Engineering analysis and design software
Bridge design and engineering

Case Study 

Seismic analysis of viaduct substructures for the Dubai Metro light rail project

  • 2D and 3D modelling of concrete viaduct structures

  • Seismic analysis to AASHTO LRFD

  • Pile and pier design moments obtained from seismic and modified BS 5400 load combinations

The Red and Green Lines of the Dubai Metro light rail scheme are being constructed as a Design-Build contract by a consortium of international contractors. Atkins, one of the world’s leading engineering and design consultancies, is the lead designer to the major civil contractor of the Dubai Rapid Link (DURL) Consortium and is carrying out the full multi-disciplinary design and project management of the civil works for the project. Atkins used LUSAS Bridge analysis software to assist with its analysis and design of various structures on the project including seismic analysis of the viaduct substructures, where maximum bending moments were derived for use in designing and reinforcing the pier and pile sections.

The Red Line runs from Jebel Ali Port, through the city centre, to Al Rashidiya - a distance of 52km in total. Of this length, some 42km is of elevated viaduct construction. The Green Line runs from Al Qusais, through the city centre, to Al Jaddaf - a distance of 24km. Of this length some 16km is of elevated viaduct construction. 

Overview

Viaducts on the Red and Green Lines comprise a combination of simply supported single-span post-tensioned precast decks of U-shaped cross-section supported on elastomeric bearings, and two and three-span continuous decks on fixed and free guided sliding pot bearings. Most viaduct spans are of a standard 28m, 32m or 36m length and are typically supported on single, circular, reinforced concrete columns of 1.75m or 2m diameter. Flared pierheads support the deck. For speed of construction most single piers are supported on 2.2m and 2.4m diameter bored monopiles. Pierheads for the single spans, twin spans and stations spans are of precast construction (requiring in-situ concrete fill and prestressing). Pierheads for single track and three-span continuous viaduct structures are constructed solely in-situ and for these structures large diameter bored piles were used. The majority of deck sections are assembled by overhead gantries but, for the pier and pile design, the temporary construction loading from the gantries was generally found to be less onerous than that caused by any potential seismic loading.

Design basis

The construction programme called for the initial design of over 1200 unique foundations in the first nine months of design to take the viaduct construction off the critical path. Initially, to keep ahead of construction, this was done using automation and conservative design methods but as time permitted more refined calculations were introduced to optimise the design of foundations yet to be constructed. Design of the viaducts was based on BS 5400 and associated standards with the AASHTO LRFD Bridge Design Specification being used for the seismic design. Using LUSAS Bridge, both 2D and 3D modelling of sections of viaduct was carried out according to span type.

Single-span modelling

Initially, 2D transverse and longitudinal models were created in LUSAS to model the simply-supported single-span structures. From these, natural frequencies were obtained for the first 3 mode shapes for use with the AASHTO LRFD design response spectrum in order to generate acceleration values for the design of pile and pier sections. For the transverse model, beam elements represented the piles, piers, and crossbeams. Pile modelling was done using the equivalent cantilever method (as opposed to modelling the soil/structure interaction as a beam with elastic springs) with appropriate static and dynamic values provided by Atkins geotechnical team. Elastomeric bearings were modelled with joint elements of appropriate stiffness. In accordance with the Design Basis Report the weight of a train acting on one track only was represented by a joint element having a mass and vertical eccentricity appropriate to the centroid of the train. Different pier heights ranging from 2m to 20m and pier diameters of 1.75m and 2m were investigated. Longitudinal models, built using similar modelling techniques to the transverse model, evaluated a series of 36m long viaduct spans. On these, beam elements also represented the deck members and used an equivalent mass density to represent the actual mass of the span as well as the additional mass of the superimposed dead load.

Typical 2D longitudinal simply-supported viaduct model

Continuous span modelling

To analyse the dynamic behaviour of numerous two and three-span continuous viaduct structures 3D models were developed from the initial 2D transverse model and used a very similar modelling methodology (see the image right). 

To allow for torsional effects the deck was modelled using thick shell elements. Whilst the deck profile varies in thickness along its length, for modelling purposes an average thickness was calculated for each part of the deck and mass density variations along the span were used to ensure that the mass of the deck was correctly distributed for the seismic assessment. 

Three simply-supported structures each side of the two or three-span continuous structure were also included in each model to reduce boundary effects, something additionally verified to be conservative.

3D modelling concept (2D modelling similar)

 

3D modelling of a multi-span continuous section of viaduct in LUSAS

3D modelling of a multi-span continuous section of viaduct in LUSAS
(with three additional simply supported spans included each side of the continuous structures)

Seismic analysis

For each 3D model an eigenvalue analysis produced the first 30 mode shapes. These were then checked to ensure the percentage of mass excited in each direction was not less than the 95% required by the AASHTO LRFD code. By using the LUSAS Interactive Modal Dynamics (IMD) facility, and specifying a CQC combination using the AASHTO response spectra and relevant damping values, the maximum bending moments at the base of all piers for the response spectra were obtained. Results from the IMD analysis were ultimately combined with modified BS5400 load combinations to give final design values. From these, pile and pier reinforcement was designed and curtailed to suit specific force moment envelopes generated for each support.

Typical deformed viaduct plot from a LUSAS Interactive Modal Dynamics analysis.

Typical deformed viaduct plot from a LUSAS Interactive Modal Dynamics analysis.

Validation of results

LUSAS output was validated using spreadsheet calculation via the SRSS method and also by an additional equivalent static analysis. Manuela Chiarello, an engineer on the project, explains: "For each model we saw how much each mode was participating to the total response of the structure and ran an SRSS analysis using a spreadsheet for just the dominant modes." She continues: "After that we used the frequency of the dominant mode and ran an equivalent static analysis using the corresponding acceleration from the AASHTO response spectrum". Whilst these methods should give close and conservative results respectively in relation to the IMD results they served to help confirm results and highlight any modelling anomalies.

David A Smith, Regional Head of Bridge Engineering at Atkins said: "We had to solve several design and programme challenges on this project to enable the viaduct substructure and decks to be erected to an agreed construction schedule." He continued: "Ultimately the use of precast concrete elements for the deck and for key substructure components, and the use of LUSAS software to assist with our design process, all helped to ensure that the viaduct construction progressed as planned.

Official opening

The Red Line was officially opened on 9 September 2009 by His Highness Shaikh Mohammad Bin Rashid Al Maktoum, Vice-President and Prime Minister of the UAE and Ruler of Dubai. Ten key stations out of a total of 29 were opened to passengers initially, with the remaining stations being opened in batches over the following few months. All Red Line stations are set to be operational by February 2010. The Green Line is scheduled to be opened in June 2010.

Other analyses undertaken by Atkins on the Dubai Metro light rail project using LUSAS include:

Aerial view of Dubai Metro Financial Centre station and footbridge

"The use of precast concrete elements for the deck and for key substructure components, and the use of LUSAS software to assist with our design process, all helped to ensure that the viaduct construction progressed as planned."

David A Smith, Regional Head of Bridge Engineering, Atkins


 

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