A novel bond stress-slip model for 3-D printed concretes

Chun-Hui He; Shu-Hua Liu; Chao Liu; Hamid Mohammad-Sedighi

doi:10.3934/dcdss.2021161

Article Contents

2022, Volume 15, Issue 7: 1669-1683. Doi: 10.3934/dcdss.2021161

This issue Previous Article Positive stability analysis of pseudo almost periodic solutions for HDCNNs accompanying $ D $ operator Next Article An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems

A novel bond stress-slip model for 3-D printed concretes

1.
School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an, China
2.
School of Science, Xi'an University of Architecture and Technology, Xi'an, China
3.
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran
4.
Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

^*Corresponding author: chaoliu@xauat.edu.cn (C. Liu) and h.msedighi@scu.ac.ir (H.M. Sedighi)
^*Corresponding author: chaoliu@xauat.edu.cn (C. Liu) and h.msedighi@scu.ac.ir (H.M. Sedighi)

Received: August 2021

Revised: September 2021

Early access: December 2021

Published: July 2022

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Abstract

This paper considers the 3D printing process as a discontinuous control system and gives a simple and coherent bond stress-slip model for a new and intelligent building 3-D printed concrete. The previous models focused on either the maximal stress or the maximal slip, however, the novel model uses an energy approach by the dimension analysis, so that the main factors affecting the bond stress-slip relationship can be clearly revealed, mainly including the concrete's properties (its porous structure and its strength), the steel bar's properties (its printing direction, its strength, its surface roughness and its geometrical property) and the printing process. It is confirmed that the proposed model, similar to the constitutive relationship in elasticity, plays a key role in concrete mechanics, and it can conveniently explain the observed phenomena from the experiment.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. Sketch of test specimen (unit: mm)

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Figure 2. Cubic specimen

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Figure 3. Test loading device

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Figure 4. Damaged shape of specimen (The main damage of the specimen is the split failure, and the pull-out failure mainly occurred in the specimens with the 45 printing direction) (a) Herringbone splitting (b) In-line splitting (c) Pull out

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Figure 5. Bond stress-slip relationship

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Figure 6. Printing direction

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Figure 7. Nonlinear bond stress-slip relationship [21]

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Table 1. Main chemical components of cementitious materials wt. %

Component	Na$ _{2} $O	MgO	Al$ _{2} $O$ _{3} $	SiO$ _{2} $	P$ _{2} $O$ _{5} $	SO$ _{3} $	Cl	K$ _{2} $O	FeO$ _{3} $	TiO$ _{2} $	SrO
Cement	0.08	0.65	4.65	20.9	0.12	2.65	0.05	0.87	65.00	3.23	0.22

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Table 2. Mix ratio of 3D printed concrete (wt. %)

Water-cement ratio	cement	Early Strength Agent	Sand	Fly ash	Silica Fume	Cellulase	PVA	Water reducing agent
0.3	26.6%	2.66%	66.46%	2.68%	1.34%	0.027%	0.0225%	0.186%

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Table 3. Mechanical properties of the casted and printed concretes

Samples	Compressive strength
Casted concrete	50.2 MPa
Printed concrete	X-direction	37.7 MPa
	Y-direction	42.9 MPa
	Z-direction	40.0 MPa

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Table 4. Mechanical properties of steel bars

Rebar type	Diameter (mm)	Yield Strength (MPa)	Ultimate strength (MPa)	Strain	Elastic Modulus (MPa)
HRB400	10	330	400	14%	2.00$\times$10$^{5}$

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Table 5. Pull-out test results of 3D printed concrete

Samples		Rebar type	$\tau_\text{max}$ (MPa)	$s_\text{max}$ (mm)	$\tau_\text{max}s_\text{max}$ (MPa$^{*}$mm)	Average (MPa$^{*}$mm)
Our group	Casted sample	HRB400	10.13	0.933	9.4512	9.4512
	Parallelly printed samples		8.75	0.93	8.1375	8.1375
	Vertically printed samples		8.22	0.99	8.1378	8.1378
	Inclined printed samples with 45°		6.15	0.80	4.92	4.92
Ref. [40]	Casted samples	BFRP Unsmooth bar	26.57	0.54	14.3478	16.7413
			28.17	0.59	16.6203
			28.74	0.67	19.2558
		BFRP Smooth bar	23.94	1.35	19.36953	22.86019
			25.71	1.42	23.60083
			24.82	1.33	25.61021
	Parallelly printed samples	BFRP Unsmooth bar	22.81	0.49	11.1769	12.37963
			24.27	0.56	13.5912
			23.79	0.52	12.3708
		BFRP Smooth bar	21.35	1.29	14.4182	16.80665
			22.79	1.32	17.94038
			21.42	1.46	18.06137
	Vertically printed samples	BFRP Unsmooth bar	20.48	0.52	10.6496	10.47707
			20.65	0.48	9.912
			19.41	0.56	10.8696
		BFRP Smooth bar	13.51	1.01	10.7561	12.68027
			18.84	1.36	13.48032
			18.91	1.27	13.80439
	Inclined printed samples with 45°	BFRP Unsmooth bar	23.59	0.58	13.6822	12.42147
			22.58	0.49	11.0642
			22.76	0.55	12.518
		BFRP Smooth bar	15.46	1.37	18.74461	16.44966
			20.07	1.25	13.83025
			21.94	1.34	16.77412

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Table 6. Effects of bars property and concretes property on the bond stress-slip relationship

Samples	D mm	$\tau_\text{max}$ MPa	$s_\text{max}$ mm	$\tau_\text{max}s_\text{max}$ MPa.mm	L mm	DL mm$^{2}$	$\tau_\text{concrete}$ MPa	$\tau_\text{max}s_\text{max}$/ ($\tau_\text{concrete} L$)
Casted	10.0	10.13	0.93	9.4512	60	600	50.2	0.003137848
Parallelly		8.75	0.93	8.1375			42.9	0.003161421
Vertically		8.22	0.99	8.1378			37.7	0.003597612
Ref.[45]	9.6	15.88	2.23	35.4124	48	461	37.7	0.019569187
Ref.[45]	10.4	18.56	1.68	31.1808	54	557	37.7	0.015444947
Ref.[46]	8.0	19.49	1.50	29.2350	40	320	36.3	0.020139846
	12.0	17.75	3.14	55.7350	60	720		0.025597042
	8.0	21.09	1.77	37.3293	20	160		0.051431937
	12.0	20.27	2.30	46.6210	30	360		0.042822632
Ref.[28]	16.0	16.42	3.72	61.0517	80	1280	35.0	0.021804189
	16.0	18.06	2.15	38.7929	80	1280	35.0	0.013854600
	16.0	11.11	3.47	38.5517	80	1280	42.5	0.011338735
	16.0	14.81	4.92	72.8652	80	1280	55.5	0.016411081
	16.0	17.36	2.67	46.3512	80	1280	60.9	0.009513793
Ref.[13]	12.0	16.48	1.08	17.7984	60	720	30.0	0.009888000
	12.0	20.43	1.50	30.6450	60	720		0.017025000
	8.0	19.03	0.32	6.08960	40	320		0.005074667
Ref.[29]	10.0	20.00	0.91	18.2000	7.8	78.3	30	0.077479779
	8.0	50.00	1.12	56.0000	19.5	156	20	0.143589744
	12.0	90.00	1.90	171.000	16.45	197.4	40	0.259878419
Ref.[26]	10.0	13.52	3.20	43.2640	50	500	35.3	0.024512181
	10.0	16.33	2.72	44.4176	100	1000		0.012582890
	10.0	14.58	0.65	9.47700	150	1500		0.001789802

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