Setting on demand for digital concrete – Principles, measurements, chemistry, validation

Cement and Concrete Research, 132

section_content: Digital fabrication with concrete has seen a rapid evolution, especially within the last few years [1] [2] [3] [4] [5] [6] [7] [8] [9]. Lagging productivity and shortages in skilled labor have been driving the construction industry towards industrialization [10]. The digitization process, which includes new additive manufacturing (AM), construction scale processes such as 3D printing, is playing a large role therein [11]. This goes along with an increasing demand for more complex construction components, and a general trend towards prefabrication. 

In this context, digital fabrication techniques are seen as a way to add value, either in the form of more complex but materially more efficient shapes [12] [13] [14] [15], or by offering increased functionality [16] [17] [18]. However, their potential of impacting construction from the productivity side has been argued to potentially be even more significant [19]. 

Layered extrusion with concrete, also called 3D printing with concrete (3DCP), has received by far the most attention of all the techniques being developed [2, 120]. The process, first pioneered by Berokh Khoshnevis and branded initially as Contour Crafting [20], is the direct transfer to concrete of the well-known fused deposition modeling (FDM) process typically carried out with thermoplastics. Other techniques include slip-forming, initially developed at ETH Zurich and known as Smart Dynamic Casting [21], and casting into weak formworks, which can all fall under the umbrella term "digital casting" [22]. One can even consider shotcrete, developed for some years already, as a form of additive manufacturing with concrete that can be (and is, in many instances) digitally controlled [23]. 

All of these new processes differ significantly from traditional casting processes by virtue of the importance of control of the yield stress, and especially with respect to its evolution over time. More specifically, the requirements of material delivery and placement are rather similar to some processes seen in traditional construction processes, but the absence of a traditional formwork requires an additional aspect, that of controlling structural build-up, to ensure structural stability during production. This aspect is commonly referred to in the literature as "buildability" [24, 25]. The introduction of this new aspect of cementitious material behaviour creates many new research challenges and emphasizes existing ones. In particular, it calls for:

1) an understanding of how yield stress evolves at the microstructural level (Section 2) 2) new testing methods to best characterize how "buildability" can be characterized (Section 3) 3) new chemical systems of rheological control, sometimes called "Set on Demand" (Section 4) 4) stability criterion for objects during and after production, in particular with regard to self-weight induced material failure or buckling (Section 5). 

These four key aspects are discussed in this paper, presenting recent advances that have enabled the production of several large-scale demonstrators, supporting the applicability of these concepts. It is hoped that the chemical, physical and mechanical insights presented will facilitate the development and upscaling of many other endeavors in digital fabrication with concrete.
section_name: Introduction

section_content: A series of advanced building processes such as slip-forming, layered extrusion and casting in weak formworks rely on predictable yield stress and its evolution over time for the control of building rates. Let us therefore first examine the fundamental and underlying principles that govern yield stress and its increase over time. Later we will see how to technologically leverage this yield stress and its growth for digital fabrication processes with concrete and mortar. 

Yield stress is, initially at least, a consequence of attractive interparticle forces at pseudo-contact points of cementitious particles, building a stress sustaining network of colloidal interactions. The yield stress resulting from these contacts depends largely on the distance between particles (changed by dispersants) and the number of contacts (a function of particle volume fraction and size). 

Under flow, parts of the contacts are broken, which is called structural breakdown. In contrast, at rest, the structure tends to buildup, at least in part. This structural build-up is a reversible process involving the formation of a network of colloidal interactions (flocculation) along with the permanent formation of hydrates (hydration) and their partially reversible connection to cement particles. This leads to the distinction between dynamic and static yield stress [26]. Dynamic yield stress is the stress needed to sustain flow, or at which flow stops, denominated τ 00 and is occurring at the time of material placing. Static yield stress is the stress needed to initiate flow from a resting material, increasing when material rests due to flocculation and hydration, denominated τ 0 (t) and applicable to materials that have been placed by the building process since the amount of time t. Thus, structural buildup or yield stress evolution at rest represents static yield stress evolution. 

Concerning the physical origin of structural build-up through hydration, two contributing mechanisms need to be distinguished: growth of hydration products at pseudo-contact points and space filling by hydration products [27]. Indeed, it is understood that some hydration products such as C-S-H are growing preferably on the surface of cement particles [28, 29], with some exceptions such as with the introduction of seeds [30], or in presence of superplasticizers [31]. With this growth occurring at the surface of particles, it is implied that it also occurs at the contact points between particles, increasing the strength of these contacts. 

Separating these two effects is not trivial and is further complicated by the question of the relative contributions from silicate and aluminate phases, the latter forming fast in time spans that are most generally of interest for structural build-up. This explains why part of the literature on the subject still deserves confirmation or revisiting. Recently, we have been able to contribute to this by showing that sucrose can postpone the hydration of C 3 S beyond the time of aluminate main activity [32, 33]. Using this trick, we studied structural build-up of pastes with varying sucrose dosages using oscillation rheometry and isothermal calorimetry to quantifying the extent of hydration during rheometric measurements. For cement pastes without superplasticizers, it was found that at long resting times, the structuration rate is dominated by the formation of hydration products and proportional to the heat rate. This indicates that, at rest, the build-up increases linearly with the amount of hydrates formed since the last deformation. However, in the induction period and on short time scales, in our experiments in the range of up to 5 min, yield stress is dominated by flocculation. Additionally, we found that the amount of hydration products formed before the last deformation only has a minor effect on the rate of structuration, indicating that growth at pseudo-contact points is indeed the main contributor to structural build-up. The structuration can be associated to the growth of hydration products bridging the cement particles in the flocculated network. These findings are in agreement with a study of Jiang et al. [34] in which strength increase at rest could be negated by mixing up to a time equivalent to the final set as measured by Vicat needle (Fig. 1 ). This is also consistent with the constant yield stress period in the induction period in the work of Mantellato where samples were remixed under the same conditions before each measurement [35]. 

The above characteristics determined on the paste level also dominate the properties of fresh and pumpable concrete, as is widely used in digital fabrication [4, 22]. Indeed, in the work by Yammine et al. [36], yield stress is shown to be dominated by hydrodynamic interactions, if the aggregate volume fraction is below a critical value (which we expect for concrete to be processed for digital fabrication). This implies the time-dependent structuration observed on pastes applies also for digital fabrication concrete. 

Admixtures and in particular superplasticizers have a big effect on yield stress and for this, we refer to the work of Mantellato [35] in which the same general exponential dependency of yield stress with solid volume fraction was found in systems with and without superplasticizer, indicating once again the existence of a scaling of yield stress with the number of contact points between particles in a given volume. Based on this it can be inferred that in superplasticised systems similar initial interactions occur, at lower attractive forces due to steric hindrance [37, 38]. However, more recent work suggests that superplasticizers simply reduce the number of contact points contributing to the overall cohesion [39]. 

For digitally controlled building processes this means that as flocculation only contributes to yield stress buildup on a timescale of some 5 min, the main contribution in additive manufacturing processes has to come from the formation of hydration products at the pseudo-contact points of particles or space filling. Approaches to deal with controlled yield stress evolution in processes are discussed in Section 4.
section_name: Physico-chemical principles of yield stress evolution

section_content: In the previous section, we presented a summary of the processes controlling yield stress and its increase over time. A summary of available static yield stress characterisation methods is given in [40]. The best-established methods offer an established physical interpretation of the measured value, are however discrete and destructive. These are the Vane method [41] [42] [43] [44], uniaxial compression test [45] as well as less regularly used penetration [46, 47], direct shear tests [45] and squeeze flow [25]. All these methods have shown to be capable to measure static yield stress at the time of placing and its evolution at rest, be it with some possible experimental limitation. In this section, we present a summary of a test method developed by Reiter [33] to continuously measure static yield stress, its validation on pastes and use on mortars. The method is based on a slow penetration test of which further details are given elsewhere [33, 48, 49]. The method uses a conical penetration tip fully submerged at the measurement start and further penetrating at a rate of 20 mm/h into a cast sample of 90 mm diameter and 120 mm height.
section_name: Measurement of structural build-up

section_content: In the slow penetration test, a penetration tip is pushed into a material sample over the course of several hours and penetration force is measured. This force is then related to yield stress. With this, continuous real-time measurements of yield stress evolution are possible with an easy to use experimental setup on a single sample. The method would typically be applied to calibrate mix designs to desired rates of structural build up, as well as to follow, the structural build-up of the first layer during production. As such, it can predict failure, acting as a quality control method for the placed concrete, can detect variations caused by changes in raw materials, or it can inform the process, giving feedback on how fast the process can build vertically, or how much set accelerator is needed for a desired vertical building rate. 

The measuring range for slow penetration in OPC cement pastes and mortars is found to lie in the range of 1-200 kPa and is ideal for capturing the yield stress range that is required for such self-support (equivalent roughly to concrete height from 7 cm to 15 m, using Eq. ( 3 )). Reiter [33] showed that penetration force and yield stress scale linearly, and more importantly that the scaling factor of this relation is in quantitative agreement with predictions from soil-mechanics. This gives confidence in the yield stress calculated from the measurement and the possibility to make reliable assessments of concrete stability. 

By modeling penetration as a geo-mechanical soil stability problem, it is possible to relate the penetration force to yield stress for plastic materials, using a bearing capacity factor N C derived for a given penetration tip. The bearing capacity factor is an analytically or numerically derived value that relates the stress at the penetration tip to the material cohesion/yield stress and depends among other on the tip geometry [33]. From this perspective, penetration tests provide cohesion measurements from a yield stress of 1 kPa upwards. The lower bound in fact reduces to about 0. 1 kPa if measurements take place at shallow depth, meaning that it can evaluate corresponding stability heights around 1 cm. However, the tests are limited to early age strength range with plastic behaviour. 

In this respect, the predictions of soil-mechanics are particularly useful as they predict the measuring range and clearly show the dominance of cohesion as well as the contribution of minor effects such as surcharge, soil-weight, heave, cone bluntness that can be relevant in other penetration setups. The soil-mechanical approach also shows that the measurement is not occurring directly on the tip surface. Rather it is carried out away from the penetration tip surface in a homogenous sample section that is constantly reaching previously undeformed material, allowing homogeneous continuous measurements. It is however suspected that wall slip can occur on the sides of the container, reducing the measured force, particularly if these have a small diameter. 

However, care should be taken as to the method limitations, as penetration force in mortars and concrete in which yield stress is dominated by frictional contacts between aggregate particles is expected to deviate from the expected linearity with the real yield stress/ compressive strength. The ratio between both depends on internal friction angle, which cannot be directly determined in a penetration test. Such frictional contacts are expected to also form by water consumption due to ongoing hydration. In the measurements of Mettler et al., this transition is shown to occur in the range of 200 kPa [46], but needed a large set of mechanical tests to observe, comparing especially penetration to compression measurements. A simple method to detect this transition is currently lacking. 

Therefore, for unknown compositions, some comparative measurements are recommended for measurement method validation and for determining the measuring range for a given composition using the discrete methods introduced above. With this in mind, slow penetration does provide reliable yield stress measurements in mortars, provided the volume fraction of sand is not too high, as shown in the next subsection.
section_name: Slow penetration test for yield stress evolution

section_content: In Fig. 2 (left), the change of penetration force is shown for mortars labelled Mx_Sy to indicate different aggregate content (x% in volumetric fraction) and superplasticizer dosage (y% of cement mass), with a water to cement ratio of 0. 38. Results are plotted for the first 3 h after water addition. Difference of initial yield stress and on-set time are better seen in the log-log scale in Fig. 2
section_name: Continuous penetration in mortars

section_content: These mortars are very different from each other. M20 has an aggregate content in the dilute regime, implying that its flow is dominated by the cement paste, while M48 is close to the percolation limit [36] of the sand used (0-2 mm crushed limestone). With increasing sand content, the initial yield stress as well as the onset of exponential yield stress increase occurs at earlier times (from curve a to b and from c to d). With increasing superplasticizer dosage, this increase occurs later and at a slower rate (from curve b to c and from d to e). This is in good agreement with literature as superplasticizers are well known to retard the onset of hydration and to reduce yield stress at early age [50] [51] [52]. The log-log scale in Fig. 2 (right) not only helps to better differentiate initial yield stresses, but additionally highlights a two-step mechanism, involving a slow evolution until approximately the time of 60-90 min, followed by exponential increase. This can be associated with the onset of hydration and a rate increasing growth of hydrates [28]. 

In Fig. 3, the evolution of yield stress calculated from uniaxial compression experiments (cylinders of diameter 90 mm, height 180 mm, loaded at a rate of 0. 2 mm/s) is shown for the different mortars as a function of time since placing. In general, the same ranking of strength evolution as in slow penetration measurements is observed. The fastest yield stress increase occurring for high solid content without superplasticizer and the slowest for mortars with high superplasticizer dosage and low aggregate solid content. In the case of the mortar with high superplasticizer content and high sand content, the measured yield stress remains substantially lower than the value measured with slow penetration and is excluded in the following analysis. 

The data in Figs. 2 and 3 provides the means to compare for mortars, the yield stress measurements from different discrete methods to the values obtained from slow penetration. As shown in Fig. 4, the correlation is quite good, showing a proportionality of the discrete measurements (fast penetration at rate of 1 mm/s with and without roughened container walls, as well as penetration test setup of Mettler et al. [46] ) with those of slow penetration (rate of 20 mm/h). The fact that this correlation includes more scatter than in the case of the pastes reported by Reiter et al. [48] can be attributed to the fact that the studied mortars are broadly different. It should be noted that the data reported in Fig. 4 (left) includes a conversion from penetration force to yield stress (or compressive strength) that involves a theoretically derived bearing capacity factor. If this term is rather taken from a best fit between the compressive strength tests and the slow penetration measurements (Table 1 ), then the correlation is much improved (see Fig. 4, right). This brings all measurements into agreement within a range of 0. 5x-2x of the theoretically predicted value. 

The theoretical bearing capacity factor can therefore be considered good enough in most applications, as most measurements then fall within a range of 2x of the prediction. However, compression tests remain fundamentally important when it is necessary to confirm that the material being tested is controlled by plastic rather than frictional behaviour. Otherwise, as explained in the previous section, the slow penetration test loses its significance. 

To illustrate the potential of slow penetration tests for digital fabrication, mortars of broadly different compositions have been measured (see Fig. 5 and Table 2 ), involving different paste matrixes, water content, initial yield stress and targeted application [33]. The compositions as used for layered extrusion and slip-forming are mortars prepared with blended cements. They contain several different admixture types and have their onset accelerated. Both of these mixtures show the earliest increase of penetration force among the tested materials (compared to Fig. 2 ), the increase being immediate and approximately linear. An SCC mortar containing a strongly retarding superplasticizer designed for transport concrete, shows only minor penetration force increase in the measuring timeframe. Furthermore, in Table 2 additional mortars for slip-forming and layered extrusion not measured in this study are listed.
section_name: (right).

section_name: From controlled setting to setting on demand

section_content: A number of advanced building processes rely on a specific evolution of yield stress and/or shear modulus over time, depending on the rate at which components are built (Section 5). Buildup is achievable foremost by hydration occurring in the placed material. Given that this needs to occur similarly for each layer, the hydration rate after placing should remain constant during the whole course of production (up to several hours). 

Providing the same kinetics for each layer is achievable with two different approaches. The first involves the continuous preparation of small quantities of concrete with high early age strength development (e. g. traditional slip-forming or dry-process shotcrete, a. k. a. "gunite") and is called controlled setting [54]. The second involves continuously taking small quantities of concrete taken from a larger batch and activating them with a set activator [4, [55] [56] [57] [58] [59] [60] [61] [62], (e. g. wet-process shotcrete). It is referred to a Setting on Demand. As most processes need < 1% of the concrete late age strength by the end of fabrication, the extent of this hydration stage can, in most cases, be limited to a minor binder phase. To allow either approach, specific cement chemistry and admixture systems are employed as reviewed by Marchon et al. [52] and Reiter et al. [40].
section_name: The need for controlled setting and set on demand

section_content: Cement hydration is a process of complex coupled chemical reactions, involving the dissolution of several anhydrous phases into a pore solution, the nucleation of hydration products from pore solution and their subsequent growth. For advanced building processes, the main periods of interest are the induction period, or open time, during which concrete can be processed, and the acceleration period or other periods of rapid hydration, in which strength builds-up and setting occurs. For most processes (except slip-forming), the transition from the induction to the rapid hydration should ideally occur at the time of placing. 

A first approach for hydration control relies on the proper choice of the mineral binder. While Ordinary Portland cement is the most used binder for concrete, it is not the only one that can be used. Alternative cements include Calcium Sulfo-Aluminate cements (CSA), Calcium Aluminate Cements (CAC), Calcium Sulfate (C$), geopolymers or alkali activated cements and magnesia cements [63] [64] [65] [66] [67]. Limiting ourselves to binders primarily containing OPC, mixes with CSA, CAC and with different gypsum sources can give a large range of early age kinetics. 

In OPC, the hydration of the main phase C 3 S is the main contributor to strength build-up, with the precipitation of calcium silicate hydrate (C-S-H) and portlandite (CH), fixing water. This substantially increases the volume of solids, in addition to providing a good cohesion between cement grains when C-S-H forms at contact points [34, 68]. At early age, C 3 A and gypsum lead to ettringite precipitation, which can also deliver strength build-up. 

A particular use of CAC is their combination with other mineral binders, especially with OPC and C$ promoting the precipitation of ettringite, something referred to as ettringite binders or binary and ternary binders [69] [70] [71] [72]. Similar blends also exist for CSA additions [63, [73] [74] [75]. Owing to the fast precipitation of ettringite in these blended cements, one way to achieve rapid setting is by using CAC or CSA as an OPC accelerator [70]. Such combinations of OPC, CAC and C$ (or CSA as a substitute for the combination of CAC and C$) can be represented in a ternary diagram. Also, as shown in Fig. 6 only a small fraction of the possible ternary binder compositions offer viable formulations. A summary of this is given by Lamberet [69]. The main points are that a high calcium sulfate content should be avoided, as it can cause expansion, a process that can cause a rapid deterioration by cracking [76, 77]. Moreover, without the addition of C$, sulfate depletion can occur, severely delaying silicate hydration in the OPC [70, 78]. Furthermore, for blended systems the use of set retarders is essential to provide even a short open time [79, 80].
section_name: Concepts for hydration control

section_content: The open time can be extended with set retarders or with admixtures for which set retardation is a side effect, such as superplasticizers [81, 82]. Set retarders for OPC can be found in a variety of sugars [83, 84], organic acids, phosphates, phosphonates [50, 85], lignosulfonates and polycarboxylate ether (PCE) superplasticizers [86, 87]. For binary and ternary CAC binders and for CSA systems involving a sulfate source, the use of citric, tartaric and phosphoric acid is a Fig. 5. Penetration force (lines) and yield stress from compressive strength (crosses) measured on mortars as used for layered extrusion, slip-forming and casting (SCC). Mixes for layered extrusion and slip-forming show a significant and immediate yield stress increase. Adapted from Lamberet [69]. 

common way to achieve retardation [88]. 

Admixtures to accelerate hydration exist in different forms [55, 89]. These admixtures act through different mechanisms, generally improving the precipitation and/or growth rate of hydration products. Overviews related to digital fabrication are given in [40] and by Marchon et al. [52].
section_name: Delaying or causing hydration onset

section_content: As opposed to the above, setting on demand offers more freedom in kinetics for the building processes. An important consideration is that the strength build-up at early age is directly proportional to the rate of hydration [32, 33, 40]. Therefore, the nature of hydration kinetics (linear, power law or exponential) should be adjusted to match the corresponding kinetic requirements for the building process under consideration. As such, if linear strength build-up is required, a constant hydration rate is sufficient. Similarly, if a rate accelerating strength gain is needed, then the hydration process should also exhibit such an acceleration. For processes only needing a limited strength build-up, such as layered-extrusion, a limited but rapid initial strength gain can also be useful. For processes where an immediate strength build-up must be avoided, as in slip-forming, strategies for delaying the action of activators are required.
section_name: Setting on demand

section_content: For set on demand in the cases where a single large batch of concrete is used, one must first extend the open time. This ensures that the cementitious system does not change substantially in terms of workability within the timeframe of manufacturing. To achieve the strength requirements, an activator is best added shortly before placing (see Fig. 7 ). This is the method mainly investigated here and which has been implemented for the building processes slip-forming and layered extrusion [61, 90]. It can be achieved by: 1) negating retardation, 2) precipitating a minor phase, or 3) accelerating the main hydration phase. Taken alone, the approach of negating retardation [91] is most often insufficient in Portland cements, as the activator addition necessitates substantial amount of water addition [40]. Hence the following sections discuss the other two options.
section_name: Achieving the strength requirements

section_content: For Ordinary Portland cement activation of the main hydration peak was studied by Thomas et al. [92] using a combination of sucrose (set retarder) and C-S-H seeds (set accelerator). As shown in Fig. 8, this allowed extension of the open time by > 30 h (from blue to green curve) and then activation of hydration by adding the seeds (from green to red curve). An advantage of accelerating the main hydration kinetics lies in the exponential increase of strength that can be obtained in the acceleration phase of hydration, along with a rather slow initial reaction. The practicability of using seeds is however limited as they are available as a dispersed suspension causing an initial increase in fluidity that is often not convenient in terms of global processing.
section_name: Accelerating the main hydration kinetics

section_content: Instead of triggering the start of massive hydration, in many cases it can be sufficient to induce the faster formation of a small amount of additional hydrates. This can be achieved by adding compounds that provide the aluminates and/or silicates missing in the aqueous phase to form these hydration products. Prominent examples are shotcrete accelerators [55]. While they are most often concentrated solutions of aluminium salts, they work through an overall similar principle as CAC suspensions, as they also provide aluminium or aluminate ions to the aqueous phase [55, 70, 71, 74, 93, 94]. 

Such accelerators act in two ways. On the one hand, they increase the precipitation of hydrates and cause a rapid initial yield stress increase (needed for processes as layered extrusion). On the other hand, they can have an indirect effect on the hydration of the main binder, for example by reducing the retarding effect of some chemical admixtures, or by providing additional growth surfaces. These compounds should therefore rather be thought of as "strength gain enhancers" rather than "cement hydration accelerators". 

While not sufficient alone, the possibility of cancelling retardation can be beneficial and other accelerators than those used for shotcrete accelerators can also achieve this through the precipitation of hydration products [53, 67]. This is illustrated in Fig. 9, where in the first case an alkali-free shotcrete accelerator and in the second case a CAC suspension cancel the retarding action of sucrose [53]. The same results have also been obtained by Das et al. [67] when using mixtures of CAC and C$ as accelerator, combining compounds need to precipitate ettringite. This can avoid the risk of sulfate depletion that could otherwise cause massive retardation of the main hydration of silicates [57, 71, 78]. 

The precipitation of a secondary phase thus leads both to a yield stress increase and the faster onset of Portland cement hydration.
section_name: Precipitation of a secondary phase

section_content: When an immediate strength gain after activation should be avoided, such as while concrete is within a slip-forming formwork or inside a mixing reactor, it is possible to use combinations of set accelerators and retarders. For example, for CAC systems, the activator can be formulated as a combination of the set accelerator LiOH, known to cause the precipitation of aluminium hydroxide, with the set retarder sodium gluconate (SG), known to prevent the precipitation of that phase (see Fig. 10 ). In this way, the onset of hydration can be controlled by modifying the ratio of sodium gluconate to lithium hydroxide.
section_name: Tailoring of activation

section_content: An early embodiment of set on demand systems is the wet process of shotcrete, where an airflow containing the accelerator is intermixed with concrete at the spraying nozzle [56]. For applications in digital fabrication, intermixing with airflow was not suitable. An alternative was developed for Smart Dynamic Casting, whereby an inline mixing reactor is used [21, 61, 95, 96] (see Fig. 11a ). 

For extrusion processes mixing chambers are closed as in the example shown in Fig. 11b. It is very important for such chambers to provide for a good homogenisation of the concrete and the accelerator. In this respect, we note that all accessible documents concerning Set on Demand approaches [60] [61] [62] 97] indicate that homogenisation is best achieved by active mechanical mixing in a chamber and by positioning the mixing chamber close to where concrete is placed [40]. It appears that at least three companies have integrated set on demand processing in their layered extrusion process, these being XTreeE [60, 62], Sika [97, 98] and Baumit [99]. How exactly these devices work is subject to some degree of speculation, neither of these actors provides details of their current design. In all cases, there appears to be a motor driving a mixing tool.
section_name: Setting on demand in processing

section_content: The set on demand system has been employed in a variety of processes that we describe as "digital casting" and for which an overview is given by Lloret et al. in the present special issue of this Journal [22]. 

The approach of a secondary precipitation of ettringite, using CAC as an accelerator, was used for layered extrusion, where vertical buildup rates of as much as 8 m/h were recently achieved. The characteristic strength build-up obtained in this case is shown in Fig. 12. a) [100]. In particular, this solution was applied to produce articulated columns of The set on demand approach is also employed for a stiffening coating of knitted textiles. In this case, the concept lies in the use of a rapid hardening calcium aluminate rich binder, that hydrates rapidly enough to prevent substantial water loss by evaporation in the thin coating. Work on this approach is preliminary, but has nevertheless contributed to enable the realisation of KnitCandela, a pavilion built in a collaboration between ETH Zürich and Zaha Hadid Architects, based on the KnitCrete technology [14]. In this project the binary binder from Fig. 13 was sprayed as a stiffening coating on the textile, subsequently allowing concrete placing [101].
section_name: Demonstrations of setting on demand

section_content: In general terms, for a structure being fabricated, the mechanical material performance in terms of yield stress and Young's modulus needs to be larger than the stresses applied by material weight throughout the structure's volume. This means that information about these properties and their evolution should be gathered (Section 3) and compared to localized stresses in the material. Both loads and mechanical performance will evolve over time, although with different kinetics. 

For the material, we distinguish two cases:

• Materials with yield stress dominated by initial yield stress and • Materials with a pronounced yield stress increase over time after placing. 

For the loads, we focus on:

• strength requirements to resist plastic collapse (depending only on hydrostatic pressure) as well as

• resistance against self-weight induced buckling failure (also de- pending on element geometry). Clearly, this approach is restrained to vertical extrusions. Other geometries, or the presence of reinforcement, formwork, friction forces, etc. would require more elaborate treatments, most of them rapidly calling for numerical modeling. The following results however have the advantage of laying simple conceptual grounds to develop first estimate engineering criterion to evaluate the risk of either material failure or buckling instability. Furthermore, it is important to remember that undesired material changes can play a major role, as for example drying and segregation (impacting for example interlayer bonds in 3DP.
section_name: Building stability

section_content: As described in Section 2, yield stress evolution at rest scales linearly with the amount of hydration products formed [27, 106, 107]. As the rate of hydration is not a constant throughout the building process, models describing yield stress should be able to capture: 1) the induction period with its slowly increasing yield stress, 2) the substantial rate increase owing to acceleration upon onset of hydration [108], and 3) the rate decrease resulting either from a reduction in the formation of hydration products or of physical interactions involved in flocculation [27]. 

Yield stress fluid models such as the Bingham model [109, 110] are applied in a widespread field of applications with τ 00 being the instantaneous concrete yield stress. Extensions to the Bingham model including structural build-up, such as by Ovarlez and Roussel [111] involving a linear build-up using a thixotropy factor A thix and by Lecompte and Perrot et al. [112] involving an extension to longer resting times and being based on growth of hydration products. 

Without considering the physico-chemical origin of build-up, an empirical approach of a power law time-dependent behaviour can be chosen:

where τ 00 is the initial yield stress, α τ is a constant and β characterises the nature of the time evolution of yield stress, whereby rate increases and decreases are respectively captured by β > 1 and 0 < β < 1), while constant rates are described by α τ or β = 0. 

The above expression is convenient for describing process relevant changes in adequate time frames and their choice can be interwound with the studied process timeframe, as is done in the following subsections. Specifically, we will use a similar expression for the increase of the elastic modulus as of the yield stress:
section_name: Yield stress evolution

section_content: A vertical element of height H (Fig. 14 ) built with a yield stress fluid should not collapse, if the yield stress at every point z along its height is higher than the shear stress from hydrostatic pressure [1, 25, 113] :

)

For example, in order to build a structure of 1 m height in 1 h with mortar (2300 kg/m3), for the pure self-support criterion, the yield stress at the bottom needs to reach = = kPa 13 0 3

and the linear yield stress increase needs to be at least: = kPa 13 / gv 3. Any onset of flow, or collapse is associated with reaching the yield stress. Also, since the pressure is highest at the bottom and that the process is self-similar, it is the bottom layer that is critical for selfsupport regardless of the building height. This means that, for a defined linear print speed, elements having a smaller cross-section lead to higher vertical rates and by consequence, require faster structuration rates. 

However, for loading close to the yield stress, substantial deformations can occur before failure [102, 114]. This can be described as a partial structural breakdown, which occurs at very low stress and causes much damage to the microstructure even before yield stress is reached [27]. This can be seen in Fig. 15 by the marked decrease of storage/shear modulus (discontinuous lines), before the yield stress is reached (maximum shear stress shown by the continuous line). Loads high enough to affect the structural build-up can occur within every layer applied during fabrication, implying that the material is not perfectly at rest and that its effective strength build-up can be slowed by successive damaging [34]. 

For most applications, large layer deformations are undesired, even if only to prevent cumulative placing errors due to excessive layer settlement. For this reason, rather than focusing purely on collapse, it can be more effective to aim at limiting deformations. A useful engineering approach for this is the introduction of a safety factor γ def to Eq. ( 3 ) that ensures that loading occurs in the linear material regime. Rheometric tests in Fig. 15 indicate indeed that the material is only "de facto stable" up to a typical shear stress to yield stress ratio of 1/3. For loading above 1/3 of the material yield stress, considering linear elastic behaviour can be an oversimplification. Thus, introducing the safety factor γ def = 3 (to be refined in future studies) should remove most of the layer settling and structural breakdown, without needing any knowledge of the thixotropic history. For the example above, the yield stress needed to support 1 m of mortar after 1 h would now be 39 kPa and the yield stress growth rate 39 kPa/h, giving the following stability criterion: g ( ) 3

def def 0, (4)
section_name: Stability with regard to self-support

section_content: For slim structures or ones built of a soft material, failure can additionally occur from buckling [2, 40, 45, [102] [103] [104] [105] 121]. Provided, that layer deformations can be considered small (no plastic deformations), then buckling occurs ideally at the Euler/bifurcation load [115]. Importantly, this approach is limited to linear-elastic materials (where Eq. ( 4 ) is fulfilled), thus excluding loading close to the strength limit, where potentially large deformations occur (as discussed above in Section 5. 2). 

For linear elastic materials it is well established that structures are more prone to buckling with increasing slenderness. Calculating the Euler load is straightforward for structures with a constant Young's modulus and a constant normal load. For axially loaded slim structures of an ideal wall of rectangular shape of length L, width b, height H and Young's modulus E, an upper limit for the critical stress σ cr can be calculated from the Euler load [102]. The correct solution of Greenhill for elastic self-weight buckling of a beam of constant Young's modulus [116] is: where E 0, min is the minimum Young's modulus required in the first layer. 

Combining Eqs. ( 2 ) and ( 5 ), we have:

which for tall elements and low starting values Young's moduli, leads to:

implying that the Young's modulus of the placed concrete should increase with t 3 on long timescales. 

In what follows we examine the more realistic situation whereby there is a gradient of material properties in the element considered. We do this with different approaches that represent alternative solutions to a mathematical problem not having a simple closed form solution.
section_name: Stability with regard to self-weight induced buckling

section_content: To account for gradients in material properties along the height, the differential equation for a vertical element describing beam stability writes as [115] :

with w the displacement along the beam length, E the Young's modulus, I the second moment of and C the normal load (compare Fig. 16 ). 

In early age concrete and for buckling under self-weight, all terms of the differential Eq. ( 8 ) may vary along the beam length, making a closed analytical solution of buckling impossible. However, scaling relationships can be extracted by separating the parameters into unitcarrying parameters and unitless functions. Solving this for the unitcarrying parameters gives the following scaling (detailed calculation in [33] ):

This scaling is valid independently of the evolution of E and of the boundary conditions and the shape of the displacement w leading to buckling. This scaling shows that for tall beams, the minimum required Young's modulus in the first layer scales with H 3 even if gradients are present. 

Similarly, as before we combined Eq. ( 2 ) with Eq. ( 9 ) and find once again that low starting values Young's moduli, the Young's modulus of the placed concrete should increase with t 3 on long timescales. Importantly, we now obtain this for the in which the material contains gradients in material properties.
section_name: Scaling solution with gradient in materials properties

section_content: Another way to quantify the Young's modulus requirement, is to consider the energy-based formulation of inner and outer potentials. The sum of potentials in a vertical unsupported element as above writes:

According to this expression, buckling should not occur as long as the second derivative of the potential with respect to the displacement (lowest energy state occurring at no horizontal displacement) is positive:

As opposed to the differential equation from the previous section, the energy-based expression can be solved with approximated expressions for E, C and w. In particular, assuming a constant vertical building rate, the Young's modulus evolution from Eq. ( 2 ) can be rewritten as a function of element height and neglecting E 0 (compare unit system introduced in Fig. 15 ): ) min 0, (12) ξ is the unit-less position along the element's height (number of deposited layers/total number of layers). 

An approximation of the buckling shape that fulfils the boundary conditions (free standing wall: w(0) = w′(0) = EIw′′(1) = (EIw′′(1))′ = 0) can be found with:

Using these approximations of Young's modulus (12) and failure shape (13) and solving in Eq. ( 11 ), the minimum requirement for the Young's modulus for the first layer of an ideal wall is then:

For a constant Young's modulus (β = 0) this solution is very close to the solution of Greenhill [116] (pre-factor 0. 125 compared to 0. 1276). The exponent of yield stress increase appears to have a minor effect on the pre-factor (increasing from 0. 125 to 0. 2 for β = 3), thus the effect of the material gradient is of secondary importance on the Young's modulus of the first layer. Much more importantly, the above result once again shows that the modulus should increase with the third power of the element height H. For constant production rates, this implies as previously, that the modulus should scale with the third power of time. The initial modulus and/or yield stress is therefore not relevant for evaluating buckling stability of tall structures, but the rate of stiffness increase is essential.
section_name: Energy based solution

section_content: As shown above, knowledge of Young's modulus is needed to predict buckling, by direct measurement or inferred from yield stress measurements. To this means, the quotient of shear stress to shear modulus at failure (yield stress) will be considered as critical strain γ cr, this being the deformation at which the structure collapses. Consequently, preventing collapse requires keeping the deformation below a critical value defined by material. 

Fundamentally for concrete at early age, yield stress and stiffness/ shear modulus do not scale directly [27]. In fact, they measure different behaviours. Yield stress indicates the maximum shear stress sustainable, while shear modulus characterises the deformation response to low shear stresses, before flow occurs (see Fig. 15 ). This discrepancy between end of the elastic limit of proportionality, its relation to static yield stress and deformation at which static yield stress is reached [44]. For the specific case of structural build-up shortly after the onset of hydration and where Young's modulus and static yield stress are already dominated by hydration product growth, preliminary measurements indicate that such a linear relationship may nevertheless exist [33]. In this case the shear modulus G(t) can be written as:

Measuring such a critical strain γ cr is difficult. Derivations from mechanical tests have limited validity due to a strong shear localization [27, 117]. The range of possible values is large and depends on the measuring procedure and particle interactions. A low bound is obtained by considering the structural breakdown of a cement paste after a long period of rest, taking the strain at which yield stress is measured, giving γ cr < 0. 01 [%] (Fig. 15 (left) and [107, 118] ). For measurements based on compression tests, values of the order of 2-4% have been reported [27] [46], but can reach 10% with some viscosity modifiers [119]. Such values can also be estimated from compression strength and Young's modulus, which are often reported in the literature. Indeed, using Eq. ( 15 ) with the yield stress to compressive strength f y conversion ( = f 3 y 0 ) and the Young's modulus to shear modulus conversion 1 ) ) the critical strain in the linear elastic regime writes as:

To define above which building height buckling with linear elastic deformations can be expected, we consider a loading in the linear elastic domain (Eq. ( 4 )) as well as a Young's modulus leading to buckling failure (Eq. ( 14 )) and combine in Eq. ( 16 ):

3 ( 5 )

From Eq. ( 17 ) we extract the building height from which we expect elastic buckling to dominate over visco-elastic collapse:

def cr (18) The extracted critical height is of similar form as the one found by Roussel [102], but accounts for material gradient in the built structure and for visco-elastic deformations to be avoided for model applicability. It expects the transition to elastic buckling failure to occur at 160% of previously expected building height. From Eq. ( 18 ), we also conclude that a small critical deformation combined with a high yield stress is optimal. In absence of hydration, admixtures such as PCEs (changing cohesion) or VMAs (introducing bridging interactions) may affect critical deformation and could cause buckling failure at lower building heights than otherwise, while critical strain is expected to be lower with ongoing hydration. 

To illustrate the above points, let us determine the critical strain by applying (15) to printing experiments by Wolfs et al. [45] who reported initial values of compressive strength and Young's modulus of f y = 6 kPa and E = 78 kPa. Taking the ratio between both provides an estimation of the critical strain of 11%, a very large value when considering elastic deformations. From this value and Eq. ( 18 ), we infer that the critical building height would be 18 cm if the filament was printed in a straight line, while Wolfs et al. measured it experimentally to be 20 cm in a cylinder (at onset of horizontal displacement). It should be stated here that as the failure observed by Wolfs was only partial, Eq. ( 14 ), valid for an unsupported wall is not valid, something that deserves further attention. Nevertheless, this suggests that (if elasticity is an acceptable assumption) buckling stability may be examined with sufficient accuracy by considering critical deformations, thus reducing the need for more complex analysis involving viscoelastic and time dependent material modeling. ) and (this paper: centre radius 150 mm, filament width 32 mm, vertical building rate 2. 8 m/h). During fabrication up to collapse, the yield stress does not significantly increase in the first case, while it increases with the building height in the second and no collapse is observed. This shows the value of set on demand systems as they can keep up with the increasing loading. Furthermore, it is observed that the non-accelerated concrete doesn't fulfil the deformation limiting criterion at the time of collapse, which could have led to visco-elastic deformations that amplified the buckling tendency. With respect to the set on demand system, while the deformation requirement is also not met, the discrepancy is much smaller, underlining that the safety factor γ def = 3 is rather conservative. From the measurements in Fig. 17, assuming visco-elastic deformation as the reason for collapse in the experiments of Wolfs et al., γ def is expected to lie around 2, while the results from this study, without observed failure indicate that γ def is smaller than 2. 5.
section_name: Critical strain-based solution

section_content: Controlled structural build-up is an important requirement for digital fabrication processes. This simultaneously requires a rapid material strength build-up after the material is deposited, but a slow buildup rate before that. To achieve these contradictory needs, controlled activation of hydration shortly before material placing, called set on demand can be used. Such approaches rely on hydration control to ensure structural stability during digital fabrication. 

Achieving this involves multiple steps of understanding and implementation. Given a building process and its manufacturing rate, the requirements of strength evolution can be derived (Section 5). To fulfil these, the understanding of physical interactions and the linear relationship between strength evolution and hydration can be used, building on the knowledge that strength gain at rest is dominated by the formation of hydration products (Section 2). On this basis, it is necessary to select the correct combination of set retarders and accelerators to achieve the desired hydration kinetics and by extension the desired strength build-up. Some solutions for this have been outlined in Section 4. 

While designing proper material compositions, as well as while producing elements, it is important to be able to quantitatively monitor the material strength gain. As explained in Section 3, our experience is that the slow penetration tests can prove to be extremely useful, particularly when analysed following the theoretical frame outlined in that section. 

Finally, in terms of stability, we have examined material loading failure as well as buckling instability. In both cases we have presented simplified ways of assessing this, offering some improvements over other state of the art approaches, while not requiring too cumbersome material testing (Section 5). Importantly, with respect to hydration control, we show that for tall elements, the material strength should increase with the third power of time even in elements with strength gradients. Using slow penetration test and selecting chemical systems to achieve this, proved to be effective for achieving large scale rapid production of tall and slender elements, which up to now was rather challenging for extrusion printing.
section_name: Conclusions

section_name: Acknowledgements

section_content: This work was developed within the National Centre for Competence in Research (NCCR Digital Fabrication, Agreement # 51NF40-141853 ) and involved many collaborations with other chairs working with digital fabrication with concrete. Specifically, the authors would like to thank constructive exchange with the following colleagues: Ena Lloret, Anna Szabo, Matthias Kohler, Fabio Gramazio, Matthias Rippmann, Philippe Block, Patrick Bedarf, Angela Yoo, Heinz Richner, Andreas Reusser, Philippe Fleischmann, Tobias Hartmann, Michael Lyrenmann. In particular, the authors would like to thank Benjamin Dillenburger for directing the project on layered extrusion and Mariana Popescu for the work done together on KnitCrete and KnitCandela. In addition we thank Axel Crettenand for pictures taken.
section_name: Acknowledgements

section_name: CRediT authorship contribution statement

section_content: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
section_name: Declaration of competing interest