Semi-probabilistic Approach Research Articles

Uncertainties in resistance models for sound and corrosion-damaged RC structures according to EN 1992-1-1

Resistance of civil engineering structures is primarily dependent on material properties, geometry and uncertainties related to an applied model. While materials and geometry can be relatively well described, the resistance model uncertainty is not yet well understood. The present paper improves the general concept for the model uncertainty from the Probabilistic model code of the Joint Committee on Structural Safety. Influences affecting results obtained by tests and models and effects of actual structural conditions are overviewed. Statistical characteristics of the uncertainties in resistance of reinforced concrete members are then provided considering simple engineering formulas based on EN 1992-1-1 models and effects of deterioration. To facilitate practical applications the partial factors for the model uncertainties are derived using a semi-probabilistic approach. It appears that the model uncertainties are substantial for shear resistances while they are less significant for the well-established models used for bending resistance and axial compression without buckling. Uncertainty in test procedures seems to be less important in common cases. The effect of the resistance uncertainties on structural reliability seems to be more significant for corrosion-damaged structures than for sound structures. Consequently the quantification of the model uncertainties is a key issue when assessing corrosion-damaged reinforced concrete structures. Further research should be focused on model uncertainties related to the models for shear and corrosion-damaged structures considering the fib Model Code 2010.

Sensitivity analysis for setting up the investigation protocol and defining proper confidence factors for masonry buildings

At present, the codified procedures for the seismic assessment of existing structures do not consider explicitly the use of sensitivity analysis that, on the contrary, is an essential tool due to the intrinsic and epistemic uncertainties involved. In particular, results of a sensitivity analysis allow, on one hand, to optimize the plan of investigations and tests, limiting it to what is really useful, and, on the other hand, to be aware of the propagation of uncertainties in the final outcome of the assessment. The paper proposes how to implement the sensitivity analysis in a systemic way, in order to define proper confidence factors, which are used within the semi-probabilistic approach of the performance-based assessment procedure. In relation to the procedures adopted by current standards, this method is aimed to overcome the following drawbacks: (1) the a priori definition of values for the confidence factor; (2) the a priori selection of parameters to which confidence factor has to be applied; (3) the weak connection between investigation and assessment. Despite the generality of most aspects of the proposed procedure, main attention is given in the paper to its application in the case of masonry existing buildings and, in particular, of those with a significant cultural value, where the minimization of invasiveness of investigations on the construction together with that of costs plays a crucial role for the aim of conservation.

Safety examination of existing concrete structures using the global resistance safety factor concept

Current design procedures for structural concrete elements are based on member level (or local) safety checks, in the sense that the safety condition is evaluated at each cross-section individually. In the examination of existing structures, the exploitation of the redundancy of the structural system and its redistribution capacity may prove necessary to fulfil the safety requirements, demanding for a system level (or global) safety evaluation. This can be achieved using nonlinear finite element analysis (NLFEA) procedures and requires a safety format different than that based on partial safety factors.In this work, a simple safety format tailored for NLFEA of existing structures is described. It is shown how to define a global resistance safety factor based on a simple semi-probabilistic approach in line with the recommendations of the new Swiss standards for existing structures [1,2] that can capture the sensitiveness of the structural system resistance, R, to the random variation of the input variables. Besides enabling the use of updated information regarding the material properties, the proposed procedure allows performing reliability differentiation based on risk analysis, being therefore suitable for the safety examination of existing bridges.The definition of the semi-probabilistic global resistance safety factor is based on the assumption of a log-normal probability density function for the resistance R and on an estimate of its coefficient of variation, vR. The existing proposals for estimating vR are reviewed and compared. For statically determined structures with a single dominant failure mode (axial compression, bending or shear) the examination values of R computed with global resistance safety factors are shown to compare well with those obtained with partial safety factors. The reliability of the examination values of R is also evaluated through a comparison with the Monte Carlo simulation procedure and it is shown that the global resistance safety factor method is sufficiently accurate. Finally, a case-study is presented illustrating the application of the proposed procedure in the structural safety examination of an existing prestressed concrete bridge.

Safety factors for the structural design of glass

The safety verification of glass structures is usually made on the basis of a deterministic approach, without assessing the underlying probability of collapse. In this article, we propose to use the semi- probabilistic method in the limit-state design of glass structures by presenting properly-calibrated values of the partial safety factors of material strength, so as to obtain a probability of failure compatible with the target values indicated for each class of consequence by Eurocode 1 (EN 1990).Starting from a micromechanically-motivated model of fracture propagation, typically used for brittle materials, experimental results conducted in a previous campaign have been interpreted using the Weibull statistical distribution, taking into account that size-effect, type of stress (e.g., uniaxial vs. bi-axial) and the insidious phenomenon of subcritical crack growth (static fatigue due to fracture growth in time without increase of load) can affect the probability of failure. Actions like wind, snow and live (anthropic) loads have been modeled using the statistical distributions recommended in international structural codes. Then, the probabilistic method of level III has been applied for the verification of paradigmatic case studies, which have served to calibrate the partial safety factors to be used in the semi-probabilistic approach. A novelty, to our knowledge, is the proposal of a multiplication coefficient for the partial safety factor of material strength, instead that for the factors of loads, to distinguish in the verification the different classes of consequences, each one characterized by the probability threshold of collapse. The results of this study will furnish the basis for the design of glass structures according to the general performance requirements established by EN 1990.

Assessment of Bridges on the Swiss National Roads

The main strategic goal in the assessment of the existing Swiss national road network is to provide a high level of availability of the roads for traffic and reduce interferences caused by construction or repair works. Therefore, renovation works tend to be executed in large maintenance sections for which the complete infrastructure is repaired in order to ensure a period of 15 years without the need for additional construction works. Before 2008, the existing bridges were maintained mostly individually under the responsibility of local cantonal administrations. Entering into the new maintenance strategy requires a careful assessment of the structural conditions. Visual inspections and laboratory testing programs are required in order to bring the structural condition of different structures to a similar level and to fulfil all standards as long as costs are not disproportional to the benefits. Structural safety is evaluated according to the new Swiss code for existing structures, SIA 269, which was published in 2011. For typical short span bridges and overpasses from the early 1970s, which represent the largest number of existing objects, focus has to be set on the shear verifications of slabs without stirrups as well as on the bending capacity of cantilever slabs. Within the structural assessment, actions, material properties, geometrical properties and structural models shall be updated. Partial safety factors can also be updated by means of semi or full probabilistic approaches, in order to verify structural safety.

Stormwater Tank Performance: Design and Management Criteria for Capture Tanks Using a Continuous Simulation and a Semi-Probabilistic Analytical Approach

Stormwater tank performance significantly depends on management practices. This paper proposes a procedure to assess tank efficiency in terms of volume and pollutant concentration using four different capture tank management protocols. The comparison of the efficiency results reveals that, as expected, a combined bypass—stormwater tank system achieves better results than a tank alone. The management practices tested for the tank-only systems provide notably different efficiency results. The practice of immediately emptying after the end of the event exhibits significant levels of efficiency and operational advantages. All other configurations exhibit either significant operational problems or very low performances. The continuous simulation and semi-probabilistic approach for the best tank management practice are compared. The semi-probabilistic approach is based on a Weibull probabilistic model of the main characteristics of the rainfall process. Following this approach, efficiency indexes were established. The comparison with continuous simulations shows the reliability of the probabilistic approach even if this last is certainly very site sensitive.

Verification of existing reinforced concrete bridges using the semi-probabilistic approach

At present existing bridges are mostly verified using simplified deterministic procedures. Application of the partial factors recommended for the design of construction works often yields conservative results and may lead to expensive repairs. More realistic verification of actual performance can be achieved using partial factors based on the semi-probabilistic approach in accordance with EN 1990 and ISO 2394. This method is easy to use and yet yields a well-balanced structural reliability. The present study intends to clarify applications of the semi-probabilistic approach in verifications of existing reinforced concrete bridges. Numerical examples supplement general procedures and illustrate how the design values and partial factors can be derived for different target reliability levels and remaining working lives.

A Simple Durability Design Method for Carbonation-induced Corrosion

The present work aims at providing a simple semi-probabilistic approach to service life design of reinforced concrete structures, in what concerns reinforcement corrosion induced by concrete carbonation. An analytical model for the initiation period, using as input parameters the accelerated carbonation resistance and the environmental class, is presented. A maximum accepted level of deterioration and reliability indexes are defined. The corresponding partial safety factors are derived from a full probabilistic approach. The performance of the proposed method is compared with that of a reference method (E 465).

Semi-probabilistic approach for assessment of the requirement for minimum hull girder section modulus

The paper presents a study on an approximate semi-probabilistic approach for assessment of any given requirement for minimum hull girder section modulus (HGSM). It consists of calculating the HGSM using as input data the reduced (due to corrosion) plates’ thicknesses and longitudinals’ cross-sections with exactly the same probability of exceedance. Its accuracy is checked against results obtained by the complete probabilistic approach developed by the author. In this paper, the requirement for minimum HGSM is based on the IMO (International Maritime Organization)-formulated permissible reduction by 10% of the as-built HGSM. A numerical example is given for a bulk carrier of 25,000 deadweight ton (25K DWT). A comparison between the results obtained by the complete probabilistic method and those obtained by the semi-probabilistic method showed that the accuracy of the semi-probabilistic method is around +8% when the 95th percentile of the corrosion wastage of plates and longitudinals is used, and around −2% when the 99th percentile of the corrosion wastage of plates and longitudinals is used. The semi-probabilistic approach is simpler than the complete probabilistic approach but has relatively high accuracy, especially for higher-order percentiles, and thus is recommended for practical use.

A method for the use of accelerated carbonation tests in durability design

This work aims to provide a simple semi-probabilistic approach to the service life design of reinforced concrete structures with respect to reinforcement corrosion induced by concrete carbonation.This paper presents an analytical model for the initiation period, calibrated with long-term carbonation results, which uses the accelerated carbonation resistance and the environmental class as input parameters. The issue of defining a limit for deterioration is discussed and a maximum accepted level of deterioration and reliability indexes are defined. The corresponding partial safety factors are derived from a full probabilistic approach. The performance of the proposed method is compared with that proposed on the fib Model Code for Service Life Design.

Comparative assessment of load–resistance factor design of FRP-reinforced cross sections

In the last decades, codes have implemented the load–resistance factor design (LRFD) approach to achieve a certain safety level in structural sections. Recently, the same philosophy established in the case of steel bars was adapted for reinforcement by innovative materials such as fiber-reinforced polymers (FRPs). LRFD is claimed to be a semi-probabilistic approach, although the implied safety is not intelligible by practitioners, being hidden into the so-called safety factors (SFs) prescribed by codes, which should account for load- and strength-affecting heterogeneities. Often, especially in the case of FRP reinforcement, the SFs differ from one code to another because of the format of the design equations. The objective of the simple study presented in the paper is to compare the safety levels, expressed in terms of conventional probability of failure, for different codes at the state-of-the art with respect to the design of FRP-reinforced concrete worldwide. The purpose is to investigate how the different equation formats, design values of material properties, and partial safety factors, affect the implicit design safety and whether it is similar among international guidelines. The study considers design of cross sections in bending at the ultimate limit state according to: ACI 440.1R-06 (US guidelines), CAN/CSA-S806-02 (Canadian guidelines), and CNR-DT 203/2006 (Italian guidelines, for which sensitivity of design to SFs is also investigated). For comparison purposes, design of steel-reinforced sections is considered according to the recent Italian regulations. Results indicate that reliability indices achieved with design procedures are generally comparable among the considered codes, and larger than that referring to steel reinforcement.

A study on reliability-based inspection planning – Application to deck plate thickness measurement of aging tankers

In order to conduct a timely and effective inspection to avoid the ultimate failure of deck plate, a reliability-based procedure for inspection planning is introduced. A review of the uncertainties in deriving the capacity of deck plate and through life degradation effects on tanker structural integrity is given. Using the Latin Hypercube sampling method to perform the Monte Carlo Simulation, the time-variant failure probabilities of deck plate are computed, then compared with target values. Based on the comparison, the time for thickness measurement of deck plate is predicted. A total of 1080 cases for nine sample tankers are analyzed to illustrate the procedure, including sensitivity and parametric studies. This paper is a sequel to the preceding paper [6], where a semi-probabilistic approach is presented to assess the time-variant ultimate strength of aging tanker’s deck plate considering corrosion wastage.

Assessment of dune failure along the Dutch coast using a fully probabilistic approach

This paper describes an investigation into the added value of a fully probabilistic approach to dune resilience assessment over the currently applied deterministic and semi-probabilistic approaches. The method is applied to the Dutch coast but is generically applicable, provided of course the sufficient availability of data. The DUROS+ model in its most basic form was used to quantitatively assess dune resilience. The Monte Carlo method was used for the probabilistic investigation. Important research questions were (1) where can the DUROS+ model in combination with the fully probabilistic approach be applied along the Dutch coast? and (2) what is the alongshore variability of failure probability using this probabilistic approach?The main conclusion of the work presented in this paper is that the fully probabilistic approach provides valuable added insight with respect to the actual failure probability of transects. At the same time it is noted that the current dune erosion model in its most basic form is not able to cover all of the Dutch coast. Reasons lie in the availability of sufficient quality boundary conditions, applicability limits associated with model assumptions and insufficient quality coastal profile information.To extend the coverage of the analysis of failure probabilities along the Dutch coast it is recommended (1) to involve more process-based model concepts that can cope with the situations DUROS+ cannot, and (2) to expand currently available data on boundary conditions.

Post-production Losses in Iodine Concentration of Salt Hamper the Control of Iodine Deficiency Disorders: A Case Study in Northern Ethiopia

Iodine is essential for good function of the thyroid, and its deficiency is of public-health importance in Ethiopia. Iodization of salt is an effective and sustainable strategy to prevent and control iodine deficiency in large populations. The effectiveness of salt-iodization programmes depends on the conservation of iodine concentration in salt at various stages of the supply-chain. The overall objective of the study was to assess the loss of iodine in salt from production to consumption and to estimate the proportion of adults, especially pregnant women, at risk of dietary iodine insufficiency. A cross-sectional study was conducted during February-April 2007 in northern Ethiopia. Iodine concentrations of salt samples from producers (n=41), retailers (n=7), and consumers (n=32) were determined using iodiometric titration. A risk assessment was conducted for dietary iodine insufficiency among adults, including pregnant women, using a semi-probabilistic approach. The concentration of iodine in the sampled salts decreased by 57% from the production site to the consumers. The assessment of exposure showed that adults in 63% (n=20) of the households, including 90% (n=29) with pregnant women, were at risk of insufficient iodine intake. A monitoring and evaluation system needs to be established to ensure adequate supply of iodine along the distribution chain. Special attention is needed for the retailers and consumers. At these levels, dissemination of information regarding proper storage and handling of iodized salt is necessary to address the reported loss of iodine from salt.

Basic concept of the factor of safety in marine structures

The basic elements involved in the determination of the factor of safety commonly used in preliminary design procedures of marine structures are outlined. The main factors affecting the magnitude of the factor of safety are highlighted. Probabilistic and semi-probabilistic approaches are briefly presented. The general equation and the main variables affecting the total safety factor are given. The different approaches used for the determination of the partial factors of safety are discussed and supported by numerical examples. Particular emphasis is placed on the characteristic and design value approaches. The variation of the factor of safety with time is illustrated. The effect of corrosion on the deterioration of the factor of safety is highlighted. The impact of the magnitude of the total factor of safety on the total life cost of the marine structure is clarified.

Simple Method for the Design of Jet Grouted Umbrellas in Tunneling

Tunnel excavation in cohesionless soils implies the use of a temporary supporting structure prior to lining installation. This temporary structure has to couple safety and economy, and can be conveniently realized using ground improvement techniques (for instance, by creating an arch of partially overlapped subhorizontal jet grouted columns). The adoption of ground improvement techniques results in structures far from having a perfect shape because they are intrinsically affected by defects (in both geometrical and mechanical characteristics), and therefore their design may hide unforeseen risks. As a consequence, this is the typical case in which sophisticated numerical analyses may just give the illusion of being refined, if possible defects are not correctly taken into account. In this paper a simple yet rational analytical method for the design of a nonclosed tunnel supporting structure that may be of some help to this aim is presented. It is done with reference to a simple two-dimensional scheme. In the first part of the paper, a design chart of optimal shape and minimum structural thickness of the cross section of the supporting structure is shown. In the second part, an iterative procedure to verify the stability or to design the minimum structural thickness of an existing supporting structure with a predefined shape is described. This method, coupled with the analysis of structural demand, allows one in principle to plot design charts. This approach can easily take into account structural defects with a semiprobabilistic approach and therefore with a chosen risk level, which is of great help to the designer at least in a preliminary design stage. The proposed semiprobabilistic procedure is applied to the case of a temporary supporting structure realized by partially overlapped subhorizontal jet grouted columns, intrinsically affected by defects in diameter and position. The variability of these geometrical parameters was considered based on the large quantity of experimental evidence collected in field trials by the writers and published elsewhere.

Framework for Durability-Based Design for Concrete-Steel Bond against Corrosion

The current understanding of the mechanics of bond resistance at the interface between concrete and plain and deformed steel bars is reviewed briefly along with the influence of corrosion on the phenomenon. Some of the available research on analytical models in both corroded and uncorroded steel bars is also reviewed. The influence of some of the significant parameters influencing the behavior of corroded bars, such as the concrete strength, crack width, extent of rebar corrosion (measured by mass loss), concrete cover thickness, bar diameter, and the loss of rebar lugs is reviewed. In addition, a preliminary framework is presented for design of reinforced concrete for durability against deterioration of bond due to steel rebar corrosion. A framework for design of structural concrete for durability against deterioration of bond at the steel-concrete interface due to corrosion of rebars is proposed. The technical note also stresses the need for more research on the above and other parameters influencing the deterioration of bond due to corrosion, before establishing a reliable design method using a semiprobabilistic approach in the design of structural concrete for other phenomena.

Proposal of a semi-probabilistic approach for storage facility design

Storage facilities are key devices in mitigating the urban drainage impact on receiving water bodies, but their design is still affected by high uncertainty. The analytical-probabilistic approach has recently raised interest, because the facility performances are directly related to probability. Starting from statistically independent storm events, distributions of the meteorological variables must be fitted. Rainfall series, recorded in three Italian raingauges, were examined for appraising two main concerns: the choice of proper probability distributions for rainfall volume and the sample sensitivity with respect to the analysis criterion. The analytical derivation of the model is then finally discussed.

Time-varying ultimate strength of aging tanker deck plate considering corrosion effect

This paper presents a semi-probabilistic approach to assess the time-varying ultimate strength of aging tanker's deck plate considering corrosion wastage. The procedure includes (1) defining the limit state function of deck plate failure, (2) determining the time-varying probability density function of corrosion wastage and values for selected severity levels of corrosion, (3) calculating the time-varying ultimate strength of deck plates corresponding to the selected levels of corrosion wastage, (4) determining the time-varying maximum nominal stress, (5) calculating when the deck plate reaches the ultimate strength limit state, and (6) determining the inspection intervals based on the risk of ultimate strength failure. A nonlinear corrosion model was proposed for deriving the time-varying probability density function of deck plates' corrosion wastage. The probability density function was determined based on a statistical analysis of the American Bureau of Shipping (ABS) corrosion wastage database [Wang G, Spencer J, Sun HH. Assessment of Corrosion Risks to Aging Oil Tankers In: 22nd International Conference on Offshore Mechanics and Arctic Engineering, Cancun, Mexico, 8–13 June 2002]. To simplify the calculations of ultimate strength, a semi-probabilistic model was adopted. Three levels of corrosion severity were considered, and the corresponding values of corrosion wastage were used instead of the probability density function. The increasing nominal stresses as ships age were also taken into account considering the loss of global hull girder section modulus. The loads of still-water-induced and wave-induced bending moments were treated as deterministic values. The ultimate strength calculation was based on the latest International Association of Classification Societies (IACS) – Common Structure Rule (CSR) formula [Common Structural Rules for Double Hull Oil Tankers, http://www.iacs.org.uk/; 2007]. Deck failure was defined as deck plate's ultimate strength becoming lower than the maximum nominal stress. An inspection should be conducted before such failure takes place. A total of nine sample tankers, designed in 1970s, 1980s and 1990s were selected for demonstrating this approach. Time to deck plate's failure by ultimate strength varies in a wide range depending on the initial designs and corrosion severity at both local plate and global hull girder levels.

A semi-probabilistic approach to the design of jet grouted umbrellas in tunnelling

A possible approach is shown for the design of jet grouted umbrellas, which are often used as temporary supports in tunnelling practice. In the current paper it is argued that such an approach should be probabilistic or semi-probabilistic. Based on published experimental data and statistical analyses of diameter and centroid position along the axis of jet grouted columns, a series of Monte Carlo simulations were carried out to find the influence of possible defects within the column in the umbrella static performance, with reference to two extreme subsoil conditions: clay and sand. Geometrical considerations on the minimum overlapping among columns necessary for continuity on the whole span of the umbrella are drawn. It is shown that, owing to defects, the real shape of jet grouted umbrellas is not that of a regular frustum of cone. It is also shown that overlapping decreases along the span. There is a critical length after which structural continuity is diffi- cult to obtain, depending on the statistical characteristics of the jet grouted columns. Defects in axis orientation have a significant effect on this critical length. Static conditions are also analysed, assuming a simplified two-dimensional arch scheme, with reference to the part of the umbrella in which continuity is guaranteed with the assumed level of confidence (95%). The minimum average thickness of the jet grouted umbrella necessary for equilibrium is found, which generally increases as the umbrella opens up along its axis. By combining geometric and static considerations, a simple yet conservative criterion to plan the number of layers of jet columns, their spacing and minimum required diameter—and therefore their initial overlapping—for the design of tunnelling supporting umbrellas is then proposed. Une méthode possible est démontrée pour l'étude de couvertures scellées par jet, utilisées fréquemment comme supports provisoires dans l'exécution de souterrains. On soutient, dans la présente communication, que cette méthode devrait être probabiliste ou semi-probabiliste. Sur la base de données expérimentales publiées et d'analyses statistiques du diamètre et de la position centroïde le long de l'axe des colonnes scellées par jet, on effectué une série de simulations de Monte-Carlo pour établir l'influence de défauts é ventuels au sein de la colonne sur les performances statiques de la couverture, relativement à deux types de sous-sol extrêmes: l'argile et le sable. On en tire des considérations géométriques sur le chevauchement minimum entre les colonnes, nécessaire pour assurer la continuité sur l'intégralité de la portée de la couverture. On démontre qu'en raison des défauts, la forme effective des couvertures scellées par jet n'est pas celle d'un cône tronqué normal. On démontre é galement que le chevauchement diminue le long de la portée. Il existe une longueur critique au-delà de laquelle il est difficile d'obtenir une continuité structurelle, en fonction des caractéristiques statistiques des colonnes scellées par jet. Les défauts dans l'orientation des axes ont un effet significatif sur cette longueur critique. Ont analyse é galement les conditions statiques, en supposant la présence d'une arche bidimensionnelle simplifiée, relativement à la partie de la couverture dans laquelle la continuité est garantie avec le niveau d'assurance (95%). L'épaisseur moyenne minimale de la couverture scellée par jet, nécessaire pour l'équilibre, est déterminée, et augmente généralement au fur et à mesure de l'ouverture de la couverture le long de son axe. Enfin, en alliant des considérations géométriques et statiques, on propose un critère à la fois simple et modeste pour planifier le nombre de colonnes à jet, leur espacement et le diamètre minimum requis – et, par conséquent, leur chevauchement initial – pour l'étude de couvertures de soutien pour la construction de tunnels.