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Realisation of complex precast concrete structures through the ...

Realisation of complex precast concrete structures

through the integration of algorithmic design and novel

fabrication techniques

Niels Martin Larsen, Ole Egholm Pedersen

Aarhus School of Architecture

David Pigram

University of Technology, Sydney

Abstract. This paper describes a novel method for constructing complex concrete

structures from small-scale individualized elements. The method was developed

through the investigation of laser cutting, folding and concrete casting in PETG

plastic sheets and funicular grid shell simulations as a generator of complex

geometry. In two full-scale experiments, grid shell structures have been designed

and built at Aarhus School of Architecture and the University of Technology,

Sydney, in 2011 and 2012. The novel design method is described as an iterative

process, negotiating both physical and digital constraints. This involves

consideration of the relations between geometry and technique, as well as the use

of form-finding and simulation algorithms for shaping and optimising the shape of

the structure. Custom-made scripts embedded in 3D-modeling tools were used for

producing the information necessary for realising the construction comprised of

discrete concrete elements.

1 Introduction

In this paper we put forward a novel technique for concrete casting in laser cut

PETG sheets. This technique is capable of generating highly complex concrete

elements, whilst maintaining a high level of precision. The method operates

through the use of dynamic relaxation as a form-generating technique. The use of

scripting tools in the realisation process enables the necessary generation of masscustomised

moulds. Due to structural optimisation, material use in the construction

is reduced, and the material waste from the production of moulds is minimised.

This is achieved through digital production techniques and the possibility of

recycling the PETG moulds. As such, the method suggests a more sustainable

approach to complex concrete structures. The first part of the paper addresses the

methodology and the system of form-generation and production. Subsequently, the

paper follows a description of the experiments carried out, including findings that


Realisation of Complex Precast Concrete Structures

were observed during experimentation. This research builds on that described in an

earlier paper by the authors [Pigram et al 2012].

With the continuous development of new production technologies, the question

arises, whether it is possible to suggest a design strategy that will allow for the

design of fully mass-customized concrete elements. Computational design

techniques and Numerically Controlled fabrication equipment enable production

that breaks away from the industrial paradigm of standardization yet these

possibilities have not had a significant influence on the production of concrete

building components. There are several reasons for developing new methods of

concrete casting as an alternative to the traditional mass-produced steel or plywood

forms. Digital design-to-production processes enable variability and increased

complexity in mould form, whilst maintaining very high precision levels. The use

of simulation software allows for the integration of structural analysis and

optimization in the design process.

The development of the novel casting method described in this paper began

with an analysis of the process of cutting flat sheets. In a pre-CAD and pre-CAM

industrial paradigm, standardization and the use of repetitive production processes

was a key determinant of achievable forms. Further, the representational and

geometric limitations of analogue drafting and orthographic projection were as

significant as material constraints in the delimiting of formal possibilities

[Benjamin 2004]. Today, several design and production techniques allow for the

fabrication of complex non-repetitive elements often alleviating the need for

construction drawings altogether.

2 Theory

The theory of Tectonics has been used as a conceptual apparatus to qualify

decisions in developing the casting method. Tectonics can be described as the

relation between material, technique, and form (Figure 1 left) [Christiansen 2004].

This definition is derived from the German architect and theorist Gottfried

Semper, who describes tectonics as the description of a unity between idea, action,

and construction [Semper 1851]. Or, generally speaking, the unification of means

and end [Frampton 1995].

In order to effectively investigate geometry and techniques related to concrete

casting, the MTF-model has been developed to include construction and the mould

(Figure 1 right). The mould has the central position in the model, because it

directly generates form. This extended model is based on a series of prior

investigations and physical experiments, carried out as part of Ole Egholm

Pedersens’s ongoing Ph.D research.


N.M. Larsen, O.E.Pedersen, and Dave Pigram

Figure 1: Left: Tectonics defined as the evaluation of relationships between material,

technique, and form. Right: A proposed relational model that places the mould in the centre

of a realisation process addressing complex shaped constructions.

3 Method

The new relational model forms the methodological basis of the research, and

helps to identify essential parameters of geometrical consequences when material

or technique is changed. Hence, the purpose of the model is to determine possible

relations between a concept (idea), the material (concrete), and the technique (a

mould material subjected to a technology), as presented in the final construction.

The arrows in the model illustrate crucial considerations when choosing which

forms, materials, and technique to work with. Three case studies are presented in

this paper, investigating how these relations might unveil new ways of casting

concrete in complex shapes, while fitting into the mode of production suggested by

the available technologies.

3.1 Method development

The method was developed by considering the relations between material

(concrete), mould geometry, and technology. Laser cutting technology was chosen

due to its digital controllability. Second, it was decided to work with moulds of

complex geometry, since concrete is a liquid that can take on any form. Folding

was selected as a logical way to generate three-dimensional form from a flat sheet

in ways that can be controlled parametrically (Figure 2) [Pedersen 2011].


Realisation of Complex Precast Concrete Structures

Figure 2: Investigations of concrete casting in PETG. Left: A basic Grasshopper script with

variable width, length and height generate the template for laser cutting. Right: Scale model

tests.

It has proved practical to divide the method into two parts. The first regards

form generation and the production of information for manufacture and assembly.

The second is concerned with production and construction. Basically: a virtual and

a physical part. In reality, the virtual and the physical parts are interlinked, which

is a key property of the method. Figure 3 shows the feedback loops crucial to the

development of the first and second case studies, see 4.2 PreVault and 4.3

PlayVault. This process diagram describes how information and material flows

through the system. The cyclic design procedure includes all aspects of the

realisation process, through form-generation, production and construction. It

breaks from a linear design process, where information concerning production and

construction is confined to the later stages of the development [Larsen 2012]. The

actual process of form-generation and production is further described in Chapter 4.

Figure 3: Process diagram


N.M. Larsen, O.E.Pedersen, and Dave Pigram

3.2 Algorithmic design

The form finding method was based on the principles for generating optimised

vault structures, as famously utilised in Antoni Gaudi’s hanging chain models for

the Sagrada Familia in Barcelona. Through physical self-organisation, the chains

take forms that contain tensile forces only forming (catenaries). When the hanging

form is inverted, the forces are translated into pure compression, resulting in

funicular forms optimised for construction in materials such as stone. A digital

form-finding process able to simulate the self-organisational behaviour of a

network of springs has been implemented in the software Processing by Iain

Maxwell and Dave Pigram for this project based on earlier research [Kaczynsky et

al 2011].

The form-finding method itself is not novel and is very similar to that

described by Kilian and Ochsendorf. The benefit of this custom implementation

comes from integration into the later workflows of creating 3-dimensional

components around the force network, completing their unrolling for laser-cutting

etc. Additional display modes have also been added to inform the real-time

adjustment of factors such as spring length used to influence the vaults final form.

The digital form-finding process takes an initial mesh or network of lines, with

arbitrary topology, and a series of fixed points as input (Figure 4 Left) and through

iteration the system arrives at an equilibrium state (Figure 4 Right). Forms

generated through the dynamic relaxation form-finding processes are optimised in

terms of compression-only force distribution from the structure's own weight. In

order to both verify the output of the form-finding software and to calculate the

structure’s performance with various applied live loads, Finite Element Analysis is

performed using Autodesk Robot Structural Analysis Professional 2012.

Figure 4: Dynamic relaxation algorithm. Left: Input mesh imported as 2D drawing. Right:

3D mesh in equilibrium state after running the dynamic relaxation simulation.

3.3 Parametric design

The wireframe geometry, generated through the ReVault simulation, is

imported into a 3D modelling software with a module for scripting. In this case

McNeel’s 3D modelling software Rhinoceros and its implementation of

IronPython were used. The geometry is developed into unique volumetric

components via custom written algorithms (Figure 5 left). Although all

components are geometrically unique, there are only two topologically distinct


Realisation of Complex Precast Concrete Structures

types: typical and base components. The latter has a thickened flat base enabling it

to stand unsupported by falsework. In the same script, input for the manufacturing

process is generated. This includes scoring lines for folding, rivet holes, flaps for

stability, holes for tube inserts to run ties to keep the elements in place through,

and the engraving of a unique number. (Figure 5 right) The 3d component model is

used for extracting the geometry of the falsework and for positioning the

individual components during the assembly.

Figure 5 left: A three-dimensional line network (dashed line) forms the basis for

parametrically generating the component geometry. Right: this geometry forms the basis for

unrolled mould templates.

4 Case studies

4.1 Case study one: Hello World

To qualify the technique for full-scale production, a feasible way of producing

discreet concrete elements in a large population was examined by Ole Egholm

Pedersen in case study one, entitled ‘Hello World’. Since the moulds would all be

unique, and therefore not reusable, a materially efficient and low or zero-waste

production method was desired. This was achieved by the use of PETG plastic,

which is part of the PET plastic family. It is easily recycled, by melting, at 260 ºC,

evaporating only CO2 and water, and its molecular structure allows for infinite use

and re-use without degradation if it is kept in a closed recycling process. In terms

of the design theory Cradle to Cradle, the PETG is used as Technical Nutrient, in a

zero-waste production [McDonough and Braungart, 2002]. Importantly it does this

while adhering to the basic requirements of being an appropriate mould material

that is easy to laser cut and easy to fold. The plastic sheet comes covered with a

thin protective film, used to protect the material against scratches during transport.

This film was left on during casting and then removed to leave a clean sheet ready

for recycling.

When exposed to fluid concrete material, 1 mm PETG sheets have a high

degree of deformation. It was practical to perform stress and deformation

simulations as part of the development of components, in order to check that the


N.M. Larsen, O.E.Pedersen, and Dave Pigram

PETG could withstand the weight and hydrostatic pressure from liquid concrete.

(Figures 6 left and center) [Pedersen 2011].

Figure 6: Calculating material deformations: Left: SolidWorks displacement analysis of a

concrete beam cast in 1mm PETG. Center: Deformations in a horizontally cast column.

Right: a parametrically defined, reinforced concrete beam spanning two meters.

Through these investigations, it was concluded that parametrically defined

concrete elements cast using the applied technique can be both complex and

accurate. (Figure 6 right). Due to deformations in large concrete components, it

was descided that further experiments should be focused around smaller concrete

components.

4.2 Case study two: PreVault

PreVault was designed around the application of small-scale components with

triangulated surfaces and a small casting height, in order to eliminate deformations

due to the hydrostatic pressure of concrete. The case study was carried out at

Aarhus School of Architecture in the fall of 2011 (Figure 7). Over the course of

three weeks the authors, with the aid of Civil Engineers Jacob Christensen, and

Ronni Madsen and 12 Master of Architecture students, designed and built a 16

square metre by 2 metre tall pavilion consisting of 110 discrete concrete elements,

cast in PETG.


Realisation of Complex Precast Concrete Structures

Figure 7: Case study two: A concrete grid shell pavilion made up of 110 discrete elements.

The developed method for form finding and component generation was applied

(Figure 8). FE analysis was used to calculate the shear forces and bending

moments in the joints influencing decisions regarding the joint design and

materials.

Figure 8: investigation of different geometries by exporting a mesh from Rhinoceros into

the ReVault software for perform dynamic relaxation, then back to Rhinoceros to generate

spatial components using a Python script. The geometry at the far right was chosen.

The final pavilion structure comprised 110 components, which were nested on 900

x 1600 millimetre sheets of PETG, laser cut, folded and reinforced. The PETG

moulds were fixed to a blueprint, generated from the digital model, which enabled

positioning of the ends of the three component arms with a tolerance of less than

one millimetre. Flaps added to the ends dictated the angle of the component arms

(Figure 9 left). A prototype test disclosed that precise falsework would be

important to position the components correctly in the compressive arc. This

falsework was generated directly from the spatial components model using

Grasshopper, a generative modelling plugin for Rhinoceros, and laser cut from

recyclable cardboard (Figure 9 right) [Pigram et al. 2012].


N.M. Larsen, O.E.Pedersen, and Dave Pigram

Figure 9: Construction. Left: Mould for base component. Right: The pavilion was

assembled on top of a digitally generated, laser-cut cardboard falsework.

4.3 Case Study Three: PlayVault

Figure 10: A complex grid shell structure made up of 190 discrete concrete elements.

PlayVault was carried out by Ole Egholm Pedersen as a workshop with 40

students over a period of two weeks at the Royal Academy of Fine Arts in

Copenhagen, Denmark (Figure 10). The case study served two purposes: To test

the method in an industrial production outside the laboratory and to explore the

potentials for the method to deal with a more complex overall form. A revised

version of the dynamic relaxation algorithm that was implemented in the ReVault

software was developed as a Grasshopper component in order to keep the digital

development of geometry within a single piece of software, namely Rhinoceros

5.0. This allowed first year students to quickly learn the workflow of drawing a

mesh, performing dynamic relaxations, and component generation (Figure 11).

This enabled many designs to be quickly proposed and evaluated by Civil

Engineer Jacob Christensen.


Realisation of Complex Precast Concrete Structures

Figure 11: development and refinement of the geometry using Rhino and a dynamic

relaxation component in Grasshopper.

During the fabrication of the second prototype, a faulty laser-cutter meant that

the cardboard falsework had to be drawn up and cut manually. This inevitably led

to a loss in precision, as well as to folding and mirroring errors that digitally

controlled cutting and marking could have avoided. As a result construction of the

falsework became immensely complicated (Figure 12).

Figure 12: Assembly of the supporting falsework present the biggest challenge during

construction.

5 Findings

The method, as tested in each case study, combines algorithmic design through

form-finding, laser cutting as a technique, and concrete as the materialization. The

process from form to construction can be retrospectively reinterpreted through the

relations model in order to structure the findings of the case studies (Figure 13).

The mould has a central position in the relations model, which is reflected in

the case studies, as the definition and development of the moulds required the most

attention. As such most of the findings relate to the relationship between the mould

design and its consequences.

Observation of the case-study structures immediately announces the material:

Concrete. Closer inspection exposes traces of score lines and rivets, revealing the

technique: laser cutting and folding. It is in this way that the material relates to the

technique: each a consequence of the overall amorphous form. The result is a

structure that can be said to be tectonic. For if the mould material been another, for

instance wood, the technique and subsequently the form, would each have been

fundamentally different.


N.M. Larsen, O.E.Pedersen, and Dave Pigram

Figure 13: The idea of catenary vaults as a form, and laser cutting as a fabrication

technology, fed into the relations model.

5.1 Concept and mould relation (Figure 13, A+B)

The folding principle was found to be a successful means for translating the

initial double-curved free form geometry into moulds to produce discrete concrete

elements. Breaking the components down into triangular surfaces introduced

additional creases that helped to provide rigidity to the mould.

During the construction of the first prototype the mould design was constructed

from three separate pieces of unrolled geometry: one for each arm. While this was

materially efficient due to improved cut-sheet nesting it was found that

approximately 40 percent of the components were incorrectly assembled. Either

the arms were incorrectly ordered or at least one arm was folded inverted (as a

valley instead of a peak or vice versa). It was determined that both of these errors

could be completely avoided through three modifications to the mould assembly

design. The first necessary modification was to only break the mould into two

parts per component, one two-armed part and one one-armed part. The second


Realisation of Complex Precast Concrete Structures

modification was to alter the rivet-hole pattern to make it asymmetrical. This

made it impossible to fold and attach the one-armed part the wrong way, which

would mirror that arm. The third and final amendment was to ensure that the part

unrolling script unrolled and oriented all components consistently such that the

arm centrelines were all valley folds.

This casting method is applicable to many component forms and their

corresponding lattice structures. The choice of Y-shaped moulds that tessellate

across a 2.5 dimensional hexagonal grid, used in all of the case studies here

described, proved to be advantageous for several reasons. By limiting material to

the periphery of the hexagon lattice a minimum of concrete is used thus achieving

a lightweight structure, physically and aesthetically. Since each component has

exactly 3 arms it is always possible to define a plane via the three end points of

these arms. Thus, the overall form, which is necessarily convex, can be made up

of flat components with the faceting happening only across the joints. Further,

because the top and bottom surfaces of each mould are parallel, the components

can be cast onto any flat surface and do not need secondary supports. This also

allowed for the simple printing of part-verification templates. Finally, because

there is no curvature across the component the total depth of the mould is

minimised which minimises both the total hydrostatic pressure exerted on the

PETG and therefore its requisite sheet thickness increasing material efficiency.

5.2 Technology and mould relation (Technique Figure 13, C+D)

The parametric definition of geometry that is directly translated into output for

the laser cutter has a very high precision that feeds directly into a standard

industrial production, as tested in the PlayVault case study and is maintained in the

final construction. Laser cutters have a limited size, which point towards designing

a large number of small concrete elements as opposed to larger elements, like

columns and beams. To withstand the pressure of large concrete elements on the

mould a thick PETG or steel sheet would be required to cast elements at a scale or

larger than the ones produced in the Hello World case study. Thicker sheets cut at

a much slower rate, they are harder to fold, and the concrete elements are

impossible to handle without a crane. Further research is needed to evaluate

whether the material and energy resources needed when casting in one-off PETG

moulds is higher than in a traditional, repetitive concrete element production, or if

the fact that the moulds can be melted at a low temperature and reused in a closed

cycle limits the overall material and energy use.

5.3 Mould and construction relation (Figure 13, E+F)

It was clear in the PlayVault case study that the current method is heavily

reliant on a very precise, digitally produced scaffold. The assembly of components

could be developed further to minimise this issue, and it is worth investigating if

the falsework could be avoided all together. The development of a robust posttensioning

system allowing ring forces to stabilise elements during construction,

like when building an igloo, is a possibility. The base components need to be fixed

around the z-axis. In the PlayVault case study base components were connected to


N.M. Larsen, O.E.Pedersen, and Dave Pigram

the ground using just one steel pin, allowing them to rotate and create distortions

throughout the construction.

5.4 Mould and concrete relation (Figure 13, G+H)

The fluid concrete can take on practically any form. Therefore it makes sense

to let the concrete elements include the complex joints where more than two lines

in the lattice geometry meet, while using midpoints between nodes in the lattice as

points for separation components.

6 Conclusion

The case study pavilions, constructed in a very short time, for low cost and

with relatively unskilled labour demonstrates that the integration of algorithmic

form-finding techniques, CNC fabrication workflows and the use of innovative

PETG folded mould techniques enables the practical realisation of complex,

freeform geometry as precast concrete element structures.

While the PreVault case study was a success in terms of precision and

structural performance, the PlayVault case study demonstrated that the proposed

method can be utilized to generate more complex forms. This case study also

showed that while it is a flexible method, it is also one sensitive to imprecision and

to scale through the accumulation of dimensional variances.

Acknowledgements

The authors wish to thank Civil Engineers Jacob Christensen, Vision+ and Ronni

Madsen, Alectia, the students of studio Digital Tectonics, 2011, Aarhus School of

Architecture, Centre for Industrialised Architecture, CINARK and the TEK1,

concrete participants, 2012 from the Royal Danish Academy of Fine Arts in

Copenhagen.

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