Local Scour Around Marine Structures: A Comprehensive Review of Influencing Factors, Prediction Methods, and Future Directions

Abstract

Local scour is a phenomenon of sediment erosion and transport caused by the dynamic interaction between water flow and seabed sediment, posing a serious threat to the safety of marine engineering structures such as cross-sea bridges and offshore wind turbines. To improve scour prediction and prevention capabilities, this review systematically analyzes the influence mechanisms of factors such as hydrodynamic conditions, sediment characteristics, and structural geometry, and discusses scour protection measures. Based on this, a comprehensive evaluation of the applicability of different prediction methods, including traditional empirical formulas, numerical simulations, probabilistic prediction models, and machine learning (ML) methods, was conducted. The study focuses on analyzing the limitations of existing methods: empirical formulas lack adaptability under complex field conditions, numerical simulation still faces challenges in validating real marine environments, and data-driven models suffer from “black box” issues and insufficient generalization capabilities. Based on the current research progress, this review presents prospects for future development, emphasizing the need to deepen the study of scouring mechanisms in complex real marine environments, develop efficient numerical models for engineering applications, and explore intelligent prediction methods that integrate data-driven approaches with physical mechanisms. This aims to provide more reliable theoretical support for the safe design, risk prevention, and scouring mitigation measures in marine engineering.

1. Introduction

Local scour is the process of sediment erosion and transport that occurs around marine structures under the action of water flow. The physical process begins with the forced separation of streamlines when the current encounters a structure, which in turn forms a complex three-dimensional system of flow structures around the structure, including a significant horseshoe vortex system downstream of the upper reaches, a strong descending current, and a lee vortex that develops behind it (Figure 1) [1]. These strong vortex structures and the high-velocity fluid region generate bed shear stresses much higher than those of the original uniform flow, which directly drive the initiation and transport of sediment particles and thus change the scour topography [2]. This phenomenon directly affects the structural stability of infrastructure and may cause serious accidents, such as the collapse of cross-sea bridges [3] and the instability of offshore wind turbine foundations [4], etc. Therefore, it is significant to study the mechanism of local scour and improve the prediction accuracy to guarantee the safe operation of hydraulic structures and optimize the protection scheme of the engineering design.

The complexity of local scour mainly stems from three key factors: flow characteristics, structure geometry, and sediment properties [5]. In terms of flow characteristics, the increase in flow velocity directly enhances bed shear stress [6]. At the same time, the periodic oscillation of waves not only reshapes the topography of scour holes through reciprocal sediment lifting [5] but also increases the pore water pressure in the long term, which results in a continuous decrease in the effective stress in the sediment skeleton. This process weakens the critical conditions for sediment initiation, thus significantly accelerating scour development [7]. At the same time, the horseshoe vortex system develops in the turbulence field and the descending current forms an erosion effect, further accelerating the local scour process [8]. In terms of structural features, structures’ size and shape characteristics significantly change the structure of the local flow field, directly affecting the scour development process [9]. Meanwhile, complex foundation configurations and spatial arrangement parameters of pile groups reshape the three-dimensional topographical characteristics of the scour through multi-body flow interference effects [10]. The influence of sediment properties on the scour process is mainly reflected in the particle size distribution and soil compactness [11,12]. Coarse particles form a protective layer on the bed surface, while the water flow more easily transports fine particles, so well-graded sediments usually show stronger scour resistance [13]. Soil compactness improves structural stability by increasing the friction and cohesion between particles, which slows down scour development [12]. It is worth noting that extreme hydrological events such as typhoon storm tides and tsunamis can instantaneously increase the flow dynamics and change the sediment transport pattern, resulting in abrupt damage to the originally stable sediment regime. This catastrophic process often exceeds the predictive capacity of conventional scour models [7,14]. For example, Wang et al. [15] pointed out that strong wave–current interactions during typhoons can trigger a series of complex sedimentary processes, such as sediment resuspension and transport, significantly altering the topography of coastal zones. These complex influencing factors and the sudden occurrence of extreme events pose a serious challenge to traditional prediction methods based on steady states and simplified assumptions.

With the breakthrough in computational power, numerical simulation has become an important tool for local scour studies. Among the existing methods, Computational Fluid Dynamics (CFD)-based single-phase models, although widely used, are often limited in simulation accuracy due to their reliance on empirical formulas [16]. Unlike the single-phase flow model, the two-phase model can reveal the micro-mechanism of scour more accurately by directly simulating the interactions between fluid and sediment particles and the inter-particle contact [17,18]. In addition, the meshless smooth particle hydrodynamics (SPH) method provides a new technological path for studying scour mechanisms, relying on its unique advantage in dealing with large deformation problems [19]. Meanwhile, empirical and semi-empirical prediction formulations developed based on experimental data are still important tools in engineering practice. However, such formulations suffer from problems with accuracy and scale effect, which makes it difficult to accurately predict the scouring process under prototypical sizes or complex working conditions [20]. To break through this limitation, ML techniques provide new data-driven solutions for scour prediction under multi-parameter coupled conditions that rely on their automatic feature extraction and complex nonlinear mapping capabilities [21]. However, its “black box” nature and reliance on high-quality, large-scale training data mean that its predictive reliability and physical interpretability remain challenging when faced with rare extreme conditions [22]. At the same time, given the inherent uncertainty of hydrological, seabed, and structural parameters, probabilistic prediction methods are increasingly being emphasized, aiming to provide a more comprehensive basis for engineering decisions from a risk assessment perspective [23].

In view of this, this paper aims to provide a deep and comprehensive review of the research on local scour around marine structures. To achieve this goal, the organization of this review is as follows: First, this paper systematically analyzes the mechanisms of key influencing factors such as hydrodynamic conditions, geometric characteristics of structures, and seabed sediment properties, and based on this, discusses the principles and applications of various scour protection measures. Subsequently, this paper critically evaluates traditional empirical formulas, multi-scale numerical simulations, data-driven machine learning models, and probabilistic risk assessment methods, exploring the theoretical foundations, advantages, and current challenges faced by each approach. Finally, based on a comprehensive summary, this paper looks forward to future research directions, focusing on innovative pathways in mechanism research, numerical models, and intelligent prediction methods, with the aim of providing systematic theoretical references and technical guidance for enhancing the safety design, risk assessment, and scouring protection capabilities of marine engineering structures.

2. Main Factors Affecting Local Scour

The development of local scour processes around marine structures is mainly influenced by fourmajor factors: hydrodynamic conditions, structural characteristics, sediment characteristics and other environmental factors. Based on the existing research results, this section systematically analyzes the mechanism of hydrodynamic elements such as flow velocity, waves, and turbulence; explores the influence of the shape, size, and arrangement of structures; and clarifies the regulatory role of the characteristics of sediments such as grain size, gradation, and compactness. Additionally, the study further analyzed the effects of tidal forces and extreme weather conditions on local scour. Based on a comprehensive understanding of these influencing factors, the study provides detailed descriptions of corresponding scour protection measures This multi-dimensional and multi-level deep analysis reveals the dynamic formation mechanism of local scour, providing a reliable theoretical basis and technical support for the design of marine engineering.

2.1. Hydrodynamic Factor

2.1.1. Flow Velocities, Waves, and Wave–Current Interactions

Flow velocity or flow intensity regulates the development of scouring processes mainly by changing the flow velocity gradient and turbulence intensity. When the flow velocity gradient increases, the fluid velocity change in the near-bed region is intensified, generating enhanced shear forces. This enhanced shear force can overcome the frictional resistance between bed particles [24], causing sediment initiation and transport with the flow, thus intensifying the erosive effect of the flow on the bed [25,26]. In addition, elevated flow velocities increase the Reynolds number, inducing a transition from laminar to turbulent flow [27], which not only enhances the pulsation and vortex effect of the water flow but also strengthens the momentum exchange between fluid layers through the synergistic effect of turbulent diffusion and molecular diffusion and ultimately changes the characteristics of the scour pattern [28].

The reciprocating motion of the wave forms a periodic oscillating flow field, which generates an alternating horizontal flow velocity field, resulting in a periodic change in the bed shear stress [29]. This dynamically changing shear stress field directly affects sediment transport by changing the critical conditions for sediment initiation and transport mechanism. It changes the development and evolution of the vortex system around the structure, affecting the formation process of the local scour hole [30]. At the same time, waves have strong sand-lifting ability, and their periodic pulsation can continuously disturb the bed surface through high-frequency reciprocating motion, even when the average flow velocity is small, prompting fine-grained sediments to lift and maintain the suspended state [31]. In addition, wave-induced periodic changes in pore water pressure reduce the effective stress of the soil skeleton, further promoting sediment lifting and transport. Under long-term wave loading, the accumulation of pore water pressure may trigger local liquefaction, accelerating the erosion rate of the scour hole and encouraging its development to a deeper level [32].

In the marine environment, waves and currents often coexist, and their interactions can significantly change the dynamics of the scour process, which is not a simple linear superposition of wave and current actions but affects the scour topography and development rate through a complex nonlinear mechanism [33]. Through experimental studies, Chen [34] found that introducing water flow significantly changes the topographical characteristics of scour holes, and the topography exhibits an obvious differential evolution pattern compared with pure wave conditions. Numerous studies [34,35,36,37] have shown that the relative wave velocity (${\mathrm{U}}_{\mathrm{c}\mathrm{w}})$ is a key dimensionless parameter controlling the scouring process, and the normalized scour depth ($\mathrm{S}/\mathrm{D}$) deepens with increasing ${\mathrm{U}}_{\mathrm{c}\mathrm{w}}$ (Figure 2), which provides an important basis for predicting the development of scour under the combined action of wave and current. Under combined wave–current action, both the generation location of the bottom horseshoe vortex and the shedding pattern of the lee vortex change, resulting in the initial formation location of the scour hole deviating from the centerline of the structure and presenting a specific spatial deflection angle, which is a phenomenon that is directly related to the regulation effect of the vortex shedding frequency in the wave–current field [38]. The study by Deng et al. [39] further demonstrated that under the combined action of waves and currents, the periodic motion of waves complicates the vortex shedding process, potentially enhancing or weakening vortex intensity in specific regions. Meanwhile, the combined wave–current effect will substantially enhance the near-bed turbulence intensity, significantly promoting sediment entrainment efficiency and transport capacity [40]. Misuriya [41] showed that the eddy shedding frequency and near-pile turbulence intensity increased significantly under combined wave–current conditions, which provided direct evidence to explain the enhanced scouring effect due to combined wave–current action. The effect of wave–current interaction on local scour is characterized by two-way coupling. On the one hand, wave–current interactions regulate the scour process by directly changing the initial sediment bed topography. On the other hand, these topography changes will, in turn, continuously modify the local hydrodynamic structure and thus regulate the scour process [42]. Through experimental studies, Du [43] found that the sand ripple-induced sediment backfilling under combined wave–current conditions accelerates the achievement of the scour equilibrium state compared to the pure flow condition. In addition, wave–current interaction induces a faster accumulation of pore water pressure around structures, creating significant upward seepage forces, and this dynamic hydraulic action can drastically reduce the effective stresses in the soil skeleton, which leads to more severe scouring effects [32]. In summary, water flow and waves jointly dominate the dynamic characteristics of the scouring process by altering the near-bottom flow field and turbulent structure, and their nonlinear coupling effects are the core challenge in scouring prediction. To date, most studies have mainly focused on the macroscopic scour characteristics, such as scour depth, equilibrium time scale, and scour topography of different structures under combined wave–current action. However, microscopic mechanisms such as turbulence evolution, horseshoe vortex dynamics, and fine-grained sediment transport under these coupled hydrodynamic conditions still lack further study. A comprehensive exploration of these issues is essential to deepen the knowledge of the physical mechanisms of scour and to improve the capability of predictive modeling.

2.1.2. Turbulence

Turbulence is a state of fluid motion consisting of vortices at different scales, which is characterized by a high degree of complexity, irregularity, and randomness, as well as strong diffusivity and energy-cascading effects [44]. Turbulence causes local scour mainly through mechanisms such as enhancing the transient shear stress on the bed surface and promoting sediment suspension and transport [45,46]. These mechanisms greatly enhance water flow’s erosion and transport capacity on the topography around structures, resulting in much higher scour rates under turbulent conditions than laminar conditions.

Turbulent energy, which is mainly derived from large-scale vortices in the main flow zone, is transferred to the near-bed region through pulsating velocities that significantly enhance the instantaneous flow velocity. This enhanced turbulent pulsation makes it easier for shear stresses to exceed the sediment initiation threshold, thereby substantially improving erosion and transport efficiency [44]. In addition, under the combined action of waves and currents, the generation location of the bottom horseshoe vortex and the detachment pattern of the lee vortex have significantly changed, resulting in more complex dynamic evolution characteristics of the turbulent-driven horseshoe vortex and other flow field structures. Studies have shown that the presence of waves can significantly alter the flow velocity and pressure distribution around structures [47]. In particular, when wave crests and troughs pass, the dramatic changes in instantaneous flow velocity and direction not only directly affect the instantaneous intensity and structure of horseshoe vortices [48] but also significantly influence the scour development process by regulating the shear stress field [49]. Particle image velocimetry (PIV) observations have found that wave pulsations cause horseshoe vortices to exhibit stronger unsteady behavior, with their core position, scale, and intensity changing dynamically with the wave cycle [48]. This dynamic change makes sediment particles more susceptible to being picked up and transported [47]. On the other hand, vortices in turbulence generate pulsation velocities perpendicular to the main flow direction, especially the upward pulsation component, which can lift sediment particles. In this process, turbulence also provides the necessary energy for sediment particles to overcome gravitational settling and remain suspended for a long time, which continues to drive the scouring process [50]. In addition, turbulence can drive the lateral and vertical transport of sediment, which enhances the collision frequency and energy exchange between particles and changes the particle arrangement structure, resulting in a decrease in their stability, which makes them more susceptible to being carried away by the water flow, thus affecting the dynamic evolution of the scour pattern [51]. For a deeper understanding of this complex process, existing studies [52,53] have mainly quantified turbulence characterization parameters to reveal their intrinsic association with scour development. Turbulence intensity, turbulence kinetic energy (TKE), and Reynolds stress, as the key parameters characterizing the microscopic velocity pulsations of the fluid, are significantly correlated with the scour rate. The study by Li [54] revealed that the trend of turbulence intensity showed a similarity between the velocity and turbulence intensity along the flow direction in front of the bridge abutment, and its near-bed relative value could be used as a key parameter to characterize the bed microdynamic processes [6]. The distribution of turbulent kinetic energy (TKE) has spatial and temporal characteristics, which decrease during the initial scouring stage but gradually increase with scouring development and peak in the upstream center of the horseshoe vortex [55]. Reynolds stress analyses indicate that peak stress is maintained at the head of the main eddy and below the horseshoe vortex, and its high-value area migrates upstream with scour development [54]. In addition, a critical shear stress model based on turbulent velocity profiles provides a new approach for sediment initiation prediction [6]. Therefore, turbulence, as the key medium for energy transfer from the mainstream to the bed surface, directly determines the initiation and suspension of sediment particles through its transient and non-uniform characteristics, making it crucial for understanding the microscopic mechanisms of scouring. Existing studies have advanced the knowledge of the turbulent structure associated with local scour, revealing the evolution of horseshoe vortex systems, the spatial variability of turbulence intensity, and its influence on scour topography. However, the knowledge of the fine structure of near-wall turbulence and its coupling mechanism with sediment is still insufficient and needs further exploration.

2.2. Influence of Structural Properties and Spatial Layout on Scour Behavior

2.2.1. Structural Size and Shape

Structure size is one of the key factors affecting local scour, which directly influences the scour process by changing the hydrodynamic conditions. The characteristics of the structure, such as diameter, width, or upper reaches area, determine the degree of obstruction to water flow, which in turn affects the formation and flow intensity of the horseshoe vortex. Studies [9,56] have shown that increased size enhances water flow obstruction and creates a larger and stronger horseshoe vortex system, and the downflow and high bed shear stress generated by the horseshoe vortex are the main driving forces of scour. In another study, structure size was found to affect local flow amplification and shear stress distribution by changing the degree of streamline constriction, with larger cross-sections leading to sharper streamline curvature and higher local flow velocities, accelerating the local scour process [57]. In addition, the structural aspect ratio has a significant effect on the development of local scour. For submerged piles, Yao [58] showed that when the aspect ratio is less than 4, the change in aspect ratio has a more significant effect on the equilibrium scour depth, and when the aspect ratio is larger, the scour depth gradually converges to the infinite height pile condition. Tafarojnoruz & Lauria [59] conducted a high-precision numerical study based on large eddy simulation (LES), which further revealed the fluid dynamics mechanism behind this effect: the influence of the pile top wake vortex is mainly limited to the “very near wake zone” close to the pile top, which dominates the initial scouring in the area immediately behind the pile; in a wider range, the shear layer separated from both sides of the pile and its induced flow structure become the dominant factors affecting the flow field and scouring topography in more distant areas. Further study of submerged composite piles by Yao [60] found that the dimensionless equilibrium scour depth increases with the increase in the ratio of the structure height to the diameter of the superstructure ($h_1/D_1$) as well as the ratio of the foundation height to the total height of the superstructure ($h_2/h_1$), and the concept of effective pile height was proposed to explain the change in the scour rate and range rule. A subsequent study by Adnan [9] on circular composite piles showed that scour depth increases with increasing foundation aspect ratio and also found that the scour process is slower when the aspect ratio is small but shows an accelerating trend as the foundation height is exposed.

The geometry of structures influences scour morphology characteristics by modulating the flow structure. It has been shown that different shapes of structures develop significantly different flow bypassing characteristics: blunt body structures induce strong horseshoe vortex systems, leading to deeper scour hole formation [56,61], whereas streamlined structures effectively inhibit flow segregation and vortex development and significantly reduce scour depth [57,62,63]. Notably, complex structures such as umbrella-shaped suction anchor foundations [64] and bucket foundations [65] exhibit superior scour resistance compared to conventional cylindrical structures, and this performance enhancement stems from their unique three-dimensional geometries that can effectively disperse turbulence energy, thus significantly inhibiting scour development. Therefore, the geometric characteristics (size and shape) of the structure directly determine its obstruction to water flow and flow patterns, thereby controlling the depth and topography of local scour.

2.2.2. Spatial Arrangement of Structures

Monopile foundation has become the main object of local scour research because of its simple structure, which establishes the theoretical foundation for group pile structure analysis. Compared with monopile, pile group scour involves the local flow field changes around the individual piles and contains the complex hydrodynamic interactions between the piles, and its scour mechanism and law are more complicated [66].

Different spatial arrangements, such as the number, spacing, and arrangement of structures, can also influence scour development. The density of structure groups affects the scouring process mainly through two mechanisms: the increased water obstruction area enhances the strength of the upstream horseshoe vortex [67]; the interactions between the structures may produce the jet effect [65] or the shielding effect [68,69], which can significantly change the depth and extent of scouring. Taking a 5 × 5 array pile as an example, Gong et al. [70] systematically studied the local scour characteristics under clear water scour conditions, focusing on analyzing the scour effects of upstream piles on downstream piles and outer piles on inner piles. Structure spacing is a key determinant of the strength of shielding and jet effects, with smaller spacing enhancing these effects, while larger spacing brings the structures closer to the scour state when independent. It is worth noting that the structure spacing ratio ($G/D$) has a nonlinear relationship with the local scour depth, and the scouring effect varies significantly under different arrangement forms. The multi-bucket jacket structure has the lowest scour depth at a spacing ratio of 2 [71], while the six-cylinder pile group arranged in series has the lowest scour depth at a spacing ratio of 3.5 [72]. In addition, different arrangement forms (tandem, side-by-side, and staggered) can result in very different scour patterns, and studies have shown that staggered arrangements may result in deeper scour downstream than upstream [73]. Different structural spatial arrangements also affect the scour hole topography; pile groups may form composite scour holes where local scour is superimposed on global scour [70], while multi-bucket foundations form spoon-shaped scour holes with a steep front slope and a gentle back slope due to narrow flow [71]. Moreover, both jacket foundations and the new hybrid gravity foundations present global scour characteristics under live-bed conditions [74], and scouring at the edges of offshore converter platforms is mainly concentrated on both sides. Under ideal forward flow conditions, scour holes tend to be symmetrically distributed, but in actual marine environments, scouring often develops asymmetrically due to factors such as the angle of attack of the water flow or non-uniform seabed conditions [75] (Figure 3). Existing studies have revealed that spatial arrangement affects the scouring process through regulated flow fields, but the quantitative influence mechanisms of spacing ratio and arrangement on vortex systems still need further research.

The arrangement of the structure will form a certain angle with the direction of natural water flow, i.e., the angle of attack of water flow, which has a significant effect on the development of local scour. The angle of attack increases the effective obstruction width of the structure, especially for a blunt body structure. The projected area of the upstream projections increases with the angle of attack, which enhances the flow obstruction effect and accelerates the local scour process [76,77]. Moreover, the angle of attack can change the formation and strength of horseshoe vortex systems, and studies have shown that strong horseshoe vortices are formed upstream of square abutments at vertical angles of attack, while oblique angles of attack may cause horseshoe vortices to weaken or even disappear [56,78]. For angled structures, oblique flow can produce a sharp streamline contraction at the corners, creating a high-velocity zone that shifts the scouring mechanism from horseshoe vortex dominance to corner jet dominance [78]. In addition, the angle of attack can influence the initial development location and expansion direction of the scour hole by changing the location of the high shear stress zone, and studies have shown that scouring starts from the side corners of the structure and extends downstream [77], causing the scour hole to no longer develop symmetrically but to show an oblique expansion trend. The above studies have shown the ability to modulate the scour depth, location, and topography by changing the effective water-blocking area, vortex structure, and local flow field characteristics of the structure. In structure groups, the angle of attack, together with the spacing and arrangement, regulates the shielding effect and jet effect, and studies have shown that the maximum scour depth of pile groups varies nonlinearly with the increase in the angle of attack [79]; similarly, the scour pattern of a tripod bucket foundation or a group of four piles is also commonly affected by the angle of attack and the gap ratio [80]. Research shows that the driving mechanism of local scour has significant multi-factor coupling characteristics. Compared with single piles, the spatial layout of structures can significantly change the overall scour behavior of pile systems through complex shielding and jet effects, and the interaction mechanism is more complex.

Figure 3. Scour topography for typical foundation types: (a) monopile (square, diamond, and elliptical) [63]; (b) bucket foundation [65]; (c) pile groups [81]; (d) offshore booster station platform [75]; (e) jacket foundation [74]; (f) six-legged gravity foundation structure [74]; and (g) umbrella suction anchor foundation [64].

Figure 3. Scour topography for typical foundation types: (a) monopile (square, diamond, and elliptical) [63]; (b) bucket foundation [65]; (c) pile groups [81]; (d) offshore booster station platform [75]; (e) jacket foundation [74]; (f) six-legged gravity foundation structure [74]; and (g) umbrella suction anchor foundation [64].

2.3. Influence of Seabed Sediment Properties on Local Scour

Sediment grain size is a key factor influencing the local scour process, and its mechanism shows significant differences across the grain size range. According to the sediment classification standard [82], the grain size can be divided into three typical intervals: clay ($d_{50}$ < 0.002 mm, where $d_{50}$ is the median diameter), silty soil ($d_{50}$ = 0.002–0.075 mm), and sandy soil ($d_{50}$ > 0.075 mm), and each interval presents different scouring characteristics. Within the range of sandy soils, through experimental research, Wang [83] showed a negative correlation between scour depth and grain size for 0.075–2.0 mm sandy soils. Two mechanisms mainly cause this phenomenon: according to Shields’ criterion [84], a decrease in grain size reduces the critical starting shear stress, making fine particles more easily transported by water flow; moreover, coarse particles can reconfigure the flow structure by increasing the bed roughness, which improves the turbulent energy dissipation efficiency and reduces the near-bed flow velocity, thus affecting the scouring process. When the particle size enters the silty soil interval (0.002–0.075 mm), Chen [85] and Qin [12] found that the silty soil produces weak cohesion due to the van der Waals forces between the particles. However, its incremental shear intensity makes it difficult to resist the shear force of the flow, so the sediments in this particle size interval still follow the law of the negative correlation between the particle size and the scour depth. The most significant change occurs in the clay interval ($d_{50}$ < 0.002 mm), when the mechanism of inter-particle interaction undergoes a qualitative change from simple mechanical friction to a complex cohesive system dominated by electrochemical interaction. The electrochemical interaction caused by the surface charge of clay particles can produce higher cohesive strength and form stable flocculent structures, which leads to an increase in bed shear strength and a significant reduction in local scour depth. Mahalder et al. [86] pointed out that the erosion process of cohesive sediment is usually described as a slow fatigue phenomenon, requiring repeated water flow events to reach the equilibrium scour depth.

Most current studies on local scour have focused on uniformly graded sediments, yet mixed sediments with non-uniform gradations are often encountered in practical engineering. Compared with uniformly graded sediments, the scour process in mixed sediments presents different influencing mechanisms, which can be summarized in two aspects: the effect of fine particle cohesion and the coarse particle armor effect [12,83]. Cohesion generated by fine particles (clay, silt) is a key factor influencing the scouring characteristics. Cohesion enhances the bed’s scour resistance, a property that reduces the scour depth of cohesive soils or clay–sand mixed soils by 15–18% compared to non-cohesive sand beds [87]. As the clay content increases, the scour characteristics of mixed sediments gradually shift from non-cohesive to cohesive, and the scour pattern changes significantly [88]. Moreover, the increase in sediment non-uniformity (measured by the geometric standard deviation ${\sigma }_g$) changes the scour characteristics. When ${\sigma }_g$ increases from 1.4 to 5.2, the maximum scour depth can be reduced by 30–50%, which is mainly attributed to the armor effect of coarse particles. After the finer particles are selectively carried away during scouring, the residual coarse particles form a protective layer on the bed surface, significantly inhibiting scour development [13]. In addition, as the content of coarse particles in the mixed sediment increases, the bed roughness increases significantly, inhibiting the development of local scour by reducing the near-bed flow velocity through the enhancement of friction and by altering the turbulent structure to promote energy dissipation. It is worth noting that even with the same median particle size ($d_{50}$), different particle gradations can lead to quite different scour resistance and scour patterns, and well-graded sediments (uniformity coefficient Cu > 5, curvature coefficient Cc = 1~3) have higher scour resistance [83]. Wang [83] revealed the law of the influence of the particle gradation on the scour resistance of a mixed soil sample. Under the condition of coarse particle-dominated gradation (45% of d = 0.5 mm), the soil samples showed strong scour resistance, while in the fine particle-dominated gradation (35% of d = 0.35 mm), the scour resistance was significantly reduced; when the ratio of coarse and fine particles was similar, the medium-sized particles became a key factor in determining the maximum depth of erosion. This suggests that the overall scour resistance of the mixed sediments is the result of the joint action of different particle sizes.

In addition to particle size and gradation characteristics, the compactness of sediments is also a key factor influencing the local scour process. Unlike the aforementioned particle characteristics that mainly determine the initial composition of the sediment, the compactness reflects the structural state of the sediment under consolidation, which directly affects its ability to resist the scouring of water by changing the mechanical properties of the sediment [89]. It has been shown that even for sediments with the same grain size composition and gradation, the difference in compactness can still lead to significant changes in scour characteristics [90], and the mechanism of action varies depending on the sediment type. For non-cohesive sediments, the increase in compactness increases the effective contact area between particles, which enhances the inter-particle friction, thus effectively inhibiting the scouring and transport of the particles by the water flow [91]; for cohesive soils, the increase in compactness enhances the inter-particle cohesion, and this enhanced cohesion prompts the particles to form more stable aggregates or denser structures, which can effectively resist the erosive action of water flow. Studies have shown that when the dry density increases from 1.49 to 1.68 g/cm³, the synergistic effect of cohesion and shear strength can reduce the average scour depth by 20–40% [85]. In addition, compactness can affect scour hole topography, with consolidated silts presenting superior scour resistance to loose silts and significantly smaller scour depths and radius, maintaining steeper scour hole topography. These mechanisms lead to an essential difference between the scour characteristics of compact sediments and loose sediments, which makes it difficult to accurately predict the scour behavior of compact sediments with the existing scour equations. There is an urgent need to develop a special prediction method. The above studies have shown a fundamental difference between dense and loose sediments regarding scour characteristics, so the key factor of compactness must be fully considered in the scour prediction model. Overall, the physical properties of seabed sediments—from particle size and gradation to overall compactness—collectively constitute an inherent ability to resist water erosion, which is the basis for determining the ease with which the scouring process begins and the rate at which it develops.

2.4. Other Factors

2.4.1. Tides

The cyclical nature of tides and their asymmetric flow characteristics affect the local scour process. Under tidal reciprocation, sediments experience a continuous scour-backfill dynamic cycle, which usually requires multiple tidal cycles to reach a stable state, a process that extends the time required to reach an equilibrium scour state [92]. Moreover, the cyclic variation of tides can significantly change the vortex distribution characteristics, which makes the scouring mechanism around the structure essentially different from the unidirectional flow. Compared with the unilateral circular scour hole formed by the unidirectional constant flow, the bidirectional vortex shedding generated by the alternating tidal fluctuation leads to the periodic scouring effect on both sides of the structure. Under the influence of the bidirectional vortex, the front and rear ends of the structure form a deep scour hole due to the strong vortex effect, while the middle area is weaker due to the convective effect of the water flow and ultimately forms a saddle-shaped scour hole characterized by two deep ends and a shallow middle [92,93]. At the same time, the scour hole slopes are always maintained in a critical stable state lower than the repose angle of the sediments due to the continuous disturbance of the periodic vortices. This phenomenon was verified in the field study of Zhang [94], where the measured scour hole slope angles in all directions were maintained in the range of 13–18° under silty seabed conditions, which is much smaller than the repose angle of this sediment (35°), and ultimately resulted in a more gentle scour hole topography. Furthermore, in asymmetric tidal environments, the difference in flow direction and strength between tidal fluctuations leads to different sand transport capacities on both sides of the structure, resulting in spatially asymmetric scour patterns. Measured data from Jeon [95] confirms that, in the area dominated by rising tides, the extension of the scour hole along the direction of the rising tides (9.8 m) significantly exceeds that in the direction of the falling tides (5.1 m), which fully reflects the effect of the asymmetric tides on the local scour patterns. It is worth noting that there is a significant difference in the scour characteristics between tidal and unidirectional flow. When the maximum peak velocity of tidal flow is used as the constant flow velocity, the development of scour slows down significantly and the final depth decreases, whereas when the RMS velocity is used, the depth of tidal flow scour may be 51% higher than that of unidirectional flow. The experiments showed that accurate simulation of the scouring effect of tidal currents requires an increase of 15–20% in the rms value of the calculated flow rate of the unidirectional flow [96], which reveals the underestimation of the role of tidal currents in the traditional constant flow prediction method, and it must be corrected by combining the dynamic flow rate characteristics.

2.4.2. Climate Change

In recent years, global climate change has increased the frequency and intensity of extreme hydrological events such as floods, typhoons, and hurricanes [14,97]. Typhoons are extreme events that significantly change the hydrodynamic environment, and the strong currents induced by typhoons can dramatically increase the surface shear force of the seabed, thus exacerbating the local scour effect. Li [14] showed that the maximum current velocity during a typhoon storm surge could reach 4.5 m/s, far exceeding the maximum possible tidal current velocity in the region (0.47–1.17 m/s), and the resulting local scour depths (2.16–16.1 m) were 1.1–2.3 times larger than those of conventional tidal conditions. At the same time, global warming-induced sea level rise has significantly increased the frequency and intensity of extreme events such as tsunamis, strong waves, and unusual currents. As the most destructive oceanic phenomenon, tsunamis affect the local scour process through two main mechanisms: the intense current field and its induced seabed seepage effect, which can significantly change scour dynamics. In the elevation wave phase, the seabed suction effect reduces the shear stress on the side of the pile foundation and inhibits scour development. In contrast, in the depression wave phase, seepage injection significantly improves the efficiency of the suspended mass transport by increasing the peak shear stress and altering the location of the boundary layer separation point, leading to the formation of deeper scour holes at the back of the pile foundation [7]. Moreover, complex vortex structures such as wake vortices and horseshoe vortices generated by the flow boundary layer separation accelerate the scouring process by continuously transporting bed sediments through strong entrainment [98]. It is worth noting that the CFD simulation study by Li [98] further showed that the scour rate around the bridge abutment was significantly and positively correlated with the tsunami period (T) and the peak flow velocity (${\mathrm{U}}_{\mathrm{m}}$), which showed a monotonically increasing characteristic with the increase in T or ${\mathrm{U}}_{\mathrm{m}}$. It can thus be seen that environmental factors such as tides and extreme weather events introduce longer time scales and stronger unsteady characteristics, requiring scour process predictions to go beyond steady-state assumptions and consider the effects of dynamic and random processes.

2.5. Scour Protection and Mitigation Measures

The development and application of effective scour protection measures are crucial for ensuring the long-term safety and stability of marine structures. The core of these measures lies in regulating the interaction between water, sediment, and structures to weaken scouring effects or enhance the scour resistance of the seabed. Based on their mechanisms of action, existing protection technologies can be broadly categorized into two main types: passive protection and active protection [99,100,101].

Passive protection technology enhances the seabed’s resistance to erosion by directly laying protective layers around structures, which are primarily divided into two categories: traditional protective surfaces and new eco-friendly protective measures. Traditional protective facing technology is most typically represented by riprap protection, which involves laying specific-sized and graded gravel around the foundation of structures [102]. This method increases bed surface roughness to dissipate water flow energy, reduce near-bottom flow velocity, and lower bed surface shear stress. Additionally, the weight of the stones helps to elevate the threshold hydrodynamic conditions [103]. However, this method poses a risk of edge scouring over the long term, which may lead to gradual degradation and failure of the protective layer [102]. To overcome these shortcomings, various innovative passive protection technologies have been developed in recent years, such as microbial-induced carbonate precipitation (MICP) technology, which uses microbial metabolism to generate calcium carbonate to bind sand particles, forming biologically active “cemented soil” in situ to enhance scour resistance [103]; cement or chemically modified soil stabilization techniques [104,105]; and ecological structures such as artificial reefs and oyster reefs that combine protective functions with ecological benefits. These technologies not only weaken local water flow but also provide habitats for marine organisms [106].

Active protection technology weakens the key hydrodynamic mechanisms of scouring (such as horseshoe vortices and downward flow) by optimizing the flow field characteristics around the structure. It mainly includes two typical methods: structural attachments and integrated new structural designs. In terms of structural attachments, anti-scour collars are highly effective active protection devices that can effectively block downstream flow and prevent the formation of horseshoe vortex systems, thereby significantly reducing scour depth [107]. Khan et al. [108] developed hooked collars that optimize the flow field structure, and sacrificial piles use auxiliary piles arranged upstream of the main piles to preemptively disrupt the incoming flow, effectively reducing the intensity of the horseshoe vortex around the main piles [109]. In the field of integrated and novel structural design, current research focuses on innovatively integrating protective functions with foundation structures, such as integrating spoilers or porous structures into pile foundations to optimize flow patterns and promote vortex dissipation [110]; Zhu et al. [111] developed a porous fan-shaped suction anchor foundation (MS²AF) that achieves synergistic optimization of flow field regulation and scour protection through structural innovation; additionally, novel anti-scour structures such as F-jacks and flexible flow deflectors have been experimentally validated to exhibit excellent protective effects [112]. These innovative technologies provide more efficient and sustainable solutions for erosion protection of marine engineering structures.

In summary, the selection of erosion protection measures must comprehensively consider hydrological conditions, geological conditions, engineering costs, and environmental impacts. Future research trends will increasingly focus on the development of new protective technologies that are multifunctional, long-lasting, economical, and environmentally friendly, as well as the integrated design of protective measures within the structural components themselves. As Bharadwaj et al. [113] noted in their review, understanding the mechanisms of action of different measures and optimizing their design are crucial for ensuring the safety of marine engineering projects.

3. Local Scour Prediction Methods

The dynamics of local scour are affected by multiple factors, and its complexity makes quantitative prediction a key challenge in engineering practice and scientific research. In this section, we will systematically sort out the theoretical foundations, applicable conditions, and research progress of existing prediction models, focusing on analyzing four types of methods: numerical models based on hydrodynamic mechanisms, empirical and semi-empirical prediction formulas, innovative applications of machine learning techniques, and probabilistic prediction methods, and comparing the advantages and limitations of each type of methods.

3.1. Numerical Modeling of Local Scour

3.1.1. CFD-Based Single-Phase Model

Local scour, as a bed erosion phenomenon caused by the interaction between water flow and structures, is a key factor threatening the safety of hydraulic engineering. Traditional research methods, such as physical model tests and empirical formulas, suffer from the shortcomings of high cost, obvious scale effects, and limited applicability, while numerical simulation methods are gradually developing into an important complementary research tool by relying on their unique advantages [114,115]. Numerical methods based on CFD reveal the formation mechanism of scour hole topography by accurately solving the key parameters such as flow velocity, pressure, and turbulence intensity in the three-dimensional flow field, providing a new perspective for the study of the scour mechanism [115]. Among them, the CFD-based single-phase model achieves efficient simulation through the following process: the CFD method is used to calculate the hydrodynamic parameters accurately, and then the sediment transport process is simulated based on the morphology model, which is iteratively calculated until reaching the equilibrium state of scouring. This method significantly improves computational efficiency while ensuring accuracy and has become the leading technical solution in current engineering applications [16].

The core of the CFD-based single-phase model lies in the dynamic interaction and iterative solution between the hydrodynamic module and the sediment morphology module. The model mainly contains two core parts: hydrodynamic simulation and sediment morphology simulation. The hydrodynamic simulation solves the Reynolds-averaged Navier–Stokes (RANS) equations to characterize the complex flow field around the structure. The sediment morphology simulation calculates the transport rates of the bed load and suspended load separately, and then updates the bed elevation by the Exner equation, and dynamically adjusts the local scour gradient above the angle of repose by using the “sand-slide” mechanism until the system reaches the equilibrium of scouring [16]. The specific process is shown in Figure 4.

In recent years, sediment morphology modeling methods have made significant progress in accuracy and applicability. In the study of sediment transport, the early models [16] only considered the effect of bed load on local scour, while the improved model proposed by Dutta [116] more accurately reflects the actual physical processes by incorporating both bed load and suspended load transport processes. Regarding bed morphology evolution simulation, Song [117] developed a novel physically based sand slide algorithm based on the slope-limited diffusion principle and applied it to the scour model. The method effectively solves the critical problem of bed slope exceeding the sediment repose angle by establishing a strict slope control mechanism. Studies on sediment properties have been extended from uniform sand to non-uniform graded sand, and Okhravi [118] accurately characterized non-uniform sand properties by discretizing the sediment bed into different grain-size components and calculating the transport rates of each component individually. At the numerical implementation level, the dynamic mesh updating technique is widely used to adjust the computational domain mesh in real time to adapt to the geometrical changes in the bed surface during the scouring process [119], in order to ensure the numerical stability of the long-term simulation. The immersed boundary method [120] avoids the mesh deformation problem by embedding complex boundaries into a fixed background mesh and can effectively deal with complex geometries and moving boundaries, which is particularly suitable for modeling local scour phenomena around complex structures. Although significant progress has been made in CFD-based single-phase models, the ability to accurately analyze the complete three-dimensional geometry of scour holes remains insufficient. In particular, under complex three-dimensional flow conditions, the accuracy of existing models in predicting scour hole morphology still needs to be improved. In addition, the high computational time cost severely limits the widespread application of these models in engineering practice. Future research should focus on developing high-precision prediction models based on physical mechanisms, optimizing the coupling method between CFD and morphology models, and improving the computational efficiency while guaranteeing reliability to provide better solutions for engineering practice.

3.1.2. Two-Phase Model

The traditional single-phase flow model adopts empirical formulas to simulate bed sediment transport, which makes it difficult to accurately describe the dynamic interactions between fluid and sediment particles, resulting in limitations in the simulation of sediment transport and bed evolution [121]. In contrast, the two-phase model can more accurately simulate the key physical processes, such as sediment initiation, suspension, settlement, and bed topography evolution, by solving the interaction between the fluid phase and the particle phase, providing a more reliable numerical simulation means for the study of local scour mechanism and engineering prediction. In the two-phase simulation framework, according to the different ways of interphase coupling, it can be divided into the Eulerian–Lagrangian and Eulerian–Eulerian methods.

The Eulerian–Lagrangian model describes the two-phase motion in different ways based on the difference in physical properties between fluid and particles. The model treats the fluid as a continuous phase and describes its motion by solving the Navier–Stokes equations in the Eulerian coordinate system; meanwhile, the particles are treated as discrete phases, and the Lagrangian coordinate system is used to track the trajectories of individual particles. By accurately coupling the interaction forces between the fluid and the particles, the model can effectively simulate the complex dynamic processes between the two phases [122]. In terms of fluid phase solution, the model establishes the Navier–Stokes governing equations based on the Eulerian framework [123]:

$${\displaystyle \frac{\partial \left({\rho }_{f}u\right)}{\partial t}}+\nabla \cdot \left({\rho }_{f}uu\right)=-\nabla p+\nabla \cdot \tau +{\rho }_{f}g+F_p$$

(1)

where $F_p$ denotes the fluid–particle interaction force. For the discrete phase description, the Lagrangian framework, based on Newton’s second law, is used to track the trajectory of individual particles while considering the influences of fluid forces and inter-particle collisions [124]:

$$m_p{\displaystyle \frac{d{v}_p}{dt}}=F_{\mathrm{drag}}+F_{gravity}+F_{\mathrm{lift}}+F_{collision}$$

(2)

The momentum exchange between the fluid and the particles exhibits a two-way coupling. The fluid affects particle motion through mechanisms such as drag and lift forces, while the reaction forces generated by the particle motion are fed back into the flow field through the Navier–Stokes equations [124]. The advantage of this model is that it can resolve the particle-scale dynamics, which is especially suitable for sparse to medium concentration particle flow, but for large-scale scouring problems, it needs to be combined with particle statistics models to reduce the computational cost [125].

In recent years, applying the Eulerian–Lagrangian two-phase model in local scour studies has made significant progress. Early studies focused on two-dimensional simple structures, and Yang [126] used a coupled model of CFD and the discrete element method (DEM) model to reveal that the scour process of submarine pipelines contains three phases: onset of scour, tunnel erosion, and lee–wake erosion. Yang found that the inter-particle interaction force plays a dominant role in the tunnel erosion phase. With the deepening of the research, the application of the model has been extended to complex engineering scenarios such as double-pile foundations [127] and offshore wind power mooring systems [122]. Regarding model optimization, Zhang [128] calibrated the DEM particle parameters by the angle of repose, which improved the model’s prediction accuracy of sediment transport behavior and established a quantitative relationship between the bed sand transport rate and the Shields number. Meanwhile, aiming at the computational efficiency problem, the researchers developed various optimization methods, among which the coarse granulation method (CGM) significantly reduces the computational volume by increasing the particle volume while ensuring the accuracy of key physical processes, and Ma and Li [129] verified that the CFD-CGDEM model can balance the computational efficiency and accuracy under different flow velocity and particle radius conditions. In addition, Ma [130] innovatively combined the porous medium model with the Darcy–Forchheimer equation to describe the far-field flow, which further enhanced the computational efficiency.

The Eulerian–Lagrangian two-phase model shows unique advantages in studying the local scour of marine structures [18,131,132]. The method can accurately simulate the macroscopic topography evolution of the scouring process and finely analyze the microscopic mechanisms, such as fluid–particle interactions and inter-particle contacts, which provides a powerful tool for studying scour problems in marine engineering. In contrast, the Eulerian–Eulerian two-phase model adopts the assumption of a continuous medium to unify the discrete particle phase and the fluid phase under the Eulerian framework, effectively solving the computational efficiency problem of large-scale particle systems. By introducing the concept of phase fraction and the model of interphase forces, the method realizes the efficient simulation of local scour under the condition of high-concentration sediment transport [133].

The Eulerian–Eulerian two-phase model treats both the fluid and particle phases as continuous media and establishes the equations for mass conservation and momentum conservation, respectively. The mass conservation equation can be expressed as follows [87]:

$${\displaystyle \frac{\partial \left({\varphi }_f{\rho }_f\right)}{\partial t}}+\nabla \cdot \left({\varphi }_f{\rho }_f{u}_f\right)=0$$

(3)

$${\displaystyle \frac{\partial \left({\varphi }_p{\rho }_p\right)}{\partial t}}+\nabla \cdot \left({\varphi }_p{\rho }_p{u}_p\right)=0$$

(4)

where ${\varphi }_f$ and ${\varphi }_p$ are the volume fractions of the fluid and particles, respectively. By introducing the coupling term between the phases, the momentum conservation equation completely describes the momentum transfer mechanism between the fluid and particle phases [87]:

$${\displaystyle \frac{\partial \left({\varphi }_f{\rho }_f{u}_f\right)}{\partial t}}+\nabla \cdot \left({\varphi }_f{\rho }_f{u}_f{u}_f\right)=-{\varphi }_f\nabla p+\nabla \cdot {\tau }_f+F_{f-p}$$

(5)

$${\displaystyle \frac{\partial \left({\varphi }_p{\rho }_p{u}_p\right)}{\partial t}}+\nabla \cdot \left({\varphi }_p{\rho }_p{u}_p{u}_p\right)=-{\varphi }_p\nabla p+\nabla \cdot {\tau }_p+F_{p-f}$$

(6)

The interphase coupling effect is realized through the drag force, particle stress, and other interaction forces [18]. With the development of Computational Fluid Dynamics technology, the Eulerian–Eulerian model based on the OpenFOAM platform is continuously optimized and shows good applicability in marine engineering scour problems. In the study of 2D structures, Fraga [18] used 2D Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations combined with the SedFOAM solver to systematically analyze the scouring characteristics of pipelines under different Shields parameters and gap ratios and verified the reliability of the model under complex geometric environments. Tofany and Wirahman [131] utilized the hybrid virtual domain-submerged boundary method to reveal the mechanism of pipe surge and jet during the early scouring process of submarine pipelines. In a three-dimensional structural study, Nagel [132] extended the model to three-dimensional space, characterized the shear stress distribution in the scour hole more accurately by the method of defining the local Shields number based on the concentration contour, and clarified the law of the sediment transport mechanism varying with the slope of the bed. For the cohesive seabed, Qin [87] introduced the influence of soil cohesion into the SedFOAM framework and developed the SedCohFOAM model, which demonstrated that cohesion can effectively inhibit scour development. Hu et al. [134] also emphasized that cohesive sediment exhibits different dynamic characteristics from non-cohesive sediment due to the cohesive force between particles, which places higher demands on the construction of two-phase flow models. However, the prediction accuracy of the scour hole topography needs to be further improved under high flow velocity conditions. These research results promote the theoretical improvement of the Eulerian–Eulerian model and lay a more solid theoretical foundation for predicting scour under complex working conditions. Although two-phase flow CFD models have advantages in terms of mechanism, their computational costs are extremely high when simulating long-term erosion evolution in real marine environments. Furthermore, they require precise settings for complex boundary conditions and multiphase flow parameters, which poses significant challenges for their direct application and verification under prototype-scale field conditions.

3.1.3. SPH Method

The SPH method, as a meshless Lagrangian particle method, has unique advantages in the field of CFD and is particularly suitable for simulation problems with complex boundary surfaces [135]. Compared with the traditional mesh methods, the SPH method discretizes the computational domain into a swarm of particles carrying physical attributes such as density, mass, and velocity. It solves numerically based on the Navier–Stokes equations, effectively avoiding the strict requirements of the mesh methods on mesh mass and density. The method is more adaptable in dealing with large deformation problems and can more accurately simulate the motion, transformation, and diffusion processes of particles [136].

Table 1. Comparative evaluation of numerical modeling approaches for local scour.

Modeling Approach	Advantages	Limitations	Applicable Conditions
CFD-based single-phase model	1. Relatively low computational costs;	1. Inability to capture microscopic mechanisms;	1. Macroscopic prediction and engineering design;
	2. Simulates macroscopic scour phenomena;	2. Reliance on empirical formulas and parameters.	2. Parametric studies and alternative comparison.
	3. Mature technology and flexible framework.
The Eulerian–Lagrangian two-phase model	1. Models microscopic mechanisms;	1. Extremely high computational cost;	1. Mechanism investigation;
	2. Captures particle kinematics;		2. Scenarios requiring detailed interactions;
	3. Considers true fluid–particle coupling;	2. Limited number of particles.	3. Low to medium sediment transport conditions.
	4. Includes inter-particle contact.
The Eulerian–Eulerian two-phase model	1. Capable of modeling the interaction of two phases, fluid and sediment, as a continuous medium;	1. Ignores the discrete nature of particles;	Suitable for high-concentration sediment transport conditions.
	2. Computational efficiency is superior to DEM for scenarios with high sediment concentrations.	2. Relies on constitutive relationships;
		3. High computational costs.
SPH method	1. Excellent at handling large deformations;	1. Higher computational costs;	Flows with complex interfaces.
	2. Avoids mesh-related issues.	2. More complex realization of boundary conditions.

describes the advantages and limitations of each local scour numerical method and the applicable conditions.

In recent years, the application of the SPH method in scour research has been deepened, and it has been gradually extended to more complex local scour problems. In the study of scour at cylindrical bridge abutments, Zhang [136] innovatively constructed the SPH multiphase flow model, treated the sediment as a non-Newtonian fluid, optimized the boundary treatment method by integrating the Herschel–Bulkley–Papanastasiou (HBP) rheological model, the Drucker–Prager criterion, and the Shield erosion criterion, and developed a new scour visualization technique, which realized the distinction between the “visible surface” and the “actual surface”. The model is accurate in flow field reconstruction and scour pattern simulation, especially in capturing the particle-scale dynamics and sediment transport process. To address the scouring problem of submarine pipelines, Yan [19] adopts the improved incompressible smooth particle hydrodynamics (ISPH) method, combined with the sub-particle scale (SPS) turbulence model and critical shear stress (CSS) erosion criterion, to effectively simulate the scouring process of submarine pipelines with different pipeline parameters and flow rates. Yan’s computational results are in good agreement with the experimental data and the numerical results of the SedFOAM, which verifies the reliability of the model. In addition, the SPH-DEM coupling method [135] was first applied to simulate the scouring of granular soil around a circular pile under steady flow conditions, and the large deformation and turbulence phenomena were accurately reproduced by characterizing the granular soil and the pile body through DEM and simulating the water body through SPH. This study verified the model’s reliability and revealed the correlation mechanism between flow, vortex, and soil erosion, which provided a new theoretical understanding of the local scour behavior of pile foundations.

The SPH method has demonstrated unique value in local scour simulation due to its mesh-free nature, complex interface handling capabilities, and advantages in sediment movement tracking. However, the large-scale engineering application of this method still faces multiple challenges: computational efficiency issues are prominent. Although parallel computing and multi-resolution SPH models [137] can partially alleviate these issues, the computational cost of SPH-DEM coupled simulations increases by an order of magnitude compared to traditional grid-based methods, severely limiting their applicability in engineering-scale or long-term evolution simulations; secondly, the accuracy and stability of the SPH method under irregular particle distributions require further optimization [138]; more critically, the inherent numerical dissipation characteristics of this method make it difficult to precisely capture the details and energy cascade of turbulent flows [139], posing significant challenges in simulating high Reynolds number strong turbulent flows. Future research should focus on breakthroughs in key technologies such as computational model optimization, including improved boundary treatment methods [140] and more advanced turbulence models [141]. Closer coupling of SPH with other numerical methods (such as FEM [142]) is also an important direction for development, in order to comprehensively capture the multi-physical field coupling effects in local scour processes and enhance the practical engineering application value of the method.

Overall, numerical scour models have become an important tool for studying local scour mechanisms and simulating dynamic processes, but their engineering applications still face significant verification issues. Current model validation primarily relies on laboratory-scale data, but scale effects and environmental differences make it difficult for the results to reflect real ocean conditions, leading to a significant reduction in the accuracy of field predictions. In particular, when simulating extreme events such as storms or tsunamis, existing models are unable to accurately characterize the complex nonlinear interactions between extreme waves and the seabed and structures, and their ability to capture transient flow field changes is also significantly insufficient, which has become a key challenge in current research. It is worth noting that due to the scarcity and inherent uncertainty of high-quality field measurement data, the reliability and applicability of simulation results from CFD, SPH, and other models also face severe challenges. To solve this problem, there is an urgent need for advanced field monitoring technology to provide high-quality real-time data. New sensor technologies developed in recent years, such as the Sensory Instrumented Particle developed by Al-Obaidi et al. [143] can track the entire process from bed particle instability to the gradual formation of scour holes in real time, providing verification data for numerical models, which is essential for calibrating the sediment initiation criteria and transport rate formulas in the model.

3.2. Local Scour Prediction Equation

Local scour is a dynamic process of water eroding the sediments around structures, which may endanger the foundation stability of structures or even lead to damage, so accurate prediction of scour depth is of key significance for the safe design and protection of offshore projects. Traditional local scour prediction mainly relies on empirical formulas obtained from laboratory small-scale model experiments. However, when these empirical formulas are applied to actual engineering projects, especially when verified with field data, there are significant deviations [144]. Qi [145] found that the 65-1R and 65-2 equations underestimate scour depths under laboratory conditions, while the HEC-18 equations tend to overestimate the results in field applications; and by comparing 30 empirical formulas, Vonkeman and Basson [146] found that these formulas have significant differences in the prediction of scour depth of bridge abutments and most of the formulas tend to overestimate the actual scour depth. This limitation mainly originates from four factors: (1) Scale effect issues: Existing formulas are mostly based on laboratory small-scale flume experiments, which are unable to fully simulate the complex water–sediment dynamics in real marine environments. More importantly, due to the temporal and spatial scale limitations of laboratories, the entire scouring process cannot be accurately simulated, leading to field measurements of equilibrium scour depth often overestimating or underestimating the predicted values derived from laboratory experiments. Additionally, the formation process of equilibrium scour depth may require several years or even longer in reality, further highlighting the differences between laboratory conditions and the real environment [20]; (2) Overly simplified theoretical foundations: Formulas typically assume uniform steady flow, ideal cylindrical structures, and uniform sand seabed, whereas real marine environments involve wave–current coupling, complex structural morphologies, and non-uniform seabed sediments. These simplifications severely weaken the physical mechanisms underlying the formulas, and existing models are unable to adequately capture the interactions among multiple factors [22]; (3) Insufficient adaptability to complex structures: Existing formulas are primarily derived under simplified conditions for single piles, but marine engineering widely employs complex structures such as pile groups, whose vortex interference effects can lead to significant differences in scour depth and topography compared to single piles. This phenomenon has been validated by field measurements and numerical simulations [147]; and (4) Limited applicability: Most formulas are based on specific experimental or field observation data. When applied to conditions beyond the scope of the original dataset, prediction accuracy significantly decreases, and applicability is greatly restricted [144]. In particular, these formulas are completely ineffective in highly transient and strongly nonlinear extreme events such as storms and tsunamis, and therefore cannot be used to predict such catastrophic scouring [148].

To improve the prediction accuracy, Amini Baghbadorani [147] proposed a multi-parameter integration model, and by integrating 367 sets of experimental data of complex bridge piers, the equations considering the interaction of columns, pile caps, and pile foundations were established, which reduced the absolute error from 108% to 28% of the traditional FDOT formula. Crowley [149], based on the theory of the attenuation of the turbulence energy spectrum, revealed the effect of particle size to structure size ratio on the equilibrium scour depth, which provided a new idea for the parameterization of the formula. Similarly, Hamidifar [150] constructed a hybrid model, such as YJAF-VRAD, by coupling ten scour equations with eight critical flow velocity models, effectively reducing the error due to critical flow velocity sensitivity. Moreover, Tang [151] utilized 71 sets of experimental data to quantify the dynamic scour process, established a process-based dynamic design method, and proposed a time evolution equation, which reduced the maximum prediction error from 162% to 34% in the traditional method. In addition, Sui [20] developed a full-scale numerical model based on field data from the Rudong wind farm in China and effectively solved the conservatism problem of small-scale tests by introducing the Reynolds number correction. To overcome issues such as scale effects in purely empirical formulas, some studies have begun to focus on semi-analytical models that combine physical mechanisms and empirical parameters. For example, Wang et al. [152] integrated the principle of sediment mass conservation, sediment transport models, and turbulence phenomenology theory to propose a semi-analytical model for predicting the development process of clear water scouring. Table 2 describes the advantages and limitations of each local scour prediction formula and the application conditions.

Although significant progress has been made in the current research on local scour prediction formulas, several key problems still need to be solved. Most of the existing improved formulations have been validated only by specific experiments or limited field data, and their universality still needs further verification. In addition, the high complexity of the scouring process and the diversity of environmental factors have not been fully quantified, resulting in models that exhibit significant instability when applied across scales or scenarios [20]. Future research should focus on exploring the multi-scale coupling mechanism between hydrodynamics and sediment dynamics, revealing the microdynamic process of local scour in-depth, and promoting the transformation of the prediction model from empirical statistics to physical mechanisms, providing a more solid theoretical foundation and technical support for the safe design of marine engineering.

Table 2. Empirical formulas for predicting equilibrium scour depth around various structures.

Formula/Model	Advantages	Limitations	Applicable Conditions
HEC-18 Equation [153]	1. Performs well for laboratory data prediction results;	1. Prediction of field data often tends to overestimate scour depth;	1. Suitable for bridge piers of simple geometry;
	2. Data support: fitted based on a large amount of laboratory data.	2. The accuracy of scour depth prediction for complex piles is low.	2. Mainly suitable for clear water scour conditions.
FDOT Equation [154]	1. Considers sediment properties;	1. The prediction accuracy is relatively low and often overestimated;	1. Suitable for bridge piers of simple geometry;
	2. Applicable to various shapes.	2. Theoretical limitations in dealing with complex piers.	2. Mainly suitable for clear water scour conditions.
65-1R and 65-2 [145]	1. Performs well in field data (especially in live-bed conditions);	1. Underestimation of scour depth for laboratory data (especially for clear water conditions);	1. Equation 65-2 generally performs better than 65-1R;
	2. Considers the effect of sediment grain size.	2. Overestimation of scour depth for large diameter abutments and large abutment–sediment ratios.	2. Equation 65-2 is recommended for medium-diameter piers (5–15 m) or moderate D/D50 ratios.
Amini Baghbadorani Equation [147]	1. Higher accuracy and lower absolute error in scour depth prediction;	1. Comprehensive data on geometric parameters of bridge piers and water flow conditions are needed;	Complex bridge pier structures with different geometric parameters.
	2. Considers complex pier structures.	2. Relatively complex calculation.
Hamidifar Equation [150]	1. Demonstrates high accuracy under multiple statistical indicators;	1. May slightly overestimate scour depths in practical applications;	1. Cylindrical piers in clear water;
	2. Low sensitivity to critical flow rates and less affected by errors in critical flow rate estimates.	2. Needs to be used in conjunction with specific critical flow equations.	2. Applicable to both lab and field.
Sui Equation [20]	1. Avoids scale effects;	Limited sediment type.	1. Single piles in a sandy environment;
	2. Considers the Reynolds number effect.		2. Specific Reynolds number range.
Crowley Equation [149]	1. Turbulent energy spectrum attenuation is considered with a theoretical basis;	1. A deeper understanding of turbulent diffusivity is needed;	1. For relatively well-defined particle and structure sizes;
	2. More explicit consideration of particle size characteristics.	2. Needs improvement at low b/D50 values.	2. Supported by turbulent diffusivity data.
Tang Equation [151]	1. Avoids dependence on the concept of equilibrium scour depth;	1. The applicability to fine-grained sand needs further verification;	1. Clean water scour conditions;
	2. Provides better flexibility and fault tolerance.	2. Accuracy at low flow intensities needs to be improved.	2. Non-uniform sand beds.

b: Pier width; D₅₀: Median Sediment Diameter; and D: pier diameter.

Table 2. Empirical formulas for predicting equilibrium scour depth around various structures.

Formula/Model	Advantages	Limitations	Applicable Conditions
HEC-18 Equation [153]	1. Performs well for laboratory data prediction results;	1. Prediction of field data often tends to overestimate scour depth;	1. Suitable for bridge piers of simple geometry;
	2. Data support: fitted based on a large amount of laboratory data.	2. The accuracy of scour depth prediction for complex piles is low.	2. Mainly suitable for clear water scour conditions.
FDOT Equation [154]	1. Considers sediment properties;	1. The prediction accuracy is relatively low and often overestimated;	1. Suitable for bridge piers of simple geometry;
	2. Applicable to various shapes.	2. Theoretical limitations in dealing with complex piers.	2. Mainly suitable for clear water scour conditions.
65-1R and 65-2 [145]	1. Performs well in field data (especially in live-bed conditions);	1. Underestimation of scour depth for laboratory data (especially for clear water conditions);	1. Equation 65-2 generally performs better than 65-1R;
	2. Considers the effect of sediment grain size.	2. Overestimation of scour depth for large diameter abutments and large abutment–sediment ratios.	2. Equation 65-2 is recommended for medium-diameter piers (5–15 m) or moderate D/D50 ratios.
Amini Baghbadorani Equation [147]	1. Higher accuracy and lower absolute error in scour depth prediction;	1. Comprehensive data on geometric parameters of bridge piers and water flow conditions are needed;	Complex bridge pier structures with different geometric parameters.
	2. Considers complex pier structures.	2. Relatively complex calculation.
Hamidifar Equation [150]	1. Demonstrates high accuracy under multiple statistical indicators;	1. May slightly overestimate scour depths in practical applications;	1. Cylindrical piers in clear water;
	2. Low sensitivity to critical flow rates and less affected by errors in critical flow rate estimates.	2. Needs to be used in conjunction with specific critical flow equations.	2. Applicable to both lab and field.
Sui Equation [20]	1. Avoids scale effects;	Limited sediment type.	1. Single piles in a sandy environment;
	2. Considers the Reynolds number effect.		2. Specific Reynolds number range.
Crowley Equation [149]	1. Turbulent energy spectrum attenuation is considered with a theoretical basis;	1. A deeper understanding of turbulent diffusivity is needed;	1. For relatively well-defined particle and structure sizes;
	2. More explicit consideration of particle size characteristics.	2. Needs improvement at low b/D50 values.	2. Supported by turbulent diffusivity data.
Tang Equation [151]	1. Avoids dependence on the concept of equilibrium scour depth;	1. The applicability to fine-grained sand needs further verification;	1. Clean water scour conditions;
	2. Provides better flexibility and fault tolerance.	2. Accuracy at low flow intensities needs to be improved.	2. Non-uniform sand beds.

b: Pier width; D₅₀: Median Sediment Diameter; and D: pier diameter.

3.3. Machine Learning

In recent years, machine learning techniques have demonstrated significant advantages in local scour prediction, providing a new way to solve the problem of insufficient accuracy of traditional empirical formulas and physical models under complex hydrodynamic conditions. The reason for this advantage lies in the fact that the scouring process under complex operating conditions involves highly nonlinear and multivariate coupled complex physical mechanisms, and this complexity makes it extremely difficult to make predictions based on traditional formulas using simplified assumptions. Studies have shown that the ML method can effectively capture the nonlinear relationship between scour depth and the influencing factors and shows superior performance under different working conditions [155]. Abd El-Hady Rady [156] used Genetic Programming (GP) and the Adaptive Neuro-Fuzzy Inference System (ANFIS) to establish a prediction model for the local scour depth of bridge abutments and found that the prediction results of the GP model matched the experimental data better than those of the traditional regression method. Similarly, Baranwal and Das [157] found that the M5Tree model had the best prediction accuracy (R² = 0.9196) under live-bed scour conditions by comparing multiple machine learning models, including ANN-PSO, ANFIS, Multivariate Adaptive Regression Splines (MARSs), and M5Tree. These results not only validate the effectiveness of machine learning in scour prediction but also reveal the differences in the applicability of different algorithms in dealing with specific problems. In practical applications, researchers have improved ANFIS by adopting a nature-inspired optimization algorithm to address the scouring problem around pipelines under wave action, significantly enhancing the model’s predictive accuracy under complex wave conditions [158]. Similarly, when predicting scouring around bridge piers in cohesive soil, the researchers proposed a random modeling strategy, which uses intelligent algorithms to learn the complex erosion behavior of cohesive soil from experimental data, resulting in a significant improvement in prediction performance [159]. These successful applications clearly demonstrate that when physical mechanisms are complex and difficult to describe using analytical formulas, machine learning methods can serve as a powerful and effective alternative or supplementary tool.

Performance optimization of machine learning models and the selection of input parameters are key problems in current research. Dang [160] used Particle Swarm Optimization (PSO) and the Firefly algorithm to improve Artificial Neural Networks (ANNs), which resulted in a significant improvement in bridge abutment scour depth prediction accuracy. The RPSO-XGBoost model developed by Eini [21] combines Red Fox Optimization (RFO) and Extreme Gradient Boosting (XGBoost) techniques, which exceeds the performance of traditional methods and quantifies the contribution of each input parameter using the SHapley Additive exPlanations (SHAP) method. In addition, in terms of input parameter sensitivity analysis, Najafzadeh and Oliveto [161] confirmed through Sobol analysis that the ratio of incoming velocity to sediment starting velocity ($\mathrm{U}/{\mathrm{U}}_{\mathrm{c}}$) is the most critical factor affecting the scour depth of the pile group. These studies not only provide an effective way for model optimization but also deepen the understanding of the physical mechanism of scour, which lays an important foundation for enhancing the interpretability of machine learning models. Table 3 describes the comparison of machine learning methods for local scour prediction.

Although machine learning shows significant potential in local scour prediction, it still faces key challenges such as data dependence, generalization ability, and interpretability. The current research mainly suffers from three limitations: Using machine learning models to analyze field data to improve the accuracy of scour depth predictions has become an important trend [162], which helps overcome the limitations of traditional methods. However, the model generalization ability is limited by the coverage and representativeness of the training data, while the scarcity of actual field measurement data severely restricts the applicability of the model [163]. This issue is particularly significant when predicting rare extreme events, as the lack of sufficient training samples leads to highly unreliable predictions by the model for such events, often resulting in significant deviations from actual outcomes. Moreover, research indicates that while data-driven models exhibit high predictive accuracy, their inherent black box nature results in insufficient physical interpretability [22], a limitation that is particularly severe in engineering applications [164]. Specifically, when the model produces incorrect predictions, the lack of understanding of its internal mechanisms makes it difficult to trace the root cause of the error, posing significant challenges for model debugging and optimization. This interpretability deficiency not only affects model reliability but also hinders a deeper understanding of the consistency of physical processes. In addition, Choi and Choi [163] found that models such as ANFIS suffer from obvious overfitting problems. Aiming at these limitations, three important development directions are extended: (1) Physics-constrained machine learning methods significantly enhance model reliability by introducing physics-consistent constraints [161], offering new approaches for scour prediction. The core of such methods lies in integrating known physical laws into model design and training processes, guiding the model to learn solutions consistent with physical laws, thereby improving predictive capability. For example, Valyrakis et al. [165] employed an adaptive neural fuzzy inference system to predict coarse-grained motion, reflecting the approach of modeling physical processes; recent studies [166,167] have further applied Physical Information Machine Learning (PIML) to solve complex fluid dynamics problems such as the Navier–Stokes equations. Future research should focus on developing PIML models for local scour multi-physical field coupling characteristics, in particular by directly embedding partial differential equations of hydrodynamics and sediment dynamics into neural network architectures to better capture the physical essence of the scour process; (2) Digital twin technology applications: For example, Wang [168] constructed a digital sink system based on AI algorithms, providing a foundation for the application of this technology; and (3) The study of time evolution laws: For example, Zhang [169] developed the MGGP model to realize the dynamic prediction of scour depth over time. Future research should focus on improving the interpretability of the model, enhancing the generalization ability, and facilitating the translation of laboratory results to engineering practice, effectively solving the complex engineering problem of local scour of marine structures.

Table 3. Comparison of machine learning methods for local scour prediction.

Machine Learning Models	Advantages	Limitations	Applicable Conditions
Neural Networks [156,160]: ANN, ANFIS, etc.	1. Powerful nonlinear mapping capability;	1. “Black box” problem;	Scenarios where the dataset is large and the signal-to-noise ratio is high, and where extreme prediction accuracy is sought.
	2. Good prediction performance;	2. Strong data dependency;
	3. Can be enhanced by optimization algorithms or integration methods.	3. Risk of overfitting.
Support Vector Machines [22,163]: SVM, SVR, etc.	1. Capable of being applied to different scour types and conditions;	1. Requires parameter tuning;	Small to medium-sized datasets with high feature dimensions.
	2. Suitable for dealing with complex nonlinear relationships.	2. Certain “black box” characteristics;
		3. Data-dependent.
Tree-Based Models [22,161,168,170]: DT, M5Tree, M5MT, GTB, REPTree, etc.	1. Intuitive and interpretable;	1. Possible overfitting;	Scenarios where physical interpretation or decision analysis of prediction results is required.
	2. Able to handle nonlinear relationships;	2. Performance is affected by the range of data;
	3. Does not require extensive data preprocessing;	3. Limited interpretability.
	4. Good predictive performance.
Boosting/Ensemble Methods [22,168,171]: RF, Boosting Model (AdaBoost, XGBoost, CatBoost, LightGBM), BRT, SGB, etc.	1. Superior predictive performance;	1. Parameter optimization requirements;	Various scour prediction tasks with extremely high requirements for prediction accuracy.
	2. Capable of handling complex nonlinear relationships and variable interactions;	2. Potential risk of overfitting;
	3. Wide range of applications.	3. Performance may vary with specific conditions.
Genetic Algorithm Models [156,161,163,169]: GEP, GP, EPR, MGGP, etc.	1. Generates explicit prediction formulas;	1. Complex and computationally expensive parameter optimization;	Exploratory research aims to discover new, concise physical laws or empirical formulas from data.
	2. Dealing with complex nonlinear problems;	2. Highly dependent on data.
	3. Superior prediction performance;
	4. Applicable to a wide range of scour conditions and structure types.
Enhanced Models Based on Optimization Algorithms [21,160,172]: ANN-PSO; ANFIS-GA; NF-GMDH-PSO; PSO-XGBoost; RFO-XGBoost; RPSO-XGBoost; RS-REPTree, etc.	1. Significantly improved prediction accuracy;	1. Higher demand for data;	When the performance of existing single models fails to meet requirements for specific issues, seek breakthroughs in performance.
	2. Excels in dealing with complex nonlinear relationships;	2. Requires parameter tuning;
	3. Broader scope of application.	3. Risk of overfitting.

ANN: Artificial Neural Network; ANFIS: Adaptive Neuro-Fuzzy Inference System; SVM: Support Vector Machine; SVR: Support Vector Regression; DT: Decision Tree; M5Tree/M5MT (M5 Model Tree); GTB (Gradient Tree Boosting); REPTree (Reduced Error Pruning Tree); RF: Random Forest; AdaBoost: (Adaptive Boosting); XGBoost: Extreme Gradient Boosting; CatBoost: (Categorical Boosting); LightGBM: (Light Gradient Boosting Machine); BRT: (Boosted Regression Trees); SGB: (Stochastic Gradient Boosting); GEP: Gene Expression Programming; GP: Genetic Programming; EPR: (Evolutionary Polynomial Regression); MGGP: (Multi-Gene Genetic Programming); PSO: Particle Swarm Optimization; and GA: Genetic Algorithm; NF-GMDH: (Neuro-Fuzzy Group Method of Data Handling); RFO: (Random Forest Optimization); RPSO: (Random Particle Swarm Optimization); RS: (Random Subspace).

Table 3. Comparison of machine learning methods for local scour prediction.

Machine Learning Models	Advantages	Limitations	Applicable Conditions
Neural Networks [156,160]: ANN, ANFIS, etc.	1. Powerful nonlinear mapping capability;	1. “Black box” problem;	Scenarios where the dataset is large and the signal-to-noise ratio is high, and where extreme prediction accuracy is sought.
	2. Good prediction performance;	2. Strong data dependency;
	3. Can be enhanced by optimization algorithms or integration methods.	3. Risk of overfitting.
Support Vector Machines [22,163]: SVM, SVR, etc.	1. Capable of being applied to different scour types and conditions;	1. Requires parameter tuning;	Small to medium-sized datasets with high feature dimensions.
	2. Suitable for dealing with complex nonlinear relationships.	2. Certain “black box” characteristics;
		3. Data-dependent.
Tree-Based Models [22,161,168,170]: DT, M5Tree, M5MT, GTB, REPTree, etc.	1. Intuitive and interpretable;	1. Possible overfitting;	Scenarios where physical interpretation or decision analysis of prediction results is required.
	2. Able to handle nonlinear relationships;	2. Performance is affected by the range of data;
	3. Does not require extensive data preprocessing;	3. Limited interpretability.
	4. Good predictive performance.
Boosting/Ensemble Methods [22,168,171]: RF, Boosting Model (AdaBoost, XGBoost, CatBoost, LightGBM), BRT, SGB, etc.	1. Superior predictive performance;	1. Parameter optimization requirements;	Various scour prediction tasks with extremely high requirements for prediction accuracy.
	2. Capable of handling complex nonlinear relationships and variable interactions;	2. Potential risk of overfitting;
	3. Wide range of applications.	3. Performance may vary with specific conditions.
Genetic Algorithm Models [156,161,163,169]: GEP, GP, EPR, MGGP, etc.	1. Generates explicit prediction formulas;	1. Complex and computationally expensive parameter optimization;	Exploratory research aims to discover new, concise physical laws or empirical formulas from data.
	2. Dealing with complex nonlinear problems;	2. Highly dependent on data.
	3. Superior prediction performance;
	4. Applicable to a wide range of scour conditions and structure types.
Enhanced Models Based on Optimization Algorithms [21,160,172]: ANN-PSO; ANFIS-GA; NF-GMDH-PSO; PSO-XGBoost; RFO-XGBoost; RPSO-XGBoost; RS-REPTree, etc.	1. Significantly improved prediction accuracy;	1. Higher demand for data;	When the performance of existing single models fails to meet requirements for specific issues, seek breakthroughs in performance.
	2. Excels in dealing with complex nonlinear relationships;	2. Requires parameter tuning;
	3. Broader scope of application.	3. Risk of overfitting.

ANN: Artificial Neural Network; ANFIS: Adaptive Neuro-Fuzzy Inference System; SVM: Support Vector Machine; SVR: Support Vector Regression; DT: Decision Tree; M5Tree/M5MT (M5 Model Tree); GTB (Gradient Tree Boosting); REPTree (Reduced Error Pruning Tree); RF: Random Forest; AdaBoost: (Adaptive Boosting); XGBoost: Extreme Gradient Boosting; CatBoost: (Categorical Boosting); LightGBM: (Light Gradient Boosting Machine); BRT: (Boosted Regression Trees); SGB: (Stochastic Gradient Boosting); GEP: Gene Expression Programming; GP: Genetic Programming; EPR: (Evolutionary Polynomial Regression); MGGP: (Multi-Gene Genetic Programming); PSO: Particle Swarm Optimization; and GA: Genetic Algorithm; NF-GMDH: (Neuro-Fuzzy Group Method of Data Handling); RFO: (Random Forest Optimization); RPSO: (Random Particle Swarm Optimization); RS: (Random Subspace).

3.4. Probabilistic Prediction Methods

Traditional deterministic methods only provide a single predicted scour depth value but do not consider the uncertainty of hydrological, sediment, and structural parameters, which may lead to a severe underestimation of risks. Therefore, probabilistic prediction methods, which quantify uncertainty, have become a research focus. This method centers on structural reliability analysis, treating key input parameters as random variables, and evaluates failure probability through limit state functions (LSFs).

In reliability analysis, Monte Carlo simulation (MCS) is the foundational method, but it is computationally expensive, especially for high-reliability structures. To improve efficiency, researchers have introduced first-order/second-order reliability methods (FORM/SORM), subset simulation (SS), and others. Tubaldi et al. [173] proposed a Markov chain-based framework to assess the failure probability of bridge piers due to scouring, effectively addressing the temporal correlation of hydrological processes. Jafari-Asl et al. [23] compared the efficiency of MCS, FORM, SS, and other methods in analyzing the scouring probability of bridge piers in clay–sand mixed sediments, finding that subset simulation significantly reduces computational costs while maintaining accuracy. The introduction of surrogate models (such as random forests and Gaussian processes) further enhances analytical efficiency, such as the RFSS method proposed by Vatani et al. [174], which uses random forests to approximate LSFs and combines it with SS to achieve high-precision reliability assessment at low cost.

In the future, probabilistic scour prediction will be more deeply integrated with machine learning and physical laws. On the one hand, models that can directly output probability distributions (such as Gaussian process regression) will be developed to quantify prediction uncertainty. On the other hand, physical constraints [175] will be embedded into probabilistic machine learning to ensure that the results are physically consistent. This evolutionary direction shifts from traditional Monte Carlo simulation (MCS) to reliability analysis assisted by efficient surrogate models, significantly enhancing the risk assessment capabilities for complex erosion problems and laying the foundation for risk-based structural design and maintenance.

4. Conclusions and Future Work

This paper systematically reviews the latest progress in the study of local scour around marine structures, focusing on key influencing factors and prediction methods. In terms of influencing factors, this paper reveals that local scour is a complex multi-physical field process driven by hydrodynamic conditions, structure characteristics, seabed sediment properties, and environmental factors. Hydrodynamics is the external driving force, in which the nonlinear effects of wave–current coupling and the transient characteristics of turbulence are key to controlling scour development. Structure characteristics determine the disturbance patterns of the flow field, with geometric dimensions, shape, and spatial layout directly influencing scour depth and topography by altering flow patterns and vortex structures. The intrinsic physical properties of seabed sediments, such as grain size, gradation, and compactness, form the foundation for resisting scour. Additionally, environmental factors such as tides and extreme weather events introduce longer time scales and stronger unsteadiness, imposing higher demands on scour prediction. In terms of prediction methods, this paper systematically reviews various techniques from traditional to advanced approaches. Empirical formulas remain applicable in initial engineering design due to their simplicity, but their reliance on simplified assumptions and laboratory-scale data results in significant limitations when applied to complex real engineering scenarios. Numerical simulation has become an important research tool due to its ability to reveal physical mechanisms, particularly two-phase flow models that can more precisely characterize fluid–structure interaction processes. However, these methods are computationally expensive and lack validation data, especially when applied at field scales. Emerging machine learning techniques, with their powerful nonlinear mapping capabilities, have demonstrated high predictive accuracy on specific datasets. However, their “black box” nature and limited generalization capabilities hinder their widespread adoption in engineering applications. Meanwhile, probabilistic prediction methods are gaining increasing attention. These methods treat key parameters as random variables, quantify prediction uncertainty, and perform reliability analysis. However, their computational resource requirements and the definition of input parameter probability distributions remain challenges. In terms of model selection, due to the uncertainty introduced by wave and tidal loads in complex marine environments, these prediction models often fail to provide a unique solution [176]. In this context, multi-model integration emerges as a breakthrough approach: by embedding the physical relationships of deterministic models into a probabilistic analysis framework, complementary advantages can be achieved [177,178]. In this integrated approach, deterministic models provide a mechanistic understanding and basic predictions of the physical processes of scouring, while the probabilistic framework quantifies the uncertainty of input parameters and their potential risks, ultimately forming a more comprehensive risk assessment system.

Although current research has made important breakthroughs, there are still several key challenges in understanding the mechanisms of local scouring and prediction methods. Future research should focus on the following areas in order to make the transition from mechanistic understanding to accurate prediction:

• Research on scour mechanisms in complex real marine environments

Recent research has made significant progress in the local scour mechanism of marine structures, but existing results are mostly based on single or simplified hydrodynamic conditions, as well as idealized structural forms and homogeneous seabed conditions. This differs significantly from the dynamic characteristics of real marine environments, and the complexity of real structures and sediments far exceeds laboratory simulation conditions. Therefore, future research should focus on the scour response mechanism of non-uniform sediments and cohesive soils under complex hydrodynamic conditions, as well as the interference effects of complex structures on local flow fields and scour patterns. At the same time, advanced field observation technologies such as fiber optic sensing and high-frequency acoustics should be used to construct high-precision real-time monitoring systems to obtain long-term, high-resolution scour dynamic data in real marine environments, thereby establishing scour evolution theoretical models that are more consistent with actual working conditions.

2.

Development and validation of high-efficiency numerical models for engineering applications

Numerical models such as CFD and SPH have achieved significant success in revealing microscopic mechanisms, but their limitations lie in their high computational costs, making them difficult to apply to long-term evolution simulations at engineering scales. Additionally, the validation of most models still relies on laboratory data, which differs from field observation results. Therefore, future research focuses on two key areas: on the one hand, developing multi-scale coupled hybrid numerical models, such as using two-phase flow models in the near-field core region and single-phase flow models in the far-field region to balance accuracy and efficiency. On the other hand, there is an urgent need to systematically compare and validate models with long-term field monitoring data and use field data for model calibration and updating to enhance the reliability of predictions in real engineering environments. Additionally, environmental variables under extreme climate conditions should be incorporated into the model framework to improve the reliability of long-term predictions.

3.

Intelligent prediction methods integrating data-driven and physical mechanisms

Recent advances in machine learning have demonstrated its high accuracy in specific scour prediction problems. However, its fundamental limitation lies in its “black box” nature, high dependence on the quality and quantity of training data, and poor generalization ability when faced with unknown operating conditions, which limit its application in engineering. Therefore, future efforts should focus on developing PIML. By integrating the governing equations of fluid dynamics and sediment transport into neural networks, models can be constructed that both learn from data and follow fundamental physical laws. Such models are expected to achieve high generalization capability under small-sample conditions and provide some physical interpretability, thereby offering reliable support for engineering decision-making.

In summary, this paper systematically sorts out the key scientific issues and technical challenges in the study of local scouring of marine structures and clarifies the mechanisms of hydrodynamics, structures, seabed, and environmental factors from a multi-physical field perspective. By comparing the advantages and limitations of traditional empirical methods, numerical simulations, machine learning techniques, and probabilistic prediction models, this paper proposes future research directions, providing a theoretical framework and methodological guidance for improving the accuracy and engineering applications of erosion prediction models in complex marine environments. This work holds significant reference value for the safe design of marine engineering structures.