Design, Robotic Fabrication and Augmented Construction of Low-Carbon Concrete Slabs Through Field-Based Reaction–Diffusion

Abstract

Constructions have a tremendous impact on global warming and are responsible for 39% of annual carbon emissions. Designers will increasingly focus on developing design methods and solutions that mitigate the impact of buildings over the next few years. Accordingly, this chapter focuses on developing an accessible computational design method to investigate the design, engineering and construction of ribbed concrete slabs with low levels of embodied carbon by minimising the use of structural materials, maximising bending resistance and surface area for recarbonation through convoluted geometry. We discuss using a Reaction–Diffusion system for performance-driven generative structural design, informed by the outputs of Finite Element Analysis in the form of scalar and vector fields. To streamline the production of geometrically complex slabs, a field-based robotic milling approach is introduced to process styrofoam concrete formworks. Mixed Reality is used to assist construction operations and realise non-standard rebar reinforcements. The results consist of proof-of-concept ribbed-slab prototypes characterised by structural efficiency, high resolution, and low-machining time.

1 Introduction

The climate emergency has radically shifted our architecture, design and construction priorities. The mitigation of climate change is a fundamental planetary goal for the survival of our ecosystem [14]. As a reflection of this, the design focus for architects and engineers is moving towards reducing embodied carbon associated with the life cycle of building materials and structures. Carbon dioxide emissions (CO2) from the manufacturing process of buildings, including material extraction, transportation, fabrication, installation, operations and end-of-life, account for 49% of the total carbon emissions from new construction [18]. Among all building materials, concrete is still necessary to fulfil the need for construction over the following decades, already being the most used material in the world after water [19]. This extensive use of concrete significantly impacts GHG, being responsible for about 8% of global emissions [7]. Replacing structural concrete with more sustainable materials is currently not a realistic and scalable option. Designing novel structures requires embodied carbon reductions through advanced design optimisation in this context. Contemporary Construction 4.0 technologies offer vast opportunities for achieving such a goal [13]. In particular through the combined use of (i) data-driven generative design; (ii) computationally-driven design to fabrication workflows that enable strategic use of building materials; (iii) smart digital twins that streamline robotic construction and Mixed Reality (MR and enhance the level of functional integration across phases. This chapter discusses integrating such features in the context of advanced structural geometry, characterised by high material efficiency and low embodied carbon.

2 Carbon-Driven Design for Horizontal Structures. Precedents and State-Of-Art

Horizontal structures, such as slabs, beams and roof elements that carry perpendicular loads to their longitudinal direction, constitute about 43% of the total use of structural concrete in buildings [3]. Minimising such structures' carbon impact is critical in achieving sustainable construction, as recent studies have documented [6, 9, 10 ]. At SDU CREATE, we conducted a study on the cradle-to-cradle life-cycle assessment of 3D concrete printed beams [8], where we formulated a design strategy for achieving carbon-efficient design: maximising bending resistance, minimising the use of material (reduction of cement and steel reinforcement), maximising the surface area of concrete for recarbonation [5]. This design rationale provides a framework for exploring geometrically convoluted ribbed slabs, where material and structural efficiency is synergistically tackled. Historically, the design of such structures has been studied in connection with the use of Principle Moment Lines (PML). In 1951, Pierluigi Nervi designed the wool-factory building Lanificio Gatti, where a pre-compressed concrete slab was reinforced using ribbed reinforcements along the direction of primary and secondary PML [1]. A similar approach was later used to design the zoology hall at the University of Freiburg, a large-span building that was efficiently constructed with this principle [2]. More recently, the integration of Finite Element Analysis (FEA) and parametric modelling environments has allowed more accessible access to such structural patterns. However, existing workflows do not support a straightforward translation of structural analysis into structural shapes. In a recent study, we demonstrated a method to generate lightweight 3D concrete printed beam elements using PML to inform the planning of a continuous printing path. Tan and Muller (2015) developed an approach to overcome common software's inconsistent generation of stress and moment lines. In this chapter, we focus on an alternative approach, where PML and other structural analyses inform the emergent shape generation of ribbed slabs, leading to an interactive exploration of efficient structural patterns.

3 Approach and Methods

One of SDU CREATE´s areas of expertise is formulating computational workflows for carbon-efficient design. The opportunities for data-driven structural morphogenesis based on FE have been discussed in multiple studies from SDU CREATE [4, 11, 12]. To render such investigations more accessible, we recently conceived a field-based approach for automating the design and fabrication of concrete slab structures (Fig. 1).

Fig. 1

Software pipeline for field-based design and fabrication of concrete ribbed-slabs

This approach analyses structural, morphological and functional properties with a set of 2D plots. These are collected as multilayer performance maps, representing scalar and vector fields. We introduce a Reaction–Diffusion (RD) system to read, interpret and react to such fields and output the underlying patterns to generate three-dimensional ribbed slabs. This avoids inflexible parametric modelling operations, which limit the exploration of topologically diverse design options.

4 Simulation and Field-Based Design

4.1 Generation of Structural Fields

A computational design pipeline was developed to explore different loading and support scenarios for a 20 by 10 m rectangular slab. Starting from given input 2D shapes, the loading and support boundary conditions, and given material properties, a linear FEA was run using Karamba for Grasshopper [15]. The analysis includes primary and secondary PMLs, intensity, and sign information. Moment principals show the direction of the highest and lowest moment of inertia along the analysed surface. Through a custom exporter which translates mesh face properties into RGB colours, a series of 2D maps were stored for the following steps of the design workflow: (i) two maps of primary and secondary moment vectors directions, where the red (R and (G channels correspond to X and Y directions of the vectors; (ii) two grayscale scalar maps showing the absolute values of the moment intensities; (iii) two grayscale scalar maps outlining the sign of the principal moments, i.e. whether it is positive or negative (Fig. 2). The analyses were applied onto two different slab cases: (01) four-point supports placed at an offset from the perimeters; (02) two diagonal linear supports evenly placed along the two axes of the rectangular slab. Both elements are calculated with their self-load and a distributed load equivalent to 6 kN/m².

Fig. 2

Slabs’ boundary conditions and field maps for the primary and secondary PML

5 Isostatics Structural Patterns with Reaction–Diffusion

In this phase, structural patterns for a ribbed slab are found with a Reaction–Diffusion (RD) system. In conventional structural design, topology and load paths for a ribbed slab are determined case by case using parametric modelling with relatively low flexibility. In our approach, an RD system was developed as a generative tool for quickly and interactively exploring isostatic structural patterns which adapt to the provided input fields. RD algorithms reproduce the chemical reaction of two or more substances spreading along a surface at a different rate [17]. When in contact, the two substances react by altering their concentration values. An anisotropic version of the Gray-Scott model was deployed to describe the variation over the time of the two substances according to parameters F and k, representing respectively the feed and kill values:

$$\begin{gathered} \frac{\partial A}{{\partial t}} = Diff_{A} \nabla^{2} A - AB^{2} + F\left( {1 - A} \right), \hfill \\ \frac{\partial B}{{\partial t}} = Diff_{B} \nabla^{2} B - AB^{2} + \left( {F + k} \right)B. \hfill \\ \end{gathered}$$

The variation of these parameters generates a highly varied range of patterns, including continuous, closed cellular, maze-like networks, and dotted configurations (Fig. 3). In this work, the growth of an RD is controlled using input fields from the preliminary structural analysis and general design to manufacturing considerations. In particular, the system needs to allow (1) the control of the directionality according to principal moments direction; (2) the variation of density according to moment intensity; (3) the dimensional control of individual rib elements according to construction and fabrication constraints. To do so, vector maps describing the principal moment curves and the scalar map of moment intensity were used to control the direction (laplacian) and diffusion rate of a pattern (F, k, and scale), respectively, obtaining anisotropic and variably dense patterns that were used as structural geometry (Fig. 4).

Fig. 3

Emerging RD patterns from variations of F and k parameters

Fig. 4

Comparison between isotropic and anisotropic growth in the employed RD

Using a Graphical User Interface (GUI), the students were to experiment and generate different patterns according to input images and tune the pattern scaling. The process was applied for primary and secondary principal moments to generate perpendicular ribs. Additionally, secondary design elements such as holes can be explored using additional grey-scale fields, controlling F and k, or used as an inlet or outlet for one of the two substances. With this exploration phase, recurrent patterns have been identified.

The anisotropic RD behaviour converges to some dominant configurations according to the parameters F and k. Independent longitudinal structural elements and a network of longitudinal structural elements (they could also be seen as one the negative of the other). For structural continuity, the network is considered a more convenient choice (Fig. 5).

Fig. 5

Selected ribbing patterns for RD Slab 01 (two ways) and RD Slab 02

6 Multi-field Design Compositing

In this phase, the three-dimensional geometry of ribbed slabs was obtained by combining the previously collected information layers. Scalar 2D maps representing design elements, structural data, and RD patterns are combined into a single height map with a compositing method for generating the slab geometry. The RD pattern was used to create a series of ribbed elements in the slab´s bottom surface to resist the tensional component induced by the bending moment. The ribs´ cross-section shape was tuned mathematically through function curves according to the size of reinforcements and needed concrete cover. The ribs´ sectional height (H) for the primary ribs was parameterised according to the moment intensity (I) to obtain a sufficient moment of inertia for any given point moment in the slab without the need for additional steel reinforcements. This is achieved with the following formulation H = RD*I*T. For the case of a two-way ribbed slab, the secondary ribs´ sectional height was parametrised on a different layer. Afterwards, the information on the cross-section height for primary and secondary ribs was combined using the maximum value at every point of the slab: h = max(h₁, h₂). The map-based compositing for the supports provided a mathematical control for the transition among the various slab parts (Fig. 6).

Fig. 6

The variable geometry of the slabs is controlled by the combined values of various maps

7 Structural Feedback and Simulation

Volumetric FEA was run in Abaqus to verify the outcomes of the design optimisation process and compare them to non-optimised slabs with the same boundary conditions and weight. The analysis tested the slabs at their Ultimate Limit State (ULS) for a distributed load of 6 kN/m². The two slab prototypes proved a reduction of the weight-to-displacement ratio of 33 and 37.5%, respectively.

8 Robotic Fabrication and Augmented Construction

8.1 Field-Based Robotic Milling of Complex Molding

Robotic CNC milling was used to manufacture styrofoam moulds bypassing conventional CAD/CAM processors. Various milling strategies were developed parametrically and tested for 7-axis robotic milling to minimise the processing time. Two main strategies were investigated. In the first one, the heightmap obtained from the multi-layer compositing method was used to determine tool orientation, density/resolution of the machining steps and the nature of robot motion (e.g. continuous/punctual). On the other hand, the second strategy started from a mesh geometry generated from the compositing, which was further processed to achieve different surface finishing patterns. The tool was oriented vertically, while angle and milling resolution were the focus parameters in the contouring method. Initial toolpath explorations involved small-scale experiments performed on 20 by 20 cm specimens, which were evaluated in terms of production time, kinematics, and visual features. Five methods were studied: (1) punch-milling with variable tool inclination and punch depth informed by the composited maps (Fig. 7a); (2) blading through a path informed by the composited maps (Fig. 7b), and through the same path manipulated with sinusoidal function; (3) parallel contouring following 45 and 90 degrees angles with different milling resolution/overstep distance (3-8 mm) (Fig. 7c) and manipulated toolpath by application of sinusoidal functions along Z and XY plane orientations; (4) geodesic offset contouring to optimise the milling resolution in relation to the geometry and (5) perpendicular contouring to the structural ribs, performed as a continuous zig-zag toolpath. After these initial tests, the geodesic offset contouring and perpendicular contouring strategies were selected to fabricate the two slabs on a scale of 1:10. They have been considered a mid-way solution between the faster toolpaths, which compromised geometric complexity and formal precision such as blading, and highly detailed but time-consuming punch-milling tool-paths.

Fig. 7

Top−Robotically fabricated styrofoam formworks with different milling strategies; Bottom−Cast concrete panels

RD Slab 01−Geodesic offset contouring. A shell mesh geometry was used to generate geodesic contours with a 10 mm offset, originating from the support points and propagating towards the centre of the slab. The obtained three-dimensional curves are then translated into robotic target frames with a point distance of 5 mm (Fig. 8).

Fig. 8

Left: Robotic toolpath for geodesic offset contouring of RD Slab 01 and mesh visualisation of the milled EPS formwork; Right: Image of the milled EPS formwork

RD Slab 02−Contouring perpendicular to structural ribs. For the second slab, the medial axis of each structural rib was extracted from the Voronoi skeleton of the RD pattern. For each region, it is then created a continuous zig-zag pattern perpendicular to the medial axis following the ribs’ slopes. The distance between the perpendicular milling paths was set to 10 mm, along which robot target frames were generated at a distance of 5 mm, keeping the same resolution settings as the first slab (Fig. 9).

Fig. 9

Left: Robotic toolpath for the contouring perpendicular to structural ribs of RD Slab 02 and mesh visualisation of the milled EPS formwork; Right: Image of a milled EPS formwork

9 Mixed Reality Bending of Reinforcement Bars

Although the provision of reinforcement bars was not necessary according to the FEA, minimal longitudinal and transversal reinforcement was included to obtain ductile structural behaviour. This was achieved by placing (i) one 4 × 50x50mm BST-500 mesh and (ii) 6 mm B550 reinforcement bars. The reinforcement layout for the individual bars was derived from an analysis of tensional areas of the RD structural patterns. This resulted in a complex three-dimensional curve network. MR allowed the user to bend and check the individual reinforcement bars quickly, a crucial pre-assembly step to ensure that parts fit together as intended. Mixed Reality (MR) was adopted to efficiently achieve the accurate bending of 3D rebars, which was manually executed with the help of a manual rebar bending device (Fig. 10). Bending sequences were communicated to users wearing a Microsoft HoloLens 2, which was a guide for manually bending the bars into their positions.

Fig. 10

Three-dimensional rebar bending in MR

10 Robotic Fabrication and Concrete Casting

The used robotic setup is a KUKA KR240 R3330 industrial robot installed on a six-metre long linear unit equipped with a 12 kW rotary spindle holding a foam rasp cutter of 20 mm diameter and 300 mm length (Fig. 11). The formwork consisted of two glued 1200 × 1200  ×  275 mm EPS 150 blocks. It was laterally restrained to a steel welding table. Both formworks were fabricated with a spindle speed of 4500 RPM and a feed rate of 450 mm/s, resulting in an average fabrication time of around four hours. The milled formworks were lightly sanded to remove residual burrs and to prepare the surfaces for applying protective coatings. A single layer of a water-based paint primer was sprayed onto the milled surface. This provided a smooth surface for applying a wax release agent and waterproofing the formwork for the casting process.

Fig. 11

Robotic milling of the styrofoam formworks for RD Slab 01

Once the surface dried, the formwork was prepared for casting by installing the bent rebars (Fig. 12), steel mesh and other 3D-printed connections for transportation. Both slabs were cast with Hi-Con UHPC having a characteristic compressive strength (F_ck) of 127 MPa. The material was prepared in 300-L batches and mixed for six minutes before being poured into the formwork. The self-compacting properties of the concrete ensured that the intricate details of mould were covered in concrete without vibration. The prototypes were left to air-cure for approximately 24 h before being de-moulded.

Fig. 12

Coated formwork of RD Slab 01 with 3D bent rebars in MR

11 Results and Discussion

Reducing embodied carbon in reinforced concrete structures is a priority for architectural designers and engineers nowadays. Radical design approaches are required to achieve sustainable targets at a global scale. Construction 4.0 principles and technologies are supporting this paradigm shift by: (i) enabling the automation of complex design operations; (ii) promoting data-driven design with early-stage structural analysis to embed fundamental engineering notions at the concept level; (iii) introducing generative design methods to effectively explore efficient design solutions; (iiii) computational design and fabrication tools becoming more accessible to architects, structural engineers, integrated designers, construction engineers.

The chapter discusses these topics, focusing on experimental activities conducted for designing and engineering ribbed concrete slabs. Several innovative features were presented. Anisotropic RD was employed for the first time to explore structural patterns interactively. Scalar and vector fields in the form of image maps were used to exchange performance data across simulation and modelling software in a synthetic format and drive structural and milling explorations. A software pipeline that connects structural analysis, generative design, robotic fabrication, and MR construction was presented. The pipeline was developed and tested during the SDU CREATE´s summer school in Experimental Architecture (2022) with students from architecture, civil engineering, integrated design, and mechanical engineering who could easily engage with complex design/engineering and fabrication tasks. Two scaled prototypes (Fig. 13) were engineered, manufactured, and successfully tested with non-linear FEA and non-destructive structural tests. The outputs show a previously unseen ribbed slab typology, which combines material and embodied carbon reduction with distinct aesthetics. Future work will further investigate the opportunities this approach opened, including an evaluation of its acoustics behaviour for future construction applications.

Fig. 13

Close-up view of RD Slab 01 (left) and global view of RD Slab 02 (right)