Fatigue Assessment of Pier Structures Under Dynamic Forces

Abstract

Pier structures in port and fishing harbor facilities require dynamic analyses during the design phase to account for external dynamic forces because of their high flexibility. Dynamic forces are frequently approximated as equivalent static forces for design purposes in practical engineering applications, but the fluctuational effects induced by these dynamic forces can be neglected. As the frequency range of wave forces acting on pier structures (0.05–1.0 Hz) significantly overlaps with the typical natural frequency range of pier structures (0.25–4.0 Hz), the response of a pier structure can be amplified because of the dynamic effects of the waves. In this study, we conducted a dynamic analysis by applying wave forces—a representative dynamic load—to a pier structure. The results were compared with those from a static analysis. A fatigue life assessment, which is often overlooked in static analyses, was also performed. The findings indicated that the concrete at the connection between the upper pier and steel piles exhibited a fatigue life of 27.3 years. The steel piles exhibited fatigue lives of 27.1 and 8.3 years depending on the weld details, falling short of the expected structural durability. Based on these results, recommendations for pier structures are proposed.

1. Introduction

1.1. Research Background

Port and fishing harbor facilities are designed with a service life of 100 years [1]. A gradual increase in the repairs, reinforcements, and reconstructions required before the intended service life has been reached has been noted. For instance, N. Pier in Yeosu, which was completed in 1979, has incurred annual repair costs exceeding USD 0.8 million since 1999. Restrictions on ship and large-vehicle traffic have been in place since 2013, with plans for demolition and reconstruction scheduled for 2025 [2]. An examination of the management costs for domestic ports and fishing harbors over a recent 5-year period (2015–2019) showed that USD 800 million had been allocated for maintenance and reinforcement costs, with expenses showing an annual upward trend [3]. These costs are expected to sharply increase because of the effects of global warming on the marine environment. South Korea experienced record-breaking conditions in 2019 when seven typhoons affected the Korean Peninsula. In August 2020, three consecutive typhoons—Bavi, Maysak, and Haishen—reached land, an unusual occurrence. The Korea Meteorological Administration introduced a new “super strong” category to its typhoon intensity classification in May 2020, indicating the growing strength of typhoons.

Considering the current situation of facilities falling short of their intended service life, an evolving marine environment is crucial when planning and designing port and fishing harbor facilities. In existing domestic design practices, various dynamic loads that affect port and fishing harbor facilities such as wave, wind, berthing, and towing forces are converted into equivalent static loads. Structures are then designed to ensure that the resulting sectional forces do not exceed the resistance capacity or allowable stress limits. Based on the dynamic characteristics of the structure, dynamic loads can either amplify or reduce responses. For instance, wave forces act on structures at various time periods and wave heights. Such continuous and repetitive dynamic loads can potentially lead to the fatigue-induced failure of a structure in the long term, affecting its natural lifespan and damping ratio in addition to the effects of its dynamic characteristics. Fatigue occurs when materials subjected to repeated varying forces fail at stress levels considerably lower than their ultimate strength; this is referred to as fatigue failure. The gradual, irreversible accumulation of damage that leads to failure is termed cumulative fatigue damage. Recent port and fishing harbor structures have been constructed using high-strength materials and precast members, offering long spans whilst reducing member heights. However, this can result in increased vibration amplitudes and potentially a greater vulnerability to fatigue. The current design criteria for domestic ports and fishing harbors lack detailed guidelines regarding structural dynamic impacts and fatigue considerations. Considering the growing influence of dynamic loads (particularly, the potential fatigue effects triggered by dynamic loads) is crucial when planning and designing ports and fishing structures.

Pier structures are frequently employed in port and fishing harbor facilities where the soil conditions are poor or the existing dock infrastructure requires expansion. These pier structures include multiple junction points between the concrete deck above and the supporting piles below and are more susceptible to dynamic load effects than other port structures such as block-type or caisson-type structures.

Figure 1 presents a relevant schematic. Pier structures experience wave forces within the 0.05–1.0 Hz range (at periods of 20.0–1.0 s). As the general natural frequency range of pier structures is 0.25–4.0 Hz (at periods of 4.0 to 0.25 s) [4,5,6], the frequencies of naturally occurring waves have been confirmed to significantly overlap with the natural frequencies of these structures. This suggests that dynamic wave effects on pier structures can amplify the structural responses. The effect of waves with frequencies similar to the natural frequencies of pier structures can lead to progressive, severe damage. A continuous wave effect can result in cumulative damage states that are similar to long-term fatigue.

1.2. Research Trends

The loads acting on coastal structures fluctuate depending on natural conditions. Wave and wind forces are not uniformly applied. Extreme impacts such as those from typhoons may affect these structures, with the degree of damage further intensified by corrosive environments. Jimenez-Martinez suggested that coastal structures should be analyzed using a probabilistic approach [9]. Studies on materials relative to fatigue have been continuously conducted. Fatigue studies have been performed on high-strength concrete, fiber-reinforced concrete, and steel–concrete composites, as well as on the fatigue behavior of reinforced concrete members in corrosive environments. The effects of concrete strength on fatigue resistance have presented conflicting research results. Certain studies suggest that high-strength concrete may be more disadvantageous in terms of fatigue compared with normal concrete [10,11], whereas other studies indicate that high-strength concrete has greater fatigue resistance [12]. The findings of previous studies suggest that compressive strength has no impact on fatigue resistance [13,14,15]. On the other hand, studies on the fatigue resistance of ultra-high-performance concrete (UHPC) and high-performance concrete (HPC) have been conducted, and Basaldella, M. et al. confirmed that UHPC can withstand more load cycles than HPC. This improvement in fatigue performance is attributed to the enhanced strain and stiffness development in UHPC and its high compressive strength and durability under cyclic loading [16]. The superior fatigue resistance of UHPC may be attributed to the fiber reinforcement rather than the increase in strength. Yu, Z. et al. evaluated that UHPC more effectively prevents the propagation of cracks even after they occur due to the presence of fiber reinforcement [17]. Daneshfar et al. conducted a study on fiber-reinforced concrete and demonstrated that increasing both the thickness of the samples and the fiber content could improve the fatigue life of concrete by up to 68% [18]. Other studies on fiber-reinforced concrete have confirmed that it positively impacts mechanical properties, fatigue life, and durability [19,20,21,22,23,24,25,26,27,28]. Recently, a study on increasing compressive strength was conducted by mixing a fiber reinforcement with waste oyster shells, silica fume, and blast-furnace slag [29]. Studies on the fatigue characteristics of steel–concrete composite members have primarily focused on bridge components. El-Zohairy et al. conducted experiments on steel–concrete composite beams subjected to one million cycles of loading and identified that the strength of shear connectors was a critical factor in controlling fatigue cracks [30]. Kuang et al. demonstrated that the strategic placement of shear connectors effectively mitigated crack formation in concrete slabs under fatigue-loading conditions [31]. Lu et al. observed that although concrete cracks had a minimal impact on fatigue life, damage to shear connectors significantly affected it [32]. Pan et al. showed that the use of engineered cementitious composites (ECCs) at steel–concrete joints improved the bond strength by 37.9% compared with conventional concrete [33]. Studies have investigated the effect of environmental factors in corrosive environments on the fatigue behavior of materials. Cui et al. demonstrated that fatigue damage was accelerated by reinforcement corrosion and that fatigue life was reduced by 77.45% in a carbonation environment [34]. Using experiments involving two million loading cycles, Zhang et al. demonstrated that the combined effects of corrosion and fatigue led to reinforcement fatigue and subsequent crack propagation [35]. Reza Kashyzadeh demonstrated that polymer concrete exhibited an 80% increase in fatigue strength compared with conventional concrete when subjected to corrosive environments [36].

Studies have been conducted on the structural safety of pier structures composed of concrete and steel members, and their behavior under dynamic wave and uplift forces. However, studies specifically addressing the dynamic behavior and fatigue effects related to pier structures are rare. Experimental studies on pier structures emerged around 2020, but these studies predominantly involved static analyses to verify the structural performance of new construction methods. Min et al. conducted a study on the horizontal cyclic loading of pier–structure connections in 2017 [37]. Their research was limited by the number of repetitions (<10 cycles), which was insufficient to reflect the dynamic load of waves.

Among the studies that have researched the dynamic behavior of mooring facilities, Park examined the fatigue safety of perforated concrete caissons under dynamic wave forces in 2012 [38]. They used a numerical wave flume program to calculate the dynamic wave pressures and verify the dynamic response of the concrete caissons. The fatigue safety of the concrete and the reinforcing bars was evaluated using the DNV code. In this study, only the self-weight, riprap, and dynamic wave pressure were considered, and, consequently, the fatigue life exceeded the allowable limits when other external factors were considered. Yang performed a comparative study on the effects of static and dynamic wave pressures on pile-type mooring facilities in 2015 [39]. They selected trestle piers and block-type dolphin structures for comparison and analyzed the static and dynamic loads using time history analysis techniques. Their results indicated that a dynamic analysis yielded larger displacements and sectional forces compared with a static analysis. The study concluded with results on displacement and sectional forces only. Subsequent research on the structural safety and fatigue of structures attributable to dynamic loads was discontinued. Ji, H.W. et al. conducted a study analyzing the lateral behavior caused by differential deflection between jetty structures. They suggested that existing studies on predicting the lateral behavior of structures under environmental and seismic loads have limitations and that more rigorous analysis is required [40]. While there has been relatively limited research on the dynamic analysis and fatigue evaluation of pier structures, extensive studies have been conducted on the foundations of offshore wind turbines, particularly jacket structures. These structures are influenced by vibrations not only from the wind turbines themselves but also from external forces such as ocean waves and wind. Consequently, fatigue evaluations have been carried out to assess the impact of these dynamic forces [41,42,43,44,45,46,47,48,49,50,51,52,53,54]. Marjan et al. analyzed the parameters affecting the lifespan of offshore jacket foundation structures and found that replacing the concrete transition piece with a lightweight steel structure increases the lifespan by 30%. Additionally, the study revealed that fatigue damage is more significant in inclined piles [48]. Tian et al. proposed a topology optimization method that considers fatigue for jacket structures, offering a design approach that achieves both lightweight structures and extended service life [49].

A review of existing research trends reveals that studies have been conducted on material fatigue, fatigue in corrosive environments, and the structural reliability of pier connections. However, only a few studies have addressed the safety of pier structures under long-term and cyclic dynamic loads. Most of these studies have focused on offshore wind turbine structures, particularly on foundation structures such as jacket-type foundations, which have been extensively explored in various research contexts. Thus, further research is required to evaluate the dynamic response and fatigue performance of pier structures subjected to dynamic loading conditions.

1.3. Research Objectives

This study conducted a comparative analysis of the static and dynamic load effects on concrete pier structures, focusing on the fatigue and structural characteristics induced by dynamic loading. In current port and fishing harbor designs, dynamic loads are often simplified into equivalent static loads. However, this approach fails to adequately account for the fatigue damage caused by continuous and fluctuating dynamic loads, such as wave forces. This deficiency can have serious implications for the long-term durability of structures. Additionally, the current domestic design standards lack detailed guidelines for fatigue assessment that consider the dynamic impacts on structures. As a result, fatigue damage due to dynamic loading is insufficiently addressed in the design and construction stages.

The objective of this study is to analyze the impact of dynamic loads, particularly wave loads, on pier structures in comparison to static loads and assess the potential for damage caused by dynamic forces. Through this analysis, we aim to identify the shortcomings of the current static load-based design approaches in addressing the effects of dynamic loading and to provide recommendations for improving the design and construction of pier structures in the future.

2. Methods

2.1. Target Structure

N. Pier BLOCK 3 (50,000 DWT), which is scheduled for reconstruction, was selected for static and dynamic comparative analysis. Figure 2 illustrates the perspective rendering and cross-sectional view of the target structure.

Table 1. Structural materials and mechanical properties.

Material	Specification	Standard Strength (MPa)	Elastic Modulus (MPa)	Unit Weight (kN/m3)	Remarks
Concrete	C40	40 (compressive strength)	30,008	24.0	Precast concrete
Concrete	C35	35 (compressive strength)	28,825	24.0	Cast-in-place
Rebar	SD400	400 (yield strength)	200,000	77.0	-
Steel pipe pile	STP355	355 (yield strength)	210,000	77.0	-

summarizes the structural materials and mechanical properties of the target structure.

2.2. Wave Force Assessment

2.2.1. Dynamic Wave Force Calculation

The CADMAS-SURF program was used to compute the dynamic wave forces. The analysis structure model comprised seven pile rows, including one front row. A two-dimensional analysis was conducted. As a result, the wave pressure on each element varied based on the permeability of the front wall. The front section consisted of wall segments 4.5 m wide, spaced at 13 m intervals. Consequently, Row 2 was expected to experience conditions closer to an impermeable-front effect, whereas Rows 2–7 were expected to be more influenced by a permeable front condition.

Figure 3 shows the velocity vectors for normal and storm waves under impermeable and permeable conditions. Based on these analysis results, the wave forces occurring at each row and each point were summarized for the structural analysis. Figure 4 depicts the time histories of the dynamic wave pressures for Rows 1 and 5 under normal and storm conditions, respectively. The right-hand side of the graph presents the dynamic wave pressure variations for each Datum Level (DL), with different DL values indicated in the legend. These wave pressures were calculated at various elevations, demonstrating the pressure fluctuations along the vertical profile of the structure under both normal and storm conditions

2.2.2. Dynamic Wave Force Input

The computed dynamic wave forces were incorporated into a structural analysis model. Time-dependent dynamic wave forces require substantial input data, leading to prolonged analysis times. As illustrated in Figure 5, time-varying wave force values were inputted at representative nodes, reducing the data volume and computational time whilst maintaining result accuracy. For example, wave pressure w₁ within the range of steel pipe pile L₁ can be input as a time-varying load P₁ at Node 1. Figure 6 illustrates the conceptual diagram of simply applying wave pressures to representative nodes. Figure 7 presents the input values of the dynamic wave pressures at DL. (+3.8) for the representative points in Rows 1 and 5.

2.3. Dynamic Properties of the Structure

The dynamic analysis was performed using 80 vibration modes and the eigen vector analysis method to evaluate the dynamic characteristics of the comparative target structure. Figure 8 describes the representative mode shapes in the X and Y directions.

A damping ratio of 0.01 was employed for the structure. Marine structures typically exhibit damping ratios between 0.01 and 0.05, with 0.01 being the recommended value in the absence of specific structural data [55]. DNV-OS-C502 guidelines indicate that a damping ratio not exceeding 0.03 can be used when actual data are unavailable [56].

3. Results

A comparative evaluation of the displacement, sectional forces, and safety was conducted for both the static and dynamic analyses.

3.1. Displacement Evaluation

The maximum displacements resulting from static and dynamic wave forces were compared for both normal and storm scenarios, based on the static and dynamic analysis outputs. Figure 9 shows the results of the dynamic wave forces.

Table 2. Maximum displacements for static and dynamic wave forces.

Category	Maximum Displacement (mm)		Remarks (B/A)
	A. Static Analysis	B. Dynamic Analysis
Normal conditions	3.442	3.971	1.154
Storm conditions	13.235	14.296	1.080

demonstrates that the dynamic analysis yielded displacements that were 15% greater under normal conditions and 8% greater under storm conditions compared with the static analysis.

Figure 10 illustrates the displacement history at locations experiencing maximum displacements under normal and storm conditions according to the dynamic analysis. The dynamic wave forces induced structural vibrations; these are shown in the figure.

3.2. Sectional Force Analysis

A comparative study of sectional forces in piles was performed for static and dynamic wave forces under both normal and storm conditions. The analysis differentiated between berthing piles (Φ812.8) and inner piles (Φ1100). Figure 11 presents the dynamic analysis results for normal wave forces under storm conditions. As summarized in

Table 3. Pile sectional forces for static and dynamic wave forces (bending moment: Mz).

Category		Bending Moment (Mz, kN-m)		Remarks Max(|B|)/A
		A. Static Analysis	B. Dynamic Analysis
Normal Conditions	Berthing pile ($\varnothing$812.8)	33.98	30.81	1.06
			−35.90
	Inner pile ($\varnothing$1100)	130.31	151.43	1.27
			−165.24
Storm Conditions	Berthing pile ($\varnothing$812.8)	146.20	129.98	1.00
			−145.65
	Inner pile ($\varnothing$1100)	515.64	496.47	1.15
			−590.90

, the results indicated that the dynamic analysis consistently produced higher sectional forces compared with the static analysis.

3.3. Regions Susceptible to Fatigue in Pier Structures

A fatigue assessment of the pier structure was conducted based on the fluctuating stresses in the key structural elements determined from the dynamic analysis. The regions susceptible to fluctuating stress were identified as connection points where the stiffness abruptly changed or where the material properties transitioned.

In pier structures, as illustrated in Figure 12, the interface between the upper structure and lower piles is anticipated to be the most vulnerable to fluctuating stress. This region not only experiences changes in stiffness and material composition but also endures the highest sectional forces and stress fluctuations in the piles. Consequently, this area was subjected to a detailed fatigue analysis. Figure 13a,b show the connection details between the upper structure and the lower piles. Detail A describes the method of integration that embedded the pile into concrete at a depth equal to its diameter. Detail B demonstrates the integration by reinforcing the pile head with rebar after minimal embedding.

3.4. Fluctuating Stress Evaluation

A detailed finite element method was employed to quantify the fluctuating stresses in the connection between the concrete and steel pipe piles. Figure 14 presents the characteristic stress distributions and stress histories of the concrete and steel pipe piles in the berthing section under normal and storm conditions. The graph illustrates the two points for each material where the maximum and minimum stresses are repeated. These points are located at the interface between the concrete and the steel pipe piles. In Detail A, the concrete points are FB-Con1 and FB-Con2, and the steel pipe pile points are FB-SP1 and FB-SP2. ABAQUS finite element software (version 2007) was used to analyze these fluctuating stresses.

Figure 15 depicts the stress distributions and histories of the inner pile cap concrete, steel pipe piles, and steel rebar (Detail B) under normal and storm conditions. In Detail B, the concrete points are IN-Con1 and IN-Con2, the steel pipe pile points are IN-SP1 and IN-SP2, and the reinforced bar points are IN-RB1 and IN-RB2.

3.5. Fatigue Life Estimation

The cumulative damage ratio was computed using Equation (1) from DNV-OS-C502 [56]. Although a cumulative damage sum of 1 indicates member fatigue failure, design standards prescribe allowable cumulative damage ratios based on environmental conditions, with 0.5 applied to areas beneath a splash zone.

$$\mathrm{D}=\sum _{i=1}^k{\displaystyle \frac{n_i}{N_i}}\le \mathsf{\eta }$$

(1)

where $\mathrm{D}$, $n_i$, $N_i$, $n_i / N_i$, and $\mathsf{\eta }$ are the cumulative damage ratio, number of stress range (${\mathrm{S}}_{\mathrm{i}}$) repetitions$,$ number of cycles to fatigue failure at the stress range (${\mathrm{S}}_{\mathrm{i}}$), damage rate from fatigue at the stress range (${\mathrm{S}}_{\mathrm{i}}$), and allowable cumulative damage ratio (0.50 for beneath a splash zone), respectively.

The number of fatigue failures (N) was calculated for concrete subjected to fluctuating stress using Equation (2) from DNV-OS-C502 [56].

$${log}_{10}\mathrm{N}=C_1{\displaystyle \frac{\left(1-\frac{{\sigma }_{max}}{C_5\times f_{rd}}\right)}{\left(1-\frac{{\sigma }_{min}}{C_5\times f_{rd}}\right)}}$$

(2)

where ${\sigma }_{max}$ is the numerically largest compressive stress, and ${\sigma }_{min}$ is the least compressive stress. Parameter ${\mathrm{C}}_1$ = 8.0 is the constant used for the fatigue life estimation of the submerged members with alternating compression–tension stress. ${\mathrm{C}}_5$ is a fatigue parameter related to the fatigue performance of concrete, ${\mathrm{C}}_5$ = 1.0 (for concrete). $f_{rd}$ is the compression strength corresponding to the specific failure mode being analyzed, $f_{rd}$ = $\mathsf{\alpha }\times {\mathrm{f}}_{\mathrm{c}\mathrm{d}}$, where $\mathsf{\alpha }=1.3-0.3\mathsf{\beta }$. $\mathsf{\beta }$ is the ratio between the numerically smallest and largest stress acting simultaneously in the local compressive zone ($0<\mathsf{\beta }<1.0$), and ${\mathrm{f}}_{\mathrm{c}\mathrm{d}}$ is the design compressive strength of concrete, ${\mathrm{f}}_{\mathrm{c}\mathrm{d}}={\mathrm{f}}_{\mathrm{c}\mathrm{n}}/{\mathsf{\gamma }}_{\mathrm{c}}$, where ${\mathsf{\gamma }}_{\mathrm{c}}$ represents the material factor (1.10). ${\mathrm{f}}_{\mathrm{c}\mathrm{n}}$ is the normalized compressive strength of concrete. When ${\mathsf{\sigma }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is tensile, ${\mathsf{\sigma }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is set to zero.

Fatigue failure cycles (N) were determined for reinforcing bars under varying stress levels using Equation (3) from DNV-OS-C502 [56].

$${log}_{10}\mathrm{N}=C_3-C_4{log}_{10}∆\sigma$$

(3)

where ${\mathrm{C}}_3 \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{C}}_4$ represent coefficients based on the rebar type and corrosion environment, respectively (${\mathrm{C}}_3=19.6 \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{C}}_4=6.0$ for straight rebars; ${\mathrm{C}}_3=15.9 \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{C}}_4=4.8$ for bent rebars). $∆\mathsf{\sigma }$ represents the stress range between the maximum and minimum rebar stress (${\mathsf{\sigma }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathsf{\sigma }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$). $\mathrm{N}$ values exceeding $2\times {10}^8$ were considered to represent infinite fatigue life.

Steel components under fluctuating stress had their fatigue failure cycles (N) computed using Equation (4) from DNV-RP-C203 [57].

$${log}_{10}\mathrm{N}=log\overline{a}-mlog\left(∆\sigma {\left({\displaystyle \frac{t}{t_{ref}}}\right)}^k\right)$$

(4)

where $m$, $log\overline{a}$, $t_{ref}$, $t$, and $k$ are the S–N curve slope, intercept of the ${log}_{10}\mathrm{N}$ axis, reference thickness (25 mm), member thickness, and thickness effect exponent, respectively (

Table 4. Steel in seawater with cathodic protection.

Detail Category	$\mathbf{N}\le {10}^7$ Cycles		$\mathbf{N}\ge {10}^7$ Cycles $\mathbf{l}\mathbf{o}\mathbf{g} \overline{\mathbf{a}};\mathbf{m}=5.0$	$\mathbf{Fatigue}\mathbf{Limit}\mathbf{at}{10}^7$ Cycles	$\mathbf{Thickness}\mathbf{Exponent},\mathbf{k}$
	$\mathbf{m}$	$\mathbf{l}\mathbf{o}\mathbf{g} \overline{\mathbf{a}}$
B1	4.0	14.917	17.146	106.97	0
B2	4.0	14.685	16.856	93.59	0
F	3.0	11.455	15.091	41.52	0.25
F1	3.0	11.299	14.832	36.84	0.25
F3	3.0	11.146	14.576	32.75	0.25

).

The values of cathodically protected steel in seawater (Table 4) from the DNV-RP-C203 guidelines were used because most steel pipe piles in pile-supported structures employing cathodic protection. The specifics adhered to the welding details for tubular members, as presented in

Table 5. Structural details (hollow sections).

Detail Category	Constructional Details	Description
B1		Non-welded section
B2		Automatic longitudinal seam welds
F		Circumferential butt-weld made from one side on a backing bar
F3		Circumferential butt-weld made from one side without a backing bar

. The steel pipes in the pile-supported structures were fabricated with diameters exceeding 800 mm via longitudinal automatic welding with roll bending (R/B) as per Detail B2. The piles were then butt-welded on-site (Details F or F3) to embed them into the foundation and attain the planned elevations.

3.6. Fatigue Life Assessment

Fluctuating stresses at concrete–pile interfaces in berthing sections and inner pile cap–pile junctions were quantified and plotted using S–N curves. Figure 16 illustrates the S–N curves and the corresponding stress occurrences for the concrete components, steel rebars, and steel pipe piles at the berthing section connections and inner sections. Figure 16a provides the S–N curve for concrete, which can be derived using Equation (2). Moreover, the fluctuating stresses at the berthing and inner sections, along with the frequency of these stresses during the service life, are depicted in the graph. Figure 16b presents the S–N curve for steel rebar, plotted using Equation (3). The graph also visualizes the stresses occurring in the inner section rebars and the frequency of these stresses throughout the service life. Finally, Figure 16c demonstrates the S–N curves for steel pipe piles based on welding details (B2, F, and F3), while also capturing the stresses acting on the steel pipe piles and their occurrence frequencies over the service life.

The fatigue life, defined as the period until fatigue failure occurs at points subjected to fluctuating stresses, can be calculated using Equation (5).

$$\mathrm{f}atiguelife={\displaystyle \frac{\mathsf{\eta }}{{\sum }_{i=1}^n\frac{d_i}{l_D}}}$$

(5)

where $\mathsf{\eta }$ represents the allowable cumulative damage ratio, and $d_i$ and $l_D$ denote the cumulative damage ratio at the stress range and design service life, respectively.

Table 6. Fatigue life of the concrete in the berthing section.

Classification	No.	$\mathbf{Stress}\mathbf{Range}\left({\mathit{S}}_{\mathit{i}}\right)$	Number of Cycles in Design Life	Number of Fatigue Failures	Damage Ratio	Cumulative Damage Ratio	Fatigue Life
Normal Condition	1	0.422	8.86 × 106	9.04 × 107	0.10	1.40	35.8 years
	2	0.324	8.86 × 106	9.13 × 107	0.10
	3	0.332	8.86 × 106	9.30 × 107	0.10
	4	0.312	8.86 × 106	9.34 × 107	0.09
	5	0.293	8.86 × 106	9.38 × 107	0.09
	6	0.273	8.86 × 106	9.42 × 107	0.09
Storm Condition	1	1.385	1.04 × 107	7.78 × 107	0.13
	2	1.051	1.04 × 107	6.64 × 107	0.16
	3	1.027	1.04 × 107	7.91 × 107	0.13
	4	0.938	1.04 × 107	7.20 × 107	0.14
	5	0.901	1.04 × 107	8.14 × 107	0.13
	6	0.681	1.04 × 107	7.91 × 107	0.13

presents the process of estimating the fatigue life of the concrete in the berthing section as a representative case.

Table 7. Fatigue life summary for concrete pile caps and pile connections.

Category			Cumulative Damage Ratio	Allowable Damage Ratio	Assessment	Fatigue Life
Berthing Part	Concrete		1.40	0.5	Fail	35.8 years
	Steel Pipe Pile	Detail B2	1.3 × 10−3		Pass	39,328 years
		Detail F	6.0 × 10−2		Pass	840 years
		Detail F3	1.9 × 10−1		Pass	257 years
Inner Part	Concrete		1.83		Fail	27.3 years
	Steel Rebar		0.01		Pass	4334 years
	Steel Pipe Pile	Detail B2	0.04		Pass	1267 years
		Detail F	1.85		Fail	27.1 years
		Detail F3	6.05		Fail	8.3 years

summarizes the cumulative damage ratios and projected fatigue lives of various components in berthing and inner parts considering stress fluctuations, including the results from Table 6.

The fatigue life analysis in Table 7 indicated that the concrete in both the berthing and inner sections exceeded the allowable damage ratios, with cumulative ratios of 1.40 and 1.83, respectively. Their fatigue lives were 35.8 years and 27.3 years, respectively, falling short of the target service life of 100 years. The cumulative damage ratio of the inner-section reinforcing bars was 0.01, well within the allowable damage ratio of 0.5, and its fatigue life was calculated to be 4334 years, confirming its safety against fatigue. On the other hand, the steel pipe piles in both sections showed a significant reduction in fatigue life depending on the welding details. For the inner section steel pipe piles, applying F or F3 welding at the point of maximum fluctuating stress caused the cumulative damage ratios to rapidly increase to 1.85 and 6.05, respectively, under the same stress variations, which far exceeded the allowable limits. The estimated fatigue lives sharply decreased to 27.1 years and 8.3 years, respectively.

4. Discussion

4.1. Interpretation of Results

This study compared the results of dynamic and static analyses under wave loads, revealing that the dynamic analysis resulted in significantly larger displacements and sectional forces. In particular, it was found that the fatigue damage at the concrete pile connection could greatly reduce the design life of the structure. These findings indicate that current static analysis-based design approaches fail to adequately consider the long-term fatigue damage caused by dynamic loads. Therefore, improvements in the planning, design, construction, and maintenance phases of structures are required to address the impact of dynamic loads. The following section outlines practical recommendations for such improvements.

4.2. Practical Implications and Proposal

The current domestic design standards for port and fishing harbor facilities state that “pile-type pier structures are flexible structures and require dynamic analysis when designing for dynamic external forces” [58]. However, these standards do not provide specific design guidelines. Based on the findings of this paper, the following improvements for pier structures are proposed:

• In this study, we observed that the concrete at the pile head—the largest fluctuating stress acting on pier structures—was vulnerable to fatigue. The following fatigue-resistance measures should be considered in the design phase: (1) apply fiber-reinforced concrete, which has been proven to enhance fatigue resistance [18,19,20,21,22,23,24,25,26,27,28], or polymer concrete [36]; (2) place shear connectors appropriately because they are effective at controlling fatigue cracks in steel–concrete composite members [31,32]; (3) use ECCs (engineered cementitious composites) to improve the bonding strength at the steel–concrete interface [33]; and (4) apply anti-corrosive coatings in this area to compensate for the reduction in fatigue life in corrosive environments [34,35].
• In the design phase, engineers should recognize that fatigue failure can occur even if the stresses on members are within safety factors based on sectional evaluations. As shown in Figure 14 and Figure 15, even if the generated stresses are minimal and within allowable limits, they can still affect the fatigue life over prolonged periods of repetition. A quasi-static analysis considering impact factors should be performed when designing structures expected to experience significant dynamic effects to amplify the dynamic load or allowable stress reduction factors for members should be applied to account for the effects of dynamic wave forces.
• As shown in Table 7, welding joints at the locations of peak fluctuating stress on piles result in a significant reduction in fatigue life. Contractors must implement strict measures during the construction phase to avoid welding joints at points where maximum fluctuating stress occurs.
• In the operational maintenance phase, facility managers should develop and implement targeted maintenance protocols for concrete–pile connections (the most fatigue-vulnerable areas) and focus their management inspection capabilities on these areas. Because of the long-term nature of fatigue failure, a system for comprehensive record-keeping and information transfer between successive managers should be established.

5. Conclusions

In this study, we conducted a dynamic analysis by applying wave forces and a primary dynamic load to pier structures and compared the results with a conventional static analysis. Displacements and sectional forces from static and dynamic loads were compared. The fatigue life of pier structures, often overlooked in static analyses, was calculated by assessing the members subjected to significant fluctuating stresses of dynamic factors. The recommendations were proposed based on the analyses of this study. Our conclusions are as follows:

• A dynamic analysis of wave forces yielded displacements 15.4% larger under normal conditions and 8.0% larger under storm conditions compared with a static analysis. The pile sectional forces were 27% and 15% higher under normal and storm conditions, respectively.
• Fatigue assessments of the concrete–pile connections in the berthing area and inner concrete–coping pile connections—which endure the highest fluctuating stresses from dynamic wave forces—revealed that the damage ratios for berthing and inner concrete were 1.40 and 1.83, respectively. These ratios substantially surpassed the permissible damage ratio of 0.5. The projected fatigue lives were 35.8 and 27.3 years, falling considerably short of the intended 100-year service life.
• For steel pipe piles, the fatigue life was observed to dramatically decrease dramatically based on the welding specifications (Detail B2: longitudinal automatic welding; Detail F: butt-welding with internal backing; Detail F3: butt-welding without internal backing). The fatigue life of steel pipe piles in the berthing area decreased to 39,328, 840, and 257 years according to each welding detail, respectively. The inner steel pipe piles reduced to 1267, 27.1, and 8.3 years, respectively.
• The welded joints in the inner piles exhibited fatigue lives of 27.1 and 8.3 years depending on the welding details, indicating that they might not attain the designed service life. Welded joints at maximum fluctuating stress points could experience fatigue failure before reaching the end of their designed service life.
• Based on the findings of this study, specific measures to enhance the fatigue resistance of pier structures have been proposed (Section 5).