Design Of Concrete Structures Research Articles

6-month evaluation of concrete aging factor using chloride migration test: Effects of binder type and w/b ratio

Service life modeling is a relevant tool in the design of durable concrete structures. Among the service life prediction models, many introduce the so-called concrete aging factor, which aims to express the reduction of concrete diffusivity over time. This paper presents an experimental assessment of the concrete aging factor up to the age of 6 months based on the chloride migration coefficient. Several concretes produced with different binder types, mineral additions, and water/binder ratios were evaluated. Concrete compressive strength and surface electrical resistivity are also addressed. The results indicate a strong influence of the type of binder and the use of mineral additions on the aging factor of the concrete – especially in concretes with water/binder ratio = 0.45. The inclusion of the aging factor in service life prediction models and the extrapolation of data obtained at the first ages of concrete for long-term analysis are discussed.

Research on the Safety Assessment of Corbel Beams of Reservoir Radial Gates Based on Real States

The radial gate corbel beam is a kind of gate support structure more often used in large and medium-sized reservoirs, but the current corresponding structural design code does not give a review calculation method for it. Because there are obvious differences between a corbel and a corbel beam in structural form and force, if the corbel beam is just simplified in the calculation as a corbel structure, it can easily lead to misjudgment of insufficient bearing capacity. This misjudgment has a significant impact on later safety assessment, danger removal, and reinforcement. Currently, there are limited studies available on the internal stress distribution of the corbel beam. In this study, taking the danger removal and reinforcement of the radial gate beam of a medium reservoir in Beijing as an example, the concrete quality of the dam was tested by the core drilling method, and two safety review methods of the corbel beam for different types of reservoirs were proposed in combination with the Code for Design of Hydraulic Concrete Structures (SL191-2008). Then, three different types of calculation model were established by the method of theoretical mechanics calculation and finite element simulation. Combined with the safety test data, the stress state of the combined stress structure of the corbel beam and gate pier under the real state was analyzed and the safety evaluation was carried out. The calculation results of these two corbel beam safety review methods were respectively reduced by 32% and 47% compared with the current calculation method. Engineering practice has proved the rationality of the two safety evaluation methods proposed in this paper, which can provide a certain reference for similar engineering reinforcement.

The Effects of Stochastic Circular Pores on Splitting Tensile Behavior of Concrete Based on the Multifractal Theory

Concrete naturally contains a large number of circular-like stochastic pores which weaken the tensile strength of concrete and change the crack propagation path. This study investigates the influences of the size distribution and the spatial distribution of stochastic pores on the fracture behavior of concrete based on the splitting tensile test. The mesoscale model of concrete containing coarse aggregate, mortar, interface transition zone (ITZ), and circular pores is established to simulate the crack initiation, propagation, and coalescence of concrete. Concrete samples with a single hole are prepared to verify the effectiveness of the numerical simulation method. Numerical tests are conducted on numerous mesoscale concrete samples with various porosities, pore size distributions, and pore spatial distributions. The numerical simulation results indicate that the tensile strength decreases with the increase of pore size at the same porosity. Based on multifractal theory, a quantitative indicator to describe the spatial distribution uniformity of concrete stochastic pores is proposed. There is a positive correlation between the spatial distribution uniformity of stochastic pores and the tensile strength. The stochastic circular pores can have a profound effect on the concrete’s fracture pattern, which results in three typical macro-crack patterns in the numerical simulation of the splitting tensile test. The presented results deepen the understanding of the influence of stochastic circular pores on the tensile mechanical properties of concrete and provide a reference for the design of concrete structures.

Experimental Study on the Sulfuric Acid Corrosion Resistance of PHC Used for Pipe Pile and NSC Used in Engineering

In order to compare and investigate the sulfuric acid corrosion resistance of concrete for PHC pipe piles and two kinds of concrete commonly used in engineering, acid accelerated corrosion tests were conducted on specimens with three different strength grades of C30, C50, and C80 in a sulfuric acid solution with pH ≈ 0.85. The appearance of the specimens was observed, and the changes in mass loss percentage, corrosion depth, and stress–stain curves under uniaxial compressive loading were calculated and obtained with the corrosion time. From the comparison of corrosion depth and mass loss percentage of the concrete specimens with three different strength grades of C30, C50, and C80, it was found that the higher the strength grade of the concrete, the more severe the corrosion degree. The shapes of the stress–strain curves of three different strength grades of concrete specimens were basically the same. As the corrosion time was prolonged, the peak stress and the elastic modulus of concrete decreased. From the perspective of long-term corrosion, C80 specimens had a relatively smaller percentage of peak stress loss and a stronger resistance to peak stress loss. The research results provide references for the durability design of concrete structures and the prediction of concrete’s service life in a sulfuric acid environment.

A general equation for estimation of time-dependent prestress losses in prestressed concrete members

Due to the inherent nature of concrete shrinkage, creep and relaxation of prestressing strands, the prestress in prestressed concrete structures decreases continuously with time, i.e., there is an apparent time-dependent prestress loss phenomenon for prestressed concrete structures. Therefore, it is an important issue for the estimation of time-dependent prestress losses in the design of prestressed concrete structures. Many current design codes provide relevant equations for the evaluation of prestress losses. For the prestressed concrete structure, in addition to the prestressing strands, a great amount of ordinary reinforcing steel is configured to enhance its load-carrying capacity. It is generally considered that no stress relaxation occurs for ordinary reinforcing steel due to its lower stress. However, the presence of ordinary reinforcing steel affects the stress distribution in the structure and thus has an obvious impact on the prestress losses, which is not considered in the prediction equations in most current codes for the design of concrete structures up to date. In this study, based on the cross-sectional analysis of prestressed concrete members that combines the age-adjusted effective modulus method of concrete creep analysis, a general equation for estimation of the time-dependent prestress losses in prestressed concrete members considering the influence of ordinary reinforcing steel is derived and simplified. When the influence of ordinary reinforcing steel is ignored, i.e., the percentage of ordinary reinforcing steel is taken as zero, the proposed equation reduces to those in Eurocode EN 1992-1-1:2004 and AASHTO LRFD 2020. In the end, an example of a T-shaped prestressed concrete girder is provided to show the application of the proposed equation for the evaluation of time-dependent prestress losses and the error resulting from the simplification of the equation. The results show that ordinary reinforcing steel has a significant effect on the time-dependent prestress losses in prestressed concrete members for the commonly used percentage of ordinary reinforcing steel, and the error arising from the simplification of the first derived equation is quite small.

Tiêu chuẩn châu Âu - nghiên cứu và ứng dụng cho kết cấu bê tông cốt thép trong điều kiện Việt Nam

Since 2018, it has been planned by the Vietnamese authorities for the preparation of a new system of the national construction codes and standards, of which the Eurocodes were recently taken into consideration to be systematically and gradually applied during the period from 2022 to 2030. Towards this orientation, significant attentions have also been paid and various number of studies on design of concrete structures to the Eurocodes have been conducted by Vietnamese researchers, which will be introduced in this paper to prepare for the comprehensive applications of the Eurocodes for concrete structures in Vietnam in the coming time when appropriable, especially the second generation of the Eurocodes will be expected to be also issued in coming years.

Stiffness of three-bar tensegrity structure

PurposeIn this paper, the main factors influencing the structure stiffness will be analyzed by studying the tangent stiffness matrix based on different requirement in engineering practice. The authors can obtain the deformation of three-bar tensegrity basic unit in different load, and gain the primary factor by comparing the deformation, which will provide reference to concrete structure design in the engineering.Design/methodology/approachThe mathematical model of tensegrity structure was built by establishing generalized node coordinates and connective matrix. Three main factors that affect the structure deformation can be obtained by analyzing the stiffness matrix, which is preload, Young's modulus, and cross-sectional area, the thinking of deformation also be sorted out. The deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering.Findings(1) When the axial external force is applied to the structure, the torsion-angle deformation of the structure is the largest, and the radial deformation of the structure is the smallest. (2) The structure stiffness can be rapidly enhanced by increasing the cross-sectional area. But the cross-sectional area can't be increased indefinitely. Because the mass will be increased once increasing the cross-sectional area, which will destroy the structure of the advantages of light weight in engineering practice.Originality/valueThe deformation analysis of the concrete structure is carried out, and it is concluded that increasing the cross-sectional area can quickly improve the stiffness of the structure, which provides a reference for the structural variable stiffness design in practical engineering.

Multiple-level earthquake-resistant design strategy for precast concrete frames with semi-rigid connections: A case study

The design of precast concrete (PC) structures with semi-rigid connections is primarily based on the design of cast-in-suit structures by adjusting the relevant parameters of PC connections. However, it is necessary to further verify whether the seismic collapse resistance capacity of these PC structures meets the requirements, and to examine how to achieve the optimal seismic resistance design of PC structures. To explore a more concise and effective design scheme for PC structures, the influence of different PC connection parameters and the number of structural stories on the collapse resistance capacity of PC structures is discussed based on a case study. In this work, we set three series of 8-story PC structures and one series of 18-story PC structures, based on different PC connection parameters. Firstly, a simplified algorithm of the inter-story drift (ISD) ratio, based on a modified Muto’s method, is performed to preliminarily screen PC structures subjected to frequent-level earthquakes, and the lower limit value of the semi-rigid connection coefficient of each series of structures can be determined. Next, based on the modal pushover analysis and the capacity spectrum, the ISD ratio of the structures subjected to rare-level earthquakes is analyzed to further screen out the structures that do not meet the specification limits. The distribution ratio of the hysteretic energy in each story of the PC structures is discussed using time history analysis. Then, in the collapse stage, based on a global damage model and incremental dynamic analysis, the collapse state points of the structure can be obtained so that the collapse probability curve of each PC structure is determined, and the collapse safety margin of PC structures can be analyzed. PC structures can be further screened based on the collapse margin ratio (CMR), and the influences of PC connection parameters on the CMR and failure path of PC structures are assessed. Finally, the optimization of structures with semi-rigid PC connections based on multilevel seismic action is realized.

Behavior and design of earthquake resistant concrete structure

Earthquake and seismic-resistant concrete structures are essential components and requirements of structural design. The performance and response of concrete structures during/after the earthquake event are significant to determine the condition of the structures as well as to identify the possibility of structural failure. The main objective is to investigate the appropriate method to evaluate the impact on the structure due to earthquakes based on closed-form solutions, and to determine its differences with the results of numerical modelling. The seismic behavior of structures is required to be designed in accordance with the minimum design requirements specified in the Standard. Seismic design, where ground behavior is considered, is presented as a significant part of design analyses, and ground movement and shaking, are associated with the ground deformation which is the primary seismic load consideration for the design of plain or reinforced concrete structures. The outcome of the longitudinal analysis provided the maximum axial and bending strain which is adopted to calculate the combined strain. These results of strain are considered with the design of concrete structures against Ultimate Limit State and Service Limit State design phases. Therefore, the results evaluate the effect of seismic design on the performance of the concrete structure.

Modeling concrete properties: New approaches in MC2020

AbstractThe fib Model Code 2020 (MC2020) is developed to serve as the basis for future international codes and standards for the design of concrete structures by summarizing international research and experience and converting this knowledge into a practical document. The chapter “Concretes” contained therein provides a clear set of application rules in combination with sufficient background information and related references. This paper gives a concise overview of the contents of the Chapter 14 “Concretes” in the 2nd draft of MC2020. Instead of presenting numerous details on changes in the text and equations compared with the previous MC2010, major fundamentals on modeling concrete behavior are indicated. New sections in MC2020 on non‐conventional concretes, durability specifications and environmental performance are covered. Extended state‐of‐the‐art chapters on concrete transport properties and durability design conclude this contribution.

Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

Owing to advancement in advanced manufacturing technology, the reinforcement design of concrete structures has become an important topic in structural engineering. Based on bi-directional evolutionary structural optimization (BESO), a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete (SRC) structures. This approach combines a minimum compliance objective function with a hybrid truss-continuum model. Furthermore, a modified bi-directional evolutionary structural optimization (M-BESO) method is proposed to control the level of tensile stress in concrete. To fully utilize the tensile strength of steel and the compressive strength of concrete, the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete. To demonstrate the effectiveness of the proposed procedures, reinforcement layout optimizations of a simply supported beam, a corbel, and a wall with a window are conducted. Clear steel trajectories of SRC structures can be obtained using both methods. The area of critical tensile stress in concrete yielded by the M-BESO is more than 40% lower than that yielded by the uniform design and BESO. Hence, the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

Approach to assessment of existing structures in the fib Model Code 2020

AbstractExisting structures often no longer meet the demands formulated in contemporary design codes with respect to structural safety and serviceability. This occurs, for instance, if the loads on existing structures, like traffic loads on bridges, are larger than assumed in the original design. A second potential reason is that structures are subject to deterioration, like alkali–silica reaction within the concrete or corrosion of the reinforcement due to chloride attack or carbonation. A third possible reason is that in recent codes, additional criteria have been introduced based on new theories and/or negative experiences with older structures. The new fib Model Code for Concrete Structures 2020 will be valid both for the design of new structures and the assessment of existing structures. This paper shows how the design and assessment of concrete structures are integrated into this new code concept.

Eco-Friendly Design and Sustainability Assessments of Fibre-Reinforced High-Strength Concrete Structures Automated by Data-Driven Machine Learning Models

In recent years, adding fibres into brittle concrete to improve ductility has gained momentum in the construction industry. Despite the significant momentum, limitations do exist in design and industrial applications, contributing to the complexity of shear behaviours in fibre-reinforced concrete and the existing empirical models that can hardly provide a reasonable prediction, especially for high-strength concrete applications. A critical review reveals that current research mostly focuses on single eigenvalue analysis and pay less attention to the different synergetic effect of fibres on high-strength concrete and normal-strength concrete. This study aims to fill the research gap by the unprecedented use of reliable models for the prediction and evaluation of structural and sustainable properties of high-strength fibre-reinforced concrete beams. To this end, this study establishes three novel deep learning (ANN, BNN, and Xgboost) models for designing and optimising the shear capacity of ‘high-strength’ fibre-reinforced concrete beams towards the circular economy. In addition to introducing a new type of novel machine learning (BNN) model, which is capable of structural design and takes into account complex design features, our study also enhances sustainability by reducing greenhouse gas (GHG) emissions. The novel prediction models unprecedentedly elicit flexural capacity, structural stiffness, carbon emission, and price, together with the shear strength for high-strength fibre-reinforced structures. Firstly, this study focuses on multiple parameters for forecasting high-strength fibre-reinforced concrete beams. In addition, the models provide more comprehensive insights into the design and manufacture of high-strength steel fibre-reinforced concrete structures in a more environmentally friendly manner. With the help of the proposed models, it will be more cost-benefit and time-efficient for the researchers to obtain the optimum design with the consideration of both structural and sustainable performance. The established models exhibit excellent prediction accuracy, and the Bayesian neural network (BNN) is found to have the best performance: R2 is 0.937, MSE is 0.06 and MAE is 0.175 in shear strength prediction; R2 = 0.968, MSE is 0.040, and MAE is 0.110 in flexural capacity prediction; R2 is 0.907, MSE is 0.070, and MAE is 0.204 in shear stiffness prediction; R2 is 0.974, MSE is 0.022, and MAE is 0.063 in carbon emission prediction; and R2 is 0.977, MSE is 0.020, and MAE is 0.082 in price prediction.

Effect of Coarse Aggregate Treatment On Characteristics of Pumice and Scoria Lightweight Concretes

This study presents an experimental investigation of lightweight concretes production using typical pumice andscoria from Kelud volcano, Indonesia as coarse aggregates. Three different treatments were evaluated to obtain an effective treatment method. Method A was a combination of preheating to the temperature of 100oC and soaking for 2 hours. Method B was a direct presoaking for 3 hours and Method C was a premixing with water in the concrete mixer for 10 minutes. These methods were based on the water content of lightweight coarse aggregates tested before. The results showedthat Method A provided the highest water content compared to Methods B and C. Similarly, it also provided the most satisfying workability during concrete production. Moreover, all physical and mechanical characteristics of hardened concrete were not affected by the coarse aggregate treatment methods given. Therefore, Method A was considered an effective treatment method. Pumice and scoria lightweight concretes constituted the structural lightweight concrete withequilibrium densities in the range of 1724 kg/m3to 1837 kg/m3. The density reduction wasbetween21% and 24% sothat they can reduce the self-weight of structural element. However, the chord modulus of elasticity, the splitting tensile strength as well as the modulus of rupture was lower than the normal concrete and must be considered throughout in the structural lightweight concrete design.

CALCULATION METHOD FOR DETERMINATION OF ADHESION LEVEL OF COMPOSITE REINFORCEMENT WITH CONCRETE

The scientific work is devoted to the interaction process of concrete and composite reinforcement, which is characterized by “adhesion-slip” dependence. It is known, that composite reinforcement does not behave in the same way as traditional steel reinforcement, because in some cases their mechanical properties differ significantly. CFRP/FGRP/BFRP products have higher strength, but a lower modulus of elasticity, so direct replacement of steel with such reinforcement is not always possible according to many constructional requirements. Adhesion forces create a complex stress-strain condition in concrete interacting with reinforcement. This condition leads to the distribution of loads along the axis of reinforcement, and, as a result, the longitudinal forces on reinforcement become variable along the entire length of the rod. A detailed analysis of the existing approaches to the problem of adhesion level of concrete and composite reinforcement is performed in article. It was determined that the complex multiparameter state of the interaction of concrete and composite reinforcement is characterized by the corresponding curves of “adhesion-slip” dependence, which can be obtained by two experimental methods (beam test method and direct pull-out test method). A theoretical research of the adhesion level of concrete and composite reinforcement (beyond the limits of cracks formation) was carried out, connected with the analysis of the distribution of deformations of concrete and reinforcement along the span of the element. Current analysis is based on the determination of a number of differential equations with a step-by-step description of adhesion level problems. The results of research can be used in future during the design and calculation of concrete structures reinforced with different types of composite reinforcement (based on basalt, glass, carbon fibers etc.), however, it is necessary to conduct further experiments into the long-term operation (behavior) of composite reinforcement over time under the influence of various factors, to establish a number of rheological aspects. Keywords: adhesion, calculation, algorithm, composite reinforcement, concrete, slip.

Evaluating the use of limestone calcined clay cement and recycled concrete aggregates for reducing the carbon footprint of concrete structures

The accelerated pace of urbanization and globalisation has led to wide scale environmental impacts. Urbanization is highly dependent on new infrastructure which relies particularly on concrete as the most used building material. The cement and concrete industries have therefore become major contributors to global CO2 emissions. Hence, there is a growing need to implement sustainable alternatives to conventional concrete which have reduced equivalent carbon dioxide (eCO2) footprints, reduce the utilisation of non-renewable resources, and which still ensure the long-term performance of modern concrete structures. This paper evaluates the viability of using two alternative materials, limestone calcined clay cement (LC3) concrete and concrete produced using recycled concrete aggregates (i.e., recycled aggregate concrete or RAC) in the design of new concrete structures. Through a comprehensive literature analysis, representative values of concrete compressive strengths and eCO2 emissions released during material manufacturing and transportation were selected. Based on these selected values, a desktop study was completed, which investigated three hypothetical reinforced concrete building designs incorporating (i) concrete with natural aggregates (i.e., the control structure), (ii) LC3 concrete and (iii) RAC. In terms of sustainability, this study found that utilizing LC3 or RAC in a new building could reduce total building eCO2 emissions by up 14%. However, the extent of this reduction was found to be dependent on the quality of the material constituents and the transportation distances associated with each material constituent. Compared to LC3 concrete, the total eCO2 associated with design scenarios utilizing RAC was highly-dependent on distance between where recycled concrete aggregates were crushed and the concrete batching plant. These results provide promising evidence to evaluate the adequacy and reliability of these new sustainable materials for wide-scale applications in the construction industry.

Experimental Verification of Load-Bearing Capacity of FRP Bars under Combined Tensile and Shear Forces

In recent decades, the number of applications of fiber-reinforced polymer (FRP) reinforcement for concrete has significantly expanded. This fact is mainly due to the FRP reinforcement cost competitiveness, the increasing availability of design provisions, and due to the advantageous physical-mechanical and chemical properties of this composite material, which open up new possibilities for the design and implementation of extremely durable elements. Currently, the most commonly used types of reinforcement bars are those containing glass FRP (GFRP) or basalt FRP fibers, which is mainly the result of their favorable price and high resistance to aggressive environments. The use of composites in construction is wide-ranging: it is possible to apply FRP bars not only in the design and strengthening of concrete structures but also in the installation of shear dowels in concrete pavement, as rock bolts or as anchors for overhanging facade components. In the case of the design of load-bearing elements subjected to a combination of tensile and shear force, it is necessary to quantify their shear resistance and concisely describe the effect of the interaction of the tensile and shear force on the load-bearing capacity of the reinforcing element. This is a broadly addressed area as regards composite laminates and fabrics, but when it comes to FRP bars, there are very few available experimental results. For that reason, this research deals with the experimental testing and quantification of the influence of the interaction of normal and shear force. The behavior of GFRP bars from two different manufacturers, with three different diameters, different surface treatments, and mechanical characteristics, was experimentally verified. The findings are presented, a material failure curve is compiled, and the results are compared with those predicted according to the available relationship for composite laminates and von Mises theory.

Some Highlights on the New Version of EN 1992-1-2 (Eurocode 2, Fire Part)

Revision process of Eurocode 2 relating to concrete structural design is ready for the final step, the Formal Vote in CEN TC 250 Structural Eurocodes at the beginning of 2023. This paper summarizes the main changes and new developments presented by this revision in prEN 1992-1-2 with regard to the version currently in force. It will focus mainly in the introduction on some changes in the structure of the document and the reduction of the number of Nationally Determined Parameters (NDPs). Additionally, some changes and novelties in the properties of concrete, reinforcing and prestressing steel with temperature are commented. Another important point is the novelties in the design and verification methods (tables, simplified and advanced), focusing in the simplified methods and an analytical formulation to find the temperature in rectangular and circular cross-sections. Finally, the new approach in the treatment of concrete spalling that simplifies and clarifies the measures to avoid it and new developments in the Annexes section are discussed.

New amendment to the Code of Practice on the design of fiber-reinforced concrete structures with non-steel fibers

Introduction. The acting version of the Code of Practice on the design of fiber-reinforced concrete structures with non-steel fibers SP 297.1325800.2017 “Fiber-reinforced concrete structures and precast products with non-steel fibers. Design rules” contain no instructions for the strength calculation of circular cross-sections with and without reinforcement under the action of bending moments and longitudinal forces. In addition, the current version provides no instructions for determining the subclass index of fiber-reinforced concrete with non-steel fibers using the residual axial tensile strength, as well as those for calculating the fire resistance of fiber-reinforced concrete structures. The absence of these provisions leads to significant difficulties in the design of individual structures made of fiber-reinforced concrete, which increases material and time expenditures.Aim. To improve the system of urban planning activities in terms of clarifying and supplementing the current regulatory documents for the design of fiber-reinforced concrete structures with non-steel fibers.Methods and materials. A draft of amendment No. 2 to SP 297.1325800.2017 was developed taking into account contemporary requirements, as well as the latest scientific research. In particular, the results of the research work concerning the fire resistance of structures made of fiber-reinforced concrete with non-steel fibers, performed by the Research Institute of Concrete and Reinforced Concrete (NIIZHB) named after A.A. Gvozdev in 2020, were taken into account. In addition, the experience of the authors and design organizations, gained during the practical application of this Code of Practice, was analyzed in order to clarify its provisions for the convenience of users.Results. The results of the work involve the draft of the amendment No. 2 to SP 297.1325800.2017, whose positions include new calculation techniques, as well as the refinements of existing calculation and construction methods. The developed amendment has passed public discussions, as well as the necessary expertise, and is being prepared for approval and enactment.Conclusion. Positions of amendment No. 2 to SP 297.1325800.2017 “Fiber-reinforced concrete structures and precast products with non-steel fibers. Design rules” can be used to develop reliable design solutions for these structures, including the achievement of a certain economic effect.

Durability Design of Concrete Structures Under Reinforce-ment Corrosion

Traditionally, the durability design of concrete structures is
 based on implicit rules (minimum concrete cover, maximum
 water/cement ratio, crack width limitation, etc.). The research on
 concrete durability during the last decades has produced a reliable
 basis for information on deterioration processes. Based on this
 knowledge, it is possible to start incorporating durability in the
 design of concrete structures. Standard reliability methods were
 used to evaluate time dependent reliability of concrete structures
 under corrosion attack.