Buildability Analysis of 3D Concrete Printing Process: A Parametric Study Using Design of Experiment Approach

Abstract

Plastic collapse and buckling are the key structural failure criteria in 3D concrete printing (3DCP). This study aims to analyze the effect of different geometrical designs and printing factors on the buildability performance of 3DCP structures. Due to the high number of variables involved, the Design of Experiment (DOE) has been used to reduce the number of simulations. In geometrical design parameters, the structure’s design is more sensitive, followed by the width and length of the printed design. The buildability increases when we move from sharp corners to more stable structures like fillets and circular geometry. For geometrical design parameters, a maximum buildability of 74% of the designed height is achieved for circular design with the highest width and lowest diameter. For printing parameters, the highest buildability of 486 mm (81%) is achieved for the lower values of printing speed and layer height. The study analyzed failure phenomena of buckling and yield strength for the tested combination of parameters. The study analyzed the sensitivity analysis of individual parameters and their combination for maximum buildability and developed the low order polynomial regression equation for each printing parameter and geometrical factors. Based on the analysis of the results, the study also proposed different new printing strategies to increase the overall performance of the printing process.

1. Introduction

3DCP is a new technology that offers numerous benefits regarding labor costs, carbon dioxide emissions into the atmosphere, the time required, the convenience of usage, and the flexibility to adjust the design as desired [1,2,3]. Environmental benefits of 3D printing include decreased manufacturing waste, a smaller carbon footprint, and support for the circular economy [4,5]. However, the trending methodology in 3D Concrete Printing (3DCP) is accompanied by extensive trial and error methods, leading to the final product’s more expensive and time-consuming development. The trial-and-error procedure is more costly for printing at a structural scale, where the failure leads to a significant loss of resources and time. In addition, the current methodology of 3DCP goes along with conservative designs, partially due to the lack of reliable simulation tools. The numerical simulation of the printing process in the virtual environment can increase the chances of successful and cost-effective printing [6,7].

Numerical and simulation models in 3DP and current state of the art: To predict structural behavior and prevent failure in 3DP structures, the material, design, and print parameters and the printing strategy may be adjusted using the results from simulation models [8]. The results can also help in optimization of the processes, such as optimal print speed for more productivity. Simulation may determine the required material qualities and printing settings for a particular design and could also help in selection of the most suitable design for printing [9,10]. The ability to forecast structural variation and determine material qualities can be used to compute the necessary material qualities and print settings for a particular design, eliminating the need for guessing and a trial-and-error method, which can lead to reducing material and time waste, machine wear, and setup time required.

The three primary categories or phases of the existing numerical models employed in the 3DCP process are mixing and delivery, material extrusion and deposition at the filament level, and structure level modeling. The fresh material’s capacity to be effectively printed is assessed at the printability stage, which is connected to the material’s mechanical and rheological characteristics [11,12]. Contrarily, buildability evaluates the final structure’s printability by increasing the printing layer without causing the printed component to collapse or deform. However, there has not been much study on how 3DCP can be printed and built. Print trials are often used to assess the buildability stage [13].

For the structural collapse in 3DP structures, the two basic failure phenomena observed in literature are elastic buckling and plastic collapse. Elastic buckling was caused by geometric instability, while plastic collapse happened when gravity-induced stresses reached the yield stress and indicated the material’s rheological yielding [13,14,15]. A second-order P-delta effect can be seen in the conjunction of the two events when elastic buckling is brought on by plastic failure at the bottom layer. For effective numerical modelling of any design at a structural scale, layers-wise modelling is required for time-dependent material properties, followed by the layer-wise activation and interaction between the layers to simulate the printing process.

Suiker [16] created a mechanistic model to investigate how the printing process parameters affected the emerging structure’s mechanical performance. The failure mechanism for straight wall structures was predicted to be either plastic collapse or elastic buckling. The model takes into account the most relevant factors, including the uneven stiffness and strength characteristics of the printing material, curing properties, print speed, the object’s geometric characteristics, and non-uniform dead weight. The research backed the model’s efficiency and proposed utilizing it to examine the impact of printing settings on the final structure. Furthermore, the study recommended using the model to validate any finite element model.

Wolfs and Suiker [17] studied the plastic collapse and elastic buckling failure of a 3D printed wall structure created by extrusion. They compared experimental wall structures using linear and exponential material curing properties to a particular FEM simulation model. The research also confirmed the accuracy of Suiker’s parametric model [16]. The FEM models produced remarkably consistent results with the experimental data for buckling failure in nearly all cases. Furthermore, the model underwent testing on designs with different printing quality and material characteristics.

Most models are printed using vertical extruding mechanisms due to the simplicity or convenience of modelling. These models can be used to estimate buildability, although their accuracy is only suitable for simple constructions like multilayers, walls with straight edges, or hollow cylindrical shapes. The first study to use a FE model to examine the mechanical behavior of recently constructed 3D printed concrete structures with independent form geometry is by Wolf et al. [18]. The study used an implicit/static solver and imported a virtual design file for the analysis. The model is partitioned into printable layers that are incrementally enabled to determine the viability of the proposed design structure. The model was built on the Mohr–Columb failure criterion and material properties that are time-dependent and exhibit linear stress–strain behavior. To determine the necessary material parameters, a direct shear test and uniaxial compression test were performed in an experimental setup. The research results demonstrated the model’s acceptable qualitative performance.

In the following work, Wolfs et al. [19] described the model with an enhanced material characteristics technique. The total printable layers were overestimated by roughly 15% before the failure due to the validation using experimental performance for a 5 m long wall structure. The study also covered how the model might deviate from the outcomes of the experiments. Vantyghem and Ooms et al. [8,20,21] have recognized and recommended additional numerical improvements to the model, such as its application to more complicated and free-form geometries. Therefore, taking the model of Wolf et al. [18] as a starting point, Vantyghem et al. [8] offered two enhanced simulation methodologies for 3DCP processes. Both models proposed multiple static implicit steps and a gradual addition of finite elements until the printing process is successfully replicated or fails. Both models also employ distinct methods of discretization. The first method, named “Voxel Print”, transforms a 3D object into a set of small unit cubes known as voxels. This method establishes a direct connection between the voxel and the mesh.

Design of Experiment (DOE) and 3DCP: Since various parameters are involved in the 3DCP process, the DOE can be a convenient approach to study the effect of different factors. The DOE approach reduces the number of required investigations [22]. In DOE terminology, the input variables are called factors, while the output is called performance. These input factors can be both categorical (or qualitative) or quantitative. The qualitative factors are the structural assumption that cannot be quantified, for example, square, hybrid square-circular structures. In contrast, quantitative factors are usually represented by numerical values. The DOE approach is applied to determine the most significant factors that affect the response [23,24]. In the 3D printing process, different quantitative and qualitative factors influence the final buildability responses.

Objective: As we get to more advanced, extensive, and valuable applications of 3DCP, the significance of predicting the ultimate mechanical performance of the produced structure increases. It is still a problematic issue, and how each process parameter and condition of the concrete printing process affects the mechanical performance of the final structure requires investigation. The objective of this study is the detailed effect of geometrical features and printing parameters on the overall buildability of the 3DCP design. The specific aim is to gain further insights, including:

• Analyze the effect of different parameters on buildability.
• Effect of each factor and its sensitivity level concerning other factors.
• Predict the model response for the configuration that was not simulated to save the execution time and to have real-time answers.
• Find the combination of input factors to maximize the final response.
• Develop the low order polynomial regression equation for each printing parameter and geometrical factors.

2. Methodology

2.1. DOE Approach for Parametric Study

Due to the high number of variables involved, the fractional factorial DOE approach has been applied where the number of variables is more than three. A Taguchi Orthogonal design was chosen, which allows for considering the subset of all the possible combinations of factors at different levels. A Taguchi Orthogonal Array (OA) design was used in this study as a general fractional factorial design. This highly fractional orthogonal design allows the matrix to be designed using a selected subset of the combination of the considered factors and their respective levels. The Taguchi technique seeks to minimize variation in a process using the DOE approach.

2.2. Geometrical Factors and Design Matrix

For geometrical design parameters, the width of printed structure (w), length of the printed form (d), and geometrical design have been considered with three different levels.

Table 1. Three factors and three levels of design matrices for geometrical factors.

d [Side/Diameter]	Geometry	Width (mm)
−1	−1	−1
−1	0	0
−1	1	1
0	−1	0
0	0	1
0	1	−1
1	−1	1
1	0	−1

represents the design matrix for the considered three factors with three levels.

Where three levels of side length (d) considered are 250 mm (−1), 300 mm (0), and 350 mm (1). For the w factor, the considered levels are 15 mm (1), 20 mm (0), and 25 mm (1). For geometrical, the three shapes considered here are square shape (−1), square width rounded side or fillet (0), and circular geometry (1), as shown in Figure 1.

2.3. Printing Parameters and Design Matrix

The two considered printing parameters for printing parameters in this study are the printing speed (v) and layer height (h). Three levels are considered for each factor, and a full factorial design approach has been used for the design matric, as seen in

Table 2. Two factors and three levels of full factorial design matric for printing factors.

Print Speed [mm/s]	Layer Height [mm]
−1	−1
−1	0
−1	+1
0	−1
0	0
0	+1
+1	−1
+1	0
+1	+1

.

The details of the selection of printing speed range are discussed in the results and discussion section, where for v the selected levels are 10 mm/s (−1), 40 mm/s (+1), and 100 mm/s (+1), while for h the considered levels are 5 mm (−1), 10 mm (0), and 15 mm (+1).

2.4. Numerical and Simulation Model

After a detailed literature review of numerical modelling, a numerical model by Vantyghem et al. [8] was used to analyze different print and geometrical constraints on the buildability performing. The general methodology of model is represented in Figure 2. The model can use any complex geometry to predict its buildability performance as a function of print speed, layer height, and geometrical design or material characteristics. In this study, the 3DCP process was simulated using two different FEM approaches. Alternative experimental methods, such as the unconfined and triaxial compression tests discussed in Wolf et al. [18], can be utilized to determine the time-dependent material characteristics required for the model. The Mohr–Coulomb material model employed various time-dependent input parameters, including Poisson’s ratio (v), density (ρ), the function of Young’s modulus over time (E(t)), the dilatancy angle (ψ), angle of internal friction (φ), and a time-dependent cohesion function (c).

3. Results and Discussions

3.1. Geometrical Parameters

For each combination of selected factors, numerical modelling and simulation were performed in the design matrix for a printing velocity of 40 mm/s and a layer height of 10 mm. For each geometry, the designed height was selected as 600 mm. The results are shown in

Table 3. Results for the geometrical parametric combination using Taguchi L9 array.

S. No	Length (Side/Diameter) [mm]	Structure	Width [mm]	Buildability [Achieved Steps Out of 100]	Buildability [Achieved Height in mm]
S1-1	250	square	15	14	84
S1-2	250	fillet	20	43	258
S1-3	250	circle	25	74	444
S1-4	300	square	20	32	192
S1-5	300	fillet	25	34	204
S1-6	300	circle	15	45	270
S1-7	350	square	25	38	228
S1-8	350	fillet	15	21	126
S1-9	350	circle	20	52	312

.

Table 3 shows the buildability results and the achieved height of the structure before failure for the considered combination. The simulation process was selected to be completed in 100 steps. Therefore, the result shows the number of completed steps before the collapse and the maximum buildability height achieved. The maximum reached buildability was 74% for the circular shape, with the most significant wall thickness of 25 mm and a minimum diameter of 250 mm. The graphical representation for each structure at the failure step is shown in Figure 3.

The response table has been calculated using the Minitab^® software to observe the impact of each factor and perform its comparative analysis,

Table 4. Response table for the response characteristic of each considered geometrical factor.

Level	Side/Dia	Structure	Width
1	262.0	168.0	160.0
2	222.0	196.0	254.0
3	222.0	342.0	292.0
Delta	40.0	174.0	132.0
Rank	3	1	2

. The technique considered the response level for each combination of the level of the factor. Delta represents the difference between the highest and the lowest response value for each factor. The rank means the relative effect of each factor and is assigned concerning the corresponding delta value.

In the observed three geometrical factors for the printed structure, the results show that the structure geometry is the most sensitive parameter to the final buildability response, followed by the width of the design. In comparison, the side or diameter length is relatively less effective than structure geometry and width.

The following regression Equation (1) has been generated for the data:

Buildability (height) = 134 − 0.480 l + 12.40 w

(1)

where l represents the factor side/diameter and w represents the width of the printed structure. However, it is essential to note that due to the high number of variables involved in the 3DCP process, the above equation is valid only for the selected materials, printing parameters, and the considered range of the geometrical factors.

The main effect plots are used to graphically analyze the effect of factors on the response (buildability here) by considering the characteristic average for each factor level. It measures the average change in the response due to changes in the individual factors—the higher the change, the higher the absolute value of the curve. Figure 4 represents the main effect plot for the considered geometrical factors.

The sensitivity of each considered factor to the buildability response can be graphically observed in Figure 4. The considered geometrical structure of square, fillet, and circular shapes can be regarded as the most sensitive parameter in the response table. The buildability decreases with an increase in the length of the considered structure while increasing with the increase in the width of the constructed wall. Similarly, the buildability increases when we move from square to more stable structures like fillets instead of a sharp corner of the square and circular geometry. Stress concentration for all three square, fillet, and circular shapes with a thickness of 25 mm is shown in Figure 5. The maximum stress concentration at the corners square cross-section can be observed. While moving towards fillet and circular cross-section, stress is distributed along with the curve structure instead of point concentration.

The interaction between different considered factor levels is shown in Figure 6. The interaction between the plots leads the factors being interrelated.

The level of one of the three levels for each element under consideration is shown on the x-axis, while the levels of the other levels are shown by various colored lines. The figure makes it easier to see how the response variable is affected by changes in the side/dia, structure, and width variables’ values. It would also reveal whether there are any significant interactions between these variables that could affect the answer. The figure aids in determining which side/dia, structure, and breadth combinations provide the best response. They may also utilize these data to create prediction models that will aid in optimizing the structure’s design and size.

3.2. Printing Parameters

For the initial study, the model has been analyzed for velocity above 40 mm/s. Three different levels of velocities and layer height have been investigated, but no significant impact has been analyzed on the printing parameters of layer height and print speed. The results show that the model is not sensitive to the printing velocity after a specific limit, as the material did not find enough time to change its properties significantly (Figure 7). For plodding printing speed, a notable change is observed in an increase in buildability. However, the effect of printing velocity on buildability is negligible after a specific limit of printing speed because the materials got enough time to develop their properties.

Therefore, to observe the impact of printing parameters factors, conditions with lower print velocity, less than 10 mm/s, have been considered. The maximum layer height considered is 15 mm, see

Table 5. Results for the printing parametric combination using Taguchi array.

S. No	Print Speed [mm/s]	Layer Height [mm]	Buildability [Achieved Steps Out of 100]	Buildability [Achieved Height in mm]
S2-1	1	5	81	486
S2-2	1	10	69	414
S2-3	1	15	65	390
S2-4	4	5	81	486
S2-5	4	10	61	366
S2-6	4	15	60	360
S2-7	10	5	67	402
S2-8	10	10	59	354
S2-9	10	15	59	354

.

The results show that a maximum buildability of 486 mm has been achieved at one mm/s and four mm/s of printing speed with a minimum layer height of 5 mm. The graphical representation for the buildability at one mm/s at the failure step is shown in Figure 8.

The sensitivity of each impact factor can be more clearly analyzed in the response in

Table 6. Response table for printing parameter of velocity and layer height.

Level	Print Speed	Layer Height
1	430.0	458.0
2	404.0	378.0
3	370.0	368.0
Delta	60.0	90.0
Rank	2	1

.

The results show that, for the considered range of printing velocity and layer height, the buildability response is more sensitive to the layer height followed by the print speed. Since the minimum values starting from 1 mm/s, the most sensitive range, have been chosen for the print speed, the results show more sensitivity of layer height as compared to the print speed. The regression equation for the considered printing factors is shown below:

Buildability [mm] = 524.0 − 6.52 v − 9.00 h

(2)

where v represents the printing velocity and h represents the printing layer height. However, it is essential to note that due to the high number of variables involved in the 3DCP process, the above equation is valid only for the selected materials, printing parameters, and the considered range of the parameter’s factors.

The graphical representation of the impact of the printing parameter can be observed in the main effect plot and interaction plot in Figure 9 and Figure 10.

It can also be observed in the interaction plot that the printing speed is more sensitive for lower printing layer height, since both contribute to a lower vertical building rate of the structure and hence provide more time for the material to be stable.

This means that the buildability can be increased with the decrease in print speed and layer height. However, other experimental factors need to be considered. For example, the reduction in printing speed and layer height might result in an increase in printing time and, therefore, printing cost, which might not be acceptable for adopting the 3DCP technique. A slow printing speed might result in lower adhesion between the layers; similarly, the lower layer height leads to high printing energy and, therefore, high printing cost.

An innovative approach like a decrease in printing velocity with an increase in height can be applied to decrease the cost due to lower print speed. This will allow the lower layers, with the most stressed conditions, to find enough time to develop their strength when they are under a high load. An alternate approach of a decrease in layer height within an increase in size can also be applied for this purpose. However, the reduction in layer height during the printing process might result in extra pressure because the nozzle might increase stress; hence, careful control of the decrease in material flow with a reduction in layer height will be necessary to control.

4. Conclusions and Future Recommendation

The significance of predicting ultimate mechanical performance for concrete 3D printing grows as we move towards more advanced, extensive, and practical applications of the technology. This study investigates the impact of printing parameters and geometrical features on the overall buildability of 3D printed structures. The DOE approach has been applied to the numerical and simulation model to investigate the performance of different geometrical and printing parameters. The study analyzed the effect of each factor and their combination for maximum buildability. Based on the study performed, the following specific conclusions can be made:

-

Buildability is sensitive to the geometrical parameters of printed structure thickness, length of the printed structure, and its geometrical design.

-

The geometrical design factor is a more sensitive parameter to buildability, followed by the width of the printed wall and the length.

-

The buildability increases with an increase in thickness of the printed structure while decreasing with the length the decreasing with an increase in the length.

-

The stability of the structures increases when we move from sharp corners (such as square geometry) to rounded corners.

-

In the considered geometries, circular geometry resulted in the highest buildability, followed by fillet (rounded corner) square shape. In contrast, the lowest buildability is reported for square shapes with sharp corners (90 degrees).

-

Buildability is sensitive to both printing speed and printed layer height in the low range of the value. In contrast, layer height is the more sensitive parameter to buildability, followed by printing velocity.

-

Buildability increases with a decrease in printing speed and reduction in the printed layer height. Both contribute to a lower vertical building rate of the structure and hence provide more time for the material to be stable.

-

The maximum buildability of 486 mm (81% of the designed height) was achieved at low printing speed and lowest layer height.

-

After a specific upper limit of printing speed and layer height, the buildability becomes independent, as the material did not find enough time to develop its time-dependent strength.

-

Like the higher limit, the effect of printing velocity on buildability is negligible after a specific lower limit of printing speed because the materials had enough time to develop their properties.

-

The buildability can be increased with the decrease in print speed or layer height. However, other experimental factors need to be considered. For example, the reduction in printing speed and layer height might increase printing time and, hence, printing cost. Similarly, a slow printing speed might result in lower adhesion between the layers. Again, the lower layer height leads to high printing energy and printing cost.

Future Recommendation

Instead of low printing speed for higher buildability, a new approach of a gradual decrease in printing velocity with an increase in height can be applied for faster printing and lower cost. This will allow the material to find enough time to develop its strength when they are under a high load. An alternate approach of a gradual decrease in layer height with an increase in height can also be applied for this purpose. However, the decline in layer height during the printing process might increase stress due to the extra pressure of printing material in the nozzle. Therefore, careful control of the decrease in material flow with a reduction in layer height will be necessary. Both models and original systems are needed to be modified to achieve these goals. The current study is valid for the studied variable of design and printing parameters, and the sensitivity of other variables can also be important and needs to be studied. Similarly, the effect of materials design parameters on the overall buildability can be considered in future studies.