Structural build-up model for three-dimensional concrete printing based on kinetics theory

doi:10.1007/s11709-024-1081-3

Front. Struct. Civ. Eng.

2024, Vol. 18

Issue (7) : 998-1014 https://doi.org/10.1007/s11709-024-1081-3

Structural build-up model for three-dimensional concrete printing based on kinetics theory

Prabhat Ranjan PREM¹(

), P. S. AMBILY¹, Shankar KUMAR¹, Greeshma GIRIDHAR¹, Dengwu JIAO²(

)

¹. Advanced Materials Laboratory, CSIR-Structural Engineering Research Centre, Chennai 600113, India
². Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong 999077, China

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Abstract

The thixotropic structural build-up is crucial in extrusion-based three-dimensional (3D) concrete printing. This paper uses a theoretical model to predict the evolution of static and dynamic yield stress for printed concrete. The model employs a structural kinetics framework to create a time-independent constitutive link between shear stress and shear rate. The model considers flocculation, deflocculation, and chemical hydration to anticipate structural buildability. The reversible and irreversible contributions that occur throughout the build-up, breakdown, and hydration are defined based on the proposed structural parameters. Additionally, detailed parametric studies are conducted to evaluate the impact of model parameters. It is revealed that the proposed model is in good agreement with the experimental results, and it effectively characterizes the structural build-up of 3D printable concrete.

Keywords structural build-up rheology thixotropy 3D printable concrete kinetics theory ultra high performance concrete

Corresponding Author(s): Prabhat Ranjan PREM,Dengwu JIAO

Just Accepted Date: 13 June 2024 Online First Date: 10 July 2024 Issue Date: 06 August 2024

Cite this article:

Prabhat Ranjan PREM,P. S. AMBILY,Shankar KUMAR, et al. Structural build-up model for three-dimensional concrete printing based on kinetics theory[J]. Front. Struct. Civ. Eng., 2024, 18(7): 998-1014.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-024-1081-3
https://academic.hep.com.cn/fsce/EN/Y2024/V18/I7/998

Model	Equation
Newton	$τ = μ p γ ˙$
Bingham [20]	$τ = τ y + μ p γ ˙$
Modified Bingham	$τ = τ y + μ p γ ˙ + c γ ˙ 2$
Herschel−Bulkley [21]	$τ = τ y + k γ ˙ n$
Power law [22]	$τ = k γ ˙ n$

Tab.1 Typical time-independent kinetics models in cement-based materials

Ref.	Breakdown	Build-up	Hydration build-up
Moore [23]	$K 2 λ γ ˙$	$K 1 (1 − λ)$	−
Worrall and Tuliani [24]	$K 2 λ γ ˙$	−	$K 3 γ ˙ (1 − λ)$
Pinder [26]	$K 2 λ 2$	$K 1$	−
Lee and Brodkey [27]	$K 2 σ a λ b$	$K 1 (1 − λ) c$	$K 3 σ d (1 − λ) e$
Yziquel et al. [28]	$K 2 σ λ γ ˙$	$K 1 (1 − λ)$	−
Mujumdar et al. [29]	$K 2 λ γ ˙$	$K 1 (1 − λ)$	−

Tab.2 Indirect kinetic models

Ref.	$η$ and $λ$	$τ$ and $λ$
Moore [23]	$λ η 0$	−
Worrall and Tuliani [24]	$λ η 0$	$τ i$
Dullaert and Mewis [30]	$λ η 0$	$λ G 0 γ e (λ, γ ˙)$
Roussel [31]	$k γ ˙ n − 1$	$(1 + λ) τ i$
Wang et al. [8]	−	$(1 + λ − λ i m) τ i$

Tab.3 Rheological and structural parameter models

Fig.1 Exponential evolution of

τ y

, adapted from Ref. [13].

Fig.2 Stages of structural build-up during 3DCP.

Fig.3 Proposed structural build-up model for 3D printable concrete.

Fig.4 Behavior of flocculation and rate of flocculation with respect to time: (a) flocculation; (b) rate of flocculation.

Fig.5 Rate of flocculation varies with time for different mix proportions.

Fig.6 Strain rate variation with time: (a) natural strain rate; (b) constant strain rate.

Fig.7 Rate of de-flocculation with increasing flowability at different scale levels (1–4): (a) natural strain rate; (b) constant strain rate.

Ref.	Binder	$τ S, i (P a)$	$w / b$	$φ 0$	$α ind ˙ 10 − 3 (j s − 1 / g m)$	Proposed Model
Ref.	Binder	$τ S, i (P a)$	$w / b$	$φ 0$	$α ind ˙ 10 − 3 (j s − 1 / g m)$	$k 3 (g ? m J − 1)$	$K 3 (× 10 − 4) (s − 1)$	$R 2$
Qian and Kawashima [44]	C	17.05	0.36	0.469	0.65−0.7[72,73]	1.556	4.746	1
Huang et al. [45]	C	25.01	0.30	0.515	–	0.753	2.519	0.99
Huang et al. [45]	C + FA	15.54	0.30	0.515	0.5−1[72,74]	0.75	1.925	0.99
Panda and Tan [46]	C + FA	760	0.45	0.482	–	2.7	6.52	0.98
Mostafa and Yahia [47]	C + SF	18.03	0.4	0.45	0.8−0.1[71]	0.36	1.296	0.98
Huang et al. [45]	C + SF	211.18	0.30	0.515	–	0.5	2.04	1

Tab.4 Hydration build-up structuration rate constants

Fig.8 Typical comparison of static yield stress concerning time for different binder materials. Data derived from [44,45, 46,47,49,50].

Fig.9 Build-up rate.

Tab.5 Mix proportion of 3D printable UHPC mixes (kg/m³)

Fig.10 (a) Test set-up for rheological characterization of printable mixes; (b) typical concrete 3D printing of U_0 specimens.

Fig.11 Prediction of static yield stress for cement paste under constant strain rate condition at rest time of 40 min. Experimental data derived from Wang et al. [39].

Fig.12 Prediction of the evolution of static yield stress for cement paste under constant strain rate conditions at a resting time of 0–130 min. Experimental data derived from Wang et al. [39].

Fig.13 Stages of structural build-up using experimental data during: (a) pumping and deposition; (b) buildability.

Parameter	U_0	U_0.5	U_1
Adj. R-Square	0.99	0.96	0.89
$τ S, i$	181.17	265.28	306.26
$λ D$	0.764	0.768	0.790
$K 1$	0.431	0.397	0.385
$K 2$	0.0194	0.0190	0.0159
$C 0$	5.00E+19	5.00E+19	5.00E+19
$C$	3.739	1.778	1.1
$K 3$	5.49E–04	7.19E–04	8.97E–04
A_thix	3.72E–01	3.39E–01	3.02E–01

Tab.6 Output parameters from the proposed model

Fig.14 Comparison of prediction of yield stress using Eq. (64) for the pumping stage and experimental data.

Fig.15 Comparison of prediction of yield stress using Eq. (69) after deposition of material and experimental data.

Fig.16 Prediction of static yield stress for 3D printable concrete under rest conditions. Data from Ref. [64].

Parameters	Case I	Case II	Case III
$τ S, i$ (Pa)	5000	5000	5000
$K 1$ (s)	$1 / 2$	$1 / 2$	$1 / 30$
$K 2$	0.005	0.005	0.005
$β$	$0. 5, 1 − 4$	$0. 5, 1 − 4$	1
$γ ˙$ (s^–1)	10,100	10	$10, 20, 30, 40$
$C 0$ (s)	$1 / 2$	–	$1 / 30$
$t 1$ (s)	–	120	120
$C$ (Pa/s)	–	–	0.154
$K 3$ (s)	–	–	$1 / 1200$

Tab.7 Input data for parametric studies

Fig.17 Rate of flocculation or de-flocculation and yield stress with natural structuration: (a) de-flocculation rate at maximum shear rate of 100 s⁻¹; (b) yield stress at maximum shear rate of 10 s⁻¹; (c) de-flocculation rate at maximum shear rate of 10 s⁻¹; (d) yield stress at maximum shear rate of 100 s⁻¹.

Fig.18 Rate of flocculation or de-flocculation and yield stress with constant strain rate: (a) de-flocculation rate at constant shear rate of 10 s⁻¹; (b) yield stress at constant shear rate of 10 s⁻¹; (c) de-flocculation rate at various constant shear rates; (d) yield stress at various constant shear rates.

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