An Analysis of the Flexural Stiffness and Horizontal Bearing Capacity of CFRP Composite Pipe Piles in Marine Environments

Abstract

Carbon-fiber-reinforced polymer (CFRP) is a composite material consisting of a resin matrix reinforced with carbon fibers. This study focuses on CFRP composite pipe piles as the subject of investigation, exploring the impact of substituting steel bars with CFRP bars on the bending performance of pipe piles through rigorous three-point bending tests. The attenuation of flexural stiffness in CFRP pipe piles under a chloride salt environment was anticipated. The lateral bearing capacity of CFRP pipe piles was calculated by introducing a stiffness degradation coefficient for the piles and utilizing the finite difference method. The findings of the analysis suggest that as the CFRP reinforcement replacement rate increases, the initial bending stiffness of the composite pipe pile experiences a corresponding decrease. After serving for 28.15 years, the steel reinforcement within the pipe pile commences rusting, resulting in a nonlinear decline in the bending stiffness of the composite pipe pile. As the service time of pipe piles increases, a higher replacement rate of CFRP reinforcement results in a slower attenuation of pile stiffness. Consequently, both the horizontal displacement at the top of the pile and the bending moment along the body of the composite pipe pile gradually increase over time. During the same service period, the higher the rate of CFRP reinforcement, the less noticeable the attenuation in the horizontal bearing capacity of the pile shaft.

1. Introduction

A large amount of chloride ions can be found in the ocean environment, and they move through concrete towards its steel surface because of differences in concentration. If the concentration of chloride ions on the surface of the steel reinforcement exceeds a certain level, corrosion will occur on the reinforcement. Consequently, as the corrosion depth of the steel increases, the bending stiffness and bearing capacity of the concrete pile undergo a decline [1]. For metal infrastructure directly exposed to the marine environment, the fatigue strength of the material is significantly reduced under the effects of external hydrostatic pressure and chloride ion corrosion [2]. The deterioration of traditional concrete piles significantly compromises the safety of highway bridges, oil platforms, and other structures that operate in corrosive marine environments over the long term. The bearing capacity and settlement effects of piles embedded in soil are also significant factors influencing the safety of pile foundations [3]. In order to solve the above problems, a new composite material is proposed for use as a substitute for traditional reinforced concrete. Carbon fibers, renowned for their light weight, exceptional strength, and corrosion resistance, are widely regarded as a promising substitute for steel [4,5,6]. Compared to traditional steel reinforcement, it exhibits superior corrosion resistance in chloride-rich environments, making it ideally suited for engineering applications and structural repairs in marine settings with high concentrations of chloride salts.

As the application of CFRP materials continues to gain traction in structural engineering, the mechanical performance of CFRP concrete components has emerged as a focal point of research among scholars globally. Liang et al. [7] determined that specimens confined by thicker fiber-reinforced polymer (FRP) exhibit higher axial strength and greater ultimate strain through compressive performance tests on recycled aggregate concrete-filled steel-tub (RACFT) square columns confined by FRPs. Waleed and Yazan [8] conducted research on deep beams strengthened with CFRP plates, demonstrating a significant enhancement in their resistance to damage and bending cracks through experimental simulations and finite element analysis. Emine A. et al. [9] conducted bending tests to investigate the influence of different types of FRP reinforcements on the flexural performance of hybrid beams and discovered that CFRP reinforcements significantly enhanced the flexural strength of hybrid beams. Job and Ramadass [10] proposed an enhanced empirical model that predicts the ultimate load capacity of deep beams strengthened longitudinally with fiber-reinforced polymer (FRP) under shear failure conditions. Ahmed et al. [11] conducted failure tests to investigate the enhancement effect of CFRP bars as stirrups on the shear strength of circular concrete specimens.

As the application of CFRP materials in concrete structures becomes increasingly widespread, they are also being utilized in pile foundations. Many researchers have carried out thorough investigations into the flexural strength, shear strength, deformation, durability, and horizontal load-bearing capacity of composite pipe piles reinforced with CFRP. Giraldo and Rayhani [12] validated the superior axial bearing capacity of FRP piles through conducting a static load test on the sides of the piles. Zyka and Mohajerani [13] proposed that the corrosion resistance and extended service life of fiber-reinforced polymer (FRP) and structurally reinforced plastic (SRP) composite piles render them an economically viable, environmentally sustainable, and practical alternative to traditional piles in marine environments. Valez and Rayhani [14] analyzed the load transfer properties of CFRP pipe piles. In comparison to traditional steel piles, the reduced stiffness of CFRP piles leads to a greater displacement of the pile top under lateral loads. However, the bearing capacity of CFRP piles is either higher than or at least comparable to that of steel piles. Zhuang et al. [15] conducted a study on the efficacy of carbon-fiber-reinforced polymer (CFRP) in enhancing the durability of composite RC piles in a marine erosion environment. Simulated tests were conducted on the pile bodies under varying degrees of theoretical corrosion, and a quantitative analysis was performed on the quality loss in the reinforcement. Alajarmeha and Manaloa [16] conducted a study on the load-bearing capabilities of glass-fiber-reinforced polymer (GFRP) longitudinal bars with varying reinforcement ratios under concentric axial compression. Furthermore, they thoroughly examined the influence of reinforcement configurations and reinforcement ratios on the axial performance of high-performance concrete. Dong et al. [17] conducted a study on the corrosion characteristics of concrete-filled CFRP–steel tube (CFRP-CFST) piles in a hot and humid environment, revealing that the external bonding of carbon fiber cloth significantly enhances the bearing capacity and durability of pipe piles. Shao et al. [18] established a chloride ion diffusion equation, combined it with the finite difference method and an uncertainty model for seismic waves, and revealed the impact of the CFRP ratio on the horizontal bearing characteristics and seismic vulnerability of pipe piles. The CFRP composite pipe pile integrates CFRP materials with concrete piles, effectively leveraging the engineering properties of CFRP. In contrast to ordinary reinforced-concrete piles, the CFRP composite pipe pile demonstrates advantages such as reduced weight, enhanced bearing capacity, superior strength, excellent corrosion resistance, and remarkable fatigue resistance.

The aforementioned research holds significant importance in analyzing the durability and lateral load-bearing capabilities of CFRP composite piles in marine environments. Nevertheless, the precise impact of the CFRP reinforcement replacement rate on the stiffness and load-bearing capacity of composite piles remains elusive. This article focuses on CFRP composite pipe piles as the subject of investigation. Through bending tests, it examines the bending performance of composite pipe piles when the reinforcement in reinforced-concrete pipe piles is replaced with CFRP reinforcement. The testing process enables the acquisition of load–deflection curves for pipe piles across various CFRP reinforcement replacement rates. Furthermore, it facilitates the analysis of the ultimate bending capacity and variation in the bending stiffness of CFRP composite pipe piles across different replacement rates. Based on this, the stiffness reduction factor of the pile body resulting from the substitution of CFRP tendons is introduced to quantitatively assess the influence of the CFRP tendon replacement rate on the initial bending stiffness of composite pipe piles. Furthermore, the reliability method is employed to forecast the initial corrosion time of these piles, particularly when subjected to lateral loads in marine environments. Utilizing the chloride diffusion model as a foundation, the impact of the CFRP reinforcement replacement rate on the rate of flexural stiffness decay in pipe piles is anticipated. Ultimately, the finite difference method is employed to compute the bending moment and displacement of the CFRP composite pipe pile during its operational lifespan.

2. Flexural Performance Test of CFRP Composite Pipe Piles

2.1. Experimental Protocol

The model pipe piles possess a length of 1200 mm, an outer diameter measuring 200 mm, an inner diameter of 100 mm, and a reinforcement cover thickness amounting to 25 mm. Each model pipe pile is furnished with eight longitudinal reinforcements. During the experiment, the replacement rates of the CFRP tendons were set at 0%, 25%, 50%, 75%, and 100%. In the model piles, the CFRP tendons were arranged in pairs, exhibiting a symmetrical layout. The design of the test pile is depicted in Figure 1.

The reinforcement materials employed consist of HRB335 [19] steel reinforcement and CFRP reinforcement, both with a diameter of 10 mm. The concrete material used in the model pipe piles incorporates high-strength Portland cement graded at 52.5, featuring an apparent density of 3150 kg/m³. River sand with a fineness modulus of 2.62 is utilized as the fine aggregate, and crushed stone fragments ranging from 5 mm to 10 mm in size, resembling melon seeds, were employed as the coarse aggregate. A naphthalene-based superplasticizer is employed to enhance the fluidity of the concrete, thereby facilitating the pouring process. The water–cement ratio for the model pipe piles stands at 0.35, and the concrete mix proportions are outlined in detail in Table 1. The completed reinforcement cage is depicted in Figure 2.

While pouring the pipe piles, concrete test blocks were simultaneously fabricated to assess the concrete. The completed cast-in-place pipe piles and concrete test blocks were placed in the same environment and maintained at a temperature of 26 °C and a humidity level of 95% for a curing period of 28 days. The completed test pipe piles after curing is depicted in Figure 3.

2.2. Experimental Procedure

The bending test for the CFRP composite pipe piles was carried out at Shanghai Zhong Cai Engineering Testing Co., Ltd. (Shanghai, China). Simultaneously, the compressive strength test was performed on the test specimens that underwent curing under identical conditions. Based on the average test results of three sets of 150 × 150 × 150 mm concrete standard test specimens, the actual compressive strength was determined to be 41.43 MPa. The compressive strength test of the concrete specimen is depicted in Figure 4. During the experimental process, the pipe piles were initially hoisted onto the steel frame support, with both ends resting securely on circular steel bearings. A steel plate, sprinkled with a small quantity of sand to enhance friction, was interposed between the pile ends and the bearings, effectively preventing any potential slippage of the pipe piles. The center point of the pipe piles was located using a ruler and marked accordingly. A small quantity of sand was sprinkled at the center point to enhance friction, and then, a saddle-shaped steel seat was affixed. The circular design of the steel saddle seat ensures uniform loading on the piles. The loading point was positioned precisely in the middle of the pipe pile model, and an anchor rod hydraulic pump was utilized along with a compatible jack to apply the desired load to the pipe piles. Three digital displacement meters were strategically placed on the upper sections of the supports at both ends of the model pipe piles, as well as on the underside of the mid-span, to gather deflection data. Prior to commencing the experiment, these meters were calibrated to zero. The magnitude of the applied load was accurately gauged through the digital readout of the anchor hydraulic pump. The test loading device is depicted in Figure 5, which depicts the graded loading approach employed. Starting from zero, the load was incrementally increased by 10 kN per level, with a 10 min interval between each loading. Upon the emergence of fine cracks in the model pipe piles, the increment was reduced to 5 kN per level, maintaining the 10 min interval. As the loading neared the ultimate capacity of the model pipe piles, the increment was further reduced to 2 kN, and the interval was shortened to 5 min. Throughout this process, the actual loading value and mid-span deflection value were meticulously recorded until the model pipe piles sustained complete failure. As the load gradually increased, cracks appeared in the concrete in the tensile zone of the pipe piles, and their deflection also increased. The initial crack in the pipe piles progressively expanded, with new cracks emerging parallel to it and extending towards the neutral axis. As the load continued to increase, the parallel cracks extended along the bending shear zone and bended towards the loading point. Finally, the concrete in the compression zone of the pipe piles was crushed, resulting in the formation of bending and inclined joints that extended along the span. The cracking and failure of the CFRP composite pipe piles that occurred during the test are illustrated in Figure 6. Under the same load level, the higher the CFRP ratio of the pipe piles, the greater the total number of cracks and their widths.

2.3. Analysis of Experimental Results

By organizing and analyzing the data gathered from the experiment, we have obtained the load–deflection curve of the pipe piles under varying CFRP reinforcement replacement rates, as depicted in Figure 7. Initially, when the load was relatively low (approximately below 40 kN), the relationship between load and deflection remained primarily linear, indicating that the concrete pipe piles were undergoing elastic deformation. As the load continued to increase, the deflection of the pipe piles also intensified, resulting in the emergence of cracks in the tensile zone of the concrete, which subsequently altered the slope of the load–deflection curve. Finally, as the load approached a critical threshold (roughly ranging from 130 to 150 kN), the pipe piles reached their failure point. At this stage, the pipe piles sustained damage, with the load value remaining constant while the deflection continued to increase, ultimately reaching the limit of its bending capacity.

Upon comparing the bending performance of pipe piles with varying CFRP reinforcement replacement rates, it becomes evident that, prior to reaching the ultimate load state, the deflection value of the pipe piles escalated with an increase in the CFRP replacement rate under identical loading conditions. Furthermore, as the CFRP reinforcement replacement rate rises, the ultimate load capacity of the composite piles diminishes, accompanied by a corresponding augmentation in deflection at the point of ultimate load attainment. This phenomenon can be attributed to the fact that the elastic modulus of carbon fiber reinforcement is inferior to that of steel reinforcement, resulting in a decrease in the stiffness of the pile body as the CFRP replacement rate increases. The ultimate load values and corresponding deflections of the composite pipe piles with various CFRP reinforcement substitution rates are shown in Table 2.

The differential equation of the piles’ deflection curve can be reduced to

(1)$EI\omega \prime \prime (x)=-M(x)$

In the formula, EI represents the stiffness of the pile shaft, ω″(x) represents the second derivative of the deflection at position x, and M signifies the bending moment at section x. A simplified diagram of the test device is depicted in Figure 1. The test piles comprise three distinct sections: AB, BC, and CD. The uniformly distributed load is imposed on section BC via a saddle-shaped steel pier. Assuming that the test specimen is simply supported at points A and D, with the support reaction forces both equal to qb/2, q represents a uniformly distributed load and b refers to the side length of the square saddle-shaped steel base, which is set as 20 cm. The bending moment equation at cross-section located at x is as follows:

(2)$\left\{\begin{array}{c}{M}_1(x)={\displaystyle \frac{qbx}{2}}, 0\le x<{\displaystyle \frac{l-b}{2}}\\ M_2(x)={\displaystyle \frac{qbx}{2}}-{\displaystyle \frac{q}{2}}{(x-{\displaystyle \frac{l-b}{2}})}^2, {\displaystyle \frac{l-b}{2}}\le x<{\displaystyle \frac{l+b}{2}}\\ M_3(x)={\displaystyle \frac{qbx}{2}}-qb(x-{\displaystyle \frac{l}{2}}), {\displaystyle \frac{l+b}{2}}\le x\le l\end{array}\right.$

where l represents the effective pile length, which is 1.0 m. Due to the smooth and continuous nature of the deflection curve, the rotation angles and deflections at points C and D are continuous. According to the boundary conditions,

(3)$\left\{\begin{array}{c}{\omega }_1\prime (x)={\omega }_2\prime (x), {\omega }_1(x)={\omega }_2(x), x={\displaystyle \frac{l-b}{2}}\\ {\omega }_2\prime (x)={\omega }_3\prime (x), {\omega }_2(x)={\omega }_3(x), x={\displaystyle \frac{l+b}{2}}\\ {\omega }_1(x)=0, x=0\\ {\omega }_3(x)=0 ,x=l\end{array}\right.$

where ω₁(x), ω₂(x), and ω₃(x) represent the deflection equations for segments AB, BC, and CD, respectively. ω₁′(x), ω₂′(x), and ω₃′(x) represent the first derivatives of the deflection equations for segments AB, BC, and CD, respectively. When at position x = l/2, the mid-span deflection ω₂ can be expressed as follows:

(4)${\omega }_2={\displaystyle \frac{(b^4+8b{l}^3-4b^{3}l)}{384EI}}q$

Here, ω₂ represents the mid-span deflection, the uniformly distributed load is q = F/b, and F stands for the numerical value of the concentrated force exerted by the hydraulic press.

The displacement–deflection relationship can be derived as follows:

(5)$EI={\displaystyle \frac{(b^3+8l^3-4b^{2}l)F}{384{\omega }_2}}$

Figure 8 presents the variation curve of the bending stiffness of the pipe piles as a function of their load, considering various CFRP reinforcement replacement rates. It can be observed that when the load is relatively small, the deflection is also minimal, resulting in a generally higher stiffness for each pile. As the load increases, the ratio of load to pile deflection tends to stabilize, with the piles’ bending stiffness approaching a more reasonable value and gradually decreasing as the load continues to rise. By defining a reasonable threshold as a change rate of less than 5% in the bending stiffness of the pile shaft, we can obtain the average value of bending stiffness within this threshold range through linear fitting. As the replacement rate increases, the bending stiffness of the composite piles exhibits varying degrees of reduction. Specifically, when compared to traditional reinforced-concrete pipe piles, the stiffness of the pipe piles with CFRP reinforcement rates of 25%, 50%, 75%, and 100% decreases by 14.5%, 33.62%, 39.78%, and 65.36%, respectively. The primary reason lies in the fact that the elastic modulus of CFRP reinforcement is inferior to that of conventional steel reinforcement, leading to a decrease in the equivalent elastic modulus of the composite pipe piles after CFRP substitution. Table 2 depicts the average bending stiffness values of each pipe pile.

To quantitatively assess the impact of CFRP reinforcement replacement rate on the initial bending stiffness of the pipe piles, we introduced the factor η_c, which is defined as the ratio of the bending stiffness of the pile shaft after replacing CFRP reinforcement to that of a fully reinforced pipe pile shaft. During the process of increasing the applied load from 60 kN to 150 kN in the experiment, the micro-disturbance error generated by the displacement meter decreased. Additionally, the magnitude of reduction in the bending stiffness of the pile body diminished as the load increased, and the changes in the bending stiffness of the pile body under various replacement rates (R_c) tended to stabilize. The statistics indicate that the measured average values of pile bending stiffness η_c, corresponding to the replacement rates of CFRP reinforcement R_c at 0%, 25%, 50%, 75%, and 100%, are 1, 0.89825, 0.68243, 0.59609, and 0.37305, respectively. Using the replacement rate of CFRP reinforcement as the horizontal axis and η_c as the vertical axis, a graph was plotted to illustrate the bending stiffness reduction coefficient of the pipe piles with varying CFRP reinforcement replacement rates. A linear fit was also performed, as depicted in Figure 9. As the CFRP reinforcement replacement rate increases, the pile shaft stiffness reduction coefficient decreases in an approximately linear manner. The equation governing the reduction in pile shaft bending stiffness due to the CFRP reinforcement replacement rate is presented as follows:

(6)${\eta }_c=1-0.00622R_c$

where R_c is the replacement rate of the CFRP tendons (%).

A more reliable η_c value can be derived from the fitting equation of linear regression, as presented in Table 2.

3. Prediction of Corrosion Initiation Time

Assuming that there is no chloride present in the reinforced-concrete pipe piles and the chloride diffusion coefficient remains constant, it is further postulated that the hollow composite piles are fully saturated when in a marine environment. Based on Fick’s second law, the diffusion equation governing the movement of chloride ions within the pipe piles is presented as follows [20]:

(7)${\displaystyle \frac{\partial C(r,t)}{\partial t}}={\displaystyle \frac{1}{r}}{\displaystyle \frac{\partial }{\partial r}}\left[r{D}_a{\displaystyle \frac{\partial C(r,t)}{\partial r}}\right]$

where C(r, t) is the chloride ion concentration (%); r is the depth from the concrete surface (m); t is the service time (s); and D_a is the apparent diffusion coefficient (m²/s). D_a is related to environmental temperature, humidity, concrete age, the effective diffusion coefficient, and other factors, and the formula is as follows [21]:

(8)$D_a=D_c\cdot f(T)\cdot f(h)\cdot f(t)$

where D_c is the effective diffusion coefficient (m²/s) affected by the water–cement ratio (w/c); f(T) is the influence function of ambient temperature; f(h) is the influence function of environmental humidity; and f(t) is the influence function of concrete age. These formulas are as follows [22,23,24,25]:

(9)$D_c={10\hspace{0.33em}}^{\left[-0.79{(w/c)}^2+3.40(w/c)-13.10\right]}$

(10)$f(T)=\exp \left[{\displaystyle \frac{U_T}{R}}({\displaystyle \frac{1}{T_{ref}}}-{\displaystyle \frac{1}{T}})\right]$

(11)$f(h)={\left[1+{\displaystyle \frac{{(1-h)}^4}{{(1-h_c)}^4}}\right]}^{-1}$

(12)$f(t)={({\displaystyle \frac{t_{ref}}{t}})}^m$

where U_T represents activation energy (35.0 kJ/mol), R is the gas constant (R = 8.314 J·mol^–1·K^–1), T_ref is the reference temperature (T_ref = 296 K), T is the ambient temperature (K), h is the ambient humidity, h_c is the reference humidity (h_c = 75%), t_ref is the reference time (t_ref = 28 days), and m is the age reduction factor of concrete, where m = 2.5(w/c) − 0.6.

According to the assumption, the chloride ion diffusion equation is expressed as the following equation [21]:

(13)$\left\{\begin{array}{l}C(r,t)=0,\hspace{0.33em}\hspace{0.33em}(t=0,\hspace{0.33em}a<r<b)\\ C_s(a,t)=C_s{t}^k,\hspace{0.33em}\hspace{0.33em}(t>0,\hspace{0.33em}r=a)\\ C_s(b,t)=C_s{t}^k,\hspace{0.33em}\hspace{0.33em}(t>0,\hspace{0.33em}r=b)\end{array}\right.$

where a is the inner radius of the pipe pile, b is the outer radius of the pipe pile, and C_s is the initial chloride concentration. It is assumed that the chloride ion concentration on the surface of the pipe pile exhibits a quasilinear variation with the k-th power of time. The chloride ion diffusion model can be expressed as follows [26]:

(14)$C(r,t)=C_s{t}^k\left[1-{\displaystyle \sum _{n=1}^{\infty }\frac{\mathsf{\pi }{J}_0({\alpha }_{n}a)U_0({\alpha }_{n}r)}{J_0({\alpha }_{n}a)+J_0({\alpha }_{n}b)}{e}^{-{\alpha }_n^2{D}_{a}t}}\right]$

where $U_0({\alpha }_{n}a)=0$ and

(15)$U_0({\alpha }_{n}r)=J_0({\alpha }_{n}r)Y_0({\alpha }_{n}b)-J_0({\alpha }_{n}b)Y_0({\alpha }_{n}r)$

where J₀ is the first kind of zero-order Bessel function and Y₀ is the second kind of zero-order Bessel function. When the chloride ion concentration on the surface of the steel reinforcement attains the threshold level (C(r, t) = C_th), corrosion is imminent, and the corresponding service duration is designated as the initial corrosion time (T_i) of the reinforcement. The corrosion limit state function F(t) is expressed as follows [20]:

(16)$F(t)=C_{th}-C(r, t)$

where C_th is the chloride threshold level. The corrosion probability limit state function is as follows:

(17)$P_f(t)=P\left[F(t)\le 0\right]=P\left[C_{th}\le C(r,t)\right]$

(18)$T_i=\left[P_f(t)\ge P_{f\max }\right]$

where T_i is the initial corrosion time of the reinforcement, P_f (t) is the failure probability function related to corrosion time, and P_fmax is the expected maximum failure probability at the beginning of corrosion.

Prior research has established that a 10% failure probability (P_fmax = 10%) is considered as the anticipated failure probability arising from corrosion in reinforced-concrete structures [27,28]. During the reliability analysis at the onset of corrosion, various random parameters, including the surface chloride concentration (C_s), chloride threshold level (C_th), and apparent diffusion coefficient (D_a), are taken into account. The dimensional parameters of the composite piles are outlined in Table 3. The random parameters for calculating the initial time of corrosion are presented in Table 4, where C_s is expressed as the percentage of surface chloride concentration relative to the weight of cement. The Monte Carlo simulation method was employed to analyze the corrosion initiation time of the CFRP composite piles, using a sampling frequency of 10,000 iterations. The entire calculation process was conducted within the MATLAB R2020a framework. Random numbers were generated for the surface chloride concentration, chloride diffusion coefficient, and chloride threshold concentration, assuming they follow a normal distribution. The surface chloride concentration varies over time, while the chloride diffusion coefficient is influenced by factors such as time, water–cement ratio, ambient temperature, and relative humidity. Notably, increases in humidity, temperature, surface chloride concentration, and water–cement ratio tend to shorten the corrosion initiation time. Conversely, higher chloride threshold levels and thicker concrete cover thicknesses contribute to delaying the corrosion initiation time [21]. As depicted in Figure 10, when the failure probability reaches P_fmax = 10%, it is anticipated that the corrosion initiation time will be approximately 28.15 years. At this juncture, the composite pipe piles will commence the first phase of chloride ion attack: the initial corrosion stage of the steel reinforcement.

4. Prediction of the Attenuation of Pile Shaft Bending Stiffness

4.1. Calculation of Critical Corrosion Depth

There is a porous layer with a thickness of δ₀ between the reinforcement and the concrete. The expansion stress (p_r) exerted on the concrete protective layer arises from the corrosion products of the reinforcement once they fill the porous layer. The stress gradually intensifies as the amount of rust products accumulates. When the p_r exceeds the tensile strength of the concrete protective layer, rust-induced expansion cracks emerge on the surface of the concrete protective layer of the CFRP composite pipe piles. The displacement of the concrete protective layer caused by the corrosion products is outlined as follows [30]:

(19)${\delta }_c={\displaystyle \frac{r_0}{E_{ef}}}\left[{\displaystyle \frac{{(r_0+c)}^2+{r_0}^2}{{(r_0+c)}^2-{r_0}^2}}+v_c\right]p_r$

where δ_c is the movement of the concrete covering layer, c is the thickness of the concrete cover, r₀ = d₀/2 + δ₀, d₀ is the initial diameter of the reinforcement, v_c is Poisson’s ratio, E_ef is the effective elastic modulus of the pipe pile, E_ef = E_c/(1 + ϕ_c), ϕ_c is the creep coefficient, and E_c is the elastic modulus of the concrete. The expression for the increment in corrosion products in steel reinforcement is as follows [20]:

(20)${\displaystyle \frac{M_r}{{\rho }_r}}-{\displaystyle \frac{M_{loss}}{{\rho }_s}}\approx \mathsf{\pi }{d}_0({\delta }_0+{\delta }_c)$

where M_r is the quality of the corrosion products, ρ_r is the density of the steel corrosion products, M_loss is the quality of the corroded reinforcement, and ρ_s is the density of the reinforcement. The expansion stress generated by the corrosion products is outlined as follows:

(21)$p_r={\displaystyle \frac{E_{ef}}{\gamma +1+v_c}}\left[{\displaystyle \frac{M_{loss}}{{\rho }_s}}\cdot {\displaystyle \frac{a_v-1}{\mathsf{\pi }{d}_0{r}_0}}-{\displaystyle \frac{{\delta }_0}{r_0}}\right]$

where a_v is the volume expansion rate of the reinforcement due to corrosion, γ = 2r₀²/[c(2r₀ + c)]. When the expansion stress generated by the corrosion products attains the critical threshold (p_cr), the concrete protective layer experiences cracking [31]:

(22)$p_{cr}=2c{f}_{ct}/d_0$

where f_ct is the tensile strength of the concrete. The critical corrosion depth x_cr of steel bars in the event of pile cracking is outlined as follows:

(23)$x_{cr}={\displaystyle \frac{M_{loss}}{\pi {\rho }_s{d}_0}}={\displaystyle \frac{r_0}{{\alpha }_v-1}}\left[{\displaystyle \frac{2c\left(\gamma +1+{\upsilon }_c\right)}{d_0}}{\displaystyle \frac{f_{ct}}{E_{ef}}}+{\displaystyle \frac{{\delta }_0}{r_0}}\right]$

The parameters pertaining to the calculation of the critical corrosion depth of the reinforcement are comprehensively outlined in Table 5. When the corrosion depth of the steel reinforcement attains 16.2 μm (x_cr = 16.2 μm), the radial expansion stress p_r generated by the corrosion products exceeds the tensile strength of the concrete protective layer surrounding the pipe pile, ultimately leading to the cracking of the concrete protective layer on the pile shaft.

4.2. Calculation of Reinforcement Corrosion Depth

The corrosion of the steel bars serves as a significant factor influencing the long-term lateral load-bearing capacity of the reinforced-concrete pipe piles in marine environments. The rate of steel consumption is intricately linked to the amount of electric current passing through the electrochemical corrosion tank. Faraday’s law offers a reliable means to estimate the extent of steel corrosion. The cross-sectional area of the steel bars diminishes due to the erosion caused by chloride ions in marine environments. The corrosion-induced mass loss in the steel reinforcement adheres to the following equation [20]:

(24)${\displaystyle \frac{d{M}_{loss}}{dt}}={\displaystyle \frac{I_{corr}M}{nF}}$

where t is the corrosion time (s), M is the atomic weight of the iron ions (M = 55.85 g/mol), I_corr is the corrosion current (A), F is the Faraday constant, and n is the valence (n = 2.5). The equation for the corrosion current of the reinforcement per unit length is as follows [20]:

(25)$I_{corr}=\mathsf{\pi }{d}_0{i}_{corr}(t)$

where i_corr is the corrosion rate (μA/cm²). The corrosion current density diminishes over time due to the formation of corrosion products on the steel surface, which impede the diffusion of chloride ions. The corrosion rate model is presented as follows [32]:

(26)$i_{corr}(t)=0.85i_{corr,0}{(t-T_i)}^{-0.29},\hspace{0.33em}t>T_i$

(27)$i_{corr,0}={\displaystyle \frac{37.5{(1-w/c)}^{-1.64}}{c}}$

By integrating the aforementioned formula, the corrosion depth of the reinforcement can be accurately determined:

(28)$M_{loss}={\displaystyle {\int }_{T_i}^t\frac{\mathsf{\pi }{d}_0{i}_{corr}(t)M}{nF}}dt$

(29)$x_i={\displaystyle \frac{M_{loss}}{\mathsf{\pi }{\rho }_s{d}_0}}={\displaystyle \frac{M}{{\rho }_{s}nF}}{\displaystyle {\int }_{T_i}^t{i}_{corr}(t)dt}$

where x_i represents the corrosion depth of the i-th reinforcement (mm). The parameters for calculating the corrosion depth are shown in Table 6. Additionally, a graphical representation of the corrosion depth of a single steel bar varying with corrosion time is depicted in Figure 11. When the corrosion duration exceeds 28.15 years, the corrosion depth exhibits a nonlinear increase with the extension of exposure time. In chloride-induced corrosive environments, CFRP bars demonstrate greater stability in terms of their elastic modulus and tensile strength compared to steel bars [33].

4.3. Attenuation Pattern of Stiffness in CFRP Composite Piles

The introduction of the bending stiffness reduction factor (η) aims to represent the attenuation of the pile shaft’s bending stiffness over time, resulting from reinforcement corrosion caused by chloride ion erosion [20].

(30)$E_p{I}_p=\eta EI$

where E_pI_p is the time-varying stiffness of the pipe pile, EI is the initial stiffness of the pipe pile, η is the reduction factor of pile stiffness caused by reinforcement corrosion, and the formula is as follows [34]:

(31)$\eta ={\displaystyle \frac{1}{A}}\Sigma A_i{\eta }_i$

(32)$A_i=\pi {(d_0/2-x_i)}^2$

where A is the sectional area of longitudinal reinforcement, and A_i is the sectional area of the i-th longitudinal bar. The formula for η_i [34] is as follows:

(33)${\eta }_i=\left\{\begin{array}{cc}1.0& 0\le x_i<0.1\\ \left(3.7-7x_i\right)/3& 0.1\le x_i<0.25\\ 0.65& x_i\ge 0.25\end{array}\right.$

Given the reduction in bending stiffness of the pile body resulting from the substitution of the CFRP tendons for steel reinforcement, the coefficient η_c is introduced to quantify the extent of the reduction in the bending stiffness of the CFRP pipe pile.

(34)$EI={\eta }_c{E}_c{I}_0$

In the equation, η_c represents the bending stiffness reduction factor of the composite pile resulting from the CFRP reinforcement replacement rate, as detailed in Table 2. E_c is the elastic modulus of concrete, I₀ is the moment of inertia, and the expression is as follows:

(35)$I_0={\displaystyle \frac{\mathsf{\pi }}{4}}(b^4-a^4)$

The specific layout of the CFRP tendons is depicted in Figure 12. The reduction coefficient attenuation of the stiffness of the pipe piles is shown in Figure 13. The bending stiffness of the pipe piles remains unaffected when the corrosion duration is shorter than 28.15 years. When the corrosion duration ranges from 28.15 years to 38.0 years, the bending stiffness reduction coefficient of the pipe piles decreases gradually at a slow rate. However, between 38.0 and 66.0 years, η experiences a sharp decline. The stress generated by the corrosion products of the steel bars within the pipe piles exceeds the tensile strength of the concrete protective layer, resulting in cracking of the layer. This cracking subsequently accelerates the diffusion rate of chloride ions and exacerbates the corrosion of the steel bars. As the degree of reinforcement corrosion intensifies, its impact on the attenuation of pile stiffness becomes increasingly pronounced. Subsequently, as the corrosion depth of the steel bars increases, corrosion products accumulate on their surface, thereby decelerating the rate of steel corrosion development and slowing down the decline in the reduction coefficient η.

The diminishing trend of the bending stiffness of the CFRP pipe piles is clearly depicted in Figure 14. Notably, under identical exposure conditions, the pile bending stiffness reduction coefficient exhibits a comparable attenuation trend. The bending stiffness of the fully steel pipe pile decays more rapidly compared to that of the CFRP composite pipe piles. This suggests that when the pile bodies are exposed to a corrosive environment, a higher ratio of CFRP reinforcement replacing steel reinforcement results in a slower rate of stiffness degradation. Under identical exposure conditions, the corrosion initiation period (T_i) for the pipe piles with varying CFRP reinforcement replacement rates remains consistent at 28.15 years. The bending stiffness of the pipe piles remains consistent prior to the initiation of reinforcement corrosion, provided that the corrosion duration is less than 28.15 years. However, once the exposure time surpasses the initial corrosion period, the degradation coefficient of the piles’ bending stiffness exhibits a nonlinear decrease as the exposure time increases. When the exposure time ranges from 0 to 28.15 years, the initial bending stiffness of the composite piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, 75%, and 100% in the pile body is 172,400 kN·m², 145,678 kN·m², 118,784 kN·m², 80,511 kN·m², and 65,167 kN·m², respectively. Evidently, as the replacement rate of CFRP reinforcement increases, the initial stiffness of the composite piles diminishes. After a corrosion period of 28.15 years, the stiffness of the pipe piles with CFRP reinforcement ratios ranging from 0 to 75% began to deteriorate. When the exposure duration surpasses 38.0 years, the bending stiffness of the pipe piles with CFRP reinforcement ratios of 0%, 25%, 50%, and 75% experiences a rapid and varying degree of decrease. In the 66th year, the flexural stiffness of the pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, 75%, and 100% decreases by 40.9%, 30.68%, 20.45%, 15.08%, and 0%, respectively, compared to their respective initial stiffnesses. After 66 years of exposure, the decay rate of the stiffness of the pipe piles begins to slow down. After 75.5 years, the flexural stiffness of the composite pile with a 25% replacement rate of CFRP reinforcement and the fully reinforced pipe pile decreases to 99,415 kN·m². Similarly, after 131.0 years, the stiffness of both the fully reinforced pipe pile and the composite pile with a 50% replacement rate of CFRP reinforcement diminishes to 9591 kN·m². Subsequently, the durability advantage of the CFRP pipe pile becomes evident, as the stiffness of the pipe piles with 25% and 50% replacement rates of CFRP reinforcement surpasses that of the fully reinforced pipe pile after 75.5 years and 131.0 years, respectively. Between 28.15 and 150 years, it can be observed that as the proportion of the CFRP tendons replacing the steel reinforcement increases, the rate of decay in the bending stiffness of the piles decreases. After 150 years of exposure, the bending stiffness of the composite pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, 75%, and 100% are 88,001 kN·m², 92,190 kN·m², 89,708 kN·m², 70,657 kN·m², and 65,167 kN·m², respectively.

5. Horizontal Bearing Capacity of CFRP Pipe Piles

The deflection control equation for laterally loaded piles is as follows [35]:

(36)$E_p{I}_p{\displaystyle \frac{d^{4}y}{d{z}^4}}+k_{h}Dy=0$

In the equation, E_pI_p is the time-varying stiffness, y is the lateral displacement, z is the depth from the pile top, D is the outer diameter of the cross-section of the pipe pile, and k_h is the foundation reaction coefficient, which is expressed as follows [35]:

(37)$k_h={\displaystyle \frac{0.65}{D}}\sqrt[12]{{\displaystyle \frac{E_s{D}^4}{E_p{I}_p}}}({\displaystyle \frac{E_s}{1-v_s^2}})$

where E_s is the elastic modulus of soil, ν_s is Poisson’s ratio of soil. The pipe pile is divided into n equal segments, and the finite difference expression is as follows:

(38)$E_p{I}_p\left[{\displaystyle \frac{y_{i-2}-4y_{i-1}+6y_i-4y_{i+1}+y_{i+2}}{d{h}^4}}\right]+k_{hi}D{y}_i=0$

(39)$y_{i-2}-4y_{i-1}+a_i{y}_i-4y_{i+1}+y_{i+2}=0$

where

(40)$a_i=6+{\displaystyle \frac{k_{hi}{L}^{4}D}{E_p{I}_p{n}^4}}$

where k_hi is the subgrade reaction coefficient, dh is the difference in step size, (dh = L/n), L is the length of the pipe pile, H is the horizontal load at the top of the pile, M is the bending moment at the pile top, and N is the axial load at the pile top. The expressions for the lateral displacement and bending moment of the pile shaft are outlined as follows [35]:

(41)$E_p{I}_p({\displaystyle \frac{d^{3}y}{d{z}^3}})=H$

(42)$-y_{-2}+2y_{-1}-2y_2+y_3={\displaystyle \frac{H{L}^3}{E_p{I}_p{n}^3}}$

(43)$E_p{I}_p({\displaystyle \frac{d^{2}y}{d{z}^2}})=M$

(44)$y_2-2y_1+y_{-1}={\displaystyle \frac{M{L}^2}{E_p{I}_p{n}^2}}$

Assuming that both the bending moment and shear force at the pile tip are zero, the following expression can be derived:

(45)$-y_{n-1}+2y_n-2y_{n+2}+y_{n+3}=0$

(46)$y_n-2y_{n+1}+y_{n+2}=0$

By utilizing the aforementioned equation, a matrix equation is established. Subsequently, finite difference processing is conducted using MATLAB R2020a to derive the distribution of bending moments and lateral displacements in horizontally loaded piles of arbitrary depth. The calculation parameters for the horizontal bearing capacity of CFRP pipe piles are shown in Table 7.

The lateral displacement of the CFRP pipe pile shafts after a corrosion duration of 30 years is depicted in Figure 15a. The horizontal displacements at the pile top of the composite piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, 75%, and 100% are measured as 72.95 mm, 78.49 mm, 86.24 mm, 105.411 mm, and 119.08 mm, respectively. When the CFRP reinforcement replacement rates are set at 0%, 25%, 50%, 75%, and 100%, the first displacement zero points of the respective composite piles occur at depths of 4.5 m, 4.1 m, 3.9 m, 3.3 m, and 3.1 m, whereas the second displacement zero points are located at depths of 15.9 m, 15.3 m, 14.5 m, 12.7 m, and 11.7 m, respectively. It is observed that as the replacement rate of the CFRP tendons increases, the horizontal displacement at the pile top also increases, with both the first and second horizontal displacement zero points exhibiting an upward trend towards the pile top. This trend can be attributed to the fact that the elastic modulus of the CFRP tendons is lower than that of the steel reinforcement. Consequently, a higher replacement rate of the CFRP tendons results in a more significant reduction in the initial stiffness of the composite pile.

The lateral displacement of the CFRP pipe pile shaft after a corrosion duration of 90 years is depicted in Figure 15b. After a corrosion duration of 90 years, the horizontal displacement at the pile tops of the composite pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, and 75% is measured to be 95.26 mm, 94.78 mm, 97.44 mm, 112.46 mm, and 119.08 mm, respectively. When compared to a service duration of 30 years, the pile top displacement of the composite pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, and 75% increases by 30.58%, 20.75%, 12.99%, and 6.69%, respectively. It is observed that as the replacement rate of CFRP reinforcement increases, the horizontal displacement increment at the top of the pipe pile decreases. After 90 years of service, the horizontal displacement at the top of the fully reinforced concrete pipe pile surpasses that of the composite pipe pile with a 25% CFRP reinforcement replacement rate. When the replacement rates of CFRP reinforcement are set at 0%, 25%, 50%, 75%, and 100%, the first displacement zero points of the respective composite piles occur at depths of 3.7 m, 3.7 m, 3.5 m, 3.3 m, and 3.1 m, whereas the second displacement zero points are located at depths of 13.5 m, 13.5 m, 13.4 m, 12.1 m, and 11.7 m, respectively. When compared to a service duration of 30 years, the composite pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, and 75% exhibit a tendency for both the first and second displacement zero points to shift towards the pile top. After 90 years of service, the horizontal displacement of the fully reinforced pipe pile surpasses that of the composite pile with a 25% CFRP reinforcement replacement rate. Both the composite pile and the fully reinforced pipe pile exhibit their first and second displacement zeros at the same depth from the pile top. Chloride ion erosion causes corrosion in the reinforcement, leading to a reduction in the bending stiffness of the composite pile. However, a higher replacement rate of CFRP reinforcement results in a slower attenuation of pile stiffness, effectively enhancing the durability of the composite pile.

After a corrosion duration of 150 years, the lateral displacement of the CFRP pipe pile is depicted in Figure 15c. After a corrosion duration of 150 years, the horizontal displacement at the pile top is observed to be 100.22 mm, 97.76 mm, 99.19 mm, 113.43 mm, and 119.08 mm, respectively, corresponding to the replacement rates of 0%, 25%, 50%, 75%, and 100% for CFRP reinforcement in the composite pipe piles. When compared to a service duration of 30 years, the pile top displacement of composite pipe piles exhibits increases of 37.38%, 24.55%, 15.02%, and 7.61%, respectively, corresponding to CFRP reinforcement replacement rates of 0%, 25%, 50%, and 75%. Evidently, as the replacement rate of CFRP reinforcement increases, the horizontal displacement increment at the top of the pipe piles diminishes. When the replacement rates of CFRP reinforcement are set at 0%, 25%, 50%, 75%, and 100%, the first displacement zero points of the respective composite piles occur at depths of 3.5 m, 3.5 m, 3.5 m, 3.3 m, and 3.1 m, respectively. Similarly, the second displacement zero points of these piles are located at depths of 13.1 m, 13.3 m, 13.1 m, 12.1 m, and 11.7 m, respectively. After 150 years of service, the horizontal displacement of the fully reinforced pipe pile surpasses that of the composite piles with CFRP reinforcement replacement rates of 25% and 50%. Notably, the composite pile with a 50% CFRP reinforcement replacement rate exhibits its first and second displacement zero points at the exact same depth from the pile top as the fully reinforced pipe pile.

In conclusion, the lateral displacement at the top of all CFRP pipe piles exhibits a gradual increase as the corrosion time elongates. For instance, when the substitution rate of CFRP reinforcement reaches 50%, the lateral displacement of the pile shaft at the pile top experiences growth from 86.24 mm to 99.19 mm within a span of 30 to 150 years. This is attributed to the severe erosion of the pile body by chloride ions as the exposure time elongates, leading to a decrease in the bending stiffness of the pile and, consequently, an augmentation in the lateral displacement of the pile top. During the same period of service, as the replacement rate of CFRP reinforcement increases, the horizontal displacement increment at the top of the pipe pile decreases. After 90 years of service, the horizontal displacement of the fully reinforced pipe pile surpasses that of the composite pile with a 25% CFRP reinforcement replacement rate. Similarly, after 150 years of service, the fully reinforced pipe pile demonstrates a greater horizontal displacement than the composite pile with a 50% CFRP reinforcement replacement rate. The corrosion resistance of the CFRP tendons is increasingly evident in mitigating the attenuation of pile stiffness.

After a corrosion duration of 30 years, the bending moment of the CFRP pipe pile is depicted in Figure 16a. After 30 years of exposure, the maximum bending moment of the pipe piles with CFRP reinforcement rates of 0%, 25%, 50%, 75%, and 100% at a depth of 1.8 to 2.2 m is 746.63 kN·m, 752.78 kN·m, 762.97 kN·m, 798.67 kN·m, and 828.86 kN·m, respectively. The maximum negative bending moments of the composite piles with CFRP reinforcement rates of 0%, 25%, 50%, 75%, and 100% are 38.98 kN·m, 45.64 kN·m, 51.82 kN·m, 60.50 kN·m, and 65.81 kN·m, respectively. The depths of bending moment zero for the composite pipe piles with CFRP reinforcement rates of 0%, 25%, 50%, 75%, and 100% are 10.9 m, 10.3 m, 9.7 m, 8.7 m, and 8.1 m, respectively. Over a period of 30 years, as the replacement rate of the CFRP tendons increases, both the maximum bending moment and the maximum negative bending moment of the pile shaft tend to rise. Over a period of 30 years, as the replacement rate of the CFRP tendons increases, both the maximum bending moment and the maximum negative bending moment of the pile shaft also increase. Additionally, the locations of the maximum bending moment, negative bending moment, and bending moment zero point become increasingly closer to the pile top position.

The bending moment of the CFRP pipe piles after a corrosion duration of 90 years is depicted in Figure 16b. After 90 years of exposure, the maximum bending moments of the composite piles with CFRP reinforcement rates of 0%, 25%, 50%, 75%, and 100% at depths ranging from 1.8 to 2.2 m are recorded as 778.84 kN·m, 777.94 kN·m, 782.95 kN·m, 813.41 kN·m, and 828.86 kN·m, respectively. The maximum negative bending moments of the pipe piles, with CFRP reinforcement rates varying from 0% to 100% in increments of 25%, are as follows: 56.47 kN·m, 56.27 kN·m, 57.42 kN·m, 63.17 kN·m, and 65.81 kN·m, respectively. The depths of the bending moment zeros for the composite pipe piles with CFRP reinforcement replacement rates of 0%, 25%, 50%, 75%, and 100% are 9.1 m, 9.1 m, 9.1 m, 8.3 m, and 8.1 m, respectively. It can be observed that as the duration of service increases, both the maximum bending moment and the maximum negative bending moment of each composite pile undergo varying degrees of augmentation. With the increasing replacement rate of CFRP reinforcement, the growth rate of both the maximum bending moment and the maximum negative bending moment in the pile body diminish. After 90 years of service, the maximum bending moment and maximum negative bending moment of the fully reinforced pipe pile surpass those of the composite pile with a 25% replacement rate of CFRP reinforcement. Notably, the zero-bending moment positions of the composite piles with 25% and 50% CFRP reinforcement replacement rates remain identical to those of the fully reinforced pipe piles.

The bending moment of the CFRP pipe piles after a corrosion duration of 150 years is depicted in Figure 16c. After 150 years of exposure, the maximum bending moments of the composite piles with CFRP reinforcement rates varying from 0% to 100% (in increments of 25%) are recorded at depths ranging from 1.8 to 2.0 m, specifically, 788.31 kN·m, 783.56 kN·m, 786.31 kN·m, 815.54 kN·m, and 828.86 kN·m, respectively. The maximum negative bending moments of the pipe piles, with CFRP reinforcement rates varying from 0% to 100% in increments of 25%, are as follows: 58.54 kN·m, 57.53 kN·m, 58.13 kN·m, 63.55 kN·m, and 65.81 kN·m, respectively. The depths of the bending moment zeros for the pipe piles with CFRP reinforcement rates of 0%, 25%, 50%, 75%, and 100% are 8.9 m, 9.1 m, 8.9 m, 8.3 m, and 8.1 m, respectively. It can be observed that with the continued increase in service time, the maximum bending moment and maximum negative bending moment of each composite pile undergo varying degrees of augmentation. Furthermore, as the replacement rate of CFRP reinforcement rises, the growth in both the maximum bending moment and maximum negative bending moment of the pile body diminishes significantly. After 150 years, the maximum bending moment and maximum negative bending moment of the fully reinforced pipe pile surpass those of the composite piles with 25% and 50% CFRP reinforcement rates. Additionally, the bending moment zero point of the fully reinforced pipe pile is situated closer to the pile top’s position compared to the composite pipe pile with a 25% CFRP reinforcement rate.

In conclusion, both the maximum bending moment and the maximum negative bending moment of the pile, which incorporates various CFRP reinforcement replacement rates, exhibit a gradual increase as the corrosion time elongates. With the increasing replacement rate of CFRP reinforcement, the growth rate of both the maximum bending moment and the maximum negative bending moment in the pile body gradually diminishes. After 90 years of service, the maximum bending moment and maximum negative bending moment of the fully reinforced pipe pile surpass those of the composite pile with a 25% CFRP reinforcement replacement rate. Similarly, after 150 years of service, the maximum bending moment and maximum negative bending moment of the fully reinforced pipe pile have exceeded those of the composite pile with a 50% CFRP reinforcement replacement rate. This is attributed to the fact that substituting steel bars with CFRP bars can mitigate the adverse effects of pile stiffness degradation caused by steel corrosion.

6. Conclusions

This article focuses on CFRP composite pipe piles as the subject of investigation, exploring the impact of substituting steel bars with CFRP bars on the bending performance of pipe piles through rigorous three-point bending tests. The attenuation of flexural stiffness in CFRP pipe piles under a chloride salt environment has been anticipated. By introducing a stiffness degradation coefficient for piles and utilizing the finite difference method, the lateral bearing capacity of CFRP pipe piles has been calculated, leading to the following conclusions:

• (1). Under the same load conditions, the deflection and crack distribution range of composite pipe piles tends to increase with the increasing replacement rate of CFRP reinforcement. The initial bending stiffness of the composite pipe pile decreases as the replacement rate of the CFRP tendons increases.

• (2). After serving in a marine environment for 28.15 years, the stiffness of composite piles exhibits nonlinear attenuation. The rate of attenuation of flexural stiffness in composite piles decreases as the CFRP ratio increases.

• (3). When the service time exceeds the initial corrosion time, the horizontal bearing capacity of the pipe pile diminishes as stiffness decreases, primarily manifesting as a gradual increase in the horizontal displacement and bending moment of the pile body. It can be observed that as the CFRP reinforcement ratio increases, the horizontal bearing capacity of the pipe pile decreases at a slower rate. After 150 years, the traditional reinforced-concrete pipe pile, which originally exhibited excellent horizontal bearing performance, is surpassed by the pipe piles with CFRP reinforcement rates of 25% and 50%.

• (4). This test did not investigate the load-bearing capacity of CFRP pipe piles after exposure to chloride ion corrosion. We recommend simulating the deterioration of CFRP pipe piles in harsh marine environments using electrochemical corrosion.

Author Contributions

Conceptualization, W.Z. and W.S.; data curation, W.Z.; formal analysis, W.Z.; investigation, W.Z.; funding acquisition, W.S.; methodology, W.Z. and W.S.; resources, W.S.; software, W.Z.; supervision, W.Z. and W.S.; validation, Y.N. and W.S.; visualization, W.Z.; writing—original draft, W.Z.; review and editing, W.Z. and Y.N. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Design schematic of the test piles. (Positions A and D are simple support points, while the area from B to C represents the load-bearing range.)

Figure 2. Completed reinforced cage with binding.

Figure 3. Completed test pipe piles after curing.

Figure 4. Compressive strength testing of the concrete specimens.

Figure 5. Loading procedure for the test pipe piles.

Figure 6. Cracking and failure of a CFRP composite pipe pile.

Figure 7. Load–displacement curve of the test piles.

Figure 8. Rigidity–load curves of the test pipe piles.

Figure 9. Fitting chart of stiffness reduction coefficient for pipe pile shafts with varying CFRP reinforcement substitution rates.

Figure 10. Failure probability of corrosion initiation time of the CFRP composite piles.

Figure 11. Corrosion depth of the reinforcement per unit length.

Figure 12. Positions of the steel reinforcement and CFRP reinforcement within the pipe piles.

Figure 13. Reduction coefficient attenuation of bending stiffness of the pipe piles.

Figure 14. Bending stiffness attenuation of the pipe piles.

Figure 15. Lateral displacement of the CFRP pipe piles under different corrosion times: (a) t = 30 years; (b) t = 90 years; (c) t = 150 years.

Figure 16. Bending moment of the CFRP pipe piles under different corrosion times. (a) t = 30 years; (b) t = 90 years; (c) t = 150 years.

Table 1

Concrete mixture proportions for the piles.

Materials	w/c	Cement	Fine Aggregate	Coarse Aggregate	Water	Water-Reducing Agent
Mixture proportions	0.35	457 kg/m3	720 kg/m3	1060 kg/m3	160 kg/m3	1.6 kg/m3

Table 2

Results of the bending test.

ReplacementRatio(%)	UltimateLoad(kN)	Deflection(mm)	BendingStiffness(kN·m2)	ReductionFactor(ηc)
0%	150	3.61	2.09 × 103	1
25%	145	3.57	1.61 × 103	0.845
50%	140	4.27	1.28 × 103	0.689
75%	135	4.53	9.27 × 102	0.467
100%	130	6.40	4.90 × 102	0.378

Table 3

Dimensional parameters of the composite piles.

Variables	Unit	Value	Description
a	mm	190	Internal radius of composite pile
b	mm	300	Outer radius of composite pile
d 0	mm	10	Diameter of steel and CFRP bars
c	mm	45	Thickness of concrete cover

Table 4

Random variables used to predict the corrosion initiation time.

Variables	Cs (%)			Da (m2/s)								Cth (%)
Distribution	Normal			Normal								Normal
Parameters	Cs	t	k	m	w/c	tref	T 1	T 2	t	hc	h	0.2 [21]
	%	year	-	-	-	day	K	K	year	%	%
μ (Mean)	0.5 [21]	-	0.37 [29]	0.2	0.35	28	296 [21]	300.15 [21]	-	75 [21]	85
σ (Variance)	0.05			0.985 × 10–13								0.02

Table 5

Parameters for determining the critical corrosion depth.

Variables	Unit	Value	Description
vc	-	0.2	Poisson’s ratio of concrete cover
δ 0	μm	12.5	Thickness of porous interface area
Ec	MPa	38,000	Modulus of elasticity for concrete
ϕc	-	2	Creep coefficient of concrete
av	-	3	Volume expansion rate of corrosion products
fct	N/mm2	2.22	Tensile strength of concrete cover

Table 6

Parameters for determining the corrosion depth of the steel reinforcement.

Variables	Unit	Value	Description
Ti	year	28.15	Corrosion initiation time
ρs	g/cm3	7.85	Steel bar density
Ms	g/mol	55.85	Quality of iron atoms
n	-	2.5	Homogenized valence of iron ions
F	C/mol	96,500	Faraday constant

Table 7

Calculation parameters of horizontal bearing capacity of CFRP pipe piles.

Variables	Unit	Value	Meaning
L	m	20	Length of composite pile
n	-	100	Number of elements
vs	-	0.3	Poisson’s ratio of soil
Es	kN/m2	6000 [36]	Elastic modulus of soil
H	kN	200	Horizontal load at pile top
M	kN·m	400	Bending moment at pile top
N	kN	6000	Vertical load at pile top

References

1. Shao, W.; Shi, D.D.; Jiang, J.P.; Chen, Y.L. Time-dependent lateral bearing behaviour of corrosion-damaged RC pipe piles in marine environments. Constr. Build. Mater.; 2017; 157, pp. 676-684. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2017.09.134]

2. Meniconi, S.; Brunone, B.; Tirello, L.; Rubin, A.; Cifrodelli, M.; Capponi, C. Transient tests for checking the Trieste subsea pipeline: Towards the field tests. J. Mar. Sci. Eng.; 2024; 12, 374. [DOI: https://dx.doi.org/10.3390/jmse12030374]

3. Ateş, B.; Şadoğlu, E. Experimental Investigation of Optimum Piles Spacing for Piled Raft Foundation in Sandy Soils. Tech. J.; 2021; 32, pp. 10477-10494.

4. Lu, C.H.; Jin, W.L.; Liu, R.G. Reinforcement corrosion-induced cover cracking and its time prediction for reinforced concrete structures. Corros. Sci.; 2011; 53, pp. 1337-1347.

5. Sen, R.; Mullins, G. Application of FRP composites for underwater piles repair. Compos. Part B.; 2007; 38, pp. 751-758. [DOI: https://dx.doi.org/10.1016/j.compositesb.2006.07.011]

6. Iskander, M.G.; Hassan, M. State of the practice review in FRP composite piling. J. Compos. Constr.; 1998; 2, pp. 116-120.

7. Liang, J.F.; Lin, S.Q.; Li, W.; Liu, D.W. Axial compressive behavior of recycled aggregate concrete-filled square steel tube stub columns strengthened by CFRP. Structures; 2021; 29, pp. 1874-1881. [DOI: https://dx.doi.org/10.1016/j.istruc.2020.12.084]

8. Waleed, A.J.; Yazan BA, T.; Abdulsamee, M.H. Behavior of reinforced concrete deep beam with web openings strengthened with (CFRP) sheet. Structures; 2020; 26, pp. 785-800.

9. Emine, A.; Elif, B.; Ferhat, A. Effects of FRP bar type and fiber reinforced concrete on the flexural behavior of hybrid beams. Constr. Build. Mater.; 2021; 279, 122407.

10. Job, T.; Ramadass, S. Improved empirical model for the strut efficiency factor and the stiffness degradation coefficient for the strength and the deflection prediction of FRPRC deep beam. Structures; 2021; 29, pp. 2044-2066.

11. Ahmed, H.A.; Hamdy, M.M.; Omar, C.; Brahim, B.; Faouzi, G. Shear resistance of RC circular members with FRP discrete hoops versus spirals. Eng. Struct.; 2018; 174, pp. 688-700.

12. Giraldo, J.; Rayhani, M.T. Load transfer of hollow Fiber-Reinforced Polymer (FRP) piles in soft clay. Transp. Geotech.; 2014; 1, pp. 63-73. [DOI: https://dx.doi.org/10.1016/j.trgeo.2014.03.002]

13. Zyka, K.; Mohajerani, A. Composite piles: A review. Constr. Build. Mater.; 2016; 107, pp. 394-410. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2016.01.013]

14. Valez, J.G.; Rayhani, M.T. Axial and lateral load transfer of fibre-reinforced polymer (FRP) piles in soft clay. Int. J. Geotech. Eng.; 2017; 11, pp. 149-155.

15. Zhuang, N.; Zhou, Y.J.; Ma, Y.M.; Liao, Y.D.; Chen, D. Corrosion Activity on CFRP-Strengthened RC Piles of High-Pile Wharf in a Simulated Marine Environment. Adv. Mater. Sci. Eng.; 2017; 9, 7185452. [DOI: https://dx.doi.org/10.1155/2017/7185452]

16. Alajarmeha, O.; Manaloa, A. Behavior of circular concrete columns reinforced with hollow composite sections and GFRP bars. Mar. Struct.; 2020; 72, 102785. [DOI: https://dx.doi.org/10.1016/j.marstruc.2020.102785]

17. Dong, H.H.; Zhou, Y.J.; Zhuang, N. Study on Corrosion Characteristics of Concrete-Filled CFRP-Steel Tube Piles under Hygrothermal Environment. Adv. Mater. Sci. Eng.; 2020; 11, 4849038. [DOI: https://dx.doi.org/10.1155/2020/4849038]

18. Shao, W.; Qin, F.L.; Shi, D.D.; Mukhtiar, A.S. Horizontal bearing characteristic and seismic fragility analysis of CFRP composite pipe piles subject to chloride corrosion. Comput. Geotech.; 2024; 166, 105977. [DOI: https://dx.doi.org/10.1016/j.compgeo.2023.105977]

19. GB50010-2010 Code for Design of Concrete Structures; China Architecture & Building Press: Beijing, China, 2015.

20. Shao, W.; Zhang, W.; Shi, D.D.; Xu, Y.Z.; Liu, E.L. Time-varying characteristics of the durability and lateral bearing behaviour of FRP bar-reinforced concrete piles in marine environments. Constr. Build. Mater.; 2021; 302, 124192. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2021.124192]

21. Shao, W.; Nie, Y.H.; Liang, F.Y.; Shi, D.D. A novel comprehensive evaluation method for the corrosion initiation life of RC hollow piles in chloride environments. Constr. Build. Mater.; 2020; 249, 118801. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2020.118801]

22. Maeda, S.; Takewaka, K.; Yamaguchi, T. Quantification of chloride diffusion process into concrete under marine environment by analysis of salt damage data base. Jpn. Soc. Civ. Eng.; 2004; 63, pp. 109-120. [DOI: https://dx.doi.org/10.2208/jscej.2004.760_109] [PubMed: https://www.ncbi.nlm.nih.gov/pubmed/39385234]

23. Stambaugh, N.D.; Bergman, T.L.; Srubar, W.V. Numerical service-life modeling of chloride-induced corrosion in recycled-aggregate concrete. Constr. Build. Mater.; 2018; 161, pp. 236-245. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2017.11.084]

24. Mangat, P.S.; Molloy, B.T. Prediction of long term chloride concentration in concrete. Mater. Struct.; 1994; 27, pp. 338-346. [DOI: https://dx.doi.org/10.1007/BF02473426]

25. Chauhan, A.; Sharma, U.K. Influence of temperature and relative humidity variations on non-uniform corrosion of reinforced concrete. Structures; 2019; 19, pp. 296-308. [DOI: https://dx.doi.org/10.1016/j.istruc.2019.01.016]

26. Shao, W.; Shi, D.D.; Tang, P. Probabilistic lifetime assessment of RC pipe piles subjected to chloride environments. J. Mater. Civ. Eng.; 2018; 30, 04018297. [DOI: https://dx.doi.org/10.1061/(ASCE)MT.1943-5533.0002512]

27. Kwon, S.J.; Na, U.J.; Park, S.S.; Jung, S.H. Service life prediction of concrete wharves with early-aged crack: Probabilistic approach for chloride diffusion. Struct. Saf.; 2009; 31, pp. 75-83. [DOI: https://dx.doi.org/10.1016/j.strusafe.2008.03.004]

28. Lu, Z.H.; Zhao, Y.G.; Yu, Z.W.; Ding, F.X. Probabilistic evaluation of initiation time in RC bridge beams with load-induced cracks exposed to de-icing salts. Cem. Concr. Res.; 2011; 41, pp. 365-372. [DOI: https://dx.doi.org/10.1016/j.cemconres.2010.12.003]

29. Costa, A.; Appleton, J. Chloride penetration into concrete in marine environment-Part II: Prediction of long term chloride penetration. Mater. Struct.; 1999; 32, pp. 354-359. [DOI: https://dx.doi.org/10.1007/BF02479627]

30. El Maaddawy, T.; Soudki, K. A model for prediction of time from corrosion initiation to corrosion cracking. Cem. Concr. Compos.; 2007; 29, pp. 168-175. [DOI: https://dx.doi.org/10.1016/j.cemconcomp.2006.11.004]

31. Papakonstantinou, K.G.; Shinozuka, M. Probabilistic model for steel corrosion in reinforced concrete structures of large dimensions considering crack effects. Eng. Struct.; 2013; 57, pp. 306-326. [DOI: https://dx.doi.org/10.1016/j.engstruct.2013.06.038]

32. Vu, K.A.T.; Stewart, M.G. Structural reliability of concrete bridges including improved chloride-induced corrosion models. Structures; 2000; 24, pp. 313-333. [DOI: https://dx.doi.org/10.1016/S0167-4730(00)00018-7]

33. Zhou, Y.W.; Zheng, X.B.; Xing, F.; Sui, L.L.; Zheng, Y.W.; Huang, X.X. Investigation on the electrochemical and mechanical performance of CFRP and steel-fiber composite bar used for impressed current cathodic protection anode. Constr. Build. Mater.; 2020; 255, 119377. [DOI: https://dx.doi.org/10.1016/j.conbuildmat.2020.119377]

34. CECS 22-2007 Standard for Durability Assessment of Concrete Structures; China Architecture & Building Press: Beijing, China, 2007.

35. Poulos, H.G.; Davis, E.H. Pile Foundation Analysis and Design; John Wiley & Sons: New York, NY, USA, 1980.

36. Haldar, S.; Sivakumar Babu, G.L. Effect of soil spatial variability on the response of laterally loaded pile in undrained clay. Comput. Geotech.; 2008; 35, pp. 537-547. [DOI: https://dx.doi.org/10.1016/j.compgeo.2007.10.004]