in other test scenarios, slope failure either did not occur during the simulated period or required longer hydraulic loading not included in the current setup. As such, conclusions about the model’s predictive ability for failure surfaces should be considered to be case-specific rather than general.

This study uses an equilibrium-based soil water retention model, which does not capture dynamic nonequilibrium suction effects that can occur under rapidly changing seepage conditions. Material heterogeneity was not included, and a full sensitivity analysis of key hydraulic parameters was outside the current scope. These are important limitations that should be addressed in the next stage of research. Future work should incorporate soil heterogeneity, perform detailed parameter sensitivity testing, and explore the impact of transient SWRC behavior to improve predictions of early infiltration and localized failure triggers. Extending simulations to cover longer time periods, fluctuating water levels, and gradual erosion processes will also help the model to replicate the delayed or progressive failures seen in real levee systems and make it more useful for practical safety assessments.