Improving the structural efficiency of textured three-dimensional concrete printing wall by architectural design

Abstract

Three-dimensional concrete printing (3DCP) technology begins to be adopted into construction application worldwide. Recent studies have focused on producing a higher concrete quality and offering a user-friendly construction process. Still, the 3DCP construction cost is unlikely to be lower than that of conventional construction, which is especially important for projects where the cost is sensitive. To broaden the 3DCP construction applications, reduction of the quantity of 3DCP material usage is needed. This work aims to perform structural analysis of several patterns of geometric textured 3DCP shell wall structures. 21 different cantilevered textured patterns of 3DCP shell wall structures were architecturally designed and then subjected to structural analysis by a finite element method (FEM). The results indicated that by designing appropriate patterns, the structural performance to weight ratio could be improved up to 300%. The study therefore offers an innovative design process for constructing 3DCP housing and suggests pre-construction analysis methods for 3DCP shell wall structures.

Graphical abstract

Keywords

3D printing / concrete / architectural design / shell wall / finite element method

1 Introduction

Nowadays, the use of automated and robotic systems has been widely adopted in the manufacturing and engineering industries, enhancing productivity and effectiveness, notably for stakeholders. Clearly, automated and robotic practices are spreading throughout the building and construction industries to evolve into Construction 4.0. Application of automated robotic arm and gantry systems using concrete, also called three-dimensional concrete printing (3DCP), for building structures including residential housing, is developing worldwide, under names that include large-scale additive manufacturing, digital concrete, and rapid manufacturing for construction. The 3DCP market has been reported as expected to grow from 3 million USD in 2019 to 1.6 billion USD by 2024 [1]. Such rapid growth of the 3DCP market is predicted as one of the key innovations of our construction industry. The adoption of 3DCP technology in building, construction, and architectural applications offers several meaningful benefits, including:

1) potentially cheaper construction, especially for an architecturally complex design, due to a lack of requirement for formwork and scaffolding during construction [2–4];

2) less labor is required when the automated system is used [5,6];

3) using less labor results in better control of the work environment and results in increased safety [7];

4) completion time is usually shorter, with better scheduling control [8,9];

5) high precision of the resulting product is achieved [9];

6) better sustainability due to increased manufacturing efficiency, reduced waste, and shorter construction time [10,11].

The adoption of the 3DCP technology in the construction and architectural industries is innovative. However, there are technological challenges in its practical implementation. Many technical knowledge fields, including architectural design, mechatronics, building and construction technology, and material science, are involved in the development of the 3DCP technology, requiring careful evaluation of processing integrity and overall technology efficiency. To have better efficiency, aspects of fresh material’s rheology, setting behavior, extrusion mix design, printing parameters, architectural and structural design, algorithmic software, industry scalability, and local building code availability, are all under investigation. For load-bearing wall application, when efficient 3DCP technology is adopted, the construction cost can be competitive with that of traditional construction techniques such as precast and prefabrication processes.

Although many studies [12,13] have reported that the cost of building a 3DCP load-bearing wall house is lower than that of traditional precast methods, 3DCP is unlikely to be used to build an affordable housing community or in a cost-sensitive area because the cost can still be too high. The authors [12] previously reported that the number of publications investigating 3DCP housing to reduce the cost was very limited. Weinstein and Nawara [13] also carried out an economic feasibility analysis of the developing countries using an Excel-based model that controlled for variables related to wealth, size, expense consumption, and concrete consumption of the citizens. They concluded that only in China and Saudi Arabia, where adequate support from national government for the public 3DCP housing community projects, could such projects be successful. Weng et al. [14] compared the cost of a 3DCP bathroom unit with the dimensions of 1.6 m × 1.5 m × 2.8 m compared with a conventional precast bathroom unit of the same size. Although the total material cost of the 3DCP bathroom unit was reportedly 46% cheaper than that of the precast unit, the formwork in their precast study was only single-use. However, in real application with affordable precast housing, the formwork will be used several times. Therefore, discarding the cost of making the formwork, the calculated cost of the 3DCP is higher than that of the precast one. As a result, housing markets in which the aesthetic appearance and unique architectural design are more important than the budget are likely to be potential 3DCP housing market segments. A flat load-bearing wall structure can be effectively built by using the traditional precast and prefabrication processes.

The current development of 3DCP technology focuses primarily on material development, fabrication, and structural reinforcement, not on design. The study of architectural design to perform better process optimization began within the last decade [15–18]. Vantyghem et al. [15] studied a post-tensioned 3DCP girder-designed structural optimization approach. They found that the optimized 3DCP structure allowed for a significant reduction of material consumption. Jipa et al. [16] also studied the structural optimization of the 3DCP formwork for a 1.8 m × 1 m × 0.15 m concrete slab, but they did not include discussion of the design of the 3DCP formwork structure. In 2021, Anton et al. [17] investigated complex choreography 3DCP columns that could be curved, branched, or nested in the Robotic Fabrication Laboratory of ETH Zürich. They reported that these columns were for stand-alone use and were not intended to perform as structural columns or in any tectonic context. Only aesthetic benefit could be achieved from these complex choreography 3DCP columns, and not structural function. Lastly, du Plessis et al. [18] reported that the 3DCP technology had bio-mimetic design elements for tectonic contexts, including overlapping, fibrous, helical, gradient, layered, tabular, cellular, and suture features. They indicated that natural mimicry of behavior by fibrous design elements was already successful in the 3DCP approach [19], so that architectural design can offer not only an aesthetic aspect but also strength and stability. Nevertheless, regarding designing biomimicry and bio-inspired design, the authors discussed that the main technology improvement aspects from the architectural field have received little interest to date.

A combined approach, with architectural design and structural analysis, has become a useful tool for least-weight and performance design determination. This also includes 3DCP technology. Prasittisopin et al. [20] conducted research on designing a nature-like 3DCP shell wall panel from the traditional double surface 3DCP wall (two outer shells and one inner truss structure) to be a structural surface element as a shell wall (one outer shell and one inner truss) structure in 2017, as shown in Fig.1. The results indicated that using the 3DCP shell wall structure, compared with that of a double surface 3DCP wall, could result in a reduction of both material consumption and printing time by more than 10%. Creating architectural design from a patterned structure could result in a significant decrease of the overall construction cost using 3DCP technology. Although the cost of cement is inexpensive, for 3DCP buildings, the mortar consumption is high and accounts for roughly 30% of the total cost. As shown in Fig.2, some industrial 3DCP companies have now begun to adopt this design concept for shell wall structures, and have publicized their designs on the Internet [21,22]. Nonetheless, there has been no structural analysis based on the fabrication of a 3DCP shell wall structure for the purpose of material reduction benefit. Additionally, the difference between Fig.1 and Fig.2 is that the structure in Fig.1 behaves like a bracing structure, allowing for more structural efficiency, while the structure in Fig.2 does not. When performance of structural analysis, as proposed in this study, is adopted into this design concept, the cost components relating to material and time are assessed. The cost-inhibited challenge is minimized such that the 3DCP construction can be widely implemented. In addition, when reducing 3DCP materials, carbon emissions can be reduced [23–25].

Because the effectiveness of architectural design of 3DCP technology is currently in need of improvement, this study presents the design and structural analysis of the geometric architectural patterns of a 3DCP shell wall structure, delivering efficient optimization in terms of material usage and printing time. The wall panel here was designed as a load-bearing structure. The structural analysis was performed on 21 load-bearing nodal model designs (also called herein cantilevered textured patterns) and 18 shell pattern designs, using the finite element method (FEM). The prototype design of a cost-efficient 3DCP solution for a public housing community was then created. The plastic prototype of the 1:20-scale affordable house was also developed as well as the 3DCP shell wall panel based on the design and structural analysis techniques used in this study. The study delivers innovative architectural design during the preconstruction design process that can maintain structural integrity while enhancing the efficiency of the manufacturing process of the load bearing 3DCP shell wall structure.

2 Design methods

2.1 Architectural design method

The study assesses several theoretical geometries to determine the physical and structural characteristics of the shells regarding their strength and load-bearing capacity. The physical and structural characteristics analyzed herein indicate the design patterns that offer improved rigidity and structural behavior for transferring and distributing external loads, as given in Tab.1. It is known that a triangle can offer the most capability in terms of holding its shape, having a stable base, and providing rigid support [26]. Several geometric patterns are shown, and each geometry contains several connecting dots and edges. The stable design of the reinforcement connection is also shown in red. The triangle polygon can support the external load as a point load to the top angle and two sides of the polygon transferred the load to the ground. The internal compression force presents in the two side of the polygon, and the base side attached to the ground presents the internal tension force as shown in Fig.3. This triangle polygons are adopted in several kinds of members of buildings, such as trusses and geodesic domes. Therefore, this study presents an analysis of structural stability using the architectural design method for different triangle model designs of the textured shell surface of 3DCP wall structures (not the supporting surface). A one-story affordable house model is designed using 3DCP wall structures and aimed to follow a local building code. The design criteria for each modular 3DCP housing unit are given as follows.

1) One-story house with 2 inhabitants living with a usable area not less than 20 m² (herein, 4.8 m × 7.2 m).

2) One bedroom sized 1.8 m × 2.0 m.

3) One kitchen sized 3 m².

4) One closet sized 0.6 m × 0.7 m.

5) One outdoor balcony.

6) The connection of each 3DCP wall panel uses a dry joint process with steel plate connected with bolt/nut system and then grouted with non-shrink grout mortar. The rebars can be added around the connection during printing.

7) Each modular unit shares the same double 3DCP wall.

8) The roof component is designed in an isosceles triangle shape, with different slopes to minimize the heat from sunlight and provide better drainage systems from rainwater.

It should be noted that the current model design method in this study is based on the state-of-the-art applicability of 3DCP technology. The current limitations of the 3DCP technology are based on:

1) the limited size of 3DCP members (a larger member can be printed with a larger printer, resulting in a lower number of connections and decreased fabrication time);

2) the type of automated printer (gantry or robotic arm); the printing time depends on the speed of the printer (for our current printer, its speed ranges between 100% and 300%); the extrusion nozzle diameter creates a low-resolution 3DCP line;

3) printing height is controlled for each layer;

4) printing path that should be in closed loop (the initial point should be the same as the ending point for each layer), in lieu of the open loop;

5) setting behavior of the material affects its buildability and the maximum slope of a cantilevered textured pattern.

2.2 Effect of cantilevered textured patterns

The architectural design method was performed based on a triangle of the modular structure using computer-aided manufacturing. It is noted that the triangle is a typical pattern for textured 3DCP wall panels. The design boundaries of the 3DCP model are as follows. As aforementioned, the maximum slope of the cantilevered textured pattern of the shell wall structure depends on the buildability and setting behavior of the 3DCP material. For the gantry printer, the maximum slope of the cantilevered or indented section was 65° to 70° from the horizontal, as reported in a previous study [27]. It should be noted here that the addition of rapid-set cements such as calcium aluminate cement and calcium sulfoaluminate cement can be performed to adjust the setting behavior [28]. The printing path was a closed-loop system, allowing the homogenous 3DCP member to have less deflection. (As discussed, the initial printing point should be the same as the ending printing point for each layer.) It should be noted that another possible printing path is a fold-back system, where adjacent layers are printed in opposite directions. The dimensions of the wall model design patterns were 1 m × 1 m × 0.12 m. The shells of the 3DCP wall structures had two surfaces: the outer shell surface having cantilevered textured patterns and the inner shell surface having either a cantilevered textured pattern or a flat surface. The Rhinoceros 5.0 software (Robert McNeel & Associates) was used to create two different pattern types: L type and V type. All the patterns were designed as solid shell wall structures. For each type, the solid 3DCP shell wall, having a length of 1 m, was then designed to have different length ratios from L/1 to L/10 and V/1 to V/10. For instance, the ratio of L/10 means the wall length was 1 m, and there were 10 cantilevered elements for each wall. Therefore, each cantilevered element had a length of 10 cm. The top view and examples of perspective solid patterns of L type and V type systems are shown in Fig.4 and Fig.5, respectively. The double wall system with flat surface, as the reference system, represented a traditional 3DCP wall panel having two flat surfaces and an inner truss for reinforcing at an angle of 65°, as shown in Fig.6. It should be noted that the mix design of the 3DCP materials was developed by SCG Cement, Thailand, and the mix ingredients can be found elsewhere [29]. The reference model design, a double wall system with a flat surface was used. The extrusion nozzle diameter used in this study was set at 3 cm. The weight of the 3DCP materials used for each pattern was calculated. The structural behavior and factors were calculated by ANSYS v18.2 software (ANSYS, Inc.) [30,31]. Daungwilailuk et al. [30] used ANSYS software to perform the FEM and they experimentally performed a large-scale loading test of 3DCP double wall panel for comparison. They made an assumption that 3DCP structure followed linear elastic behavior. The mesh that they generated in the software had 1028002 nodes and 599623 elements. Each 3DCP layer was designed to be perfectly bonded. Their results exhibited good agreement between the results from the FEM and the experimental study. These parameters were then used in this study. However, it should be noted here that, as with cantilever structures, the tensile strength can be formed, which can be the limitation of the study. The input material parameters of the 3DCP material are given in Tab.2. The assumption of the related internal forces includes only the compression loading from the roof structure of the 3DCP house. The dead load was assumed to be 50 kg/m² for the weight of the steel roof structure and 15 kg/m² for the weight of ceramic roof tile. The input vertical dead load was 65 kg/m². The compression live load was 50 kg/m³. The total loading was calculated as (1.4 × dead load) + (1.7 × live load) which was equal to 176 kg/m². The maximum stress values of different wall design patterns were reported. For each pattern, the estimated material used in fabricating 1 m × 1 m × 0.12 m wall was then calculated. It should be noted here that not all patterns were steel-reinforced. This concept is generally applied where microfiber is added to the cementitious material.

2.3 Effect of wall patterns

After running a structural analysis, the cantilevered textured patterns, the type, and the length ratio that were structurally safe while consuming less material were then used for designing the wall patterns. The dimensions of the wall model design patterns were 1 m × 1 m × 0.12 m. The diameter of the extrusion nozzle was set at 3 cm. This is the typical nozzle size used for the printer in this study. The solid shell walls of the 3DCP structures had two sides: the outer shell having cantilevered textured patterns and the inner shell having either cantilevered textured or flat surfaces. The Rhinoceros 5.0 software was used. The grid line was then designed for each wall pattern, as shown in Fig.7.

When varying the wall design patterns, all possible patterns (generally using the length ratio of 3 to 5 as discussed in the previous section) were studied under the discussed limitations of the current 3DCP technology, as shown in Fig.8–Fig.12. It is noted that the possible patterns were discussed with the printing team before design. P01 to P05 patterns were created for the five wall patterns. The P01 pattern had the cantilevered elements as cantilever point from 4 sides (like a diamond shape). The P01 pattern (Fig.8) consisted of 4 different types, these being: 1) angle-to-angle and one-side texture, 2) angle-to-angle and two-side texture, 3) angle-to-face and one-side texture, and 4) angle-to-face and two-side texture. For the P02 pattern (Fig.9), the cantilevered element was designed switching from 1 side of the P01 pattern to 1 vertical face. As for P01 pattern, the P02 pattern could be designed for 4 different types, these being: 1) angle-to-angle and one-side texture, 2) angle-to-angle and two-side texture, 3) angle-to-face and one-side texture, and 4) angle-to-face and two-side texture. For the P03 pattern (Fig.10), the designed pattern had cantilevered and indented elements but not as many as the P01 and P02 patterns. This allows the P03 pattern to have a larger triangle pattern. The designs of the P03 pattern could be varied into 6 different types, these being: 1) angle-to-side angle, angle-to-top-bottom-side, and one-side texture, 2) angle-to-side angle, angle-to-top-bottom-side, and two-side texture, 3) angle-to-side-top-bottom angle and one-side texture, 4) angle-to-side-top-bottom angle and two-side texture, 5) angle-to-side and one-side texture, and 6) angle-to-side and two-side texture. The P04 pattern (Fig.11) was designed using hexagonal (or 6 triangles) cantilevered elements. Two types of the P04 pattern can be designed here: 1) angle-to-angle and one-side texture and 2) angle-to-angle and two-side texture. The P05 pattern (Fig.12) appears quite similar to the P02 pattern, but instead of having the cantilevered element as vertical face, the P05 pattern has this as a horizonal face. The design of the P05 pattern can be classified into 2 different types, these being: 1) angle-to-angle and one-side texture and 2) angle-to-angle and two-side texture. It should be noted that both one- and two-side textures used the same mixture proportion.

The FEM was used to structurally determine all patterns from P01 to P05 after they were designed. The ANSYS software was then performed, and input 3DCP material parameters were used as given in Tab.2. An assumption of 3DCP patterns for structural analysis was linear elastic behavior. The mesh was generated in the software with 1028002 nodes and 599623 elements, and each 3DCP layer was designed to be perfectly bonded. Other wall systems varied from the reference system. Each type of model design was simulated to have a gravity loading of 176 kg/m². It is noted that the gravity loading value was used in the calculation assuming the cross-sectioned area of the wall to be 1 m × 0.12 m. This gravity loading value represents the calculated weight of the actual roof structure of the building (i.e., ceramic roof tile). Fig.13 shows an example of FEM results from the maximum in-plane stress calculation from vertical loading of the P01 Type 1 model, of which its structural efficiency is maximum.

3 Result and discussion

This result and discussion section is presented in two parts: 1) the effect of different cantilevered textured patterns and 2) the effect of different wall patterns.

3.1 Effect of cantilevered textured patterns

Fig.14 and Fig.15 show the effects of different cantilevered textured patterns of the L type and the V type on the maximum stress values. The maximum stress value calculated in this study represents the load carrying capacity of the 3DCP wall’s cantilevered textured patterns. Results for different patterns shown in Fig.14 indicate that the maximum stress value calculated for the L/2 system is higher than those of the L/3, L/1, L/4, L/5, L/6, L/8, L/7, L/9, and L/10 systems. Compared to the maximum stress value of the double wall (reference) system, the L/2 system has 3% higher, and the L/3 system has less than 1% higher, maximum stress value. For the others, the maximum stress values are lower than the double wall system, with differences ranging between 2% and 19%. The L/1 system has the cantilevered element far out of the plane (1 × cot65° = 0.47 m from the surface of the shell wall); therefore, it is believed that the centroid locates far out from the body, resulting in the instability of the structure. Both L/2 and L/3 systems provide better structural stability, while still being able to perform as a surface-bracing structures, because the centroid seems to locate closer to the plane. For the L/4 to the L/10 systems, the cantilevered elements are unlikely to perform well as surface-bracing structures although the centroid is in plane. The L/2 system offers the highest load carrying capacity because the system has structural efficiency regarding the in-plane centroid and surface-bracing structure. Note that the positions of the centroid in x and y directions can be calculated in the following equations.

For x direction

(1)\mathrm{L}\mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}:x_{\mathrm{N}}=\frac{L}{N^2}\times \left[\frac{2N}{3}+\sum \left(i-1\right)\right],

(2)\mathrm{V}\mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}:x_{\mathrm{N}}=\frac{V}{N^2}\times \left[\frac{N}{2}+\sum \left(i-1\right)\right],

where x_{\mathrm{N}} is the position of the centroid locating in the 3DCP wall system in x direction; L is the length of the L system; V is the length of the V system; N is the number of the length ratio; and i is the integer value.

For y direction

(3)\mathrm{L}\mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}:y_{\mathrm{N}}=\frac{L}{N}\times \mathrm{c}\mathrm{o}\mathrm{t}\theta ,

(4)\mathrm{V}\mathrm{t}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}:y_{\mathrm{N}}=\frac{L}{N+1}\times \mathrm{c}\mathrm{o}\mathrm{t}\theta ,

where y_{\mathrm{N}} is the position of the centroid locating in the 3DCP wall system in y direction; and \theta is the angle of the cantilevered textured patterns of 65°.

For Fig.15, results indicate that the maximum stress value of the cantilevered textured pattern of the V/1 system is higher than those of the V/2, V/3, V/5, V/4, V/6, V/8, V/7, V/10, and V/9 systems. The maximum stress value of double wall system for the V/1 system is 6% higher than that of the double wall system. The other 9 patterns (from V/2 to V/10) have calculated maximum stress values lower than that of the double wall system, with differences ranging between 2% and 23%. Only the V/1 system has better structural performance than that of the double system. This is due to the in-plane centroid of the V/1 system and its surface-bracing structure.

Results indicate that, apart from the L/1 and V/1 systems, all other L type systems have higher maximum stress values than all other V systems at the same length ratio. The L type systems have maximum strength values ranging from 1% to 13% higher than those of the V type systems. It is believed that the L type system has better structural performance at the same length ratio because the perpendicular distance from the plane of cantilevered elements of L type systems is twice as large as the that for the V type systems. For this reason, the L type systems act as the surface-bracing structure and have better stability than the V type systems. However, this is not the case for the L/1 system compared with the V/1 system. The L/1 system has the perpendicular distance of 0.47 m from the plane of cantilevered elements, and the V/1 system has the perpendicular distance of 0.235 m from the plane of cantilevered elements. Although the L/1 system may better perform as the surface-bracing structure, the centroid is not located inside the body. Unlike the V/1 system, its centroid is inside the body of the wall. The V/1 system has better structural performance than that of the L/1 system. This is due to both in-plane centroid of the V/1 system and its surface-bracing structure.

The influences of cantilevered textured patterns of L type and V type on the amount of 3DCP material used for printing are shown in Fig.16 and Fig.17, respectively. Results indicate that the amount of 3DCP material changes when the cantilevered textured pattern is altered. In Fig.16, when the length ratio of the cantilevered textured pattern increases (meaning that the cantilevered or indented element becomes smaller), more 3DCP material is consumed. This is because a more textured pattern leads to a longer printing path. The amount of 3DCP material used increases significantly from 169 kg in the L/1 system to 286 kg in the L/10 system. It should be noted here that when designing the shell wall structure with more texture, not only is the 3DCP material consumption significantly increased, but the printing time can also considerably increase. Our previous research showed that total printing time was reportedly reduced by 10% when changing the design of wall pattern from a double wall system to a shell wall structure [20]. Additionally, in general, the 3DCP machine automatically prints at a slower rate when designing the printing angular shapes or curvature elements than when printing the flat surfaces or straight elements. When printing a more complex textured wall with several angular angles or curvature elements, the printing time increases. Both increase in material cost and total printing time directly affect the cost-efficiency of a 3DCP construction, which may result in construction becoming cost-prohibited with this new technology. Comparing the cantilevered textured patterns to the double wall system, the results exhibited that the cantilevered textured patterns consumed less 3DCP material than the double wall by nearly 50%. When printing time reduced, many cost components can decrease. These cost components include machine depreciation cost, electric energy cost, cost of operators, waiting time for storing concrete to develop strength, and cost related to finishing the surface when needed.

Results of the V type systems, as shown in Fig.17, indicate that when the length ratio of the cantilevered textured pattern increases, more 3DCP material is consumed. These results conform with the results in Fig.16. This occurs because more textured patterns require longer printing paths. The amount of 3DCP material used increases significantly from 162 kg in the L/1 system to 272 kg in the L/10 system. Comparing the shell wall structure to the double wall system, results indicate that the V type systems consume less material, ranging from 53% to 90%, than the double wall system. It should be noted here that the V/1 system uses less material than the double wall system by 54% while having better structural performance by about 6%. The architectural model design greatly benefits the 3DCP process in both increasing its strength and reducing the volume of 3DCP material. Comparing the L type systems and the V type systems, results indicate that all L type systems consume more 3DCP volume than all V type systems at the same length ratio. The calculated ratios of 3DCP material used for V type systems with the L type systems ranges are between 92% and 96%. The textured pattern of the shell wall structure can influence the volume of 3DCP material.

The maximum stress (or load-carrying capacity) to weight ratio of material or structure is one of the important parameters in construction and building technology, especially for complex structures, wide-span buildings, and high-rise buildings. This maximum stress to weight ratio represents the effectiveness of selected materials or structures for buildings and leads to holistic effectiveness of structural technology. Many studies have proposed the optimization of this ratio by introducing a new material usage [32–34] and by designing architectural elements [35,36]. The benefits of maximizing this ratio can be either direct or indirect for both architectural and civil engineering aspects include: lightweight structure, durable structure, increased usable area, ease of transport and lifting, reduced curing time of concrete structures for lifting, safer construction for workers, and a more sustainable solution [37–41].

Fig.18 and Fig.19 show the influences of different cantilevered textured patterns on the maximum stress to weight ratio of L type and the V type systems, respectively. Results in Fig.18 indicate that the maximum stress to weight ratios of all L type systems decrease when the length ratios increase. More texture on the cantilevered element leads to a reduction of the maximum stress to weight ratio. The L/1 system provides the highest value of the maximum stress to weight ratio, and this value can be reduced up to 51% (for the L/10 system). Comparing the cantilevered textured patterns to the double wall system, results indicate that the cantilevered elements of the L/1 to L/7 systems can result in increased maximum stress to weight ratios up to 75% (for L/1 system). However, the L/8, L/9, and L/10 systems have the maximum stress to weight ratios 3%, 9%, and 14% lower than that of the double wall system, respectively. The architectural design of the 3DCP wall can significantly alter the effectiveness of the load-carrying capacity to weight ratio of the structure.

For Fig.19, results indicate that when the length ratios of the cantilevered textured patterns of the V type systems increase from V/1 to V/10, their maximum stress to weight ratios significantly decrease by 57%. The architectural design of cantilevered element of V type systems also significantly affects their structural performance, resulting in improved structural effectiveness of 3DCP shell wall structure. Comparing the cantilevered textured patterns to the double wall system, results indicate that the cantilevered elements of the V/1 to V/8 systems can result in increased maximum stress to weight ratios of up to 200% (for the V/1 system). However, the V/9 and V/10 systems have the maximum stress to weight ratios 10% and 14% lower than the double wall system, respectively. When comparing the results of the L type systems from Fig.18) with the V type systems from Fig.19, results indicate that at the same length ratio, the V/1 to V/8 systems have higher maximum stress to weight ratios than the L/1 to L/8 systems. These ratios of the V type system are higher than those of the L type systems by a range of 4%–14%. However, for length ratios of 9 and 10, the L type systems have similar maximum stress to weight ratios with the V type systems, where the difference of ratio values of both systems is less than 1%.

From the analysis discussed in this section, the length ratios of the cantilevered textured patterns of the 3DCP shell wall structure of 2–7 were selected to design the wall patterns in the next section. The system having the length ratio of 1 is neglected here because it does not provide any texture, and the systems having the length ratios more than 7 are not considered because their maximum stress to weight ratios are lower than that of the double wall system. It should be noted again that several models of the shell wall structures were designed, based on the current limitations of the 3DCP process and the machine. Once 3DCP technologies, such as material performance at a higher slope (more than 65°, as used in this study), and the machine printing a higher resolution without collapsing, are improved, then a wide variety of textured shell wall structures can be designed.

3.2 Effect of wall patterns

Fig.20 shows the influences of 3DCP wall patterns designed on the maximum stress values calculated by the FEM. The patterns consist of both one- and double-side textured walls. Results indicate that different 3DCP wall patterns affect the maximum stress values. The maximum stress values of the P01, P02, P03, and P04 wall patterns range from 223480 to 244580 Pa, 228970–228980, 147550–190458, and 103770–118090 Pa, respectively. The average maximum stress value of all P02 wall types is 3%, 28%, 25%, and 53% higher than those of the P01, P02, P04, and P05 wall patterns, respectively. The P01 Type 2 wall pattern has the highest maximum stress valve. Hence, this P01 Type 2 pattern provides the highest structural performance of the 3DCP wall pattern.

The effects of 3DCP wall patterns on the volume of 3DCP material consumed are shown in Fig.21. Results indicate that when changing the wall patterns, the 3DCP material’s volume is significantly altered. The average value of 3DCP material volume used in the P01 systems for all types is 11% lower than that in the P02 systems and 20% lower than that in the P05 systems. But the average values of 3DCP material volume used by the P01 systems of all types are 11% higher than those in the P03 systems and 16% higher than those in the P04 systems. Comparing the volume of 3DCP material between one-side textured systems and two-side textured systems, the results indicate that most of the one-side textured systems consume a lower amount of material for printing than the two-side textured systems, except for the P05 systems. The average volume of 3DCP material used for printing the one-side textured systems is around 4% lower than that for the two-side textured systems. The two-side textured wall systems typically have texture on both sides, resulting in a larger amount of material use. However, for the P05 wall systems, the one-side textured system consumes 5% less 3DCP material than the two-side textured system. This is because when printing the one-side textured wall system, its thickness is larger, on average, than the average thicknesses in the two-side textured system. The wall thickness variation may also affect its structural performance. It should be noted here that when printing the two-side textured system, the wall thickness should be designed properly. The two-side textured wall may result in less material and a very small thickness from the cantilever texture of both sides. This leads to a reduction in structural performance.

Fig.22 shows the effects of the maximum stress to weight ratio when the 3DCP wall pattern is varied. Results indicate that designing different wall patterns can result in a very large variation in the maximum stress to weight ratio values. Their variation ranges from 404 to 1274 Pa/kg, which is approximately a 315% difference. The average value of the maximum stress to weight ratio of the P01 systems for all types is approximately 9%, 22%, 27%, and 159% higher than those of the P02, P03, P04, and P05 systems, respectively. The P01 systems are the most efficient 3DCP shell wall structures regarding the structural efficiency. Less material used for printing results in less printing time and reduced material cost. From the cost estimation of pervious 3DCP construction, the 3DCP material accounts for around 33% of the total construction cost. It is also reported that the 3DCP material cost component was approximately 44% of the total construction cost for a 3DCP bathroom unit as discussed by Weng et al. [14]. The material cost is the major component of the cost of constructing a 3DCP building. Their study revealed that the cost of 3DCP construction can be reduced by 16%–22% without loss of any structural building performance.

The P01 Type 2 (two-side textured) system is the 3DCP shell wall structure with the most structural efficiency, among all analyses. Fig.23(a) shows the 3DCP panel of the P01 Type 2 wall with a size of 1 m × 1 m × 0.12 m. Fig.23(b) shows the FEM model of the P01 Type 2 wall system with respect to its maximum stress as modeled by ANSYS software. The lateral or out-of-plane loads were ignored here because the structure was aimed at a one-story 3DCP house. The one-story 3DCP house is purposedly built for an affordable community. Additionally, the FEM for assessing the lateral loads of buildings was not analyzed for the real 3DCP wall structure projects. As aforementioned, in earlier studies, the FEM using ANSYS software was adopted to analyze the structural behavior of 3DCP [20,26]. In the previous study, the FEM results exhibited good agreement with the large-scale test of the printed textured wall structures. After determining the structural efficiency in this work, the final prototyping design model of 3DCP housing of the P01 Type 2 system was then created and is shown in Fig.24. This prototype was printed by the commercial 3D plastic printer (FullScale Max400). The plastic used here was Acrylonitrile Butadiene Styrene filament with a diameter of 1.75 mm. The model was designed having the scale of 1: 20 relative to the dimensions of the real 3DCP house (4.80 m (W) × 7.20 m (L) = 34.56 m²). The height of the wall is 3 m. It should be noted that the large-scale building structure using 3DCP was not assessed here due to site and funding limitations. The images of the 3DCP modular public affordable housing design are shown in Fig.25 and Fig.26.

4 Conclusions

The study presents the results of using architectural design and structural analysis methods to improve structural efficiency in modeled geometric 3DCP textured shell wall systems. The various cantilevered texture patterns and wall patterns were assessed. From this study, conclusions are as follows.

1) The proposed architectural design of the 3DCP shell wall structure could significantly alter the maximum stress, volume of 3DCP material used, and effectiveness of the strength to weight ratio of the structure, relative to traditional 3DCP double surface wall practice. Strength is sufficient for a load-bearing structure, while the weight is significantly reduced.

2) Decreasing the length ratio of the cantilevered textured patterns leads to better structural performance.

3) The shell wall patterns could affect the strength to weight ratio by more than 300%.

4) One-side textured wall patterns consumed more material for printing than was the case for the two-side textured patterns, by about 4%.

5) Little knowledge had been previously reported for architectural design to improve structural efficiency from the current research and development program of 3DCP technology.

The results from this study can beneficially offer enhanced process efficiency for textured 3DCP building structures and increase the utilization of 3DCP in construction as a cost-efficient construction solution. Hence, it is recommended that these modeling processes, from architectural design to structural analysis, should be performed during the preconstruction stage of 3DCP constructions. Ongoing studies include evaluation of the whole 3DCP modular unit structure with two-side textured shell wall pattern using the FEM and performing a cost-feasibility analysis of the modular house.

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