Prediction Methodology for the Service Life of Concrete Structures in Marine Environment: From Materials to Performance

Taotao Feng; Yanchun Miao; Yongshan Tan; Zhiqiang Yang; Tongning Cao; Fengjuan Wang; Jinyang Jiang

doi:10.1016/j.eng.2025.03.010

Engineering ›› 2026, Vol. 61 ›› Issue (6) :109 -119. DOI: 10.1016/j.eng.2025.03.010

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Prediction Methodology for the Service Life of Concrete Structures in Marine Environment: From Materials to Performance

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Abstract

The conventional method for analyzing the durability of concrete structures is complex and time-consuming. The values of durability parameters are closely linked with the specific mix proportions of concrete and its service environment. For a reliable service life assessment, it is crucial to accurately determine critical physical indicators within the design model, such as the chloride diffusion coefficient, the time-dependent index of chloride diffusion coefficient, and the critical chloride concentration. However, efficiently and reliably deriving these physical parameters remains a significant challenge. This study develops three-dimensional (3D) heterogeneous models of cement-based materials from the microscale to the mesoscale to quantitatively calculate the chloride diffusion coefficient of concrete at the macroscale. Then, a dataset containing more than 2000 groups of marine concrete was analyzed to reliably determine the values and distribution types of relevant durability parameters. Finally, service life evaluations based on the theoretical model of chloride diffusion and reliability theory are applied to the marine concrete structure in Northeast Asia. This methodology bypasses the lengthy process of conventional exposure testing, demonstrating enhanced efficiency and providing a novel approach to the durability assessment of concrete structures in the marine environment.

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Service life / Durability parameters / Chloride diffusion coefficient / Data set

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Taotao Feng, Yanchun Miao, Yongshan Tan, Zhiqiang Yang, Tongning Cao, Fengjuan Wang, Jinyang Jiang. Prediction Methodology for the Service Life of Concrete Structures in Marine Environment: From Materials to Performance. Engineering, 2026, 61 (6) : 109-119 DOI:10.1016/j.eng.2025.03.010

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1. Introduction

Concrete structures constitute the primary structural typology in civil engineering. In marine environments, these structures are prone to prolonged chloride corrosion, which can precipitate the corrosion of internal steel reinforcements before the structures achieve their intended service life [1], [2], [3]. Designing concrete structures to meet service life requirements provides an effective and economical approach to ensuring the secure and sustained operation of these structures. Therefore, investigating durability assessment methodologies is pivotal in enhancing corrosion resistance and achieving the expected service life of concrete structures. Predicting the durability of concrete structures is a complex and time-consuming endeavor. The prevailing theoretical foundation for service life analysis is the chloride diffusion theory derived from Fick’s second law, extensively applied in the durability assessments of various marine engineering projects [4]. In addition to the reliability of theoretical models, the accuracy of values assigned to each durability parameter within the model significantly influences the dependability of the analysis results. Currently, the durability parameters in the chloride diffusion theory equation, such as the chloride diffusion coefficient and the chloride binding capacity, are predominantly derived through experimental methods. Among these, the most common approach is the natural diffusion method [5], which includes a series of procedures such as prolonged exposure, grinding sampling, and chemical titration. Thus, the natural diffusion method is characterized by its labor-intensive and time-consuming nature and is heavily influenced by the standardization of experimental procedures, impacting the reliability of service life assessments.

With advances in computer technology, scholars have obtained promising results using numerical simulation methods to study chloride transport behavior in concrete materials. Liu et al. [6] employed the CEMHYD3D program to develop a hydration microstructure model for concrete, effectively predicting the chloride diffusion coefficient of hardened paste. In addition, Carrara and De Lorenzis [7] quantitatively analyzed the chloride diffusion coefficient of the interface transition zone (ITZ). Jiang et al. [8] employed the CEMHYD3D model to construct a microstructure model of ultra-high-performance concrete with cracks and explored the effects of crack self-healing behavior on the transport properties of the matrix. At the mesoscale, Yu and Lin [9], as well as Du et al. [10] developed a two-dimensional (2D) mesoscopic finite element model of concrete based on ideal circular aggregate particles, simulating the transport behavior of chloride within the concrete. Actually, the chloride diffusion coefficient is directly related to the multiscale structural characteristics of concrete. Despite the effectiveness of numerical simulation methods, current research has primarily focused on the chloride transport properties at a single scale, such as the paste or concrete scale. There was a lack of consideration for the interrelated characteristics across different scales; consequently, the model parameters were often empirically determined, leading to limited applicability. In addition, most studies focused solely on the chloride diffusion coefficient without extending the analysis to the service life assessment of concrete structures. Consequently, it becomes challenging to provide guidance for the durability design of concrete structures.

Durability parameters, such as the surface chloride concentration and environmental degradation factors, are influenced not solely by the composition of the concrete material but also by the exposure environment, which includes temperature, humidity, and external loads [11]. Using short-term durability parameters determined under laboratory-standard conditions to assess the long-term service performance of concrete structures in actual complex environments may yield less accurate analytical outcomes [12], [13], [14], [15], [16]. Therefore, it is essential to determine the evolution of concrete durability parameters in actual service environments to assess the structural service life. However, concrete exposure tests are lengthy processes. It is necessary to propose a reliable and efficient method for assessing the durability of concrete structures in marine environments.

In this study, a methodological framework for the durability assessment was proposed, based on the composition of concrete raw materials and the structural service environment. Initially, multiscale structural models of concrete are developed, grounded in the physical and chemical properties of the raw materials. The chloride diffusion coefficients for paste, mortar, and concrete are calculated at various scales. This enables the quantitative prediction of the chloride diffusion coefficients in concrete from the raw material composition. In addition, considering the characteristics of the service environment in Northeast Asia, marine durability parameters are examined by analyzing pertinent data from existing literature. This process involves identifying the values and distribution types of parameters within the chloride diffusion equation. Finally, considering Northeast Asia a case study, the service life of marine concrete structures is evaluated based on chloride diffusion theory and reliability theory. This comprehensive approach combines material composition and environmental characteristics to analyze the service life of concrete structures in marine environments. Accordingly, this study aims to present a novel method for assessing the durability of concrete structures in the marine environment. The method targets the determination of durability parameter values based on concrete mix proportions and service environment characteristics, and subsequently calculates the service life of the structures. It addresses the time-consuming and labor-intensive limitations of traditional experimental methods, offering new perspectives for the reliable life design of these structures.

2. Materials and methods

2.1. Raw materials

Ordinary Portland cement (OPC; P.O. 42.5) was utilized as the cementitious material, and the chemical compositions are detailed in Table 1, whereas Fig. 1(a) displays the particle size distribution. River sand and basalt serve as fine and coarse aggregates, respectively, with their gradation curves shown in Fig. 1(b). Tap water is used in the mixing process. The mix proportions are listed in Table 2.

2.2. Sample preparation

When preparing concrete samples, the cement and aggregates were mixed dry in a mixer for 2 min. Water was then introduced, followed by an additional 5 min of mixing. The resultant concrete slurry was poured into a plastic test mold measuring 100 mm (length) × 100 mm (width) × 100 mm (height). After vibrating the concrete slurry, it was left to cure in the air for 24 h. Following demolding, the hardened concrete specimens were transferred to a standard curing room for 56 d.

2.3. Chloride diffusion depth in concrete

After the standard curing period, epoxy sealing was applied to five surfaces of the concrete specimens. The exposure test was then conducted using a 3.5% sodium chloride solution to simulate seawater conditions. After 60 d of exposure, the concrete specimens were ground to obtain powdered samples, with a grinding depth of 50 mm and each layer being 5 mm thick, as depicted in Fig. 2. The total chloride concentration at various depths within the concrete was then determined based on the standard JTS/T 236-[17]. It is noteworthy that the test results represented the total chloride concentration, without considering the chloride binding effect.

2.4. Method for service life analysis of marine concrete structures

The predominant service life analysis models currently used for concrete structures are the DuraCrete [18] and Life-365 [19] methods. However, the DuraCrete design model exhibits several characteristics: ① It assumes that the chloride diffusion coefficient (D_t) decreases over time, which contradicts the observation that D_t tends to stabilize after a certain age; ② it presumes constant boundary conditions, but in reality, the surface chloride concentration (C_s) gradually increases and stabilizes over time; ③ it does not consider chloride binding; and ④ the environmental influence coefficient is derived from short-term test data, which may be unreliable. For the Life-365 method, it relies on laboratory data to evaluate the durability of concrete structures in natural environments but fails to address concrete degradation from actual conditions, nor does it consider the chloride binding capacity. Xu et al. [20], Ma et al. [21], Yu et al. [22], [23], and Feng et al. [24] developed a chloride diffusion model that effectively incorporates the chloride binding capacity and the environmental effect. In addition, it accounts for the time-varying characteristics of C_s and D_t, as shown in Fig. 3. The mathematical representation of the model is depicted in Eq. (1), and it has been successfully applied in the durability design for a service life of 100−120 years for concrete structures in the Dalian Bay subsea immersed tube tunnel [20], [25]. In this study, Eq. (1) is the theoretical model for conducting durability analyses of concrete structures in marine environments.

(1)$\frac{\partial C_{\mathrm{f}}}{\partial t}=\frac{K D_{0} t_{0}^{m}}{1+R_{\mathrm{b}}} t^{-m} \frac{\partial^{2} C_{\mathrm{f}}}{\partial x^{2}}$

where x is the diffusion depth of chloride; C_f is the free chloride concentration at the depth of x; t is the exposure time; K is the deterioration coefficient; t₀ is the reference time; D₀ is the chloride diffusion coefficient at t₀; m is the time-dependent index of the chloride diffusion coefficient; and R_b is the chloride binding capacity.

Reliability theory has been found to have a common application in the analysis of engineering structures. Concerning durability issues stemming from chloride corrosion, the critical chloride concentration (C_cr) and C_f on the steel surface represent the resistance factor and load effect, respectively, from which a functional relationship can be derived as follows:

(2)$ Z=C_{\text {cr }}-C_{\mathrm{f}}$

where Z is reliability function.

If C_cr is less than or equal to C_f, the failure probability (P_f) can be computed as follows:

(3)$ P_{\mathrm{f}}=\phi(-\beta)$

where β is the reliability index; Φ(·) is the normal distribution function.

3. Results and discussion

3.1. Multiscale numerical simulation of the chloride diffusion coefficient

3.1.1. Microscale: The chloride diffusion coefficient of hardened paste

The CEMHYD3D model was utilized at the microscopic level to reconstruct the hydration microstructures of hardened cement paste. According to the water-to-cement ratio, casting, phase separation, and hydration steps were performed. As the reaction progresses, the microstructure continuously evolves, forming new phases and providing insights into phase composition and spatial distribution within the hardened matrix. The microstructures at a hydration age of 60 d were established based on the mineral composition of the cement and the mix proportions provided in Table 2, as depicted in Fig. 4(a). Within the matrix, only the pores and calcium silicate hydrate (C-S-H) gels contributed to chloride transport, with the remaining phases being non-transport phases. The chloride diffusion coefficients for high-density C-S-H (HD C-S-H) and low-density C-S-H (LD C-S-H) gels were found to differ significantly; thus, it became essential to distinguish between HD C-S-H and LD C-S-H gels in the hydration products. This study proposed that LD C-S-H primarily formed within open capillaries during the early and intermediate stages of hydration, while HD C-S-H predominantly developed in confined regions during the later stages of hydration. Therefore, for newly formed C-S-H, if its location prior to hydration was within a pore, it was classified as LD C-S-H; if cement particles filled its location prior to hydration, it was classified as HD C-S-H. Following the methodology outlined in the Ref. [26], the C-S-H gel was categorized into HD C-S-H and LD C-S-H gels, as illustrated in Fig. 4(b).

After establishing the microstructure, a simulation of chloride transport behavior can be conducted. Chloride diffusion within concrete can be described using Fick’s second law. Under conditions of one-dimensional (1D) diffusion, the governing equation is formulated as follows:

(4)$ \frac{\partial C(x, t)}{\partial t}=D \frac{\partial^{2} C(x, t)}{\partial x^{2}}$

where C is the chloride concentration; D is the chloride diffusion coefficient; C(x,t) is the total chloride concentration at position x and time t.

When applying Eq. (4), it is crucial to satisfy one prerequisite, which is that the D value remains constant with exposure age. In chloride diffusion into concrete, the continuous hydration of cementitious materials leads to a gradual densification of the microstructure. Therefore, the diffusion coefficient decreases with increasing time. In this study, concrete specimens underwent immersion tests after 56 d of curing, at which point the hydration degree of concrete was relatively high, and the pore structure development could reach a stable state. In addition, the exposure duration of the concrete was limited to 60 d, during which time the pore structure would exhibit minimal changes. Therefore, it was approximated that the chloride diffusion coefficient remained constant during this short period.

When the initial condition and boundary condition were given by Eq. (5).

(5)$ \left\{\begin{array}{l} C(x, 0)=C_{0} \\ C(0, t)=C_{\mathrm{s}} \end{array}\right.$

The analytical solution to the Eq. (4) can be expressed as follows:

(6)$ C(x, t)=C_{0}+\left(C_{\mathrm{s}}-C_{0}\right)\left[1-\operatorname{erf}\left(\frac{x}{2 \sqrt{D t}}\right)\right]$

where erf is error function.

ABAQUS, a sophisticated, large-scale general finite element analysis software (Dassault Systèmes, French), is celebrated for its robust computational prowess. The study investigated the transport process of chloride in hardened paste by employing the mass diffusion module within ABAQUS. C₀ in the specimens was set to zero in the model. C_s acted as the boundary condition for the chloride diffusion equation, with its value equivalent to a seawater concentration of 3.5%. Although C_s does not necessarily equal the solution concentration, its specific value does not influence the calculation results of the chloride diffusion coefficient. Pores, HD C-S-H, and LD C-S-H gels were identified as the transport phases within the hardened paste. Based on the Ref. [27], the chloride diffusion coefficients for these phases were determined to be 1.72 × 10⁻⁹, 1.2 × 10⁻¹³, and 1.77 × 10⁻¹² m²·s⁻¹, respectively. The chloride diffusion coefficients in the remaining non-transport phases were set to zero. Through numerical simulations, the three-dimensional (3D) spatial distribution of chloride in the hardened paste of A35 mix proportion at different exposure times was depicted in Fig. 5. Then, statistical analysis of chloride concentrations at various cross-sections yielded concentration distribution curves for the hardened pastes, as illustrated in Fig. 6.

The chloride diffusion analysis equation (Eq. (6)) was then utilized to perform regression analysis on the curves in Fig. 6. The calculated average values of the chloride diffusion coefficients for mixes A35 and A45 were 3.2 × 10⁻⁵ and 1.0 × 10⁻⁴ mm²·s⁻¹, respectively.

3.1.2. Mesoscale: The chloride diffusion coefficient of mortar

After the calculation of the chloride diffusion coefficients of hardened paste, the analysis shifted to the transport characteristics of chloride within the mortar. The development of a 3D packing model for fine aggregate particles laid the foundation for numerical simulations concerning the transport properties of mortar. Given the typically polyhedral nature of aggregates, this study employed random polyhedra to reconstruct aggregate particles. Detailed algorithms are discussed in the Refs. [28], [29]. The model was represented as a cube with edges measuring 5 mm, and the particle sizes of the fine aggregates conformed to the actual gradation curve. The resulting packing model, with a side length of 5 mm, is illustrated in Fig. 7(a). At the mesoscale, mortar comprised the matrix, fine aggregates, and the ITZ. Subsequently, the packing model underwent grid partitioning using hexahedra as characteristic elements. The 2D schematic depiction of the grid partitioning is illustrated in Fig. 7(b), with detailed algorithmic methodologies outlined in the Refs. [30], [31]. Considering computational efficiency, a characteristic element size of 50 μm was selected, resulting in a grid count of 1 000 000, a partitioning condition deemed feasible for computing efficiency. Employing the algorithms described above, the 3D mesoscale model of mortar, featuring fine aggregates, matrix, and ITZ, is depicted in Fig. 8.

In the analysis of chloride diffusion behavior in mortar, aggregates acted as non-transport phases, and the diffusion coefficients for the hardened paste were derived from the simulation results of the previous section, specifically, 3.2 × 10⁻⁵ and 1.0 × 10⁻⁴ mm²·s⁻¹ for A35 and A45 mix proportions, respectively. Due to the minimal thickness of ITZ in mortar, the diffusion coefficients for the ITZ aligned with those of the paste. Establishing boundary conditions at the mortar surface, with a specifically set 3.5% chloride content, facilitated 1D chloride diffusion within the matrix. Fig. 9, Fig. 10 illustrate the 3D spatial distribution and concentration profiles of chloride in the mortar at various exposure times. The average diffusion coefficients for the mortar mixtures A35 and A45 are calculated using Eq. (6) as 9.28 × 10⁻⁶ and 2.92 × 10⁻⁵ mm²·s⁻¹, respectively.

3.1.3. Macroscale: The chloride diffusion coefficient of concrete

Simulating chloride transport in concrete was analogous to that used for mortar. A 3D cubic packing model of coarse aggregates with a side length of 50 mm was established, relying on coarse aggregates’ volume fraction and particle size distribution, as illustrated in Fig. 11(a). For computational efficiency, the number of characteristic elements was set to 100 × 100 × 100. The resultant concrete mesoscale model is depicted in Fig. 11(b). At the concrete scale, coarse aggregates were treated as non-transport phases. The diffusion coefficients for mortar were sourced from the calculations in the previous section, namely 9.28 × 10⁻⁶ and 2.92 × 10⁻⁵ mm²·s⁻¹ for A35 and A45 mix proportions, respectively. The ITZ’s diffusion coefficient is determined depending on the Ref. [32], as stated in Eq. (7).

(7)$ D_{\mathrm{ITZ}}=D_{\text {mortar }} \times\left(139.4 / t_{\mathrm{ITZ}}+1.0\right)$

where D_ITZ is the chloride diffusion coefficient of ITZ; D_mortar is the chloride diffusion coefficient of mortar matrix; t_ITZ is the thickness of the ITZ, with its value taken as the length of the characteristic element.

Through numerical simulations, the 3D spatial distribution of chloride concentration within A35 concrete at different exposure ages is demonstrated in Fig. 12. In addition, by statistically analyzing the concentration values at various diffusion depths, the chloride concentration distribution curves for a 60 d exposure period are depicted in Fig. 13. A comparison between the experimental results of the chloride concentration distribution curves and the simulated results demonstrated a high degree of agreement, indicating that the multiscale model can effectively analyze the diffusion behavior of chloride within concrete. Based on the numerical simulation results, as per Eq. (6), the chloride diffusion coefficients for concrete mixes A35 and A45 were calculated to be 5.87 × 10⁻⁶ and 1.71 × 10⁻⁵ mm²·s⁻¹, respectively.

It is worth noting that neither the experimental nor the simulation methods employed in this study account for the chloride binding effect. Therefore, the obtained diffusion coefficients represented the total chloride diffusion coefficients (D_t,t). However, the free chloride diffusion coefficient (D_t,f) is generally utilized in the service life analysis model. Yu et al. [33] compiled 508 sets of measured data from indoor exposure and actual marine engineering scenarios to establish a correlation between these two parameters. Through their analysis, they derived a relationship between D_t,f and D_t,t as follows:

(8)$ D_{\mathrm{t}, \mathrm{f}}=0.6355 D_{\mathrm{t}, \mathrm{t}}^{0.9621} \quad\left(R^{2}=0.9328\right)$

Using Eq. (8) for transformation, the D_t,f values for concrete mixes A35 and A45 were determined to be 3.49 × 10⁻⁶ and 1.06 × 10⁻⁵ mm²·s⁻¹, respectively. R² is the coefficient of determination.

3.2. Durability parameters of concrete structures in marine environments

The theoretical equation for chloride diffusion includes five critical durability parameters, specifically the m, k, K, C_cr, and R_b. Subsequent analyses utilized the Northeast Asia region as the service environment to determine the values and distribution patterns of these parameters through a combined approach of literature review and statistical methods.

3.2.1. Time-dependent index of the chloride diffusion coefficient

The chloride diffusion coefficient is a fundamental parameter in the service life analysis of marine concrete structures and can be represented using the following power function, as depicted in Eq. (9).

(9)$ D_{\mathrm{t}}=D_{0}\left(\frac{t_{0}}{t}\right)^{m}$

Yu et al. [33] performed a statistical analysis of chloride diffusion data, encompassing 2207 sets from global marine concrete samples with exposure times ranging from 7 d to 91 years. Through statistical analysis, the researchers determined that when concrete mix proportions and exposure environments were not considered, the universal value of m was determined to be 0.6304. Given the large sample size and the broad range of exposure times, selecting this m-value for the service life assessment was reasonable.

3.2.2. Time-dependent constant of surface chloride concentration

C_s was used as the boundary condition for the theoretical equation of chloride diffusion. Numerous experimental findings indicated that C_s evolved from a low concentration to a high concentration, gradually reaching saturation [34], [35], [36], [37], [38]. Yu [39] found that C_s increases over time based on a power function.

(10)$ C_{\mathrm{s}}=k t^{\frac{1-m}{2}}+C_{0}$

Xu et al. [40] analyzed C_s data from 144 groups of marine concrete in laboratories, exposure stations, and global engineering structures, establishing that the relationship between C_s and exposure time can be effectively modeled using Eq. (10). Feng et al. [24] collected long-term data from the literature on the C_s value of marine concrete in the Northeast Asia area, where the exposure ages ranged from 2 to 82 years. Fig. 14 [24] illustrates the time-varying model of C_s values for statistical concrete within the splash zone. The analysis identifies the k for C_s in the splash zone, with a determined value of 0.2567.

3.2.3. Degradation coefficient

During the structural service process, external loads and environmental factors such as freeze-thaw cycles would induce the formation of microcracks within the concrete, accelerating chloride diffusion [41]. In addition, corrosive media such as sulfate and magnesium salts present in seawater further influence the transport behavior of chloride in concrete [42]. The K, defined as the ratio of the chloride diffusion coefficient under actual service conditions to that under laboratory conditions, is commonly employed to reflect the influence of the service environment on the diffusion coefficient. The DuraCrete project guidelines provide environmental coefficients affecting the chloride diffusion coefficient shown in Table 3 [18]. These coefficients consider the influence of cement type and marine exposure regions. In reality, the service environment of the structure, including factors such as temperature, humidity, and wind loads, significantly affects the deterioration coefficient. Consequently, the K-value of concrete is directly correlated with the geographical location of the structure. Investigating marine concrete in the pertinent seas of Northeast Asia is imperative to achieve a reasonably accurate K-value. Feng et al. [24] and Feng [43] explored the chloride diffusion coefficient of a concrete wharf operating for 11 years in Dalian, China. The K-value of the concrete in the wharf’s splash area was established at 1.52. Hence, this value of 1.52 was utilized for the life analysis.

3.2.4. Critical chloride concentration

The C_cr leading to the corrosion of steel reinforcement was influenced by factors including the type and dosage of cementitious materials, the internal moisture content of the concrete, the surface properties of the reinforcement, as well as environmental conditions such as temperature and humidity. Despite efforts, there remained no unified value for the C_cr [44], [45], [46]. The Fourth Harbor Engineering Research Institute of the China Communications Construction Company conducted field surveys and sampled analyses on concrete from several typical marine engineering projects and exposure stations in northern China. Through on-site surveys and analyses, a statistical range for the C_cr in splash zones was determined to be between 0.057% and 0.064% [47]. Zhang et al. [47], drawing on the outcomes of exposure tests, investigations of harbors and docks, and comprehensive laboratory experiments, have derived recommended values for the C_cr in concrete structures within the northern coastal regions of China. In particular, for concrete in splash zones, the C_cr value of 0.060% is proposed. For durability design, both the Life-365 service life prediction model [19] and the Chinese Civil Engineering Society standard “CCES 01-2004: Guide to Durability Design and Construction of Concrete Structures” [48] stipulate that the C_cr for concrete is 0.05% of its mass fraction. In the analysis of the service life of marine concrete structures, Yu et al. [22], Xu et al. [20], and Funahashi [49] also adopted a C_cr of 0.05% of the concrete’s mass fraction. This value is lower than the research findings mentioned above, rendering it safer for durability design. Therefore, the recommended value of 0.05% by mass of concrete for the C_cr was adopted.

3.2.5. Chloride binding capacity

Chlorides in concrete were categorized into two types: free chloride, which can move freely within the pores and threaten the reinforcement steel, and bound chloride, primarily reacting with aluminate or directly adsorbed by hydration products [50]. The binding action of chloride can delay its arrival at the surface of the reinforcement steel, effectively prolonging the initiation of steel corrosion [51]. In the context of the durability design standard for concrete structures [52], Eq. (11) was employed to determine the value of R_b. Based on the functional relationship, the R_b values for concrete mixes A35 and A45 were determined to be 0.22 and 0.10, respectively.

(11)$ \begin{array}{l} R_{\mathrm{b}}=\left(1.3+0.06 m_{\mathrm{FA}}-28.5 \times 10^{-4} m_{\mathrm{FA}}^{2}+28.5 \times 10^{-6} m_{\mathrm{FA}}^{3}\right) \\ \times(0.49-0.92 w / b) \end{array}$

where m_FA denotes the content of fly ash; w/b represents the water to binder ratio.

3.2.6. Distribution types of durability parameters

When analyzing the service life of concrete structures using reliability theory, it is imperative to consider the distribution types of durability parameters. A comprehensive literature review was conducted to ascertain the distribution characteristics of each parameter, as listed in Table 4 [18], [20], [21], [24], [25], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [40], [77], [78], [79], [80], [81]. The eight durability parameters (x₀, C₀, R_b, C_s, C_cr, D₀, m, and K, where x₀ is the thickness of the concrete protective layer), various distribution types such as normal, lognormal, and uniform distributions can be employed for description, with normal distribution being predominant among these distributions. Therefore, for the theoretical model of chloride diffusion, it was postulated that, apart from exposure time, all other durability parameters conform to a normal distribution.

3.3. Service life assessment based on the theoretical model of chloride diffusion and reliability theory

This study was conducted against the backdrop of the Northeast Asia region, investigating the service life of marine concrete structures in the splash zone. Within the theoretical model, the coefficient of variation for parameters conforming to a normal distribution was set to 20%. The specific model parameters are detailed in Table 5.

GB/T50476 [81] specifies that the failure probability range for structures is 5%-10%. Accordingly, the service life of structures is determined by the instances at which the steel bars’ corrosion probability (i.e., the failure probability) reaches 5% or 10%. Fig. 15 presents the calculation results of the service life of the concrete structures with different mix ratios. It indicates that under a 5% corrosion probability, the service life of concrete structures A35 and A45 is 11.2 and 0.5 years, respectively. In addition, under a 10% corrosion probability, the service lives extend to 12.6 and 0.6 years for A35 and A45, respectively. An increase in the water-binder ratio from 0.35 to 0.45 significantly decreases the service life of the concrete structures.

In summary, this study determines the chloride diffusion coefficient of concrete based on its mix proportions. In conjunction with the structural service environment, the values of the remaining durability parameters are established. Finally, an assessment of the service life of concrete structures is conducted. Significant enhancements in analytical efficiency are achieved by avoiding the time-consuming and labor-intensive experimentation process, thus offering new perspectives for the durability analysis of concrete structures in the marine environment.

4. Conclusions

This study establishes a set of evaluation methods to predict the service life of marine concrete structures based on a multiscale diffusivity model and a data set of durability parameters. The material models for hardened paste, mortar, and concrete are initially developed. The chloride diffusion coefficient of concrete is calculated using the multiscale transition method, and the results reveal that its value is close to that under test conditions. Then, data from more than 2000 groups of marine concrete are analyzed to reliably determine the values and distribution types of relevant durability parameters in the theoretical equation of chloride diffusion. Finally, the service life of marine concrete structures in Northeast Asia is predicted based on the chloride diffusion theory and reliability theory. This methodology enables the prediction of the service life of structures based on concrete mix proportions and service conditions, significantly enhancing the efficiency of durability analysis.

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