Algorithm-aided design of bridge abutment

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Bachelor’s thesis

Degree Programme in Construction Engineering Autumn 2021

Nikita Smirnov

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Degree Programme in Construction Engineering Abstract

Author Nikita Smirnov Year 2021

Subject Algorithm-aided design of concrete bridge abutment Supervisors Eetu Partala, Ahmad Shagerdi

A bridge abutment is a bridge substructure that retains the embankment and carries the vertical and lateral loads from the superstructure to the foundation. The modeling process of a bridge abutment using traditional design methods is time-consuming and vulnerable to project updates that may lead to full remodeling. Using the design process of anabutment for a concrete girder bridge as an example, the thesis presents the innovative way of modelling that solves these problems.

This Bachelor’s thesis aimed to develop a parametric design tool for creating a 3D geometry of a concrete seat-type bridge abutment using an algorithm-aided design approach. The thesis consists of a preliminary study of algorithm-aided design, bridge design considerations and features of the bridge abutment which are later embodied in a design tool.

As a result, a fully functional design tool was developed using a visual programming tool called Grasshopper. The tool is developed to be used at an early stage of the project when the future shape of the abutment is being designed. The tool includes the built-in manual which allows bridge designers to use it even without knowledge of parametric design software. With this tool, bridge designers can easily create and modify the 3D geometry of the concrete bridge abutment by changing input parameters. The functionality of the tool was proved by creating two different geometry configurations of the concrete bridge abutment, which showed the speed and accuracy of modeling of the desired geometry.

Keywords Bridge abutment, parametric design, Grasshopper Pages 38 pages

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1 INTRODUCTION

Today design approaches that are applied in the construction industry are far more advanced than a pair of decades ago. BIM (Building Information Modeling) technology, which seemed then a revolutionary, has already become a common method for controlling building design processes. However, modeling is still a relatively new invention compared to structural design.

Despite constant development, some aspects of modeling are still lacking flexibility and effectiveness.

Talking about bridge design, it refers to the preliminary design phase which has always been an utterly time-consuming part in civil engineering projects. During this phase bridge designers are developing the optimal design solution to the bridge which is a quite time- consuming procedure. Considering how complex the geometry of bridges can be, even a single change may lead to remodeling everything from scratch. As a rule, remodeling affects the whole design process and may result in cost overruns and delays. The solution to this problem is the use of an alternative design approach where a quick adaptation to changes is key.

And such a solution is Algorithm-Aided Design (AAD) or parametric design. It is a relatively new design approach slowly being introduced into the construction industry. Parametric design has proven itself particularly well in bridge design where the use of this approach implies the creation of a parametric model of the bridge that can easily adapt to changes in geometry. Moreover, the use of parametric design allows easy exploration of many design alternatives. This brings tremendous flexibility for the bridge designers allowing them to develop more optimal and cost-effective solutions in the preliminary design phase.

1.1 Thesis objective

In this study, algorithm-aided design is applied to the concrete bridge abutment design. The work focuses on how standard design processes can be simplified with the use of algorithms, a set of mathematical rules and instructions that help to perform certain tasks. The main goal of the thesis is to create a strong and efficient modelling tool for a concrete bridge abutment with a detailed step-by-step guide for the modelling workflow.

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1.2 Work limits

The modelling tool is developed in the program for parametric design and used to create a geometrical 3D model of the concrete bridge abutment. By changing input parameters, the bridge designer is able to create and modify a geometric model having the full control over every dimension of the geometry. The modelling tool is used in the early design stage therefore it is limited only to creating the geometry model. The created geometry will be transferred to Tekla Structures for design stages such as the design of reinforcement and structural analysis. The creation of bridge abutment accessories and devices such as bearings, expansion joints, drainage and cable pipes are not in the scope of the tool. The creation of the tool is based on design regulations and building standards developed by the Finnish Transport Infrastructure Agency, several finished projects and knowledge of the experienced bridge designers.

2 BIM DESIGN

Nowadays, BIM is used by a great number of architects, engineers, and contractors. Global construction trends are increasing the complexity of AEC (Architecture, Engineering and Construction) projects, while advances in technology are allowing industry professionals to work more efficiently. BIM is an intelligent model-based process that connects architects, engineers, and contractors and therefore they can more efficiently design, build, and operate infrastructure and buildings. Designers use BIM to create digital 3D models (Figure 1) that contain information about the physical and functional properties of the model components.

The information in a model defines the design elements and establishes the behaviour and relationships between model components. The models support building and construction design during all stages and enable better management and analytics than traditional manual processes. (Autodesk Building Solutions, 2021)

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Figure 1. BIM model of Isoisänsilta (The Construction Index, 2019)

2.1 BIM in Bridge Design

For the past decades, BIM has increased the quality and completion time by avoiding inefficient workflow. As a result, various engineering projects have benefitted from using the features provided by BIM; however, its use in bridge construction has been limited for some time. According to (Chen et al., n.d.), the reasons for this were mainly the following. First, unlike building structures, BIM standards for infrastructure projects were lacking. Second, most of the common BIM modeling software had a lack of flexibility for adapting future model changes. In contrast to vertical structures, bridges are horizontal structures that have a complex geometry and irregular shapes. In case when design requirements need to be changed, usually the model must be rebuilt instead of just being modified.

In recent years, the situation in terms of BIM in bridge design has changed. The design of bridges is gradually moving to model-based design. This means that instead of working on several different models concurrently only one central model is used.

A good example is a Motorway 4 Kirri-Tikkakoski project (Figure 2) that is currently being in the process of construction and will be completed by 2023. This project includes the design of 29 bridges of different types using a BIM-based design approach. As a result, the use of model-

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based design had a very positive effect on all parties involved in the project. Thanks to the use of such approach, it was possible to avoid the creation of a great number of detailed drawings and sending them for inspection and approval. In total, this means saving from 20 to 25 weeks off the construction schedule. (Tekla Structures, 2021)

Figure 2. BIM models of Kirri-Tikkakoski project bridges. (Tekla Structures, 2021)

2.2 Algorithm-aided design

Algorithm-aided design (AAD) or parametric design is a computer-aided design approach in which some aspects of the design are solved as a result of an algorithmic process. In modeling or solving difficult functionality problems, the design process can be simplified using algorithm-assisted method. The greatest benefit of using this method is achieved in creating complex geometry or performing time-consuming repetitive tasks. (Tanska & Österlund, 2014)

In modeling where algorithmic processes are used, geometry generation is controlled by user- defined scripts and graphs that are composed in either textual or graphical syntax. (Humppi &

Österlund, n.d., p. 602) The process of creating scripts in parametric modeling software is called visual scripting. The visual scripting reminds coding, but instead of textual commands graphical components are used.

One of the biggest benefits of using visual scripting is its ease of use. It is not important to know how the components work, but it is only needed to know the input and output of the components. In the picture below, a point (input) is needed to get an output (cylinder) (Figure 3).

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Figure 3. Geometry of cylinder made by using visual scripting.

The use of AAD allows easy exploration of many design alternatives particularly in the early phase of design. In this study, the main focus in AAD is the use of algorithms to generate the geometry that would be too complex to handle by manual modeling. However, for the further design stages the parametric data and the geometry still need to be exported and exchanged separately to other design tools.

2.3 Rhinoceros and Grasshopper

McNeel Rhinoceros, colloquially Rhino, is the three-dimensional modelling program for NURBS (Non-uniform Rational B-spline) surfaces and lines. NURBS are mathematical representations of 3D geometry that can precisely describe any shape, ranging from a basic 2D line, circle, arc, or curve to the most complicated 3D organic free-form surface or solid.

(McNeel R. & Associates, 2021)

Grasshopper is a visual scripting tool integrated into Rhino. Using Grasshopper, the algorithm is created visually by linking ready-made program components to each other. Each component has a specific function such as creating a line out of two points or dividing a curve into equal segments. There are hundreds of different components and by combining them, a large variety of diverse geometry can be created. It is possible to createone’s own component inside the Grasshopper’s environment, however, it requires the more advanced study of programming languages.

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Figure 4. The interface of Rhino and Grasshopper.

2.4 Tekla Structures and Tekla live-link

Tekla structures is a structural BIM software offered by Tekla Corp.; a Finnish company founded in 1966. The initial name of this construction product was Xsteel, which was introduced in the mid-1990s. Since then, there have been many changes. In the early 2000s, Tekla added precast concrete design and detailing features. Later, in 2004 it was renamed Tekla Structures to reflect the expanded support for timber, steel, reinforced concrete and structural engineering. (Eastman, 2011, p. 88)

Nowadays, it is not only software that allow to design structures, but it is also a tool that helps to manage construction processes. Tekla Structures is used throughout projects, from buildings and infrastructure conceptual planning to fabrication of structural elements. It is used for design, detailing, drawing creation, maintenance, information management etc. Also, Tekla supports a very broad range of exchange formats that allows to work together with other applications.

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While being a powerful tool, its full functionality is still difficult to learn. Moreover, it is not able to edit complex multicurve surfaces that frequently appear in bridge design. For now, it is only possible to import and use them as a reference. This problem can be solved with Tekla live-link.

As it is already known, Rhino is able to work with complex geometry while Tekla is not. Tekla live-link is a connecting link between Tekla Structures and Rhino. This Grasshopper plugin adds Tekla components to the Grasshopper environment which enables algorithmic modeling for Tekla Structures. Practically this means that complex geometry is being designed in Rhino using Grasshopper, but further design stages are being done in Tekla Structures. Figure 5 shows a linked workflow between these tools.

Figure 5. Workflow between Rhino, Grasshopper and Tekla Structures.

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3 BRIDGE DESIGN

Since ancient times, on the way of urban planning and development of civilization, the humanity has encountered all sorts of obstacles, be it rivers, rocks, ravines or gorges. To overcome these obstacles, people came up with one of the greatest structures – a bridge.

A bridge is an artificial structure that connects two points. This implies that connecting two banks, a permanent route of communications is formed, which gives impetus to progress in the development of states, their interaction with each other, the establishment of trade relations, the simplification of the movement of transport, the development of industry, agriculture and their provision. (Magomedova, 2017, p. 84-86)

Bridge design has evolved through the adoption of well-established practices, codes and building methods. Today, bridge design has undergone significant advances in engineering and technology, however, design principles remain unchanged. Bridges are still being designed considering three main factors: cost-efficiency, safety and aesthetics.

3.1 Bridges in Finland

According to Finnish Transport Infrastructure Agency, a bridge is a speciality structure that leads a vehicle, train, pedestrians, or other traffic over an obstacle and has a span of at least 2 meters. Speciality structures are all structures that require plans based on strength calculations and whose structural damage due to design or construction error may pose a danger to people or the transport system. In addition to bridges, typical speciality structures are railway junctions, quays, tunnels and retaining walls. (RIL 179-2018, 2018, p. 39)

In Finland most of the road, railway and pedestrian bridges are owned by Finnish Transport Agency and municipalities. The rest of the bridges are owned by private road administrations and Metsähallitus. The Finnish Transport Agency was in charge of 15 079 road bridges and 2 495 railway bridges at the start of 2019. (Väylävirasto, 2020)

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3.2 Bridge main dimensions

The main dimensions of a bridge refer to standardized dimensional concepts that deal with, among other things, the overall dimensions of the bridge, traffic engineering dimensions, heights, and angles and distances. (RIL 179-2018, 2018, p. 40)

• Bridge span (Jännemitta) – distance between two consecutive support lines measured along the centerline of the bridge

• Clear span (Vapaa-aukko) - the smallest horizontal distance between two consecutive supports parallel to the center line of the bridge

• Effective width (Hyödyllinen leveys) – the smallest distance between the railings of the bridge

• Free vertical height – the smallest height difference between the lower surface of the superstructure and the design level of road surface

• Permissible vertical height – the maximum permissible height of a vehicle passing under the bridge

• Overall width (B) – distance between outer edges of the load-bearing structure of the bridge superstructure

• Overall length (L) – the maximum distance between the ends of the wing walls or similar structures, measured along the edge lines of the bridge

• Skew – the angle between the superstructure support line and a line perpendicular to the bridge centreline

• Intersection angle – the angle between the centreline of the bridge and support line

3.3 Bridge types

The choice of the bridge type is mainly based on site characteristics, price, and owner preferences. The appearance, safety, and maintenance costs are also considered. Bridge types can be classified according to various criteria such as the purpose of use, building material, service life, length, and the static functionality of the structure. In Finland, bridges are usually classified according to their static functionality of the structure. There are five categories of bridge types that are being designed and built in Finland. (RIL 179-2018, 2018, p. 45-46)

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• Tubular and portal frame bridges

• Bending bridges

• Compression bridges

• Suspension bridges

• Special bridges

Figure 6. Distribution of bridges by their type (Väylävirasto, 2020)

In Finland concrete is a predominant building material. Over 60% of the Finnish bridges are made of concrete. (RIL 179-2018, 2018, p. 46) Bridges that are built using other building materials also have at least concrete foundations. The high compressive strength of concrete makes it a suitable material, especially for compression bridges. Also, the use of concrete allows designers to achieve a variety of structural forms, enabling the creation of aesthetically pleasing bridge structures.

Tubular and portal frame bridges are the most common bridge types. The use of tubular bridges varies from the creation of small unobstructed water flows to large railway

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underpasses. Portal frame bridges are used to create an underpass for light traffic. Both bridge types are cost-effective and fast to build. Simple structure eliminates the need for frequent maintenance. (RIL 179-2018, 2018, p. 47)

Figure 7. Pipe bridge (1), portal frame bridge (2). (RIL, 2018)

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Bending bridges carry traffic load by the bending capacity of the superstructure. The typical building material used in the construction of bending bridges is reinforced concrete and prestressed concrete. The most common bending bridges in Finland are concrete slab and girder bridges. More than a third of road bridges in Finland is the concrete slab bridges that are typically used as an underpass and junction bridge. The optimal length of a slab bridge is 8-20 meters, whereas the optimal length of a girder bridge starts from 15 meters and may reach 100 meters due to prestressed steel cables laid inside the concrete. Besides slab and girder bridges, bending bridges include box girder and truss girder bridges. (RIL 179-2018, 2018, p. 49)

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Figure 8. Slab bridge (1), (Väylavirasto, 2020). Girder bridge (2), (Author).

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Compression bridges include arch and tied-arch bridges. These bridges are always under compressive stresses. The roadbed of this bridge type might be located below, in the middle, or above the arch. In Finland, arch bridges are mainly used to overcome water obstacles. The optimal span length of arch bridges is usually 60 – 70 meters. Concrete is the most common building material for the arch bridge in Finland, however, steel and wood are still competitive alternatives. (RIL 179-2018, 2018, p. 55)

Figure 9. Arch bridge (1), tied-arch bridge (2). (RIL, 2018)

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Suspension and cable-stayed bridges are also used to overcome water obstacles; however, their span length is significantly bigger. The cost-effective span length of a cable-stayed bridge starts from 200 meters. Due to its high construction costs and deflection properties cable- stayed bridge is not designed as a railway bridge. Suspension bridges have the longest span lengths among all bridge types. In Finland, most of the suspension bridges were built in the

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1960s. The longest span length among all bridges built in Finland can be found in Kirjalansalmi – 220 meters. (RIL 179-2018, 2018, p. 56) The difference between a suspension and cable- stayed bridges lies in how the cables are connected to the supporting towers. In cable-stayed bridges, the cables are attached to the tower, which alone bears the load. In suspension bridges, cables are hung between the towers and anchored at each end of the bridge to the ground.

Figure 10. Kirjalansalmi bridge (1), cable-stayed bridge (2). (RIL, 2018)

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Special bridges include movable, temporary, auxiliary, and ponton bridges. Movable bridges are used on waterways and canals where the free vertical height of the bridge is not sufficient for waterway traffic. Temporary bridges are usually a modular structure that is used during the construction period when a regular bridge is inaccessible. The span length of that bridge type may reach 40 meters. Auxiliary bridges are temporary bridges that are used mainly for the repair of the railway bridge. (RIL 179-2018, 2018, p. 57)

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Figure 11. Movable bridge (1), temporary bridge (2). (RIL, 2018)

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3.4 Bridge structural parts

The main structural parts of the bridge are divided into superstructure, substructure, equipment and devices, and bridge site structures. These parts are defined on the basis of their function.

The superstructure is a main structural part of the bridge. Its primary objective is to withstand the imposed loads and transfer them to the substructure. (RIL 179-2018, 2018, p. 44) The superstructure includes beams, girders, cables, trusses, stringers, bearings, and stiffeners.

Superstructure also includes secondary components that are used to provide lateral stability for the main components. Secondary components are lateral bracings, struts, cross-frames and diaphragms. (WisDOT Bridge Manual, Part 2, Chapter 5) Different types of road surfaces, parapet walls and handrails are also considered to be a part of the superstructure. (RIL 179- 2018, 2018, p. 44)

The substructure of the bridge includes all elements that support the superstructure.

Substructure elements transfer the superstructure reaction loads down to the foundation soil or bedrock. Also, substructure elements control deflections and settlement so as not to cause serviceability problems for the riding surface or unintended overloads of the

superstructure. Three main substructure components are abutments, piers, and wing walls.

(WisDOT Bridge Manual, Part 2, Chapter 5)

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Bridge equipment and devices are structures or components that maintain the functionality, safety and service life of the bridge and support the operation of superstructure and

substructure. Bridge devices include bearings, different kind of expansion joints, transition plates, drainage pipes, measuring equipment. (RIL 179-2018, 2018, p. 45)

Bridge site structures are structures that are mainly outside the bridge but are necessary for the long-term durability of the bridge site. These structures include ramps with upholstery, gutters and wells, embankments and stairs. (RIL 179-2018, 2018, p. 45)

3.5 Bridge abutment

A bridge abutment is a substructure type that supports both ends of the superstructure and, at the same time, provides a lateral stability by resisting lateral loads such as earth pressure and wind load. There are numerous types of bridge abutments used in bridge construction.

The choice of abutment type is dependent on bridge geometry, roadway requirements, construction costs, geotechnical restrictions, aesthetic requirements, etc. From the view of the connection between abutment and bridge deck, bridge abutments can be divided into two categories: integral abutment and seat-type abutment (Figure 12).

Figure 12. Integral and seat-type bridge abutments.

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The integral abutment is rigidly connected to the bridge superstructure. When the bridge is subjected to transitional movement, backfill soil absorbs the energy. This type of abutment is mainly constructed for short bridges where expansion joints are not required.

The seat-type abutment is built separately from the bridge superstructure. The superstructure seats on the bridge seat through bearing devices. This type of abutment allows the bridge designer to control the bridge displacement between the bridge superstructure and abutment. It makes this type of abutment widely used for long bridge structure especially for prestressed concrete bridges and steel bridges. This type of abutment is constructed when - there is not enough space on the end of embankment ramp due to the length of the

bridge and the dimensions of the underpass

- bridge superstructure requires a bearing support and a movement joint device - bridge has a very oblique angle

The type of bridge abutment being design in this thesis is a seat-type abutment built for reinforced concrete girder bridge.

3.5.1 Abutment design features and considerations

In abutment design, great attention is paid to the bridge superstructure as it determines the shape and the main dimensions of the abutment.

Figure 13. Structural elements of bridge abutment in different colours.

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The abutment represents several structural elements cast into a uniform wall structure. Each element has its own design features and depending on the structural design may be cast using different concrete classes. For example, the main body of abutment is cast using concrete strength class C30/37 and corrosion class P3, whereas edge beams on top of the wing walls are cast using concrete strength class C35/45 and corrosion class P50. This is due to the fact that edge beams are closer to the road and more often exposed to salt that damages concrete.

(RIL 179-2018, 2018, p. 319)

The footing is typically a rectangular reinforced concrete slab that evenly distributes the loads from the bridge to the underlying rock or soil. The design feature of the abutment footing is an inclined top surface. It is needed to allow water to drain and not to accumulate next to the front wall. The excessive water near the foundation may lead to the damages of the concrete.

Figure 14. Footing of the abutment (1), inclined top surface of the footing (2).

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The front wall is the most massive structural element of the abutment. It is a basis for the other elements and, it transfers the superstructure reaction loads to the foundation and retains much of the backfill soil behind the abutment. The shape of the front wall reminds the small letter “r” which is due to savings in building material. The top surface of the front wall is called a bridge seat. This is where the bearings that support the end of the span are placed.

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Figure 15. Front wall of the abutment (1), bearing device (2), (Mageba-group, 2021).

One of the design features of the front wall are drain grooves. To avoid water accumulation near bearing devices small grooves are being cut in concrete to allow water to drain. Water can drain both through the grooves and drain pipes that are installed in the front wall before concrete pouring (Figure 16).

Another design feature of the front wall is a small room for the maintenance and repair of expansion joint (Figure 16). This room is designed when one of the following conditions is met:

• The main girder of the bridge is tensioned and access to the tendon anchor is needed

• A modular expansion joint is used in bridge abutment

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Figure 16. Drain pipe cast inside front wall (1), maintenance and repair room (2). (RIL, 2018)

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The backwall is a vertical wall that rises above the bridge seat and provides a horizontal brace that retains soil from penetration into a connecting point of the bridge deck. It also provides support for transition slabs and for expansion joint devices. A transition slab is a reinforced concrete slab that prevents the settlement of soil of the embankment. A small console on the inner side of the backwall is a design feature of this element.

Figure 17. Backwall of the abutment (1), typical dimensions of console (2).

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The top extension of the abutment is used as a basis for the expansion joint which is an important component in the structure where the elements move due to thermal expansion, loads, and other environmental factors.

Figure 18. Top extension of the abutment (1), modular expansion joint (2), (Mageba, 2021).

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The wing walls support the end embankment laterally, which improves stability of the embankment at the end of the bridge. The design feature of the wing wall is the shape of the wing wall. Depending on structural design, wing walls can be sloped and extended from the front wall, sloped and extended from the front wall with offset or can be straight and the height of the whole bridge abutment. The slope of the wing walls is dependent on slope of the embankment which is usually 1:1,5.

Figure 19. Wing wall shape variations.

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The edge beams are located on top of the wing walls and repeat the geometry of the bridge deck. The design feature of the edge beam is an inclined top surface. In most cases, the slope of that inclination is 1:20. Also, the edge beam might have a drip inducer, a small groove on an underside surface. The function of that groove is to interrupt the flow of water along the surface thereby causing it to drip off.

Figure 20. Edge beam of the abutment (1), drip inducer (2), (Väylävirasto, 2019).

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4 PARAMETRIC DESIGN TOOL FOR BRIDGE ABUTMENT

A parametric design tool for designing bridge abutment was developed in this thesis. The tool is able to create various shapes of bridge abutment by changing input parameters. The tool was developed on the basis of reviewed building regulations and standards. The developing process was supervised by an experienced bridge designer. He made sure that the tool met all the requirements. Also, during the development process the tool’s workability was reviewed by several bridge designers who gave some comments on the tool. The received comments were considered, and some aspects of the tool were improved. Besides the tool itself, a step- by-step guide was composed and embodied inside the tool. It eliminates the need to have separate documents open, making the design process more convenient.

4.1 Concept

Figure 21 shows the concept of the algorithm for creating a bridge abutment.

Figure 21. Scheme of algorithm creation

The centerline and cross-section of the bridge are imported into Rhino. Based on imported geometry, the algorithm creates a geometry of a bridge deck by extruding its cross-section

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along the centerline. It is needed to visualize a bridge to which the abutment is being designed.

After centerline and bridge cross-section were imported, the designer places support lines.

Besides being a target line for placing an abutment cross-section, these lines allow the designer to regulate the skew angle of the end of the bridge span.

The cross-section of the abutment in its turn is created of separate cross-sections of each structural element. The cross-section of the wing walls is created based on the bridge cross- section. The algorithm literally repeats the specific part of the bridge deck cross-section. Both abutment and wing walls cross-sections are created on the XY plane. Further, an algorithm adjusts the position of cross-sections to the target plane. In the case of the abutment cross- section, the target plane is perpendicular to the cross-section of the bridge deck end. The target plane of the wing walls is the same plane as the cross-section of the bridge deck end.

After the geometry position is adjusted the algorithm extrudes two-dimensional geometry into a volumetric three-dimensional geometry. The cross-section of the abutment is extruded along the support line and the cross-section of the wing walls is extruded along the edge lines that are parallel to the centerline of the bridge. The extruded geometry is then cut by the algorithm to give a final shape to the bridge abutment.

4.1 Tool setup

One of the goals of this thesis was to create a step-by-step guide for the parametric design tool. Before using the tool, it is important to set it up correctly otherwise the algorithm will not create a geometry in the right way.

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Figure 22. Roadline and bridge cross-section import.

In Step 1 the designer should import the cross-section of the bridge deck into the Rhino. The cross-section itself should be created in the right order that is shown in Figure 22. After the cross-section is imported, the designer should set the geometry in Grasshopper.

In Step 2 the designer should check that the correct line is selected. By clicking on component in Grasshopper one of the lines is highlighted in the Rhino. The correct line is also shown in the cross-section view. Both steps 1 and 2 are temporary solution for the tool workability. For now, it is one of the most complicated parts of the algorithm because in this part the algorithm partly repeats the geometry of the bridge cross-section. The wrong sequence of points or the wrong line might lead to malfunction of the algorithm. To avoid this, the development of the tool involves adding a bridge cross-section generator that will replace the first two steps and allow more reliable functionality of the tool.

In Step 3 the designer should import the roadline into Rhino and set it in Grasshopper.

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Figure 23. Edge beam curves setup.

In step 4 designer should check that the correct curves are selected since the algorithm constructs edge beams and wing walls along these curves. The correct curves are shown in Figure 23. Sometimes edge curves are not parallel to the roadline and have own shape at the end of the bridge. In this case, the designer can import his own curves that correspond to the right position and set it in Grasshopper. As a result, the geometry of the wing walls will follow these curves.

Figure 24. Support line setup.

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In step 5 designer should set the support lines that are perpendicular to the roadline and created in a certain direction relative to the curve. The correct direction of the support line is shown in the Figure 24. After every support line is set, the algorithm instantly generates the geometry of the bridge abutment. The created geometry might be correct initially or flipped and not showing as it should. In this case, the designer should toggle the Grasshopper component between true or false. This action is associated with the construction of geometry on different planes. By switching the toggle, the algorithm creates geometry on the correct one.

Figure 25. Regulation of skew angle and bridge deck gaps.

After the tool is set, the designer can pick the skew angle of the abutment and set the gaps between bridge deck and abutment.

4.2 Input data

The algorithm creates a geometry of a bridge abutment based on the parametric input values.

Each structural element of the abutment has its own set of input values that define the dimensions of its geometry. Changing the input values changes the width, height, length, and tilt angle of certain parts of the structural element. The values that need to be parameterized were determined during the study of bridge abutment design features. Based on reviewed building standards and with the help of experienced bridge designers it was also determined the allowable range of the values.

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Some of the values are constant or strictly dependant on others. Although these values cannot be changed, they need to be visible during the design process. For this, the cross-sectional view (Figure 26) of the bridge abutment and wing wall was created. In this view, the designer can see the overall cross-section of the geometries, the needed dimensions and how it is modifying in real-time while changing the input parameters. Also, an additional feature was added to the design tool. To assist a bridge designer both side views of a bridge deck and a 3D roadline of the bridge were projected onto a 2D plane. The roadline assists in design by showing how much space is between the top surface of the road and the top part of the abutment. The projected side view of the bridge deck shows the exact position of the bridge end span.

Figure 26. Cross-section view in Rhino.

4.2.1 Input values for the front wall

This section presents the input values that define the geometry of the front wall. Parameters that are presented in Figure 27 were determined on the basis of building standards. Some of the input values in the following sections have additional information that describes their function more precisely.

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Figure 27. Input values for the front wall.

1. Slope of the bridge seat

Depending on building conditions the designer has option to change the slope of the bridge seat from 0.01 to 0.05 or not to have the slope at all.

2. Width of the bridge seat

In some cases the support line may not pass through the centre of the front wall therefore, an extra option to define the width of the bridge seat considering the eccentricity was created.

3. Depth of the drain groove 4. Width of the drain groove

By itself, size of the drain groove is small. For example, it might be 25mm in depth and 100mm in width. But if increase that groove up to 200mm in depth and 750mm in width, it transforms into a bottom part of the maintenance and repair room.

5. Width of the backwall base

The base determines the thickness of the backwall.

6. Height of the front wall console edge

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7. Slope ratio of the console

The designer has option to choose between 1:1, 1:1.5 and 1:2 slope ratio.

8. Thickness of the front wall

The input value number 8 defines the thickness from the support line to inner surface of the front wall. As the thickness from the support line to the outer surface is known the algorithm adds the values and shows the actual thickness of the front wall in the cross-sectional view.

9. Height of the front wall

4.2.2 Input values for the backwall

There are no standards regarding backwall dimensions except for the console for the transition slab. Dimensions in Figure 28 that are possible to parameterize were determined on the basis of reviewed similar examples of bridge abutments.

Figure 28. Input values for the backwall.

1. Pour level

Pour level is a place where front wall and backwall are connected. During

construction process the backwall is poured after front wall. It is needed to provide a temporary access to the connection point between bridge deck and bridge seat.

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2. Height of the backwall

3. Distance from the top of backwall to transition slab console 4. Console enlargement

Regardless of the standard dimension of the transition slab console, that input allows designers to increase the size of the console.

4.2.3 Input values for the top extension

There is also no fixed dimension or standards in the design of top extension. The input parameters in Figure 29 were also determined on the basis of reviewed examples.

Figure 29. Input values for the top extension.

While designing a top extension, the designer is able to adjust the top surface of that extension to the roadline. The algorithm automatically creates a geometry of the top extension that corresponds a roadline. Thickness value that cannot be parameterized is shown in the cross- sectional view.

1. Thickness of the top extension

In case if the top beam is not adjusted to the roadline it is possible to regulate the thickness of the beam by changing the input value 1.

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2. Extension of the top extension

In case if bridge abutment has a maintenance and repair room the top beam can be extended towards the bridge deck creating a ceiling for the room.

3. Width of the middle part of the top extension 4. Width of the chamfered edge of the top extension 5. Vertical offset of the roadline

This line shows the level of edge beam. To have it visible, designer should set the correct value shown under the Input value 5.

4.2.4 Input values for the footing

Figure 30 show the input values that are in charge of foundation geometry. The parameters were determined on the basis of building regulations and reviewed examples.

Figure 30. Input values for the foundation.

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1. Width of the outer edge of the footing 2. Height of the outer slope

3. Thickness of the footing 4. Width of the footing 5. Height of the inner slope

6. Distance from the left wing wall 7. Distance from the right wing wall

The total length of the foundation is shown in the cross-sectional view.

4.2.5 Input values for the edge beams

Input values for the edge beam are shown in Figure 31. Dimensions that the designer is able to parameterize were determined partly on the basis of building standards and worked examples.

Figure 31. Input values for the edge beam

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1. Edge beam offset

In most of the cases this value is 200mm.

2. Thickness of the wing walls 3. Input value 3

4. Gap between edge beam and a cheek wall

Cheek wall is a part of the wing wall that protects the bridge connecting point.

4.2.6 Input values for the wing wall

It is possible to parametrize both of the wing walls separately. Before changing the values, the designer can choose between two types of wing walls available in the tool: sloped and straight.

1. Height of the wing wall edge.

The typical value of the edge varies from 700 mm to 1000 mm. This input parameter is only applied to the sloped wing wall.

2. Total length of the wing wall.

3. Distance from the front wall to the start of the slope.

Figure 32. Input values for the wing walls.

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4.3 Design tool testing

During the development process, the tool was subjected to constant testing. It was necessary to verify that the geometric model of the concrete bridge abutment is created successfully and has a good quality. The parametric design software that was used allow seeing the results live and therefore, it was easy to determine the errors and malfunctions of the algorithm.

During the tests, one main disadvantage was determined. Successful creation of the geometry is dependent on the input, therefore geometry that is being imported into Rhino should strictly correspond to the conditions of importing. This may add some difficulties to bridge designers because not every bridge cross-section corresponds to the conditions, or it needs time to adapt the geometry. The solution to this problem is the creation of an alternative method of importing geometry.

The way that the tool was tested lied in trying to reproduce the geometry of the bridge abutments of the already finished projects. Also, it was tested for the possible error by randomly changing input values. Thanks to this method it was possible to detect and correct malfunctions in the algorithm in the early stages of development.

The most common mistake that was detected during the test, was an incorrect positioning of coordinate planes what lead to the incorrect cutting of geometry. One of the key features that makes this tool useful is the ability to change the skew angle of the bridge end. The implementation of this feature was quite problematic due to the insufficient knowledge of how to orient the coordinate planes in a correct way.

Figure 33 shows some random variations of bridge abutment geometry that was made during the tests. The main focus of the testing was to ensure that the final model was as accurate as possible and was ready to be imported to other design tools.

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Figure 33. Randomly generated bridge abutment geometries.

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4.4 Future utilization

The developed tool is the first working version of it. The real functionality should be tested in a real project to determine its strengths and weaknesses. Based on the results, the tool will be finalized. But the development of the tool does not end there. In the future, the functionality of the tool is planned to be expanded. The possible expansion of the tool includes combining it with other parametric design tools used inside a construction company. A uniform modeling tool will decrease the time spent on modeling and increase the quality of the design. Also, the development idea includes adding automatization for the creation of reinforcement and drawings.

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5 CONCLUSION

Algorithm-aided design is a relatively new design approach in the construction industry. Some aspects of it are still complicated and need to be deeply studied. However, it is safe to say that AAD is the next era in BIM. Gradually design offices adapt this technology to their needs and as a result, they find a great alternative that is more effective and less time-consuming than the traditional design approach. The potential of AAD is enormous. This thesis represented some of the possibilities that AAD has.

The aim of the thesis was to create a design tool using an algorithm-aided design approach.

The software that was used in this thesis is Rhino 6 and Grasshopper. The object for the design was a concrete bridge abutment – a substructure of the bridge that supports the end span of the superstructure. Bridge design features and considerations were studied in order to investigate the aspects of bridge abutment design. The data obtained served as a basis for the determination of input parameters, and those, in turn, for the creation of a geometric model of a bridge abutment.

During the development process, the main problems arose due to insufficient knowledge of parametric design software capabilities. In this regard, it took some time to learn the program before starting to develop the tool. Nevertheless, the study progressed without any significant problems. There is enough material related to parametric design and available in the public domain, to start learning it from scratch.

As a result, a fully functional design tool was created using an algorithm-aided design approach. In addition to the tool, a step-by-step guide was developed. The guide allows bridge designers to set the tool correctly before starting to use it. By using the tool, the designer gains full control over every dimension of the geometry. Unlike the traditional modeling approach, the use of this tool significantly reduces the time spent on modeling and modifying the model.

To prove it, a skilled modeler was asked to give an approximate value of how much time it would take to model a simple bridge abutment that does not have a skew angle and any equipment. According to his approximation it would take from 10 to 15 hours of modeling whereas the use of a parametric approach reduces that time up to an hour. Considering how

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complex geometry can be it might take much more time to model it in Tekla Structures.

Moreover, it was noted that the capabilities of Tekla Structures do not allow to modify the geometry as quickly as it can be done using an algorithm-aided approach.

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