DESIGNERS’ GUIDES TO THE EUROCODES
DESIGNERS’ GUIDE TO EUROCODE 8: DESIGN OF BRIDGES FOR EARTHQUAKE RESISTANCE EN 1998-2
BASIL KOLIAS DENCO S.A, Greece
MICHAEL N. FARDIS University of Patras, Greece
ALAIN PECKER Ge´odynamique et Structure, France
Series editor Haig Gulvanessian CBE
Published by ICE Publishing, 40 Marsh Wall, London E14 9TP
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Preface Aim of the Designers’ Guide This Designers’ Guide to EN 1998-2:2005 covers the rules for the seismic design of bridges, following in a loose way the contents of this EN Eurocode. It highlights its important points without repeating them, providing comments and explanations for its application, as well as background information and worked-out examples. However, it does not elaborate every single clause in EN 1998-2:2005, neither does it follow strictly the sequence of its clauses.
Layout of this guide All cross-references in this guide to sections, clauses, subclauses, paragraphs, annexes, figures, tables and expressions of EN 1998-2 and EN 1998-5 are in italic type, which is also used where text from EN 1998-2 and EN 1998-5 has been directly reproduced (conversely, quotations from other sources, including other Eurocodes, and cross-references to sections, etc., of this guide, are in roman type). Numbers within square brackets after cross-references in the margin refer to Parts 1, 2 and 5 of EN 1998: EN 1998-1 [1], EN 1998-2 [2], EN 1998-5 [3]. Expression numbers specific to this guide are prefixed by D (for Designers’ Guide), for example, Eq. (D3.1), to prevent confusion with expression numbers from EN 1998.
Acknowledgements This Designers’ Guide would not have been possible without the successful completion of EN 1998-2:2005. Those involved in the process were: g g
national delegates and national technical contacts to Subcommittee 8 of CEN/TC250 the Project Team of CEN/TC250/SC8 that worked for the conversion from the ENV to the EN: namely PT4, convened by Alex Plakas.
v
Contents Preface Aim of the Designer’s guide Layout of this guide Acknowledgements
v v v v
Chapter 1
Introduction and scope 1.1. Introduction 1.2. Scope of Eurocode 8 1.3. Scope of Eurocode 8 Part 2 1.4. Use of Eurocode 8 Part 2 with the other Eurocodes 1.5. Additional European standards to be used with EN 1998-2:2005 1.6. Assumptions 1.7. Distinction between principles and application rules 1.8. Terms and definitions – symbols References
1 1 1 2 2 3 4 4 4 4
Chapter 2
Performance requirements and compliance criteria 2.1. Performance-based seismic design of bridges 2.2. Performance requirements for new bridges in Eurocode 8 2.3. Compliance criteria for the non-collapse requirement and implementation 2.4. Exemption from the application of Eurocode 8 References
5 5 7 8 16 16
Chapter 3
Seismic actions and geotechnical aspects 3.1. Design seismic actions 3.2. Siting and foundation soils 3.3. Soil properties and parameters 3.4. Liquefaction, lateral spreading and related phenomena References
19 19 29 30 32 36
Chapter 4
Conceptual design of bridges for earthquake resistance 4.1. Introduction 4.2. General rules for the conceptual design of earthquake-resistant bridges 4.3. The choice of connection between the piers and the deck 4.4. The piers 4.5. The abutments and their connection with the deck 4.6. The foundations References
37 37 38 43 53 59 64 65
Chapter 5
Modelling and analysis of bridges for seismic design 5.1. Introduction: methods of analysis in Eurocode 8 5.2. The three components of the seismic action in the analysis 5.3. Design spectrum for elastic analysis 5.4. Behaviour factors for the analysis 5.5. Modal response spectrum analysis 5.6. Fundamental mode analysis (or ‘equivalent static’ analysis) 5.7. Torsional effects in linear analysis 5.8. Effective stiffness for the analysis 5.9. Calculation of seismic displacement demands through linear analysis 5.10. Nonlinear analysis References
67 67 68 69 69 73 92 98 100 107 110 117 vii
Chapter 6
viii
Verification and detailing of bridge components for earthquake resistance 6.1. Introduction 6.2. Combination of gravity and other actions with the design seismic action 6.3. Verification procedure in design for ductility using linear analysis 6.4. Capacity design of regions other than flexural plastic hinges in bridges of ductile behaviour 6.5. Overview of detailing and design rules for bridges with ductile or limited ductile behaviour 6.6. Verification and detailing of joints between ductile pier columns and the deck or a foundation element 6.7. Verifications in the context of design for ductility based on nonlinear analysis 6.8. Overlap and clearance lengths at movable joints 6.9. Seismic links 6.10. Dimensioning of bearings 6.11. Verification of abutments 6.12. Verification of the foundation 6.13. Liquefaction and lateral spreading References
119 119
Chapter 7
Bridges with seismic isolation 7.1. Introduction 7.2. Objective, means, performance requirements and conceptual design 7.3. Design seismic action 7.4. Behaviour families of the most common isolators 7.5. Analysis methods 7.6. Lateral restoring capability References
171 171 171 174 174 185 191 191
Chapter 8
Seismic design examples 8.1. Introduction 8.2. Example of a bridge with ductile piers 8.3. Example of a bridge with limited ductile piers 8.4. Example of seismic isolation References
193 193 193 210 221 249
Index
251
119 122 124 129 129 132 135 140 142 155 159 164 167
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance ISBN 978-0-7277-5735-7 ICE Publishing: All rights reserved http://dx.doi.org/10.1680/dber.57357.001
Chapter 1
Introduction and scope 1.1.
Introduction
Design of structures for earthquake resistance penetrated engineering practice for buildings much earlier than for bridges. There are several reasons for this. First, seismic design is of relevance mainly for piers, but is secondary for the deck. The deck, though, receives in general far more attention than the piers, as it is more important for the function and the overall cost of the bridge, while its engineering is also more challenging. So, seismic considerations, being relevant mainly for the less important components of bridges, have traditionally been of lower priority. Second, a good number of bridges are not so sensitive to earthquakes: the long-span ones – which are also the subject of lots of attention and of major design and engineering effort – are very flexible, and their long periods of vibration are outside the frequency range of usual ground motions. At the other extreme, short bridges, with one or only few spans, often follow the ground motion with little distress, and normally suffer only minor damage. However, with the very rapid expansion of transportation networks, the new priorities in land use – especially in urban areas – and the sensitivities of recent times to protection of the environment, bridge engineering has spread from the traditional field of short crossings of rivers, ravines or other natural barriers or of over- and underpasses for motorways to long viaducts consisting of a large number of spans on equally numerous piers, often crossing territories with different ground or soil conditions. The heavy damage suffered by such types of engineering works in the earthquakes of Loma Prieta in 1989 and Kobe in 1995 demonstrated their seismic vulnerability. More recent events have confirmed the importance of proper seismic design (or lack of it) for bridge projects. Owing to these developments, recent decades have seen major advances in the seismic engineering of bridges. It may now be claimed with a certain amount of confidence that the state-of-the-art in the seismic design of bridges is catching up with that of buildings, which is more deeply rooted in common design practice and codes. Europe, where even the moderate-to-high seismicity countries of the south lacked modern seismic design codes for bridges, has seen the development of EN 1998-2:2005 as a modern and complete seismic design standard, on par with its counterparts in California, Japan and New Zealand. Part 2 of Eurocode 8 (CEN, 2005a) is quite advanced from the point of view of the state-of-the-art and of seismic protection technology, not only compared with the pre-existing status at national levels but also with respect to the other parts of the new European seismic design standard (EN Eurocode 8) that address other types of civil engineering works. It is up to the European community of seismic design practice to make good use of it, to the benefit of the seismic protection of new bridges in Europe and of its own professional competiveness in other seismic parts of the world. This Designers’ Guide aspires to help this community become familiar with Part 2 of Eurocode 8, get the most out of it and apply it in a cost-effective way.
1.2.
Scope of Eurocode 8
Eurocode 8 covers the design and construction of earthquake-resistant buildings and other civil engineering works – including bridges, but excluding nuclear power plants, offshore structures and large dams. Its stated aim is to protect human life and property in the event of an earthquake and to ensure that structures that are important for civil protection remain operational.
Clauses 1.1.1(1), 1.1.1(2) [1] Clause 1.1.1(1) [2]
Eurocode 8 has six Parts, listed in Table 1.1. Among them, only Part 2 (CEN, 2005a) is covered in this Designers’ Guide.
Clauses 1.1.1(4), 1.1.3(1) [1] 1
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
Table 1.1. Eurocode 8 parts Part
EN
Title
1
EN 1998-1:2004
2 3
EN 1998-2:2005 EN 1998-3:2005
4 5
EN 1998-4:2006 EN 1998-5:2004
6
EN 1998-6:2005
Design of structures for earthquake resistance. seismic actions, rules for buildings Design of structures for earthquake resistance. Design of structures for earthquake resistance. retrofitting of buildings Design of structures for earthquake resistance. Design of structures for earthquake resistance. retaining structures, geotechnical aspects Design of structures for earthquake resistance.
1.3. Clauses 1.1.1(2)– 1.1.1(4), 1.1.1(6) [2]
General rules, Bridges Assessment and Silos, tanks, pipelines Foundations, Towers, masts, chimneys
Scope of Eurocode 8 Part 2
Part 2 of Eurocode 8 (CEN, 2005a) has as its sole object the seismic design of new bridges. It focuses on bridges having a deck superstructure supported directly on vertical or nearly vertical concrete or steel piers and abutments. The seismic design of cable-stayed or arched bridges is only partly covered, while that of suspension bridges, timber bridges (strictly speaking, bridges on timber piers), masonry bridges, moveable bridges or floating bridges is not covered at all. Part 2 of Eurocode 8 also covers the design of bridges with seismic isolation. Unlike existing buildings, whose seismic assessment and retrofitting is covered in Eurocode 8 (CEN, 2005b), existing bridges are not addressed at all.
1.4. Clauses 1.1.2(1)– 1.1.2(3) [1]
g g g
Clauses 1.1(1), 1.1(2) [3]
Use of Eurocode 8 Part 2 with the other Eurocodes
Part 2 of Eurocode 8 builds on the general provisions of Part 1 (CEN, 2004b) for: the general performance requirements seismic action analysis methods and procedures applicable to all types of structures.
All the general or specific provisions of Part 5 of Eurocode 8 (CEN, 2004a) regarding: g g g g
siting of the works properties and seismic verification of the foundation soil seismic design of the foundation or of earth-retaining structures seismic soil–structure interaction
apply as well. Clause 1.2.1 [1,2] Eurocode 8 is not a stand-alone code. It is applied alongside the other relevant Eurocodes in a Clauses 1.2.2, 1.2.4 [2] package referring to a specific type of civil engineering structure and construction material.
For bridges, there are four Eurocode packages: g g g g
2/2: 3/2: 4/2: 5/2:
Concrete bridges Steel bridges Composite bridges Timber bridges.
To be self-sufficient, each package includes all the Eurocode parts needed for design, as follows: g
2
Several EN Eurocodes are included in every single bridge package: – EN 1990: ‘Basis of structural design’ (including Annex A2: ‘Application for bridges’) – EN 1991-1-1: ‘Actions on structures – General actions – Densities, Self weight and Imposed loads for buildings’ – EN 1991-1-3: ‘Actions on structures – General actions – Snow loads’
Chapter 1. Introduction and scope
– – – – – – – –
g
g
g
EN 1991-1-4: ‘Actions on structures – General actions – Wind actions’ EN 1991-1-5: ‘Actions on structures – General actions – Thermal actions’ EN 1991-1-6: ‘Actions on structures – General actions – Actions during execution’ EN 1991-1-7: ‘Actions on structures – General actions – Accidental actions’ EN 1991-2: ‘Actions on structures – Traffic loads on bridges’ EN 1997-1: ‘Geotechnical Design – General rules’ EN 1997-2: ‘Geotechnical Design – Ground investigation and testing’ EN 1998-1: ‘Design of structures for earthquake resistance – General rules, seismic actions, rules for buildings’ – EN 1998-2: ‘Design of structures for earthquake resistance – Bridges’ – EN 1998-5: ‘Design of structures for earthquake resistance – Foundations, retaining structures, geotechnical aspects’. Additional EN-Eurocodes are included in the Concrete Bridges package (2/2): – EN 1992-1-1: ‘Design of concrete structures – General – General rules and rules for buildings’ – EN 1992-2: ‘Design of concrete structures – Concrete bridges – Design and detailing rules’. Additional EN-Eurocodes included in the Steel Bridges package (3/2): – EN 1993-1-1: ‘Design of steel structures – General rules and rules for buildings’ – EN 1993-1-5: ‘Design of steel structures – Plated structural elements’ – EN 1993-1-7: ‘Design of steel structures – Strength and stability of planar plated structures subject to out of plane loading’ – EN 1993-1-8: ‘Design of steel structures – Design of joints’ – EN 1993-1-9: ‘Design of steel structures – Fatigue’ – EN 1993-1-10: ‘Design of steel structures – Selection of steel for fracture toughness and through-thickness properties’ – EN 1993-1-11: ‘Design of steel structures – Design of structures with tension components’ – EN 1993-2: ‘Design of steel structures – Steel bridges’. EN-Eurocodes which are included in addition in the Composite Bridges package (4/2) are: – EN 1992-1-1: ‘Design of concrete structures – General – General rules and rules for buildings’ – EN 1992-2: ‘Design of concrete structures – Concrete bridges – Design and detailing rules’ – EN 1993-1-1: ‘Design of steel structures –General rules and rules for buildings’ – EN 1993-1-5: ‘Design of steel structures – Plated structural elements’ – EN 1993-1-7: ‘Design of steel structures – Strength and stability of planar plated structures subject to out of plane loading’ – EN 1993-1-8: ‘Design of steel structures – Design of joints’ – EN 1993-1-9: ‘Design of steel structures – Fatigue’ – EN 1993-1-10: ‘Design of steel structures – Selection of steel for fracture toughness and through-thickness properties’ – EN 1993-1-11: ‘Design of steel structures – Design of structures with tension components’ – EN 1993-2: ‘Design of steel structures – Steel bridges’ – EN 1994-1-1: ‘Design of composite steel and concrete structures – General rules and rules for buildings’ – EN 1994-2: ‘Design of composite steel and concrete structures – General rules and rules for bridges’.
Although package 5/2, for timber bridges, does include Parts 1, 2 and 5 of Eurocode 8, EN 19982:2005 itself is not meant to cover timber bridges.
1.5.
Additional European standards to be used with EN 1998-2:2005
Part 2 of Eurocode 8 makes specific reference to the following product standards: g g g
Clause 1.2.4 [2]
EN 15129:2009: ‘Antiseismic Devices’ EN 1337-2:2000: ‘Structural bearings – Part 2: Sliding elements’ EN 1337-3:2005: ‘Structural bearings – Part 3: Elastomeric bearings’. 3
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
Although EN 1337-5 ‘Structural bearings – Part 5: Pot bearings’ is not specifically referenced, it is also to be used, as relevant.
1.6. Clauses 1.3(1), 1.3(2) [1,2]
1.7. Clause 1.4 [1,2]
Distinction between principles and application rules
Eurocode 8 refers to EN 1990 for the distinction between principles and application rules. Accordingly, reference is made here also to Designers’ Guides to other Eurocodes for elaboration. It is noted, though, that, in practice, the distinction between principles and application rules is immaterial, as all provisions of the normative text are mandatory: non-conformity to a single application rule disqualifies the entire design from being considered to accord with the EN Eurocodes.
1.8. Clauses 1.5, 1.6 [2]
Assumptions
Eurocode 8 refers to EN 1990 (CEN, 2002) for general assumptions, so reference is made here to Designers’ Guides to other Eurocodes for elaboration. Also, Eurocode 8 adds the condition that no change to the structure (not even one that increases the force resistance of members) should take place during execution or afterwards without proper justification and verification.
Terms and definitions – symbols
Terms and symbols are defined in the various chapters of this Designers’ Guide wherever they first appear. REFERENCES
CEN (Comite´ Europe´en de Normalisation) (2002) EN 1990: Eurocode – Basis of structural design (including Annex A2: Application to bridges). CEN, Brussels. CEN (2004a) EN 1998-5:2004 Eurocode 8 – Design of structures for earthquake resistance – Part 5: Foundations, retaining structures, geotechnical aspects. CEN, Brussels. CEN (2004b) EN 1998-1:2004. Eurocode 8 – Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings. CEN, Brussels. CEN (2005a) EN 1998-2:2005 Eurocode 8 – Design of structures for earthquake resistance – Part 2: Bridges. CEN, Brussels. CEN (2005b) EN 1998-3:2005 Eurocode 8 – Design of structures for earthquake resistance – Part 3: Assessment and retrofitting of buildings. CEN, Brussels.
4
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance ISBN 978-0-7277-5735-7 ICE Publishing: All rights reserved http://dx.doi.org/10.1680/dber.57357.005
Chapter 2
Performance requirements and compliance criteria 2.1.
Performance-based seismic design of bridges
Paraphrasing – for the particular purpose of the seismic design of bridges – the fib 2010 Model Code ib, 2012) – the seismic performance of a bridge refers to its behaviour under seismic action: the bridge must be designed, constructed and maintained so that it adequately and in an economically reasonable way performs in earthquakes that may take place during its construction and service. More specifically, the bridge must: g g
g
remain fit for the use for which it has been designed withstand extreme, occasional and frequent seismic actions likely to occur during its anticipated use and avoid damage by an exceptional earthquake to an extent disproportionate to the triggering event contribute positively to the needs of humankind with regard to nature, society, economy and wellbeing.
Accordingly, three categories of performance are addressed by the fib 2010 Model Code ( fib, 2012): g
g
g
Serviceability: the ability of the bridge and its structural components to perform, with appropriate levels of reliability, adequately for normal use after or even during seismic actions expected during its service life. Structural safety: the ability of the bridge and its structural components to guarantee the overall stability, adequate deformability and ultimate load-bearing resistance, corresponding to occasional, extreme or exceptional seismic actions with appropriate levels of reliability for the specified reference periods. Sustainability: the ability of the bridge to contribute positively to the fulfilment of the present needs of humankind with respect to nature, society and people, without compromising the ability of future generations to meet their needs in a similar manner.
In performance-based design, the bridge is designed to perform in a required manner during its entire life cycle, with performance evaluated by verifying its behaviour against specified requirements, based in turn on stakeholders’ demands for the bridge performance and required service life. Performance-based design of a new bridge is completed when it has been shown that the performance requirements are satisfied for all relevant aspects of performance related to serviceability, structural safety and sustainability. If the performance of a structure or a structural component is considered to be inadequate, we say we have ‘failure’. The Eurocodes introduce limit states to carry out performance-based design for serviceability and safety (CEN, 2002). Limit states mark the boundary between desired and undesirable structural performance of the whole structure or a component: beyond a limit state, one or more performance requirements are no longer met. For the particular case of seismic design, limit states are defined conceptually for all transient situations in the service life or the execution of the bridge during which the earthquake acts in combination with any relevant persistent or transient actions or environmental influences. They correspond to discrete representations of the structural response under a specified exposure for which specific losses/damages can be associated. In practice, they use simplified models for the exposure and the structural response ( fib, 2012). 5
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
The Eurocodes recognise (CEN, 2002): g g
serviceability limit states (SLSs) ultimate limit states (ULSs).
SLSs are those beyond which specified requirements for the bridge or its structural components related to its normal use are no longer met. If they entail permanent local damage or permanent unacceptable deformations, the outcome of their exceedance is irreversible. It is considered to be serviceability failure, and may require repair to reinstate fitness for use. According to the fib 2010 Model Code ( fib, 2012), in seismic design at least one – but sometimes two – SLSs must be explicitly considered, each one for a different representative value of the seismic action: g
g
The operational (OP) limit state: the facility (bridge or any other construction work) satisfies the operational limit state criteria if it has suffered practically no damage and can continue serving its original intention with little disruption of use for repairs; any repair, if needed, can be deferred to the future without disruption of normal use. The immediate use (IU) limit state: the facility satisfies this if all of the following conditions apply: – the structure itself is very lightly damaged (i.e. localised yielding of reinforcement, cracking or local spalling of concrete, without residual drifts or other permanent structural deformations) – the normal use of the facility is temporarily but safely interrupted – risk to life is negligible – the structure retains fully its earlier strength and stiffness and its ability to withstand loading – the (minor) damage of non-structural components and systems can be easily and economically repaired at a later stage.
ULSs are limit states associated with the various modes of structural collapse or stages close to it, which for practical purposes are also considered as a ULS. Exceedance of a ULS is almost always irreversible; the first time it occurs it causes inadequate structural safety, that is, failure. ULSs address (CEN, 2002; fib, 2012): g g
life safety protection of the structure.
In seismic design, ULSs that may require consideration include ( fib, 2012): g g g g
reduction of residual resistance below a certain limit permanent deformations exceeding a certain limit loss of equilibrium of the structure or part of it, considered as a rigid body (e.g. overturning) sliding beyond a certain limit or overturning.
In seismic design there may be several ULSs, with different consequences of limit state failure, high or medium. According to the fib 2010 Model Code ( fib, 2012), in seismic design at least one – but normally both – of the following ULSs must be explicitly considered, each one for a different representative value of the seismic action: g
6
The life safety (LS) limit state: this is reached if any of the following conditions are met (but not surpassed): – the structure is significantly damaged, but does not collapse, not even partly, retaining its integrity – the structure does not provide sufficient safety for normal use, although it is safe enough for temporary use – secondary or non-structural components are seriously damaged, but do not obstruct emergency use or cause life-threatening injuries by falling down – the structure is on the verge of losing capacity, although it retains sufficient load-bearing capacity and sufficient residual strength and stiffness to protect life for the period until the repair is completed
Chapter 2. Performance requirements and compliance criteria
g
– repair is economically questionable and demolition may be preferable. The near-collapse (NC) limit state: this is reached if any of the following conditions are met: – the structure is heavily damaged and is at the verge of collapse – although life safety is mostly ensured during the loading event, it is not fully guaranteed as there may be life-threatening injury situations due to falling debris – the structure is unsafe even for emergency use, and would probably not survive additional loading – the structure presents low residual strength and stiffness but is still able to support the quasi-permanent loads.
A representative seismic action, with a prescribed probability of not being exceeded during the design service life, should be defined for each limit state considered. According to the fib 2010 Model Code ( fib, 2012), multiple representative seismic actions appropriate for ordinary facilities are: g
g g g
For the operational (OP) limit state: a ‘frequent’ seismic action, expected to be exceeded at least once during the design service life (i.e. having a mean return period much shorter than the design service life). For immediate use (IU): an ‘occasional’ earthquake, not expected to be exceeded during the design service life (e.g. with a mean return period about twice the design service life). For life safety (LS): a ‘rare’ seismic action, with a low probability of being exceeded (10%) during the design service life. For near-collapse (NC): a ‘very rare’ seismic action, with very low probability of being exceeded (2–5%) in the design service life of the structure.
For facilities whose consequences of failure are very high, the ‘very rare’ seismic action may be appropriate for the life safety limit state. For those which are essential for the immediate postearthquake period, a ‘rare’ seismic action may be appropriate for the immediate use or even the operational limit state ( fib, 2012). A fully fledged performance-based seismic design of a bridge as outlined above for the case of the fib 2010 Model Code ( fib, 2012) will serve well the interests and objectives of owners, in that it allows explicit verification of performance levels related to different level of operation (including loss) of the bridge under frequent, occasional, rare or quite exceptional earthquakes. However, the design process may become too complex and cumbersome. Therefore, even the fib 2010 Model Code ( fib, 2012) recognises that, depending on the use and importance of the facility, competent authorities will choose how many and which limit states should be verified at a minimum and which representative seismic action they will be paired with. The seismic design of a bridge, or at least certain of its aspects, may be conditioned by just one of these limit states. However, this may hold on a site-specific but not on a general basis, because the seismicity of the site controls the relative magnitude of the representative seismic actions for which the multiple limit states should be verified. In closing this discussion on the performance-based design of bridges, a comment is required on sustainability performance: it is not explicitly addressed in the first generation of Eurocodes, but will be in the next one, as the European Union recently added ‘Sustainable use of resources’ to the two essential requirements of ‘Mechanical resistance and stability’ and ‘Resistance to fire’ for construction products that must be served by the Eurocodes. The fib 2010 Model Code ( fib, 2012), which has raised sustainability performance to the same level as serviceability and structural safety, speaks about it still in rather general terms. At any rate, the sustainabilityconscious bridge designer should cater in the conceptual design phase for aesthetics and the minimisation of environmental impact (including during execution) and during all phases, from concept to detailed design, for savings in materials.
2.2.
Performance requirements for new bridges in Eurocode 8
Part 2 of Eurocode 8 (CEN, 2005) requires a single-level seismic design of new bridges with the following explicit performance objective:
Clauses 2.1(1), 2.2.2(1), 2.2.2(4) [2] 7
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
g
The bridge must retain its structural integrity and have sufficient residual resistance to be used for emergency traffic without any repair after a rare seismic event – the ‘design seismic action’ explicitly defined in Parts 1 and 2 of Eurocode 8; any damage due to this event must be easily repairable.
Although called a ‘non-collapse requirement’, in reality this corresponds to the life safety, rather than to the near-collapse, limit state of the general framework of performance-based seismic design outlined in the previous section, since sufficient residual resistance has to be available after the design seismic event for immediate use by emergency traffic. Clause 2.1(1) [1,2]
As we will see in more detail in Section 3.12.2 of this Guide, the ‘design seismic action’ of structures of ordinary importance is called the ‘reference seismic action’; its mean return period is the ‘reference return period’, denoted by TNCR . Eurocode 8 recommends basing the determination of the ‘design seismic action’ on a 10% exceedance probability in 50 years, corresponding to a ‘reference return period’ of 475 years.
Clause 2.2.2(5) [2]
If the seismicity is low, the probability of exceedance of the ‘design seismic action’ during the design life of the bridge may be well below 10%, and at any rate difficult to quantify. For such cases, Eurocode 8 allows for consideration of the seismic action as an ‘accidental action’; also, in these cases it tolerates more damage to the bridge deck and secondary components, as well to the bridge parts intended for controlled damage under the ‘design seismic action’.
Clauses 2.1(2)–2.1(6) [2] Clause 3.2.1(3) [1]
Again as detailed in Section 3.12.2 of this Guide, Eurocode 8 pursues enhanced performance for bridges that are vital for communications in the region or very important for public safety, not by upgrading the performance level, as suits the general framework of performance-based seismic design delineated in the previous section, but by modifying the hazard level (increasing the mean return period) for the ‘design seismic action’ under which the ‘non-collapse requirement’ is met. This is done by multiplying the ‘reference seismic action’ by the ‘importance factor’ gI , which by definition is gI ¼ 1.0 for bridges of ordinary importance (i.e. for the reference return period of the seismic action).
Clauses 2.2.1(1), 2.2.3(1), 2.3.1(1) [2]
Part 2 of Eurocode 8 calls also for the limitation of damage under a loosely defined seismic action with a high probability of exceedance; such damage must be minor and limited only to secondary components and to the parts of the bridge intended for controlled damage under the ‘design seismic action’. However, this requirement is of no practical consequence for design: it is presumed to be implicitly fulfilled if all the criteria for compliance with the ‘non-collapse requirement’ above are checked and met. This should be contrasted with new buildings, for which Part 1 of Eurocode 8 (CEN, 2004) provides explicit checks under a well-defined ‘damage limitation’ seismic action. However, these damage checks (inter-storey drifts) normally refer to non-structural elements that are not present in bridges.
Clauses 2.3.4(1), 2.3.4(2) [2]
Although not explicitly stated, an additional performance requirement for bridges designed to face the ‘design seismic action’ by means of ductility and energy dissipation is the prevention of the near-collapse limit state in an extreme and very rare, as yet undefined, earthquake. This implicit performance objective is pursued through systematic and across-the-board application of the capacity design concept, which allows full control of the inelastic response mechanism.
2.3. Clauses 2.2.2(3), 2.3.2.2(4) [2]
Clause 2.2.2(5) [2]
8
Compliance criteria for the non-collapse requirement and implementation
2.3.1 Design options to meet the bridge performance requirements For continued use after the ‘design seismic action’ (e.g. by emergency traffic), the deck of the bridge must remain in the elastic range. Damage should be local and limited to non-structural or secondary components, such as expansion joints, parapets or concrete slabs providing topslab continuity between adjacent simply-supported spans, most often built of precast concrete girders. The latter may yield during bending of the deck in the transverse direction. If the seismic action is considered in the National Annex as ‘accidental’, because the probability of exceedance of the ‘design seismic action’ during the design life of the bridge is well below 10%
Chapter 2. Performance requirements and compliance criteria
or undefined, Eurocode 8 allows as an exemption some inelastic action in and damage to the bridge deck. It is today commonplace that the earthquake represents for the structure a demand to accom- Clauses 2.4(3), 2.4(4), 6.6.2.3(1) [2] modate imposed dynamic displacements – primarily in the horizontal direction – and not forces. Seismic damage results from them. The prime aim of seismic design is to accommodate these horizontal displacements with controlled damage. The simple structural system of bridges lends itself to the following options: To place the deck on a system of sliding or horizontally flexible bearings (or bearing-type devices) at the top of the substructure (the abutments and all piers) and accommodate the horizontal displacements at this interface. 2 To fix or rigidly connect horizontally the deck to the top of at least one pier but let it slide or move on flexible bearings at all other supports (including the abutments). The piers that are rigidly connected to the deck are required to accommodate the seismic horizontal displacements by bending. These piers develop inelastic rotations in flexural ‘plastic hinges’, if they are not tall and flexible enough to accommodate the horizontal displacements elastically. 3 To accommodate (most of ) the seismic horizontal displacements in the foundation and the soil, either through sliding at the base of piers or through inelastic deformations of soil– pile systems of the foundation. 4 To rigidly connect the deck with the abutments (either monolithically or via fixed bearings or links) into an integral system that follows the ground motion with little additional deformation of its own. It then makes little difference if any intermediate piers are also integral with the deck or support it on bearings. 1
Option 4 (usually termed ‘integral bridges’) is encountered only in relatively short bridges with one or very few spans. It is dealt with in Section 5.4 of this Designers’ Guide as a special case.
Clauses 4.1.6(9), 4.1.6(10) [2]
Part 5 of Eurocode 8 explicitly allows horizontal sliding of footings with respect to the soil (as long as residual rotation about horizontal axes and overturning are controlled), but this is an unconventional design option adopted for major bridges, notably the 2.45 km continuousdeck Rion-Antirrion bridge with a design ground acceleration of 0.48g. For typical bridges, a non-reversible sliding of one foundation support may entail serious problems. Part 5 of Eurocode 8, as well as Part 2, also allows inelastic deformations in foundation piles. This may be the only viable option if the deck is monolithic with strong and rigid wall-like piers placed transverse to the bridge axis.
Clauses 5.4.1.1(7), 5.4.2(7) [3] Clause 4.1.6(7) [2]
Most common in practice are options 1 and 2, which are therefore considered as the two fundamental options for the seismic design of bridges. Option 1 is considered in Part 2 of Eurocode 8 as full seismic isolation, with the piers designed to remain elastic during the ‘design seismic action’.
Clauses 2.3.2.1(10), 4.1.6(11) [2]
In option 2, the piers are normally designed to respond well into the inelastic range, mobilising ductility and energy dissipation to withstand the seismic action. Design based on ductility and energy dissipation capacity is seismic design par excellence. It is at the core of Part 2 of Eurocode 8, where it is called ‘design for ductile behaviour’, as well as of this Designers’ Guide.
Clauses 2.2.2(2), 2.2.2(4), 2.3.2.2(1), 2.3.2.2(2), 2.3.2.2(7), 4.1.6(6) [2]
Ductility and energy dissipation under the ‘design seismic action’ is entrusted by Part 2 of Eurocode 8 to the piers, and is understood to entail a certain degree of damage at the plastic hinges (spalling of the unconfined concrete shell outside the confining hoops, but no buckling or fracture of bars, nor crushing of confined concrete inside the hoops). However, as this damage is meant to be reparable, it should be limited to easily accessible parts of the pier. Parts above the normal water level (be it in a sleeve or casing) are ideal. Those at a shallow depth below grade but above the normal water table are also accessible. Those embedded deeper in fill but above the normal water level are still accessible but with increased difficulty. Part 2 of Eurocode 8 does not distinguish in great detail between these cases. It considers, though, as accessible the base of a pier deep in backfill but as inaccessible parts of the pier which are deep in water, or piles under large pile-caps; to reduce damage in such regions
Clauses 2.2.2(4), 2.3.2.2(3) [2]
9
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
under the ‘design seismic action’, it divides seismic design forces by 0.6 should plastic hinges form there. 2.3.2 Design of bridges for energy dissipation and ductility 2.3.2.1 Introduction Section 2.3.2 refers to one of the two fundamental options for the seismic design of bridges, namely to option 2: that of fixing horizontally the deck to the top of at least one pier but to let it slide at the abutments and accommodate the seismic horizontal displacements through bending of the piers, with ductile and dissipative flexural ‘plastic hinges’ forming at their ends.
Clauses 2.3.5.2(1), 2.3.5.2(2), 2.3.6.1(8) [2]
2.3.2.2 Design of the bridge as a whole for energy dissipation and ductility It has already been pointed out that the earthquake is a dynamic action, representing for a structure a requirement to sustain certain displacements and deformations and not specific forces. Eurocode 8 allows bridges to develop significant inelastic deformations under the design seismic action, provided that the integrity of individual components and of the bridge as a whole is not jeopardised. Design of a bridge to Eurocode 8 for the non-collapse requirement under the ‘design seismic action’ is force-based, nonetheless. The foundation of force-based seismic design for ductility and energy dissipation is the inelastic response spectrum of a single-degree-of-freedom (SDoF) system having an elastic–perfectly plastic force–displacement curve, F d, in monotonic loading. For given period, T, of the elastic SDoF system, the inelastic spectrum relates: g g
the ratio q ¼ Fel/Fy of the peak force, Fel , that would have developed if the SDoF system were linear elastic, to the yield force of the system, Fy the maximum displacement demand of the inelastic SDoF system, dmax , expressed as ratio to the yield displacement, dy (i.e. as the displacement ductility factor, md ¼ dmax/dy).
Part 2 of Eurocode 8 has adopted a modification of the inelastic spectra proposed in Vidic et al. (1994):
md ¼ q md ¼ 1 þ ðq 1Þ md ¼ 1
1:25TC 5q 4 T
if T 1:25TC
ðD2:1aÞ
if T , 1:25TC
ðD2:1bÞ
if T , 0:033 s
ðD2:1cÞ
where TC is the ‘transition period’ of the elastic spectrum, between its constant spectral pseudoacceleration and constant spectral pseudo-velocity ranges (see Section 3.1.3). Equation (D2.1) expresses Newmark’s well-known ‘equal displacement rule’; that is, the empirical observation that in the constant spectral pseudo-velocity range the peak displacement response of the inelastic and of the elastic SDoF systems are about the same. With F being the total lateral force on the structure (the base shear, if the seismic action is in the horizontal direction), the ratio q ¼ Fel/Fy is termed in Eurocode 8 the ‘behaviour factor’ (the ‘force reduction factor’ or the ‘response modification factor’, R, in North America). It is used as a universal reduction factor on the internal forces that would develop in the elastic structure for 5% damping, or, equivalently, on the seismic inertia forces that would develop in this elastic structure and cause, in turn, the seismic internal forces. In this way, the seismic internal forces for which the members of the structure should be dimensioned can be calculated through linear-elastic analysis. In return, the structure must be provided with the capacity to sustain a peak global displacement at least equal to its global yield displacement multiplied by the displacement ductility factor, md , that corresponds to the value of q used for the reduction of elastic force demands (e.g. according to Eqs (D2.1)). This is termed the ‘ductility capacity’, or the ‘energy-dissipation capacity’ – as it has to develop through cyclic response in which the members and the structure as a whole dissipate part of the seismic energy input through hysteresis. 10
Chapter 2. Performance requirements and compliance criteria
2.3.2.3 Design of plastic hinges for energy dissipation and ductility In force-based seismic design for ductility and energy dissipation, flexural plastic hinges in piers are dimensioned and detailed to achieve a combination of force resistance and ductility that provides a safety factor between 1.5 and 2 against substantial loss of resistance to lateral (i.e. horizontal) load. To this end, they are first dimensioned to provide a design value of moment and axial force resistance Rd , at least equal to the corresponding action effects due to the seismic design situation, Ed , from the analysis: Ed Rd
Clause 2.3.3(1) [2]
(D2.2)
The values of Ed in Eq. (D2.2) are due to the combination of the seismic action with the quasi-permanent gravity actions (i.e. the nominal permanent loads and the quasi-permanent traffic loads, as pointed out in Section 5.4 in connection with Eq. (D5.6a) for the calculation of the deck mass). As linear analysis is normally applied, Ed may be found from superposition of the seismic action effects from the analysis for the seismic action alone to the action effects from that for the quasi-permanent gravity actions. After having been dimensioned to meet Eq. (D2.2), flexural plastic hinges in piers are detailed to provide the deformation and ductility capacity necessary to meet the deformation demands on them from the design of the structure for the chosen q-factor value. The measure used for the deformation and ductility capacity of flexural plastic hinges is the curvature ductility factor of the pier end section, whose supply-value is
mf ¼ fu/fy
Clauses 2.3.5.1(1), 2.3.5.3(1), 2.3.5.3(2), 2.3.6.1(8), Annex B, Annex E [2]
(D2.3)
where fy is the yield curvature of that section (computed from first principles) and fu its ultimate curvature (again from first principles and the ultimate deformation criteria adopted for the materials). At the other end, the global displacement demands are expressed through the global displacement ductility factor of the bridge, md , connected to the q factor used in the design of the bridge through the inelastic spectra, in this case Eqs (D2.1). The intermediary between mf and md is the ductility factor of the chord rotation at the pier end where the plastic hinge forms, mu . Recall that the chord rotation u at a pier end is the deflection of the inflexion point with respect to the tangent to the pier axis at the end of interest, divided by the distance between these two points of the pier, termed the ‘shear span’ and denoted by Ls . So, the chord rotation u is a measure of member displacement, not of the relative rotation between sections. If the pier is fixed at its base against rotation and supports the deck without the intervention of horizontally flexible bearings (i.e. if it is monolithically connected or supported on the pier through fixed – e.g. pot – bearings), the chord rotation at the hinging end of the pier is related as follows to the deck displacement right above the pier top, d, in the common cases of: Pier columns monolithically connected at the top to a very stiff deck with near-fixity there against rotation for seismic response in the longitudinal direction and inflexion point at the column mid-height (see Section 5.4, Eqs (D5.4) if the deck cannot be considered as rigid compared with the piers in the longitudinal direction); the horizontal displacement of that point is one-half of that of the deck above, d, and the shear span, Ls , is about equal to one-half of the pier clear height, Hp ; Ls Hp/2; therefore, at the plastic hinges forming at both ends of the pier, u 0.5d/Ls ¼ d/Hp . 2 Multiple-column piers monolithically connected at the top to a very stiff deck or a cap beam with near-fixity there against rotation for seismic response in the transverse direction; the situation is similar to case 1 above, so in the transverse direction Ls Hp/2 and u 0.5d/Ls ¼ d/Hp . 3 Piers supporting the deck through fixed (e.g. pot) bearings at the top and working as vertical cantilevers with a shear span Ls about equal to the pier clear height, Ls Hp and u ¼ d/Ls ¼ d/Hp . 4 Single-column piers monolithic with the deck and working in the transverse direction of the bridge as vertical cantilevers; if the rotational inertia of the deck about its longitudinal axis and the vertical distance between the pier top and the point of application of the deck 1
11
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
inertia force are neglected (see Section 5.4, Eqs (D5.5) for the case they are not), the situation is similar to case 3 above, so in the transverse direction Ls Hp and u ¼ d/Ls ¼ d/Hp . In a well-designed bridge, all piers will yield at the same time, turning the bridge into a fully fledged plastic mechanism. Then, in all cases 1 to 4 above, md ¼ d/dy will be (about) equal to mu ¼ u/uy:
md mu
(D2.4)
In a plastic hinge model of the inelastic deformation of the pier, all inelastic deformations are lumped in the plastic hinge, which is considered to have a finite length Lpl and to develop constant inelastic curvature all along Lpl . Then, for a linear bending moment diagram (constant shear force) along the pier, the chord rotation at its yielding end(s) is Lpl Ls u ¼ fy þ f fy Lpl 1 3 2Ls
ðD2:5Þ
giving, for uy ¼ fyLs/3 (purely flexural elastic behaviour), 3Lpl Lpl mu ¼ 1 þ mf 1 1 Ls 2Ls
ðD2:6Þ
Equation (D2.6) is inverted as
mf ¼
fu md 1 ¼1þ fy 3lð1 0:5lÞ
ðD2:7Þ
where l ¼ Lpl/Ls . Then, if the pier plastic hinge length Lpl is estimated through appropriate empirical relations, Eqs (D2.1) and (D2.7) translate the q factor used in the design of the bridge into a demand value for the curvature ductility factor of the piers. Note that Part 1 of Eurocode 8 has adopted for concrete members in buildings the following conservative approximation of Eqs (D2.6) and (D2.7):
mu ¼ 1 þ 0.5(mf 1)
i.e. mf ¼ 2mu 1
(D2.8)
dating from the ENV version of the concrete buildings part of Eurocode 8 (ENV 1998-1-3:1994). Clauses 2.3.5.4(1), 2.3.5.4(2) [2]
Clauses 2.3.3(1), 2.3.4(1), 2.3.4(2), 2.3.6.2(2) [2]
If linear analysis is used alongside the design spectrum involving the q factor, the required value of the curvature ductility factor of the piers is presumed to be provided if the detailing rules of Part 2 of Eurocode 8 are applied, prescriptive or not. If nonlinear analysis is used instead, the inelastic chord rotation demands obtained from it are compared with appropriate design values of chord rotation capacities, obtained by setting f ¼ fu in Eq. (D2.5). Details are given in Chapter 6. 2.3.2.4 Capacity design for the ductile global response The bridge’s seismic design determines how the (roughly) given peak global displacement demand of the design seismic action is distributed to its various components. Eurocode 8 uses ‘capacity design’ to direct and limit this demand only to those best suited to withstand it. Capacity design imposes a hierarchy of strengths between adjacent components or regions, and between different mechanisms of load transfer in the same member, so that those items capable of ductile behaviour and hysteretic energy dissipation are the first ones to develop inelastic deformations. More importantly, they do so in a way that precludes the development of inelastic deformations in any component, region or mechanism deemed incapable of ductile behaviour and hysteretic energy dissipation. The components, regions thereof or mechanisms of force transfer to which the peak global displacement and deformation energy demands are channelled by capacity design are selected,
12
Chapter 2. Performance requirements and compliance criteria
taking into account the following aspects: Their inherent ductility. Ductile components, regions thereof or mechanisms of force transfer are entrusted through ‘capacity design’ for inelastic deformations and energy dissipation, while brittle ones are shielded from them. Flexure is a far more ductile mechanism of force transfer than shear, and can be made even more so through judicious choice of the level of axial force and the amount, distribution and ductility of longitudinal and transverse reinforcement. 2 The role of the component for the integrity of the whole and the fulfilment of the performance requirements of the bridge. The foundation and connections between components (bearings, links, holding-down devices, etc.) securing structural integrity are most important for the stability and integrity of the whole; the integrity of the deck itself determines the continued operation of the bridge after the earthquake. 3 Accessibility and difficulty in inspecting and repairing any damage. Accessible regions of the piers (above the grade and the water level) are the easiest to repair without disruption of traffic. 1
On the basis of the above aspects, a clear hierarchy of the bridge components and mechanisms of force transfer emerges, determining the order in which they are allowed to enter the inelastic range during the seismic response: the deck, the connections between components and the foundation are to be shielded from inelastic action; the last is channelled to flexural plastic hinges at accessible ends of the piers. Capacity design ensures that this order is indeed respected. As we will see in more detail later, it works as follows. The required force resistance of the components, regions thereof or mechanisms of force transfer to be shielded from inelastic response is not determined from the analysis. Simple calculations (normally on the basis of equilibrium alone) are used instead, assuming that all relevant plastic hinges develop their moment resistances in a way that prevents preemptive attainment of the force resistance of the components, etc., to be shielded from inelastic action. 2.3.2.5 How elastic deformations in flexible bearings or the foundation ground affect the ductility of the bridge Assume that the deck is supported on a ductile pier that can develop a curvature ductility factor mfo in the plastic hinge(s) and a chord rotation ductility factor muo , and has elastic lateral stiffness Kp if fixed at the base:
Annex B [2]
(a) For a single-column pier presenting flexural rigidity (EI )c in a vertical plane in the transverse direction of the bridge and supporting a deck mass with a radius of gyration rm,d about its centroidal axis (r2m,d ¼ ratio of tributary rotational mass moment of inertia of the deck about the deck’s centroidal axis to the tributary deck mass): "
Kp H
9r2m;d 8Ls
3ðEIÞc ! # 2 þ Ls H þ ycg þ ycg
ðD2:9aÞ
In Eq. (D2.9a), ycg is the distance from the soffit of the deck to the centroid of its section, and Ls is the shear span at the pier base (see Eq. (D5.5) in Section 5.4 for this particular case). (b) For a pier consisting of n 1 columns, each one with height H and presenting the rigidity (EI )c within the plane of bending considered, all having the top fixed to the soffit of a very stiff deck: Kp ¼ 12Sn(EI )c/H3
(D2.9b)
Single-column piers (n ¼ 1) in the transverse direction of the bridge are not addressed by this case but by case 1 above and Eq. (D2.9a). 13
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
(c) For a pier as in case 2 above but with the top of its n 1 columns pin-connected to the deck, instead of being fixed to it: Kp ¼ 3Sn(EI )c/H3
(D2.9c)
Assume also that one or more additional components intervene between the deck and the ground in series with the pier, all designed to remain elastic until and after the pier yields (e.g. through capacity design according to the previous section). The generic elastic stiffness of these components is denoted as Kel . Such components can be: g
g
the compliance of the ground – if the foundation itself has horizontal stiffness Kfh (base shear divided by the horizontal displacement of the foundation) and rotational stiffness Kff (moment divided by the rotation at the pier base), giving horizontal stiffness at the top of the pier Kff/H2 – and/or an elastic (e.g. elastomeric) bearing with horizontal stiffness Kb (Kb ¼ GA/t if the bearing has horizontal section area A, and its material – the elastomer – has total thickness t and shear modulus G) – needless to say, this case does not combine with piers of case 2 above, which have their top fixed to the soffit of the deck.
The deck sees down below a total stiffness K such that X 1 1 1 1 1 1 H2 ¼ þ ¼ þ þ þ K Kp Kel Kp Kb Kfh Kff
ðD2:10Þ
If the pier yields at a base shear Vy , the displacement of the deck at yielding is
dy ¼
Vy Vy X Vy ¼ þ K Kp Kel
ðD2:11Þ
After the pier yields, additional horizontal displacements are due to the inelastic rotation(s) of its plastic hinge(s) alone, giving an inelastic displacement of the deck: Vy md dy ¼ muo 1 þ dy Kp
ðD2:12Þ
where md is the global displacement ductility factor of the bridge at the level of the deck. According to Eqs (D2.4), (D2.6) and (D2.7), there is proportionality between (md 1), (mu 1) and (mf 1). Therefore, Eqs (D2.9)–(D2.11) state that, to achieve the same target value md of the global displacement ductility factor of the bridge at the level of the deck, the curvature ductility demand at a plastic hinge of a pier should increase from mfo to X Kp mf ¼ 1 þ mfo 1 1 þ Kel
ðD2:13Þ
The horizontal stiffness of an elastic bearing is several times smaller than that of an ordinary pier. So, Eq. (D2.13) gives unduly large values of the curvature ductility demand that a plastic hinge in the pier may have to bear for the bridge to achieve the q factor values normally used in the seismic design of bridges for ductility. So, if piers are intended to resist the design seismic action through ductility and energy dissipation, elastic bearings have no place on top of them. By the same token, ductile piers should be nearly fixed to the ground: compliance of the foundation will penalise detailing of their plastic hinges for the target q factor of seismic design for ductility. The same conclusion can be reached through energy considerations. The pier is an assembly of components in series, only one of which (the pier shaft having stiffness Kp) possesses the capability of hysteretic energy dissipation. The other components (elastic bearings at the pier top and foundation compliance, having a composite stiffness Kel) should remain within the elastic range. As the same shear force acts on all components in series, the strain energy 14
Chapter 2. Performance requirements and compliance criteria
input in each component at any instant of the seismic response is proportional to their flexibilities, 1/Kp and 1/Kel , respectively. When the portion of the energy input in the dissipative component is small compared with the input in the series system, the dissipation capability of the whole assembly is also small. In other words, the behaviour of such assemblies becomes practically elastic. 2.3.3
Seismic design of bridges for strength instead of ductility: limited ductile behaviour Part 2 of Eurocode 8 gives the option to design a bridge to resist the seismic action through strength alone, without explicitly resorting to ductility and energy dissipation capacity. In this option, the bridge is designed: g g g
Clauses 2.3.2.1(1), 2.3.2.2(1), 2.3.2.3(1), 2.3.3(2), 2.3.4(3), 2.3.5.4(3) [2]
in accordance with Eurocodes 2, 3, 4 and 7, with the seismic action considered as a static loading (like wind) without capacity design considerations, except for non-ductile connections or structural components (fixed bearings, sockets and anchorages of cables and stays), but observing: – some minimum requirements for the ductility of steel reinforcement or steel sections and for confinement and bar anti-buckling restraint in potential plastic hinges of concrete piers – simplified rules for the ULS verification in shear.
The seismic lateral forces are derived from the design response spectrum using a behaviour factor, q, not higher than the value of 1.5 attributed to material overstrength. In fact: (a) if the bridge seismic response is dominated by upper modes (as in cable-stayed bridges) or (b) concrete piers have: – axial force ratio hk ¼ Nd/Ac fck (axial load due to the design seismic action and the concurrent gravity loads, Nd , normalised to product of the pier section area and the characteristic concrete strength, Ac fck), higher than or equal to 0.6, or – shear-span ratio, Ls/h, in the direction of bending less than or equal to 1.0,
Clauses 2.3.2.3(2), 4.1.6(3), 4.1.6(5) [2]
then the behaviour factor, q, is taken equal to 1.0. As design seismic forces are derived with a value of the behaviour factor, q, possibly greater than 1.0, structures designed for strength and little engineered ductility and energy dissipation capacity are termed ‘limited ductile’, in lieu of ‘non-ductile’. Part 2 of Eurocode 8 recommends (in a note) designing the bridge for ‘limited-ductile’ behaviour in cases of ‘low seismicity’ (see below), but does not discourage the designer from using this option in other cases as well. It specifies the option as the only possible one, no matter whether the bridge is a ‘low-seismicity’ case or not, in two very specific but also quite common cases:
Clauses 2.3.7(1), 2.3.2.1(1), 2.4(2), 2.4(3), 4.1.6(3), 4.1.6(9)–4.1.6(11) [2]
when the deck is fully supported on a system of sliding or horizontally flexible bearings (or bearing-type devices) at the top of the substructure (the abutments and all piers), which accommodate the horizontal displacements (see option 1 in Section 2.3.1 and the influence of non-dissipative components in Section 2.3.2.5 above), or 2 when the deck is rigidly connected to the abutments, monolithically or via fixed bearings or links (listed as option 4 in Section 2.3.1 of this Guide). 1
2.3.4 The balance between strength and ductility The option described in Section 2.3.3 above, namely to design for strength alone without engineered ductility and energy dissipation capacity, is an extreme, specified by Part 2 of Eurocode 8 only for cases a and b and 1 and 2 well delineated in Section 2.3.3. Outside of these specific cases, the designer is normally given the option to opt for more strength and less ductility (i.e. for ‘limited-ductile’ behaviour) or vice versa (for ‘ductile’ behaviour).
Clause 2.3.2.1(1)
Equations (D2.1) show that, except for short-period bridges, the magnitude of the design seismic forces decreases when the global displacement ductility factor, md , increases. So, there is an 15
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
apparent economic incentive to increase the available global ductility, to reduce the internal forces for which the components of the bridge are dimensioned. Moreover, if the lateral force resistance of the bridge is reduced, by dividing the elastic lateral force demands by a high qfactor value, the verification of the foundation soil, which is done for strength rather than for ductility and deformation capacity, is much easier. Last but not least, a bridge with ample ductility supply is less sensitive to the magnitude and the details of the seismic action, and, in view of the large uncertainty associated with the extreme seismic action in its lifetime, may be a better earthquake-resistant design. On the other hand, there are strong arguments for less ductility and dissipation capacity in seismic design and more lateral force resistance instead. Ductility necessarily entails damage. So, the higher the lateral strength of the bridge, the smaller will be the structural damage, not only during more frequent, moderate earthquakes but also due to the design seismic action. From the construction point of view, detailing piers for more strength is much easier and simpler than detailing for higher ductility. Also, some bridge configurations may impart significant lateral force resistance. In others (notably when the deck is rigidly supported on tall and flexible piers), the dominant vibration modes may fall at the long-period tail of the spectrum, where design spectral accelerations may be small even for q 1.5, and dimensioning the piers for the resulting lateral force resistance may be trivial. Last but not least, if the bridge falls outside the framework of common structural configurations mainly addressed by Eurocode 8 (e.g. as in arch bridges, or those having some inclined piers or piers of very different height, especially if the height does not increase monotonically from the abutments to mid-span), the designers may feel more confident if they narrow the gap between the results of the linearelastic analysis, for which members are dimensioned and the nonlinear seismic response under the design seismic action (i.e. if q 1.5 is used). Clauses 3.2.1(4) [1] Clause 2.3.7(1) [2]
2.3.5 The cases of ‘low seismicity’ Eurocode 8 recommends in a note designing the bridge for ‘limited ductile’ behaviour if it falls in the case of ‘low seismicity’. Although it leaves it to the National Annex to decide which combination of categories of structures, ground types and seismic zones in a country correspond to the characterisation as ‘cases of low seismicity’, it recommends in a note as a criterion either the value of the design ground acceleration on type A ground (i.e. on rock), ag (which includes the importance factor gI), or the corresponding value, agS, over the ground type of the site (see Section 3.1.2.3 of this Guide for the soil factor, S). Moreover, it recommends a value of 0.08g for ag , or of 0.10g for agS, as the threshold for the low-seismicity cases.
Clauses 2.2.1(4), 3.2.1(5) [1]
2.4.
Exemption from the application of Eurocode 8
Eurocode 8 itself states that its provisions need not be applied in ‘cases of very low seismicity’. As in ‘cases of low seismicity’, it leaves it to the National Annex to decide which combination of category of structures, ground types and seismic zones in a country qualify as ‘cases of very low seismicity’. It does recommend in a note, though, the same criterion as for the ‘cases of low seismicity’: either the value of the design ground acceleration on type A ground (i.e. on rock), ag , or the corresponding value, agS, over the ground type of the site. It recommends a value of 0.04g for ag , or of 0.05g for agS, as the threshold for the very low seismicity cases. Because the value of ag includes the importance factor gI , ordinary bridges in a region may be exempted from the application of Eurocode 8, while more important ones may not be. This is consistent with the notion that the exemption from the application of Eurocode 8 is due to the inherent lateral force resistance of any structure designed for non-seismic loadings, neglecting any contribution from ductility and energy dissipation capacity. Given that Eurocode 8 considers that, because of overstrength, any structure is permitted a behaviour factor, q, of at least 1.5, implicit in the value of 0.05g for agS recommended as the ceiling for very low seismicity cases is a presumed lateral force capacity of 0.05 2.5/1.5 ¼ 0.083g. If a National Annex states that the entire national territory is considered as a ‘case of very low seismicity’, then Eurocode 8 (all six parts) does not apply at all in the country. REFERENCES
CEN (Comite´ Europe´en de Normalisation) (2002) EN 1990: Eurocode – Basis of structural design (including Annex A2: Application to bridges). CEN, Brussels. 16
Chapter 2. Performance requirements and compliance criteria
CEN (2004) EN 1998-1:2004: Eurocode 8 – Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings. CEN, Brussels. CEN (2005) EN 1998-2:2005: Eurocode 8 – Design of structures for earthquake resistance – Part 2: Bridges. CEN, Brussels. fib (2012) Model Code 2010, vol. 1. fib Bulletin 65. Fe´de´ration Internationale du Be´ton, Lausanne. Vidic T, Fajfar P and Fischinger M (1994) Consistent inelastic design spectra: strength and displacement. Earthquake Engineering and Structural Dynamics 23: 502–521.
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Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance ISBN 978-0-7277-5735-7 ICE Publishing: All rights reserved http://dx.doi.org/10.1680/dber.57357.019
Chapter 3
Seismic actions and geotechnical aspects 3.1.
Design seismic actions
3.1.1 Introduction As pointed out in Section 2.2 of this Guide, Eurocode 8 entails a single-tier seismic design of new bridges, with verification of the no-(local-)collapse requirement under the ‘design seismic action’ alone. So, whatever is said in Section 3.1 refers to the ‘design seismic action’ of the bridge. Note, however, that in its two-tier seismic design of buildings and other structures, Part 1 of Eurocode 8 (CEN, 2004a) adopts the same spectral shape for the different seismic actions to be used for different performance levels or limit states. The difference in the hazard level is reflected only through the peak ground acceleration to which each spectrum is anchored. The seismic action is considered to impart concurrent translational motion in three orthogonal directions: the vertical and two horizontal ones at right angles to each other. The motion is taken to be applied at the interface between the structure and the ground. If springs are used to model the soil compliance under and/or around spread footings, piles or shafts (caissons), the motion is considered to be applied at the soil end of these springs. 3.1.2 Elastic response spectra 3.1.2.1 Introduction The reference representation of the seismic action in Eurocode 8 is through the response spectrum of an elastic single-degree-of-freedom (SDoF) oscillator having a given viscous damping ratio (with 5% being the reference value). Any other alternative representation of the seismic action (e.g. in the form of acceleration time histories) should conform to the elastic response spectrum for the specified value of the damping ratio.
g
Clauses 3.1.1(2), 3.1.2(1)–3.1.2(3) [2]
Clause 3.2.2.1(1) [1] Clause 3.2.1(1) [2]
Clause 7.5.4(3), Table 7.1 [2]
Because: g
Clause 2.1(1) [2] Clauses 2.1(1), 2.2.1(1) [1]
earthquake ground motions are traditionally recorded as acceleration time histories and seismic design is still based on forces, conveniently derived from accelerations,
the pseudo-acceleration response spectrum, Sa(T ), is normally used. If spectral displacements, Sd(T ), are of interest, they can be obtained from Sa(T ), assuming simple harmonic oscillation: Sd(T ) ¼ (T/2p)2Sa(T )
(D3.1)
Spectral pseudo-velocities can also be obtained from Sa(T ) as Sv(T ) ¼ (T/2p)Sa(T )
(D3.2)
Note that pseudo-values do not correspond to the real peak spectral velocity or acceleration. For a damping ratio of up to 10% and for a natural period T between 0.2 and 1.0 s, the pseudovelocity spectrum closely approximates the actual relative velocity spectrum. 3.1.2.2 Design ground accelerations – importance classes for reliability differentiation Clauses 3.2.1(2), In Eurocode 8 the elastic response spectrum is taken as proportional (‘anchored’) to the peak 3.2.2.1(1),3.2.2.3(1)[1] acceleration of the ground: 19
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
g g
Clause 2.1(3) [2] Clause 3.2.1(3) [1]
the horizontal peak acceleration, ag , for the horizontal component(s) of the seismic action or the vertical peak acceleration, avg , for the vertical component.
The basis of the seismic design of new bridges in Eurocode 8 is the ‘design seismic action’, for which the no-(local-)collapse requirement should be met. It is specified through the ‘design ground acceleration’ in the horizontal direction, ag , which is equal to the ‘reference peak ground acceleration’ on rock from national zonation maps, multiplied by the importance factor, gI , of the bridge: ag ¼ gIagR
(D3.3)
For bridges of ordinary importance (belonging to importance class II in Eurocode 8), by definition gI ¼ 1.0. Clauses 2.1(4)–2.1(6) [2]
Eurocode 8 recommends classifying in importance class III any bridge that is crucial for communications, especially in the immediate post-earthquake period (including access to emergency facilities), or whose downtime may have a major economic or social impact, or which by failing may cause large loss of life, as well as major bridges with a target design life longer than the ordinary nominal life of 50 years. For importance class III, it recommends gI ¼ 1.3. Bridges that are not critical for communications, or considered not economically justified to design for the standard bridge design life of 50 years, are recommended by Eurocode 8 to be classified in importance class I, with a recommended value gI ¼ 0.85.
Clause 2.1(3), The reference peak ground acceleration, agR , corresponds to the reference return period, TNCR , Annex A [2] of the design seismic action for bridges of ordinary importance. Clauses 2.1(1), 2.1(3), Note that, under the Poisson assumption of earthquake occurrence (i.e. that the number of earth2.1(4) [1]
quakes in an interval of time depends only on the length of the interval in a time-invariant way), the return period, TR , of seismic events exceeding a certain threshold is related to the probability that this threshold will be exceeded, P, in TL years as TR ¼ –TL/ln(1 P)
(D3.4)
So, for a given TL (e.g. the conventional design life of TL ¼ 50 years) the seismic action may equivalently be specified either via its mean return period, TR , or its probability of exceedance in TL years, PR . Values of the importance factor greater or less than 1.0 correspond to mean return periods longer or shorter, respectively, than TNCR . It is within the authority of each country to select the value of TNCR that gives the appropriate trade-off between economy and public safety in its territory, as well as the importance factors for bridges other than ordinary, taking into account the specific regional features of the seismic hazard. Part 1 of Eurocode 8 recommends the value TNCR ¼ 475 years. The mean return period, TR(ag), of a peak ground acceleration exceeding a value ag is the inverse of the annual rate, la(ag), of exceedance of this acceleration level: TR(ag) ¼ 1/la(ag)
(D3.5)
A functional form commonly used for la(ag) is
la(ag) ¼ Ko(ag) k
(D3.6)
If the exponent k (the slope of the ‘hazard curve’ la(ag) in a log-log plot) is approximately constant, two peak ground acceleration levels ag1 , ag2 , corresponding to two different mean return periods, TR(ag1), TR(ag2), are related as ag1 TR ðag1 Þ 1=k ¼ ag2 TR ðag2 Þ 20
ðD3:7Þ
Chapter 3. Seismic actions and geotechnical aspects
The value of k characterises the seismicity of the site. Regions where the difference in the peak ground acceleration of frequent and very rare seismic excitations is very large, have low k values (around 2). Large values of k (k . 4) are typical of regions where high ground acceleration levels are almost as frequent as smaller ones. Tall free-standing piers, decks built as free cantilevers or incrementally launched, etc., may be much more vulnerable to earthquake than after completion of the full bridge. It is up to the designer or the owner of the bridge to specify the seismic performance requirements before completion of the project and the corresponding compliance and verification criteria. Equation (D3.4) may be used then to determine the mean return period of the seismic action that has a given probability of being exceeded P (e.g. P ¼ 0.05) in the full duration of the bridge construction, Tc , to be used in Eq. (D3.4) in lieu of TL . This mean return period may be used as TR(ag1) in Eq. (D3.7), to compute the peak ground acceleration, ag1 , with a probability P of been exceeded during construction. In that case, ag2 ¼ agR and TR(ag2) ¼ TNCR . 3.1.2.3 Horizontal elastic response spectrum The Eurocode 8 spectra include ranges of: g g g
Annex A [2]
Clauses 3.2.2.1(3), 3.2.2.2(1) [1]
constant spectral pseudo-acceleration for natural periods between TB and TC constant spectral pseudo-velocity between periods TC and TD constant spectral displacement for periods longer than TD .
The elastic response spectral acceleration for any horizontal component of the seismic action is described in Parts 1 and 2 of Eurocode 8 by the following expressions: Short-period range:
T 2:5h 1 0 T TB : Sa ðT Þ ¼ ag S 1 þ TB
ðD3:8aÞ
Constant spectral pseudo-acceleration range: TB T TC : Sa ðT Þ ¼ ag S 2:5h
ðD3:8bÞ
Constant spectral pseudo-velocity range: TC T TD : Sa ðT Þ ¼ ag S 2:5h
TC T
ðD3:8cÞ
Constant spectral displacement range: TD T 4 s: Sa ðT Þ ¼ ag S 2:5h
TC TD T2
ðD3:8dÞ
where ag is the design ground acceleration on rock and S is the ‘soil factor’. pffiffiffiffiffiffiffiffiffiffiffiffi h ¼ 10=ð5 þ jÞ 0:55 (Bommer and Elnashai, 1999) is a correction factor for viscous damping ratio, j, other than the reference value of 5% (from Parts 1 and 2 of Eurocode 8); the value j ¼ 5% is considered to be representative of cracked reinforced concrete. The viscous damping values specified in Part 2 of Eurocode 8 for components of various structural materials are shown in Table 3.1.
Clause 3.2.2.2(3) [1] Clauses 4.1.3(1), 7.5.4(3) [2]
Note the uniform amplification of the entire spectrum by the soil factor, S, over the spectrum for rock. By definition, S ¼ 1 over rock. The value agS plays the role of effective ground acceleration, as the spectral acceleration at the constant spectral acceleration plateau is always equal to 2.5agS. The values of the periods TB , TC and TD (i.e. the extent of the ranges of constant spectral pseudoacceleration, pseudo-velocity and displacement) and of the soil factor, S, are taken to depend mainly on the ground type. In the Eurocodes the term ‘ground’ includes any type of soil and
Clauses 3.2.2.2(2), 3.1.2(1), [1] 21
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
Table 3.1. Values of viscous damping for different structural materials Material
Damping: %
Reinforced concrete components Pre-stressed concrete components Welded steel components Bolted steel components
5 2 2 4
rock. Parts 1 and 2 of Eurocode 8 recognise five standard ground types, over which it recommends values for TB , TC , TD and S, and two special ones, as listed in Table 3.2. Clauses 3.1.2(1)– 3.1.2(3) [1]
The characterisation of the ground is based on the average value of the shear wave velocity, vs,30 , at the top 30 m (CEN, 2004a): 30 vs;30 ¼ X hi
ðD3:9Þ
v i ¼ 1;N i where hi and vi are the thickness (in metres) and the shear wave velocity at small shear strains (less than 10 6) of the ith layer in N layers. If the value of vs,30 is not known, for soil types B, C or D Part 1 of Eurocode 8 allows the use of alternatives to characterise a soil: for cohesionless soils especially, the SPT (Standard Penetration Test) blow-count number may be used (e.g. according to the correspondence of SPT to vs,30 in Ohta and Goto (1976)); for cohesive soils, the undrained cohesive resistance (cu). Clause 3.1.2(4) [1]
Clause 3.2.2.2(2) [1]
The two special ground types, S1 and S2, require the carrying out of special site-specific studies to define the seismic action (CEN, 2004a). For ground type S1, the study should take into account the thickness and the vs value of the soft clay or silt layer and the difference from the underlying materials, and should quantify their effects on the elastic response spectrum. Note that soils of type S1 may have low internal damping and exhibit linear behaviour over a large range of strains, producing peculiar amplification of the bedrock motion and unusual or abnormal soil–structure interaction effects. The scope of the site-specific study should also address the possibility of soil failure under the design seismic action (especially at ground type S2 deposits with liquefiable soils or sensitive clays) (CEN, 2004a). The values of TB , TC , TD and S for the five standard ground types A to E are meant to be defined by each country in the National Annex to Eurocode 8, depending on the magnitude of earthquakes contributing most to the hazard. The geological conditions at the site may also be taken into account in addition, to determine these values. In principle, S factors that decrease with increasing spectral value because of the soil nonlinearity effect may be introduced. Instead of spectral amplification factors that decrease with increasing design acceleration Table 3.2. Ground types in Part 1 of Eurocode 8 for the definition of the seismic action
A B C D E S1 S2
22
Description
vs,30: m/s
NSPT
cu: kPa
Rock outcrop, with less than 5 m cover of weaker material Very dense sand or gravel, or very stiff clay, several tens of metres deep; mechanical properties gradually increase with depth Dense to medium-dense sand or gravel, or stiff clay, several tens to many hundreds of metres deep Loose-to-medium sand or gravel, or soft-to-firm clay 5–20 m surface alluvium layer type C or D – underlain by stiffer material (with vs . 800 m/s) .10 m thick soft clay or silt with plasticity index .40 and high water content Liquefiable soils; sensitive clays; any soil not of type A to E or S1
.800 360–800
– .50
– .250
15–50
70–250
180–360 ,180
,15
,100
–
,70
10–20
Chapter 3. Seismic actions and geotechnical aspects
Table 3.3. Recommended parameter values in Part 1 of Eurocode 8 for standard horizontal elastic response spectra Ground type
Spectrum type 1
A B C D E
Spectrum type 2
S
TB: s
TC: s
TD: s
S
TB: s
TC: s
TD: s
1.00 1.20 1.15 1.35 1.40
0.15 0.15 0.20 0.20 0.15
0.4 0.5 0.6 0.8 0.5
2.0 2.0 2.0 2.0 2.0
1.0 1.35 1.50 1.80 1.60
0.05 0.05 0.10 0.10 0.05
0.25 0.25 0.25 0.30 0.25
1.2 1.2 1.2 1.2 1.2
(spectral or ground) as in US codes, the non-binding recommendation of a note in Part 1 of Eurocode 8 is for two types of spectra: g g
Type 1: for moderate- to large-magnitude earthquakes. Type 2: for low-magnitude ones (e.g. with a surface magnitude less than 5.5) at close distance, producing over soft soils motions rich in high frequencies.
The values of TB , TC , TD and S recommended in a non-binding note in Part 1 of Eurocode 8 for the five standard ground types A to E are given in Table 3.3 They are based on Rey et al. (2002) and European strong motion data. There are certain regions in Europe (e.g. where the hazard is contributed mainly by strong intermediate-depth earthquakes, as in the part of the eastern Balkans affected by the Vrancea region) where the two recommended spectral shapes may not be suitable. The lower S values of type 1 spectra are due to the larger soil nonlinearity in the stronger ground motions produced by moderate to large-magnitude earthquakes. Figure 3.1 depicts the recommended type 1 spectral shape. The values recommended in Part 1 of Eurocode 8 for the period TD at the outset of the constant spectral displacement region seem rather low. Indeed, for flexible structures, such as bridges with tall piers or supported only on movable bearings, they may not lead to safe-sided designs. Accordingly, Part 2 of Eurocode 8 calls the attention of designers and national authorities to the fact that the safety of structures with seismic isolation depends mainly on the displacement
Clause 7.4.1(1) [2] Clause 3.2.2.5(8) [1]
Figure 3.1. Elastic response spectra of type 1 recommended in Eurocode 8, for a peak ground acceleration on rock equal to 1g and for 5% damping 4 Soil A Soil B Soil C Soil D Soil E
3.5 3
Sa /ag
2.5 2 1.5 1 0.5 0
0.5
1
1.5
2
2.5
3
3.5
T: s
23
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
demands on the isolating system that are directly proportional to the value of TD . So, as allowed in Part 1 of Eurocode 8 specifically for design with seismic isolation or energy dissipation devices, Part 2 invites its National Annex to specify a value of TD for bridges with such a design that is more conservative (longer) than the value given in the National Annex to Part 1. If the National Annex to Part 2 does not exercise this right for national choice, the designer may do so, taking into account the specific conditions of the seismically isolated bridge. Clause 3.2.2.5(4) [1]
Clauses 4.1.7(1)– 4.1.7(3) [2]
A safeguard against the rapid decay of the elastic spectrum for T > TD , is provided by the lower bound of 0.2ag recommended in Part 1 of Eurocode 8 for the design spectral accelerations (see Eqs (D3.12c) and (D3.12d) below). 3.1.2.4 Elastic spectra of the vertical component The vertical component of the seismic action needs to be taken into account only in the seismic design of (CEN, 2005): g g g g
Clause 3.2.2.3(1) [1] Clause 3.2.2.2(1) [2]
prestressed concrete decks (acting upwards) any bearings any seismic links piers in zones of high seismicity: – if the pier is already taxed by bending due to permanent actions on the deck or – the bridge is located within 5 km of an active seismotectonic fault (defined as one where the average historic slip rate is at least 1 mm/year and there is topographic evidence of seismic activity in the past 11 000 years), in which case site-specific spectra that account for near-source effects should be used.
Eurocode 8 gives in Part 1 a detailed description of the vertical elastic response spectrum, as follows: Short-period range: 0 T TB : Sa;vert ðT Þ ¼ avg
T 1þ 3h 1 TB
ðD3:10aÞ
Constant spectral pseudo-acceleration range: TB T TC : Sa;vert ðT Þ ¼ avg 3h
ðD3:10bÞ
Constant spectral pseudo-velocity range: TC T TD : Sa;vert ðT Þ ¼ avg 3h
TC T
ðD3:10cÞ
Constant spectral displacement range: TD T 4 s: Sa;vert ðT Þ ¼ avg 3h
TC TD T2
ðD3:10dÞ
The main differences between the horizontal and the vertical spectra lie: g g
in the value of the amplification factor in the constant spectral pseudo-acceleration plateau, which is 3 instead of 2.5 in the absence of a uniform amplification of the entire spectrum due to the type of soil.
The values of control periods TB , TC , TD are not the same as for the horizontal spectra. Part 1 of Eurocode 8 recommends in a note the following non-binding values of TB , TC , TD and the design ground acceleration in the vertical direction, avg: g g
24
TB ¼ 0.05 s TC ¼ 0.15 s
Chapter 3. Seismic actions and geotechnical aspects
g g g
TD ¼ 1.0 s avg ¼ 0.9ag , if the type 1 spectrum is considered as appropriate for the site avg ¼ 0.45ag , if the type 2 spectrum is chosen.
The vertical response spectrum recommended in Eurocode 8 is based on work and data specific to Europe (Ambraseys and Simpson, 1996; Elnashai and Papazoglou, 1997). The ratio avg/ag is known to be higher at short distances (epicentral or to causative fault). However, as distance does not enter as a parameter in the definition of the seismic action in Eurocode 8, the type of spectrum has been chosen as the parameter determining this ratio, on the basis of the finding that avg/ag also increases with increasing magnitude (Ambraseys and Simpson, 1996; Abrahamson and Litehiser, 1989), which in turn determines the selection of the type of spectrum. 3.1.2.5 Topographic amplification of the elastic spectrum Eurocode 8 provides for topographic amplification (ridge effect, etc.) of the seismic action for all types of structures. According to Part 1 of Eurocode 8, topographic amplification of the full elastic spectrum is mandatory for structures (including bridges) of importance above ordinary. An informative annex in Part 5 of Eurocode 8 (CEN, 2004b) recommends amplification factors equal to 1.2 over isolated cliffs or long ridges with a slope (to the horizontal) less than 308, or to 1.4 at ridges steeper than 308. However, as a bridge on a ridge is fairly rare, the need to account for such an effect would be exceptional. 3.1.2.6 Near-source effects ‘Directivity’ effects of the seismic motion along the direction of rupture propagation are usually observed near the seismotectonic fault rupture in a land strip parallel to the fault. This may show up at the site as a large velocity pulse of long period in the direction transverse to the fault. The general rules of Eurocode 8 in Part 1 do not provide for near-source effects. However, Part 2 of Eurocode 8 (CEN, 2005) requires elaboration of site-specific spectra that take into account near-source effects if the bridge is within 10 km horizontally from a known active fault that may produce an event of moment magnitude higher than 6.5. In this respect, it gives a default definition of an active fault as one where the average historic slip rate is at least 1 mm/year and there is topographic evidence of seismic activity within the Holocene period (i.e. during the past 11 000 years).
Clause 3.2.2.1(6) [1] Annex A [3]
Clause 3.2.2.3(1) [2]
For bridges less than 15 km from a known active fault, the Caltrans Seismic Design Criteria (Caltrans, 2006) increase spectral ordinates by 20% for all periods longer than 1 s, while leaving them unchanged for periods shorter than 0.5 s, with linear interpolation in the period range in between. Although not stated in Caltrans (2006), this increase, known as the directivity effect, should only be restricted to the fault normal component of the ground motion, leaving the fault parallel component unaffected (Sommerville et al., 1997). It should be noted that near-source effects are quite usual in seismic-prone areas. 3.1.2.7 Design ground displacement and velocity The value given in Part 1 of Eurocode 8 for the design ground displacement, dg , corresponding to the design ground acceleration, ag , is based on the assumption that the spectral displacement within the constant spectral displacement range, derived as (T/2p)2Sa(TD) with the spectral acceleration at T ¼ TD given from Eq. (D3.8c), entails an amplification factor of 2.5 over the ground displacement that corresponds to the design ground acceleration, ag . Taking (2p)2 40, we obtain (for ag in m/s2, not in g) dg ¼ 0:025ag STC TD
Clause 3.2.2.4(1) [1] Clauses 3.3(6), 6.6.4(3) [2]
ðD3:11Þ
Equation (D3.11) gives estimates of the ratio dg/ag that are rather on the high side compared with more detailed predictions as a function of magnitude and distance on the basis of Bommer and Elnashai (1999) and Ambraseys et al. (1996). The design ground velocity vg may be obtained from the design ground acceleration ag as follows: vg ¼ STC ag/2p
Clause 6.7.4.(3) [2]
(D3.12) 25
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
Clauses 2.1(2), 3.2.4(1), 4.1.6(1) [2] Clause 3.2.2.5(4) [1]
3.1.3 Design spectrum for elastic analysis For the horizontal components of the seismic action the design spectrum in Eurocode 8 is: Short-period range: 0 T TB : Sa;d ðT Þ ¼ ag S
2 T 2:5 2 þ 3 TB q 3
ðD3:13aÞ
Constant spectral pseudo-acceleration range: TB T TC : Sa;d ðT Þ ¼ ag S
2:5 q
Constant spectral pseudo-velocity range: 2:5 TC TC T TD : Sa;d ðT Þ ¼ ag S b ag q T Constant spectral displacement range: 2:5 TC TD TD T: Sa;d ðT Þ ¼ ag S b ag q T2
ðD3:13bÞ
ðD3:13cÞ
ðD3:13dÞ
The behaviour factor, q, in Eqs (D3.13) accounts for ductility and energy dissipation, as well as for values of damping other than the default of 5% (see also Section 2.3.2 of this Guide). The value 2/3 in Eq. (D3.13a) is the inverse of the overstrength factor of 1.5 considered in Eurocode 8 to always be available even without any design measures for ductility and energy dissipation. The factor b in Eqs (D3.13c) and (D3.13d) gives a lower bound for the horizontal design spectrum, acting as a safeguard against excessive reduction of the design forces due to flexibility of the system (real or presumed in the design). Its recommended value in Part 1 of Eurocode 8 is 0.2. Its practical implications may be particularly important, in view of the relatively low values recommended by Eurocode 8 for the corner period TD at the outset of the constant spectral displacement range. Clause 3.2.2.5(5) [1], Clause 4.1.6(12) [2]
Clauses 3.2.3(1), 3.2.3(2) [2] Clauses 3.2.3.1.1(1), 3.2.3.1.1(2), 3.2.3.1.2(4) [1] Clauses 3.2.3.1.1(3), 3.2.3.1.2(3), 3.2.3.1.3(1) [1] Clauses 3.2.3(1), 3.2.3(2), 3.2.3(4), 3.2.3(8) [2]
26
The design spectrum in the vertical direction is obtained by substituting in Eqs (D3.13) the design ground acceleration in the vertical direction, avg , for the effective ground acceleration, agS, and using the values in Section 3.1.2.4 for the three corner periods. There is no clear, well-known energy dissipation mechanism for the response in the vertical direction. So, the behaviour factor q in that direction is taken equal to 1.0. 3.1.4 Time-history representation of the seismic action Representation of the seismic action merely by its 5%-damped elastic response spectrum is sufficient for linear or nonlinear static analysis. For a nonlinear dynamic (response-history) analysis, time histories of the ground motion are needed, conforming on average to the 5%-damped elastic response spectrum defining the seismic action. Eurocode 8 (Parts 1 and 2) requires as input for a response history analysis an ensemble of at least three records, or pairs or triplets of different records, for analysis under two or three concurrent components of the action. Part 1 of Eurocode 8 accepts for this purpose historic, ‘artificial’ or ‘simulated’ records, while Part 2 mentions only historic, ‘modified historic’ or ‘simulated’ records. ‘Artificial’ (or ‘synthetic’) records can be mathematically produced using random vibration theory to match almost perfectly the response spectrum defining the seismic action (Gasparini and Vanmarcke, 1976). It is fairly straightforward to adjust the phases of the various sinusoidal components of the artificial waveform, as well as the time evolution of their amplitudes (‘envelope function’), so that the artificial record resembles a specific recorded motion. This is the ‘modified historic’ type of record mentioned in Part 2 of Eurocode 8. Figure 3.2 shows an example of such a record and Figure 8.47 another one. Note, however, that records that are equally rich in all frequencies are not realistic. Moreover, an excitation with a smooth
Chapter 3. Seismic actions and geotechnical aspects
Figure 3.2. Herzegnovi X record from the 1979 Montenegro earthquake modulated to match the Eurocode 8 type 1 spectrum for ground type C with a peak ground acceleration of 0.1g 1
Modified Hercegnovi
0.6
Target spectrum Modified Hercegnovi
3
0.8
2.5 2
0.2
Sa: m/s2
a: m/s2
0.4 0
1.5
–0.2
1
–0.4 –0.6
0.5
–0.8 –1
0
2
4
6 Time: s
8
10
12
0
0
0.5
1
1.5 2 Period, T: s
2.5
3
response spectrum without peaks or troughs introduces a conservative bias in the response, as it does not let the inelastic response help the structure escape from a spectral peak to a trough at a longer period. Therefore, historic records are favoured in Part 2 of Eurocode 8. Records ‘simulated’ from mathematical source models, including rupture, propagation of the motion through the bedrock to the site and, finally, through the subsoil to the surface are also preferred over ‘artificial’ ones, as the final record resembles a natural one and is physically appealing. Obviously, an equally good average fitting of the target spectrum requires more – appropriately selected – historic or ‘simulated’ records than ‘artificial’ ones. Individual recorded or simulated records should, according to Part 1 of Eurocode 8, be ‘adequately qualified with regard to the seismogenetic features of the sources and to the soil conditions appropriate to the site’ (Part 1 of Eurocode 8). In plainer language, they should come from events with the magnitude, fault distance and mechanism of rupture at the source consistent with those of the design seismic action (Part 2 of Eurocode 8). The travel path and the subsoil conditions should preferably resemble those of the site. These requirements are not only hard to meet but may also conflict with conformity (in the mean) to the target spectrum of the design seismic action. The requirement in Part 1 of Eurocode 8 to scale individual historic or simulated records so that their peak ground acceleration (PGA) matches on average the value of agS of the design seismic action may also be considered against physical reality. It is more meaningful, instead, to use individual historic or simulated records with PGA values already conforming to the target value of agS. Note also that the PGA alone may be artificially increased or reduced, without affecting at all the structural response. So, it is more meaningful to select the records on the basis of conformity of spectral values alone along the lines of Part 2 of Eurocode 8 (CEN, 2005), as described below. If pairs or triplets of different records are used as the input for analysis under two or three concurrent seismic action components, conformity to the target 5%-damped elastic response spectrum may be achieved by scaling the amplitude of the individual records as follows (see Figures 8.48 and 8.49 for an application example): g g
g
Clauses 3.2.3(3), 3.2.3(6), 3.2.3(7) [2]
For each earthquake consisting of a triplet of translational components, the records of horizontal components are checked for conformity separately from the vertical one. The records of the vertical component, if considered, are scaled so that the average 5%damped elastic spectrum of their ensemble is at least 90% of the 5%-damped vertical spectrum at all periods between 0.2Tv and 1.5Tv , where Tv is the period of the lowest mode having a participation factor of the vertical component higher than those of both horizontal ones. For analysis in 3D under both horizontal components, the 5%-damped elastic spectra of the two horizontal components in each pair are combined by applying the SRSS rule at each period value. The average of the ‘SRSS spectra’ of the two horizontal components of 27
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
p the individual earthquakes in the ensemble should be at least 0.9 2 1.3 times the target 5%-damped horizontal elastic spectrum at all periods from 0.2T1 up to 1.5T1 , where T1 is the lowest natural period of the structure (the effective period of the isolation system in seismically isolated bridges) in any horizontal direction. If this is not the case, all individual horizontal components are scaled up, so that their final average ‘SRSS spectrum’ exceeds by a factor of 1.3 the target 5%-damped horizontal elastic spectrum everywhere between 0.2T1 and 1.5T1 . Clause 3.2.3.1.2(4) [1] Note in this respect that for analysis under a single horizontal component, Part 1 of Eurocode 8
requires the mean 5%-damped elastic spectrum of the applied motions to not fall below 90% of that of the design seismic action at any period from 0.2T1 to 2T1 . Clause 4.2.4.3(1) [2] If the response is obtained from at least seven nonlinear time-history analyses with (triplets or Clause 4.3.3.4.3(3) [1] pairs of ) ground motions chosen in accordance with the previous paragraphs, the relevant veri-
fications may use the average of the response quantities from all these analyses as the action effect. Otherwise, it should use the most unfavourable value of the response quantity among the (three to six) analyses.
Clauses 3.3(1)–3.3(8), Annex D [2]
3.1.5 Spatial variability of the seismic action Unlike typical buildings, bridges are extended structures. Therefore, it is very likely that the foundation supports experience different ground motions owing to the spatial variability of the seismic motion. This phenomenon is known by the generic term ‘decorrelation’. Decorrelation of seismic motions arises from three different causes: The travelling wave effect: except for vertically propagating waves, the seismic waves exhibit an apparent velocity in the horizontal direction, causing out-of-phase motions along the bridge, even when the amplitude remains the same. 2 Scattering of waves, especially at high frequencies: waves travelling through a heterogeneous soil medium are scattered (diffracted and/or reflected) at every heterogeneity, no matter whether a small lens or an abrupt change in the mechanical characteristics of the media. As the frequency increases, the wavelength decreases and the waves perceive and are affected by smaller heterogeneities. Scattering causes the motion at two adjacent locations to be different. 3 Propagation through different soil profiles under each pier location: if the bridge foundations are not very close to each other, the soil profile under them may be different, causing different soil amplification from the bedrock. 1
Effects 1 and 3 can, theoretically, be accounted for (although under simplifying assumptions), if the direction of propagation of the seismic waves is given and the soil profiles are accurately known. Effect 2 does not lend itself to calculation, without complete knowledge of the subsoil conditions between the seismic source and the bridge. Effect 1 can easily be modelled, by shifting the ground motion time histories by a time lag equal to the distance between the piers divided by the apparent travelling wave velocity. Analytical studies and observations suggest that the apparent wave velocity is not equal to the wave velocity in the upper soil layers, but rather to the wave velocity at a significant depth (in the rock medium where the rupture initiates); typical values exceed 1000 m/s. Effect 3 can be computed through one-dimensional site response analysis. For effect 2, only random vibration models with empirically determined parameters can be used. Informative Annex D in Part 2 of Eurocode 8 presents the theory for the generation of incoherent ground motions, including all three effects above, as well as the mathematical tools for the analysis of the bridge response under multi-support excitations. However, because the theory is complex, requiring specific tools for its numerical implementation and statistical site data for the determination of model parameters, the code allows the use of a simplified approach to take into account the spatial variability of seismic motions along the bridge. This spatial variability should be taken into account whenever the soil properties along the bridge vary and the ground type according to Table 3.2 differs from one pier to another, or if the length of a continuous deck exceeds Lg/1.5, where Lg is the correlation distance (beyond which the motion may be assumed to be fully uncorrelated). Recommended values of the correlation distance are given in Table 3.4. 28
Chapter 3. Seismic actions and geotechnical aspects
Table 3.4. Values recommended in Part 5 of Eurocode 8 for the distance beyond which ground motions may be considered as uncorrelated Ground type
A
B
C
D
E
Lg : m
600
500
400
300
500
The simplified methodology consists of combining via the SRSS (square root of the sums of the square) rule the dynamic effects of a uniform ground motion acting at every foundation, to the effects of differential displacements imposed statically at each foundation point. Two patterns are used for the static imposed displacements, and the results of the most unfavourable one are retained: g
g
a pattern with foundation displacements all in the same direction and proportional to the distance along the bridge and to the ground displacement, but inversely proportional to the correlation distance, combined with a small offset at any intermediate pier a pattern with displacements alternating between consecutive piers.
The same patterns of imposed displacements, with an increased safety factor, are also used in the checks of deck unseating at movable joints (see Eq. (D6.34) in Sect. 6.8.1.2). Unlike certain truly dynamic approaches, the simplified method above cannot capture dynamic features of the spatial variability of the seismic action, as it is essentially a pseudo-static ‘addition’ of imposed support displacements. It accounts, however, to a certain degree of approximation, for all three main effects of the spatial variability (Sextos et al., 2006; Sextos and Kappos, 2009).
3.2.
Siting and foundation soils
3.2.1 Introduction Significant damage to foundations may be caused by soil-related phenomena: fault rupture, slope instability near the bridge, liquefaction or densification of the soil due to the ground shaking. Except in very few cases, such adverse effects cannot be accommodated by a foundation design. Therefore, these ground hazards should be thoroughly investigated and properly mitigated to the largest possible extent.
Clause 4.1.1(1) [3]
3.2.2 Seismically active faults Seismological evidence suggests that, where seismogenic activity is confined in the upper 20 km or Clause 4.1.2(1), (2) [3] so of the Earth’s crust, co-seismic surface rupture tends to occur only if the earthquake has a Clause 3.2.2.3(1) [2] moment magnitude Mw over about 6.5. Therefore, in Europe, surface faulting is a rather rare event, except in Turkey and maybe in Greece or Italy. As pointed out in Part 5 of Eurocode 8, assessment of the surface fault rupture hazard at a site requires special geological investigations, to show that there is no active fault nearby. Official documents published by competent national authorities may, of course, map the seismically active faults. Note, though, that there are no absolute criteria to characterise a fault as seismically active and to consider a site as close to it. It is suggested in Part 5 of Eurocode 8 that evidence of movement in the late Quaternary period (10 000 years) or lack of it is used as a criterion, while Part 2 of Eurocode 8 defines an active fault as one where the average historic slip rate is at least 1 mm/year and there is topographic evidence of seismic activity in the Holocene period (i.e. in the past 11 000 years). A distance of several tens of metres may be used as the criterion for the immediate vicinity to a fault. 3.2.3 Slope stability When a structure is to be built near a natural or man-made slope, a verification of the slope stability under the seismic action shall be carried out. Although the stability checks recommended in Part 5 of Eurocode 8 aim at ensuring a prescribed safety factor, the underlying criterion is an ultimate limit state (ULS) beyond which the permanent displacements it entails become unacceptable. This is reflected in the method of analysis proposed in Part 5 of Eurocode 8 for achieving a safety factor above 1.0, notably a pseudo-static approach with seismic forces taken as equal to
Clauses 4.1.3.1(1), 4.1.3.1(2), 4.1.3.3(1), 4.1.3.3(3)–4.1.3.3(6), 4.1.3.3(8), 4.1.3.4(4), Annex A [3]
29
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
the product of the potential sliding mass multiplied by 50% of the design PGA at the soil surface, agS, including the topographic amplification factor of Section 3.1.2.5, if relevant. The 50% fraction has been chosen empirically and with back-analysis of observed performance of slopes in earthquakes. It nevertheless reflects the observation, first pointed out by Newmark in his 1965 Rankine lecture, that when the maximum seismic action, equal to the product of the potentially sliding mass multiplied by the PGA, is slightly exceeded, only permanent displacements occur without a catastrophic failure. With the recommended value of the ground acceleration, 0.5agS, it is expected that the induced displacements will not exceed a few centimetres. The design seismic inertia forces in the horizontal and vertical direction are given by FH ¼ 0.5agSM FV ¼ +0.5FH FV ¼ +0.33FH
(D3.14) if avg . 0.6ag if avg 0.6ag
(D3.15a) (D3.15b)
where M is the potentially sliding mass and agS includes the topographic amplification factor of Section 3.1.2.5, if relevant. The seismic design resistance of the soil should be calculated with the soil strength parameters divided by the appropriate partial factor, defined in the National Annex to Part 5 of Eurocode 8. It is essential not to overlook the applicability conditions of the pseudo-static method of analysis, that is: g g
The geometry of the topographic profile and the ground profile are reasonably regular. The ground materials of the slope and the foundation, if water saturated, are not prone to developing significant pore water pressure build-up that may lead to loss of shear strength and stiffness degradation under seismic conditions. The same limitation applies to certain unusual soils, such as sensitive clays, although the mechanism of strength degradation is different.
For high values of agS it may prove hard to verify the slope stability using the pseudo-static method. If so, the designer may opt for computing the actual induced permanent displacements and checking whether they are acceptable. A simplified way to estimate the displacements is the Newmark sliding block method. This entails the preliminary choice of the most critical sliding surface and the associated ‘critical’ value of agS for which the safety factor drops to 1.0. With the selection of appropriate time histories for the ground motion, double integration of the difference of the input acceleration and the critical one is carried out over the time intervals during which the former exceeds the latter. The outcome may be taken as the permanent slope displacement along the chord of the critical circular failure surface. More refined analyses, accounting for the seismic response of the slope in the evaluation of the rigid block acceleration, may be warranted in some cases. One essential requirement for the application of pseudo-static analysis or of the Newmark sliding block method is that the soil strength does not vary significantly during the earthquake. When the strength is reduced by a pore pressure build-up, it may be evaluated through the expression Du tan wr ¼ 1 0 tan w sv
ðD3:16Þ
where wr is the reduced friction angle, Du the pore pressure increase estimated from empirical correlations or preferably from experimental tests, and s v0 is the effective vertical stress.
3.3.
Soil properties and parameters
3.3.1 Introduction: the meaning of soil property values Many geotechnical tests, particularly field tests, do not allow determining directly the value of basic geotechnical parameters or coefficients, notably for strength and deformations. Instead, 30
Chapter 3. Seismic actions and geotechnical aspects
these values are to be derived via theoretical or empirical correlations. Part 2 of Eurocode 7 (CEN, 2007) defines derived values as: Derived values of geotechnical parameters and/or coefficients are obtained from test results by theory, correlation or empiricism. Derived values of a geotechnical parameter then serve as input for assessing the characteristic value of this parameter in the sense of Eurocode 7 – Part 1 and, further, its design value, by applying the partial factor gM (‘material factor’). The philosophy regarding the definition of characteristic values of geotechnical parameters is given in Part 1 of Eurocode 7 (CEN, 2003): The characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state . . . the governing parameter is often the mean of a range of values covering a large surface or volume of the ground. The characteristic value should be a cautious estimate of this mean value. These excerpts from Eurocode 7 reflect the concern that we should be able to keep using the values of the geotechnical parameters traditionally used, whose determination is not standardised (they often depend on the judgment of the geotechnical engineer). However, two remarks are due in this connection: on one hand, the concept of a ‘derived value’ of a geotechnical parameter (preceding the determination of the characteristic value) has been introduced, but, on the other, there is now a clear reference to the limit state involved and the assessment of a spatial mean value, as opposed to a local value; this might appear as a specific feature of geotechnical design which, indeed, involves ‘large’ surface areas or ‘large’ ground volumes. Statistical methods are mentioned in Eurocode 7 only as a possibility: If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%. The general meaning is that the characteristic value of a geotechnical parameter should not be very different from the values traditionally used. Indeed, for the majority of projects, the geotechnical investigation is such that no meaningful statistical treatment of the data can be performed. Statistical methods are, of course, useful for very large projects where the amount of data justifies their use. 3.3.2 Soil properties Eurocode 8 considers both the strength properties and the deformation characteristics. It further recognises that earthquake loading is essentially of short duration. Consequently, most soils behave in an undrained manner. In addition, for some of them the properties may be affected by the rate of loading.
Clauses 3.1(1)–3.1(3) [3]
3.3.2.1 Strength parameters For cohesive soils, the relevant strength property is the undrained shear strength, cu . For most of them this value can be taken as equal to the conventional ‘static’ shear strength. However, on the one hand some plastic clays may be subject to cyclic degradation of strength, but, on the other, some clays may exhibit a shear strength increase with the rate of loading. These phenomena should ideally be given due consideration in the choice of the relevant undrained shear strength. The recommended partial factor gM on cu is equal to 1.4. For cohesionless soils, relevant strength properties are the drained friction angle, w0 , and the drained cohesion, c0 . They are directly usable for dry or partially saturated soil. For saturated soils, they require knowledge of the pore water pressure variation during cyclic loading, u, which directly governs the shear strength through the Mohr–Coulomb failure criterion:
t ¼ (s u) tan w0 þ c0
(D3.17)
The evaluation of u is very difficult. Therefore, Part 5 of Eurocode 8 gives an alternative approach, namely using the undrained shear strength under cyclic loading, tcy,u , which may be determined 31
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
from experimental correlations with, for instance, the soil relative density or any other index parameter, such as the blow counts number, N, in a standard penetration test (SPT). The recommended values for the partial factors gM are: g g
Clauses 3.2(1)–3.2(4), 4.2.3(1)–4.2.3(3) [3]
gM ¼ 1.25 on tan(w0 ) and tcy,u gM ¼ 1.4 on c0 .
3.3.2.2 Stiffness and damping parameters The soil stiffness is defined by the shear wave velocity, vs , or equivalently the soil shear modulus G. The main role played by this parameter is in the classification of the soil profile according to the ground types in Table 3.2 of Section 3.1.2.3 in this Guide. Additional applications that require knowledge of the shear stiffness of the soil profile include the evaluation of: g g
soil–structure interaction site response analyses to define the ground surface response for special soil categories (profile S1).
In the applications listed above, it is essential to recognise that soils are highly nonlinear materials and that the relevant values to use in calculations are not the elastic ones but secant values compatible with the average strain level induced by the earthquake, typically of the order of 5 10 4 to 10 3. Part 5 of Eurocode 8 proposes the set of values in Table 3.5, depending on the peak ground surface acceleration. Note that the fundamental variable governing the reduction factor is the shear strain and not the peak ground surface acceleration. However, in order to provide useful guidance to designers, the induced strains have been correlated to PGAs. In addition to the stiffness parameters, soil internal damping should be taken into account in soil–structure interaction analyses. The soil damping ratio also depends on the average induced shear strain, and is correlated to the reduction factor for the stiffness, as listed in Table 3.5.
3.4. Clauses 4.1.4(1)– 4.1.4(3) [3]
Liquefaction, lateral spreading and related phenomena
3.4.1 Nature and consequences of the phenomena Liquefaction is a process in which cohesionless or granular sediments below the water table temporarily lose strength and behave as a viscous liquid rather than a solid, during strong ground shaking. Saturated, poorly graded, loose, granular deposits with low fines content are most susceptible to liquefaction. Liquefaction does not occur randomly: it is restricted to certain geological and hydrological environments, primarily recently deposited sands and silts in areas with a high ground water level. Dense and more clayey soils, including well-compacted fills, have low susceptibility to liquefaction. The liquefaction process itself may not necessarily be particularly damaging or hazardous. For engineering purposes, it is not the occurrence of liquefaction that is of importance but the potential of the process and of associated hazards to damage structures. The adverse effects of liquefaction can be summarised as follows: g
Flow failures, when completely liquefied soil or blocks of intact material ride on a layer of liquefied soil. Flows can be large and develop on moderate to steep slopes.
Table 3.5. Average soil damping ratios and reduction factors (+1 standard deviation) for the shear wave velocity vs and the shear modulus G within the upper 20 m of soil in Part 5 of Eurocode 8 (for soil with vs , 360 m/s)
32
Ground acceleration, agS: g
Damping ratio: %
vs/vs,max
Gs/Gs,max
0.1 0.2 0.3
3 6 10
0.9 (+0.07) 0.7 (+0.15) 0.6 (+0.15)
0.8 (+0.1) 0.5 (+0.2) 0.36 (+0.2)
Chapter 3. Seismic actions and geotechnical aspects
g
g
g g
g g
Lateral spreading, with lateral displacement of superficial blocks of soil as a result of the liquefaction of a subsurface layer. Spreading generally develops on gentle slopes, and moves towards a free face, such as an incised river channel or coastline. It may also occur through the failure of shallow liquefied layers subjected to a high vertical load on part of the ground surface due to a natural or artificial embankment or cut. Ground oscillation: where the ground is flat or the slope too gentle to allow lateral displacement, liquefaction at depth may disconnect overlying soils from the underlying ground, allowing the upper soil to oscillate back and forth in the form of ground waves. These oscillations are usually accompanied by ground fissures and the fracture of rigid extended structures, such as pavements and pipelines. Loss or reduction in bearing capacity, when earthquake shaking increases pore water pressures, which in turn cause the soil to lose its strength and bearing capacity. Soil settlement, as the pore water pressures dissipate and the soil densifies after liquefaction. Settlement of structures may occur, owing to the reduction in the bearing capacity or the ground displacements noted above. In piled foundations the postearthquake settlement of the liquefied layer due to pore pressure dissipation induces negative skin friction along the shaft, in all layers above the liquefied layer. Increased lateral pressures on retaining walls, when the soil behind a wall liquefies and behaves like a ‘heavy’ fluid with no internal friction. Flotation of buried structures, when buried structures, such as tanks and pipes, become buoyant in the liquefied soil.
Other manifestations of liquefaction, such as sand boils, can also occur, and may pose a risk to structures, particularly through loss or reduction in the bearing capacity and settlement. Liquefaction has been extensively studied since 1964. The state of the art is now well established and, more importantly, allows reliable prediction of the occurrence of liquefaction. So, this aspect is fully covered in Part 5 of Eurocode 8, including a normative annex for the use of SPT measurements for the evaluation of the undrained cyclic strength of cohesionless soils. However, in addition to the SPT, other techniques are allowed for the determination of the soil strength, such as cone penetration tests (CPTs) and shear wave velocity measurements. Laboratory tests are not recommended, because to obtain a reliable estimate of liquefaction resistance, very specialised drilling and sampling techniques are needed, beyond the budget of any common project. It should, however, be noted that there have been numerous developments in liquefaction assessment methodologies in recent years (e.g. Seed et al., 2003; Idriss and Boulanger, 2008). So, the methods described in Part 5 of Eurocode 8 may be potentially unconservative, especially for materials with a high fines content. It is therefore recommended that an expert is involved in the liquefaction assessment. 3.4.2 Liquefaction assessment Clauses 4.1.4(3)– The verification of the liquefaction susceptibility is carried out under free field conditions, but 4.1.4(6), 4.1.4(10), with the prevailing situation during the lifetime of the structure. For instance, if a tall platform is going to be built to prevent flooding of the site, or the water table will be lowered 4.1.4(11), Annex B [3] on a long-term basis, these developments should be reflected in the evaluation. The recommended analysis is a total stress analysis in which the seismic demand, represented by the earthquake-induced stresses, is compared with the seismic capacity (i.e. the undrained cyclic shear strength of the soil – also called liquefaction resistance). The shear stress ‘demand’ is expressed in terms of a cyclic stress ratio (CSR), and the ‘capacity’ in terms of a cyclic resistance ratio (CRR). In both ratios the normalisation is with respect to the vertical effective stress, s v0 . A soil should be considered susceptible to liquefaction whenever CRR , l CSR, where l is a factor of safety, with a recommended value of 1.25. The CSR is evaluated with a simplified version of the Seed–Idriss formula, which allows a rapid calculation of the induced stress along the depth, without resorting to a dynamic site response analysis: CSR ¼ 0:65ðag S=gÞsv =s 0v
ðD3:18Þ 33
Designers’ Guide to Eurocode 8: Design of Bridges for Earthquake Resistance
where sv and s v0 are the overburden pressure and the vertical effective stress at the depth of interest. Equation (D3.18) may not be applied for depths larger than 20 m. The liquefaction resistance ratio, CRR, may be estimated through empirical correlations with an index parameter, such as the SPT blow count, the static CPT point resistance or the shear wave velocity. Note that all of these methods should be implemented with several corrections of the measured index parameter for the effects of the overburden at the depth of measurement, the fines content of the soil, the effective energy delivered to the rods in SPTs, etc. In normative Annex B in Part 5 of Eurocode 8, the CRR is assessed based on a corrected SPT blowcount, using empirical liquefaction charts relating CRR ¼ t/s v0 to the corrected SPT blow count N1(60) for an earthquake surface magnitude of 7.5. Correction factors are provided in Annex B [3] for other magnitudes. Clause 4.1.4(7), 4.1.4(8) [3]
A soil may be prone to liquefaction if it presents certain characteristics that govern its strength and the seismic demand is large enough. Taking the opposite view, Part 5 of Eurocode 8 introduces cumulative conditions under which the soil may be considered as not prone to liquefaction and liquefaction assessment is not required: g
Low ground surface acceleration, agS , 0.15g, and – soils with a clay content higher than 20% and a plasticity index above 10% or – soils with a silt content higher than 35% and a corrected SPT blow count of over 20 or – clean sands with a corrected SPT blow count higher than 30.
The assessment of liquefaction is also not required for layers located deeper than 15 m below the foundation. This does not mean that those layers are not prone to liquefaction, although susceptibility to liquefaction decreases with depth; it means, instead, that because of their depth their liquefaction will not affect the structure. Although it is not spelled out in Eurocode 8, obviously this condition is not sufficient by itself: it should be complemented with a condition on the foundation dimensions relative to the layer depth. Clauses 4.1.4(12)– 4.1.4(14) [3]
If soils are found to be susceptible to liquefaction, mitigation measures, such as ground improvement and piling (to transfer loads to layers not susceptible to liquefaction), should be considered to ensure foundation stability. The use of pile foundations alone should be considered with caution, in view of: g g g
Clauses 4.1.4(12)– 4.1.4(14) [3]
the large forces induced in the piles by the loss of soil support in the liquefiable layers the post-earthquake settlements of the liquefied layers causing negative skin friction in all layers located above the inevitable uncertainties in determining the location and thickness of such layers.
3.4.3 Liquefaction mitigation If soils are found to be susceptible to liquefaction and the consequences are considered unacceptable for the structure (excessive settlement, loss of bearing capacity, etc.), ground improvement should be considered. Several techniques are available to improve the resistance to liquefaction: soil densification, soil replacement, sand compaction piles, drainage (gravel drains), deep soil mixing (lime–cement mixing), stone columns, blasting, jet grouting, etc. The most commonly used among these are stone columns and soil densification, the latter through vibroflotation, dynamic compaction or compaction grouting. Some techniques, such as stone columns, offer the advantage of combining several effects, for example, densification and drainage. Not all techniques are appropriate for any soil condition. The most appropriate ones should be chosen taking into account the depth to be treated, the fines content of the soil and the presence of adjacent structures. Attention should also be paid to the efficiency, durability and cost of the solution. For instance, dynamic compaction is better suited for shallow clean sand layers; jet grouting and stone columns may be used to improve the soil and offer a good load-bearing layer under shallow foundations; compaction grouting, albeit more costly, is very efficient for almost any soil, etc. Methods based on drainage should be considered with care, as drainage conditions may change in time and clogging may occur, especially in environments with large fluctuation of the water table.
34
Chapter 3. Seismic actions and geotechnical aspects
Figure 3.3. Assessment of volumetric strain Cyclic shear strain, γcyc: % –3
Volumetric strain due to compaction, εc: %
10 10–3
10–2
N1 < 40
