Research on the Preparation and Mechanical Properties of Solidified 3D Printed Concrete Materials

Abstract

Three-dimensional (3D) printing is an innovative manufacturing process based on 3D digital models that involves layer-by-layer addition of materials. In recent years, 3D printing has made good progress in the field of construction, thereby leading to more stringent requirements for materials. In this study, we first compare different equipment and materials used for 3D printing concrete. Subsequently, the mix ratio of extruded and cured 3D printed concrete is studied by using flow and slump as the main evaluation indexes. Through a universal test, the influence of different dosages of water reducer, retarder, and latex powder on the performance of 3D printed concrete (compression resistance strength) is studied. Furthermore, the optimum mix ratio for fiber reinforced concrete is determined, based on which axial pull-out, axial compression, and three-point bending tests are performed to elucidate the peak compressive strength, load–displacement curve, and mechanical properties of 3D printed concrete. By employing the ABAQUS finite element software, the shaft pulling force and axial compression of 3D printed concrete are simulated and analyzed to determine the parameters influencing the bonding performance of different 3D printed concrete layers. Moreover, the influence of water reducer and sand–glue ratio is observed to be greater than that of water gel ratio and sodium gluconate. The testing results showed that the mechanical strength of 3D printed concrete is lower than that of poured concrete. Meanwhile, bending and compressive strengths of 3D printed concrete and poured concrete are quite different.

1. Introduction

Three-dimensional (3D) printing is a manufacturing process based on 3D digital models that involves layer-by-layer addition of materials [1,2]. This technology has the potential to effectively solve the problems associated with traditional building construction such as lengthy construction periods, low efficiency, wastage of manpower, and material resources, environmental pollution, and the difficulty to shape complex components. However, 3D printing has not been adequately developed for application in building construction; the theoretical research on printing material is lacking, and the influence of admixtures on the mechanical properties of 3D printed concrete needs further research [3]. Distinct from the traditional concrete preparation process, 3D printing of concrete is essentially a pouring process. A predetermined shape is printed by using the machine settings, and its height [4] can be controlled by altering the thickness of the print and number of layers. Related literature has also reported the instable performance of 3D printed concrete by changing the mix ratio of 3D printed concrete to alter its mechanical properties. The researchers at Loughborough University [5] developed a high-performance fiber-enhanced 3D printed concrete with fine aggregates, explored the admixture ratio, and identified factors influencing its performance. They designed multiple sets of concrete materials that were suitable for the 3D printing process and comprised different mix ratios to print large-scale free-form components, evaluate the feasibility of the concrete for the 3D printer, and determine the most optimum mix ratio of the concrete; they also identified parameters most optimum for printing, namely: a gel ratio of 1.5, a water–glue ratio of 0.26, a fly ash [6] proportion of 20%, a silica ash proportion of 10%, a polypropylene fiber content of 1.2 kg/m³ [7], a water-reducing agent proportion of 1%, and a retarder proportion of 0.5%. Based on the optimal fit ratio, the opening time and mechanical properties of 3D printed concrete have also been studied. The opening time is controlled at 100 min and the compressive strength of the concrete exceeds the preset target, reaching 110 MPa at 28 d and 125 MPa at 56 d. Overall, the 3D printed concrete prepared at Loughborough University meets the performance requirements of 3D printed high-performance fiber reinforced concrete, and no collapse or tilt occurs.

In addition to the admixture ratio, some experts and practitioners have also studied the nozzle shape, printing rate, and object complexity [8], while testing the compression and tension strength of concrete. Furthermore, compression strength, bending strength, and other mechanical properties of the 3D printed specimen are also affected by the printing direction; therefore, these specimens exhibit anisotropy. Moreover, the printing time interval [9] has different effects on the interlayer strength, compressive strength, and flexural strength of the 3D printed concrete in different directions. Printing times of 10, 20, and 30 min reveal that the compression and bending strengths of 3D printed concrete are related to the surface water content [10] at the interlayer interface; therefore, increasing the interlayer delay time augments its strength. The compressive strength in the vertical direction lies between the compressive strength observed in other directions, regardless of the delay time.

Theoretically, mechanical properties of 3D printed mortar cannot be similar to those of traditional cast-in-place concrete. In fact, loading results in different directions exhibit anisotropy in 3D printed concrete. Feng et al. [11] used gypsum as the printing gel material for mechanical testing. They concluded that when loading in the X, Y, and Z directions, the damage form of the printing specimen is similar; although there are hourglass cracks on the left and right sides, the compressive strength along the X direction (printer head movement) and the elastic modulus are the largest.

There are various standardized methods and specifications for studying the mechanical properties of conventional concrete; however, their applicability to mortar strength testing remains uncertain. In general, the current test methods developed for concrete differ in terms of the sample form and size, mix ratio, material, time, and direction of the nozzle device. Adding fiber material can also enhance the mechanical properties of 3D printed concrete by increasing the compactness. Its anisotropy changes significantly with an increase in the fiber content. With the help of high-precision computed tomography scanning, Yanfeng et al. [12] have studied the mechanical characteristics of 3D printed concrete based on fine structural characteristics such as concrete interface area and pore defect distribution. The test results show that the initiation and expansion of cracks tend to occur due to the existence of many internal pores, voids, and weak interlayer surfaces produced in the construction process, which is the direct cause of the mechanical anisotropy of cracks.

This paper elucidates the mechanical properties of 3D printed concrete with two main objectives:

• Determining the influence of different admixtures on the performance of concrete through single-factor experiments: an orthogonal combination test [13] has been used to analyze the interaction between different factors to determine the basic mix ratio of printed concrete. According to the requirements of the 3D printing process, fiber optimization is conducted, and the mix ratio of fiber-reinforced concrete is determined.
• Analyzing the difference in the failure mode and ultimate compressive strength of the 3D printed concrete under different load directions: This objective is achieved by conducting the axial pull-out [14], axial compression [15], and three-point bending tests [16]. By numerically simulating a cohesion [17], mechanical properties of the 3D printed concrete are analyzed. Consequently, a 3D printed beam is developed, the mechanical properties of this beam are analyzed, and the feasibility of different printing paths [18] is explored. Overall, the study findings provide a theoretical basis for elucidating the mechanical properties of 3D printed concrete.

2. Materials and Methods

2.1. Introduction of Equipment

The equipment used in this study [19] consists of four modules: control system, motion system, extrusion system, and data processing system. The control system provides the commands and has the following functions: microprocessor function, external input function, G code interpretation function, axis linkage function, mechanical signal processing function, human–computer interaction interface, etc. The motion system is used to realize three-dimensional movement of the nozzle, which is applied to actual printing. The extrusion system consists of a pumping device, feeding pipeline, mixer, and nozzle [20], as shown in Figure 1.

The printing process employed here can be divided into three stages: data preparation, concrete preparation, and model printing. In the data preparation stage, the component model is drawn using BIM, after which the files are exported in the STL format. Next, the model is sliced up to the design layer depth, and then the printing path required to generate the G code file is determined. Subsequently, the concrete mixture is added to the pumping device, and the drive control system smoothly transports the mortar through the pump pipe-nozzle. The dense concrete filament is printed first, which ensures that the structural components are built layer by layer. The printing process is shown in Figure 2.

The admixtures used in this experiment, such as water reducer [21], glue powder, and retarder [22,23], improve the tension strength of the component and reduce the number of microcracks. The low activity of fly ash [24] in additives reduced the initial concrete strength. To increase the activity of fly ash in concrete, CH powder and fly ash can be mixed together with a 6 mm basalt fiber [25] and 15 mm fiberglass [26]. Concrete curing temperature is 20 ± 2 °C, while humidity is not less than 95%. Maintenance is performed every 7 d and 28 d.

3D printing of concrete considers extrudability, constructability, and ease of implementation as the performance indices. The cement used here (RSC42.5 grade fast hard-sulfur aluminate cement) [27] is produced by Wuxi Chengde Yue Building Materials Co., LTD. The main performance indicators are shown in

Table 1. Performance indices of sulphoaluminate cement.

Compression Strength (MPa)		Rupture Strength (MPa)		Specific Area	Setting Time
3 d	28 d	3 d	28 d	(m2/kg)	Start	Stop
21.5	52.5	6.8	12.4	542	10	25

. The aggregate used in this study exhibits a quartz sand content of 30–40%, and it has been provided by the Tai Xuefeng, Chengdu, Sichuan province. Its main component is SiO_2, and the corresponding performance indices are shown in

Table 2. Performance indices of quartz sand.

Material	Burning Reduces Quality (%)	Water Absorption (%)	Hardness	Density (kg/m3)
Quartz sand	0.03	1.3	7.5	2640

. The secondary fly ash and CH powder selected in the test have been provided by Hengyuan New Material Co., Ltd.; their performance indicators are shown in

Table 3. Physical performance indices of fly ash.

Material	Sulfur Anhydride (%)	Burning Vector (%)	Stacking Density (g/cm)	Density (g/cm3)	Moisture Content (%)	Fineness (%)
Fly ash	2.1	2.8	1.12	2.55	0.125	16

and

Table 4. Performance indices of CH mineral powder.

Material	Specific Area (m2/kg)	Density (kg/m3)	Burning Vector (%)	Flow Ratio (%)	Activity Index for 7 Days (%)	Activity Index for 28 Days (%)
CH mineral	422	2.86	1.3	75	105	114

, respectively.

2.2. Test Methods

2.2.1. Orthogonal Test Design

An orthogonal test has been conducted by selecting the representative test points and analyzing the results of the typical test to identify the most optimum production process. The materials used in this study are 300 g of cement, 100 g of mineral powder [28], 100 g of fly ash, 1 g of concrete foaming agent, and 10 g of latex powder. The L16 (44) orthogonal table has been used for testing, where 16, 4, and 4 represent the number of trials, levels, and factors, respectively.

Table 5. Value of each influencing factor at different levels.

Level	Influencing Factors
	Water to Glue Ratio/1	Sand to Glue Ratio/1	Water Reducer/%	Retarder/%
1	0.26	0.7	0.05	0.1
2	0.28	0.9	0.15	0.2
3	0.30	1.1	0.25	0.3
4	0.32	1.3	0.35	0.4

shows the value of different influencing factors at different levels, while

Table 6. Result of the orthogonal test.

Test Number	Influencing Factors
	Water to Glue Ratio	Sand to Glue Ratio	Water Reducer/%	Retarder/%
ZJ-1	0.26	0.7	0.05	0.1
ZJ-2	0.26	0.9	0.15	0.2
ZJ-3	0.26	1.1	0.25	0.3
ZJ-4	0.26	1.3	0.35	0.4
ZJ-5	0.28	0.7	0.15	0.3
ZJ-6	0.28	0.9	0.05	0.4
ZJ-7	0.28	1.1	0.35	0.1
ZJ-8	0.28	1.3	0.25	0.2
ZJ-9	0.30	0.7	0.25	0.4
ZJ-10	0.30	0.9	0.35	0.3
ZJ-11	0.30	1.1	0.05	0.2
ZJ-12	0.30	1.3	0.15	0.1
ZJ-13	0.32	0.7	0.35	0.2
ZJ-14	0.32	0.9	0.25	0.1
ZJ-15	0.32	1.1	0.15	0.4
ZJ-16	0.32	1.3	0.05	0.3

represents the orthogonal table. The additive percentage has been measured as the mass percent.

2.2.2. Single-Axial Test

A uniaxial test [29], which is divided into a tension test and compression test, has been conducted using a 200 kN WDW testing machine with a load-control loading mode; the loading rate is 0.02 kN/s. The specimen preparation process is shown in Figure 3.

3. Results and Discussion

3.1. Analyses of Orthogonal Test Results

The extreme difference analysis method [30] has been used in this study to elucidate the orthogonal test results, with flow and slump being the primary evaluation indexes [31] while compressive strength and bending strength [32] are the secondary evaluation indexes. The test results are shown in

Table 7. Orthogonal test results.

Test Number	Flow/mm	Slump/mm	Compressive Strength at 3rd Day/MPa	Compressive Strength at 28th Day/MPa	Flexural Strength at 3rd Day/MPa	Flexural Strength at 28th Day/MPa
ZJ-1	170	160	33.3	56.1	6.6	11.9
ZJ-2	155	145	20.1	48.3	5.4	10.1
ZJ-3	155	110	21.8	49.4	4.9	8.1
ZJ-4	145	70	17.4	41.2	4.4	8.5
ZJ-5	218	230	16.9	46.7	5.1	6.1
ZJ-6	175	180	23.6	51.5	6.1	10.4
ZJ-7	155	160	18.0	43.4	4.5	9.5
ZJ-8	145	70	23.3	50.0	6.0	9.1
ZJ-9	248	270	25.2	51.6	6.5	9.2
ZJ-10	215	230	21.3	48.7	5.7	11.2
ZJ-11	168	175	22.7	49.7	6.0	9.5
ZJ-12	145	85	22.3	48.4	5.8	8.9
ZJ-13	280	290	22.8	48.2	5.6	9.1
ZJ-14	235	265	18.3	44.7	5.2	8.0
ZJ-15	180	220	19.6	47.9	5.4	7.3
ZJ-16	160	160	22.5	49.7	5.9	10.1

.

3.2. Analysis of the Extreme Difference between Flow and Slump

According to the test results in Table 4, the influence of different factors on the flow and slump of concrete is analyzed. Results of the analysis are shown in

Table 8. Influence of various factors on flow.

Numbering	Flow/mm
	Water to Glue	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	156.3	229.0	168.2	176.3
K2	173.2	195.0	174.5	187.0
K3	194.0	164.5	195.7	187.0
K4	213.8	148.8	198.8	187.0
Range R	57.50	80.20	30.50	10.70

and

Table 9. Influence of various factors on slump.

Numbering	Slump/mm
	Water to Glue	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	121.25	237.50	168.75	167.50
K2	160.00	205.00	170.00	170.00
K3	190.00	166.25	178.75	182.50
K4	233.75	96.25	187.50	185.00
Range R	112.50	141.25	18.75	17.50

.

The extreme difference values exhibit the following relationship for both slump and flow: sand–glue ratio > water gel ratio > water reducing agent > sodium gluconate [33]. When the permeability ratio [34] of sand glue ratio is 0.8 and 1.1, flow and slump do not meet the requirements of 3D printing and should not be considered. Furthermore, the mixing amount should be controlled between 0.9 and 1.1.

Based on Figure 4a, the water–glue ratio has a contrasting effect on flow and slump when compared to the effect that the sand–glue ratio has. With an increase in the water–glue ratio, there is a flow and slump increase in a linear trend. When the water–glue ratio is 0.28, the flow degree is 173.2 mm and the slump degree is 160.0 mm, which meets the 3D printing requirements; meanwhile, the water–glue ratio is determined to be 0.28.

Figure 4c,d indicate that the flow rate and slump slowly increase as the contents of the water reducer [35] and sodium gluconate increase. When the sodium gluconate content exceeded 0.2%, there was no effect on the flow rate, while the slump was increased by 0.20% to 0.30%. Meanwhile, the sodium gluconate content is 0.23%, and the water reducer content is controlled to range between 0.15% and 0.23% according to the printing requirements; the specific dose is dependent on the simulated intensity.

3.3. Differential Analyses of Compressive Strength

The extreme differential analysis [36] is used in this study to analyze the influence of each factor on the compressive strength of concrete at day 3 and 28, and the analysis results are shown in

Table 10. Influence of various factors on the compressive strength at 3 d.

Numbering	Compressive Strength at 3 d/MPa
	Water to Glue Ratio	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	23.40	24.55	25.52	22.97
K2	20.45	21.07	19.52	22.48
K3	22.88	20.52	22.15	20.63
K4	20.80	21.38	19.88	21.45
Range R	2.95	4.02	5.65	2.35

and

Table 11. Influence of various factors on the compressive strength at 28 d.

Numbering	Compressive Strength at 28 d/MPa
	Water to Glue Ratio	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	48.75	50.65	51.75	50.42
K2	50.17	48.30	47.83	49.05
K3	49.60	49.88	48.92	48.63
K4	47.63	47.33	47.65	48.05
Range R	2.55	3.33	4.10	2.37

.

The extreme difference values exhibit the following relationship for compressive strength at both 3rd and 28th day: water reducing agent > sand–glue ratio > water–gel ratio > sodium gluconate. The key to control compressive strength is to alter the contents of water reducer and gel ratio.

3.4. Extreme Difference Analysis of Bending Resistance Strength

According to the test results in Table 6, the influence of each factor on the bending strength of concrete at 3 d/28 d was analyzed. Results of the analysis are shown in

Table 12. Influence of various factors on flexural strength after 3 d.

Numbering	Flexural Strength at 3 d/MPa
	Water to Glue Ratio	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	5.325	5.950	6.150	5.525
K2	5.425	5.600	5.425	5.750
K3	6.000	5.200	5.650	5.400
K4	5.525	5.525	5.050	5.600
Range R	0.675	0.750	1.110	0.350

and

Table 13. Influence of various factors on flexural strength after 28 d.

Numbering	Flexural Strength at 28 d/MPa
	Water to Glue ratio	Sand to Glue Ratio	Water Reducer	Sodium Gluconate
K1	9.650	9.075	10.475	9.575
K2	8.775	9.925	8.100	9.450
K3	9.700	8.600	8.600	8.875
K4	8.625	9.150	9.575	8.850
Range R	1.075	1.325	2.375	0.725

.

The extreme difference values exhibit the following relationship for flexural strength at both 3rd and 28th day: water reducing agent > sand–glue ratio > water–gel ratio > sodium gluconate. As shown in Figure 5, sand gel ratio of 1.1 and retarder content of 0.2% are reasonable.

In summary, based on the requirements of the 3D printed concrete with regard to flow, slump, and setting or hardening time, the mix ratio of 3D printed concrete is determined (

Table 14. Mix ratios of 3D printed concrete.

Water-to-Glue Ratio	Sand-to-Glue Ratio	Cement	Fly Ash	Mineral Powder	Water Reducer	Retarder	Latex Powder	Defoamer
/%	/%	/%	/%	/%	/%	/%	/%	/%
0.29	1	60	20	20	0.20	0.23	2	0.2

).

3.5. Uniaxial Test Results and Discussion

3.5.1. Tension Test

Cracks are produced in a small area of the middle section during the dog bone test, where the nature of damage is brittle and the axial tension ceases. The peak load of each test piece is recorded to determine the mechanical properties under axial pull. Meanwhile, the cross-sectional area and tension strength of different specimens are calculated, as shown in

Table 15. Results of the axial tension test.

Category	Specimen Number	Peak Load (kN)	Cross-Sectional Area (mm2)	Tensionon Strength (Mpa)	Average Strength (Mpa)
Specimen printed horizontally	LH-1	0.365	19.5 × 28.9	1.33	1.41
	LH-2	0.412	18.9 × 30.7	1.51
	LH-3	0.387	19.4 × 29.6	1.39
Specimen printed vertically	LV-1	0.889	19.4 × 31.4	1.46	1.56
	LV-2	0.841	18.9 × 28.7	1.55
	LV-3	0.978	19.8 × 29.4	1.68
Poured specimen	LX-1	0.831	18.7 × 30.4	1.86	1.91
	LX-2	0.944	19.3 × 29.1	2.12
	LX-3	0.721	19.1 × 29.2	1.75

.

The load–displacement curves of the horizontally printed, vertically printed, and poured specimens are shown in Figure 6.

The average tension strength of the three specimens exhibits the following order: pouring specimen > vertically printed specimen > horizontally printed specimen. The average tension strength of the horizontally printed specimen and vertically printed specimen is 73.8% and 81.7%, respectively. The 3D printed specimen comprises strip concrete layers, which tend to be weak inside the specimen, resulting in reduced tension strength. Bonding modes of horizontally and vertically printed specimens tend to differ, and so does the bonding performance between any two layers. Since vertically printed specimens are formed under the action of gravity, their integrity is better than that of horizontally printed specimens. Meanwhile, horizontally printed specimens exhibit lower tension strength than that of vertically printed specimens [37].

3.5.2. Single-Axial Compression Test

Nine test specimens have been designed in this study, among which three sets of specimens are subjected to either the Z-axis, X-axis, or Y-axis loading. The Z-axis is perpendicular to the concrete layers, the X-axis is parallel to the concrete layers and oriented toward the printing direction, and Y-axis is parallel to the concrete layers and perpendicular to the X-axis. Three poured specimens have been set up as control groups. Peak load of each specimen is summarized in

Table 16. Results of axial compression testing.

Category	Specimen Number	Peak Load (KN)	Cross-Sectional Area (mm2)	Compressive Strength (Mpa)	Average Strength (Mpa)
Z-axis loading	CZ1	73.23	39.2 × 40.7	45.9	43.5
	CZ2	64.94	38.3 × 41.7	40.7
	CZ3	69.95	39.4 × 40.5	43.8
X-axis loading	CX1	76.46	39.2 × 40.3	48.4	48.5
	CX2	79.75	38.9 × 39.5	51.9
	CX3	73.38	39.8 × 40.7	45.3
Y-axis loading	CY1	80.59	39.1 × 40.1	51.4	48.9
	CY2	73.66	38.4 × 40.9	46.9
	CY3	77.37	38.8 × 41.2	48.4
Poured specimens	C1	86.62	40.3 × 40.1	53.6	53.7
	C2	90.64	39.4 × 41.3	55.7
	C3	84.32	39.8 × 40.9	51.8

, and the cross-sectional areas of all specimens have been measured to accurately calculate their compressive strength.

According to the test results, the load–displacement curve of each test group is drawn (Figure 7).

The compressive strength of samples loaded in Z-axis, X-axis, and Y-axis directions is 43.5 Mpa, 48.5 Mpa, and 48.9 Mpa, respectively. Meanwhile, that of the cast-in-place reinforced concrete is 53.7 Mpa. The compressive strengths in the direction of X and Y axes are similar, while being greater than that observed in the Z axis direction; therefore, anisotropy is evident. Due to the different bonding modes (extrusion bonding and stacking bonding) between the layers of 3D printed concrete, different printing directions, such as X and Y directions, the force is parallel to the printing layer during the compression test, and the complete printing layer makes the value measured in the direction of X and Y greater than the Z direction. Along with the weight and load of the upper print layer, concrete compaction and short column effect, therefore these results were observed.

4. Finite Element Simulation

There are few test blocks in this test, and due to the influence of laboratory temperature difference and humidity, the mechanical performance test of different batches of test blocks is different, which is not universal. According to the 3D printed concrete data measured in Chapter 3, the data show that the mechanical properties of the concrete optimized after the mixing ratio are close to those of C55 concrete. According to previous studies, concrete with similar strength generally has similar mechanical properties and change trend. Considering the uncertainty in the process of making and curing of concrete test block, the data may have large errors, which may lead to large error for finite element, and is not suitable for finite element [38], so C55 strength concrete is used to simulate the change trend of mechanical properties of concrete after optimized mix ratio. The finite element part adopts C55 concrete parameters (

Table 17. Concrete material parameters.

Density (kg/m3)	Poisson’s Ratio	Elastic Modulus (MPa)	Standard Value for Cube Compressive Strength (MPa)	Standard Value for TensionStrength (MPa)
2500	0.2	35500	35.5	2.74

), and the finite element division of 3D printed concrete is considered a homogeneous material. This test is special, and the results of this simulation are only valid for the concrete mix ratio in this study.

The stress–strain relationship of concrete is indicated using Equations (1) and (2):

$${\sigma }_c=\left(1-d_c\right)E_0{\epsilon }_c$$

(1)

$${\sigma }_t=\left(1-d_t\right)E_0{\epsilon }_t$$

(2)

where ${\sigma }_c$ is the uniaxial compressive stress, $d_c$ represents the uniaxial compression damage evolution, $E_0$is the elastic modulus, ${\epsilon }_c$ is the uniaxial compressive strain, ${\sigma }_t$ is the uniaxial tension stress, $d_{t }$ represents the uniaxial tension damage evolution, and ${\epsilon }_t$ is the uniaxial tension strain.

The plastic damage model represents the constitutive model of 3D printed concrete, whose stress and strain have been calculated using Equations (3) and (4). Meanwhile, the damage factors $D_c$ and $D_t$ are calculated using Equations (5) and (6):

$${\tilde{\epsilon }}_c^{pl}={\tilde{\epsilon }}_c^{in}-\frac{D_c}{\left(1-D_c\right)}\frac{{\sigma }_c}{E_0}$$

(3)

$${\tilde{\epsilon }}_t^{pl}={\tilde{\epsilon }}_t^{ck}-\frac{D_t}{\left(1-D_t\right)}\frac{{\sigma }_t}{E_0}$$

(4)

$$D_c=1-\sqrt{1-d_c}$$

(5)

$$D_t=1-\sqrt{1-d_t}$$

(6)

where ${\tilde{\epsilon }}_c^{pl}$ is the equivalent plastic compressive strain, ${\tilde{\epsilon }}_c^{in}$ is the inelastic compressive strain, $D_c$ is the compression damage factor, ${\sigma }_c$ is the concrete single-axis compressive stress, $E_0$ is the elastic modulus, ${\epsilon }_t$ is the uniaxial tension strain, ${\tilde{\epsilon }}_t^{pl}$ is the equivalent plastic tension strain, ${\tilde{\epsilon }}_t^{ck}$ is the tension cracking strain, $D_t$ is the tension damage factor, and${\sigma }_t$ is the single-axis tension stress.

The remaining parameters of the concrete plastic damage model are shown in

Table 18. Other parameters of the plastic damage model.

Expansion Angle	Flow Potential Eccentricity	Ratio of Biaxial CompressiveStrength to Uniaxial Compressive Strength	K	Viscous Parameters
40	0.1	1.16	0.66667	0.005

.

4.1. Tension Simulation of Components

Mechanical properties of 3D printed concrete during shaft pulling are simulated using the ABAQUS finite element software. The Revit software is used to establish the concrete model [39], whose size parameters are the same as those of the specimen in Section 2.2. A full fixed constraint is applied to the bottom of the model, and the reference point is set at the top. The coupling instruction is used to couple the force on the specimen surface subjected to axial pulling with the reference point and apply an upward load to the point. The adhesion unit is placed between the disassembly layers; since it only 0.1 mm thick, it is negligible in size when compared to the Axle test model (Figure 8). The normal strength of the model Cohesive unit is 1.35 MPa and its tangential strength is 1.2 MPa. Convergence analysis of the finite element model mesh is conducted before geometric meshing, while 3.0 mm, 4.0 mm, 5.0 mm, 6.5 mm, and 8.0 mm are selected as the mesh sizes.

Considering the accuracy and calculation efficiency of the simulation results, a grid of size 4.0 mm is selected, and the calculation results are shown in Figure 9.

Numerical simulations show that the bond layer of 3D printed concrete breaks under vertical tension, which is consistent with the fracture pattern of the uniaxial tension test in Section 3.5. By calculating the reaction force at the reference point, the tension strength of the horizontally and vertically printed structures is determined to be 1.35 MPa and 1.48 MPa, respectively. The simulated and experimental results have been compared in Figure 10 and

Table 19. Comparative analysis of axial tension test and numerical simulation.

Testing Number	Strength (MPa)		Simulated Intensity (MPa)	Difference between the Experimental and Simulated Values (%)
	Experimental Values	Mean Values
LH-1	1.33	1.41	1.35	4.4%
LH-2	1.51
LH-3	1.39
LH-4	1.46	1.56	1.48	5.4%
LH-5	1.55
LH-6	1.68

.

The average tension strength of horizontally printed specimens is 1.41 MPa, which is greater than the simulated value by 4.4%. Meanwhile, the average tension strength of vertically printed specimens (1.56 MPa) is greater than the simulated value by 5.4%. This may be due to the addition of glass fiber, it ensures that there is a closer bonding between the layer. Due to the effect of gravity in vertical printing, the tensile force is greater compared with horizontal printing, but due to the thin thickness of the component, the performance of vertical printing is slightly higher than that of horizontal printing, but it is not obvious. The gap in the two directions is only 1%, and this data is not necessarily general considering the errors in the test block preparation process. The test block printed in two directions is less than 6% wrong than the simulated value, which is acceptable. Therefore, the simulation can be used instead to analyze the change of its mechanical properties.

4.2. Axial Compression Simulation

The axial tension model is a 40 mm side-length cube. Based on the 3D-printing concrete process, the model is divided into four layers and two columns, and each layer of concrete is 10 mm thick and 20 mm wide (Figure 11). The Cohesive unit is set between the disassembly layers and is 0.1 mm thick; it exhibits a normal strength of 1.35 MPa and tangential strength of 1.2 MPa.

4.2.1. Z-Axis Compression Simulation

Here, a grid of size 2.0 mm is selected. For finite element simulation of the axial pressure test, cloud maps depicting concrete compression damage, bonding unit damage, and Mises stress have been extracted from results, as shown in Figure 11 and Figure 12.

Figure 12 shows that compression damage is the highest (close to 1) and causes cracks in the specimen. Since downward cracks occurred in the vertical bonding layer, the cohesive unit was damaged, and the concrete cracked. The compression damage in the horizontal two-layer cohesion is l and some units fail at the edge of the vertical bonding unit, which is consistent with the cloud map depicting concrete compression damage.

Figure 13 shows that the maximum stress value of the specimen subjected to axial compression is 50.60 MPa, and the edges at the upper and lower ends and at the middle part of the specimen are large. Meanwhile, high stress is observed at the edge of both ends of the specimens, causing the concrete to break and fall off; vertical cracking is also observed in the middle parts. Overall, the simulation results are consistent with the experimental results.

The load–displacement curves of specimens subjected to Z-axis loading compression are compared with the simulation results, as shown in Figure 14 and

Table 20. Comparative analysis of Z-axial compression testing and numerical simulation.

Specimen Numbering	Strength (MPa)		Simulated Intensity (mpa)	The Ratio of the Test Value to the Simulated Value (%)
	Test Values	Experimental Average
CZ1	45.9	43.5	44.5	97.8%
CZ2	40.7
CZ3	43.8

.

Table 20 shows the average of Z-axial compression strength of different specimens, as well as the simulated compression strength. According to the tensile test, the concrete performance of the optimized mix ratio should be slightly higher than that of C55 concrete, but the compression test value of Z axis is less than the simulated value, and it is 97.8% of the simulated value. This may be because in the preparation process of 3D printed concrete compression test block, often used by printing out the strip concrete and then cutting the test block. In this process, the edge of the test block receives downward pressure, and due to the influence of the printing layer first starting to solidify, it may lead to the weak bonding between the layers of the test block edge, and the performance can-not give full play in the compression test, and the fixed force is relatively small compared with the simulation.

4.2.2. X-Axis Compression Simulation

Cloud maps depicting concrete compression damage, bonding unit damage, and Mises stress caused by X-axis loading are shown in Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9.

Figure 15 shows that compression damage gradually weakened from the edge to the middle. The compression damage at the edge is close to 1, where the concrete layer suffers from crushing damage and cracks are formed. The concrete layer produced vertical cracks throughout the specimen, and compression damage at the two edges of the cohesion is close to 1. Overall, the bonding unit is damaged, and the concrete specimen is cracked, which is in accordance with the cloud map depicting concrete compression damage.

Figure 16 shows that the maximum stress value of the specimen subjected to axial compression is 56.33 MPa, and that the stress values at the upper and lower edges of the specimen and at the vertical adhesive layer are large. During the experimental test, concrete breaks and falls off, and vertical cracks appear on the two adhesive layers at the edge, which is consistent with the simulation results. The load–displacement curve of the output reference point fit well with the test results, as shown in Figure 17.

Experimental and simulated results have been summarized in

Table 21. Comparative analysis of X-axial compression testing and numerical simulation.

Specimen Number	Strength (MPa)		Simulated Intensity (MPa)	Difference between the Experimental and Simulated Value (%)
	Test Values	Experimental Average
CX1	48.4	48.5	47.2	102.8%
CX2	51.9
CX3	45.3

.

Table 21 shows that the experimental value is greater than the simulated value by 102.8%. Compared with the Z-axis loading test, the X-direction loading test has cracks, but the bonding between the layers is better due to the addition of glass fiber, and the fixation test value should be greater than the simulated value. According to the division between finite element units, the compression test in the X-axis direction is compressed by 8 bonded concrete bars, so the simulation value should be greater than that of the Z-axis simulation, which is consistent with the measured data and simulated data.

4.2.3. Y-Axis Compression Simulation

Similarly, cloud maps depicting concrete compression damage, bonding unit damage, and Mises stress caused by Y-axis loading are shown in Figure 18 and Figure 19.

Figure 18 shows that the simulation results of Y-axis loading compression are similar to those of the X-axis loading compression. The compression damage of the two concrete layers at the edge is the largest, and vertical cracks are generated in the bonding layer on both sides of the specimen. The bonding layer on both sides of the specimen is completely damaged, which is consistent with the simulation results.

Figure 19 shows that the maximum stress value of the specimen subjected to axial compression is 56.26 MPa. The stress values at the upper and lower edges of the specimen and at the vertical bonding layer are relatively large, which is consistent with the simulation results. The load–displacement curve of the reference point shows a good fit with that of the test data, as shown in Figure 20.

The experimental and simulation results are summarized in

Table 22. Comparative analysis of Y-axial compression testing and numerical simulation.

Specimen Number	Strength (MPa)		Simulated Value (MPa)	Difference between the Experimental and Simulated Value (%)
	Test Values	Experimental Average
CY1	51.4	48.9	47.1	103.8%
CY2	46.9
CY3	48.4

.

Table 22 shows that the experimental mean is greater than the simulated values, or 103.8% of the simulated values.

Compared to the compression test of the Z-axis, the result of the Y-axis compression test is larger than the simulated value, which may be due to the result of horizontal printing. The test value is from large to small, respectively. X > Y > Z, but the simulation results are Y > X > Z. According to the division of the finite element units, the Y-axis test, as it is the whole concrete strip, should be the largest value in the test, which is the same as the simulation results. However, from the perspective of the test data, the big difference between the test groups, this may be because the maintenance is not strictly accurate to 18–22 °C, humidity cannot strictly guarantee above 95%, and cutting blocks cannot avoid the bond between layer and layer, the solid test has particularity, this test is only applicable to the corresponding situation in this paper. Compared with other materials printing, such as 3D metal printing, 3D concrete printing accuracy is poor, and the size between the test blocks is also a certain difference, which also has a certain impact on the final result and cannot guarantee that it is an ideal situation. In the simulation results of the three directions, the error does not exceed 4%, and some partly reflects the mechanical properties. In conclusion, it is feasible to simulate the stress performance of concrete with similar strength, such as C55 concrete.

5. Conclusions

This study presents the preparation procedures and mechanical properties of extruded and cured 3D printed concrete materials The optimized mix design is valid only for the used materials, and the following conclusions were drawn based on the results obtained:

• Different additives and their contents have varying effects on the strength of concrete. On one hand, excessive additive content causes extremely fast concrete setting, while blocking the 3D printer nozzle. On the other hand, moderate additive may have no impact on the concrete performance. Therefore, it is very necessary to choose appropriate additives.
• Through a single-factor experiment, an orthogonal test, and fiber optimization of 3D printed concrete, the most optimum mix ratio is determined in this study (3D printed concrete: cement: fly ash: CH powder: water reducing agent: sodium gluconate: latex powder: concrete foaming mass ratio = 0.29:1:0.6:0.2:0.2:0.002:0.0023:0.02:0.002), wherein the glass fiber volume is 0.3%.
• Twenty-one 3D printed concrete specimens and nine poured concrete specimens are subjected to axial pull-out, axial compression, and three-point bending tests. The mechanical strength of all 3D printed samples is less than that of the poured concrete specimens. Moreover, bending and compression strengths revealed that 3D printing via compression is more efficient. The bonding strength of the 3D printed concrete can be further optimized by mixing the properties of other fibers.
• In the pulled simulations, numerically simulated data of 3D printed concrete fit the experimentally obtained data of concrete, thereby verifying the feasibility of using cohesion to simulate the bonding performance of 3D printed concrete. The simulated tension strength of the horizontally and vertically printed structures is 1.35 MPa and 1.48 MPa, respectively. The error is within the acceptable range.
• In the simulation of the compression part, because there are big differences between 3D printing concrete blocks, so the data does not apply to the finite element model, compared with the error of the optimal value of the concrete, and the similar strength of C55 concrete to a certain extent correctly reflects the change trend of 3D printing concrete, and the difference between different axes.
• The preparation of 3D printed concrete materials is a complex process. There are many other admixtures and mineral admixtures that can affect the properties of printed materials. Therefore, determining the impact of other varieties of admixtures and mineral admixtures on the properties of printing materials requires further exploration; the proposed optimized mixture is valid only for the used materials. Meanwhile, the proposed test method is also not perfect; however, it can be improved in future studies.