7.1. Introduction

Widely developed over the last two decades, additive manufacturing (AM) through the three-dimensional concrete printing (3DCP) of structural elements represents an important step in the automation process of the construction industry. This innovative technique makes it possible to build structures with a high degree of geometric freedom, saving materials and reducing costs and delivery times, compared with traditional construction methods.

In the 3D printing process, the preparation of the geometry of the printed structure, the choice of the material formulation (especially cementitious) and the configuration of the printer with the process parameters are an essential first step before manufacturing. According to this procedure, the digital prototype based on computer-aided design (CAD) of the printed structure is a prerequisite. This virtual geometric model is then transformed into a standard format and cut into layers before being manufactured by the printer. Implementing the programs that control the trajectories and speed of movement of the printer (e.g. the robots) in the digital tools is the primary task in this preparation stage.

Due to the novelty of this technique, there is still a lack of knowledge concerning the specific relationships between design, material and process parameters. Indeed, these parameters interact strongly and significantly influence the quality of the manufactured product. The first attempt to find the optimum 3D printing parameters for a given design is based on a trial-and-error approach using a range of print speeds, printed layer dimensions and material composition. However, as soon as the design changes, or new materials become available, this costly procedure has to be restarted, and the print parameters modified as required. Consequently, such an approach limits the development and application of 3D concrete printing on a large scale in practice. If this layer-by-layer manufacturing technique is to be competitive with concrete casting, it must enable a reduction in manufacturing cost and time, without compromising the geometric freedom and structural safety of printed objects. So, alongside the development of geometric modeling and virtual printing simulation tools, it is necessary to integrate 3D printing process modeling into this numerical approach to predict the behavior of deposited layers and structural failure during fresh concrete printing – a phenomenon frequently observed in several trials. In fact, the ability to anticipate the risk of failure of the printed structure thanks to digital modeling in the design phase means that an appropriate layer size and printing speed can be chosen beforehand. During the printing process, these numerical predictions can be updated to enable the right strategy decisions to be made, as well as updating the printing parameters to maximize the success of this innovative construction technique.

The main aim of this chapter is to present an overview of the tools, approaches and recent results of numerical modeling in the field of 3D concrete printing. After summarizing digital tools for geometric modeling and virtual printing, we will detail the state of the art in digital modeling of the 3D printing process. This final section focuses on both the structure and the deposited layer. Finally, after a discussion of recent advances and existing limitations, some potential avenues are presented to guide future research in this field.

7.2. Designing the geometric model of a virtual object

The AM process for concrete structures involves several stages, from the design of the geometric model of a virtual object to the production of the real object and its finishing for commissioning (Abdulhameed et al. 2019). The first step is to design a model using 3D drafting software, respecting the specifications required for the design of the object to be created. Converted into an STL (stereolithography or standard tessellation language) format, this 3D model is then cut into layers and each layer translated into consecutive motion commands using a specific language such as G-Code, which is familiar from CNC (computer numerical control) milling. This code provides the printer with instructions on the path of movement (or tool trajectory) and the corresponding speeds of the printing process. The second step is to configure the machine and prepare the necessary materials before starting production. The final step is to evaluate the printed object in terms of its visual appearance and performance. If quality requirements are not met, adjustments may need to be made to the digital model, machine or materials.

Digital tools offer a variety of functionalities that facilitate the design of innovative structures through AM. A parametric approach, for example, has been adopted at Loughborough University, enabling great adaptability of the parameters involved (robot movement speed, printed layer size) in the concrete 3D printing process (Wolfs 2015). This approach has proved capable of identifying the relationships between these parameters automatically using the simulated annealing optimization technique. For this purpose, a script is fully generated in Grasshopper, a graphical algorithm editor, which is a plugin for Rhinoceros (McNeel 2010), including all printing parameters (material properties, geometry and loads). This script is then sent to the calculation software, which is controlled by the Python programming language. Using the script created by Grasshopper, Python controls the execution of both the structural analysis during 3D printing and the algorithm for optimizing printing time and the quantity of concrete used. Various research projects have made use of this methodology, such as the work of Lim et al. (2016), where Grasshopper was successfully used to generate curved layered print trajectories and transfer them to the robotic arm to print the designed model.

In the context of the construction sector’s move toward digitalization, the integration of BIM (building information modeling) with 3D printing activities has become a challenge for many research efforts. BIM is an in-depth approach to building construction management that covers all phases of the construction lifecycle, from planning to construction and eventually maintenance (Eastman 2011). It encompasses essential information such as geometric data, resources, equipment, materials and manufacturing data (Wu et al. 2016). Consequently, implementing a BIM-based additive construction procedure can significantly reduce turnaround times. For example, it can facilitate the immediate application of design changes to 3D printing in construction (Ding et al. 2019). In addition, BIM’s ability to store and organize data relating to material delivery, printer control and finishing operations can be used to fully automate the process (Tay et al. 2017; Teizer et al. 2018).

An optimized approach that streamlines the use of BIM in the 3D printing process is proposed in Anane et al. (2021). The suggested approach consists of a tightly coupled approach from BIM software realized using the Rhino.Inside.Revit plugin (Vandezande et al. 2012). The print script is developed in Rhinoceros using Grasshopper, since it is much more widely used in the digital manufacturing environment. Consequently, the print simulation and command lines are instantly generated with Rhino.Inside.Revit, that is, Rhino running in Revit’s memory space. The Speckle plugin can be used for collaboration between different stakeholders in a project and will be used to transmit geometric information and exchange print data in real time between the software it supports. The augmented reality representation of 3D printing simulation could be used by Fologram, a real-time connection between mixed reality devices and Rhino and Grasshopper (Fologram for Rhino and Grasshopper n.d.; https://www.food4rhino.com/en/). The result of this process illustrates the simultaneous visualization of the developed 3D print model in four columns from left to right: in Rhinoceros, Revit, Speckle web viewer and in augmented reality, thanks to Fologram. However, this approach still has certain limitations when it comes to mesh transfer, since 3D printing is based on meshes, which are often data intensive.

7.3. Digital modeling of the 3D printing process

Numerical modeling of the 3D concrete printing process is a complex task, involving the prediction of the behavior of components and/or the entire concrete structure during printing. Indeed, to accurately model the entire printing process, the numerical study must be carried out at two critical levels of the process: the material deposition level at the deposited layer scale and the printed structure level. However, modeling the behavior of fresh concrete during the printing process, whose nature varies from a viscous fluid state (as in the extrusion and material deposition steps) to a solid state after deposition of the printed layers, presents a first obstacle. Furthermore, from a numerical point of view, simulating behavior from the material to the structural scale is very costly and always presents a major challenge for engineers and researchers. Consequently, there is no universal model in the literature to represent the behavior of fresh concrete, and numerical modeling of the 3D printing process is very often carried out separately at each scale. For the purposes of this chapter, we will limit our synthesis to the two scales aimed at predicting structural stability (i.e. buildability) during 3D printing and behavior at the deposited layer scale.

7.4. Discussions on recent advances, limitations and future research directions

The growing involvement of the academic and industrial sectors in the field of 3D concrete printing is gradually addressing the specific technical challenges associated with this innovative construction process. As previously presented, the numerical modeling tools developed have made it possible to detect and predict various failure modes throughout the printing process, whether they occur at the scale of a printed layer or of the entire structure. Numerical modeling has proved to be a valuable option for optimizing the 3D printing process, as it enables a systematic assessment of the influence of the entire range of materials, geometric parameters and process parameters.

Accurate prediction of structural behavior during printing relies on understanding each parameter involved in printing, such as material behavior and properties, geometric features and the printing environment. For example, the numerical study of the buckling of a 3D-printed structure by Wolfs et al. (2018), considering the time-dependent MC elasto-plastic behavior of the material, overestimated the printed heights before failure. The authors explain that compacting the material prior to the experimental tests (unconfined compression and direct shear tests) can lead to an overestimation of the material properties, which in turn can lead to an overestimation of the height before failure and an underestimation of the lateral deformations. Furthermore, in Wolfs and Suiker (2019), numerical predictions lose accuracy due to the influence of thermal heating of the 3D printer during the long printing process, which has not yet been incorporated into experimental characterization or numerical analyses.

Deviations between predictions and print tests can also be explained by various sources of uncertainty, such as uncertainties in material property measurements, imperfections or spatial variation in the geometry (e.g. width, thickness and position) of deposited layers, which are neglected in predictions. According to the results of experimental tests (such as the uni-axial compression test and the direct shear test) carried out by Wolfs et al. (2018), a non-negligible dispersion in the shear strength and Young’s modulus of concrete at young age was noted, where a coefficient of variation (COV) of around 20% was indicated for each parameter. This uncertainty is linked to the heterogeneous nature of mortars and the transition state from fresh concrete (viscous fluid) to solid state, which is extremely difficult to accurately characterize. In addition to the uncertainty in material properties, Suiker et al. (2020) have also shown that the eccentricity of printed layers can significantly affect elastic buckling failure during printing.

Until now, the analysis of the behavior of the printed structure has been based on a deterministic problem using mean values of fresh concrete properties calibrated from laboratory tests. Variations (or uncertainties) in these properties are neglected, while a perfect rectangular cross-section of the layer is considered, ignoring the geometric imperfections that occur during deposition. Furthermore, in most cases, numerical tools are used to predict the behavior and especially the heights before failure of the printed structure, but they are not yet exploited for their capabilities and potentials, particularly in optimizing the 3D concrete printing process. The first attempt to take into account the uncertainty of fresh concrete properties in buildability analyses and 3D printing process design optimization can be found in Kruger et al. (2020). In this contribution, the authors used the probabilistic approach such as the first-order reliability method (FORM) to assess the impact of the large variation in material properties ignored by the classical deterministic design model. The optimal solution for layer thickness and printing speed was determined in order to minimize printing time. However, this latest study only considers the plastic failure mode, and the elastic buckling phenomenon is not addressed.

In this context, Diab’s thesis (Diab 2023) was carried out within the Lamé laboratory, as part of the European Interreg CIRMAP project (CIrcular economy via customizable furniture with Recycled Materials for public Places). In this research work, a comprehensive reliability analysis procedure was developed with the aim of enhancing the predictive capability of numerical simulations and increasing their applicability in optimizing the 3D concrete printing process (Diab et al. 2023, p. 202). More specifically, the analyses carried out by stochastic modeling make it possible to estimate the probability of different failure modes of concrete structures during the printing process, taking into account various uncertainties, such as those of the mechanical properties of fresh concrete. In the proposed procedure, uncertainties must first be quantified. For example, in the contribution by these present authors (Diab et al. 2022), the probabilistic inversion technique based on Bayesian theorem was adopted to quantify uncertainties in the elasto-plastic behavior of fresh concrete. Based on the uniaxial compression and shear test results of Wolfs et al. (2018, p. 20), Bayesian inference is used to determine the a posteriori statistical distribution of five parameters that characterize the structure’s two failure modes during printing (i.e. plastic failure and elastic buckling), as illustrated in Figure 7.1.

The results of the uncertainty quantification step are then used as input data for stochastic modeling of the printed structures. While the Monte Carlo simulation (MCS) approach is widely known as the benchmark for reliability analysis, it nevertheless requires a very large number of direct evaluations of the structure’s response, which is numerically very costly. To reduce the considerable time required for these stochastic analyses, the MCS can be combined with a model reduction technique developed on the basis of machine learning. Recently, in contributions by the present authors (Diab et al. 2022, 2023), the combination of the Kriging meta-modeling technique with MCS has been adapted to the field of 3D concrete printing. The main idea of this technique, named AK-MCS, is to iteratively build the response surface of the structure on a very reasonable number of samples of random parameters (i.e. the five mechanical property parameters of fresh concrete). In each iteration, the estimation of the probability of failure of the structure by the MCS can be easily achieved by interpolating the results of the constructed metamodel. After each iteration, a new, more appropriate sample of random parameters is added to reconstruct the metamodel. This AK-MCS stochastic modeling procedure continues until the estimated probability converges. As an example, Figure 7.1 shows the results of deterministic modeling and stochastic analysis of a straight concrete wall during printing. The availability of the analytical solution in this case of a simple structure (Suiker 2018) validates, on the one hand, the results of deterministic modeling by FE and, on the other hand, the applicability of the MCS performed on a million samples verifies the effectiveness of the AK-MCS. The same results for the estimated probabilities of two failure modes (i.e. plastic failure, elastic buckling) were obtained by both methods, but stochastic modeling by AK-MCS requires fewer than a hundred direct assessments of the printed structure.

Reliability analyses of complex structures using the Kriging metamodel have been carried out in Diab et al. (2022, 2023). For example, in Diab et al. (2023), a numerical investigation with rectangular section walls verifies the geometrical effect on the risk of structural failure during printing. Figure 7.3 shows that the probability of plastic collapse of the square wall (m/n = 1) can be significantly higher than that of elastic buckling at a certain printing height. Conversely, for the rectangular wall with a large horizontal length ratio (e.g. m/n = 2.5), the probability of elastic buckling is much higher than that of plastic failure. Elastic buckling has also been identified as the dominant mode of failure in the case of a chair (Diab et al. 2022). Parametric studies have shown that the probability of elastic buckling depends strongly on the layer width of the printed chair, while the effect of printing speed and layer thickness is moderate (Figure 7.14).

The effect of the printing strategy, such as the layer pressing technique, is also taken into account in the reliability analyses. In addition to uncertainty in the mechanical properties of fresh concrete, probabilistic predictions of structural failure of rectangular walls consider the propagation of uncertainty related to the layer pressing strategy (e.g. uncertainty in extrusion speed, effective layer geometry and pressing force). Nevertheless, within the adopted range of random input parameters, it appears that the effect of the layer pressing strategy is less than that of the mechanical properties of the fresh concrete. Quantitatively, the global sensitivity analysis using Sobol indices identifies the parameters that most affect the probability of the two failure modes. The results in Figure 7.5 show, in the case studied, a strong influence of material properties, notably initial Young’s modulus on the probability of elastic buckling, or initial cohesion and friction angle on the probability of plastic failure of printed structures.

The final stage of the methodology developed in Diab’s thesis (Diab 2023) involves combining the AK-MCS technique with an optimization approach for the 3D printing process. In current developments, the chosen technique, named Kriging-QMC (Moustapha et al. 2016; Do et al. 2021), is based on quantile calculations of each failure mode and aims to optimize design parameters such as printing speed and deposited layer width by minimizing the amount of concrete and printing time. The first application in the case of the straight wall shows a good match between this Kriging-QMC technique and the well-known two-level optimization method using the MCS, which is, however, numerically very costly. Validation of this Kriging-QMC design optimization technique provides an effective tool for optimizing the 3D printing process for more complex concrete structures. An attempt to calibrate safety factors from these results to facilitate engineering applications is also envisaged.

It is important to point out that different assumptions have been adopted in these reliability analysis and design optimization studies using stochastic modeling. On the one hand, the variation in the mechanical properties of the fresh concrete in each layer during printing has been ignored to facilitate numerical modeling. This means that each deposited layer is considered homogeneous, and the mechanical properties of the printed structure vary only in the direction of extrusion. A more rigorous study of the variation in mechanical properties within each deposited layer (Nguyen-Van et al. 2021; Ooms et al. 2021; Vantyghem et al. 2021) would increase the accuracy of predictions. On the other hand, in our FE numerical studies, shell-type elements were chosen instead of volume elements, given the small thickness of the concrete structure compared to other dimensions. Although the 3D model using volumetric elements can provide the most accurate results of the structure’s response, the simplified model based on surface elements enables us to reduce calculation time enormously, particularly in the context of probabilistic analyses and design optimization using stochastic modeling. It should also be noted that, in these current studies, the geometric imperfection and possible spatial heterogeneity of the geometry (e.g. thickness and width) of printed layers is not taken into account, and only the analysis of bifurcation buckling has been undertaken.

The developments and applications of numerical tools in the 3D printing process for concrete structures as previously presented have demonstrated the effectiveness of numerical modeling in this field. Its high performance, particularly in predicting the behavior of complex structures in the design phase and during printing, offers great advantages over studies based on analytical solutions. However, a major limitation of this numerical approach is the considerable increase in computational time and resources, depending on the volume of the large-scale structure, the desired accuracy and the target objective. This limitation largely explains why numerical studies have been focused on each specific scale (e.g. deposited layer scale, structure scale) and why, to date, there is no universal model or tool that can predict the entire 3D printing process. The challenge for the development of such a tool is further increased by taking into account physical phenomena (e.g. the influence of temperature, relative humidity, etc.), which have been very rarely discussed to date.

Despite its constant development, the implementation of 3D concrete printing in real construction projects remains complex. Indeed, the engineering principles governing construction, as in the building sector, are highly standardized and regulated, and relate as much to the materials used as to the amount of structural reinforcement and the methodology of the construction technique. Compliance with these specific regional standards and codes is essential to guarantee the safety and integrity of the structure in accordance with its design, location and function. However, as a new technology, 3D concrete printing does not yet have standardized construction rules to establish a clear framework for its use in construction projects. The concrete 3D printing community presents the first attempt to create norms and standards (Buswell et al. 2020) to broaden the technology’s adoption in the industry. In addition, 3D printing companies have found ways to overcome the certification hurdle in order to bring their projects to fruition. For example, a bridge was produced using the Eindhoven University of Technology printer (TU/e) and certified for public use after validation by testing on a scale model (Salet et al. 2018). The current procedure is based on extensive testing of materials and the final structure to provide a satisfactory guarantee of safety and compliance with traditional codes. However, this strategy requires much more material, contradicting the aim of this new technology to reduce material consumption during construction and limiting the development and application of 3D concrete printing on a large scale in practice. Similarly, in 2016, taking advantage of the architectural freedom offered by 3D concrete printing, XtreeE 3D printed a pillar of complex geometry for a public building, which could not have been easily manufactured with any other technology (Gaudillière et al. 2020). However, in the absence of specific regulations, only the outer wall of the structure was 3D printed, serving as a mold for the concrete cast inside. The result was an oversized final structure, since only the material poured inside was taken into account in the structural analysis, and the printed material was considered to play no mechanical role. These cases underline the need for regulations and an optimization process to ensure proper design.

The development and optimization of numerical simulation tools and procedures for industrial-scale applications is therefore a major objective for 3D printing. While maintaining the necessary accuracy of predictions, these numerical tools need to be able to deliver results continuously and almost instantaneously. This is an essential prerequisite for decision support and real-time optimization of the 3D printing process. The stochastic optimization procedure could be widely useful for establishing design regulations for structures built using 3D printing. To approach this objective, a number of options could be considered:

• Results from numerical modeling at the CFD layer scale could be better exploited to characterize the interaction between different printing parameters (e.g. extrusion speed, deposited layer width and thickness and nozzle geometry). These numerical tools can also be used to quantify the uncertainty of these printing parameters and of the force imposed by the layer pressing technique, which are not yet accessible.
  
• Consideration of geometric imperfections and spatial heterogeneity in the mechanical properties and self-weight of printed layers in probabilistic modeling would improve predictions at the structural scale. However, the necessary use of volume elements, which is numerically very costly, will be an obstacle to overcome in these simulations. Enhancing the capability of numerical tools by combining them with model reduction techniques using machine learning algorithms would be essential in this context.

From a strategic point of view, using the approach based on direct assessments of the structure’s behavior seems to be very difficult, if not inapplicable, for real-time optimization of the 3D printing process. While this approach could be very useful in the design phase prior to manufacturing, another approach should be adopted to study and optimize the structure during the printing phase. Artificial intelligence (AI), using deep learning tools, is a very promising approach. Thanks to this method, it would be possible to characterize and quantify (in real time) the various parameters (e.g. mechanical properties of fresh concrete, nozzle pressure on already printed layers, etc.) using continuous measurement data during printing (e.g. measurements of vertical displacement or deformation of the structure, etc.). These results would provide important data for the optimization of structure printing, which would be carried out in a continuous and sequential manner. More precisely, corresponding to a given iteration or point in time during the printing phase, updating the input parameters and their associated uncertainties would help verify the predictions and decisions of the previous iteration. These would then be taken into account to predict the behavior and optimize the printing of the structure in the next iteration. The effectiveness of such an approach would closely depend on the performance of the deep learning technique and also on the quality and quantity of the data gathered from the printing tests, which are also supplemented by the results of prior numerical predictions.

7.5. Conclusion

Digital tools play an essential role in the three-dimensional printing process for concrete structures. From the design phase of the geometric model in the virtual environment to the construction of the actual structure and finishing for commissioning, these tools are becoming an essential choice for this new construction technique. The recent development of digital tools makes it possible, on the one hand, to automate all the various stages of the 3D printing process (design, layering of the virtual geometric model, definition of printer trajectories and speeds); and, on the other hand, to directly supply input files for the digital modeling of components and/or the printed structure.

This chapter summarizes the state of the art in numerical modeling of the 3D printing process, focusing on the scale of the structure and the printed layer. On a large scale, the interest of numerical modeling lies in predicting failure modes such as elastic buckling and plastic collapse of the structure, phenomena commonly observed during printing. The results obtained at this scale demonstrate the performance of numerical studies based largely on the finite element method, adopting the material’s elasto-plastic behavior model. At the filament scale, numerical modeling involves predicting the shape of the deposited layers. In all studies at this level, a viscous behavior represented by a Newtonian or non-Newtonian fluid model is chosen to characterize the state of fresh concrete, while simulations can be carried out using finite volume or finite element-particle methods. Numerical predictions have demonstrated their ability to simulate the cross-section of the printed layer, which depends not only on the parameters and strategy of the printing process but also on the properties of the material and its interaction with the existing layer. The ability to characterize the quality of the contact surface roughness between successive layers, or the pressure force under the nozzle, is also an advantage of numerical modeling at this scale.

However, numerical predictions sometimes differ significantly from experimental results. The difference can be explained by an overestimation of the mechanical properties of fresh concrete calibrated on the basis of experimental tests, or by the influence of thermal phenomena not yet taken into account in numerical simulations. Among the various ways of improving the predictive capacity of numerical modeling, the stochastic analysis approach offers a promising avenue. On the one hand, this type of reliability analysis approach makes it possible to quantify sources of uncertainty, such as the uncertainty of the mechanical properties of concrete at a young age, and their propagation to the responses of printed structures. On the other hand, by combining them with the appropriate algorithms, stochastic modeling can be used to optimize the printing process corresponding to a chosen confidence level. Moreover, the ability to calibrate safety factors on the basis of these optimization results would contribute to the standardization of construction using the 3D printing process.

The future development and enhancement of digital tools must meet the need for real-time optimization and/or decision support of the printing process, while maintaining the necessary precision. The use of AI, in which data is collected from measurements during the printing process and from digital simulations at different scales in the design phase, would enable this objective to be approached.

7.6. References

1. Abdulhameed, O., Al-Ahmari, A., Ameen, W., Mian, S.H. (2019). Additive manufacturing: Challenges, trends, and applications. Advances in Mechanical Engineering, 11(2), 1–27.
   
2. Anane, W., Iordanova, I., Ouellet-Plamondon, C. (2021). The use of BIM for robotic 3D concrete printing. In Canadian Society of Civil Engineering Annual Conference. Springer, Singapore.
   
3. Buswell, R.A., Da Silva, W.L., Bos, F.P., Schipper, H.R., Lowke, D., Hack, N., Kloft, H., Mechtcherine, V., Wangler, T., Roussel, N. (2020). A process classification framework for defining and describing digital fabrication with concrete. Cement and Concrete Research, 134, 106068.
   
4. Chang, Z., Schlangen, E., Šavija, B. (2020). Extended lattice model to simulate the printing process of 3D printed cementitious materials. In Second RILEM International Conference on Concrete and Digital Fabrication: Digital Concrete 2020. Springer, Cham.
   
5. Chang, Z., Xu, Y., Chen, Y., Gan, Y., Schlangen, E., Šavija, B. (2021). A discrete lattice model for assessment of buildability performance of 3D-printed concrete. Computer-Aided Civil and Infrastructure Engineering, 36(5), 638–655.
   
6. Chang, Z., Zhang, H., Liang, M., Schlangen, E., Šavija, B. (2022). Numerical simulation of elastic buckling in 3D concrete printing using the lattice model with geometric nonlinearity. Automation in Construction, 142, 104485.
   
7. Comminal, R., Serdeczny, M.P., Ranjbar, N., Mehrali, M., Pedersen, D.B., Stang, H., Spangenberg, J. (2019). Modelling of material deposition in big area additive manufacturing and 3D concrete printing. In Joint Special Interest Group Meeting between Euspen and ASPE Advancing Precision in Additive Manufacturing. The European Society for Precision Engineering and Nanotechnology, Cranfield, Bedfordshire.
   
8. Comminal, R., da Silva, W.R.L., Andersen, T.J., Stang, H., Spangenberg, J. (2020a). Influence of processing parameters on the layer geometry in 3D concrete printing: Experiments and modelling. In RILEM International Conference on Concrete and Digital Fabrication. Springer, Cham.
   
9. Comminal, R., da Silva, W.R.L., Andersen, T.J., Stang, H., Spangenberg, J. (2020b). Modelling of 3D concrete printing based on computational fluid dynamics. Cement and Concrete Research, 138, 106256.
   
10. Diab, Z. (2023). Application d’outils numériques à l’analyse probabiliste de la constructibilité et à l’optimisation du procédé d’impression 3D. PhD Thesis, Université d’Orléans, Orléans.
    
11. Diab, Z., Do, D.P., Rémond, S., Hoxha, D. (2022). Uncertainty quantification of concrete properties at fresh state and stability analysis of the 3D printing process by stochastic approach. In RILEM International Conference on Concrete and Digital Fabrication. Springer, Cham.
    
12. Diab, Z., Do, D.-P., Rémond, S., Hoxha, D. (2023). Probabilistic prediction of structural failure during 3D concrete printing processes. Materials and Structures, 56(4), 73.
    
13. Ding, Z., Liu, S., Liao, L., Zhang, L. (2019). A digital construction framework integrating building information modeling and reverse engineering technologies for renovation projects. Automation in Construction, 102, 45–58.
    
14. Do, D.P., Tran, N.T., Hoxha, D., Vu, M.N., Armand, G. (2021). Kriging-based optimization design of deep tunnel in the rheological Burger rock. In IOP Conference Series: Earth and Environmental Science, Turin, 833, 012155.
    
15. Eastman, C.M. (2011). BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers and Contractors. John Wiley & Sons, New York.
    
16. Fologram for Rhino and Grasshopper (n.d.). [Online]. Available at: https://www.food4rhino.com/en/.
    
17. Gaudillière, N., Dirrenberger, J., Duballet, R., Bouyssou, C., Mallet, A., Roux, P., Zakeri, M., Xtree, E.R. (2020). Industrialising concrete 3D printing: Three case studies. In Design Transactions: Rethinking Information Modelling for a New Material Age, Sheil, B., Thomsen, M.R., Tamke, M., Hanna, S. (eds). UCL Press, London.
    
18. Keita, E., Bessaies-Bey, H., Zuo, W., Belin, P., Roussel, N. (2019). Weak bond strength between successive layers in extrusion-based additive manufacturing: Measurement and physical origin. Cement and Concrete Research, 123, 105787.
    
19. Kruger, J., Zeranka, S., van Zijl, G. (2019). 3D concrete printing: A lower bound analytical model for buildability performance quantification. Automation in Construction, 106, 102904.
    
20. Kruger, J., Cho, S., Zeranka, S., Viljoen, C., van Zijl, G. (2020). 3D concrete printer parameter optimisation for high rate digital construction avoiding plastic collapse. Composites Part B: Engineering, 183, 107660.
    
21. Le, T.T., Austin, S.A., Lim, S., Buswell, R.A., Law, R., Gibb, A.G., Thorpe, T. (2012). Hardened properties of high-performance printing concrete. Cement and Concrete Research, 42(3), 558–566.
    
22. Lim, S., Buswell, R.A., Valentine, P.J., Piker, D., Austin, S.A., De Kestelier, X. (2016). Modelling curved-layered printing paths for fabricating large-scale construction components. Additive Manufacturing, 12, 216–230.
    
23. Liu, H., Ding, T., Xiao, J., Mechtcherine, V. (2022). Buildability prediction of 3D–printed concrete at early-ages: A numerical study with Drucker–Prager model. Additive Manufacturing, 55, 102821.
    
24. McNeel, R. (2010). Rhinoceros 3D, Version 6.0. Robert McNeel & Associates, Seattle, WA.
    
25. Moustapha, M., Sudret, B., Bourinet, J.-M., Guillaume, B. (2016). Quantile-based optimization under uncertainties using adaptive Kriging surrogate models. Structural and Multidisciplinary Optimization, 54, 1403–1421.
    
26. Nerella, V.N., Hempel, S., Mechtcherine, V. (2019). Effects of layer-interface properties on mechanical performance of concrete elements produced by extrusion-based 3D-printing. Construction and Building Materials, 205, 586–601.
    
27. Nguyen-Van, V., Panda, B., Zhang, G., Nguyen-Xuan, H., Tran, P. (2021). Digital design computing and modelling for 3-D concrete printing. Automation in Construction, 123, 103529.
    
28. Ooms, T., Vantyghem, G., Van Coile, R., De Corte, W. (2021). A parametric modelling strategy for the numerical simulation of 3D concrete printing with complex geometries. Additive Manufacturing, 38, 101743.
    
29. Panda, B., Lim, J.H., Tan, M.J. (2019). Mechanical properties and deformation behaviour of early age concrete in the context of digital construction. Composites Part B: Engineering, 165, 563–571.
    
30. Papanastasiou, T.C. (1987). Flows of materials with yield. Journal of Rheology, 31(5), 385–404.
    
31. Perrot, A., Rangeard, D., Pierre, A. (2016). Structural built-up of cement-based materials used for 3D-printing extrusion techniques. Materials and Structures, 49, 1213–1220.
    
32. Perrot, A., Pierre, A., Nerella, V.N., Wolfs, R.J.M., Keita, E., Nair, S.A.O., Neithalath, N., Roussel, N., Mechtcherine, V. (2021). From analytical methods to numerical simulations: A process engineering toolbox for 3D concrete printing. Cement and Concrete Composites, 122, 104164.
    
33. Reinold, J., Nerella, V.N., Mechtcherine, V., Meschke, G. (2019). Particle finite element simulation of extrusion processes of fresh concrete during 3d-concrete-printing. In Sim-AM 2019: Second International Conference on Simulation for Additive Manufacturing. CIMNE, Barcelona.
    
34. Reiter, L., Wangler, T., Roussel, N., Flatt, R.J. (2018). The role of early age structural build-up in digital fabrication with concrete. Cement and Concrete Research, 112, 86–95.
    
35. Roussel, N. (2018). Rheological requirements for printable concretes. Cement and Concrete Research, 112, 76–85.
    
36. Roussel, N., Spangenberg, J., Wallevik, J., Wolfs, R. (2020). Numerical simulations of concrete processing: From standard formative casting to additive manufacturing. Cement and Concrete Research, 135, 106075.
    
37. Salet, T.A., Ahmed, Z.Y., Bos, F.P., Laagland, H.L. (2018). Design of a 3D printed concrete bridge by testing. Virtual and Physical Prototyping, 13(3), 222–236.
    
38. Spangenberg, J., da Silva, W.R.L., Comminal, R., Mollah, M.T., Andersen, T.J., Stang, H. (2021). Numerical simulation of multi-layer 3D concrete printing. RILEM Technical Letters, 6, 119–123.
    
39. Suiker, A.S.J. (2018). Mechanical performance of wall structures in 3D printing processes: Theory, design tools and experiments. International Journal of Mechanical Sciences, 137, 145–170.
    
40. Suiker, A.S.J., Wolfs, R.J., Lucas, S.M., Salet, T.A. (2020). Elastic buckling and plastic collapse during 3D concrete printing. Cement and Concrete Research, 135, 106016.
    
41. Tay, Y.W.D., Panda, B., Paul, S.C., Noor Mohamed, N.A., Tan, M.J., Leong, K.F. (2017). 3D printing trends in building and construction industry: A review. Virtual and Physical Prototyping, 12(3), 261–276.
    
42. Teizer, J., Blickle, A., King, T., Leitzbach, O., Guenther, D., Mattern, H., König, M. (2018). BIM for 3D printing in construction. Building Information Modeling: Technology Foundations and Industry Practice, 421–446.
    
43. Vandezande, J., Krygiel, E., Read, P. (2012). Autodesk Revit Architecture 2013: Essentials. John Wiley & Sons, New York.
    
44. Vantyghem, G., Ooms, T., De Corte, W. (2021). VoxelPrint: A grasshopper plug-in for voxel-based numerical simulation of concrete printing. Automation in Construction, 122, 103469.
    
45. Wangler, T., Lloret, E., Reiter, L., Hack, N., Gramazio, F., Kohler, M., Bernhard, M., Dillenburger, B., Buchli, J., Roussel, N. (2016). Digital concrete: Opportunities and challenges. RILEM Technical Letters, 1, 67–75.
    
46. Wolfs, R.R. (2015). 3D printing of concrete structures. Master’s Thesis, Eindhoven University of Technology.
    
47. Wolfs, R.J.M. and Suiker, A.S.J. (2019). Structural failure during extrusion-based 3D printing processes. The International Journal of Advanced Manufacturing Technology, 104, 565–584.
    
48. Wolfs, R.J.M., Bos, F.P., Salet, T.A.M. (2018). Early age mechanical behaviour of 3D printed concrete: Numerical modelling and experimental testing. Cement and Concrete Research, 106, 103–116.
    
49. Wolfs, R.J.M., Bos, F.P., Salet, T.A.M. (2019a). Hardened properties of 3D printed concrete: The influence of process parameters on interlayer adhesion. Cement and Concrete Research, 119, 132–140.
    
50. Wolfs, R.J.M., Bos, F.P., Salet, T.A.M. (2019b). Triaxial compression testing on early age concrete for numerical analysis of 3D concrete printing. Cement and Concrete Composites, 104, 103344.
    
51. Wolfs, R.J., Salet, T.A., Roussel, N. (2021). Filament geometry control in extrusion-based additive manufacturing of concrete: The good, the bad and the ugly. Cement and Concrete Research, 150, 106615.
    
52. Wu, P., Wang, J., Wang, X. (2016). A critical review of the use of 3D printing in the construction industry. Automation in Construction, 68, 21–31.