Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2022.38.0104 Acta Polytechnica CTU Proceedings 38:104–109, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague RELIABILITY APPROACHES AFFECTING SUSTAINABILITY OF EXISTING STEEL STRUCTURES Miroslav Sýkora∗, Vitali Nadolski Czech Technical University in Prague, Klokner Institute, Department of Structural Reliability, Šolínova 7, Prague, Czech Republic ∗ corresponding author: miroslav.sykora@cvut.cz Abstract. Steel structures are second most numerous in the stock of existing buildings. In contrast to dominating concrete buildings, they are typically lightweight and are more sensitive to alterations in use or loads. While the sustainability principles require to maintain and keep using these structures, structural assessments often indicate insufficient reliability and need for replacements. The submitted contribution shows that the most important reliability considerations affecting the sustainability of existing steel structures consist of specifying (1) appropriate target reliability level, (2) verification methods, and (3) intervention procedures. The study focuses on the first two aspects. (1) Optimum target reliability can be specified by probabilistic optimisation considering sustainability aspects including structural costs, and expected consequences of replacement and of possible failure. It is shown that lower reliability levels might be considered for the assessment of existing structures than for the design of new structures, with benefits for sustainability in construction. Regarding (2), the most efficient verification methods are based on advanced probabilistic ap- proaches. It is demonstrated that sustainability may be significantly affected by the selection of assessment methods. Advanced reliability approaches commonly reduce assessment requirements by 10–15 %. Sustainability indicators are mostly related to the key aspects (1) and (2). Using the advanced methods may bring a significantly positive contribution to sustainability, particularly when an upgrade of the existing structure is associated with high economic cost and significant environmental impact. Keywords: Existing structures, adjusted partial factors, probabilistic approaches, reliability. 1. Introduction Steel structures are second most numerous in the stock of existing buildings. In contrast to dominat- ing concrete buildings, steel structures are typically lightweight and are more sensitive to changes in use and adjustment of loads. Some of the existing struc- tures are more than 100 years old and protected for their heritage value. While the sustainability princi- ples require to maintain and keep using these struc- tures, structural assessments often indicate insufficient reliability and need for replacements. This situation may be solved by applying advanced reliability as- sessment methods that mitigate the conservativeness of simplified methods utilised in engineering prac- tice. In agreement with this, the Global Consensus on Sustainability in the Built Environment [1] requires facilitating and rewarding the use of advanced anal- yses and methods of structural reliability to achieve sustainability in construction. Applications of advanced assessments of existing structures may contribute to achieving the Sustain- able Development Goals (SDGs). In October 2015 the United Nations adopted Resolution 70/1 Trans- forming Our World: the 2030 Agenda for Sustainable Development to balance the three aspects of sustain- able development: economic, social, and environmen- tal. Improved assessments of existing structures can particularly help contribute to reach SDG 12 Ensure sustainable consumption and production patterns. Rel- evant targets presented in the resolution include (a) achieving the sustainable management and effi- cient use of natural resources by 2030, and (b) substantially reducing waste through prevention, reduction, recycling and reuse. The assessment may positively contribute to sus- tainability in construction, facilitating to keep existing structures in service. The assessment of existing steel bridges may be improved by specifying • appropriate target reliability level, • verification methods, and • intervention procedures. This study focuses on the first two aspects: (1.) opti- mum target reliability can be specified based on proba- bilistic optimisation considering sustainability aspects including structural costs, expected consequences of replacement and of possible failures. Regarding (2.), the most efficient verification methods are based on advanced probabilistic approaches, considering actual load conditions and properties of the structure and related failure consequences. This study investigates benefits of applying advanced methods in the reliabil- ity assessment of an existing steel structure, critically comparing the obtained results with those based on the partial factor method for structural design. 104 https://doi.org/10.14311/APP.2022.38.0104 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 38/2022 Reliability approaches affecting sustainability . . . Basic variable X Dist. µX/Xk VX Yield strength fy LN 1.09 5 % Geometry a N 1.0 3 % Resistance model uncertainty θR LN 1.15 6 % Permanent load G N 1.0 5 % Ground snow (1-year maxima) q1 Gum 0.4 50 % Snow load – time-invariant component C0 LN 0.8 20 % Load effect model uncertainty θE LN 1.0 7.5 % µX – mean, VX – coefficient of variation, N – normal distribution, LN – lognormal distribution with the lower bound at the origin, Gum – Gumbel distribution (max. values), Xk – characteristic value of basic variable. Table 1. Probabilistic models of basic variables considered in the case study. 2. Adjusted partial factors General guidelines for adjusting and updating par- tial factors are provided by the basic Eurocode EN 1990 [2]. Partial factors may be adjusted considering structure-specific (information about materials, di- mensions, permanent actions, system behaviour etc.) and site-specific conditions (e.g. information about variable loads). The assessment values are obtained as fractiles corresponding to probability from general- ized values of sensitivity factors and a selected target reliability level. For more details see [3]. 3. Probabilistic reliability analysis A generic limit state function for members of steel structures may be written as follows: g(x) = θRR − θE [G + C0qref ], (1) where the notation of the basic (random) variables is as follows: θR and θE uncertainties in resistance and load effect models respectively, R resistance of the cross-section or of a structural member, G permanent load, C0 time-invariant component (e.g shape factor for the roof snow loads), and qref time-variant component of the variable load related to a reference period tref (e.g. maxima of the ground snow loads). Probabilistic models for basic variables given in Ta- ble 1 are selected taking into account in situ measure- ments and data in JCSS Probabilistic Model Code [4] and previous studies [5]. The results of numerous studies indicate that a Gumbel distribution is often an appropriate model for annual maxima. The back- ground report for Eurocodes [6] proposes the gener- alised values for annual maxima that are adopted here (Table 1). The statistical parameters for different reference periods are recalculated using general equations for Gumbel distribution. Snow load on the roof is ob- tained from the ground snow load by using shape, thermal and exposure factors. Uncertainties related to these coefficients are described here by the time- invariant coefficient C0 according to [6]. The model for load effect uncertainty, θE is based on the JCSS Probabilistic Model Code [4]. 4. Case study – reliability analysis of roof girder of existing steel building In this section, reliability requirements following from the fixed partial factors (FPF) provided in EN 1990, adjusted partial factors (APF) (Section 2), and prob- abilistic method (PM) (Section 3) are critically com- pared. Reliability assessment is performed considering a 10-year remaining service life (equal to a considered reference period). Target reliability index is recom- mended according to EN 1990 [2]. However, these recommendations are intended to be used primar- ily for the design of members of new structures. In general, lower reliability levels can be accepted for existing structures in comparison to structural design as follows from the general principles of structural reliability provided in ISO 2394:2015 [7]. Optimisa- tion of the target reliability for existing structures by implementing cost optimization procedures and criteria for human safety is presented in [8]. Two reli- ability levels are recommended – the minimum level below which the structure is considered unreliable and should be upgraded – reliability index β0; and the target level indicating an optimum upgrade strategy – βup. For middle Consequence Class (CC2) βup = 3.3 and β0 = 2.8 are considered [8]. EN 1990 [2] is the basic document that suggests the load combinations and relevant partial factors. The following partial factors are recommended for structural design for permanent loads: γG = 1.35 and ξ = 0.85 and for variable loads γQ = 1.5 and Ψ0 = 0.5 (snow). The load combination rule 6.10(a,b) is applied; for the considered load ratios (see below) relationship (6.10b) with a reduced permanent action effect is dominating. 105 Miroslav Sýkora, Vitali Nadolski Acta Polytechnica CTU Proceedings APF APF∗ APF APF∗ PM PM (β0,10 = 2.8) (β0,10 = 2.8) (βup,10 = 3.3) (βup,10 = 3.3) (β0,10 = 2.8) (βup,10 = 3.3) γG 1.07 1.10 1.08 1.11 1.12 1.13 γQ 1.10 1.40 1.24 1.64 1.42 1.65 γM0 0.97 0.84 1.00 0.85 0.85 0.86 ∗ Adjusted partial factors calculated with the actual values of the sensitivity factors (αR = 0.2, αG = 0.2, and αQ = 0.95). Table 2. Comparison of partial factors (χ = 0.8). Figure 1. Variation of sensitivity factors with χ. Using the adjusted partial factors and the proba- bilistic method (the First Order Reliability Method FORM), partial factors are derived to provide for the target reliability index. To cover a wide range of load combinations, load ratio χ is introduced. The load ra- tio χ denotes the ratio of characteristic variable loads to the total characteristic load. The load ratio may vary within the interval from nearly 0 (underground structures, foundations) up to nearly 1 (local effects on crane girders). For steel structures, 0.5 ≤ χ ≤ 1 is expected [9]. The values of the partial factors are presented in Table 2 for χ = 0.8. The main deficiency of the APF is that the gener- alised sensitivity factors are applied. More precisely, it is possible to determine the values of the partial factors using the actual values of the sensitivity fac- tors obtained by FORM. Figure 1 displays variation of the sensitivity factors with the ratio χ. For adjusted partial factors the sensitivity factor could be recom- mended αE = -0.95 for the snow load, αE = -0.2 for the permanent load and αR = 0.2 for resistance. The results the APF and PM become close when using these values of the sensitivity factors. The geometrical characteristic (hereinafter referred to as a reliability requirement) of a cross-section Wi, such as section modulus, required to satisfy the limit state in accordance with a particular approach to reliability verification the selected system of partial Figure 2. Variation of wi with χ (APF based on the actual values of sensitivity factors – αR = 0.2, αG = 0.2, and αQ = 0.95). factors is calculated from limit state function: g(x) = Wfyk/γM0 − [γGGk + γQC0Sk]. (2) Figure 2 displays variation of the standardised ratio wi = Wi/WEN with χ, where WEN is the reference value based on the partial factors recommended in Eurocodes for structural design. When wi < 0, the reliability requirements according to approach “i” are lower than those according to Eurocodes for structural design. Figure 2 shows that the adjusted partial factors (APF) and probabilistic method PM lead to the relia- bility requirements lower than EN. The decrease in re- quirements is attributed to the use of the lower target reliability level for existing structure β0 (lower than in EN) and case-specific probabilistic distributions for basic variables that reduces the conservativeness of fixed partial factors. In contrast, the requirements for upgrades according to APF and PM (considering βup) are close to those based on EN. The area between the curves for assessment (β0) and upgrade (βup) in Figure 2 is associated with the situations when the application of the advanced methods is expected to provide sustainability benefit. In these situations, EN assessment requires an upgrade with economic and environmental impacts while the advanced methods authorise a continued use of the structure “as it is”. For the structures designed according to the Czech standards valid before Eurocodes has been introduced, ratio wi is expected to range approximately from 0.75 (χ close to unity) to 0.85 (χ close to 0.3) when the 106 vol. 38/2022 Reliability approaches affecting sustainability . . . roof snow load is the leading variable action. These estimates are based on the results of detailed relia- bility analysis of existing steel roofs exposed to snow loads in the Czech Republic [10]. Such low wi-values are attributed to increased design roof snow loads as introduced by Eurocodes. 5. Discussion on appropriate sustainability indicator for assessment of existing structures This example provides first insights into the sustain- ability benefits possibly gained by applying advanced reliability methods and considering the target reliabil- ity levels optimised for existing structures. The fun- damental decision in reliability assessments – whether the existing structure can be used without upgrade or upgrade is needed – is analysed focusing on the roof girder investigated in Section 4. Various sustain- ability indicators have been proposed to quantify the effects of decisions about structures on sustainabil- ity. For instance, Müller et al. proposed a simplified measure – building material sustainability potential (BMSP) [11]. To focus on the main aspects and allow for analysing a range of the assessment situations of practical relevance, this simple indicator is considered: BMSP = P × SL/EI, (3) where P performance; SL service life; and EI environmental impact. It is assumed that the existing structure under con- sideration fully provides its function if an Ultimate Limit State (ULS) criterion is fulfilled, P = 100 %. When the ULS condition is violated, the structure should be closed, P = 0 %. Service life is measured in years with a reference level considered here as 50 years, and then SL = 100 %. If a service life is estimated as 25 years, then SL reduces to 50 %. Very small environ- mental impact is assumed when the existing structure is continuously used without upgrade, EI ≈ 0, while EI increases proportionally with the level of strength- ening, EI > 0. When comparing two alternatives, BMSPA > BMSPB should indicate alternative A being preferable. However, it can be argued whether BMSP is an appropriate indicator for comparing decision alterna- tives about existing structures since the environmental impact is close to zero for a “no upgrade” alternative and BMSP converges to infinity. To further illustrate the need for modification of BMSP, let us assume that: • Benefit (P × SL) and environmental impact related to maintenance and upgrade (EI) can be both ex- pressed in monetary terms; typically the former as a gain and the latter as a loss. • The benefit from using the structure, (P0 × SL0), may be much larger than the environmental impact EI0 that is now related to maintenance only; as an example (P0 × SL0) = 100 units and EI0 = 1 unit; the total gain from using the structure is thus 99 units over service life. • In the case of upgrade, performance level may be retained, service life may be doubled and likewise related benefit, P0 × SLup = 200 units. The up- grade may have significant environmental impact; for instance 10-times increased compared to “no up- grade”, EIup = 10EI0 = 10 units. The total gain is then 190 units, nearly doubled in comparison to “no upgrade”. In this example, BMSP for the structure “as it is” and upgraded would be: BMSP0 = 100/1 = 100 > BMSPup = 200/10 = 20 and the “no upgrade” strategy should be preferred. However, a comparison of the total gains clearly points to the opposite. Based on these arguments, it is thus proposed to modify the sustainability indicator for decision making about existing structures when benefits and losses can be expressed in the same units: SI = P × SL − (EI + C). (4) The term in brackets denotes the expected losses. Newly introduced cost C should cover all expenses related to maintenance and possible upgrade. When the owner (particularly the society) saves financial re- sources, these may be utilised to implement measures positively contributing to sustainability. Focusing on the girder analysed in Section 4, Fig- ure 3 displays variation of sustainability indicator SI, benefit expressed as SL, and losses C with ratio w that is the property of the girder “as it is”. The trends of SI, SL, and C are estimated on the basis of the assumptions discussed below. As a reference level, the maximum benefit is assumed to be related to service life of 50 years, SLmax = 100 units. No distinction between performance levels is made – the girder just needs to comply with reliability requirements and then the building can be fully used; P is thus disregarded hereafter. Assumptions related to losses, C: (1.) Based on the detailed analysis in [9], upgrade cost is assumed to correspond to about 40 % of the total benefit, 40 units, out of which 50 % is fixed cost independent of w (costs of surveys, assessment, administration and management, economic losses due to business interruption or replacement of users, etc.). Maintenance is disregarded for simplification. Environmental impact was ignored in [9]. 107 Miroslav Sýkora, Vitali Nadolski Acta Polytechnica CTU Proceedings Figure 3. Variation of sustainability indicator SI, benefit SL, and loss C with ratio w (neglected EI). (2.) Focusing initially on application of the partial factor method according to Eurocodes (“EN”), up- grade is needed for w < 1 while no structural in- tervention takes place otherwise. Full upgrade is assumed to be associated with w = 0.6; upgrade cost then linearly decreases with increasing w and drops to zero for w = 1 when the existing girder complies with the EN requirements. (3.) For 0.6 ≤ w < wβ0 = 0.8 (Figure 2), similar assumptions for upgrade cost apply when the ad- vanced methods are used. Reliability of the girder is below β0 and an upgrade is necessary. As the opti- mum upgrade level is slightly below to that required by EN, wadv,upgrade ≈ 0.9–0.95 (Figure 2), Cadv(w) is slightly lower than CEN (w). For w ≥ wβ0, no upgrade is needed. Assumptions related to benefit, SL: (4.) For w < 1, EN requires upgrading. The upgrade is assumed to provide for a service life of 50 years. When w ≥ 1, the existing girder meets the EN re- quirements and it is again assumed to have a service life of 50 years. (5.) For 0.6 ≤ w < wβ0, SLadv is also 100 units as upgrade provides for a 50-year service life. For w = wβ0 the girder exactly complies with β0 for tref = 10 years (Section 4) and thus a 10-year ser- vice life is guaranteed, yielding SLadv(wβ0) = 20 units. When w increases above wβ0, tref can be increased to comply with the β0-requirement. For w = 0.98, a 50-year service life is reached, SLadv(w ≥ 0.98) = 100 units. Comparison of SI-values – evaluated according to Equation (4) and plotted in Figure 3 – indicates that: • For 0.6 ≤ w < wβ0 and w ≥ 1, the use of advanced methods has a small effect on the SI-values. • For wβ0 ≤ w < 0.96 (marked in Figure 3 as “A”), Figure 4. Variation of sustainability indicator SI, benefit SL, and losses (EI+C) with ratio w (including EI). the use of advanced methods seems to lead to lower SI-values as a service life lower than 50 years would be authorised. In this case with a relatively low upgrade cost, upgrading seems beneficial. • For 0.92 ≤ w < 1 (marked as “B”), the advanced methods provide benefit as upgrade is unnecessary while the EN-based assessment indicate otherwise. In [9] no account for environmental impact was taken. During upgrade, environmental impact may cover for instance material consumption, transporta- tion of materials and equipment and related fuel con- sumption and emissions etc. To illustrate the effect of environmental impact, let us consider that (EI + C) for full upgrade is 2.5-times higher than in the pre- vious case, (EI + C) = 100. All other assumptions remain unchanged. Figure 4 portrays variation of SI, SL, and (EI + C) with w. It appears that in- creased upgrade cost (EI + C) significantly change the obtained SI-values: • While for 0.6 ≤ w < wβ0 there is again a small difference between SIadv and SIEN , for wβ0 ≤ w < 1 area “A” nearly vanishes and area “B” remains – the use of the advanced methods is beneficial. • For w ≥ 1, there is again no difference between using the advanced methods or EN. It is emphasised that the example presented in this section is intentionally simplified focusing on the main aspects of decision making and implications for sustainability. Situations when decision making may be more complex include: • For very low resistance (w < wβ0), the girder is considered unreliable and decision should be made whether it should be replaced or should be upgraded; the example indicates that environmental impact plays a significant role in this decision making. 108 vol. 38/2022 Reliability approaches affecting sustainability . . . • For low but possibly acceptable resistance (wβ0 < w < 1), the girder may be considered reliable with a reduced service live. It should be then decided whether the girder can be preserved, upgraded or replaced by a new structure. • Even for sufficient resistance (w ≥ 1), upgrading or replacement may be considered to reach a longer service life of the structure. However, this deci- sion should be made with caution as useful service life of buildings is mostly affected by a number of factors causing obsolescence that are beyond the control of civil engineers (economic, functional or technological obsolescence, failure to meet legal re- quirements) [12]. Large investments in the attempt to achieve long service life from the reliability perspective may then be in vain. Within further research, the obtained results will be verified considering a wide range of factors to quantify the overall sustainability impact of various assessment strategies by a full probabilistic approach as proposed by Webb and Ayyub [13]. Also, the use of surveys results should generally reduce uncertainties in basic variables and increase reliability estimates for existing structures, making it possible to avoid or minimise structural interventions. 6. Conclusions While the sustainability considerations require to maintain and keep using existing structures, struc- tural assessments often indicate insufficient reliability levels and need for replacements. The submitted con- tribution investigates how this situation may be solved by applying advanced reliability assessment methods. It is demonstrated how the advanced methods may bring a significant positive contribution to sustain- ability, particularly when an upgrade of the existing structure is associated with high economic cost and large environmental impact. It is newly proposed to modify the sustainability indicator for decision mak- ing about existing structures considering associated benefits and losses expressed in the same units. Case studies show that the application of advanced probabilistic approaches reduces the assessment re- quirements by 20–25 % when the minimum reliability level is accepted, and by 5–10 % when the optimum reliability level for upgrades is considered. It is demon- strated that the application of advanced reliability methods may allow continued use of existing struc- tures when conservative methods of structural design may indicate needs for upgrading. Acknowledgements This study has been supported by the Ministry of Culture of the Czech Republic under Grant DG18P02OVV033 “The Methods for Achieving the Sustainability of Industrial Heritage Steel Bridges”. References [1] M. H. Faber, W. Schmidt. GLOBE – Global consensus on sustainability in the built environment, 2020. (Adopted by JCSS and sup-ported by RILEM, IABSE, fib, CIB, ECCS and IASS), [2022-11-15]. https://www.rilem.net/globe [2] EN 1990, Eurocode – Basis of structural design, 2002. CEN, Brussels, p. 87. [3] R. Caspeele, M. Sykora, D. L. Allaix, R. Steenbergen. The design value method and adjusted partial factor approach for existing structures. Structural Engineering International 23(4):386–393, 2013. https: //doi.org/10.2749/101686613X13627347100194 [4] Joint Committee on Structural Safety. JCSS Probabilistic model code, 2022. (periodically updated, online publication), [2022-11-15]. https://www.jcss- lc.org/jcss-probabilistic-model-code/ [5] V. Nadolski, A. Rózsás, M. Sýkora. Calibrating partial factors – methodology, input data and case study of steel structures: Methodology, input data and case study of steel structures. Periodica Polytechnica Civil Engineering 63(1):222–242, 2019. https://doi.org/10.3311/PPci.12822 [6] CEN TC250/Ad Hoc Group Reliability of Eurocodes (convenor – Ton Vrouwenvelder) Technical Report for the reliability background of Eurocodes, 2021. P. 165. [7] ISO 2394, General Principles on Reliability for Structures, ISO, Geneve, Switzerland, 2015. [8] fib C. TG3.1, Partial Factor Methods for Existing Structures (fib bulletin 80), fib, 2016. [9] M. Sykora, D. Diamantidis, M. Holicky, K. Jung. Target reliability for existing structures considering economic and societal aspects. Structure and Infrastructure Engineering 13(1):181–194, 2017. https://doi.org/10.1080/15732479.2016.1198394 [10] M. Holický, J. Marková, M. Sýkora. Reliability of light-weight roofs exposed to snow load [In the Czech original: Spolehlivost lehkých střech zatížených sněhem]. Stavební obzor 16(3):65–69, 2007. [11] H. S. Mueller, M. Haist, J. S. Moffatt, M. Vogel. Design, material properties and structural performance of sustainable concrete. Procedia Engineering 171:22–32, 2017. https://doi.org/10.1016/j.proeng.2017.01.306 [12] D. Diamantidis, M. Sykora, E. Bertacca. Obsolescence rate: Framework, analysis and influence on risk acceptance criteria. In Proceedings IALCCE 2018, pp. 379–386. 2019. [13] D. Webb, B. M. Ayyub. Sustainability quantification and valuation. II: Probabilistic framework and metrics for sustainable construction. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 3(3):E4016002, 2017. https://doi.org/10.1061/AJRUA6.0000894 109 https://www.rilem.net/globe https://doi.org/10.2749/101686613X13627347100194 https://doi.org/10.2749/101686613X13627347100194 https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://www.jcss-lc.org/jcss-probabilistic-model-code/ https://doi.org/10.3311/PPci.12822 https://doi.org/10.1080/15732479.2016.1198394 https://doi.org/10.1016/j.proeng.2017.01.306 https://doi.org/10.1061/AJRUA6.0000894 Acta Polytechnica CTU Proceedings 38:104–109, 2022 1 Introduction 2 Adjusted partial factors 3 Probabilistic reliability analysis 4 Case study – reliability analysis of roof girder of existing steel building 5 Discussion on appropriate sustainability indicator for assessment of existing structures 6 Conclusions Acknowledgements References