The Failure Mechanism Concept – An Innovative ULS Design Approach

Matthias SCHUELLER

Principal, P.Eng. Infinity Engineering Group North Vancouver, BC, Canada MSchueller@infinity-engineers.com

Matthias Schueller, born 1964, received a structural engineering degree from the University of Darmstadt, Germany, a Ph.D. from the University of Stuttgart, Germany and an MBA from the University of Phoenix, USA. He is the designer of innovative pedestrian, roadway, and pipeline bridges.

Summary The Failure Mechanism Concept (FMC) is an innovative plastic design approach which encourages designers to investigate probable failure mechanisms and intentionally define the weakest link along primary load paths. The FMC is very useful for Integral Bridges (structures without bearings and expansion joints), but even for conventional bridges the method offers new opportunities to design structures with lower construction and maintenance costs, improved durability, and a higher safety margin against failure. The over 1 km long Deh Cho Bridge crossing the Mackenzie River in Canada (see Figure 1) has been designed using the FMC design approach. As a result, a continuous superstructure was achieved thereby avoiding two costly expansion joints in the main span.

Keywords: conceptual bridge design; plastic design; integrity; redundancy; ductility; durability; reliability.

Fig. 1: Rendering of the Deh Cho Bridge near Fort Providence, Northwest Territories, Canada

1. Introduction Many modern bridge design standards clearly define the acceptable degree of safety (safety margin) required to avoid structural failure. Standards using the Load Factor and Resistance Design (LFRD) approach specify load and resistance factors for selected Ultimate Limit State (ULS) scenarios. Designers typically verify for relevant ULS load combinations that factored demands do not exceed the factored resistance of critical sections. An investigation of potential failure mechanisms is generally not conducted except in progressive failure or forensic investigations [1], [2].

Plastic design approaches are not new; however, existing design concepts usually consider only one material or only a few specific components of the structure [3], [4]. Conversely, the FMC investigates every single structural component along critical load paths. Therefore, a global perspective is incorporated into the design process and the interaction between main elements such as the foundations, substructure, superstructure, and pylons is considered when deriving capacities of critical sections. This holistic design approach requires significant knowledge about the structural behaviour of relevant components such as pile foundations, bearings, shock-transmission-units, and cables. As such, knowledge becomes vital when designing for the imperative goal: avoiding unpredictable structural failures.

2. Conceptual Bridge Design Conceptual bridge design is one of the most important stages in the design process. Experienced designers devote relevant time to this early stage in order to avoid time consuming and costly revisions that may be required if an immature concept advances to the final design and construction stages. Conceptual bridge design is a complex task. A sound concept should appropriately address design criteria & standards, deploy an economical fabrication & construction method, make efficient use of material & labour, create a reliable & durable structure, allow for inspection & maintenance, and find general acceptance from a technical, economical, and aesthetical point of view.

Successful bridge design concepts primarily focus on an advantageous structural system and a fast paced economical erection method. An excellent example is the widely accepted cable-stayed bridge concept with one main span and two relative short back spans [5], [6].

Close attention must be paid to the overall structural system and structural detailing. The bridge’s long-term performance (serviceability, durability, reliability, maintenance requirements etc) depends directly on the structure’s resilience to resist wear & tear, pollution, and detrimental effects caused by the environment. Structural systems are typically defined in the conceptual bridge design phase; however, structural detailing is not necessarily a part of this early design phase. Nevertheless, designers must ensure that constructible and reliable solutions for any kind of anticipated structural details are achievable. Expensive or excessive design, fabrication, and construction issues should be avoided by any means.

Stability is often a major concern; this is particularly true if during construction the structural system is changed several times before the final configuration is achieved. Specialized erection engineers typically investigate critical construction stages in great detail and specify additional temporary equipment required to ensure safe construction procedures and stages. However, even in the early conceptual design phase a profound understanding of reasonable and reliable construction methods is crucial for a cost-effective design approach. This is particularly true if a novel bridge concept is being developed.

The FMC has a notable influence on the efficiency of structural systems during service and construction. It is an excellent tool to verify structural resistance during the conceptual bridge design phase as it considers the entire structural system and requires the designer to visualize major load paths and adjust for optimum Structural Performance. The key word is Structural Performance. The FMC approach is more than a simple stress check or verification that factored demands are not exceeding factored capacities; the FMC is a design tool. Using accepted plastic design principles the method animates the designer’s structural perception and allows intelligent structures that are able to develop a predictable and controlled failure mechanism if overloaded.

3. Plastic Design Principles

3.1 Idea and Challenges

The general idea is twofold: Plastic design principles can be used in order to (1) determine the Ultimate Sectional Capacity of a member and (2) activate the Structure’s Ultimate Capacity.

3.1.1 Ultimate Sectional Capacity

The Ultimate Sectional Capacity is exhausted if any additional load would trigger a failure of the critical section. Plastic design principles are commonly used for the design of structural concrete, structural steel, or composite members to determine the Ultimate Sectional Capacity if local sectional buckling can be excluded. Modern design standards do not precisely predict the Ultimate Sectional Capacity; instead, material resistance factors are specified in order to establish a generic safety margin against failure.

3.1.2 Structure’s Ultimate Capacity

The Structure’s Ultimate Capacity is exhausted if any additional load triggers a collapse of the structure. It should be noted that a collapse does not necessarily occur immediately if the Ultimate Sectional Capacity at one or more locations is exhausted. For instance, a multi-span continuous

beam may have the ability to resist additional loads even if the Ultimate Sectional Capacity at a certain location for a given load configuration is already exhausted. If this is the case then the structure may have reserves and designing for higher loads could be justified despite the fact that one or more sections are overloaded. However, the elastic distribution of forces (predominantly moment and shear) is no longer valid and some design standards apply restrictions. Generally the plastic activation of a Structure’s Ultimate Capacity relies on three factors: Integrity, Redundancy, and Ductility.

3.2 Integrity

Achieving integrity through proper detailing, as demonstrated for concrete box girders in [7], is of fundamental importance for any bridge structure. Integrity ensures that a structure does not experience an unforeseen local failure which may trigger a global collapse before the anticipated ultimate capacity is exhausted. Even the most sophisticated design approach is ineffective if the structure suffers an impetuous collapse due to a lack of integrity. For instance, several columns of the Hanshin expressway in Kobe collapsed during the 1995 earthquake due to premature termination of the longitudinal reinforcement and inadequate concrete confinement [8]. This incident demonstrates why the absence of structural integrity along a primary load path may have fatal consequences. For the design of structural concrete, Strut-and-Tie Models [9] and the Modified-Compression-Field Theory [10] have been proven to be excellent design tools. Skilled designers use them to visualize the flow of forces, verify zones of stress concentrations, and design reinforcement. It is noteworthy that many modern design standards have recognized the fact that a primary load path (load chain) is only as strong as the weakest link and included important information on proper detailing and methods which emphasize structural integrity.

3.3 Redundancy

Without redundancy a Structure’s Ultimate Capacity is governed by the Ultimate Sectional Capacity of the critical section. For example, a statically determinate system lacks redundancy and will collapse if demands exceed the structural capacity at one critical location. Conversely, redundant structural systems, or in other words statically indeterminate systems, have load reserves so long as the elastic distribution of forces do not trigger an unlikely failure mechanism which activates several plastic hinges at the same time. However, in order for structures to take advantage of the redundancy principle, overloaded sections require ductility so that the structure’s reserved strength can be activated through the redistribution of internal forces.

3.4 Ductility

Ductility is defined as the ability of a section to endure significant deformations (predominantly rotations and elongations) without forfeiting its structural capacity in terms of moment, shear, and axial force resistance. A ductile sectional response is essential for avoiding sudden brittle failure modes and allowing the activation of secondary redundant load paths.

4. Failure Mechanism Concept

4.1 Motivation

The I-35 Mississippi River Bridge in Minneapolis, Minnesota, USA [11] and the Boulevard De La Concorde Overpass in Laval, Quebec, Canada [12] are examples of unpredicted sudden bridge collapses causing the loss of human lives. Typical engineers learn from these regrettable incidents more than from thousand examples of well functioning structures. However, the question remains: Are unpredictable collapses avoidable?

No structure is or will be “absolute safe”. The level of safety (margin against failure) is typically defined by widely accepted safety concepts prescribed by design standards or other design criteria. The commonly used ULS design approach is assuming fictitious load scenarios serving the sole purpose of verifying that the required level of safety is achieved or exceeded. However, engineers should be encouraged to develop new methods to decrease the probability of an unforeseen collapse without exceeding financial budgets and timelines.

4.2 Design Philosophy

The FMC goes beyond the ULS design philosophy adopted by modern codes. The FMC investigates failure mechanisms along primary load paths. A primary load path is defined as a structure’s preferred way of resisting loads (natural load path). Objective is the development of a structure which announces a serious problem before a collapse is possible.

Structural integrity and redundancy are the foundation of the FMC. Considering the structure as a whole and investigating possible failure mechanisms are paramount. This Big Picture design approach will provide designers with valuable information about the structure’s behaviour when reaching its structural capacity. Sudden failures along primary load paths should be avoided by deliberately defining weak sections with ductile failure mechanisms. The so defined weak sections shall act as fuses safeguarding the structure by activating additional redundant load paths. This Fuse Design Approach shall trigger noticeable deformations so that the structure’s critical condition is clearly identifiable before lives are endangered.

4.3 Design Criteria

Like any other design method the Fuse Design Approach is based on assumptions. Since the FMC is investigating the structural behaviour of the entire structure conservative design assumptions at a certain design section may lead to an overall unconservative design approach. For example, if the resistance of a section designated as fuse is calculated using factored resistances (ULS design approach) the fuse may be behave stronger than anticipated and its function as fuse is questionable.

Therefore, the design criteria shall reflect lower-bound (under-strength) and upper-bound (over-strength) considerations when verifying the structural capacity of fuse sections. It is recommended to design the fuse in accordance with ULS design criteria (under-strength) for primary load path demands and to use over-strength design values when specifying the Fuse Limit State (FLS) for the activation of secondary load paths. Structural tuning may be required to achieve an overall well balanced structural system responding appropriately to the different design scenarios (ULS and FLS).

4.4 Limitations

The FMC design approach mandatorily requires statically indeterminate structural systems (such as integral bridges [13] or moment frames) allowing the activation of redundant secondary load paths. The method is relevant for the design of primary (natural) load paths in order to avoid sudden local failures triggering a chain reaction and resulting in a fatal collapse. It is not recommended for members irrelevant for overall structural integrity.

5. Deh Cho Bridge

5.1 Description

The Deh Cho Bridge is a 1045 m long structure crossing the Mackenzie River near Fort Providence in the Northwest Territories, Canada [14], [15]. The symmetrical span arrangement is 90 m – 3 x 112.5 m – 190 m (navigation channel) – 3 x 112.5 m – 90 m (see Figure 2). The 190 m long main span is cable assisted allowing a constant superstructure depth of only 4.5 m over the entire length of the bridge. The superstructure (with expansion joints only at the abutments) has a maximum slope of 3.5% and consists of two vertical Warren trusses and Chevron bracings (for cross frames and two lateral bracings at top and bottom chord level). This adaptation of an “open” steel box girder is designed to carry two lanes of traffic while acting compositely with an 11.3 m wide by 235 mm thick precast concrete deck.

Two steel A-pylons located at the tallest piers are flanking the main span. Each A-pylon is supported by spherical bearings allowing a pendulum movement of the pylon in the longitudinal bridge direction (see Figure 3). Four groups of three stays each, arranged in two cable planes, are anchored at each pylon head using sockets with pin connections. The stays (locked coil cables with 100 mm diameter) are anchored at the third points of the main span and at the centres of the back spans using a truss outrigger system.

Fig. 2: New Articulation Scheme for the Deh Cho Bridge

The Deh Cho Bridge can be classified as an “Extradosed Bridge System” [16] since the superstructure has a significant bending stiffness and is locally reinforced with stays and king posts. As such, the Deh Cho Bridge has a very different structural behaviour compared to a similar looking traditional cable-stayed bridge system which does not require a stiffening girder because its outer backstays are anchored at a pier location [17].

The eight piers of the Deh Cho Bridge are founded on spread footings which overlay the river bed. The piers consist of a lower solid concrete cone (reinforced with an outer steel shell protecting the concrete against ice forces) and an upper steel head. Each steel head has a base, two inclined legs, and a tie-beam connecting the legs at the top thus forming an inverted open triangle in the transverse bridge direction. All of the steel head components (base, legs, and tie-beam) are custom made hollow boxes using 40 mm thick steel plates. The lower concrete cone and the steel head are connected at the pier’s “bottle neck” (called the Pier Connection Detail, see Figure 3) with post-tensioned bars which ensure that the connection stays tight and sealed under service conditions.

Fig. 3: Pier 4 South of the Deh Cho Bridge (Pier 4 North similar)

Fig. 4: Cross Section at the Pier Connection Detail

5.2 Problem

The original concept had numerous design issues, and therefore Infinity Engineering Group (IEG) was retained by the Deh Cho Bridge Corporation (DCBC) to redesign the superstructure, pylons and stays. The original superstructure design had been conceived with two complex expansion joints in the main span. For cost, durability, and comfort reasons, IEG preferred a continuous superstructure from abutment to abutment. This concept required a new articulation scheme compatible with the original substructure. It was found that the piers were very stiff and “over-reinforced” (concrete compression zone crushes before steel in the tension zone starts yielding) at the Pier Connection Detail thus giving rise to a brittle failure mode if overloaded due to bending in the longitudinal bridge direction.

5.3 Solution

5.3.1 New Articulation Scheme

The new articulation scheme (see Figure 2) utilizes conventional disk bearings at the piers and abutments. The bearings guide the superstructure in the transverse direction but allow longitudinal movements due to temperature changes. Pier 4 North (one of the main span piers) is the only location where the superstructure is longitudinally restrained. At the remaining piers, except the piers nearest to each abutment, so called Lock-Up Devices (LUDs) are employed. The LUDs ensure that temperature displacements are allowed without generating noteworthy restraining demands, but for longitudinal impact forces due to gusty winds or braking loads, the devices rigidly connect the superstructure to the piers.

5.3.2 Pier Retrofit

As a consequence of the new articulation scheme, Pier 4 North had to be checked in order to verify that it was capable of resisting all longitudinal load effects arising from steady forces. The Canadian Highway Bridge Design Code [18] does not explicitly define steady transitory loads in the horizontal direction; therefore, it was decided to use the 100-year return wind (with a gust factor of 1.0) as the governing ULS design load for a steady longitudinal force effect. It was found that the Pier Connection Detail of Pier 4 North was not capable of resisting the new design force and that a pier retrofit design was required. The retrofit design focused on the following structural aspects: (1) a favourable local and global failure mechanism, (2) resistance and ductility of the Pier Connection Detail, and (3) splices between steel head components (base, legs, and tie beam).

A favourable local and global failure mechanism was created by providing sufficient rotational capacity for Pier 4 North and the adjacent piers equipped with LUDs. In the event of an overload the LUDs would be activated on account of large superstructure displacements, and load sharing could be achieved through the capability of the piers to endure plastic deformations. The design limit for the longitudinal displacement was set to 225 mm which corresponds to the maximum play in the LUDs at Pier 2 South. This ensures that even Pier 2 South can be engaged before any of the previously engaged piers start to give up a portion of their resistance.

In order to meet the rotational demands, the resistance and ductility of the Pier Connection Detail due to bending and axial force was improved by: (a) applying high strength grout in the compression zone, (b) activating some of the high strength bars in the joint as compression reinforcement, (c) utilizing the outer steel shell as external compression reinforcement by ensuring that buckling does not occur and (d) limiting the number of high strength bars activated in the tension zone.

During the retrofit design, it was found that the pier splices between steel head components had been originally designed with a resistance below 75% of the member’s capacity and were therefore deemed to be in noncompliance with the design code. The Fuse Design Approach was applied to overcome this conflict. Sealing welds were added to each splice; however, the welds were designed to resist only the forces up to those triggering plastic deformation in the Pier Connection Detail. The integrity of the system was ensured by applying under-strength values for the welds in the splices and over-strength values for components in the Pier Connection Detail.

5.3.2 Improvements

This unique structural system spawned by the FMC allows the structure to mobilize several redundant load paths for longitudinal force effects and provides valuable information to engineers long before a critical condition is reached.

The pier retrofit design using the FMC significantly improved the structure’s behaviour during ULS: The retrofitted piers undergo a ductile local failure mechanism if overloaded. Load sharing (achieved through the capability to endue plastic deformations) is possible without reducing structural resistance locally or globally. Plastic pier deformations and significant superstructure displacements provide engineers with important information so countermeasures can be taken. The Fuse Design Approach justified an economical solution for the retrofit of pier splices without compromising reliability, durability, and aesthetic quality of the piers. Most importantly the FMC did not change the bridge’s general appearance or caused extra cost. On the contrary, it provided the foundation for a very cost effective new structural system with a continuous superstructure over the entire bridge length.

6. Conclusions The FMC is a design tool using Plastic Design Principles in order to achieve innovative and cost efficient structures with predicable and ductile failure mechanisms. The FMC is not restricted to any specific material or structure. It is a new interpretation of existing safety concepts without compromising accepted safety margins. The technique is useful for designing new structures, rehabilitation and seismic retrofit of existing structures or forensic investigations. Design goal is the creation of an intelligent structure being capable of enduring local failures, showing early evidence of structural deficiencies, and thus saving lives and increasing return on investment.

Fig. 5: Deh Cho Bridge Superstructure under Construction, Picture taken by Michael Owen

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Structural Engineering International, Issue 2, 2006, pp. 113-117.

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[11] National Transportation Safety Board, Collapse of I-35W Highway Bridge, Minneapolis, Minnesota, August 1, 2007, Highway Accident Report NTSB/HAR-08/03, Washington DC, 2008, p. xiii.

[12] Commission d’Enquête sur le Viaduc de la Concorde, Commission of Inquiry into the Collapse of a Portion of the de la Concorde Overpass, Government of Quebec, 2007, pp. 5-7.

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[14] SCHÜLLER M., “Ganzheitliches Entwerfen im Brückenbau – Deh Cho Bridge im Norden Kanadas” Brückenbau – Construction & Engineering, Vol. 4/2009 and 1/2010, Verlagsgruppe Wiederspahn, Wiesbaden 2010, pp. 77-80.

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[16] MEISS K.U., Anwendung von Strukturoptimierungsmethoden auf den Entwurf mehrfeldriger Schrägseilbrücken und Extradosed Bridges, Verlag Grauer, Beuren und Stuttgart, 2007, pp. 2-3 and pp. 5-26.

[17] SINGH P., SCHUELLER M., and OPPEL S., “Deh Cho Bridge – The Northern Link”, Larsa’s 4D Journal, October, 2009, p. 1 and pp. 4-6.

[18] CAN/CSA-S6-06, Canadian Highway Bridge Design Code, Canadian Standards Association, Ontario, 2006, pp. 39-113.