Seismic design of concrete bridges: Some key issues to be

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016

Seismic design of concrete bridges: Some key issues to be addressed during the evolution of Eurocode 8 - Part 2 Konstantinos I. Gkatzogias PhD Candidate, Research Centre for Civil Engineering Structures, Department of Civil Engineering, City, University of London, UK, [email protected]

Andreas J. Kappos Professor, Department of Civil Engineering, City, University of London, UK, and Aristotle University of Thessaloniki, Greece, [email protected] 1. Introduction As of 2015, Eurocodes have entered the next stage of their development aiming at the publication of the second generation of the relevant EN Standards in 2020-21. The evolution of the Eurocodes has been scheduled by CEN in four overlapping phases, each involving different standards. The main objectives of the evolution process are: (a) revision of the existing codes with a view to improving the ‘ease of use’, increasing harmonisation through the reduction of National Determined Parameters (NDPs), covering aspects of the assessment, re-use and retrofitting of existing structures, strengthening the requirements for robustness, and development of new Eurocodes (i.e. on structural glass) also incorporating ISO standards (e.g. wave and current actions on coastal structures) and the steps towards the development of codes on membrane structures and fibre-reinforced polymers (FRPs) applications; (b) essential maintenance of the existing Eurocodes and publication of relevant amendments to the existing standards in case emergent safety issues arise, and (c) promotion of the use of Structural Eurocodes, including states outside Europe. CEN/TC 250 has recently launched phase 3 of the systematic review of existing Eurocodes which includes among others (see Table 1) the review of Eurocode 8 Part 2 (EN1998-2) (CEN 2005).

Table 1 Phases and corresponding EN1998 parts addressed in the Eurocode evolution process

Phase EN1998 Part Project Team 1 EN1998-1:2004 General rules, seismic actions and rules for buildings PT1 (material-independent chapters, i.e. Ch. 1-4, 10)

EN1998-3:2005 Assessment and retrofitting of buildings and bridges PT3 2 EN1998-1:2004 General rules, seismic actions and rules for buildings PT2 (material dependent chapters, i.e. Ch. 5-9) EN1998-5:2004 Foundations, retaining structures and geotechnical aspects PT4

3 EN1998-2:2005 Bridges PT6 EN 1998-4:2006 Silos, tanks and pipelines PT5 EN 1998-6:2005 Towers, masts and chimneys

4 - No parts of EN1998 involved - In this context, this paper contributes to the ongoing CEN public enquiry and feedback process on EN1998-2, attempting to identify some issues associated with the seismic design of concrete bridges

mailto:[email protected]

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 designed for ductile behaviour of the piers that need, in the authors’ view, some revision, namely: the criteria for regular/irregular bridge response and the associated behaviour factor q (EN1998-2: §4.1.8), and the capacity design verification of the deck (EN1998-2: §5.6.3.6). The relevant clauses of EN1998-2 are critically presented and examples of the code-prescribed procedures implemented in an actual bridge designed according to ‘standard’ European practice are used to point out associated pitfalls and suggest some possible remediation. Further suggestions for changes (both technical and editorial) in EN1998-2 are currently being put forward by the UK Mirror Group for this code, led by the senior author. 2. Regular and irregular seismic behaviour of ductile bridges 2.1. Code provisions Seismic design of bridges for ductile behaviour according to EN1998-2 aims to ensure a relatively uniform distribution of inelastic deformation demand among the selected dissipating zones (i.e. the pier ends), and hence increase the reliability of elastic response spectrum analysis (Bardakis & Fardis 2011) performed using design spectra that are reduced by a global q-factor. As a means to this end, a ‘regularity’ index ri is defined according to Eq. (1) at each intended plastic hinge location of a ductile member (i) and principal horizontal direction of the bridge as the ratio of the elastic bending moment demand (qMEd, where MEd is derived from analysis for the reduced by q response spectrum) at the hinge of the considered member to the design flexural resistance MRd of the same section with its actual reinforcement, both terms accounting for the concurrent action of the non-seismic action effects in the seismic design situation.

,

,= Ed i

iRd i

Mr q

M (1)

Representing an approximate measure of local ductility demand, the extreme values of ri (rmin, rmax) among the intended plastic hinges are used subsequently to quantify the ‘regularity’ of the inelastic deformation demand distribution in each principal direction of the bridge. A bridge is considered to have ‘regular’ seismic behaviour in the considered direction when the condition of Eq. (2) is satisfied, and irregular behaviour otherwise;

max0

minρ ρ= ≤

rr

(2)

The limiting value ρ0, introduced to ensure that sequential yielding in the intended plastic hinges will not cause unacceptably high ductility demands on one member, is set as an NDP with a recommended value of 2.0. In the light of of the previous considerations, ‘irregularity’ of structural response is associated with widely varying overstrength among piers or, more precisely, with allocation of strength (to at least one pier) in excess of the seismic demand, and is treated in EN1998-2 either by decreasing the allowable q-factor to qr according to Eq. (3), thus penalising the ‘irregular’ bridge, or by requiring nonlinear response history analysis (NLRHA) of the bridge.

0ρρ

=rq q (3)

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 Irrespective of the efficiency of the adopted measure compared to others (e.g. AASHTO 2011, Guirguis & Mehanny 2013, Ayala & Escamilla 2013) in harmonising inelastic demands among piers, implications from the implementation of ri indices resulting in overdesigning members, may arise either from the designer’s subjective interpretation of the above code prescriptions and/or from detailing constraints. It should be noted that based on the code-adopted phraseology it is not clear whether Eq. (2) should consider ri indices calculated at all the intended plastic hinge locations or just the indices at the critical hinge location per ductile member. For example, adoption of the same longitudinal reinforcement ratio ρl at the top and bottom of single-column piers monolithically connected to the deck (a common bridge configuration) will normally result in ‘irregular’ behaviour in the transverse direction of a straight bridge, even in the case of piers with similar height, if ri are calculated at both pier ends. ‘Regularity’ is also affected by the minimum reinforcement ratio (ρl,min) applied in the design of piers. Since ρl,min is not specified in EN1998-2, EN1992-1-1 (CEN 2004a) applies. In practice, however, the EN1992 limit is often perceived by practitioners as too low, thus usually replaced with the 1% limit prescribed for buildings in EN1998-1-1 (CEN 2004b), which is rather high for bridge pier columns. Adoption of relatively high ρl,min promotes in general ‘irregularity’ among piers of unequal height irrespective of the considered direction of the bridge. The previous implications are further illustrated in the next section through a simple application of the relevant clauses to an actual 3-span bridge with single-column piers monolithically connected to the deck, and a possible treatment of the issue is subsequently proposed.

2.2. Implementation of EN1998-2 provisions to a typical bridge The selected structure (Fig. 1) previously used by the authors in the development of different performance-based design procedures (e.g. Kappos et al. 2013, Gkatzogias & Kappos 2015a, b), is a 3-span structure of total length equal to 99 m; the 10m wide prestressed concrete box girder deck has a 7% longitudinal slope and it is supported by two single-column R/C piers of cylindrical section (and equal diameter) and clear height of 5.9 and 7.9m. The deck is monolithically connected to the piers and rests on the abutments through elastomeric bearings allowing movement of the deck in any direction. The bridge rests on firm soil and both piers and abutments have surface foundations (footings).

Fig. 1 Overpass T7 (Egnatia Motorway, N. Greece) and finite element modelling

The EN1998-1 ‘Type 1’ elastic spectrum corresponding to subsoil class ‘C’ and a PGA of 0.21g was selected as the basis for seismic design, while the output of the performance-based methodology presented in Gkatzogias and Kappos (2015a) regarding the bearings (plan dimensions of 350×450mm with total thickness of elastomer tr=88 mm) was adopted herein, focusing on the transverse response of the bridge and ignoring SSI effects.

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 Four different cases corresponding to different diameter (D) of the columns were investigated, i.e. D=1.2, 1.4, 1.6, and 2.0 m. Response spectrum analyses (RSAs) were first performed under the design spectrum assuming an initial (i.e. maximum allowable) value of q accounting for the effect of the normalised axial force (nk) (whenever required) and the reduced equivalent cantilever height (i.e. the shear span ratio as in Eurocode terminology) of the pier columns in accordance with EN1998-2. Pier stiffness was initially estimated by taking into account the effects of axial load ratio using the diagrams adopted by Caltrans (2013). The superstructure was assumed to respond essentially elastically, as far as its flexural stiffness is concerned, while its torsional stiffness was set equal to 20% of the uncracked section torsional stiffness (Katsaras et al. 2009), considering cracking due to torsion. Based on analysis results, i.e. required longitudinal reinforcement ratio (ρl,req) (accounting also for second order effects) and flexural response of the pier columns, refined values of q and as were calculated. Pier stiffness was redefined according to EN1998-2 Annex C (CEN 2005) on the basis of the flexural strength MRd. Some iterative RSAs were subsequently performed until all relevant design quantities were stabilised (i.e. as, q-factor, pier stiffness, ρl,req). The ‘regularity’ of the structural response was finally evaluated on the basis of Eqs. (1) - (3) considering all intended plastic hinge locations (i.e. both ends of the pier). Selected results of the procedure are presented in Table 2. It is noted that the reinforcement demand at the base of each pier was also adopted at the pier top, which is a common design approach in low to medium height columns; the critical (i.e. largest) requirement specifying the adopted ρl in the pier is denoted in blue. Two alternative strategies were explored with regard to the minimum amount of longitudinal reinforcement ρl,min; the first is the EN1998-1 value of 1% and the second is the maximum of the values specified in EN1992-1-1 and in the EN1998-2 Handbook (Fardis et al. 2012) (Eq. (4));

( )( )( )

,min,EC 2,min

,min,HB

max 0.10 ,0.002 (CEN2004a)max

: (Fardis . 2012)l Ed yd c

ll Rd c ctm Ed c

N f A

M W f N A et al

ρρ

ρ

= = ≥ +

(4)

Conformity to the criterion included in the lower part of Eq. (4) is deemed to ensure a minimum local ductility in the potential plastic hinge region by providing a sufficient amount of steel reinforcement (ρl,min,HB), and hence a design value of flexural strength of the pier section, MRd, not less than the cracking moment represented by the right-hand part of the inequality; Wc is the elastic section modulus, fctm is the mean value of the concrete tensile strength, NEd is the axial force in the seismic design situation (positive if compressive), and Ac is the area of the concrete section. According to Eqs. (1) – (3) and Table 2, consideration of ri indices calculated at both pier ends resulted in ‘irregular’ bridge response, and hence in further reduction of q (accounting for as and nk effects) to qr (accounting in addition for ‘irregularity’) and cost-ineffective designs, in five out of the eight investigated cases. In fact, the degree of ‘irregularity’ increases as the difference between the moment resistance of the pier section and the seismic demand increases, either due to the increase of the diameter of the pier section or due to the adoption of higher ρl,min ratios (see right-hand side of Table 2). Allocation of strength in excess of the seismic demand results in almost elastic response at the top of the piers (ri ≤ 1.0), increasing ρ, and limiting the inelastic response at their base compared to the allowable q. On the other hand, the effect of the ‘irregularity’ is eliminated in the D=1.2m case wherein the seismic demand exceeds the minimum requirements in almost all locations (i.e. the adopted ρl,min has no effect in qr) and the shear span ratio of pier columns approximates half of their height.

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016

Table 2 Comparative evaluation of ‘irregularity’ indices for different design approaches

* T: top, B: base

The ‘irregularity’ in structural response implied in the cases of D=1.4, 1.6, 2.0 m in Table 2, due to the consideration of ri indices at the pier top, is generally in contrast with the expected structural performance of the considered bridge. Its structural configuration indicates a relatively regular seismic response under horizontal seismic actions since both pier columns have the same diameter and similar height (hP1/hP2~0.75). More important, extensive evaluation of alternative design approaches (including a deformation-based and a force-based approach) and different diameter of piers (within the range considered herein) using nonlinear dynamic analysis (Gkatzogias & Kappos 2015a, b) consistently resulted in similar ductility demand in the piers; e.g. the ratio of curvature ductility demand at the base of the short column to the corresponding ductility demand at the base of the tall column was found between 0.80 and 1.10. The above implication can be alleviated if ρ is calculated on the basis of ri indices that are specified only for the critical location (i.e. location of maximum seismic demand) of each ductile member; ρcr and qr,cr corresponding to the latter approach are also provided in Table 2 indicating

Pier ρ l,req ρ l,min,EC2 r i ρ q r ρ cr q r,cr ρ l,req ρ l,min,EC8 r i ρ q r ρ cr q r,cr

Section (‰) (‰) - - - - - (‰) (‰) - - - - -P1

T* - 2.00 0.69 - 10.00 0.32

P1B* - 2.00 1.91 - 10.00 1.43

P2T - 2.00 1.04 - 10.00 0.48

P2B - 2.00 2.09 - 10.00 1.41


Section (‰) (‰) - - - - - (‰) (‰) - - - - -P1

T - 2.00 1.41 - 10.00 0.86

P1B - 2.00 2.60 1.65 10.00 2.03

P2T - 2.00 2.08 - 10.00 1.27

P2B 2.12 2.00 3.10 3.58 10.00 2.30


Section (‰) (‰) - - - - - (‰) (‰) - - - - -P1

T - 2.00 2.04 - 10.00 1.46

P1B 2.97 2.00 3.25 4.70 10.00 2.60

P2T 2.05 2.00 2.14 1.68 10.00 2.13

P2B 9.85 2.00 3.24 8.57 10.00 3.13


Section (‰) (‰) - - - - - (‰) (‰) - - - - -P1

T 4.65 2.07 2.16 4.65 10.00 2.16

P1B 13.63 2.11 3.18 13.63 10.00 3.18

P2T 14.06 2.07 2.31 14.06 10.00 2.31

P2B 24.09 2.11 3.20 24.09 10.00 3.20

D=1.2 m (n k ~0.33)q =3.22 q =3.22

1.48 3.22 1.01 3.22 1.48 3.22 1.01 3.22

4.54 1.39 1.02 3.16

D=2.0 m (n k ~0.12)

3.02 1.091.99 3.00

q =3.16q =3.00

D=1.6 m (n k ~0.19)

2.20 2.88 1.19 3.17 2.66 2.46 1.13 3.28

q =3.28q =3.17

D=1.4 m (n k ~0.24)

1.59 3.29 1.00 3.29 2.14 3.14 1.20 3.35

q =3.35q =3.29

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 ‘regularity’ in seismic response (which is in agreement with NLRHA results), and thus, avoiding further reduction of q-factors and ensuing over-conservatism. Results presented in Table 2 may also be indicative of systems with significantly unequal pier heights (e.g. piers pinned to the deck) wherein ri are considered only at the critical locations of each ductile member; in this case high ρl,min ratios will have an adverse effect irrespective of the considered direction amplifying ‘irregularity’ among piers and thus penalising critical sections with lower q-factors. In this respect, lower ρl,min ratios on the basis of Eq. (4) are expected to attain more rational and cost-efficient designs, noting however that ρl,min,HD was not found critical in any of the cases studied herein. 3. Deck capacity design verifications 3.1. Code provisions Modern codes (e.g. AASHTO 2011, Caltrans 2013, CEN 2005) require an explicit verification of the elastic response of ‘capacity protected’ members (e.g. the deck) when the components of the bridge energy dissipation system (e.g. the pier ends) reach their overstrength. EN1998-2 in particular, requires that non-significant yielding will occur in the deck under the ‘capacity design effects’ determined from equilibrium conditions at the intended plastic mechanism, when all intended flexural hinges develop an upper fractile of their flexural resistance (i.e. overstrength). A general procedure for the estimation of the ‘capacity design effects’ in each principal direction of the bridge considering both signs of the excitation is provided in Annex G of the code. It involves:

• Calculation of pier overstrength (MP,R=γοMRd) corresponding to each horizontal direction of the seismic action (E) with the sign considered (i.e. E+ or E-). The overstrength factor (γο) is defined according to Eq. (5);

( )( )2

1.35 if 0.1 if 0.11.35 1 2 0.1

γ ≤= >+ −

ko

kk

nnn

(5)

The flexural strength (MRd) should account for the interaction with the axial force and possibly with the bending moment in the orthogonal direction, both resulting from the analysis in the seismic design situation (i.e. ‘G+0.2Q+P+E’, where G, Q, P represent permanent, traffic, and prestressing actions, respectively).

• Calculation of the change of action effects of the plastic mechanism (herein the flexural moment of the deck, ΔMD,C) corresponding to the increase of the moments of the pier plastic hinges (ΔMP,R), from the values due to the permanent actions (Mp,G+0.2Q+P) to the overstrength moments (Mp,R);

, , , 0.2+ +∆ = −P R P R P G Q PM M M (6)

ΔMD,C should be evaluated from equilibrium conditions at the intended plastic mechanism; simplifications with respect to this step are also provided;

• Calculation of the deck capacity design moment MD,C by superimposing ΔMD,C to the permanent action effects MD,G+0.2Q+P;

, , , 0.2+ += ∆ +D C D C D G Q PM M M (7)

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 Implementation of the procedure in the previously considered 3-span bridge and subsequent verification using a more refined approach based on NLRHA are presented in the following sections.

3.2. Implementation of the EN1998-2 provisions In verifying the deck of the considered bridge (§2.2) against significant yielding, bearings were considered having plan dimensions of 350×450 mm and tr=44 mm, and pier columns having D=2.0 m and ρl=15‰ (at both ends). The previous configuration, corresponding to the ‘as-built’ state of the bridge (Gkatzogias & Kappos 2015a,b), was selected with a view to evaluating the Eurocode requirements in the case of an ‘actual’ bridge deck designed according to European practice and supported on fairly ‘strong’ piers that may compromise the requirement for non-significant yielding in the deck. The code provisions described in §3.1 were first applied in the longitudinal direction of the considered bridge; relevant results and critical combinations to be checked (in blue) are presented in Table 3 using the sign convention of Fig. 2(a).

Fig. 2 (a) Longitudinal cross-section of T7 at a typical pier-to-deck connection and sign convention, (b) vertical eccentricity of the prestressing force (P) with regard to the centre of gravity of section A-A, (c) intended plastic mechanism under the longitudinal component of seismic action The effect of prestressing (considered herein as part of the external actions) was taken into account to form MD,G+0.2Q+P; the range of the prestressing force (i.e. Pmin and Pmax values in Table 3) was selected on the basis of the load combinations provided in the final design report of the actual bridge, whereas the secondary effects of prestressing were ignored. MDz,G+0.2Q+P moments were calculated by considering the eccentricity of the tendons with regard to the centre of gravity (CG) in y-direction (Fig. 2(b)). It is noted that in the considered bridge, the pier overstrength does not depend on the sign of the excitation (cylindrical column pier and circular reinforcement pattern), while the effect of the out-of-plane bending moment and the variation of the axial force in the flexural strength of the piers is expected to be small,

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 and thus ignored (i.e. the pier overstrength was calculated in uniaxial bending under NG+0.2Q). ΔMp moments (see Table 3 and Eq. (6)) account for the direction of the seismic action (i.e. E+ or E-) and the sign of the response quantities (i.e. M+ or M-). ΔMD,C were evaluated from equilibrium conditions at the intended plastic mechanism of Fig. 2(c), while MD,C moments were calculated using Eq. (7).

Table 3 Calculation of capacity design effects according to EN1998-2

Fig. 3 Intended plastic mechanism under the transverse component of seismic action

M z,G+0.2Q M Rd,z γ ο M P,R,z M P,R,x ΔM *†(kNm) (kNm) (kNm) E x+ E x - (kNm) (kNm)

A1-A1L -24665 - - - -15743 10231 - 32863

A1-A1R -28338 - - - 20659 -19368 - 35861

P1T -2751 18907 1.35 25540 28292 -22789 - -

P1B 1619 19031 1.35 25719 -27338 24100 25719 -25719

A2-A2L -28341 - - - -17839 21302 - 42276

A2-A2R -24158 - - - 7642 -14684 - 41337

P2T 4513 18857 1.35 25471 20958 -29984 - -

P2B -2811 19033 1.35 25722 -22911 28533 25722 -25722

M z,G+0.2Q+P M z,G+0.2Q+P M G+0.2Q+P † M D,C †(kNm) E x+ E x - (kNm) E x+ E x - (kNm) (kNm)

A1-A1L -16036 -31780 -5805 -7421 -23165 2810 - 32863

A1-A1R -19710 949 -39078 -11095 9564 -30463 - 35861

P1T -2751 - - -2751 - - - -

P1B 1619 - - 1619 - - - -

A2-A2L -19712 -37551 1590 -11097 -28936 10205 - 42276

A2-A2R -15530 -7887 -30213 -6915 728 -21598 - 41337

P2T 4513 - - 4513 - - - -

P2B -2811 - - -2811 - - - -

SectionΔM z * (kNm)

P max = -18840 kN P min =-37650 kN

SectionM D,C,z (kNm) M D,C,z (kNm)

*ΔM P,R in piers, ΔM D,C in deck †M x in piers, M y in deck

Longitudinal Transverse

P = P min or P max


ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 The procedure suggested in EN1998-2 appears to be less straightforward when applied in the transverse direction of a bridge given that the definition of the intended plastic mechanism may not be obvious. More specifically, as the complexity of the system increases, e.g. the number of piers, significance of higher modes effect, non-simultaneous yielding among pier columns of different geometry/detailing or between column ends, the EN1998-2 assumption that all intended pier column plastic hinges reach their overstrength at the same time can result to a significant overestimation of the ‘capacity design effect’ on the deck. In the relatively simple case of T7, if yielding of pier columns is assumed at both ends (i.e. top and base), the application of the code procedure will result in deck capacity design moments (i.e. MD,C) in the order of 200,000 kNm, hence significantly overestimating the relevant values found through nonlinear dynamic analysis of the bridge (i.e. in the order of 35,000 kNm, see §3.3 and Table 4). In view of the previous consideration, the plastic mechanism presented in Fig. 3 was assumed, involving yielding only at the base of pier columns. Results of MD,C moments are presented in Table 3; deck moments presented in the table are valid irrespective of the value of the prestressing force P, due to the symmetry in the deck section geometry and detailing with respect to y-axis (note the zero eccentricity of the prestressing force in z-axis due to the symmetric pattern of tendons in Fig. 2(b)). Similarly, pier and deck flexural moments about x- and y-axis, respectively, under ‘G+0.2Q+P’ are equal to zero.

3.3. Verification of deck ‘capacity design’ flexural moments A more refined approach involving nonlinear dynamic analysis was subsequently used to verify MD,C moments calculated in §3.2. Pier overstrength was specified through moment-curvature (M-φ) analysis as the ultimate flexural strength using mean values of material strength. M-φ analysis of pier sections was performed with the aid of the computer program RCCOLA.NET (Kappos & Panagopoulos 2011) and the built-in ‘Section Designer’ (SD) utility of SAP2000 (CSI 2013) by adopting the same stress-strain laws for confined concrete (Kappos 1991) and reinforcing steel (Park & Sampson 1972); comparative results are presented in Fig. 4. Instead of adopting simplified assumptions with regard to the plastic mechanism, the deck bending moments MD due to ‘G+0.2Q+E’ were directly obtained from NLRHA of a partially inelastic model (PIM) of the bridge (Gkatzogias & Kappos 2015a) wherein the energy dissipation zones of the piers (top and base of columns) were modelled as yielding elements, with their strength and stiffness defined according to bilinear approximations of the M-φ curves (based on the equality of areas under the ‘exact’ and the bilinear curve); remaining parts of the bridge were modelled as elastic members. The bridge model was analysed under five artificial motions compatible to the EN1998-1 ‘Type 1’ elastic spectrum (subsoil class ‘C’) (Fig. 5) and properly scaled up to a seismic intensity that entails a seismic demand at the base of the short (critical) pier approximately equal to its flexural capacity. Analysis was carried out using the Ruaumoko3D software (Carr 2006); further information regarding the bridge modelling can be found in Gkatzogias & Kappos (2015a, b). Pier flexural moments at column ends under a spectrum compatible motion (SIM1) are plotted against time in Fig. 6, with a view to illustrating the validity of the plastic mechanism considered in §3.2 under the transverse component of seismic action. Although the maximum values (represented in the graph with solid dots) are recorded at different time intervals, it is seen that at t≈4.2 s pier flexural moments are close to the maximum recorded values. This implies that the inconsistency in ‘capacity design’ deck moments among the plastic mechanisms that include or exclude yielding at the pier top (see §3.2) derives

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 mainly from the fact that column sections at the pier top remain elastic under the specific intensity rather than from the asynchronous maximisation of bending moments.

Fig. 4 (a) Detailing of pier column in Overpass T7, (b, c) equivalent sections analysed with RCCOLA and SD (grey: unconfined concrete, blue confined concrete), (d, e) comparison of exact and bilinear M-φ curves extracted from RCCOLA and SD at the base of Pier 1

Fig. 5 Spectral matching of the mean acceleration (left) and displacement (right) spectrum to the EN1998-1 elastic spectrum for a suite of five artificial recordings Relevant results and critical combinations to be checked (in blue) are presented in Table 4 under the longitudinal (using the sign convention of Fig. 2(a)) and transverse component of seismic action. Moments retrieved from NLRHA correspond to the average of maximum and minimum values recorded

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ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 during the five NLRHAs at each specific location (hence not satisfying joint equilibrium) while classification in Ex+ or Ex- columns of Table 4 was made on the basis of the deformed profile of the bridge at the instant of each peak. MD,G+0.2Q+P+E (i.e. ‘capacity design’) moments were calculated by considering the eccentricity of the tendons with regard to the centre of gravity (CG) in y-axis; MD moments correspond to the MD,C values of the EN1998-2 ‘capacity design’ provisions in Table 3.

Fig. 6 Response history of Pier 1 flexural moments under the artificial recording SIM1 resulting in the development of the pier flexural capacity at the base of the columns

Table 4 Calculation of capacity design effects based on NLRHA

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M z,G+0.2Q M Rd,z γ ο M P,R,z * M P,R,x * M Ez †‡(kNm) (kNm) (kNm) E x+ E x - (kNm) (kNm)

A1-A1L -24665 - -47266 -8800 - -34524

A1-A1R -28338 - -9477 -45196 - -33826

P1T -2751 29148 28660 -28732 - -20350

P1B 1619 29325 -29082 29036 29325 30014

A2-A2L -28341 - -46558 -7446 - -31358

A2-A2R -24158 - -14122 -41822 - -30262

P2T 4513 29098 28022 -27854 - -24366

P2B -2811 29316 -28336 28276 29316 -29988

M z,G+0.2Q+P M z,G+0.2Q+P M G+0.2Q+P ‡ M D,Ez ‡(kNm) E x+ E x - (kNm) E x+ E x - (kNm) (kNm)

A1-A1L -16036 -38637 -171 -7421 -30022 8444 - 34524

A1-A1R -19710 -848 -36567 -11095 7767 -27952 - 33826

P1T -2751 - - -2751 - - - -

P1B 1619 - - 1619 - - - -

A2-A2L -19712 -37929 1183 -11097 -29314 9798 - 31358

A2-A2R -15530 -5493 -33193 -6915 3122 -24578 - 30262

P2T 4513 - - 4513 - - - -

P2B -2811 - - -2811 - - - -

*based on M-φ analysis †based on NLRHA ‡M x in piers, M y in deck

P max = -18840 kN P min =-37650 kN P = P min or P max

SectionM Dz,G+0.2Q+P+E (kNm) M Dz,G+0.2Q+P+E (kNm)


SectionM z,G+0.2Q+E †(kNm)


ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 Comparison of the deck capacity design moments presented in Tables 3 and 4, reveals that although the code-based approach cannot always predict the location of the critical moment, it can provide conservative estimates of the critical moment magnitude. EN1998-2 capacity moments were found in most cases approximately 1 to 5% higher than the relevant values derived from NLRHA. Deck capacity design moments were overestimated compared to the NLRHA values only in the case of the transverse component of seismic action (~23%) and in one case of positive flexure (Fig. 2(a)) under the longitudinal component of seismic action (~34%). Nevertheless, both previous cases were not found critical with regard to the non-significant yielding requirement of EN1998-2 (see the following section).

3.4. Evaluation of the ‘non-significant yielding’ criterion M-φ analysis of the A-A deck section (Fig. 2) was performed in order to evaluate the fundamental requirement of EN1998-2 for ‘non-significant’ yielding of the deck under the ‘capacity design effects’. The ‘actual’ detailing of section A-A and the section modelled in SD (CSI 2013) are presented in Fig. 7; it is noted that tendons were not modelled since the prestressing effect has been previously (§3.2, 3.3) considered as part of the external actions whereas confinement of the concrete within the web of the box girder section was ignored. The latter assumption was adopted for the sake of simplicity (evaluation of the ductility capacity was not an issue in this investigation) as it is expected to have a minor effect on the flexural strength and initial stiffness of the deck section.

Fig. 7 Detailing of Overpass T7 deck section A-A (top) and section modelling in SD (bottom)

In Figs. 8, 9, the ‘exact’ and bilinear M-φ curves of the deck section A-A are presented for different levels of prestressing force (i.e. Pmin, Pmax) in the case of positive/negative moments about z- and y-axis, representing flexure of the deck under the longitudinal and transverse component of seismic action, respectively. The magnitude of bending moments that correspond to the critical combinations of ‘capacity design effects’ (i.e. MD,C and MD values in blue in Tables 3 and 4) for both the EN1998-2 and the NLRHA-based approach, along with the cracking moments (i.e. moments at the instant of the first crack) are also presented in the diagrams. Considering Fig. 8, deck yield moments were found in general higher than the capacity design moments under both levels of prestressing force, however, only a minor

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 exceedance of the capacity design moment is observed in the case of Pmax and negative flexure of the deck, corresponding well within the cracked state of the deck section. On the other hand, capacity design moments for ‘Pmin – negative flexure’ correspond to the onset of cracking while the deck section remains in all cases uncracked under positive flexure. Under the transverse component of seismic action (Fig.9), capacity design moments (independent of P according to Tables 3, 4) were found in general lower or approximately equal to the cracking moments.

Fig. 8 ‘Exact’ and bilinear Mz-φz curves of deck section A-A under Pmin, Pmax (solid dots represent deck cracking moments), compared with the deck ‘capacity design’ moments (dashed lines) obtained from the EN1998-2 and the NLRHA-based approach

Fig. 9 ‘Exact’ My-φy curves of deck section A-A under Pmin, Pmax (solid dots represent deck cracking moments), compared with the deck ‘capacity design’ moments (dashed lines) obtained from the EN1998-2 and the NLRHA-based approach

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ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 Results presented in Figs. 8, 9 indicate that the target performance for non-significant yielding in the deck is generally achieved. However, the proximity of flexural demand to the yield moments of the deck raises some serious concerns with regard to the common assumption adopted in EN1998-2 (and the US codes) that prestressed concrete deck sections remain uncracked under the design seismic actions. In fact, non-significant yielding of the deck under the ‘capacity design effects’ cannot ensure that cracking in deck sections will be avoided under the seismic design situation and the validity of analysis results (e.g. non-conservative estimation of displacement demand) may be reduced, especially in cases of increased seismic intensity and relatively low level of prestressing forces. It should be noted that the issue discussed is by no means specific to the longitudinal response of straight bridges as implied by the case studied herein, since the out-of-plane flexural demand of the deck is expected to be significantly higher in the common case of straight/curved-in-plan bridges wherein the displacement response of the deck is restrained at the abutments. Pending further investigation on the issue and unless a more stringent criterion is adopted during the capacity design verifications of the deck (e.g. non-cracking instead of non-significant yielding), explicit verification of the flexural stiffness of the deck would be in order when assessing displacement demand under the seismic design situation. 4. Conclusions EN1998-2 provisions focusing on the assessment of ‘regularity’ in seismic response, and the capacity design verification of the deck in bridges designed for ductile behaviour of the piers were scrutinised herein and implemented in a 3-span bridge with a view to identifying associated implications and problems, and suggesting some possible remediation. Regarding the regularity criterion and the associated reduced behaviour factor qr adopted by EN1998-2, consideration of ri indices calculated only for the critical location of each ductile member along with use of a rationally selected minimum longitudinal reinforcement ratio are suggested as a means of avoiding conservative and cost-ineffective designs deriving from excessive and unnecessary reductions of the design q-factor which it turn result from a ‘blind’ interpretation of the EN1998-2 provisions. Capacity design verification of an ‘actual’ bridge deck supported on relatively ‘strong’ piers (through a monolithic connection) according to the EN1998-2 provisions and a more refined approach involving NLRHA and M-φ analysis of pier and deck sections indicate that the target performance prescribed by the Code (i.e. no significant yielding of the deck) is achieved, since the ‘capacity design effects’ are found lower than the relevant yield moments of the deck. However, certain pitfalls are also identified. More specifically, the definition of the intended plastic mechanism in the transverse direction of the bridge may not be obvious, especially as the complexity of the system increases, while the estimation of deck bending moment demands corresponding well within the cracked state of deck sections renders questionable the validity of analysis when the flexural stiffness of the deck is calculated on the basis of uncracked sections, and indicates the need for further investigation on this important issue.

ΕΠΕΣ Ελληνική Επιστημονική Εταιρία Ερευνών Σκυροδέματος (ΕΠΕΣ) – ΤΕΕ / Τμήμα Κεντρικής Μακεδονίας Πανελλήνιο Συνέδριο Σκυροδέματος «Κατασκευές από Σκυρόδεμα» Θεσσαλονίκη, 10-12 Νοεμβρίου 2016 References AASHTO (2011), “Guide Specifications for LRFD seismic bridge design, WA, USA. Ayala, G. and Escamilla, M. A. (2013), “Modal irregularity in continuous reinforced concrete bridges.

Detection, effect on the simplified seismic performance evaluation and ways of solution”, Eds. Lavan, O. and De Stefano, M., Seismic Behaviour and Design of Irregular and Complex Civil Structures, Springer, pp. 103-118.

Bardakis, V. G. and Fardis, M. N. (2011), “Nonlinear Dynamic v Elastic Analysis for Seismic Deformation Demands in Concrete Bridges having Deck Integral with the Piers”, Bulletin of Earthquake Engineering, Vol. 9, No. 2, pp. : 519–536.

Caltrans (2013), “Seismic design criteria, (ver. 1.7)”, CA, USA. Carr, A. J. (2006), “Ruaumoko 3D: Inelastic dynamic analysis program”, University of Canterbury, New

Zealand. CEN (2004a), “Eurocode 2. Design of concrete structures–Part 1-1: General rules and rules for buildings

(EN 1992-1-1)”, Brussels. CEN (2004b), “Eurocode 8. Design of structures of structures for earthquake resistance–Part 1: General

rules, seismic actions and rules for buildings (EN 1998-1)”, Brussels. CEN (2005), “Eurocode 8. Design of structures of structures for earthquake resistance–Part 2: Bridges

(EN 1998-2)”, Brussels. CSI (Computers and Structures Inc.) (2013), “SAP2000: Three dimensional static and dynamic finite

element analysis and design of structures”, CSI, CA, USA. Fardis, M. N., Kolias, B. and Pecker, A. (2012), “Designer’s Guide to Eurocode 8: Design of Bridges

for Earthquake Resistance EN 1998-2”, ICE Publishing, London, UK. Gkatzogias, K. I. and Kappos, A. J. (2015a), “Deformation-based seismic design of concrete bridges”,

Earthquakes & Structures, Vol. 9, No. 5, pp.: 1045-1067. Gkatzogias, K. I. and Kappos A. J. (2015b), “Performance-based seismic design of concrete bridges”,

SECED Conference on Earthquake Risk and Engineering towards a Resilient World, Cambridge. Guirguis, J. E. B. and Mehanny, S. S. F. (2013), “Evaluating Code Criteria for Regular Seismic Behavior

of Continuous Concrete Box Girder Bridges with Unequal Height Piers”, Journal of Bridge Engineering, Vol. 18, No. 6, pp.: 486-498.

Kappos, A. J. (1991), “Analytical prediction of the collapse earthquake for R/C buildings: Suggested methodology, Earthquake Engineering & Structural Dynamics, Vol. 20, No. 2, pp.: 167–176.

Kappos, A. J. and Panagopoulos G. (2011), “RCCOLA.NET - A program for the inelastic analysis of reinforced concrete cross sections”, Aristotle University of Thessaloniki, Greece.

Kappos, A. J., Gkatzogias, K. I. and Gidaris, I. G. (2013), “Extension of direct displacement-based design methodology for bridges to account for higher mode effects”, Earthquake Engineering & Structural Dynamics, Vol. 42, No. 4, pp.: 581–602.

Katsaras, C. P., Panagiotakos, T. B. and Kolias, B. (2009), “Effect of torsional stiffness of prestressed concrete box girders and uplift of abutment bearings on seismic performance of bridges”, Bulletin of Earthquake Engineering, Vol. 7, No. 2, pp.: 363-375.

Park, R. and Sampson, R. A. (1972), “Ductility of reinforced concrete column sections in seismic design”, Journal of the ACI, Vol. 69, No. 9: 543-551.

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