INTERTWINING SYSTEMS FOR THE CREATION OF THICK CONCRETE SHELLS - INTERSTITIAL ITERATIONS

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abstract

The question about the definition of the interstitial space is introduced into the conceptual reflection on concrete shells. The in-between space is no longer considered a residue – an inevitable consequence of other interactions.

Gordon Pask notes in “The Architectural Relevance of Cybernetics� that earlier pure architecture was descriptive (a taxonomy of buildings and methods) and prescriptive (as in the preparation of plans) but it did little to predict or explain. In contrast, the cybernetic theory has an appreciable predictive power. This predictive and explanatory power leads the investigations and the experiments for the creation of a thick concrete shell.

The thick concrete shell is the result of the combination of existing and innovative systems. Controlling systems shape the space configuration according to variable architectural requirements, defining the size and geometry through a parametric highly controlled procedure. Controlled systems formulate the void, carving away material from the concrete volume, resulting in a new material topology this of a reticulated three - dimensional concrete lattice. These entwining systems inject new methodologies to the design of concrete shells fuelling the process in an architectural and material level.

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Thin concrete shell era

pg. 8 - 11

Thick concrete shell era

pg. 12 - 21

Controlling systems

pg. 22 - 35

Controlled systems

pg. 35 - 51

New Materiality

pg. 52 - 55

Intertwining systems

pg. 56 - 67

Conclusion: Collision of forces

pg. 68 - 69

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thin concrete shell era

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fig. 1: Algeciras Market Hall, Algeciras, Spain, 1934

fig. 2 & 3: Restaurant los Manantiales, Mexico City, 1958

fig. 4: Deitingen Service Station, Solothurn Switzerland, 1968

fig. 5: CNIT, La Defense, Paris, 1958

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thin concrete shell era

The modern era of the concrete shell construction begun in 1920’s when the use of the new material reinforced concrete spread throughout the world as it was relatively inexpensive and easy to cast into compound curves. The curved shapes are naturally strong structures allowing wide areas to be spanned without the use of internal support giving an open unobstructed interior. Many of the concrete shells rely wholly on the shell structure itself without any ribs or additional reinforcement. This construction approach gave new possibilities in realization of concrete shells.

Before the World War II one of the first who looked into thin concrete shells in innovative way was Eduardo Torojja. A market hall in Algericas (figure 1), is the first thin concrete shell realised in 1933, it is a lowered semi- spherical dome with an octagonal plan and a diameter span of 4.9m. The thickness of the structure was in the minimum point 10mm.

After the end of World War II, the suitable conditions occurred that were in the need of structures that offer economical material use like shells. Despite the labour intensive construction of complex shapes a blooming period for the concrete shell construction begun. The reduction of material use contemplated in the totality of the economic report. The race for the creation of thinner shells and more complex geometries started, contributing in rapid evolution on methodologies and forms.

In the 50’s, an important figure in the thin concrete shell scenery completed his first works in Mexico, Felix Candela. He worked on the hyperbolic parabolic shaped shells and double curvature forms. The complicated forms he suggested were geometrically defined by lines, this permitted an inexpensive construction method relatively easy to realize since for the formwork planar pieces of wood were used (figure 2 ,3).

Nicolas Esquillan, a French Engineer, keeps until today the record for the biggest span in concrete shell construction. In 1958 he completed the CNIT in Paris- La Defense (figure 4), a groined vault, formed from the intersection of three parabolic cylinder segments covering a total area of 900000m2 .

Heinz Isler is considered as the founder of modern free-form design and shape optimization. His greatest contribution though was free-form structures realised from hanging membranes. Hanging models give the best performance due to the fact that they are in pure compression, this was the principle he worked on and based many of his works by experimenting in different scale the results he obtained from the physical models (figure 5).

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fig. 6: ouroboros, symbol of circularity

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The overview of the methodology and work of the modern era of concrete shells from the 20’s until the 70’s when the interest for concrete shells in architecture faded, shows that the input – output principle in problem solving was applied. A linear system procedure was followed updating the input information with every evolution in order to respond to the challenge of creating more complex geometries, cheap construction methods and optimum material usage. The input was the material, the form and the design requirements. The process was subjective and personalized to each designer’s views. Different process of calculating the complexity of curvatures existed, experimental like Isler or Mathematical like Candela, the construction method was adapted accordingly. The output either in the architectural scale or as a design product gave feedback for the next steps; this is obvious through most of these architects work evolution.

The modern era of shell construction started before the World War II and bloomed in the 50’s and 60’s, in the same period when Wiener developed the first order of Cybernetics, established the principles of systems. The first order of cybernetics represents goal directed behaviour of the system whether organic or constructed. Every system has goals and acts and aims towards these goals. There is an input and an output. The environment around affects the aim and specific information returns to the system the so called “feedback”. (figure 6) System measures the difference between the state and the goal, detects the errors and corrects the action to aim towards the goal again. The procedure is repeated until the goal is achieved.

Design is a cybernetic process. It relies on a simple feedback loop: think, make, test, It requires iteration through the loop. It seeks to improve things, to converge on a goal, by creating prototypes of increasing fidelity.[1]Gordon Pask “The architectural relevance of Cybernetics” defines an architect as a system designer, studying the organizational system properties of development, communication and control. Perceiving and creating architecture through systems was highlighted through with the genesis of the Cybernetics theory and a whole new field of studies emerged.

1. Dubberly H. , Pangaro P., “Cybernetics and Service-Craft: Language for Behavior-Focused Design”,Kybernetes: The International Journal of Systems & Cybernetics, v. 36, No. 9-10. (2007), pp. 1301-17

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thick concrete shell era

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fig. 7 & 8 : Toyo Ito, Meiso no Mori Municipal Funeral Hall Kakamigahara-shi

fig. 9 : thin and thick shell

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thick concrete shell era

The challenge on concrete shells started many decades ago and still continues through the work of contemporary architects like Toyo Ito (figure 7, 8). Their work evaluates the contemporary requirements, exploits the advanced design and construction technology available nowadays. Most certainly concrete shells have still a significant part in the contemporary architecture scenery and are calling for a challenge that will change their prospect.

As mentioned before concrete shells were mainly used for their ability to span large areas without the use of internal support while relying wholly on the shell structure itself rarely using ribs or reinforcement. The use of concrete shells defines strictly the relation of the inside and outside space, few openings mostly arcs following the curve that the shell structure needs to obtain in order to be mechanically efficient.

Taking into account the new technologies that are available now comparing to then and the acquired cognition from new fields of research the thin concrete shell leaves a big margin of questioning in its creation and its applications. Reformulations and a new perspective are almost obligatory.

The relation of space and architecture is far from settled as space is layered and evolving, containing diverse informational and other kinds of ‘flows’. [2] For Plato the in-between space is lacking any substance or identity of its own, falls in between the ideal and the material; it is the receptacle or nurse that brings matter into being, without being material; it nurtures the idea into its material form, without being ideal.

In- between space is here fluctuating enclosed by the inside and outside space, it needs to expand and claim its territory in the spatial organisation (figure 9).

2. Digicult, http://www.digicult.it/digimag/issue-063/italiano-scoprire-gli-spazi-interstiziali-parte-1/, (accessed 22 July 2014).

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ventilation

fig. 11 : thick shell functions

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Inserting the problematic of defining in-between space in thin concrete shell conception brings the possibility to make more than a thin concrete shell, a skin of concrete. Design a three - dimensional concrete lattice that challenges the perception of concrete shells as large scale objects used for spanning large areas. It inspires the design of a structure that creates openings, space subdivisions and perforations (figure 11). Various configurations can be also composed for water draining and gardens, in a smaller scale for insulation and ventilation. Multiple functions occur by carving away material to create void.

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Inhabitable Cells Space Subdivision

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Thermal insulation

Natural Ventilation

Water Store

Green landscape Structure

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fig. 12 : Designed Particles Aggregations ( Eichi Matsuda, Uniy 4, AA London)

fig. 13 : configuration with light ( Eichi Matsuda, Uniy 4, AA London)

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Architectural systems commonly seek to form clearly defined and seemingly permanent material assemblies [2] Loose granulates in concrete can be considered and researched as material systems. A large arrangement of components can complete architectural tasks. The architect’s role is to modulate and observe their behaviour on the particle and system level. To observe how a shapeless material generates form and geometry and finally space. These elements have the ability to adjust to the internal and external system influences (figure 12, 13).

The preceding thematology, material systems and interstitial space, constitute two eminent topics in the architectural scenery. One belongs to the experimental research approach and the other one is theoretical, questioning the configuration of space.

Material systems bring suggestions, maybe even solutions in the query for interstitial space. When architecture is designed in the conceptual boundaries of material systems interstitial space emerges. It becomes the space between the aggregates, the void in their arrangement.

2. Hensel M., Menges A., “ Aggreates�, Architectural Design, v.78 No 2(March/ April 2008), pp. 81-89

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Controlling system

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fig. 14: functional organisation of a living organism

fig. 15: ouroboros, symbol of circularity of multiple systems

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Controlling system

As the interstitial space expands the thickness of the concrete sections follows adjusting to the requirements. The idea of thin concrete shells is abandoned and a new type of concrete shell emerges. The system becomes more complicated and encloses more information and elements that belong to other systems.

Systems as described in the second-order of cybernetics nest one first-order cybernetic system within another. The inner or lower-level system is controlled by the outer or higher-level system. The goal of the controlled system is set by the action that the controlling system follows. Addition of more levels (or “orders”) repeats the nesting process. What is system for one process is environment for another one. There is no absolute distinction between system and environment. The observed system is enclosed in an observing system. The observer has an active role of regulating the observed system to respond in multiple and complex environment changes. This complexity of nesting systems prevails in the thick shell design.

Empirically a large proportion of the complex systems one can see have hierarchical structure. Or one perceives them as hierarchies in order to solve some complex problems. A complex system can be presented as a hierarchy in order to make proper control of the systems. This approach of hierarchisation is very desirable in many cases due to the fact that it has many useful properties such as near decomposability that is simplifying description and analysis of the system. [3] This complexity of nested systems dispenses a distinctive perception on the “thick” concrete shell. The reticulated concrete shell is the result of nested systems which combine information and processes of existing conceptual and construction methods and the implementation of new ones.

3. Burmakin E., Course at Helsinki University of Technology “Architecture of Complex Systems“, 15 January 2003, http://neocybernetics.com/report145/Chapter4.pdf

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fig. 17: membrane guyed with aditional linear elements - Frei Otto

fig. 18 & 19: stabilised membrane with additional linear support - Frei Otto

fig. 16: single membrane with additional linear support

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fig. 20 & 21: multiplicity of possible design s - Frei Otto

In the interpretation of the “thick” concrete shell system a layering of different systems intertwining in a non- linear way can be identified. In order to have a clearer and “simplified” viewing of these systems the whole procedure can be resolved in two interplaying categories of sub-systems, the controlling and the controlled. The upper controlling system is consisted of a double inflated membrane – pneumatic structure on which a form finding procedure has been applied in order to achieve structural patterns, space subdivision and other particular customisations of the initial form.

Pneumatic structures have priory been used as form finding method and as formwork for concrete shells by Frei Otto and Dante Bini respectively but they also represent an extensive field of studies by other architects and engineers.

Frei Otto was one of the pioneers in pneumatic structures investigations. His curiosity led him in creating numerable models experimenting on the potentials of the pneumatic forms. For the study on anticlastic areas different initial plane structures where tested (figure 20, 21). Very significant is his work on the Investigation of linear reinforcement on pneumatic membranes which fuelled the structural and design problematic (figure 18, 19).

In a similar way various methods of form finding are applied on the interior membrane of the controlling system. Anchor points that keep the bottom membrane grounded are applied, where subdivisions or inner open space are required. The delineation of the border where the main openings are created is realised by the use of supporting arches between the two membranes. This method allows formulating a kind of a beam that supports the ending of the reticulated volume of the thick shell. Springs are used for the reinforcement of the concrete shell where necessary.

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fig. 22 : physical model - form - finding method - springs

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In a similar way various methods of form finding are applied on the interior membrane of the controlling system. Anchor points that keep the bottom membrane grounded are applied, where subdivisions or inner open space are required. The delineation of the border where the main openings are created is realised by the use of supporting arches between the two membranes. This method allows formulating a kind of a beam that supports the ending of the reticulated volume of the thick shell. Springs are used for the reinforcement of the concrete shell where necessary.

The top layer – exterior membrane acts as an offset of the interior one in order to keep a control of the complex behaviour of the liquid material. The offset form accepts alterations when it is desired to formulate differently the interior and exterior face of the reticulated volume.

As shown in figure 24, through simulation a highly controlled procedure is achieved. The stiffness of the elastic membranes, the length of the springs and the positioning of the anchor points are parametrically regulated.

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anchor points on the edges anchor points in the main area for creating subdivisions free edges for side openings

anchor points on the edges areas with varying topography creating diverse curvatures anchor points in the main area for creating subdivisions free edges for side openings areas with varying topography creating diverse curvatures

fig. 23 : form finding methods

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borders------arches for side openings

borders------free edges for side openings

subdivision------anchor points

topology------forces apply for creating various curvature

fig. 24 : parametrically defined form finding methods

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fig. 25 : sketch fo Bini system construction method (Dante Bini , 1965)

fig. 26

fig. 28

fig. 27

fig. 29 fig. 26-29: bini shell construction process (The Architectural Review, January 2013, www.architectural-review.com )

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Dante Bini developed a system that transforms the pneumatic structure of a simple dome membrane to a form work for the creation of concrete shells. Dante Bini pioneered ‘air structures’: gigantic balloons that could be covered with a thin layer of concrete then inflated to form domes in a matter of hours (figure 25).

Bini Dome fabrication involves the construction of a ring beam and ground floor slab. The ring beam cleverly contains a ‘cast in’ egg-shaped void to hold the main membrane in place during inflation, as well as air inlets and outlets. The internal pneumatic form Pneumoform of nylon-reinforced neoprene is then laid over the slab on top of which a complex network of crisscrossing helical springs is stretched across the diameter. The springs have no specific structural function, but control the even distribution of steel reinforcement bars (which are threaded through the springs) and also maintain an even concrete thickness by holding the mix in place. A top layer of membrane is rolled on the poured concrete, the bottom membrane is inflated with air and the whole system rises up to the final position where vibration is applied until the air is fully dissipated from the concrete mixture.

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force:2 force:2 force:2

1st membrane

force:2 force:2 force:10 force:10 force:2 force:10

2nd membrane

fig. 30: definition of the 1st and 2nd membrane

2nd membrane

1st membrane

fig. 31: geometrical definition of the two membranes

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Similar to the Bini - shell, in this case the membranes modulate the in-between space where the material – concrete and the reticulating components (the air cells) will attain final shape and position according to the controlling system and forces that dominate. The air pressure applied on the interior membrane creates a strong support in order to hold the dead weight of liquid concrete until it goes dry. The controlling subsystems are in an immediate interaction with the adjoining system, the in-between layer in which an energetic materiality is formulated.

The preceding examples give an idea of the complexity that already prevails in the functionality of the controlling sub-systems of the higher level of regulation.

The interrelation of existing conceptual and construction tools produce a challenging complexity that fuels the two controlling sub-systems conception. In Cybernetics this kind of combination of actions is known as Heuristics a set of instructions for searching out an unknown goal by incremental exploration, to some known criterion.

Consequently, acquired cognition becomes part of an unconscious activity this type of activity is difficult to detect and to be controlled. [4]

4. Abramovitz R., von Foerster H. (1995) “Cybernetics of cybernetics : or, The control of control and the communication of communication.� Minneapolis : Future Systems, Inc., pp. 200

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Controlled system

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controlling system

controlled system stochastic level controlled system deterministic level

controlling system

fig. 32: controlling and controlled system

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Controlled system

The lower sub - systems are designed to fit variables and constraints that are given for various conditions defined by the upper sub-systems. Different size of spheres (filled with air) are placed in different parts of the structure providing variability in the reticulation where needed. The in-between space associates an organized system of various sizes of spheres representing the primary reticulation of the concrete volume and a system of smaller spheres with a more stochastic organization. The primary reticulation relies on a stable organisation of the spheres that follows the architectural requirements of the thick shell. This way the openings, the subdivisions and the formulation of interior space are ensured in combination with the form-finding methods applied on the controlling system. Additionally initial perforation for ventilation, water drain and garden capsules is realised and further completed by the second stochastic layer of spheres.

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fig. 33 : close hexagonal and cubic packing

fig. 34 : studies on optimum packing density for the creation of sustainable concrete mixture

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Sphere packing studies are essential to the understanding of the intricate organisational behaviour of the spheres mainly in the stochastic sub-system. The two main characteristics of a sphere packing is the geometrical configuration and the packing density. The creation of the optimum packing has long been an issue for mathematicians. The optimum packing of spheres is of immediate interest with the research on the organisation of spheres as it provides the smaller negative space and therefore the minimal volume (figure 33).

The reticulating cells of the in-between system can be inspected as aggregates in the mixture of concrete with the particularity that the particles create voids in the concrete volume. The particle packing between coarse and fine aggregate elements has been a engaging subject of study by material scientists in order to recognize the behaviour of components in the liquid concrete. Computational simulations on this subject represent and calculate the aggregates particles as spheres.

Precisely the packing density of coarse and fine aggregate has been catalogued in a methodical way in order to anticipate the behaviour of such particles in concrete mixtures. The importance of predicting such mixtures is essential for the production of sustainable concrete mixtures that require less water and less cement paste, therefore reducing the CO2 emission (figure 34). The optimum packing of aggregates is also crucial since it directly affects the strength modulus of elasticity, creep and shrinkage of concrete.

Due to the close packing that is achieved through the interconnection of complementary elements, it has been proven that the void ratio of a mixture with different size of aggregate is more efficient than the packing of same size aggregates.

Packing of exclusively fine aggregates results to dry concrete mixtures and have big volumetric changes while drying, on the other hand coarse aggregates mixtures create ‘rocky’ mixtures that are prone to segregation.[5]

5. Quiroga P. , Fowler D., “ Proportioning methods for concrete with high microfines”, (Univeristy of Texas, published 2004, Post Ph. D. Thesis)

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total sphere volume total sphere volume

Volume = 3.4 m3

total sphere volume Volume = 3.4 m3 Volume = 3.4 m3 top view top view top view

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interstitial v Volume = 0

Volume = 0.6 m3

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Iteration 03 4503 spheres total Iteration Cumulative 45 spheres total sphere Volume = 3.5 m3 Cumulative sphere Volume = 3.5 m3 interstitial volume Volume = 0.4 m3 + interstitial volume Volume = 0.4 m3

Iteration 03 45 spheres t Cumulative

Iteration 04 147 Iteration 04spheres total Cumulative 147 spheres total sphere Volume = 3.5 m3 Cumulative sphere Volume = 3.5 m3 interstitial volume Volume = 0.2 m3 interstitial volume

Iteration 04 147 spheres Cumulative

interstitial v Volume = 0

interstitial v Volume = 0.

+ Volume = 0.2 m3

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Towards Recursion 147 spheres total Cumulative sphere Volume = ?

total sphere volume Volume = 3.4 m3

interstitial volume Volume =? fig. 35 : apollonian gasket 3D packing - reticulation of a sphere volume top view

top view

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fig. 36 : random generation of spheres - processing script +

Towards Recursion 147 spheres total Cumulative sphere Volume = ?

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Iteration 02 21 spheres t Cumulative

Iteration 02 2102 spheres total Iteration Cumulative 21 spheres total sphere Volume = 3.2 m3 Cumulative sphere Volume = 3.2 m3 interstitial volume + Volume = 0.6 m3 interstitial volume

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interstitial v Volume = 1.

Volume = 1.0 m3

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Towards Recursion spheres total Towards147 Recursion Cumulative 147 spheres total sphere Volume = ?

Cumulative sphere Volume = ? interstitial volume Volume =? interstitial volume

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Iteration 01 16 spheres t Cumulative

Iteration 01 1601 spheres total Iteration Cumulative 16 spheres total sphere Volume = 2.8 m3 Cumulative sphere Volume = 2.8 m3 interstitial volume + Volume = 1.0 m3 interstitial volume

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interstitial volume Volume = ?

A particular interest is found in the apollonian gasket packing as there is a close connection to the reference image of polymer foam that leads the investigation for the concrete lattice of the thick shell. Figure (38) shows the reticulation of a spherical volume in a recursive way. This result is acquired from the negative space of different size sphere packing by the complementary interlocation of small spheres in-between big spheres. There are endless iterations of placing smaller and smaller spheres, with an endless recursivity showing that the negative resulting lattice could be minimised in a big extend.

The Apollonian packing methodology combined with the Voronoi – Delanay principles has already been used in the calculation of optimum aggregates packing.

In this case the Voronoi network is a “navigation map� of the interparticle volume.

Following such packing model high bulk density can be achieved, though the most interesting point of such investigation is the fractal nature of the resulting assembly.

In order to get away from the traditional approach of searching for the optimum degree of aggregate packing for a given particle size distribution researchers developed a method of random packing. The problem is transferred on finding the best particle distribution and corresponding degree of packing. The centre of the particle is randomly placed on the grid of a cubic lattice. The generation of adjoining particles is random with a restriction of maximum and minimum size. The procedure is repeated until the cubic lattice is full.

Figure 36 shows the sequence of filling a cube by creating randomly the centre point of the adjoining sphere. The script can be adjusted in order to create tangent or intersecting spheres this way minimising the remaining interstitial space and maximising the packing density.

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fig. 37 : polymer foam ( Caroline M. Zeyfert, School of Chemistry, Durham University)

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volume limitation volume limitation

volume limitation volume limitation volume limitation

volume limitation

fig. 38 : deformation of the 2D grid

fig. 39 : deformation in 3D configuration

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The mixture of different size particle already conducts a certain complexity in the calculation of the behaviour of the components. Additionally, the complex dynamic behaviour of the cells is accentuated by the particular material that encloses the void, the latex. Elasticity and deformation studies are necessary to acquire a fundamental understanding of the collective behaviour of dislocations and point defects (figure 37, 38). Different factors need to be added to the contact point of particles such as friction, deformation, stiffness, elasticity and damping. These characteristics give specific behaviour to the simulated particle, defining considerably the final packing.

Computational simulation of the aggregates models is essential to the understanding of the inspiring structure. The forces are the basic experimental setup for the packing systems. This can be gravity, airflows or vibrations. The boundary conditions are equally important. The roughness of the walls of the colliding surface is directly affecting the friction and therefore the behaviour of the component.

Physics engines give the possibility of simulating the behaviour of complex soft body interactions, calculating with accuracy the elasticity, stiffness, deformation and friction. The simulation of various size proportions corresponding to aggregates studies give interesting results on understanding how to achieve the maximum reticulation of the concrete volume. The packing reflects the combination of three fractions of big (coarse), intermediate and small (fine) spheres.

Through these simulation, the assumption that following a recursive procedure the optimum packing can be achieved, is invalidated. The optimum packing is obtained when the proportion of dominating big spheres is applied (graph 1).

Physical models prove that the behaviour of latex balloons is digitally simulated in the closest possible precision. The speed and elastic deformation are really similar to the one captured during the execution of the physical models(figure 41). The selforganisation of the spheres is reflecting the packing that is achieved through the computational model.

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20-60-20 | 364 spheres

20-40-40 | 253 spheres

20-20-60 | 217 spheres

no pressure

14-28-56 | 537 spheres

9.83 0.43

void volume void ratio

60-20-20 | 497 spheres

40-40-20 | 382 spheres

40-20-40 | 275 spheres

9.03 0.39

8.91 0.38

no pressure

33-33-33 | 277 spheres

8.21 0.35

void volume void ratio

9.54 0.41

10.04 0.43

9.82 0.42

9.67 9.42

fig 40 : packing proportions following aggregates studies

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PROPORTIONS

PACKING 9.83

9.54

2 1

9.82 9.67

graph 1: void ratio of packing configurations

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9.67

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fig. 41 : comparison of empirical and computational simulation

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fig. 42 : interfacial transition zone

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fig. 43: micro analysis of transition zone in concrete

fig. 44 : latex sphere - no transition zone

fig. 45 : grooves on latex sphere for the creation of a transition zone

fig. 46 : micro fibres on latex sphere for the creation of a transition zone

When looking at the microscopic level into the relation of liquid paste and aggregates the complexities of the concrete structure begin to appear. It becomes obvious that the materiality of aggregates in ordinary concrete mix affects the final composition. On a macroscopic scale, it is a mixture of cement paste, fine aggregates in a range of sizes and shapes, large aggregates in a range of gradations, and various types of void spaces. At the microscopic and sub microscopic level, concrete is heterogeneous.

The paste is observed to be a mixture of different types of crystalline structures. Various behaviour of concrete under stress can be explained only when the cement pasteaggregate interface is treated as a third phase of the concrete structure. Therefore, in order to study the structural behaviour of concrete, it is most helpful to view this complex mass as a three-phase composite structure. Coherent mortar phase and fine aggregate are bonded to an aggregate phase. The aggregate phase is constituted by coarse or large aggregate. The transition zone (ITZ) represents the interfacial region between the particles of coarse aggregate and the hydrated cement paste(figure 42, 43).

In the case of packing elastic spheres the ITZ doesn’t exist since the composition of the particles is not a crystalline structure and its molecular synthesis doesn’t interact with water. Rubber material is waterproof and has the ability to repel any liquid material off its surface. The creation of a transitional zone though is possible by adding a texture on the exterior face of the particles as shown in figure (48-50). For instance, the creation of grooves on the material can trap the paste and create a second outer layer on the sphere. Micro-fibres on the particles surface can also act like hair and retain the liquid paste. Capturing the liquid paste on the particles’ skin results to a more homogenous behaviour of this new materiality.

The attempt to connect the heterogeneous materials that compose this mix is equally preventing the danger of segregation in the concrete mix. Segregation is the separation of some size groups of aggregates from the mortar in isolated locations with corresponding deficiencies of these materials in other locations. When such concentrations occur, the concrete mix proportioned on the basis of uniform distribution of all particles is no longer adequate. Aggregates packing is directly associated with the problem of segregation in concrete and many studies have been conducted on the subject.

The previous simulations show the aggregation of the elastic spheres, their association in space. The empirical knowledge gained from physical models gives a good understanding of segregation. This phenomenon can be avoided in the case of the elastic spheres. Applying pressure on the spheres helps keeping them in constant touch between them, creating a compact mix of the heterogeneous components.

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fig. 47 : components of the new materiality

fig. 48: new materiality on a shell

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new materiality

Gordon mentions in “The science of structures and Materials “, that materials with no typical mechanical properties don’t have any typical properties because the material is designed to suit not only each individual structure but each place in that structure. The adaptability of the in-between controlled system in this case is the key in the functionality of this new materiality. The size and the properties of the components of the material are adapted according to the requirements.

During the modern era of thin concrete shells, materiality was minimally investigated since the basic priority was the construction of the optimum and more challenging design. Material science gave us a better understanding of what are the possibilities of matter, revealing its inner forces and variable states. It becomes more and more a necessity to include this cognition and take it into account. It is essential to detach from the idea of material being a receptacle of form [7] and start integrating its dynamic behaviour in the design it-self.

In ‘Material Complexity’ DeLanda accentuates that the emphasis is not only, on the spontaneous generation of form, but on the fact that this morphogenetic potential is best expressed, not by the simple and uniform behaviour of materials, but by their complex and variable behaviour. It is about bringing together heterogeneous materials without trying to create any homogenization (figure 47). Creating a new materiality with undiscovered potentials that is capable to bring advanced structural solutions and new topological potential in space.

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sections showing the distribution of the reticulating components on a shell

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intertwining systems

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fig. 49 : inflation of the lower membrane - injection of noise in the system

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intertwining systems

Controlling and controlled systems influence each other in an immediate way in different timing phases of the construction process. Principles of self- organization apply during this process, since the interlocation of the particles in the agglomeration undergoes fluctuations until the system reaches a stable condition.

Ross Ashby describes the principle of self – organisation as “a dynamic system, that independently of its type or composition, always tends to evolve towards a state of equilibrium.” It is a spontaneous process of organization, the development of new complex structures takes place primarily in and through the system it-self. All parts contribute evenly to the resulting, arrangement, even if it seems that the position or size of some of them is more consequent that others. Each component self regulates its position and behaviour and simultaneously affects the adjoining ones.

The particles are packed between the two membranes using specific pouring points or injecting them with specific air pressure in order to control better their distribution and organisation. A first state of equilibrium is reached until the moment the air pressure is applied on the interior membrane (Figure 49). The output of the interstitial system is then placed in a non-equilibrium environment which has the tendency to change until it reaches its stable condition. The “noise” forces the system to deviate from its preferred trajectory and administers impending change. In a smaller extend internal variation processes - fluctuations occur also to the primary deterministic system. Due to the infusion of energy both systems will enter a transient state but the vacillation in the self-organization of the spheres is restricted from their size, initial position and potential stabilisation.

Depending on the pressure the strength of the “noise” that is injected in the packing system is different and the consequent deformation of the particles varies.

Simulations showed that the deformation of the particles is bigger on the ones that are in immediate contact with the membranes (the object that applies the force – “noise)”.

Moreover, the application of same pressure on various packing configurations showed that the bigger spheres size agglomeration shows smaller deformation comparing to the smaller ones. The material stiffness of the particles and the air pressure inside the elastic sphere is the same for all of them. The surface tension changes because of the size of the particles; this phenomenon explains how the bigger balls are stiffer and more tolerant to the forces (Figure to). .

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fig. 51 : attractors on the configuration of the concrete shell

fig. 52: vector forces creating singularities ( Open processing, http://www.openprocessing.org/sketch/34320 )

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Additional noise is injected in the controlled system when the last element of the interstitial composition is added, the liquid. Within the moments of perturbation these systems oscillate around a value until the desired state of equilibrium is reached again. The transient state is driven by attractors that pull the system into regions of dynamic state space, allowing the components to drift along fitness landscapes.[6]

The fitness landscape represents the state space; every point in the space has a certain “height corresponding to its fitness value. The attractors correspond to the local minima (potential valleys) or maxima (fitness peaks) of the potential function.

The system will always move downwards in the potential landscape. Once reached the locally lower point, all remaining will point upward. The system will be trapped and not able to leave the bottom of the valley unless another force, “noise” is injected.

In the case of the controlled systems attractors are mainly elements of the controlling upper systems. The curvature of the initial shape of the two membranes is variously altered by the form-finding methods applied according to the requirements (figure 51). Anchor points and springs may create steep changes in the geometry; these variations drive the liquid to interact in a different way according to the morphology.

The attractor forces will stop affecting the system when the pouring procedure is over and the liquid finds its way following the curvature through the interstitial space, the void that needs to be filled. In figures 53 the section of the shell is translated into a fitness landscape. The liquid follows this landscape interacting differently to the valleys and peaks formulated by the attractors.

For self-regulatory structures that are based on interactions stabilization of the system finding the balance among tensions is the ultimate goal. When the equilibrium state occurs and no more noise is injected, then according to the second law of thermodynamics the death of the system will follow. In our case the “death” is the solid state the system will secure in, the final topology, the three - dimensional concrete lattice.

6. Principia Cybernetica Web, http://pespmc1.vub.ac.be/, (accessed April 2014)

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fig. 53: liquid simulation in a box

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fig. 54: liquid simulation on a shell - the curvatures act like attractors for the liquid

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fig. 55: liquid simulation on a section of the shell

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fig. 56: liquid simulation on a section of the shell

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collision of forces

Having control and understanding over the systems human designs is one of the main quests that humanity pursues for centuries. Through evolution it became obvious that systems enclose self-organising features and therefore stochastic formations. Self - organising systems in a way combine features of control and randomness. There is definitely no deterministic procedure followed, that makes the result difficult to predict. However the behaviour of the components has patterns and qualities that are identifiable.

Identifying architecture as a set of systems starting from design to fabrication makes the procedure more predictable and descriptive. The methodology is translated into systems; therefore its combination with new innovative structures is facilitated.

These existing organizations constitute the groundwork, the vertebral bone in the creation of the nested systems. Their credibility proves to be a big advantage since they have long been tested in architecture. They are the foundation for the investment in a new conceptual procedure that has high probabilities to be successful.

One of the well-established systems in architecture is this of the thin concrete shells. The design and construction methodologies can be translated into predetermined arrangements and used as a tool for further investigations. The highest potential of concrete shells hasn’t been reached yet. The conceptual stimulus for a new approach results from the collision of the intellectual problematic of interstitial space with new research and methodologies. As the questions on interstitial space and its spatial status expand, the space it - self expands and claims its rightful territory.

“Hence, we may need to nurture again our ability to deal with variation as a creative force, and to think of structures that incorporate heterogeneous elements as a challenge to be met by innovative design.” [7]

There are various emerging methodologies that wait to be absorbed into an architectural potentiality. For the conception of the thick concrete shell the complexity of a new heterogeneous materiality is translated into a system as well and incorporated in the already classified methodologies in architecture. It represents an innovative force that is injected in the structure. The entwining systems represent a well – greased machine. It has the ability to assimilate the assorted composition of the systems’ components into a highly controlled design procedure.

Preceding Architectural accomplishments are actually a catalogue of systems more accurately a hibernating archive of systems, this must be assimilated. They are the stable foothold for the next steps and a solid receptacle for new experiments.

6. De Landa M. (1995) ‘Uniformity and Variability: An Essay in the Philosophy of Matter’ , Doors of Perception 3: On Matter Conference, Netherlands Design Institute, Amsterdam, Holland, 07-11.11.95., pp7

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bibliography 1. Abramovitz R., von Foerster H. (1995) “Cybernetics of cybernetics: or, The control of control and the communication of communication.” Minneapolis: Future Systems, Inc. 2. Anishchik, S. , Medvedev N. , Three-Dimensional Apollonian Packing as a Model for Dense Granular Systems, Physical Review Letters, v. 75, Issue 23, pp. 4314-4317 3. Burmakin E., Course at Helsinki University of Technology “Architecture of Complex Systems“, 15 January 2003, http://neocybernetics.com/report145/Chapter4.pdf 4. Chilton J.(2000) “Heinz Isler / John Chilton.” London: Thomas Telford 5. Dewar J. D. (1999) “Computer modelling of concrete mixtures.” London: E & FN Spon 6. De Landa M. , “ Material Complexity”, Digital Tectonics, (presentation at University of Bath, UK, (02.03.02) 7. De Landa M. (1995) “ Uniformity and Variability: An Essay in the Philosophy of Matter” , Doors of Perception 3: On Matter Conference, Netherlands Design Institute, Amsterdam, Holland, 07-11.11.95 8. Dubberly H. , Pangaro P., “Cybernetics and Service-Craft: Language for BehaviorFocused Design”, Kybernetes: The International Journal of Systems & Cybernetics, v.

36, No. 9-10. (2007) 9. Digicult, http://www.digicult.it/, ( July 2014) 10. Gordon J.E. (1988) “The science of structures and Materials.” New York : Scientific American Library 11. Herzog T. (1977) “Pneumatic structures : a handbook for the architect and engineer.”

London : Crosby Lockwood Staples 12. Mohammed M. H. , Pusch R. , Nadhir Al-Ansari, S. Knutsson, “Optimization of Concrete by Minimizing Void Volume in Aggregate Mixture System“,Journal of Advanced Science & Engineering Research;Sep2012, Vol. 2 Issue 3 13. Heylighen F. , “ Cybernetics and second order of Cybernetics” , Encyclopaedia of physical science & technology 4, (Academic Press, New York, 2001)

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14. Otto F., Rasch B., Schanz S., (1995) “Finding Form: Towards an Architecture of the Minimal.” Germany : Axel Menges 15. Principia Cybernetica Web, http://pespmc1.vub.ac.be/, (accessed April 2014) 16. Pask G. , “ The Architectural Relevance of Cybernetics”, Architectural Design , v.39 (Sept.1969) 17. Pask G., “ Heinz Von Foerster’s Self Organisation, the Progenitor of Conversation and Interaction Theories ”, System Reasearch, v.13 N 3 (1996) 18. Smith C. S. (1968 ) ‘Matter versus Materials: A Historical View’. In: Science162 19. Sobolev K., Amirjanov A., Hermosillo R. , Lozano F.,” The Modelling Of Dense Packing Of Aggregates As An Approach To Optimizing The Proportioning Of Concrete Mixtures”, International Centre for Aggregates Research (ICAR) 2004 12th Annual Symposium Research Papers 20. Sonja A.A.M. Fennis, Joost C. Walraven, “Using particle packing technology for sustainable concrete mixture design” HERON Vol. 57 (2012) No. 2 21. The Architectural Review, http://www.architectural-review.com/, (April 2014) 22. Weiner R. (1950) “The human use of human Beings : Cybernetics and society.”

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figures fig. 1: Algeciras Market Hall, Algeciras, Spain, 1934. http://anengineersaspect. blogspot.co.uk/2012/09/42-eduardo-torroja-y-miret-structures.html fig. 2 & 3: Restaurant los Manantiales, Mexico City, 1958. http://mcis2 princeton.edu/candela/works.html fig. 4:Deitingen Service Station, Solothurn Switzerland, 1968. http://blog buildllc.com/2009/04/heinz-isler-a-few-important-things/ fig. 5:CNIT, La Defense, Paris, 1958. http://www.pinterest.com/ pin/314829830172544674/ fig. 6:ouroboros, symbol of circularity http://www.presidentsmedals.com/Entry-12420 fig. 7: Toyo Ito, Meiso no Mori Municipal Funeral Hall Kakamigahara-shi http://www.ccaa.com.au/sub/cplusa/articles issue/10/meiso-no-mori-crematorium/ fig. 8: Toyo Ito, Meiso no Mori Municipal Funeral Hall Kakamigahara-shi http://openbuildings.com/buildings crematorium in-kakamigahara-profile-45079 fig. 9 : thin and thick shell, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 11: thick shell funtions, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 12: Designed Particles Aggregations ( Eichi Matsuda, Uniy 4, AA London) http://www.achimmenges.net/?p=4403 fig. 13 : configuration with light ( Eichi Matsuda, Uniy 4, AA London) http://www.achimmenges.net/?p=4403 fig. 14: functional organization of a living organism ( Rodney Clough) , http:/ ada.evergreen.edu/~arunc/texts/cybernetics/heinz/constructing/ constructinghtml fig. 15:ouroboros, symbol of circularity of multiple systems, http://www.presidentsmedals.com/Entry-12420 fig. 16:single membrane with additional linear support. Herzog T. (1977) ‘Pneumatic structures : a handbook for the architect and engineer.’ London : Crosby Lockwood Staples.pp 26 fig. 17:membrane guyed with aditional linear elements - Frei Otto. ibid pp. 106 fig. 18 & 19: stabilised membrane with additional linear support - Frei Otto. ibid. pp 25 fig. 20 & 21: multiplicity of possible design s - Frei Otto. ibid. pp 100 fig. 22 : physical model - form - finding method - springs, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 23 : form finding methods, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014

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fig. 24 : parametrically defined form finding methods, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 25 :sketch fo Bini system construction method (Dante Bini , 1965), http://www.architectural-review.com/essays skill-inflatable-concrete-domes/8641827.article fig. 26-29: bini shell construction process (The Architectural Review, January 2013, www.architectural-review.com ), http://www. architectural-review.com/essays/skillinflatable-concrete-domes/8641827.article fig. 30: definition of the 1st and 2nd membrane, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 31: geometrical definition of the two membranes, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 32: controlling and controlled system, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 33 : close hexagonal and cubic packing, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 34 : studies on optimum packing density for the creation of sustainable concrete mixture, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 35 : apollonian gasket 3D packing - reticulation of a sphere volume, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 36 : random generation of spheres - processing script, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 37 : polymer foam ( Caroline M. Zeyfert, School of Chemistry, Durham University), S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 38 : deformation of the 2D grid, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 39 : deformation in 3D configuration, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig 40 : packing proportions following aggregates studies, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 graph 1: void ratio of packing configurations, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 41 : comparison of empirical and computational simulation, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 42 : interfacial transition zone, http://ciks.cbt nist.gov/garbocz/paper95/node2.html

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fig. 43: micro analysis of transition zone in concrete,http:// faculty.washington.edu/nemati/ fig. 44 : latex sphere - no transition zone, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 45 : grooves on latex sphere for the creation of a transition zone, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 46 : micro fibres on latex sphere for the creation of a transition zone, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 47 : components of the new materiality, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 48: new materiality on a shell, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 49 : inflation of the lower membrane - injection of noise in the system, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 50 : levels of deformation according to the pressure, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 51 : attractors on the configuration of the concrete shell, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 52: vector forces creating singularities, Open processing, http://www.openprocessing.org/sketch/34320 fig. 53: liquid simulation in a box, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 54: liquid simulation on a shell, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014 fig. 55 & 56: liquid simulation on a section of the shell, S.Sifakis, I.Kuzu, C.Zaccagnini, GAD M.Arch 2013-2014

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The question about the definition of the interstitial space is introduced into the conceptual reflection on concrete shells. The in-between space is no longer considered a residue – an inevitable consequence of other interactions.

The predictive and explanatory power of Cybernetics leads the investigations and the experiments for the creation of a thick concrete shell. The thick concrete shell is the result of the combination of existing and innovative systems. Controlling systems shape the space configuration according to variable architectural requirements, defining the size and geometry through a parametric highly controlled procedure. Controlled systems formulate the void, carving away material from the concrete volume, resulting in a new material topology this of a reticulated three - dimensional concrete lattice. These entwining systems inject new methodologies to the design of concrete shells fuelling the process in an architectural and material level.

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