Experimental Study of 3D Concrete Printing Configurations Based on the Buildability Evaluation

Abstract

Different formulations for 3D printable cementitious composites have been developed for extrusion-based printing. However, there is a lack of configuration guides for actual printing operations, which integrate one printable material and one printing system closely. Three testing methods for configuration determination were proposed and tested with three material proportions, with initial setting times of 2, 8, and 13 min, respectively. The building index (BI) measures the layer stacking stability based on the material, scale, and device. The height reduction test (HRT) quantifies the shortening in the height of the printed filaments. The leaning angle (LA) refers to the maximum slope of the stacked layers. In this study, results showed the critical values were (a) 0.167 for the height reduction ratio (HRR), (b) 40° for LA, and (c) 0~19.1, 0~61.1, and 0~99.4 for BI of the three mixtures. They were the meta parameters used to guide the CAD sketching, material development, and printing configurations, including the printing speed and layer height.

1. Introduction

Three-Dimensional printing technology with digital, customized, and new material features is a promising emerging technology. After more than 20 years of development, 3D printing technology has been used in many fields such as aerospace, medical equipment, metal parts, etc., with its high accuracy, short production cycle, and diverse materials [1,2]. The research on and application of 3D concrete printing (3DCP) technique (3DCPT) have been accelerating, from Pegna using steam injection to cement powder dating back to 1997 [3], to contour craft technology [4] printing curved walls in 2004, and Shanghai Winsun Ltd. printing various types of houses as well as many recent applications all around the world [5]. Compared with traditional building construction, 3DCP technology has the following potential advantages: (1) high degree of mechanical automation with short construction times, safety, cleaning, and accuracy; (2) no frame required, and resource consumption is relatively reduced; (3) labor-saving; (4) light weight, high strength and multi-functionality can be achieved through structural design; and (5) high customization can realize both standardization and personalization in construction products.

Printable material needs to possess the required properties, including print-ability, pump-ability, build-ability, and open time [6], with which the printing equipment can pump the mortar to the printing mechanism, print/extrude the material to the platform, and build a layer-by-layer structure with proper bonding strength between layers in an open time. The material should possess the following characteristics: (1) have good fluidity to be pumped from a remote container, (2) can be easily extruded from a nozzle to the printing bed, (3) keep its finished shape with neither obvious fractures nor cracks [7], (4) gain early strength as fast as possible to bear the continuous load from the following layers, and (5) good bonding with adjacent filaments/layers. Because of the advancement of printing devices, many material proportions have been formulated with acceptable printing results. The mixture in the extruding technique is pre-mixed, and a paste is formed before printing, which remains in paste form on the printing platform. The paste passes through the nozzle to be “printed” in the form of thin filaments, under the operations of pumping, squeezing, and vibrating. Several studies on rheology have been carried out to help design printable materials [8,9,10]. Bentz et al. [11] stated that the material should have high compressive yield stress to bear the load from upper layers during the process of hydration; however, Panda et al. argued that the high yield stress can make the extrusion operations difficult [12].

Many studies evaluated buildability simply based on the number of layers printed or height achieved in a single printing process without failure [13,14,15]. It is worth noting that buildability also depends on the workability and mix proportions. Khalil et al. [16] reported that a high buildability of 30 layers can be achieved using calcium sulfoaluminate cement. Panda improved their printing from 13 to 20 layers by using high-volume fly ash mixtures [17]. Wolfs et al. [18] included limestone filler, additives, rheology modifiers, and a small number of polypropylene fibers to the printing materials and managed to print 30 layers without collapse.

On the other hand, Rahul et al. [7] and Kazemian et al. [19] evaluated the buildability by measuring the height reduction of the bottom layer from a two-layer printed specimen. To quantitatively characterize the buildability, Ma et al. [20] determined the factor as the ratio of vertical deformation of 20 stacked layers to the optimal height. Perrot et al. [8] proposed the buildability as the printed height. They established a linear relationship between the static yield stress and the buildability, but factors such as material density, gravity, and the geometry of the tested specimen were kept constant. Arunothayan et al. [21] defined good buildability when the lower layers showed no vertical distortion, layer failure, or excessive deformation in a seven-layer printing test. To achieve good buildability, Wolfs et al. [18] suggested that the printing materials with low- to zero- slump should be used. Bentz et al. [11] stated that the buildability can be improved by decreasing the material density as well as the slump. Nevertheless, the printing failure still would happen with zero-slump material due to the elastic buckling and plastic collapse.

However, from the technical point of view, it is not suitable to quantify the buildability by how many layers are printed or how high the achieved structure is. It should be noted that the printing height or layers can be increased remarkably by lowering the printing speed or extending the time interval [22] without considering the bonding between layers. The range of the 3D printer also limits the printing height of one printing process. The buildability reported in the literature is evaluated based on printing 10 to 30 layers. The buildability of 3DCP should refer to the ability to create a complex architectural object rather than simple layer stacking, meaning that the buildability is an evaluation of one printing operation rather than of the printable material. Moreover, the printing operation involves the printable material and the printing equipment. In actual printing activities, one mixed material can not be extrudable with a small nozzle tip, but be printable with a large one. It can not be stackable with fast printing speed but buildable with slow printing speed. Thus, the “printable” material is closely related to the 3D printer regarding the configurations. Thus, the success of printing is heavily affected by the printing device (PD), printable material (PM), and the printed object (PO).

Once the PM has been developed and the PO is given, the PD configurations should be precise regarding the motion speed, extruding speed, layer thickness, etc. in the form of the toolpath, which is generated by the printing software (i.e., slicing software) with a group of configurations. Better configurations can help optimize the toolpath to achieve better printing results to fit the designed geometry of the PO. A typical printing process is illustrated in Figure 1. Unfortunately, it is hard to find guidelines among the existing studies regarding concrete printing configurations. Additionally, most of their printers utilize control boards from the plastic 3D printing technique (fused deposition modeling, FDM). The toolpath generator (TPG) needs a configurable set of melting temperature, filament diameter, filling pattern, and maximum speed. However, they are not suitable for concrete printing. Therefore, it is urgent to clear the current confusion to guide 3D concrete printing activities.

To establish standard criteria for the printing configuration guidelines, the following three methods were proposed:

• Building index (BI): It evaluates the geometry-keeping ability. The BI can help determine the parameters for the material development and the printing configuration based on the printing scale and the material mix. The buildability can be quantified as the range of BI for one printable material;
• Height reduction test (HRT): This quantifies the slumping criteria of the printed filaments in terms of height reduction ratio (HRR) instead of the traditional slump test; and
• Leaning angle (LA): It is the angle between the vertical line and the filament-stacking direction to quantify the buildability of the material for printing complex geometry.

3DCP must be a system that combines materials, devices, and software. Studies should be conducted both on the material and printing equipment. This study proposes buildability evaluation methods for a printing operation in terms of the PM, PD, and PO. The determinations of the printing configurations were discussed, and theoretical requirements for 3DCP were proposed to ensure that (1) the mix proportion is well developed; (2) a smooth extrusion with uniform filament size and free of fractures and cracks is achieved, and (3) precise positioning of the extruder/nozzle by the motion control system can be guaranteed. The results of this study can fill the knowledge gap by proposing suitable methods to evaluate and guide printing activities, including material development, printing configurations, and geometric design.

2. Materials and Equipment

2.1. Mix Proportion

The cementitious materials used in this study were ordinary portland cement (OPC 42.5 R, purchased from Foshan China) and sulfoaluminate cement (SAC, 42.5 R, purchased from Shanghai, China). The purpose of using SAC was to meet the requirements of (1) fast setting to keep the designed geometry, (2) high early strength to bear the continuous layer weight, and (3) low shrinkage to prevent cracks along the interfaces between layers and lines [23].

Table 1. Chemical composition (wt.%) of OPC and SAC.

	CaO	SiO2	Al2O3	MgO	Fe2O3	SO3	IL	TiO2	Na2O	K2O	Others
OPC	55.01	23.44	7.19	2.24	2.96	2.87	3.48	0.27	0.32	0.89	1.33
SAC	44.48	7.82	20.02	1.94	1.46	17.9	4.31	-	-	0.70	1.37

shows the chemical composition of both OPC and SAC materials.

Fine sands with a diameter from 210 $\mathsf{\mu }\mathrm{m}$ to 250 $\mathsf{\mu }\mathrm{m}$ were used as the aggregates. Polypropylene fiber (PFB, round interface, 98% carbon content, density 1.7 g/cm³, tensile strength 4900 MPa, tensile modulus 228 GPa, fiber diameter of 7 $\mathsf{\mu }\mathrm{m}$, length ranging from 3–6 mm) was used to increase the tensile and flexural strength of the printed outputs. High-range water-reducing agent (HRWR, polycarboxylic acid superplasticizer) and thickening water-retaining agent (HPMC, hydroxypropyl methylcellulose) were chosen to improve the printability of paste by improving the viscosity [24,25]. A defoaming agent (DFA) decreased the air bubbles generated during the mixing and extruding processes.

2.2. 3D Printer

A frame-type 3D printer was designed and built using an open-source 3D printing control motherboard with a mechanical accuracy of 0.1 mm in three alignments of X, Y, and Z axes. The printer was operated at a maximum movement speed of 100 mm/s in the XY plane, with a maximum printing size of 60 cm × 60 cm × 1500 cm. The resolution of the motion system was 0.1 mm, acceptable for the concrete printing operations. The control unit of the printer was based on the RepRap open-source project, ensuring precise motion positioning and stable execution for a smooth printing process. A round nozzle with a diameter of 10 mm was developed to achieve good geometry and relatively high printing accuracy. The extrusion bin was fed locally by hand instead of remote pump feeding. The developed extruder with a two-segment screw is shown in Figure 2. The large screw blade is for material feeding, and the small screw is for extrusion.

3. Experimental Program

The mixed proportions of the printing mortar are listed in

Table 2. Mix proportions of the printing mortar.

No.	W/C	OPC/g	SAC/g	Fine Sand/g	HRWR/g	HPMC/g	DFA/g	PFB/g
OSS1	0.37	1440	960	1600	19.2	8	2	40
OSS2	0.37	1680	720	1600	19.2	8	2	40
OSS3	0.37	1800	600	1600	19.2	8	2	40

. The mixtures were designed to meet printability requirements, with a constant water-cement ratio (W/C) of 0.37. Different proportions of SAC (0.4, 0.3, and 0.25 by weight of cement) were added, and the effects on initial setting times were examined. The dried fibers were blow-treated for better dispersion before being added to the dry mix. All solid components, apart from fibers, were dry mixed for 10 min. Then, the treated fiber was added, followed by wet mixing for another 10 min. The raw paste was then placed inside the nozzle container, and the printing process was started immediately.

3.1. Printing Procedures

Different samples were printed to study various application scenarios. STL files were exported with CAD software DesignSpark Mechanical 4.0 (deviation: 0.75 mm and angle tolerance: 8°), and the printing command G-codes were generated with the software Simplify 3D. The designed height of each layer was 5.0 mm. Five kg of cementitious mortar was prepared and fed into the material bin manually after the printer was powered on and installed the printing toolpath file. Some of the mortar samples were incorporated with pigment to create colored POs. The printing process is described in Figure 3.

3.2. Basic Testing Methods

The initial setting times of the prepared pastes were determined by the Vicat needle apparatus according to ASTM C191. The fluidity of the fresh mortar was evaluated using the flow table test according to ASTM C230. ImageJ, a Java-based image processing program commonly used in the biomedicine domain for microscopic measurements, was used to measure layer height and leaning angle.

The printing components were of different geometries; then, the generated toolpath might include various motion speeds, non-extruding motions, or rapid changes in direction. In addition, neighbored filaments had an inter-supporting effect of increasing the layer stacking ability, as shown in Figure 4a. Thus, this study was conducted on the basis of single-walled hollow cylinders, as in Figure 4b, with which the 3D printing would have a stable motion speed, a constant extruding speed, and a non-stop printing toolpath with a spiral-up printing method [26]. Furthermore, the toolpath did not have sudden corners to avoid collapse due to the material being pulled by the nozzle motion. Therefore, data accuracy of the BI, HRR, and LA would be guaranteed.

A printing height ratio (PHR) was employed to evaluate the height quality of printed products, as shown in Equation (1) and Figure 4b, referring to the actual average height of the printed product divided by its designed height $H_{designed}$. The printed product was considered acceptable (Pass) if the $PHR\ge 90\%$, whereas it was unacceptable (Fail) if the $PHR<90\%$.

$$PHR=\frac{h_1+h_2+h_3+h_4}{H_{designed}\times 4}\times 100\%$$

(1)

3.3. Configuring Methods

3.3.1. Building Index (BI)

Buildability is about the ability of the PO to maintain the printed geometry itself with fast-setting and early strength to bear its own weight and that from subsequent layers. As said in Section 1, neither the maximum number of layers nor the height of the PO can be used to evaluate buildability since they are highly dependent on the configuration of the PD.

In this study, the building index (BI) was defined by how many layers/loops can be finished within the initial setting time duration $T$.

$$BI=\frac{T}{t_{loop}}$$

(2)

where $t_{loop}$ stands for the loop time, indicating the (average) time for one-layer fabrication to combine the printing scale (total length of the filaments in one layer) of the PO and the printing speed of PD. As shown in Figure 5, for a hollow cylinder with a diameter of $D$ at a printing speed (nozzle motion speed) of $V$, the loop time can be determined as:

$$t_{loop}=\frac{D\times \pi }{V}$$

(3)

and the BI can be further expressed as:

$$BI=\frac{T}{t_{loop}}=\frac{T\times V}{D\times \pi }$$

(4)

The BI includes the initial setting time of PM, the printing scale of the PO, and the printing speed of the PD. It is easy to understand that: (1) for one fixed printing scale, if the printing speed is increased, the PO is more likely to collapse, since more layers are stacked on; (2) for a fixed printing speed, the smaller the printing scale, the more layers would be stacked on the previous printing layer, and the more likely the PO will collapse; (3) if the $t_{loop}$ is fixed in one printing activity, the higher the $T$, the more likely the PO will collapse. Thus, lowering $BI$ would lead to 3D printing success.

To evaluate the BI, three groups of specimens were prepared with the designated layer height, filament width, and total height of 5.0 mm, 15 mm, and 30 layers, respectively. The first group with different SAC contents was prepared, and they were expected to show different initial setting times. The specimens were 100 mm diameter cylinders made of OSS1, OSS2, and OSS3 at a printing speed of 50 mm/s and marked as D100V50OSS1, D100V50OSS2, and D100V50OSS3. The numbers 100 and 50 after the letters D and V show the diameter of the specimen and the printing speed, respectively. The second group of specimens of identical size was prepared at different printing speeds, ranging from 20 mm/s to 50 mm/s with an increment of 10 mm/s. They were made of mix OSS3 and marked as D100V20OSS3, D100V30OSS3, D100V40OSS3, and D100V50OSS3. The third group of specimens was prepared with different cylinder diameters ranging from 50 mm to 200 mm with an interval of 50 mm. They were printed with the mixture OSS3 at a printing speed of 40 mm/s and marked as D50V40OSS3, D100V40OSS3, D150V40OSS3, and D200V40OSS3. In addition, other supplementary specimens were produced to fulfill the orthogonal test requirements for diameter, speed, and initial setting time, as well as to provide more data for analysis, as listed in

Table 3. The cylinder samples for the BI tests.

Sample Group	Sample Name	Diameter	V (Speed)	Mixture
D100V50T@	D100V50OSS1	100	50	OSS1
	D100V50OSS2			OSS2
	D100V50OSS3			OSS3
D100V@OSS3	D100V20OSS3	100	20	OSS3
	D100V30OSS3		30
	D100V40OSS3		40
	D100V50OSS3		50
D@V40OSS3	D50V40OSS3	50	40	OSS3
	D100V40OSS3	100
	D150V40OSS3	150
	D200V40OSS3	200
Other specimens excluding above samples	D50V20-, D50V30-, D50V40-, D50V50-, D100V20-, D100V30-, D100V40-, D100V50-, D150V20-, D150V30-, D150V40-, D150V50-, D200V20-, D200V30-, D200V40-, D200V50-,			OSS1 OSS2 OSS3

.

3.3.2. Height Reduction Test (HRT)

In traditional concrete research, the slump test is used to evaluate the workability of the mortar (about 10 Kg for the slump experiment). However, in a 3DCP process, the amount of material being printed/extruded is relatively small (about 300 g for 100 mm length of printed filament); thus, the ordinary slump test for a large amount of mortar is not suitable to characterize the PM. In this study, a height reduction test (HRT) was proposed to quantify the height loss of the extruded filaments and find the critical value.

The extruded fresh mortar should fill the gap between the nozzle tip and the upper surface of the previously printed layer, as shown in Figure 6a. Otherwise, the printed line will not follow the designated route, especially at turning points, as shown in Figure 6c,d. In a printing process, $h$ is defined as the designed layer height and $H$ as the gap height reserved for a layer. The $H$ would be larger than $h$, due to the slump of previous layers, thus creating more room for the subsequent layer. The gap height tolerance (GHT) $\delta$ is defined as: $\delta =\left(H-h\right)/h ,H\ge h$. Wolfs et al. [18] suggested that the printing materials with low- to zero- slump should be used, then $H\to h$, meaning $\delta \to 0$, and based on the authors’ experience, for printing ordinary geometry, the $\delta$ should be less than 0.2, meaning that $H$ should be less than $1.2h$. Otherwise, the extruded filament cannot land in the designated plane by free fall, as indicated in the red circle shown in Figure 6d.

The printing technology has been developed for complex components that have many turns in the printing route. misplacement would lead to inconsistency with the designed geometry and, eventually, a collapse failure, as shown in Figure 7, as the accumulated height error increases. It is essential since most of the printing toolpath has the same fixed height for each layer, marked as same-layer-height printing.

The extruded material would have a slight slump. To determine the slumping requirement, a parameter, height reduction ratio (HRR) $r$, was proposed as defined in Equation (5). It is easy to conduct an HRT to obtain the height ratio $x$, which is the measured real height of a printed filament divided by its designed height $h$. Then, the HRR can be expressed as:

$$HRR=r=1-\frac{real height measured}{h}=1-x$$

(5)

Three groups of HRTs have been conducted, with a time gap of 10 min, 20 min, and 15 h, respectively. The criteria of the HRR $r$ were theoretically calculated and verified by a printing simulation, which was conducted via Microsoft Excel with VBA (Visual Basic for Applications) program. Detailed calculation and simulation of HRR for the conditions when BI = 1 and BI > 1 are provided in later sections.

3.3.3. Leaning Angle (LA)

It is challenging to manufacture leaning sections without supports. A leaning angle (LA) test was proposed to find a critical angle for geometry design in 3D printing activities/applications. The LA defines the angle between the layer-stacking direction and a vertical line, as in Figure 8a. A series of cone buckets with LA α ranging from 10° to 50° were printed according to the sketch design shown in Figure 8b. The Pass and Fail of a leaning angle are determined by Equation (1) and Figure 4a. The maximum LA from the Passed buckets would help the sketch design for a decorative vase printing.

4. Results and Discussion

4.1. Basic Properties

The initial setting times for mixes OSS1, OSS2, and OSS3 were 2, 8, and 13 min, respectively. As expected, the initial setting times decreased with the increasing content of SAC. The average flow diameters of the corresponding samples were 138 mm, 143 mm, and 160 mm, in an acceptable range for mixtures having a smooth surface and high buildability, as concluded by Tay et al. [27]. It can be seen in Figure 9a that the printed layers or circumferential lines are of high consistency, without obvious fractures, cracks, or settlement. Moreover, a regular width of the printed filament can be seen in Figure 9b, indicating high printing quality [7,16]. Therefore, it is believed that the material proportion and the printer achieved acceptable printability, with accurate mechanical positioning, controllable extruding operation, and stable material properties, based on which the buildability could then be further studied.

The printed cylinder D200V40OSS3 consisted of 30 layers and took about 8 min to print. The height of each printed layer and the accumulative height measured by ImageJ are shown in Figure 10. The average height was 4.96 mm, with a standard deviation of 0.42. It should be pointed out that the first layer and the last layer were excluded from the measurements because of the spiral-up printing method used. The layer height results show that the layer stacking operation was successful and stable, as the printer could extrude the material evenly at a stable printing speed. Therefore, the printer and the material proportion were considered suitable for further evaluation.

4.2. The Printed Samples

The samples were printed as shown in Figure 11. Some of the sample material fell off when printing, as indicated by the red arrows, and some had several layers fail, as indicated by the red boxes. The printing times were determined by the sample diameter and the printing speed. The printing times are listed in

Table 4. The printing times for each sample according to its diameter and printing speed.

	V = 20 mm/s	V = 30 mm/s	V = 40 mm/s	V = 50 mm/s
D = 50 mm	3.13 min	2.12 min	1.60 min	1.10 min
D = 100 mm	7.52 min	5.03 min	4.17 min	2.68 min
D = 150 mm	11.82 min	8.03 min	5.80 min	4.78 min
D = 200 mm	15.98 min	10.85 min	8.15 min	6.53 min

.

4.3. Building Index

Figure 12a shows the effect of diameters, initial setting times, and printing speeds on the BI values. The BI values increased with decreasing diameter, increasing initial setting time, and increasing printing speed. However, not all of the specimens were printed successfully, as shown in Figure 11. The failure and success cases are indicated as red and black dots in Figure 12a, respectively. The printing failed at $BI=76.4$ for material mix OSS2 in group D100V50T@, at $BI=124.2$ for the printing speed at 50 mm/s in group D100V@OSS3, and at $BI=198.7$ for the cylinder diameter at 50 mm in group D@V40OSS3. The printing succeeded at $BI=19.1$ for material mix OSS2 in group D100V50T@, at $BI=99.4$ for the printing speed at 50 mm/s in group D100V@OSS3, and at $BI=99.4$ for the cylinder diameter at 50 mm in group D@V40OSS3. Therefore, printing would definitely succeed with $BI$ lower than the success points and fail with $BI$ higher than the failing points for each group.

Figure 12b shows the relationship between BI and the loop time, based on different initial setting times for mixes OSS1, OSS2, and OSS3. It can be seen from the figure that the longer the initial setting time, the wider the acceptable range of $BI$. The mix OSS3 with 13 min of initial setting time had the largest acceptable BI range of 99.4, whereas the mix with the shortest initial time only showed a BI range of 19.1.

As shown in Figure 12a, results from the three independent groups show that the lower BI could guarantee successful printing. It could be explained from the BI definition in Equation (4) that: the printed filaments would have more time to obtain strength to maintain geometry before the next layer is stacked on, leading to better buildability with a lower printing speed $v$, larger printing scale $D$, or shorter initial setting time $T$.

Therefore, for one printing application with a known printing scale $D$, if the printing speed of the 3D printer is fixed, the material should be developed with a low initial setting time in the acceptable range of the material printability. If the material mix proportion is fixed, the printing speed should be lower in the acceptable range of the total printing time of the application. For the PD in this study, the BI ranges of the OSS1, OSS2, and OSS3 were 0–19.1, 0–61.1, and 0–99.4, respectively.

A BI of around 50 was chosen to print different sizes of cylinders with mix OSS3 as the PM. Four cylinders with diameters of 50 mm, 100 mm, 150 mm, and 200 mm were sketched and sliced with different printing speeds to guarantee a BI of around 50. Each printed cylinder consisted of 30 layers. All four printings succeeded without collapse or obvious slump, as shown in Figure 13.

Table 5. Data and calculation of the printed cylinders with material mix OSS3.

	Unit	D = 50 mm	D = 100 mm	D = 150 mm	D = 200 mm
Printing speed *	mm/s	10.1	18.6	27.9	37.2
$t_{loop}$	s	15.5	16.9	16.9	16.9
BI		50.2	46.2	46.2	46.2

* The printing speed is the average value. The TPG generated the speed of each toolpath according to the given maximum speed and the CAD file.

summarizes the required printing time and the calculated BI.

The loop time in Equation (3) can be controlled to be equal to or longer than the initial setting time, meaning $BI\le 1$. In this case, the printed filament could have enough time to gain early strength and maintain its geometry without collapse. However, the time for layer bonding $t_{bonding}$, as illustrated in Figure 5, would be extended reversely, decreasing the interface bonding strength [28,29] and the mechanical properties of the PO. To obtain a good bonding, the printing speed needs to be higher, leading to a bigger BI and a high mechanical property of the PO. Fortunately, the layer bonding would be enhanced by other techniques, such as inserting rebars [30] or nails [31]. Therefore, the BI needs to be chosen carefully to balance successful printing with the mechanical properties of the printed results.

In normal printing activities, the $t_{loop}$ may choose the average loop time of the printing component, or the whole printing time divided by the layer amount, as in Table 5. Those data can be found in the TPG software. For solid components, such as in the sketch in Figure 4a, the loop time for one layer could be:

$$t_{loop}=\frac{material mass of one layer \left(gram\right)}{the nozzle extruding speed \left(gram per s\right)}$$

Besides the $t_{loop}$, there are many time data in the 3DCP, related to the yield stress, slumping, setting, and bonding behavior of the fresh material, among which only the initial/final setting time are universal characterizing methods, indicating a material starting to lose plasticity and completely losing plasticity, respectively. The final setting time is later than the open time, out of the printability range. Thus, the initial setting time was the suitable parameter in the BI at this stage. Although some materials have zero slump and there is no height reduction in each printed layer, the printing failure still would happen due to the elastic buckling and plastic collapse [32,33], since the distribution of the individual material, after being stirred by the blades, extruded by the screw, and sheared by the nozzle tip, is not sufficiently uniform. More studies should be conducted on the timing data to upgrade the BI equation by balancing the yield stress, slumping, setting, and bonding behavior.

Nevertheless, compared to the existing buildability characterizing methods that simply quantify layer amount [10,13], height achievement [8], or height reduction [7,20], the BI in Equation (4) considers and balances the printing speed and printing size and results in a dimensionless value. BI is related to the material and its PD and the nozzle tip specified, and it evaluates the working range of PM and PD. In other words, BI characterizes not only the material but also the printing system. For one developed PM, BI could be one configuration for generating the best toolpath from variable sizes of PO.

Furthermore, the BI in this study was only for an extruding mechanism stirring, shearing, and pushing the material out of the nozzle tip, as utilized in this study and other similar studies [34,35], and may not be suitable for piston-like extruders [36,37,38].

4.4. Height Reduction Test

The HRT results are shown in Figure 14, manifesting that the mix proportion in this study had nearly zero slumps after 15 h for mixture OSS3. The criteria values for the HRR are discussed and simulated as follows.

4.4.1. HRR for $BI\le 1$

Assuming that the PM would stop slumping and obtain enough strength before the next layer is printed, meaning the $BI\le 1$, and the PD supplies stable printing and precise positioning, the printing operation starts from 1-Positioning, 2-Printing, 3-Material slump, and repeats 1, 2, 3 for the next layer, until the last layer N, as in Figure 6b. Data on the height for each step can be represented as shown in

Table 6. Height data during the printing process.

Layer No.	1. Nozzle Positioning	2. Printing	3. Material Slump	Accumulated Height
	Nozzle Position *	H, Gap Height **	Layer Height after Slump ***
0	h	h − 0	h (1 − r)	h (1 − r)
1	2 h	2 h − h (1 − r)	(2 h − h (1 − r)) (1 − r)	h (1 − r) + (2 h − h (1 − r)) (1 − r)
N	(N + 1) h	(1 + r1 + r2 + … + rN) h	(1 − rN+1) h	(N − r1 − r2 − … − rN+1) h

* Nozzle height, the position of nozzle in the Z direction for each layer, achieved by the motion system, i.e., same-layer-height printing. ** Gap height reserved for this layer equals the nozzle position subtracted by the accumulated height in the previous layer. *** Real height of this layer after being printed and undergoing the material slump.

.

The prepared gap height for layer N is $H=\left(1+r^1+r^2+\cdots +r^{N-1}+r^N\right)\times h={\sum }_{i=0}^N{r}^i\times h$. As mentioned earlier, $H$ should be less than $1.2 h$ when GHT $\delta <0.2$. For the layer $N\to \infty$, the formula ${\sum }_{i=0}^N{r}^i, r\in \left(0,1\right)$ is convergent to $\frac{1}{1-r}$; thus, the HRR can be derived as:

$$HR{R}_{BI=1}=r_{BI=1}=\frac{\delta }{\delta +1}$$

(6)

Hence, the height reduction ratio can be solved for $r<0.167$, meaning that it is acceptable to print the mortar having less than 16.7% height reduction after extrusion, under a printing GHT $\delta$ = 0.2.

4.4.2. HRR for $BI>1$

The discussion above is theoretically based on $BI\le 1$. In a real printing operation, the material would undergo a further slump after the following layers are stacked on and show much more height reduction under the weight from the subsequent layers if it cannot gain strength early enough. One layer would have many slump steps/times ($BI=n>1$) after being printed, and its height shrinkage ratio for each step/time could be marked as $x_i \left(i=1,2,\cdot \cdot \cdot ,n\right)$. Taking a two-step slump ($BI=2$) as an example, the printed filament has a height of $H$ after being printed, a height of $\left(H\times x_1\right)=H{x}_1$ after the first step/slump at time $T1$, and $\left(H{x}_1\right)\times x_2=H{x}_1{x}_2$ after the second step at $T2$, and keeps its height $H{x}_1{x}_2$ from $T3$ and on. The $x_n$ indicate the height slump ratio, $x_n\in \left(0,\left.1\right)\right.$. The height data for each layer are graphed in Figure 15, as the $Tn$ indicates the printing time on each layer. Then, the HRT of this two-step slump material would be $HR{T}_{BI=2}=1-x_1{x}_2$. Furthermore, when $BI=n$, the height reduction ratio would be:

$$HR{R}_{BI=n}=r_{BI=n}=1-x_1{x}_2\cdot \cdot \cdot x_n=1-{{\displaystyle \prod }}_{i=1}^n{x}_i x_i\in \left(0,\left.1\right)\right.$$

(7)

At the time $T12$, the previous 11 layers all finish their two-step slump and keep the stable height $H_n{x}_1{x}_2$. Thus, when $n=1$, Equation (7) would be the same as Equation (5). When $n\ge 2$, it only needs to solve the product of $x_n$ (${\prod }_{i=1}^n{x}_i$), without considering any single value of $x_n$. Therefore, the two-step slump printing can be considered one-slump printing for enough layers printed and a multi-layer slump in the same pattern. Regarding Equation (6), the $HR{R}_{BI=n}$ can be derived as:

$$HR{R}_{BI=n}=r_{BI=n}=\frac{\delta }{\delta +1}(n>1)$$

(8)

4.4.3. HRR Printing Simulation

To verify Equation (6), a VBA code in Excel simulated the printing process and the slump steps when $BI=n$ ranging from 1 to 100, by finding the minimum ${\prod }_{i=1}^n{x}_i$, via traversing $x_i$, where $i\in \left(1,n\right)$, $n\in \left(1,100\right)$, and $x_i\in \left(0,1\right)$.

As shown in Figure 16, the slump steps and the $x_i$ are in columns A and B, while the printed filaments are simulated and shown in columns J to ZZ. Each layer takes two steps to finish its slump and stop losing height, with HRR $x_1$ and $x_2$, where $0<x_1,x_2<1$, as shown in cells B8 and B9. Then, the total height reduction ratio can be calculated as in cell D7 by $r=1-x_1{x}_2$. Twenty layers are listed in the Excel file. Column F lists the layer counting number, column G lists the accumulated height for the current layer, and the cells of column H are the gap heights reserved for the new layer.

In the first printing cycle, layer 1 was printed and shown in column J, having the $x_1$ slumped in J8. In the second printing cycle, layer 2 was printed and shown in column K with $x_1$ slumping in K9, while layer 1 continues with $x_2$ slumping in J9. In the third printing cycle, layer 3 was printed and shown in column L, and has $x_1$ slumping in L10, while layer 2 continues its $x_2$ slumping in cell K10 and layer 1 remains at its height. The subsequent simulation continues the same pattern. After each layer has been “printed”, the accumulated height and the gap height for the next layer are calculated.

The VBA “printing” code runs for every combination of $x_1$ and $x_2$, each ranging from 0 to 1.0, with an increment of 0.001. One “printing” succeeds only if each gap height $H<1.2$, and the minimum $x_1\times x_2$ with succeeding “printing” can be found for the maximum HRR = $1-x_1\times x_2$. Eventually, the simulated printing calculation found that HRR is 0.167 for this two-step slump material when GHT $\delta =0.2$. The same $HRR=0.167$ was then calculated for $BI>2$.

In addition, several simulations were conducted for $BI>0$ with $\delta \in \left(0,0.3\right)$ and obtained the same result with Equation (8), proving that the multi-layer slump can be considered as a one-layer slump to characterize the HRR criteria.

Conclusively, based on the “printing” simulation and theoretical calculation, the HRR of PM can be correlated with the printing GHT $\delta$ as shown in Equation (9), regardless of the multi-step slump and the compression from self-weight and weight from subsequent layers in a printing process.

$$HRR=r=\frac{\delta }{\delta +1}$$

(9)

For the GHT $\delta$ = 0.2, the criteria value of HRR is 0.167. For printing complex geometry, the GHT should be smaller, and the material with low HRR is then required.

In actual printing practice, the height reduction ratio test will be conducted on the maximum $BI$ layers, and the HRR can be calculated as:

$$HR{R}_{BI}=r_{BI}=1-\frac{real height measured on BI layers }{h\times BI}$$

(10)

The slump of the cementitious material cannot be avoided since the force of gravity on the particles is stronger than the cohesion in the material matrix at the beginning of the hydration, even if most of the PMs have admixtures of thickener to increase their viscosity. Like BI, HRR is not for the material only, but related to the GHT $\delta$, the requirement for the printing accuracy of PO, a reasonable and direct basis for the specific slump data of the PM. Thus, the HRR is more suitable than the height deformation tests of 20 layers [20], 7 layers [21], or 2 layers [7,19]. Furthermore, with the precise slumping data, the height of the printed filaments can be predicted, and a more complex toolpath can be realized, such as by varying the layer height [39]; then the height tolerance can be larger than needed.

4.5. Leaning Angle

The cone buckets with LA α ranging from 10° to 50° were printed as shown in Figure 17a. It can be observed that the print failed and collapsed when LA was higher than 40°. Thus, the max LA of this material is 40°, and the leaning angle in the sketch design can not be higher than 40° for the material and the printer in this study. A blue vase, shown in Figure 17b, was then designed and printed successfully with a maximum LA of 36°. Increasing the LA by optimizing the material formulation can aid the design of more complex geometry, by, for example, decreasing the setting time or viscosity, which would make extruding difficult, leading to low printability. An acceleration technique could be invented to speed up mortar setting, such as by dosing with accelerating admixtures [40] at the nozzle tip. The layer thickness was fixed at 5 mm for all the printings. The result data would vary when using other layer thicknesses.

Horizontal bridge-like geometry could be printed if the LA reached 90°, which is common and achievable in plastic extrusion printing. However, it is difficult to reach 90° LA for cementitious material. In plastic printing, the process involves a rapid (nozzle moving speed at 100 mm/s) physical change from high-temperature liquid (~200 °C for ABS material) to low-temperature solid (room temperature) using a small amount of material (nozzle diameter 0.4 mm) and, therefore, easy to dissipate heat. Contrarily, the printing of cementitious materials involves a much slower chemical change and requires a larger nozzle size.

Thus, the 3DCP technique can not directly print horizontal overhang, such as a roof, but it could be possible with some specific printing strategies proposed by Khoshnevis [4] and Apis-Cor.com [5]. Supporting material, such as wax, can be introduced with another extruder to help achieve better buildability. Roofs were printed with manual support of sand and waxes by Khoshnevis et al. [41]. The second nozzle can print waxes to support the printed concrete, and the waxes can be removed by heating, while the multi-nozzle techniques are common in plastic printing.

4.6. Applications of the BI, HRR, and LA

BI, HRR, and LA can be treated as the meta parameters of the 3DCP, as in Figure 18. They can fill the gap of the printing configurations to close the loop of the 3D printing operation. In the printing operation, the PD is ready, and the PM is ready and changeable; then, the LA, HRR, and BI can be pre-tested with this study, as in the point p0. For an actual printing request, parameters can be exported from the designed PO: max LA, height tolerance, layer height, layer size, printing speed, and mechanical requirements. Then, the verifications can be conducted at points p1, p2, and p3, from which the results can guide the updating of the PM proportion or PO sketch. Eventually, the final output PO can be fabricated from point p4.

Many complex geometries for decorative applications have been successfully printed, as shown in Figure 19. The designated resolution can determine the maximum LA, the HRR, and the nozzle size; then, the mix proportion can be furtherly confirmed. The corresponding BI can be determined by the nozzle size and material proportion by the cylinder-printing tests. The optimized printing speed would be obtained to guarantee printing success. It would be configured variably on different layers to guarantee the same BI throughout the printing process.

5. Conclusions

Traditional material testing methods may not be suitable for this printing technique. This study proposed the height reduction test (HRT), building index (BI), and leaning angle (LA) to guide the configuration of cementitious printing based on the existing material mixtures OSS1, OSS2, and OSS3 and a laboratory printing device with a nozzle size of ∅15 mm. More studies should be conducted when the material mix proportion and extruding mechanism vary. The main conclusions are summarized as follows:

• Building index (BI) was proposed to evaluate the layer stacking ability of the PM and PD by counting how many layers were printed in the initial setting time. BI can be used to guide the printing configuration and material development. The acceptable ranges of BI for mixes OSS1, OSS2, and OSS3 in this study were 0~19.1, 0~61.1, and 0~99.4, respectively.
• The height reduction test (HRT) measures the height reduction percentage (height reduction ratio) of a PO. It is suitable for the slump evaluation of printed filaments, with more practical significance for the development of PM than the common slump test. Theoretical calculation and numerical simulation verified that the criteria HRR $r$ and gap height tolerance (GHT) $\delta$ have a relationship of $r=\frac{\delta }{\delta +1}$ for a PM, and 0.167 is the criteria value for regular geometry printing with $\delta =0.2$.
• Leaning angle (LA) tests guide the design of CAD sketches to increase the buildability of applications.
• BI, HRR, and LA can work as the meta parameters of the 3DCPT to guide material development and printing configurations, including the printing speed and layer height.