Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments: An application of the three-parameter Weibull distribution model

Chu-Jie Jiao; Cheng-Gong Lu; Xiu-Cheng Zhang; Xue-Fei Chen

doi:10.1016/j.cscm.2025.e05543

Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments: An application of the three-parameter Weibull distribution model

Chu-Jie Jiao (Co-first Author)
, Cheng-Gong Lu (Co-first Author)
, Xiu-Cheng Zhang
, Xue-Fei Chen^*

^*Corresponding author for this work

Department of Architecture and Civil Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

2 Downloads (CityUHK Scholars)

Abstract

Understanding the degradation mechanisms and patterns of concrete is crucial for predicting the service life of concrete structures. Researchers have focused on establishing quantitative correlations between deterioration and time. Traditionally, Fick's second law and chloride diffusion models have been key in durability design. However, the three-parameter Weibull distribution, widely used in reliability analysis, has been underutilized in assessing reinforced concrete durability. To address this, this study investigates the corrosion degradation behavior of reinforced concrete exposed to a coupled salt solution environment (0.32 mol/L NaCl and 0.4 mol/L MgSO₄), utilizing electrochemical testing and a three-parameter Weibull reliability model. The electrochemical results indicated a gradual increase in the corrosion current density, reaching a critical threshold of 10 μA·cm⁻² after 720 days, marking the onset of significant corrosion. The predicted reliability lifespan of C35 reinforced concrete under these aggressive conditions was estimated to be approximately 760 days. To estimate the Weibull parameters (shape parameter U, scale parameter V, and location parameter δ), three parameter estimation methods were employed: the Correlation Coefficient Optimization Method (CCOM), Maximum Likelihood Method (MLM), and Method of Moments (MEM). Among these, CCOM and MLM provided consistent and stable estimates, while MEM exhibited larger estimation errors. The reliability curves derived from CCOM and MLM displayed similar trends, with reliability maintaining a constant value in the initial phase and then rapidly decreasing after 730 days. These findings not only deepen the understanding of reinforced concrete’s corrosion behavior in aggressive environments but also suggest that CCOM and MLM are the most reliable methods for parameter estimation in cases with limited sample sizes.

© 2025 The Authors. Published by Elsevier Ltd.

Original language	English
Article number	e05543
Number of pages	13
Journal	Case Studies in Construction Materials
Volume	23
Online published	11 Nov 2025
DOIs	https://doi.org/10.1016/j.cscm.2025.e05543
Publication status	Published - Dec 2025

Funding

This project was financially supported by the Major Cultivation Project of Scientific Research and Innovation Platforms in Gansu Province Universities (Grant No. 2024CXPT-19): development and technology transfer of a multifunctional integrated building maintenance system. This project was also funded by the [Natural Science Foundation of Fujian] under grant number [NO. 2023J01999].

Research Keywords

Concrete Degradation
Durable Performance
Three-Parameter Weibull Distribution
Durability Evaluation and Life Prediction

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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title = "Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments: An application of the three-parameter Weibull distribution model",

abstract = "Understanding the degradation mechanisms and patterns of concrete is crucial for predicting the service life of concrete structures. Researchers have focused on establishing quantitative correlations between deterioration and time. Traditionally, Fick's second law and chloride diffusion models have been key in durability design. However, the three-parameter Weibull distribution, widely used in reliability analysis, has been underutilized in assessing reinforced concrete durability. To address this, this study investigates the corrosion degradation behavior of reinforced concrete exposed to a coupled salt solution environment (0.32 mol/L NaCl and 0.4 mol/L MgSO₄), utilizing electrochemical testing and a three-parameter Weibull reliability model. The electrochemical results indicated a gradual increase in the corrosion current density, reaching a critical threshold of 10 μA·cm⁻² after 720 days, marking the onset of significant corrosion. The predicted reliability lifespan of C35 reinforced concrete under these aggressive conditions was estimated to be approximately 760 days. To estimate the Weibull parameters (shape parameter U, scale parameter V, and location parameter δ), three parameter estimation methods were employed: the Correlation Coefficient Optimization Method (CCOM), Maximum Likelihood Method (MLM), and Method of Moments (MEM). Among these, CCOM and MLM provided consistent and stable estimates, while MEM exhibited larger estimation errors. The reliability curves derived from CCOM and MLM displayed similar trends, with reliability maintaining a constant value in the initial phase and then rapidly decreasing after 730 days. These findings not only deepen the understanding of reinforced concrete{\textquoteright}s corrosion behavior in aggressive environments but also suggest that CCOM and MLM are the most reliable methods for parameter estimation in cases with limited sample sizes. {\textcopyright} 2025 The Authors. Published by Elsevier Ltd.",

keywords = "Concrete Degradation, Durable Performance, Three-Parameter Weibull Distribution, Durability Evaluation and Life Prediction",

author = "Chu-Jie Jiao and Cheng-Gong Lu and Xiu-Cheng Zhang and Xue-Fei Chen",

year = "2025",

month = dec,

doi = "10.1016/j.cscm.2025.e05543",

language = "English",

volume = "23",

journal = "Case Studies in Construction Materials",

issn = "2214-5095",

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Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments: An application of the three-parameter Weibull distribution model. / Jiao, Chu-Jie (Co-first Author); Lu, Cheng-Gong (Co-first Author); Zhang, Xiu-Cheng et al.
In: Case Studies in Construction Materials, Vol. 23, e05543, 12.2025.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments

T2 - An application of the three-parameter Weibull distribution model

AU - Jiao, Chu-Jie

AU - Lu, Cheng-Gong

AU - Zhang, Xiu-Cheng

AU - Chen, Xue-Fei

PY - 2025/12

Y1 - 2025/12

N2 - Understanding the degradation mechanisms and patterns of concrete is crucial for predicting the service life of concrete structures. Researchers have focused on establishing quantitative correlations between deterioration and time. Traditionally, Fick's second law and chloride diffusion models have been key in durability design. However, the three-parameter Weibull distribution, widely used in reliability analysis, has been underutilized in assessing reinforced concrete durability. To address this, this study investigates the corrosion degradation behavior of reinforced concrete exposed to a coupled salt solution environment (0.32 mol/L NaCl and 0.4 mol/L MgSO₄), utilizing electrochemical testing and a three-parameter Weibull reliability model. The electrochemical results indicated a gradual increase in the corrosion current density, reaching a critical threshold of 10 μA·cm⁻² after 720 days, marking the onset of significant corrosion. The predicted reliability lifespan of C35 reinforced concrete under these aggressive conditions was estimated to be approximately 760 days. To estimate the Weibull parameters (shape parameter U, scale parameter V, and location parameter δ), three parameter estimation methods were employed: the Correlation Coefficient Optimization Method (CCOM), Maximum Likelihood Method (MLM), and Method of Moments (MEM). Among these, CCOM and MLM provided consistent and stable estimates, while MEM exhibited larger estimation errors. The reliability curves derived from CCOM and MLM displayed similar trends, with reliability maintaining a constant value in the initial phase and then rapidly decreasing after 730 days. These findings not only deepen the understanding of reinforced concrete’s corrosion behavior in aggressive environments but also suggest that CCOM and MLM are the most reliable methods for parameter estimation in cases with limited sample sizes. © 2025 The Authors. Published by Elsevier Ltd.

AB - Understanding the degradation mechanisms and patterns of concrete is crucial for predicting the service life of concrete structures. Researchers have focused on establishing quantitative correlations between deterioration and time. Traditionally, Fick's second law and chloride diffusion models have been key in durability design. However, the three-parameter Weibull distribution, widely used in reliability analysis, has been underutilized in assessing reinforced concrete durability. To address this, this study investigates the corrosion degradation behavior of reinforced concrete exposed to a coupled salt solution environment (0.32 mol/L NaCl and 0.4 mol/L MgSO₄), utilizing electrochemical testing and a three-parameter Weibull reliability model. The electrochemical results indicated a gradual increase in the corrosion current density, reaching a critical threshold of 10 μA·cm⁻² after 720 days, marking the onset of significant corrosion. The predicted reliability lifespan of C35 reinforced concrete under these aggressive conditions was estimated to be approximately 760 days. To estimate the Weibull parameters (shape parameter U, scale parameter V, and location parameter δ), three parameter estimation methods were employed: the Correlation Coefficient Optimization Method (CCOM), Maximum Likelihood Method (MLM), and Method of Moments (MEM). Among these, CCOM and MLM provided consistent and stable estimates, while MEM exhibited larger estimation errors. The reliability curves derived from CCOM and MLM displayed similar trends, with reliability maintaining a constant value in the initial phase and then rapidly decreasing after 730 days. These findings not only deepen the understanding of reinforced concrete’s corrosion behavior in aggressive environments but also suggest that CCOM and MLM are the most reliable methods for parameter estimation in cases with limited sample sizes. © 2025 The Authors. Published by Elsevier Ltd.

KW - Concrete Degradation

KW - Durable Performance

KW - Three-Parameter Weibull Distribution

KW - Durability Evaluation and Life Prediction

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001618500600001

U2 - 10.1016/j.cscm.2025.e05543

DO - 10.1016/j.cscm.2025.e05543

M3 - RGC 21 - Publication in refereed journal

SN - 2214-5095

VL - 23

JO - Case Studies in Construction Materials

JF - Case Studies in Construction Materials

M1 - e05543

ER -

Reliability life analysis of reinforced concrete structures (RCS) in salt corrosion environments: An application of the three-parameter Weibull distribution model

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Research Keywords

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