# Performance Analysis of 3D Concrete Printing Processes through Discrete-Event Simulation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}and then in a 12-floor building of 10,920 m

^{2}. To analyze the 3D printing process, discrete-event simulation was used while considering different variables such as extrusion speed and the locations of a robot mounted on tracks. The results show that when comparing the time taken for a conventional construction system to construct concrete walls and the maximum duration for 3D-printed walls, this method is 45% faster than traditional construction for a small building, but for a big building, there is a difference of 40% in favor of conventional construction; however, this was when using only 1 robot for the whole building. After running the same analyses but using 3 robots instead of 1, the total 3D concrete printing time for the big building was 80% faster in favor of the 3D concrete printing process.

## 1. Introduction

## 2. Literature Review

#### 2.1. Construction 4.0

#### 2.2. Additive Manufacturing

#### 2.3. 3DCP and the Use of Robotic Arms

#### 2.4. Simulation of Processes

#### 2.5. Simulation of AM Processes

## 3. Methodology

#### 3.1. Modeling of Different Configurations for 3D Printing Concrete Walls

^{TM}software (version 22.1, 2022, Orem, UT, USA).

#### 3.1.1. Export of the Structural Model from Revit to AutoCAD

^{TM}reads .dwg files (created with AutoCAD) for use as a template, which is not present in Revit. Thus, the floor plans from Revit were obtained by exporting them to AutoCAD and then to FlexSim

^{TM}.

#### 3.1.2. Analysis of the Different Possible Locations for the Mobile Robot

- (a)
- Operational area for the robot

- (b)
- Device operation without collision

- (c)
- Starting points for motion trails

- (1)
- The mobile device must be located within the area of collision-free operation.
- (2)
- The maximum reach of the mobile device must overlap with the area on which to be worked.
- (3)
- When moving, the device must not collide with existing structures.

#### 3.1.3. Simulation of Various Configurations and Locations in FlexSim^{TM}

^{TM}is a DES program, while the robot extrudes continuously, so there may be a disjunction in their ways of working. However, the latter operates by placing the arm at specific points traced on the tracking path, as found in previous studies [10]. That is, the movement of the extrusion is continuous, but it is programmed to move with points of separation, that is, in a discrete way.

^{TM}according to what was defined in the flowchart. This code was explicitly run for the second floor of the small building; however, the process was the same for the rest of the floors, except for locations, trajectories, and movements, which do not need a different algorithm to be implemented. Furthermore, this procedure allows other work areas and scope for the robotic arm, which translates into different locations and queue nodes. The FlexSim

^{TM}routines can be found in Appendix A. Therefore, the following provides an explanation of the groups shown in the flow diagram shown in Figure 8, and the code in FlexSim

^{TM}can be found in Appendix A.

- $n$ = the number of rounds of the printing bead;
- $b$ = Width of the printed bead (in meters);
- $B$ = Width of the wall (in meters).

- $n$ = the number of rounds of the printing bead;
- $L$ = Total length of the bead (in meters);
- $l$ = Length of the element (in meters).

- $t$ = Time to extrude an element (in seconds);
- $L$ = Total length of the bead (in meters);
- $s$ = Printing speed of the robot (in meters per second).

^{TM}, the “Load” command is adjusted to the mentioned speeds. In addition, a “Custom” code is added so that the robot advances the queue as it places the elements. Finally, to finish this stage, a “Decide” code is inserted to check if it reaches the last queue of the extrusion zone according to the position.

^{TM}“Experimenter” tool should be used to obtain different simulation times. In this case, 100 values were obtained and used in the statistical analyses.

#### 3.2. Experimental Design

^{TM}. To introduce them as replicates in the factorial analysis, and to study the effects caused by the different configurations, a factorial-type experimental design with three factors was performed. In the factorial analysis, to analyze the performance of a mobile robot that prints 3D concrete walls, the three factors used were robot extrusion speed, crawler displacement speed, and type of location of the mobile robot, denoted by the letters A, B, and C, respectively.

_{1}being the minimum speed, A

_{2}the average speed, and A

_{3}the maximum speed at which the robot can work for the extrusion, whereas B

_{1}, B

_{2}, and B

_{3}are the travel speeds of the tracked vehicle, respectively. On the other hand, different ways in which the robot can be located were analyzed, where the locations were grouped into two types of locations: C

_{1}and C

_{2}. In other words, each floor has two ways to place the mobile robot, C

_{1}and C

_{2}, obtaining m and n numbers of locations, respectively. In summary, Table 2 shows the factors and their respective levels in coded units.

## 4. Analysis of Results

^{TM}, and studying the most influential variables, resulting in simulation times. In this section, we will analyze those results.

#### 4.1. Locations of the Robot

#### 4.2. Results of the Experimental Design

^{TM}, for each configuration of robot extrusion speed and crawler travel speed, 100-time values were obtained that varied according to the triangular distribution considered for each test level, and in turn, for each location.

#### 4.2.1. Goodness-of-Fit

**Null Hypothesis a (H0a):**

**Alternative Hypothesis a (H1a):**

^{TM}, and a distribution fitting was performed using the Excel plug-in Crystal Ball

^{TM}. Then, considering a confidence value of 95%, the null hypothesis would not be rejected when the p-values of the Anderson–Darling, Kolmogorov–Smirnov, and chi-square statistics were greater than a significance level α of 0.05. By comparing the p-value results with the given significance level, it was possible to accept the null hypothesis; therefore, the time data for each floor fit the probability distributions shown in Table 4. Thus, the mean (µ) and standard deviation (σ) parameters per floor were obtained from the distributions fitted and shown in Table 5.

#### 4.2.2. Factor Analysis and Variance

#### 4.2.2.1. Factor Analysis of Three Factors

#### 4.2.2.2. Factor Analysis of Three Factors

**Null Hypothesis b (H0b):**

**Alternative Hypothesis b (H1b):**

**Null Hypothesis 0c (H0c):**

**Alternative Hypothesis c (H1c):**

**Null Hypothesis d (H0d):**

**Alternative Hypothesis d (H1d):**

**Null Hypothesis e (H0e):**

**Alternative Hypothesis e (H1e):**

**Null Hypothesis f (H0f):**

**Alternative Hypothesis f (H1f):**

**Null Hypothesis g (H0g):**

**Alternative Hypothesis g (H1g):**

**Null Hypothesis h (H0h):**

**Alternative Hypothesis h (H1h):**

#### 4.2.2.3. Graphs of the Factor Analyses

- (a)
- Main effect plots

- (b)
- Interaction graphs

#### 4.2.2.4. Optimization of Simulation Time

#### 4.3. Comparison between Conventional Construction Methodologies and AM

^{3}, including the fabrication and placement of reinforcement, the assembly and placement of formworks, and the pouring of concrete, in addition to considering the permanence of the formworks, 4.78 days are used. For a working day of 9 hours, 4.78 days correspond to 43.02 hours.

^{3}(Small building) and 2082.93 m

^{3}(Big building).

^{3}, this amount must be extrapolated to the volume to build the two buildings considered in this study to know the approximate duration when conventional construction is used, as shown in Table 11 and Table 12. According to Table 11, using the conventional system for the small building gives a time of 5.08 days or 45.72 hours. On the other hand, as shown in Table 12, for the construction of the big building, 182.74 days or 1,645 hours were spent.

#### 4.4. Discussion

## 5. Conclusions

^{TM}is a simulation methodology that can be easily extrapolated to other construction projects by setting the locations of the “Queues”. Regarding the experimental design, the goodness-of-fit test served to investigate the probabilistic behavior that the simulation demonstrated in addition to delivering a mean value and standard deviation for each speed and location of the robot, showing that the times for the small building corresponded to a normal distribution and those of the big building to a log-normal distribution.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

**Table A1.**Simulation times in hours according to the combination of variables for floor 1 of the small building.

A1 | A2 | A3 | |||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

B1 | B2 | B3 | B1 | B2 | B3 | B1 | B2 | B3 | |||||||||||||||||||

C1 | 37.28 | 37.27 | 37.25 | 37.26 | 37.25 | 37.27 | 37.25 | 37.23 | 37.25 | 19.89 | 19.89 | 19.90 | 19.88 | 19.88 | 19.88 | 19.87 | 19.88 | 19.88 | 12.80 | 12.79 | 12.79 | 12.77 | 12.78 | 12.78 | 12.78 | 12.77 | 12.78 |

37.29 | 37.26 | 37.28 | 37.28 | 37.25 | 37.25 | 37.22 | 37.26 | 37.24 | 19.92 | 19.91 | 19.91 | 19.89 | 19.86 | 19.89 | 19.88 | 19.86 | 19.88 | 12.80 | 12.79 | 12.80 | 12.78 | 12.78 | 12.78 | 12.78 | 12.77 | 12.77 | |

C2 | 37.26 | 37.27 | 37.25 | 37.23 | 37.26 | 37.24 | 37.25 | 37.20 | 37.22 | 19.90 | 19.90 | 19.90 | 19.86 | 19.86 | 19.89 | 19.89 | 19.87 | 19.88 | 12.79 | 12.78 | 12.79 | 12.78 | 12.78 | 12.77 | 12.77 | 12.77 | 12.77 |

37.27 | 37.28 | 37.24 | 37.25 | 37.25 | 37.26 | 37.25 | 37.24 | 37.25 | 19.89 | 19.90 | 19.89 | 19.88 | 19.88 | 19.87 | 19.86 | 19.85 | 19.88 | 12.80 | 12.79 | 12.79 | 12.77 | 12.78 | 12.78 | 12.77 | 12.77 | 12.77 |

**Table A2.**Simulation times in hours according to the combination of variables for floor 2 of the small building.

A1 | A2 | A3 | |||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

B1 | B2 | B3 | B1 | B2 | B3 | B1 | B2 | B3 | |||||||||||||||||||

C1 | 36.62 | 36.62 | 36.61 | 36.63 | 36.62 | 36.60 | 36.61 | 36.60 | 36.59 | 19.54 | 19.56 | 19.54 | 19.55 | 19.52 | 19.54 | 19.54 | 19.52 | 19.53 | 12.56 | 12.56 | 12.57 | 12.54 | 12.55 | 12.55 | 12.55 | 12.55 | 12.54 |

36.61 | 36.61 | 36.62 | 36.58 | 36.61 | 36.59 | 36.60 | 36.62 | 36.62 | 19.54 | 19.53 | 19.55 | 19.53 | 19.54 | 19.55 | 19.53 | 19.54 | 19.53 | 12.57 | 12.57 | 12.56 | 12.55 | 12.56 | 12.55 | 12.55 | 12.56 | 12.55 | |

C2 | 36.61 | 36.60 | 36.63 | 36.61 | 36.61 | 36.62 | 36.62 | 36.58 | 36.58 | 19.55 | 19.54 | 19.55 | 19.53 | 19.54 | 19.54 | 19.52 | 19.53 | 19.55 | 12.55 | 12.56 | 12.57 | 12.55 | 12.55 | 12.55 | 12.55 | 12.54 | 12.55 |

36.65 | 36.60 | 36.60 | 36.61 | 36.62 | 36.59 | 36.60 | 36.60 | 36.61 | 19.54 | 19.54 | 19.54 | 19.53 | 19.52 | 19.54 | 19.53 | 19.52 | 19.53 | 12.57 | 12.57 | 12.56 | 12.56 | 12.56 | 12.55 | 12.54 | 12.55 | 12.54 |

**Table A3.**Simulation times in hours according to the combination of variables for the standard floor of the big building.

A1 | A2 | A3 | |||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

B1 | B2 | B3 | B1 | B2 | B3 | B1 | B2 | B3 | |||||||||||||||||||

C1 | 412.8 | 412.8 | 412.8 | 412.7 | 412.7 | 412.7 | 412.7 | 412.7 | 412.7 | 282.9 | 282.9 | 282.9 | 282.8 | 282.8 | 282.8 | 282.8 | 282.8 | 282.8 | 229.8 | 229.8 | 229.8 | 229.7 | 229.7 | 229.7 | 229.7 | 229.7 | 229.7 |

412.8 | 412.8 | 412.8 | 412.8 | 412.7 | 412.7 | 412.7 | 412.7 | 412.7 | 283.0 | 282.9 | 282.9 | 282.8 | 282.8 | 282.8 | 282.8 | 282.8 | 282.8 | 229.8 | 229.8 | 229.8 | 229.7 | 229.7 | 229.7 | 229.7 | 229.7 | 229.7 | |

C2 | 410.0 | 410.1 | 410.0 | 409.8 | 409.9 | 409.9 | 409.8 | 409.8 | 409.8 | 281.0 | 281.0 | 281.0 | 280.8 | 280.8 | 280.8 | 280.8 | 280.8 | 280.8 | 228.3 | 228.2 | 228.3 | 228.1 | 228.1 | 228.1 | 228.0 | 228.0 | 228.0 |

410.0 | 409.9 | 410.0 | 409.8 | 409.8 | 409.8 | 409.8 | 409.8 | 409.8 | 281.0 | 281.0 | 281.0 | 280.8 | 280.8 | 280.8 | 280.7 | 280.8 | 280.8 | 228.2 | 228.2 | 228.3 | 228.1 | 228.1 | 228.1 | 228.0 | 228.0 | 228.0 |

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**Figure 1.**Small building: (

**a**) first-floor simulation; (

**b**) second-floor simulation; and (

**c**) final model.

**Figure 6.**(

**a**) Side view of robot’s reach (mm); (

**b**) ABB robot on tracked CyBe vehicle (adapted from [42]).

**Figure 9.**Type of configuration analysis for the small building: (

**a**) S11, (

**b**) S12; (

**c**) S21; and (

**d**) S22 (blue arrows show the direction in which the robot moves on crawler; red circles show the operating radius of the robot in each position, and blue numbers show the different positions of the robot).

**Figure 10.**FlexSim

^{TM}modeling of the printing sequence for analysis type S11 (green arrows are the directions where the robot moves, and black squares are the multiple robot locations).

**Figure 11.**Locations for the analysis type B12 for exterior walls (

**a**) and interior walls (

**b**) (blue arrows show the direction in which the robot moves on crawler; red circles show the operating radius of the robot in each position, and blue numbers show the different positions of the robot).

**Figure 12.**Printing sequence for analysis type B12 (green arrows are the directions where the robot moves, and black squares are the multiple robot locations).

**Figure 13.**Pareto charts of standardized effects for (

**a**) floor 1—small bldg.; (

**b**) floor 2—small bldg.; and (

**c**) standard floor—big bldg.

**Figure 19.**Interaction graph of variables concerning time for the standard floor of the big building.

Small Building | Big Building | |
---|---|---|

Number of floors | 2 | 12 |

Area per floor | 154.53 m^{2} | 910 m^{2} |

Total area | 309.06 m^{2} | 10,920 m^{2} |

Height of the walls | 2.75 m | 2.75 m |

Total height | 5.5 m | 33 m |

Factors | Coded Levels | ||
---|---|---|---|

A: Speed of the robot | A_{1} | A_{2} | A_{3} |

B: Speed of the crawler | B_{1} | B_{2} | B_{3} |

C: Location type | C1 C_{2} |

Description | Type of Analysis |
---|---|

Small building, floor 1, analysis 1 | S11 |

Small building, floor 1, analysis 2 | S12 |

Small building, floor 2, analysis 1 | S21 |

Small building, floor 2, analysis 2 | S22 |

Big building, floor 1 (standard), analysis 1 | B11 |

Big building, floor 1 (standard), analysis 2 | B12 |

Analysis | Robot Minimum Speed (0.1 m/s) | Robot Average Speed (0.225 m/s) | Robot Maximum Speed (0.35 m/s) | ||||||
---|---|---|---|---|---|---|---|---|---|

S_{min} Crawler (0.3 m/s) | S_{avg} Crawler (0.83 m/s) | S_{max} Crawler(1.4 m/s) | S_{min} Crawler(0.3 m/s) | S_{avg} Crawler (0.83 m/s) | S_{max} Crawler(1.4 m/s) | S_{min} Crawler (0.3 m/s) | S_{avg} Crawler (0.83 m/s) | S_{max} Crawler (1.4 m/s) | |

S11 | Normal | Normal | Normal | ||||||

S12 | |||||||||

S21 | |||||||||

S22 | |||||||||

B11 | Log-normal | Log-normal | Log-normal | ||||||

B12 |

**Table 5.**Average values and standard deviations of times in hours per floor according to the type of analysis.

Analysis | Robot Minimum Speed (0.1 m/s) | Robot Average Speed (0.225 m/s) | Robot Maximum Speed (0.35 m/s) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

S_{min} Crawler (0.3 m/s) | S_{avg} Crawler(0.83 m/s) | S_{max} Crawler (1.4 m/s) | S_{min} Crawler(0.3 m/s) | S_{avg} Crawler (0.83 m/s) | S_{max} Crawler (1.4 m/s) | S_{min} Crawler (0.3 m/s) | S_{avg} Crawler (0.83 m/s) | S_{max} Crawler (1.4 m/s) | ||||||||||

µ | σ | µ | σ | µ | σ | µ | σ | µ | σ | µ | σ | µ | σ | µ | σ | µ | σ | |

S11 | 37.271 | 0.014 | 37.249 | 0.014 | 37.245 | 0.014 | 19.902 | 0.007 | 19.880 | 0.007 | 19.875 | 0.007 | 12.799 | 0.005 | 12.777 | 0.005 | 12.773 | 0.005 |

S12 | 37.260 | 0.014 | 37.245 | 0.014 | 37.244 | 0.014 | 19.891 | 0.007 | 19.876 | 0.007 | 19.875 | 0.007 | 12.788 | 0.005 | 12.773 | 0.005 | 12.772 | 0.005 |

S21 | 36.618 | 0.014 | 36.606 | 0.014 | 36.604 | 0.014 | 19.545 | 0.007 | 19.534 | 0.007 | 19.531 | 0.007 | 12.564 | 0.005 | 12.552 | 0.005 | 12.550 | 0.005 |

S22 | 36.617 | 0.014 | 36.606 | 0.014 | 36.603 | 0.014 | 19.544 | 0.007 | 19.533 | 0.007 | 19.531 | 0.007 | 12.563 | 0.005 | 12.552 | 0.005 | 12.550 | 0.005 |

B11 | 412.824 | 0.036 | 412.723 | 0.036 | 412.703 | 0.036 | 282.916 | 0.019 | 282.815 | 0.019 | 282.795 | 0.019 | 229.794 | 0.012 | 229.693 | 0.012 | 229.673 | 0.012 |

B12 | 409.996 | 0.036 | 409.807 | 0.036 | 409.769 | 0.036 | 280.995 | 0.019 | 280.806 | 0.019 | 280.768 | 0.019 | 228.244 | 0.012 | 228.055 | 0.012 | 228.017 | 0.012 |

Source | p-Value | ||
---|---|---|---|

Floor 1—Small Bldg. | Floor 2—Small Bldg. | Standard Floor—Big Bldg. | |

Model | 0.000 | 0.000 | 0.000 |

Linear | 0.000 | 0.000 | 0.000 |

Robot speed | 0.000 | 0.000 | 0.000 |

Crawler speed | 0.000 | 0.000 | 0.000 |

Location type | 0.004 | 0.538 | 0.000 |

2-way interaction | 0.477 | 0.934 | 0.000 |

Robot speed ∗ crawler speed | 0.192 | 0.892 | 0.284 |

Robot speed ∗ location type | 0.553 | 0.947 | 0.000 |

Crawler speed ∗ location type | 0.905 | 0.421 | 0.000 |

3-way interaction | 0.976 | 0.677 | 0.721 |

Robot speed ∗ crawler speed ∗ location type | 0.976 | 0.677 | 0.721 |

**Table 7.**Optimal conjugations of variables to minimize simulation time in hours for floor 1 of the small building.

Solution | Robot Speed | Crawler Speed | Location Type | Time Fit | Composite Desirability |
---|---|---|---|---|---|

1 | 0.35 | 1.4 | 2 | 12.7700 | 1.00000 |

2 | 0.35 | 1.4 | 1 | 12.7750 | 0.99980 |

3 | 0.35 | 0.83 | 2 | 12.7767 | 0.99973 |

4 | 0.35 | 0.83 | 1 | 12.7783 | 0.99966 |

5 | 0.35 | 0.3 | 2 | 12.7900 | 0.99918 |

**Table 8.**Optimal conjugation of variables to minimize simulation time in hours for floor 2 of the small building.

Solution | Robot Speed | Crawler Speed | Location Type | Time Fit | Composite Desirability |
---|---|---|---|---|---|

1 | 0.35 | 1.4 | 2 | 12.5450 | 0.999793 |

2 | 0.35 | 1.4 | 1 | 12.5500 | 0.999585 |

3 | 0.35 | 0.83 | 1 | 12.5500 | 0.999585 |

4 | 0.35 | 0.83 | 2 | 12.5533 | 0.999447 |

5 | 0.35 | 0.3 | 2 | 12.5633 | 0.999032 |

**Table 9.**Optimal conjugations of variables to minimize simulation time in hours for the standard floor of the big building.

Solution | Robot Speed | Crawler Speed | Location Type | Time Fit | Composite Desirability |
---|---|---|---|---|---|

1 | 0.35 | 1.4 | 2 | 228.018 | 0.999955 |

2 | 0.35 | 0.83 | 2 | 228.067 | 0.999693 |

3 | 0.35 | 0.3 | 2 | 228.243 | 0.998737 |

4 | 0.35 | 1.4 | 1 | 229.677 | 0.990982 |

5 | 0.35 | 0.83 | 1 | 229.687 | 0.990928 |

Variables | Small Building | Big Building | |
---|---|---|---|

Floor | Floor 1 | Floor 2 | Standard floor |

Time per floor | 12.77 h | 12.545 h | 228.018 h |

Total time | 23.315 h | 2736.216 h |

Activity | Duration |
---|---|

Rebar fabrication | 1.06 days |

Rebar installation | 0.95 days |

Placement of wall formwork | 1.87 days |

Concrete pouring | 0.20 days |

Waiting time before removing formworks | 1.00 days |

Total duration | 5.08 days |

Activity | Duration |
---|---|

Rebar fabrication | 45.27 days |

Rebar installation | 40.41 days |

Placement of wall formwork | 79.63 days |

Concrete pouring | 8.72 days |

Waiting time before removing formworks | 8.72 days |

Total duration | 182.74 days |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Forcael, E.; Martínez-Chabur, P.; Ramírez-Cifuentes, I.; García-Alvarado, R.; Ramis, F.; Opazo-Vega, A.
Performance Analysis of 3D Concrete Printing Processes through Discrete-Event Simulation. *Buildings* **2023**, *13*, 1390.
https://doi.org/10.3390/buildings13061390

**AMA Style**

Forcael E, Martínez-Chabur P, Ramírez-Cifuentes I, García-Alvarado R, Ramis F, Opazo-Vega A.
Performance Analysis of 3D Concrete Printing Processes through Discrete-Event Simulation. *Buildings*. 2023; 13(6):1390.
https://doi.org/10.3390/buildings13061390

**Chicago/Turabian Style**

Forcael, Eric, Paula Martínez-Chabur, Iván Ramírez-Cifuentes, Rodrigo García-Alvarado, Francisco Ramis, and Alexander Opazo-Vega.
2023. "Performance Analysis of 3D Concrete Printing Processes through Discrete-Event Simulation" *Buildings* 13, no. 6: 1390.
https://doi.org/10.3390/buildings13061390