My title https://doi.org/10.14311/APP.2022.36.0206 Acta Polytechnica CTU Proceedings 36:206–215, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague PROBABILISTIC MODELS FOR RESISTANCE VARIABLES IN fib MODEL CODE 2020 FOR DESIGN AND ASSESSMENT Miroslav Sýkoraa, ∗, Wouter Botteb, Robby Caspeeleb, Dimitris Diamantidisc, Aurelio Muttonid, Raphaël D. J. M. Steenbergenb, e a Czech Technical University in Prague, Klokner Institute, Šolínova 7, 166 08 Prague, Czech Republic b Ghent University, Faculty of Engineering and Architecture, Department of Structural Engineering and Building Materials, Technologiepark-Zwijnaarde 60, 9052 Zwijnaarde, Belgium c OTH Regensburg, Faculty of Civil Engineering, Galgenbergstrasse 30, 93053 Regensburg, Germany d École Polytechnique Fédérale de Lausanne, School of Architecture, Civil and Environmental Engineering, Station 18, CH-1015 Lausanne, Switzerland e TNO Delft, Department of Structural Reliability, P.O. Box 155, NL-2600 AD Delft, Netherlands ∗ corresponding author: miroslav.sykora@cvut.cz Abstract. The fib Model Code offers pre-normative guidance based on the synthesis of international research, industry and engineering expertise. Its new edition (draft MC 2020) will bring together coherent knowledge and experience for both the design of new concrete structures and the assessment of existing concrete structures. This contribution presents an overview of the main developments related to the partial factors for materials. In the draft MC2020, the partial factors are presented in tables for clusters of cases depending on consequence classes and variability of basic variables. Furthermore, formulas and background information are provided to facilitate updating of the partial factors. This contribution discusses the different assumptions adopted in MC 2020 for design and assessment. Main changes with respect to the previous version are related to description of the difference between in-situ concrete strength and the material strength measured on control specimens, and to modelling of geometrical variables. The presented comparison of the requirements imposed by Eurocodes and MC 2020 for design reveals insignificant differences. The assessment requirements may be decreased by about 25% when the conditions specified in MC 2020 are satisfied. Hence, the revised MC 2020 will provide designers and code makers with wider possibilities to utilise actual data and long-term experience in assessments of existing structures. Keywords: Assessment of existing concrete structures, Eurocodes, fib Model Code 2020, partial factors, probabilistic models, reliability, updating. 1. Introduction fib (International Federation for Structural Concrete) has been systematically revising its flagship document - fib Model Code (MC). The MC offers pre-normative guidance, synthesis of international research with in- dustry and engineering expertise, and advanced tools for international code writers as well as industry prac- titioners. The main aspiration of its new edition (draft MC 2020) is to bring together coherent knowledge and experience for both design and assessment and to pro- vide a single code for both new and existing concrete structures [1]. The fib MC serves as a pre-standard, in- tended to provide the basis for development of future Eurocodes and other international standards. Under fib Commission 3 Existing Concrete Struc- tures, Task Group 3.1 is drafting the MC 2020 sections on: • Reliability requirements (target reliability levels for various limit states in design and assessment and different consequence classes) and • The partial factor method for design and assess- ment. This contribution presents an overview of the main developments related to the latter topic, focusing on resistances. It is demonstrated that the revised MC 2020 should provide designers and code makers with wider possibilities to utilise actual data and long- term experience in the assessment of existing concrete structures. 2. Probabilistic models for resistances 2.1. General The draft MC 2020 section on the partial factor method is focused on the analysis of basic structural elements such as beams, slabs and columns through simplified (analytical) models. The safety formats 206 https://doi.org/10.14311/APP.2022.36.0206 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 36/2022 Probability of fib Model Code 2020 resistance variables fc on control specimens Vfc = 0.1 Conversion factor for in-situ cast concrete (μη = 0.95, Vη = 0.12) Concrete section area (μa ≈ 1 and Va ≈ 0.04) DESIGN Resistance model uncertainty – column crushing (μθR = 1.02, VθR = 0.07) fc in-situ Vfc,is = 0.08 or 0.15fc in-situ Vfc,is = 0.08 or 0.15 Concrete section area (μa ≈ 1 and Va ≈ 0.01) Concrete section area (μa ≈ 1 and Va ≈ 0.01) ASSESSMENTASSESSMENT Resistance model uncertainty – column crushing (μθR = 1.02, VθR = 0.07) Figure 1. Basic variables considered in resistance model for short columns in design and assessment situations. to be applied in conjunction with advance numeri- cal models are also addressed by MC 2020 but they remain beyond the scope of this contribution. MC 2020 emphasises the importance of updating of the models applied in reliability verifications consider- ing all available information about the structure. How- ever, to assist routine applications, the Model Code also provides the conventional probabilistic models for parameters of resistances and load effects considered to be applicable for common reinforced concrete (RC) structures with a reasonable level of approximation. These conventional models are mostly based on the probabilistic models assumed in the background docu- ment to the revised prEN 1992-1-1:2021 for design and assessment of concrete structures [3] and they are con- sistent with those provided by the JCSS Probabilistic Model Code [4], and with the recommendations of fib bulletin 80 [5]. Focusing on non-deteriorated RC structures, the flexural resistance of members and the resistance of short columns under compression, R, are obtained as the product of a resistance model uncertainty, θR, geometrical property, a, and of material strength, f : R ≈ constant × θR × a × f (1) where the strength f can cover the factor, η, ac- counting mainly for the difference between the com- pressive concrete strength measured on control spec- imens (fc) and the in-situ strength (fc,is), and then fc,is ≈ η × fc. The resistance R is assumed to be lognormally distributed. It is assumed that reinforcement properties are gov- erning bending failures whereas concrete compres- sive strength dominates in compressive crushing of columns without significant second order effects. Fig- ure 1 shows the basic variables considered in the re- sistance model for short columns in design and assess- ment situations. The flexural resistance, dominated by reinforcement yielding, is described in a similar way. Table 1 provides the probabilistic models for resis- tance parameters considered in MC 2020. µ denotes the bias of a variable - systematic deviation of random values of the variable from its characteristic (nominal) value, considered as the ratio of mean to characteristic (nominal) value; V is a coefficient of variation. 2.2. Material properties The models for concrete strengths, fc and fc, is, and the conversion factor, η, provided in Table 1 are re- lated to ordinary strength concretes (cylinder concrete strengths approximately up to 100 MPa) and stan- dard quality related to in-situ cast RC structures. For high-strength or precast concretes or other than standard execution quality, other models may apply [6]. The coefficient of variation (CoV) of concrete strength commonly decreases with increasing mean strength; see also [7]. For instance, Torrenti and Dehn [8] proposed for in-situ cast concrete: Vf c ≈ 0.1 × (fc/40 MPa)3/2 (2) The value of µη in Table 1 represents concretes in tops of columns; for other governing regions the bias may be increased to 1.0 or up to 1.05 for bottoms of columns. Similarly, for smaller members (h < 450 mm) lower biases µη = 0.95 may be considered while 207 M. Sýkora, W. Botte, R. Caspeele et al. Acta Polytechnica CTU Proceedings Basic variable X Situation Dist. Bias µX Coeff. of variation VX Note Concrete compressive strength measured on control specimens (in-situ cast concrete), fc Design LN exp(1.645Vf c)= 1.18 0.1 µf c = 1.10 and Vf c = 0.06 could be considered for precast concrete. Concrete compressive in-situ strength, fc, is Assessment LN exp(1.645Vf c,is)= 1.14 − 1.28 0.08− 0.15 To be estimated from core tests. Conversion factor for in-situ cast concrete, η Design LN 0.95 0.12 Based on [2]. For precast concrete, lower coefficient of variation can apply. Yield strength of steel reinforcement, fy Design and assessment LN [exp(1.645Vf y )] = 1.08 0.045 No conversion factor is commonly applied (µη = 1 and Vθ = 0). Concrete section area, Ac Design N 1 0.04 The case of normal uncertainty in geometry considered as the default case, width of the column ∼ 300 mm. MC 2020 provides guidance for other cases. Assessment N 1 0.015 Should be based on measurements in the existing structure. Normal uncertainty in geometry as adopted for design may be consi- dered in the absence of measurements. See Sec- tion 3 for details. Effective depth, d Design N 1 0.04 Normal uncertainty in geometry as the default case, effective depth ∼ 200 mm. MC 2020 provides guidance for other cases. Assessment N 1 0.01 To be based on measurements in the existing structure. Normal uncertainty may be considered in the absence of measurements. Flexural resistance model uncertainty, θR Design and assessment LN 1.09 0.045 Considered to derive γs in both design and assessment situations. Resistance model uncertainty for crushing of columns without significant 2nd order effects, θR LN 1.02 0.07 Considered to derive γc in both design and assessment situations. Table 1. Probabilistic models for resistance parameters considered in draft MC 2020. 208 vol. 36/2022 Probability of fib Model Code 2020 resistance variables for larger members (h ≥ 450 mm), more favourable values may be applied (e.g. µη = 1.03). MC 2020 indicates that the conversion factor can be influenced by the effects of non-standard quality of execution, various types of binding materials, seasonal aspects, size of the structure etc. More details including an ex- tensive literature review and the analysis of available test results can be found in the background document to prEN 1992-1-1 [3]. Note that the conversion factor η is implicitly covered by test results for in-situ com- pressive strength, fc, is, and µη = 1 and Vη = 0 are considered when the model for fc, is is based on core tests. 2.3. Geometrical variables Regarding geometrical variables, it is assumed that the section area, Ac, relates to the failure modes gov- erned by concrete crushing (typically columns under compression) while the effective depth, d, should be taken into account when reinforcement yielding is dom- inating (typically bending of beams or slabs). The case of normal uncertainty in geometry is considered as the default case for design. For the section area of a square column with fully correlated dimensions b × b, no bias is assumed and the CoV of Ac can be obtained as: VAc = 2Vb = 0.04 × (300 mm/b)2/3 (3) When the two widths are statistically independent, the factor of 2 should be replaced by √ 2 and thus: VAc = 0.0283 × (300 mm/b)2/3 (4) In the case of doubts about a level of correlation, use of Equation 3 is recommended. When considering normal uncertainty in geometr y, the statistical characteristics of effective depth can be considered as a function of its nominal value, dnom: µd = 1 − 0.05 (200 mm/dnom)2/3 Vd = 0.05 (200 mm/dnom)2/3 (5) It is further considered that uncertainty in geometry may be reduced when a decisive geometrical property is measured in the existing (finished) structure. This is considered as the default case for the assessment of existing structures. µAc = 1 and VAc = 0.015 may then be considered for the section area, and µd = 1 and Vd = 0.01 for the effective depth. Further, uncertainty in geometry can also be re- duced when an increased execution quality and quality control are required. For instance, when higher exe- cution quality is reached (ensuring that the geometri- cal deviations of Tolerance Class 2 according to EN 13670 on execution of concrete structures are fulfilled), µAc = 1 and VAc = 0.02 may be considered for the section area. For the effective depth, the following characteristics may be considered: µd = 1 − 0.025 (200 mm/d)2/3 Vd = 0.025 (200 mm/d)2/3 (6) It can be shown that the partial factor for concrete, γC , is insignificantly affected by the variability of the section area in common cases. In contrast, CoVs of the effective depth, yield strength and model uncer- tainty for bending are of a similar magnitude and the variability of the effective depth should be adequately considered when determining the partial factor for reinforcement, γS . Considering a reference period of 50-years, a recommended value of the sensitivity fac- tor for resistance is αR = 0.8 and the target reliability index for design and Consequence Class 2 (medium failure consequences) is β = 3.8 in MC 2020. Assum- ing that the three resistance variables (fy , d, θR) have a similar effect on the design or assessment value of the flexural resistance, the sensitivity factor for the effective depth is estimated as αd = 0.8/ √ 3 = 0.46 and its design value should approximately correspond to a 4% fractile, Φ(0.46 × 3.8) = 4 % (with Φ denoting the cumulative distribution function of the standard- ised normal distribution). For assessment situations, target reliabilities lower than those for design are considered in MC 2020 and a slightly higher fractile would characterise the assessment value of the effec- tive depth. To provide indications for both situations, Figure 2 displays 5% fractiles of the effective depth as a function of its nominal value, dnom (the fractiles are normalised with respect to dnom). The models for effective depth described in this section are applied. Figure 2. Effective depth - 5% fractiles as a function of nominal value. Figure 2 shows that the probabilistic models rec- ommended for the effective depth in MC 2020 (for d = 200 mm) yield rather lower estimates for the cases of improved quality and particularly for normal 209 M. Sýkora, W. Botte, R. Caspeele et al. Acta Polytechnica CTU Proceedings uncertainty that are primarily relevant for design sit- uations. In the latter case for dnom = 1000 mm, the design value of effective depth increases by about 8% in comparison to the reference case based on dnom = 200 mm. In contrast, measurements in the existing structure are associated with the smallest uncertainty and the highest design or assessment value of effective depth is obtained. Regarding considerations of the variability of effec- tive depth in design, MC 2020 provides an additional simplification. The variability of d may be ignored (µd = 1 and Vd = 0) if the design resistance is based on the design value of effective depth obtained as dd = dnom − ∆d where: • dnom is determined on the basis of the nominal cover. • ∆d is the deviation of the effective depth with: ▷ ∆d = 15 mm for reinforcing and post-tensioning steel, ▷ ∆d = 5 mm for pre-tensioning steel 2.4. Model uncertainties In the background document to prEN 1992-1-1 [3], the statistical characteristics for resistance model un- certainties adopted in MC 2020 (Table 1) are based on the comparison of test and model results. The model uncertainty is estimated as the ratio of test resistance to a model estimate [9]. For short columns with negligible second order effects, Moccia et al. [6] investigated cases without and with eccentricity for cylinder concrete strengths up to 100 MPa. They found a bias of 1.02 and CoV of 0.087. The latter is affected by the test variability and the uncertainties in the test parameters. Considering typical variabilities for these effects, the VθR-value reduced to 0.07. The statistical characteristics for flexural resistance, µθ R = 1.09 and VθR = 0.045, were derived in the background document [2] in a similar way. Bending tests were considered for various reinforcement steel classes and calculated strains around 1-1.5%. Both bias and CoV tend to increase with increasing calcu- lated strain. In the draft MC 2020, the resistance model uncer- tainties are assumed to have a lognormal distribution [4]; for further information see also Annex A of fib bulletin 80 [5] or the numerical study by Sykora et al. [10]. Note that slightly less favourable resistance model uncertainty characteristics (bias around unity and higher CoV) are indicated in MC 2020 complex situations analysed by advanced numerical models [11]. 3. Updating of probabilistic models When specific information about the structure under investigation is available, the probabilistic models for materials and actions and subsequently related partial factors can be updated. Particularly in the assessment of an existing structure, uncertainties in resistances and load effects can often be reduced on the basis of inspections, measurements, and tests. The experience from practical applications suggests that it is often highly beneficial when in-situ concrete strength is investigated and hence the important uncertainty in the conversion factor is eliminated. However, it is also possible that uncertainties to be considered in the reliability verification of the existing structure exceed those considered for a relevant design situation and the partial factors adopted for design might be insufficient. The prospective Eurocode on the reliability assess- ment of existing structures, prEN 1990-2:2021, makes distinction between the preliminary and detailed as- sessment; the latter being in the main focus of this con- tribution. Regarding the updating of basic variables, the preliminary assessment is typically conducted as- suming the default characteristics of basic variables similar to those for new structures while these char- acteristics are updated for the detailed assessment or in the case of doubts about an appropriate model for the basic variable. If justified to be relevant for the structure un- der investigation, prior information can be combined with new information obtained e.g. by measurements and/or tests through Bayesian updating. MC 2020 provides no information about the strength of the prior information provided by the presented conven- tional models. Following the background document to the reliability basis in Eurocodes [12], it might be as- sumed that the MC 2020 resistance models are based on prior information associated with the equivalent sample sizes n′ = 1 to 5 for the mean values (biases) and v′ = 3 to 10 for standard deviations. Typically, lower values apply for concrete and higher for steel reinforcement. More details can be found in the JCSS Probabilistic Model Code [4] and the JCSS monograph on assessment of existing structures [13]. 4. Recommended values of partial factors in draft MC 2020 The draft MC 2020 elaborates on a partial factor method for the reliability assessment of new or existing structures conforming to ISO 2394:2015 for structural reliability principles and EN 1990:2004 for basis of structural design. 4.1. Partial factors for design For design with respect to Ultimate Limit States (ULSs), the partial factor for materials is obtained according to MC 2020 as: γM = Rk/Rd ≈ [exp(−1.645 Vf )]/[ µθR µa µη exp(−αR β √ V 2θR + V 2a + V 2η + V 2 f ] (7) 210 vol. 36/2022 Probability of fib Model Code 2020 resistance variables CC γC γS γG - self-weight γG - other permanent loads γQ (imposed) γQ (wind) CC1 1.4 1.1 1.2 1.3 1.3 1.6 CC2 1.5 1.15 1.25 1.35 1.5 1.85 CC3 1.6 1.175 1.25 1.4 1.7 2.1 Table 2. Recommended values of partial factors for design according to MC 2020 and various CCs. CC γC γS γG - self-weight γG - other permanent loads γQ (imposed) γQ (wind) CC1 1.1 0.975 1.125-1.2 1.25-1.3 1.0 1.05 CC2 1.15 1.0 1.125-1.225 1.275-1.325 1.075 1.15 CC3 1.15 1.0 1.15-1.25 1.3-1.375 1.25 1.3 Table 3. Recommended values of partial factors for assessment of existing structures according to MC 2020. where a denotes a decisive geometrical property and the subscripts "k" and "d" refer to characteristic and design value, respectively. Equation 7 assumes that: • The resistance is obtained as the linear product according to Equation 1. • The characteristic value of the material property (commonly strength) corresponds to a 5% fractile of the respective lognormal distribution. • Unity characteristic values are considered for re- sistance model uncertainty and conversion factor, respectively. • Statistical uncertainty is reflected in the estimate of characteristic resistance. The same assumptions apply also for relationship (8) in Section 4.2. Table 2 provides the recommended values of the partial factors for design according to MC 2020 for low, medium and high consequence classes (CC1 to CC3 respectively); γG denotes the partial factor for permanent load effects and γQ for variable load effects. A detailed discussion on the partial factors for load effects is beyond the scope of this contribution but selected values are provided in Table 2 and in Table 3 in Section 4.2 to allow for comparisons with the design requirements of Eurocodes in Section 5. For the sake of brevity, the following discussion is focused on CC2 only. The partial factors for materials in Table 2 are derived using relationship (7) and considering: • The probabilistic models provided in Section 2. • A 50-year reference period along with the target re- liability index β = 3.8 (CC2) and sensitivity factors αR = 0.8 for resistance and αE = −0.7 for load effects. The partial factors in Table 2 are in broad agreement with the values provided by Eurocodes. Important for many concrete structures is that γG for self-weight can be reduced to 1.25. In contrast, the γQ-value for wind action effects is increased. Note that EN 1990:2002 and prEN 1990:2021 keep partial factors for materials fixed across CCs and differentiates by adjusting partial factors for unfavourable load effects only. The background documents for MC 2020 further demonstrate that similar values of the partial factors are obtained when the informative annual target re- liability indices β given in MC 2020 are taken into account along with the sensitivity factors adjusted for a 1-year reference period - αR = 0.7 and αE = 0.8. Note that MC 2020 provides partial factors for a number of other design situations such as the cases with higher execution quality, effective depth consider- ably exceeding 200 mm and effective depth measured in the finished structure. The draft MC 2020 emphasises that the recom- mended values of the partial factors for design or assessment may only be applied when the conditions of the structure under consideration comply with the assumptions adopted therein. Examples of the cases when the γ-values should be updated include: • Changes of the target reliability level and/or of the sensitivity factors • Decreased or increased variability of a basic variable such as a material property, geometry, load effect or model uncertainty • Basic variables having other probabilistic distribu- tions than those assumed when deriving the γ-values In particular for existing structures, the partial factors often need to be updated considering structure- specific information. Higher-level methods should be applied when structure-specific conditions deviate from those com- monly accepted. The more advanced approaches in- clude the design (assessment) value method (using e.g. Equation 7), a full-probabilistic approach (with up- dated models for basic variables and without making assumptions on the values of the sensitivity factors), or risk analysis (by which the target level can be optimised for the particular structure). 211 M. Sýkora, W. Botte, R. Caspeele et al. Acta Polytechnica CTU Proceedings 4.2. Partial factors for assessment In order to identify the need for a safety measure to achieve a required reliability level at ULS for the existing structure, a relationship similar to Equation 7 is considered for the partial factor for concrete: γM = [exp(−1.645 Vf is)]/[ µθR µAc exp(−αR β √ V 2θR + V 2 Ac + V 2 f is ] (8) where the in-situ concrete compressive strength evaluated from core tests, fc, is, is considered and the conversion factor is not included. Table 3 provides the recommended values of the par- tial factors for assessment to verify the need of safety measure(s) (termed as "assessment of the existing structure" hereafter for brevity) under the assump- tions provided below. The partial factors for materials in Table 3 are derived using the Equation 8 and considering: • The probabilistic models provided in Section 2 along with Vf c,is = 0.15 and Vf y = 0.045, and various levels of the load effect model uncertainty (on which the γG-values are dependent while the γQ-values are affected insignificantly) • An annual reference period along with the target reliability index β = 3.3 (CC2) and modified sensi- tivity factors αR = 0.7 and αE = −0.8 Regarding decisive geometrical parameters, related uncertainties are described in MC 2020 for two cases: A) measurements in the finished structure and B) normal uncertainty. Following Section 2.2, the par- tial factors in Table 3 are based on µa/anom = 1, Vac = 0.015, and Vd = 0.01 in case A). In case B), it is assumed that reliability verification adopts informa- tion on geometry from documentation that is checked by in-situ measurements, but the geometry of the de- cisive section is not directly verified. µAc/Ac,nom = 1, µd/dnom = 0.95, Vac = 0.04, and Vd = 0.05 are then considered. The draft MC 2020 specifies that the partial factors in Table 3 should only be applied when: • Concrete compressive strength is verified by ade- quate destructive tests (following standards on the evaluation of concrete in-situ strength such as EN 13791:2019). • The type and amount of reinforcement is verified. • Degradation does not affect structural behaviour significantly. Additionally to the conditions described in Section 4.1, updating of the recommended values may be needed e.g. due to structural damage including dete- rioration, differences in material properties, detailing provisions or execution tolerances. Note that the partial factors for resistance may need to be increased to cover epistemic uncertain- ties related to the lack of knowledge about important details that may have a significant influence on struc- tural behaviour such as actual geometry or amount of reinforcement in joints of frames. In these cases, a sensitivity analysis can help to explore the effect of such uncertainties on structural behaviour. As an ex- ample, assumptions for representative favourable and unfavourable situations might be made and structural analysis can then reveal the effect of this uncertainty on structural resistance. The draft MC 2020 further emphasises that human safety may require reliability levels higher than those provided in the MC for the assessment (such as annual β = 3.3 for CC2) if structural failure is expected to result in human losses. In particular, for special cases e.g. with many persons at risk or with large failure consequences, higher target levels might be more appropriate and the partial factors given in Table 3 should be increased. It is seen from Table 3 that all MC 2020 partial factors for the assessment are considerably lower than those provided in the MC and in Eurocodes for design. As an example of the important change, γS reduces from 1.15 to 1.0. This decrease can be associated with two differences between design and assessment situations of similar importance: 1. The probability of the fractile associated with the design (assessment) value of resistance increases by an order of magnitude - from Φ(αR × β) = Φ(0.8 × 3.8) = 1.18 ‰ for design to Φ(0.7 × 3.3) = 1.04% for the assessment. 2. The effective depth is assumed to be measured in the existing structure and the bias and CoV be- comes more favourable than in design (cf. Figure 2 indicating the difference of about 10% for normal uncertainty and measurements in the finished struc- ture). In addition, MC 2020 again provides partial factors for other assessment situations (concrete strengths with low variability when Vf c,is = 0.08 or reliability assessments based on information about geometry from verified documentation). 5. Comparison of design and assessment requirements In this section, the requirements imposed by the rec- ommended values of the partial factors according to Eurocodes ("EC", primarily intended for design), draft MC 2020 for design (MC design), and for assessment (MC assessment) are compared. Table 4 provides the overview of the values considered in this section, focusing on CC2 only. The comparison is made on the basis of a fundamen- tal reliability condition, Rd = Ed, for compression of the short column with a dominating concrete contri- bution according to Equation 9 and for bending of the beam with a dominating reinforcement contribution according to Equation 10: 212 vol. 36/2022 Probability of fib Model Code 2020 resistance variables Reference γC γS γG - permanent loads γQ (imposed) γQ (wind) EC* 1.5 1.15 1.35 1.5 1.5MC design 1.3** 1.85 MC assessment 1.15 1.0 1.25**,*** 1.075 1.15 *Considered here to be primarily intended for design. **Considering self-weight and other permanent actions equally important. ***Averaged over low and normal levels of load effect model uncertainty, rounded. Table 4. Overview of partial factors considered in comparison of design and assessment requirements (CC2). Ac fck/γC = γG Gk + γQ Qk = γG(1 − κ) + γQ κ = Ed(κ) (9) As fyk dnom/γS = γG Gk + γQ Qk = Ed(κ) (10) where κ = Qk/(Gk + Qk)is the load ratio based on the characteristic values of load effects; and Ed = design (assessment) values of the load effect. The ratio of section or reinforcement area required by MC assessment to the requirement by Eurocodes becomes: ρc,ex = Ac,ex Ac,EC = γC,ex Ed,ex(κ) fck,is γC,EC Ed,EC (κ) fck ≈ 1.15 γC,ex Ed,ex(κ) γC,EC Ed,EC (κ) (11) ρc,ex = Ac,ex Ac,EC = γS,ex Ed,ex(κ) fyk dm γS,EC Ed,EC (κ) fyk dnom ≈ 1.05 γS,ex Ed,ex(κ) γS,EC Ed,EC (κ) (12) In Equation 11, EC is based on the character- istic value of concrete strength from control spec- imens, fck = µf c exp(1.645 Vf c) ≈ 0.85 µf c con- sidering Vf c = 0.1. MC assessment applies the characteristic value of in-situ strength affected by the bias of the conversion factor. When the effect of concrete aging is-mostly conservatively- ignored, the characteristic value might be estimated as fck,is ≈ µη µf c exp(1.645 Vf c,is) which leads to fck,is ≈ 0.74 µf c for µη = 0.95 and Vf c,is = 0.15, and to fck/fck,is ≈ 1.15. For MC design based on fck, this effect plays no role and Equation 11 reduces to ρc,des = γC,des Ed,des(κ)/[γC,EC Ed,EC (κ)]. In Equation 12, all three approaches are based on the same characteristic value of yield strength, fyk, and there is no numerical effect on ρs-values. EC is based on the nominal value of effective depth, dnom, while MC assessment assumes that in-situ mea- surements provide its mean, dm. According to Sec- tion 2.3, it is then considered dnom/dm ≈ 1.05. For MC design based on dnom, Equation 12 reduces to ρs,des = γS,des Ed,des(κ)/[γS,EC Ed,EC (κ)]. When evaluating ρ-values, the load ratio is a study parameter considered in the range from 0.1 to 0.7 characteristic for RC structures [14] and the values of partial factors are considered according to Table 4. Figure 3 displays the variation of ratio ρ for MC design. When ρ < 1, MC design leads to lower requirements than EC. In this case, there is no difference between flexural resistance and columns under compression as the same material factors are provided by EC and MC design (cf. Table 4). In the case with imposed loads, MC design leads to nearly same levels as EC (the former being lower by 1-3%). For wind pressure (and similarly for snow loads), MC design (50 y.) requires higher resistances (5-15%) as the γW -value is significantly increased in comparison to EC. Figure 3. Variation of ratio ρ for MC design. Figure 4 displays the variation of ratio ρ for MC assessment. In this case, MC assessment is below EC for all situations. In comparison to flexural resistance, 213 M. Sýkora, W. Botte, R. Caspeele et al. Acta Polytechnica CTU Proceedings Figure 4. Variation of ratio ρ for MC assessment. systematically lower levels are obtained for columns in compression. For flexural resistance, 75-80% of the ref- erence EC level is mostly reached for variable action- dominated or permanent action-dominated structures, respectively. For columns, the level drops to 70-75%. For both failure modes, slightly lower levels are ob- tained for imposed loads. The ρ-ratios shown in Figure 4 can be considered low and consequently the reliability levels associated with MC assessment might be questioned. Such re- duced requirements are attributed mainly to a lower target reliability adopted in the MC for assessment. As an example, for κ = 0.5 and wind pressure, the γc-value increases from 0.74 (obtained for β = 3.3) to 0.83 (β = 3.7). A smaller effect is related to re- duced uncertainty as the measurements in the existing structure are assumed. 6. Discussion Besides the partial factors for design and assessment discussed in this contribution, the draft MC 2020 pro- vides guidance for a number of other design and as- sessment situations. While new parts of an upgraded structure are to be designed in a way proposed for new structures, a specific approach for the reliability assessment of existing parts of the upgraded structure is provided. This approach is based on requirements adopted also for assessment in Section 4.2, addressing the need of concrete core tests, the verification of the actual reinforcement, and a check of the degradation. However, in contrast to Section 4.2, the target relia- bility levels for design are considered and dimensions are assumed to be measured in-situ in all cases (as is common practice before structural interventions). The draft MC 2020 provides detailed guidance for the specification of the target reliability levels consid- ering annual or 50-year reference periods, somehow recommending the use of the former one. While both reference periods can be considered in design situa- tions, in assessment situations MC 2020 focuses only on annual reference period and recommends annual target levels (requiring that the annual target reliabil- ity should be fulfilled in every year of a service life of the structure). For the two reference periods, different values of the sensitivity factors are recommended. 7. Summary and concluding remarks The partial factors for materials, permanent load ef- fects, and variable load effects are presented in draft fib MC 2020 in tables for the clusters of cases depending on consequence classes and variability of basic vari- ables. Formulas and background information facilitate updating of the recommended values, i.e. adjusting the partial factors for structure-specific conditions. The key inputs for deriving the partial factors include the probabilistic models of basic variables. Different assumptions may then need to be adopted in design and assessment situations; the main differences are related to the considerations of the concrete strength measured in control specimens (design) and in-situ compressive concrete strength (assessment) as well as to the models for geometrical properties. The presented comparison of the requirements im- posed by Eurocodes and MC 2020 for design reveals on average insignificant differences (with somewhat increased partial factors for snow and wind loads and reduced partial factor for permanent actions in the Model Code). As a key new feature in the draft MC 2020, a lower target reliability is recommended for the assessment and the respective assessment require- ments may decrease by about 25%. The conditions specified in MC 2020 should then be satisfied, includ- ing in-situ verification of concrete strength, reinforce- ment, and effects of degradation. An important principle when developing MC 2020 proposals was that the Model Code should be con- sistent with Eurocodes, primarily with prEN 1990 for basis of design and assessment and prEN 1992- 1-1 for design and assessment of concrete structures including bridges. Regarding specific issues for con- crete structures, MC 2020 often offers more detailed guidance than Eurocodes. In particular, the revised MC 2020 will provide designers and code makers with wider possibilities to utilise actual data and long-term experience in assessments of existing structures. Acknowledgements This study is based on the developments of fib COM 3 TG 3.1. 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Heron 63(3): 243-302, 2018. https://heronjournal.nl/63-3/2.pdf. 215 https://doi.org/10.1002/suco.201700198 https://doi.org/10.1002/suco.201900562 www.jcss.byg.dtu.dk https://doi.org/10.1002/suco.202000211 https://doi.org/10.1002/suco.201700244 https://doi.org/10.1002/suco.201900153 https://doi.org/10.1016/j.probengmech.2015.09.008 https://doi.org/10.1016/j.probengmech.2015.09.008 https://doi.org/10.1002/suco.201700169 https://doi.org/10.1002/suco.202100420 Acta Polytechnica CTU Proceedings 36:206–215, 2022 1 Introduction 2 Probabilistic models for resistances 2.1 General 2.2 Material properties 2.3 Geometrical variables 2.4 Model uncertainties 3 Updating of probabilistic models 4 Recommended values of partial factors in draft MC 2020 4.1 Partial factors for design 4.2 Partial factors for assessment 5 Comparison of design and assessment requirements 6 Discussion 7 Summary and concluding remarks Acknowledgements References