Predictive strength of ready‐mixed concrete: Exemplified using data from the Norwegian market

Engen, Morten; Hendriks, Max A.N.; Köhler, Jochen; Øverli, Jan Arve; Åldstedt, Erik; Mørtsell, Ernst; Sæter, Øyvind; Vigre, Roar

doi:10.1002/suco.201700950

Cited by 12 publications

(17 citation statements)

References 28 publications

(36 reference statements)

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“…The crack widths that are of primary interest from the experimental study and that are comparable to the characteristic crack width, w k , are the 95%‐fractile of the crack widths measured, w 0.95 , for each RC tie. To obtain this value, the statistical method of Engen et al was used to account for the uncertainty related to the limited number of section average crack width measurements for each formed crack. Generally, the mean and the variance of the crack width for a formed crack i with n i section average crack width measurements can be estimated as:

{\overset{false¯}{y}}_{i} = \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} y_{i, j,}

…”

Section: Experimental Studymentioning

confidence: 99%

Experimental and theoretical investigation of crack width calculation methods for RC ties

Tan

Eileraas

Opkvitne

et al. 2018

Structural Concrete

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This paper theoretically and experimentally investigates the semi‐empirical formulas recommended by Eurocode 2 (EC2), fib Model Code 2010 (MC2010), and Eurocode 2 with the German National Annex (DIN) for calculating crack widths in reinforced concrete. It is shown that the formulas can be derived from the principles for the idealized behavior of RC ties. However, instead of explicitly solving the resulting differential equations, the use of simplifications leads to inconsistent formulas. An experimental study was carried out involving the testing of eight RC ties to discover the modeling uncertainty of the formulas. It was found that EC2 substantially overestimated the crack widths for the RC ties. MC2010 and DIN seemed to predict the crack widths better, but gave rather a large number of nonconservative crack width predictions. These experimental results, combined with the theoretical study, suggest that a more consistent calculation model should be formulated by explicitly solving the resulting differential equation.

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{\overset{false¯}{y}}_{i} = \frac{1}{n_{i}} \sum_{j = 1}^{n_{i}} y_{i, j,}

…”

Section: Experimental Studymentioning

confidence: 99%

Experimental and theoretical investigation of crack width calculation methods for RC ties

Tan

Eileraas

Opkvitne

et al. 2018

Structural Concrete

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“…A typical value applicable to different strength classes was used for the concrete cylinder strength. The V may seem slightly high compared to the results reported by, say, [25], but may be realistic in the case of a deteriorated structure. Furthermore, a sensitivity study by one of the authors [15] showed only a minor influence of Young's modulus on the anchorage capacity.…”

Section: Geometric and Physical Uncertaintymentioning

confidence: 55%

Partial safety factors for the anchorage capacity of corroded reinforcement bars in concrete

Blomfors

Ivanov

Honfí

et al. 2019

Engineering Structures

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al (2018) Partial safety factors for the anchorage capacity of corroded reinforcement bars in concrete Engineering Structures, 181: 579-588 http://dx. ABSTRACTMany reinforced concrete bridges in Europe and around the world are damaged by reinforcement corrosion and the annual maintenance costs are enormous. It is therefore important to develop reliable methods to assess the structural capacity of corroded reinforced concrete structures and avoid unnecessary maintenance costs. Although there are advanced models for determining the load carrying capacity of structures, it is not obvious how they should be used to verify the performance of existing structures. To confidently assess the bond of corroded reinforcement in concrete, for example, the calculation model must give a sufficient safety margin. When designing new structures, semi-probabilistic approaches (such as the partial safety factor method) are adopted to achieve the target reliabilities specified in structural design codes. This paper uses probabilistic methods to develop partial factors for application in an existing bond model, to assess the safety of corroded reinforced concrete structures. The response of the bond model was studied using Monte Carlo (MC) simulations for several design cases, with probability distributions fitted to the results. Partial factors were then derived, based on these distributions. Furthermore, an MC-based simulation technique called "importance sampling" was used to study the reliability of several deterministic bond assessments conducted using these partial factors. The results show that deterministic assessments which use the proposed partial factors lead to a safety level at least equal to the target value. The results presented in this paper will support the assessment of reinforced concrete structures with anchorage problems and give a reasonable approximation of the anchorage capacity with sufficient safety margin. When generalised to cover other failure modes and structural configurations, this will enable better utilisation of damaged structures and lead to major environmental and economical savings for society. 1.

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“…Note that in the literature, usually only one experimental outcome is reported for each experimental setup, such that in Table 1,

m_{i} = m = 1

, and the generalized estimator in Equation () takes the form in Equation (). There are, however, examples of experimental campaigns being repeated by independent researchers.

θ_{ik} = {(\frac{R_{\exp}}{R_{NLFEA, k}})}_{i}

When Equation () is used, the contributions to the estimate from within‐ and between‐model uncertainty can be quantified by following a hierarchical approach as suggested by 6 …”

Section: Quantification Of the Modelling Uncertaintymentioning

confidence: 99%

“…It can be shown that

y

can be represented by a

t

‐distributed random variable with expected value and variance given in Equations () and (), where

ν_{k} = n_{k} - 1

are the degrees of freedom. See for example 6 for derivations. The mean and coefficient of variation of

θ

can be estimated from Equations () and (), where the errors of approximation in Equations () and () are <2% for

V_{θ_{k}} < 0.2 .

μ_{{normaly}_{k}} = normalE ([], y_{k}) = {\overset{true¯}{y}}_{k}

σ_{{normaly}_{k}}^{2} = VAR ([], y_{k}) = \frac{ν_{k} ((), ν_{k} + 2)}{((), ν_{k} - 2) ((), ν_{k} + 1)} s_{k}^{2}

μ_{θ_{k}} = normalE ([], θ_{k}) \approx \exp {\overset{true¯}{y}}_{k}

V_{θ_{k}} \approx \sqrt{VAR ([], y_{k})} = s_{k} \sqrt{\frac{ν_{k} (ν_{k} + 2)}{(ν_{k} - 2) (ν_{k} + 1)}}

The effect of the degrees of freedom, that is, the number of observations or the decreasing statistical uncertainty, on the ratio between the calculated standard deviation

σ_{y}

and the sample standard deviation

...

…”

Section: Quantification Of the Modelling Uncertaintymentioning

confidence: 99%

“…See for example 6 for derivations. The mean and coefficient of variation of

θ

can be estimated from Equations () and (), where the errors of approximation in Equations () and () are <2% for

V_{θ_{k}} < 0.2 .

μ_{{normaly}_{k}} = normalE ([], y_{k}) = {\overset{true¯}{y}}_{k}

σ_{{normaly}_{k}}^{2} = VAR ([], y_{k}) = \frac{ν_{k} ((), ν_{k} + 2)}{((), ν_{k} - 2) ((), ν_{k} + 1)} s_{k}^{2}

μ_{θ_{k}} = normalE ([], θ_{k}) \approx \exp {\overset{true¯}{y}}_{k}

V_{θ_{k}} \approx \sqrt{VAR ([], y_{k})} = s_{k} \sqrt{\frac{ν_{k} (ν_{k} + 2)}{(ν_{k} - 2) (ν_{k} + 1)}}

The effect of the degrees of freedom, that is, the number of observations or the decreasing statistical uncertainty, on the ratio between the calculated standard deviation

σ_{y}

and the sample standard deviation

s_{y}

is shown in Figure 2. Since the statistical uncertainty is significant if the estimate is based on a low number of observations, the resulting coefficient of variation should always be estimated using Equation ().…”

Section: Quantification Of the Modelling Uncertaintymentioning

confidence: 99%

See 1 more Smart Citation

Treatment of modelling uncertainty of NLFEA in fib Model Code 2020

Engen

Hendriks

Monti

et al. 2021

Structural Concrete

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When non‐linear finite element analyses are used in design of new or assessment of existing concrete structures, one should account for the modelling uncertainty before conclusions are drawn based on the results. The present article describes the basis for how this topic is treated in the draft of fib Model Code 2020. There are two components of the modelling uncertainty: (i) within‐model, and (ii) between‐model. The within‐model uncertainty was estimated from a range of series of benchmark analyses gathered from the literature. Each series was assumed analyzed in a consistent manner, termed as the solution strategy. The main result for the within‐model component, is a set of prior parameters for Bayesian updating. In an application setting, the prior parameters should be updated after validating the selected solution strategy with a suite of relevant benchmark analyses, before using the mean and coefficient of variation in the Global Factor Method or calculating the modelling uncertainty factor γRd to be used in the Partial Factors Method. Finally, results from blind‐prediction competitions were studied. With the present data, it cannot be concluded that a‐priori knowledge of the experimental outcome reduces the uncertainty in the prediction. Hence, there is no need for compensating for this effect by a separate partial factor.

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Predictive strength of ready‐mixed concrete: Exemplified using data from the Norwegian market

Cited by 12 publications

References 28 publications

Experimental and theoretical investigation of crack width calculation methods for RC ties

Experimental and theoretical investigation of crack width calculation methods for RC ties

Partial safety factors for the anchorage capacity of corroded reinforcement bars in concrete

Treatment of modelling uncertainty of NLFEA in fib Model Code 2020

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