Conclusiones y recomendaciones

4.1. Introduction

During the conceptual design phase, the layout of the structure is established, the structural materials for its various parts are selected and the construction technique and procedure are decided. Conceptual design concludes with a preliminary sizing of all members, in order to allow the next phase of the design process to be carried out, namely the analysis for the calculation of the effects of the design actions (including seismic) in terms of internal forces and deformations in structural members. Analysis is followed by the detailed design phase (notably the verification of member sizes, the dimensioning of the reinforcement, etc., on the basis of the calculated action effects) and the preparation of material specifications, construction drawings and any other information that is necessary or helpful for the implementation of the design.

Conceptual design is of utmost importance for the economy, safety and fitness for use of the structure. In addition to technical skills and knowledge, it requires judgement, experience and a certain intuition. Although conceptual design cannot be taught, several authoritative documents (recently, fib, 2009, 2012) give general principles and guidance. Useful general sources for bridges are fib (2000) and (2004), and, for their seismic design, Priestley et al. (1996) and fib (2007).

The conceptual design of a bridge is controlled mainly by that of the deck, which in turn is governed by its use, the preferred construction technique (Table 4.1), aesthetics, topography and – of course – cost issues. The three last considerations significantly influence the conceptual design of the piers as well. Gravity loads and the construction technique control the design of the deck. The deck spans and their erection, alongside the terrain, determine the number and location of the piers. In seismic regions, the piers themselves and their connection to the deck are governed by the seismic action. In addition, seismic considerations are taken into account for some aspects of the deck design, notably its continuity across spans and sometimes its connec-tion with the abutments and the piers. Before delving into these purely seismic aspects, it is worth recalling that one of the prime objectives of the conceptual design of a bridge for non-seismic loads is to reduce the deck dead load, as this is normally the prime contributor to the action effects in the deck, the piers and the foundation for the combination of factored gravity loads (the persistent and transient loads combination in Eurocode terminology). This is first pursued through the choice of the material(s) and the shape of the deck section; once these are chosen, an effort is made to reduce its dimensions by using higher-strength materials, external prestres-sing (if relevant), etc. Needless to say, although the conceptual and detailed seismic design of bridges concerns mainly the piers and the way they are connected to or support the deck, reducing the deck’s self-weight is of prime importance for the bridge seismic design as well:

both seismic force and displacement demands increase with the deck mass (they are normally approximately proportional to its square root), and there is good reason to reduce it.

As pointed out in Section 2.3.1 of this Guide, the prime decision in the conceptual seismic design of the bridge is how to accommodate the horizontal seismic displacements of the deck with respect to the ground. Four options were highlighted there, repeated below for completeness:

1 to support the deck on all abutments and piers through bearings (or similar devices) that can slide or are horizontally very flexible

Clauses 2.4(1)–2.4(3) [2]

Clauses 2.4(4), 2.4(9), 2.4(10) [2]

2 to fix the deck to the top of at least one pier (but not at the abutments) and let those piers accommodate the horizontal seismic displacements through inelastic rotations in flexural

‘plastic hinges’

3 to let the base of the piers slide with respect to the soil or allow inelastic deformations to develop in foundation piles

4 to lock the bridge in the ground, by fixing the deck to the abutments as in an integral system that follows the ground motion with little additional deformation of its own.

Option 3 is not central in Part 2 of Eurocode 8, and is not dealt with in detail in this Designers’

Guide. Option 4 is also a rather special case, applicable only to short bridges with up to three spans – but often with only one. It is dealt with separately in Sections 4.5, 5.4 and 6.11.3 of this Guide. Options 1 and 2 are the main ones. The first amounts to effectively isolating the deck from ground shaking; it is treated in Eurocode 8 as seismic isolation. The second option relies on ductility and energy dissipation in the piers. This chapter – and most of the rest – focuses on these two options.

The features of conceptual design affecting the seismic behaviour and design of a bridge the most are:

1 (for multi-span bridges) the continuity of the deck across spans over the piers 2 (for bridges with a concrete deck) whether the deck is monolithic with the piers.

To a certain extent these features are related to the method used for the erection of the deck (see Table 4.1). It is very unlikely – or even impossible – for continuous decks to lose support and drop from the piers. Even unseating from some bearings – which is also unlikely – will not have cata-strophic consequences, and may be easily reversed. Unseating and dropping can be ruled out if the deck is monolithically connected to the piers. In that case, the prevention of horizontal movement between the deck and the top of the piers profoundly affects the seismic response of the bridge, which is then dominated by the inelastic deformations and behaviour of the piers. It also affects its seismic design, which is then based on the ductility of the piers. Monolithic or rigid connection of the deck to the pier tops also affects the bridge performance under non-seismic actions. The effect may be favourable (e.g. the performance under braking or centrifugal traffic actions in railway bridges) or negative (e.g. the restraint of thermal or shrinkage deformations in a long deck on stiff piers, which may even be prohibitive for the bridge).

4.2. General rules for the conceptual design of earthquake-resistant bridges

4.2.1 Deck continuity

The most important goal of the seismic design of a bridge is to keep the deck in place under the strongest conceivable seismic action. In multi-span bridges, one of the risks to be faced by the Table 4.1. Span range, erection speed and continuity of the deck across spans and with the piers for different erection techniques

Prefabricated girders 10–50 25–100^a Normally not Normally not

On scaffolding/falsework on grade 5–50 5–10 Normally yes Yes or no On mobile launching/casting girder

or gantry (span-by-span)

30–60 10–50 Yes Yes or no

Free/balanced cantilever

Cast-in-situ deck segments 60–300 6–15 Yes Normally yes

Prefabricated deck segments 40–160 20–60^a Incremental launching

Without temporary props 30–70 10–30 Yes Normally not

With temporary props 70–120 10–30

aSpeed depends on the capacity of the prefabrication plant

seismic design is local loss of support of the deck, due to unseating from a pier. The best way to prevent drop of a part of a multi-span deck from one or more piers is by providing continuity of the spans over all piers: a deck continuous from abutment to abutment. An exception may be made in very long bridges – of several hundred or over a thousand metres – where intermediate movement joints may be judiciously introduced. Such joints may be essential if it is considered likely that a strong earthquake may induce significantly different movement at the base of adjacent piers, notably if the bridge straddles a potentially active tectonic fault or crosses non-homogeneous soil formations. Intermediate movement joints may be placed within a span as Gerber-type hinges with sufficient seat length. More often they are placed between two spans whose ends are supported through separate bearings on the same pier. In such a layout the movement joint should be wide enough to prevent pounding between the ends of the two spans, in addition to providing sufficient support length against unseating (see also Section 6.8.1.3).

Apart from breaking up the full continuity of the deck and increasing the chances of a drop-off, intermediate movement joints increase the uncertainty of the seismic response: the parts of the bridge separated by the movement joints (the ‘frames’ of the bridge in US parlance) may vibrate out of phase and experience pounding at the joints. Opening and closing of joints is a nonlinear phenomenon, and capturing its effects may require a nonlinear analysis (normally in the time domain). To take some of these effects into account without recourse to nonlinear time-history analysis, the Caltrans Seismic Design Criteria (Caltrans, 2006) requires using, in addition to a stand-alone model of each and every bridge ‘frame’ between adjacent movement joints, two global models that consider their interactions:

g a ‘compression’ model with all movement joints taken as closed

g a ‘tension’ model where movement joints are considered to be open and connected only through the axial stiffness, EA/L, of any cable restrainers linking the deck in the longitudinal direction across joint(s).

For bridges with several intermediate movement joints, Caltrans (2006) further requires the use of several elastic multi-’frame’ models, each one encompassing not more than five ‘frames’ plus a

‘boundary frame’ or abutment at each end; ‘frames’ beyond the ‘boundary’ ones are represented by massless springs, and analysis results for ‘boundary frames’ are ignored, while adjacent models overlap by at least one ‘frame’ beyond a ‘boundary frame’. The objective of this complex series of analysis is to better capture the out-of-phase motion of ‘frames’ and to account for the important normal modes and periods of vibration of each ‘frame’ without resorting to an unduly large number of nodes from abutment to abutment. Despite its complexity, the above procedure may not capture important features of the system response for the following reasons:

g pounding between ‘frames’ or the activation of cable restrainers linking them are unilateral nonlinear phenomena that cannot be approximated by ‘envelope’ linear models

g if the bridge is long enough to have several intermediate deck separation joints, the effect of the spatial distribution of the seismic ground motion may be quite important and worth accounting for, even when such joints are provided.

As Part 2 of Eurocode 8 requires none of this analysis complexity, the sole reason for highlighting here the provisions in Caltrans (2006) is to stress the uncertainty of the seismic response of bridges with intermediate movement joints and the complexity of the analysis that this entails.

Reducing the uncertainty of the response is an important goal of conceptual design, and in this case it is served well by avoiding such joints.

Deck spans composed of prefabricated girders, be they of concrete, steel or composite (steel–

concrete), are normally simply supported on the piers. Adjacent spans can be connected by encapsulating their ends in bulky cast-in-situ crossheads. However, this is not a common practice. Normally, continuity of adjacent spans is pursued through a cast-in-situ topping slab continuous over the joint between two girder ends (see also Section 5.5.1.4). Figure 4.1 depicts an example. The slab should have sufficient out-of-plane flexibility to allow different rotations at the ends of the adjacent spans due to traffic, creep (and the ensuing moment redistribution) and pier head rotation. This detail provides continuity of the pavement for motorist and

Clauses 2.3.2.2(4), 4.1.3(3) [2]

passenger comfort and makes redundant intermediate roadway joints and the maintenance they entail. It also ensures the continuity of seismic displacements of the deck and prevents impact between adjacent spans under seismic actions. Finally, it serves as a sacrificial seismic link between the two spans against span drop-off after unseating. It is of note that the precast girders of the twin 2.3 km-long Bolu viaduct were spared from dropping and triggering a cascading collapse despite their unseating in the Duzce (TR) 1999 earthquake (Figure 4.2(a)), due to their continuous topping slab. Part 2 of Eurocode 8 (CEN, 2005) makes specific reference to such continuity slabs and their modelling.

It is normal practice to support prefabricated girders on a transversely stepped top surface of the pier or the bent-cap or on corresponding concrete plinths, in order to achieve a transverse slope Figure 4.1. Precast girders simply supported on pier and connected for continuity via topping slab

Pier Cross beam Slab cast over the webs on a 2 cm expanding polystyrene layer

Bearings

Figure 4.2. Bolu viaduct in Duzce (TR) 1999 earthquake: (a) unseating of precast girders; (b) suspension from the continuity top slab prevented span drop-off

of the top surface of the deck without differentiating the depth among the girders. By contrast, a step of the pier top in the longitudinal direction is not a proper means to accommodate a differ-ence in depth between two adjacent deck spans simply supported on the pier as, during the longitudinal seismic response, the deeper of the two decks may ram the step. Instead, the depth of the shallower deck should be increased over the support (through a deeper cross-head) to that of the deeper, so that both can be supported at the same horizontal level.

4.2.2 Uniform seismic demands on piers – piers of different height 4.2.2.1 Introduction

For reasons of aesthetics, all piers or pier columns of a bridge usually have the same cross-sectional dimensions. If the bridge has several piers with the same type of rigid connection to the deck (i.e. all monolithically connected, or supporting it on fixed bearings) as in option 2 of Sections 2.3.1 and 4.1, differences in pier height are translated into differences in pier flexibility in a given horizontal direction (longitudinal or transverse), as flexibility is approximately pro-portional to the third power of the pier height. This has certain implications for the longitudinal or the transverse seismic response of the bridge. Some of these are unfavourable, and should be avoided at the conceptual design stage, as highlighted in the following sections.

4.2.2.2 Conceptual design of bridges with piers of different heights for favourable longitudinal response

The longitudinal inertia forces on an approximately straight deck (even one along which the tangent to the axis does not change direction by more than 608) are about collinear. Owing to the high axial rigidity of the deck, no matter where they originate, these forces are shared by the individual piers (approximately) in proportion to their longitudinal stiffness. If the pier columns have the same cross-sectional dimensions, shorter ones will undertake larger longitudi-nal seismic shears and develop higher seismic moments (which are approximately inversely pro-portional to the square of the pier height), requiring more vertical reinforcement than the rest.

This will further increase the effective stiffness of the shorter piers (cf. Section 5.8.1), and may lead to a vicious cycle. In addition, regardless of the exact amount of their reinforcement, the shorter piers will yield earlier and develop larger ductility demands than the others, possibly failing sooner. Note that the shorter piers are normally towards the two ends of a long deck, and, if rigidly connected to it, they constrain its thermal, creep and shrinkage deformations, inducing in the deck high tensile forces and suffering themselves from the associated longitudinal shears. The measures proposed below for the mitigation of non-uniform longitudinal seismic demands in piers are quite effective in reducing these longitudinal constraints and their effects.

Conceptual design offers various ways around the problems posed by different pier heights:

g If the height differences are rather small, the free height of the shorter piers may be increased to be approximately the same as in all others. The added height may be in an open (preferably lined) shaft under grade. The base of these piers should always be easily accessible for inspection and repair of any damage, and above groundwater level.

Figure 4.3 shows an example.

g If the pier heights are very different, rigid connection of the deck to the piers (monolithic or through fixed bearings) may be limited to a few piers of about the same height – normally the tallest ones. The deck may be supported on all other piers via bearings that are flexible in the longitudinal direction (elastomeric or sliding). Often, the tallest piers are around the deck mid-length; so, this choice helps to relieve the stresses building up in the deck and the piers due to the thermal and shrinkage movements of the deck in the longitudinal direction. A typical example is the bridge in Figure 4.4. The deck is

continuous from abutment to abutment, with a total length of 848 m for the east-bound carriageway and 638 m for the west-bound one, both with a radius of curvature of 450 m, interior spans of about 55 m and end ones of about 44 m. It was cast span-by-span on a mobile casting girder launched from pier to pier. Each deck is monolithically connected to the five centre-most and tallest piers, but tangentially sliding on the rest and at the abutments (see Figure 4.5).

g The cross-section of the shorter piers and of the upper part of the taller ones may be chosen to present much smaller lateral stiffness in the longitudinal direction than the lower part. In this way, the longitudinal stiffness of the piers can be balanced despite substantial

Clauses 2.4(4), 2.4(6), 2.4(7) [2]

differences in height. A usual choice for the longitudinally flexible part of the pier is a

‘twin blade’ consisting of two parallel wall-like piers in the transverse direction. The lower and stiffer part (possibly of very different heights in various piers) may be a hollow box.

Figure 4.6 shows a schematic, and Figure 4.7 a real example, of a balanced cantilever construction (where the ‘twin-blade’ piers offer additional advantages). Depending on the relative length of its ‘twin-blade’ and hollow box parts, plastic hinges may form either at the very base of the pier or at the base of each of the individual columns of the upper

‘twin-blade’ part, or at both, one after the other. These possibilities should be taken into account in the capacity design of the pier. All these potential plastic hinge regions (including the top of the individual columns of the ‘twin blades’) should be detailed for ductility.

g If the deck is supported on all piers through elastomeric bearings, the stiffness of piers with different heights may be harmonised by tailoring the total thickness t of the elastomer so that the bearing stiffness K_b¼ GA/t counterbalances the difference in pier stiffness, Kp, giving approximately the same composite stiffness from Eq. (D2.10) for all piers (see point 2 in Section 4.3.3.5). Note, however, that the large flexibility of the elastomeric bearings controls the horizontal stiffness of such bridges (see also Section 2.3.2.5 of this Guide).

g If the section of pier columns is hollow, its thickness may be adjusted to balance the difference in pier height and achieve either approximately uniform shear forces or

approximately uniform maximum moments among the piers. However, as the pier stiffness is not very sensitive to the thickness of the hollow section, only small differences in the pier height can be the accommodated in this way.

4.2.2.3 Transverse response of bridges with piers of different heights

The transverse inertial forces are distributed all along the deck. The seismic action effects they induce in piers depend not only on their relative transverse stiffness but also on their tributary deck length and the in-plane flexural rigidity of the deck, which is normally high but does not dominate the transverse response as much as the axial deck stiffness does for the longitudinal

The transverse inertial forces are distributed all along the deck. The seismic action effects they induce in piers depend not only on their relative transverse stiffness but also on their tributary deck length and the in-plane flexural rigidity of the deck, which is normally high but does not dominate the transverse response as much as the axial deck stiffness does for the longitudinal