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Scope and aims
Structure of report
An extensive part of this report was dedicated to the literature review. Though actually the most interesting part is the one which concerns to the results of the vulnerability of bridge of the case study, it is not admissible to neglect all the general considerations based on an extensively research in technical text, through which was possible to determine the specific structure, the method and the phases of construction, the type of analysis to be carried out and in which way the results have to be read. Indeed close attention is needed in interpreting the results due to limitations of the specific case under consideration and at the same time because of the need to generalize the specific results for use on a larger scale of projects.
In the "literature review" section of the report a general study about bridges has been developed. This has been done investigating the history, the evolution, as well as the technologies and trends of bridge design, with particular attention to recent developments in California. Construction techniques have also been analyzed in more details referring to many important projects, based on international literature, scientific journals and technical books.
Then the "earthquake" section was covered.
In the section about Codes of practice an overview of the most important aspects has been made and few tables of interested have been attached to justify the choices made in the case study.
Type of Analysis of previous papers
The second part, elaborated with the support of the software SAP2000 BRIDGE Modeler, follows the development of the project of a common bridge in California according to the local and currents codes of practice.
An extensive literature review was conducted to understand which is the state of the research and the interest of the codes in assured performance behavior of the bridges during phases of construction.
Among all the engineering sciences, bridge engineering is one of the most complex because involves in itself a lot of disciplines, from technical to aesthetic, from environmental to social, from economic to political aspects. Without any doubt the technical and the economic factors are those that strongly influence engineer's choices in designing a bridge, but they do not cover all the design process. Using Troitsky words "Planning and designing bridges is part art and part compromise" (Chen, Lian Duan, 1999).
For understanding recent trends in bridge design and construction it is of high importance to consider the development that bridge engineering has undergone during centuries. History illustrates that social and economical changes in a nation have been reflected on bridge engineering development. At different historical moments, various types of bridges have been built for many purposes with the new technologies at each time. From the 19th century, due to the big industrial growth, bridges have been built essentially as part of the transportation system. During the 20th century, bridge engineering has been characterized by big changes in the structural solutions and methods of constructions because of the diffusion of the reinforced concrete. The designers had finally a large possibility of choices between materials, methods of constructions and technologies of analysis. This led to the actual scenario where multiple type of bridges are in operation highlighting the wide creativity of bridge engineers.
Designing a bridge, the main important parameters to take in account in choosing the best solution are: location, span, material, type of foundation, scheme of the bridge, type of superstructure, type of supports, method of construction. Regarding materials, nowdays timber is used only for temporary bridges, then for ordinary bridges the choice is between reinforced concrete and steel. Depending on the span of the structure one material is to be preferred to the other. For spans between 65ft and 330ft reinforced concrete gives the best compromise, for spans greater than 330 ft steel is recommended. The span influences also the system of the bridge: for small and medium spans a beam bridge is commonly used, for spans longer than 160 ft an arch system could be adviced and a suspended bridge can be the solution for very long span bridges. These are only indication, and every single case has to be evalued considering limitations due to location, codes, cost and typical bridge of the area. It is a good rule of practice to consider typical projects recent designed in the area in which there is the purpose of insert a new bridge structure, if the medium-span is the one of interest. (Chen, Lian Duan, 1999).
Figura 1 - Comparative Bridge Costs in California January 2010. (Caltrans Construction Statistics)
Figura 2 - 2009 Bridge Trends in California. (Caltrans Construction Statistics)
4.2 Structural Types
This paragraph intends to provide a list of the several commonly used types of bridges, highlighting the differences for geometry, analysis, economy. This list is not to be intended complete, as other type of bridges may be design, in which case, specific deep studies have to be done in order to analyse the particular solution.
According to Raina it is possible to categorize bridges in six different types of superstructure regarding the material which is made of.
Materials commonly used for building the superstructure of permanent bridges are:
Mix of steel and reinforced concrete or mix of reinforced concrete and prestressed concrete
Special superstructures with cables
For each material there are possibilities of different kinds of sections.
1. Reinforced Concrete Superstructures can be simple span or continuous span; balanced cantilever, arch or frame, tipically utilized for short span bridges. Some parts may be precast.
Solid Slab - Used for spans between 5 and 14 meters
Slab and girder (T-beam bridges) - Used for spans between 14 and 25 meters
Hollow box girder - Used for spans between 25 and 70 meters - Characterized by a high torsional resistance, is suitable for curved paths.
2. Prestressed Concrete Superstructures can be simple, balanced or free cantilever, or continuous span. It is possible to have segmental cast in situ or precast solutions. Prestressed Concrete superstructures cover medium spans.
Hollow slab - Used for spans between 10 and 25 meters
Slab and girder (Girder bridges)
Hollow box girder
3. Masonry superstructures have been associated with arch bridges in the past centuries.
This type of bridges is not of relevant importance for this study, which is relative to new bridges under construction.
4. Steel Superstructure typically consists in a steel truss deck and covers long spans.
5. Composite superstructures can have the following deck types:
Longitudinal plate girder and transverse beam girder with concrete slab
Longitudinal and transverse beam girder with concrete slab
Longitudinal box girder with concrete slab
The deck arrangement can be simple span or continuous span, or arch and covers medium and long spans.
5. Special superstructure
Cable stayed bridges
These structures are of relatively new conception and in last century have been used for long span solutions.
Figura 3 - a) Reinforced Concrete solid slab; b) Voided Slab
Figura 5 -
4.3 Methods of construction
Figura 6 - Balanced CAntilever Segmental Construction
Conventional construction: using falsework
Cast in place segmental construction
Precast segmental construction
Figura 7 - Precast beam method
Figura 8 - Full span precast method
Figura 9 - Span by span erection on falseworks
Figura 10 - Balanced cantilever method with launching gantry
Figura 11 - Span by span erection with launching gantry
Figura 12 - Balanced cantilever method with cranes
Figura 13 - Balanced cantilever method with lifting frames
Figura 14 - Form traveller method
Figura 15 - Incremental launchig method
4.4 New trends
According to Caltran's informations, in California the majority of bridges have been built with the cast-in-place (CIP) technique (See also fig.x?). This method of construction provides a good compromise between bridge cost and seismic performance of the structure. Commonly CIP system requires big effort in design and preparation at the site; often needs framework to support and long time for casting and finishing. An ever-increasing requests of new way of transportation has been registered due to the rapid growth of population and the high economic standards, added to the aging of infrastructures and the introduction of new seismic design criteria. The transportation planners are searching for new solutions that can accelerate highway and bridge construction in alternative to the traditional ones. Caltrans engineers are looking at precasting to try to achieve the Accelerating Bridge Construction (ABC); they are developing research and studies to understand the effectiveness of precast solutions in reducing construction time on site and delays in the decongestion of traffic. In the beginning, Caltrans was concerned about the behavior of the precast structures in high seismic zones, because there was not a long tradition in the earthquake prone areas. Precasting has been usually considered having too many points of connection which are weaknesses for seismic performance capabilities. The University of California-San Diego conducted tests on the seismic behavior of precast segmental bridge and the results showed that this kind of method gives desirable performances also for high seismic zones. (Aspire, Spring 2007) In the last 3 years few projects have been completed successfully in California with prefabricated elements, and even if they costed 30% more than it they were built with traditional CIP method, the reduced time-on-site guarantees a overall gain.
Figura 16 - Segments wait in storage behind the completed spans - Otay River Bridge, San Diego (2007)
4.5 Economic analysis and Quantity trends
Figura 17 - Bridge Construction Index Trend in California. (Caltrans Construction Statistics)
In the figure above is graphically shown the trend of the Bridge Construction Cost Index in California over the last 45 years. It is evident how the index cost has been increasing over the decades, although sometimes decrements have been registered. This is possibly due to periods of regressions in the economy of the State or due to improvements in various technical aspects of construction and consequently in the adoption of new, cheaper and better designed solutions.
It is very difficult to forecast the cost of bridge engineering works, as they are related to a lot of uncertainty parameters like economic situation, inflation, local environment. By the way an effort in this sense has been done to have some costs of
4.7 Seismic Codes
WHICH SEISMIC CODE?????
AASHTO Standards Specifications give provisions of minimum requirements for conventional bridges with span not exceeding 300ft. There are some general indications about cable-stayed bridges, suspended bridges, arch bridges but these are not fully covered.
The fundamental principles on which the Standards are based on are the following points:
Structural performance should be ensured without significant damage (elastic range) under small and moderate earthquakes
Design has to be carried out applying realistic ground motion accelerations
Large earthquake should not cause collapse
The Codes are valid for all United States and the seismic risk varies a lot through the Country. Reading the acceleration contours on the hazard map (fig.20?) the acceleration coefficient A, relative to the place of interest, is determined dividing by 100 the value read; the map is based on a return period of 475 years for events with 10% probability of exceedence in 50 years. Four Seismic Performance Categories (SPC) from A to D (AASHTO SDC) or from 1 to 4 (AASHTO LRFD) are defined (fig.20?) on the base of the Acceleration Coefficient (A) and two Importance Classification (IC) parameters categorize every bridge as Essential (I) or Critical (II) regarding its importance (fig. 22?). To take into account the soil conditions a Site Coefficient (S) has to be used in the design process for all type of foundation for approximates the effect of the soil modification on the structural behavior (fig.22?). S coefficient varies from 1 to 2 for soils from rock to soft clays or silts. For those cases in which is not possible to determine the characterization of the site, a soil Type II with S=1.2 should be assigned. With this specifications the elastic seismic response coefficient Csm has to be calculate for the Tm period of vibration of the structure that corresponds to the mth mode. Csm is defined by the Code (22.214.171.124 AASHTO LRFD) as a function of A, S and Tm. Seismic design forces for substructure and connections have to be determined dividing the elastic forces by the appropriate Response Modification Factor given for each Importance Category of bridge. To consider the variability of the directions in which the earthquake may occur, two combinations of orthogonal seismic forces have to be apply to the superstructure of the bridge with the proportion of 100% and 30% in each direction. The Code (AASHTO LRFD) defines a vertical support as a column if the ratio of the clear high to the maximum dimension of the cross section is not less than 2.5. If the ratio is less than 2.5, the requirements for piers have to be satisfied. A pier can be analysed as a pier in its strong direction and as a column in the weak one.
Figura 20 - Seismic performance zones (Table 3.10.4-1, AASHTO LRFD)
Caltrans estimates substructure's capacity through non linear "push-over" analysis.
Figura 21 - Seismic performance zones (Table 3.10.4-1, AASHTO LRFD)
Figura 22 - Bridge importane categories (AASHTO LRFD)
Figura 23 - Soil profile (AASHTO LRFD)
Figura 24 - Site coefficient (AASHTO LRFD)
4.8 Analysis Method
The objective of seismic design is to define forces which structures are subject to, calculate elastic and inelastic deformations, study the ductile behavior of the structure and verify the ability of the single elements to resist. Different methods of analysis were found in the literature review with different assumptions and for different scopes. Briefly it will be given a list of the methods covered by the codes.
ESA - Equivalent Static Analysis
EDA - Elastic Dynamic Analysis
ISA - Inelastic Static Analysis
Structural System Global Analysis
Stand-Alone "Local" Analysis
Transverse Stand-Alone Analysis
Longitudinal Stand-Alone analysis
ESA - Equivalent Static Analysis - can be used to estimate the displacement demands of those structure with uniform stiffness, responding by the predominant mode of vibration, where dynamic analysis would not give significantly different results. (Cetinkaya, Nakamura,Takahashi,2005)
EDA - Elastic Dynamic Analysis - can be used to estimate the displacement demands of those structures where ESA does not give a good response of the dynamic behavior. The effect of applying design spectral acceleration likely results in stresses exceeding the linear range. This is due to the contribution of the soil, yielding in the structural elements, expansion of the joints.
According to recent Caltrans specifications (Caltrans SDC (v.1.5)) an Ordinary Bridge can be analyzed either with Equivalent Static Method or Linear Elastic Dynamic Method for estimating the displacement demands. For establish the displacement capacity of the elements a nonlinear analysis is required to take into account the ductility of the structure.
The case study has been chosen after evaluating the trends in bridge construction in California in the last ten years. The trend shows that the majority of bridges designed in recent past are of medium span, built with the cast in place technique. A very high percentage of these are prestressed box girder built by segments with the balanced cantilever erection method. Since the interest of this study is aimed at predicting the likely behavior of the bridges that will be probably built in the next future in California, the choice was made in that direction. Precast!!!!!NEW TRENDS
The main objective of this study is to study the vulnerability of the bridge under the seismic load if the earthquake is going to occur during the construction phases. Before doing this, however, is fundamental to be sure that the bridge (case of study), after work completion and during life time under live loads, will respond satisfying all safety criteria required by the current local codes.
We are talking about small earthquakes if the performance behavior of the structure has to stay in the elastic range, because this is a principle that governs the bridge design according to the codes of practice.
5.1 Structural System
The solution adopted consists in a prestressed cast on site concrete box girder constructed with the segmental balanced cantilever method, with a mixed system of prestressing cables in post-tension.
5.2 Stages of Construction
One of the most significant aspect of the bridge under consideration, that affects the all the design phases, is the definition of the bridge behavior during construction in the sequential progression of structural configurations. Therefore, issues relating to structural analysis during construction and those due to the actions in the final phase, have been examined in depth.
The modeling has been conducted
The capacity demand of vertical supports is a complex function of a lot of variables including:
Ground motion characteristic
Required design level
Period of vibration of the structure
Elastic damping coefficient
Soil condition and foundation type
The geology of the ground and the morphology of the site play a key role in the design stage and govern the choices to be made in terms of foundations, maximum span length and construction type.
A subsurface investigation in the vicinity of piles and abutments is necessary to identify a suitable foundation type. The economic aspect is also affected because, depending on the geological situation, in case of high risk of liquefaction or slope stability the cost of foundations can vary greatly and reach very high costs in proportion to the total cost of the structure. In the case study taken into consideration, there was no possibility to determine the required type of the foundations due to the lack in knowledge of the geology of the soil.
The feasible foundation options that could be proposed are many and, depending on the particular one chosen, they could significantly change the behaviour of the structure under seismic load. It was therefore preferred to leave the type of foundations as undefined and study the behaviour of the superstructure (piers and abutments) by assigning a good degree of restraint at the base of the substructure. Basically in the analysis model the base of the substructure has been fully restrained neglecting the possibility of deformation. This decision is based on the assumption that a fully fixed restraint (as the one simulated/assigned in the analysis model) will never occur in reality, regardless the type of foundation chosen; this means that the reactions at the base obtained from the model will be higher than the ones expected in reality, guarantying a conservative approach of the study. On the other hand the scope of this study is not the full design of the bridge, but the variation of the seismic vulnerability during the construction process, hence the previous assumptions, constant during the study of all construction stages, do not affect the final results. This means that making sure that the limitations deriving from these assumptions are taken into consideration, it has been possible to interpret the results appropriately as described in the following paragraphs.
5.4 Analysis procedure
The project of the bridge should be feasible in the near future at the location indicated and therefore the completed structure has to be able to withstand to all the loads defined by the codes, including seismic loads. Therefore, the first phase of this study involved the design of the bridge sections by analyzing bending, shear and torsion in superstructure and substructure.
Usually, while conducting a push-over analysis, the structure is pushed till collapse is reached. This means that the structure would be allowed to pass the linear state and undergo to the non-linear one with the progressive formation of plastic hinges. Plastic hinges are a exemplification of cracking and initial damages in the structure. Wherever they occur, is not admissible to have cracks in the structure during construction of the bridge. For this reason the capacity of the piers to resist to seismic loads during construction has been evaluated through "linear" pushover analysis. Therefore the structure behavior has always been considered linear and when plastic hinges started occurring, which means that the structure was dissipating energy while cracking, the pushover has been stopped because the piers were considered damaged.
Since the structure was reproduced with a 3-dimensional model, two different pushover analysis were carried on: one in the longitudinal direction and one in the transverse direction. The two chosen directions correspond to the first and the second mode of vibration of the bridge. Longitudinal pushover analysis was performed applying a slowly increasing seismic load on the superstructure of the bridge in the same direction of the span, and transverse pushover analysis similarly in the perpendicular direction.
TABLE OF MODES OF VIBRATION AND PERIODS FROM SAP
6.1 Summary of pushover analysis results
6.2 Discussion of pushover results
The push-over graphs show
The effect of push-over direction
6.3 Relative vulnerability relationships
Summary and Conclusion
The discussion in this study was carried out looking at a single bridge and making some simplifications (assumptions of fixity supports, two orthogonal directions of seismic forces, no admissible damage, linear behavior) to limit the number of variables that could affect the analysis. The previous push-over results refer to different models for the different construction phases of the same bridge. It would be hazardous coming to the conclusion that these results are representative of all bridge behaviors. Surely this study can be considered a good starting point for further investigation to be carried out on bridges with different characteristics for compare and group them in classes with analogue behavior to reach a generals conclusions about seismic vulnerability during construction.