A review of rheological properties and influencing factors of 3D printed concrete
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摘要: 3D打印混凝土具有绿色环保、生产高效智能、节约人力、无需模板等优势，是推动建筑行业工业化升级向智慧化和数字化发展的重要途径之一。对应混凝土3D打印的三个重要阶段：泵送、挤出和建造，决定其制备成功的可打印性主要包含可泵送性、可挤出性和可建造性，然而，这些特性之间存在着矛盾与平衡，且与流变性能密切相关。因此，混凝土流变性能是3D打印混凝土的重要影响因素，也是制约3D打印技术在土木工程中广泛应用的主要因素。目前，已有许多关于3D打印混凝土流变性能的研究，但对于3D打印混凝土流变性能的测试方案和影响因素等关键研究方向尚未形成全面的认识。基于此，本文首先汇总分析了3D打印混凝土流变参数(屈服应力、塑性黏度和触变性)的测试方案、测量范围和表征模型。其次，对3D打印混凝土流变性能的影响因素(原材料性能与配合比、打印参数和温度)进行了分析，提出了调控流变参数的方法。最后，展望了3D打印混凝土流变性能研究的未来发展方向。Abstract: 3D printed concrete has the advantages of green environmental protection, efficient and intelligent production, labor saving, and no formwork, and is one of the important ways to promote the industrialization and upgrading of the construction industry to intelligent and digital development. Corresponding to the three important stages of 3D printing for concrete: pumping, extrusion and construction, the printability that determines the success of its preparation mainly includes pumpability, extrudability and buildability. However, there are contradictions and balances between these characteristics, and they are closely related to rheological properties. Therefore, the rheological properties of concrete are vital important factors for 3D printed concrete, and it is also the main factor restricting the wide application of 3D printing technology in civil engineering. At present, there are many researches on the rheological properties of 3D printed concrete, however, there is still no comprehensive understanding for the key research directions such as the test scheme and influencing factors of the rheological properties of 3D printed concrete. Therefore, this paper first reviewed the test protocols, measuring ranges and models for rheological parameters (yield stress, plastic viscosity and thixotropy) of 3D printed concrete; Secondly, the factors affecting rheological properties of 3D printed concrete were analyzed, influencing factors include raw material properties, mix proportion, printing parameters and temperature, and the method of controlling rheological parameters is obtained. Finally, the problems in the research of 3D printed concrete rheological properties are pointed out and improvement measures are proposed, as well as its development trend and application prospect are prospected.
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Key words:
- 3D printed concrete /
- rheological property /
- yield stress /
- plastic viscosity /
- thixotropy
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图 2 动态屈服应力和塑性黏度测试方法及其流变曲线：(a)和(b) 线性剪切法及其剪切应力-剪切速率曲线[53]；(c)和(d) 阶梯式剪切法及其剪切应力-剪切速率曲线[81]
Figure 2. The test method and rheological curve of dynamic yield stress and plastic viscosity: (a) and (b) the test method and shear stress-shear rate curve of linear shear method[53]; (c)and (d) the test method and shear stress-shear rate curve of step shear method[81]
表 1 静态屈服应力演化模型对比
Table 1. Comparison of static yield stress evolution models
Models Equations Fitting time Disadvantage Fitting cases of 3D printed concrete Roussel[65] $ {\tau }_{0}\left(t\right)={\tau }_{\mathrm{0,0}}+{A}_{thix}{t}_{rest} $
$ {A}_{thix}=\dfrac{{\tau }_{0}}{\mathrm{T}} $Within 40 min after resting Its fitting time is short Perrot et al.[69] Perrot[66] $ {\tau }_{0}\left(t\right)={\tau }_{\mathrm{0,0}}+{A}_{thix}{t}_{c}\left({\mathrm{e}}^{{t}_{rest}/{t}_{c}}-1\right) $ From resting to printable time limit It lacks the fitting of the re-flocculation period Perrot et al.[69]、Shahmirzadi et al.[70] Kruger[52] $ {\tau }_{S}\left(t\right)={\tau }_{D,i}+{R}_{thix}t $ (t≤$ {\mathrm{\tau }}_{\mathrm{r}\mathrm{f}} $)
$ {t}_{rf}=\dfrac{{\tau }_{S,i}-{\tau }_{D,i}}{{R}_{thix}} $
$ {\tau }_{S}\left(t\right)={\tau }_{S,i}+{A}_{thix}(t-{t}_{rf}) $ (t>$ {t}_{rf} $)Period of re-flocculation and after 40 min of resting It needs to derive trf and can only fit the time of resting for 40 minutes Kruger et al.[52, 58]、De Vlieger et al.[40] Note:τ0,0: initial static yield stress, trest: resting time, T: thixotropic parameter, τ0(t): time-varying static yield stress,tc: characteristic time;τs(t): time-varying static yield stress, τD,i: initial dynamic yield stress, τS,i: initial static yield stress, t: time since cessation of agitation, trf: time period over which re-flocculation occurs. 
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表 2 Bingham模型、改进Bingham模型和Herschel-Bulkley 模型对比
Table 2. Comparison of Bingham model, modified Bingham model and Herschel-Bulkley model
Models Equations Advantage Disadvantage References Bingham $ \tau ={\tau }_{0}+\eta \gamma $ It is a linear model to facilitate data processing It is not suitable for shear-thinning and shear-thickening fluids [36, 42, 74] Modified Bingham $ \tau ={\tau }_{0}+\eta \gamma +c{\gamma }^{2} $ It has high fitting accuracy and avoids the case of τ0 < 0 It sometimes lacks of transformation formulae [76, 82, 83] Herschel-Bulkley $ \tau ={\tau }_{0}+m{\gamma }^{n} $ It can fit most experimental data with high fitting accuracy It has mathematical limitations on shear-thickening fluids, sometimes fitting τ0<0 [36, 42, 61, 76, 83, 84] Note: τ: shear stress; γ: shear rate; τ0: dynamic yield stress; η: plastic viscosity; c: second order parameter; m: consistency factor; n: flow index(n < 1: shear thinning fluid; n > 1: shear thickening fluid)
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表 3 塑性黏度表征模型
Table 3. Plastic viscosity characterization models
Plastic viscosity characterization models Equations Notes Hu and De Larrard[90] $ \eta ={\eta }_{0}\left(1+{k}_{{\mathrm{s}}}{p}_{{\mathrm{s}}}\right){\left(1-\dfrac{{\phi }_{{\mathrm{F}}}}{{\alpha }_{{\mathrm{F}}}}\right)}^{-2.5{\alpha }_{{\mathrm{F}}}}{\left(1-\dfrac{{\phi }_{{\mathrm{C}}}}{{\alpha }_{{\mathrm{C}}}}\right)}^{-k{\alpha }_{{\mathrm{C}}}}{\left(1-\dfrac{{\phi }_{{\mathrm{G}}}}{{\alpha }_{{\mathrm{G}}}}\right)}^{-k{\alpha }_{{\mathrm{G}}}} $
$ {\phi }_{{\mathrm{F}}}=\dfrac{{V}_{{\mathrm{F}}}}{{V}_{0}+{V}_{{\mathrm{F}}}} $ ，$ {\phi }_{{\mathrm{C}}}=\dfrac{{V}_{{\mathrm{C}}}}{{V}_{0}+{V}_{{\mathrm{F}}}+{V}_{{\mathrm{C}}}} $ ，$ {\phi }_{{\mathrm{G}}}=\dfrac{{V}_{{\mathrm{G}}}}{{V}_{0}+{V}_{{\mathrm{F}}}+{V}_{{\mathrm{C}}}+{V}_{{\mathrm{G}}}} $
$ {\alpha }_{xmax}=1-0.45{\left(\dfrac{{d}_{{\mathrm{x}}}}{{D}_{{\mathrm{x}}}}\right)}^{0.19} $ ，x=F、C、GIt fits with general accuracy Mahmoodzadeh and Chidiac[95] $ {\eta }_{{\mathrm{r}}}=1+{\eta }_{i}\lambda $
$ \lambda ={y}^{3}\dfrac{4\left(1-{y}^{7}\right)}{4(1+{y}^{10})-25{y}^{3}(1+{y}^{4})+42{y}^{5}} $
$ y\left(\phi \right)={\left(\phi /{\phi }_{\max}\right)}^{1/3}\left(1-{K}_{{\mathrm{P}}}\right) $
$ {K}_{{\mathrm{P}}}={C}_{{\mathrm{P}}}\dfrac{{m}_{{\mathrm{c}}}}{{m}_{{\mathrm{w}}}} $It is more accurate to fit than the former Zhao et al.[93] $ \eta =46.8 F-21.09 A-24.71 R+147.09 $ It is not widely applicable Li et al.[94] $ {\eta }_{r}=\dfrac{D}{PFT}\times \dfrac{{\left(1-\dfrac{\phi }{{\phi }_{{\mathrm{m}}}}\right)}^{-4}}{{\left(a+b\times \dfrac{\phi }{{\phi }_{{\mathrm{m}}}}\right)}^{{\mathrm{c}}}} $ It is a semiquantitative model Note: η: plastic viscosity, η0: the plastic viscosity of water, ks and k: fit by curve, ps: maximum proportion of water reducing agent, F、C、G: respectively represents silica fume, cement, aggregate, $ \phi $: volume density, V: Volume fraction, $ {\alpha }_{xmax} $: Maximum particle packing density; ηr: relative plastic viscosity, ηi: intrinsic viscosity, CP: fitting parameter, mc and mw: the mass of cement and water in the mixture respectively; F: flatness, A: angularity, R: roughness; D: equivalent diameter, PFT: paste film thickness, $ \phi $: fine aggregate volume fraction, $ {\phi }_{m} $: packing density, a、b、c: the dimensionless fitting parameters obtained from the regression analysis.
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表 4 材料比例对3D打印混凝土流变性能的影响
Table 4. Effect of material ratio on rheological properties of 3D printed concrete
Material ratio Rheological parameter Ratio Growth rate/% References Sand-binder ratio Static yield stress 0.8→1.2 847 Shahmirzadi et al.[70] 0→1.5 130 Liu et al.[57] Dynamic yield stress 0.6→1.5 173 Zhang et al.[45] 1.0→1.8 23 Mohan et al.[102] Dlastic viscosity 0.6→1.5 29 Zhang et al.[45] 1.0→1.8 153 Mohan et al.[102] Thixotropy 0.6→1.5 −22 Zhang et al.[45] 0→0.67 213 Liu et al.[57] 0.8→1.2 180 Shahmirzadi et al.[70] Water-binder ratio Static yield stress 0.38→0.40 −35 Mazhoud et al.[38] 0.22→0.28 −90 Tran et al.[34] Plastic viscosity −97 Thixotropy 0.38→0.40 −33 Mazhoud et al.[38]
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表 5 化学外加剂对3D打印混凝土流变性能影响
Table 5. Effect of chemical admixtures on rheological properties of 3D printed concrete
Chemical admixtures Rheological parameter Content/wt.% Growth rate/% References Superplasticizer Static yield stress 6.1→6.9 −33 Ibrahim et al.[59] 1.26→1.48 −73 Kruger et al.[52] Dynamic yield stress −130 6.1→6.9 −32 Ibrahim et al.[59] Viscosity modifier Shear yield stress 0→0.4 1000 Chaves et al.[106] 0.14→0.48 150 Chen et al.[107] Tensile yield stress 100 Bulk yield stress 0→0.4 141 Chaves et al.[106] Static yield stress 0→0.3 81 Liu et al.[74] Dynamic yield stress 105611 Plastic viscosity 176 Dynamic yield stress 0→1 190 Long et al.[80] Plastic viscosity 21 Thixotropy 130 Retarder Static yield stress 0→0.25 −36 Chen et al.[53] Dynamic yield stress −24 Plastic viscosity −14 Static yield stress −37 Dynamic yield stress −27 Plastic viscosity −15 0→0.1 15 Zhang et al.[35] Dynamic yield stress −80 Thixotropy −85 Accelerator Static yield stress 0→10 50 Yuan et al.[39] Note: If it is not specified in detail, the content in the table defaults to the quality content of the cementing material.
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表 6 纳米填料对3D打印混凝土流变性能影响
Table 6. Effect of nanofillers on rheological properties of 3D printed concrete
Nanofillers type Rheological parameter Content/(wt.%) Growth rate/% References Nano silica Static yield stress 0→3 137 Kruger et al.[138] 0→1 900 Mendoza Reales et al.[139] Dynamic yield stress 0→3 145 Kruger et al.[138] Thixotropy −44 0→1 800 Mendoza Reales et al.[139] Nano calcium carbonate Static yield stress 0→4 188 Liu et al.[62] Nano clay Static yield stress 0→0.5 57 Panda et al.[56] 0→1 494 Dai et al.[28] 0→2 755 Arunothayan et al.[29] Dynamic yield stress 0→1 140 Dai et al.[28] Plastic viscosity 220 Apparent viscosity 0→0.5 39 Panda et al.[56] 0→2 101 Arunothayan et al.[29] Thixotropy 0→0.5 176 Panda et al.[56] 0→1 105 Dai et al.[28] Carbon nano tube Static yield stress 0→0.1 143 Zhao et al.[15] Dynamic yield stress 122
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表 7 纤维对3D打印混凝土流变性能的影响
Table 7. Effect of fibers on rheological properties of 3D printed concrete
Fiber type Rheological parameter Content Growth rate/% References Polyvinyl alcohol fiber Bulk yield stress 0→2.2wt.% 81 Chaves et al.[106] Shear yield stress 0→1.6wt.% 75 Dynamic yield stress 0→0.5wt.% 25 Chougan et al.[135] Polypropylene fiber Static yield stress 0→9wt.% 69 Ibrahim et al.[59] Dynamic yield stress 97 0→5.4 Kg/m3 1667 Tran et al.[34] Plastic viscosity 107 Steel fiber Initial shear yield stress 0→2 vol.% 395 Arunothayan et al.[29] Thixotropic stress 494 Thixotropy 293
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表 8 矿物掺和料对3D打印混凝土流变性能影响
Table 8. Effect of mineral admixtures on rheological properties of 3D printed concrete
Types of mineral admixtures Rheological parameter Content/wt.% Growth rate/% References Silica fume Static yield stress 0→10 140 Panda et al.[153] Dynamic yield stress 0→2 70 zhang et al.[35] 0→10 650 Guo et al.[43] Plastic viscosity 0→2 30 zhang et al.[35] 0→12 1320 Liu et al.[74] Thixotropy 0→2 33 zhang et al.[35] 0→10 185 Panda et al.[153] 0→10 767 Guo et al.[43] Fly ash Static yield stress 50→80 −57 Panda et al.[154] 0→20 −45 Aydin et al.[61] Dynamic yield stress 0→40 −62 Xu et al.[30] 0→20 −73 Aydin et al.[61] Apparent viscosity 0→40 −201 Xu et al.[30] 50→80 −20 Panda et al.[154] Thixotropy 0→20 −90 Aydin et al.[61] Limestone packing Static yield stress 0→15 44 Dey et al.[155] 0→70 123 Wang et al.[55] Dynamic yield stress 141 0→30 182 Nair et al.[152] Plastic viscosity 0→70 238 Wang et al.[55] 0→30 30 Nair et al.[152] Blast furnace slag Static yield stress 0→10 128 Panda et al.[153] 0→10 726 Guo et al.[43] Dynamic yield stress 61 Plastic viscosity 196 Metakaolin Static yield stress 0→3 75 Chen et al.[36] 0→10 285 Duan et al.[31] Dynamic yield stress 0→3 27 Chen et al.[36] 0→10 129 Duan et al.[31] Plastic viscosity 49 Thixotropy 0→3 62 Chen et al.[36] 0→10 5457 Duan et al.[31] Note: If it is not specified in detail, the content in the table defaults to the quality content of the cementing material.
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