3D Modular Construction Made of Precast SFRC-Stiffened Panels

Abstract

A new concept of a 3D volumetric module, made up of six plane stiffened self-compacting fiber-reinforced concrete (SFRC) panels, is here studied. Experimental campaigns are carried out on SFRC material and on the thin-slab structures used for this modular concept. The high volume of steel fibers (80 kg/m³) used in the formulation of this concrete allow a positive strain hardening to be obtained in the post-cracking regime observed on the bending characterization tests. The high mechanical material characteristics, obtained both in tension and compression, allow a significant decrease in the module slabs’ thickness. The tests carried out on the 7 cm thick slab demonstrate a high load-bearing capacity and ductility under bending loading; this is also the case for shear loading configuration, although without any shear reinforcements. Numerical simulations of the material mechanical tests were conducted using Abaqus code; the results corroborate the experimental findings. Then, simulations were also conducted at the structural level, mainly to evaluate the behavior and the bearing capacity of the thin 3D module stiffened slabs. Finally, knowing that the concrete module truck transport can be a weak point, the decelerations induced during transportation were characterized and the integrity of the largest 3D module was demonstrated.

1. Introduction

The industrialized approach to construction aims to reduce delays and operating costs, improve quality, and reduce environmental impact, while reducing energy consumption and overexploitation of resources. Industrialized 3D (or volumetric) modular construction would make it possible to respond to some challenges. It consists of the construction of an entire building using 3D modules that are positioned and stacked using a crane. This allows for rapid construction and therefore for stealth construction sites. The large reduction in noise, soil, and air pollution reduce environmental impacts comparative to traditional onsite construction [1]. Despite challenges such as the lack of standardized regulations, modular construction is expanding in countries such as China, Australia, Singapore, the United States, Japan, and the United Kingdom, adapting to spatial constraints and increasing urban densification [2,3,4]. The current trend of the modular construction concepts with 3D volumetric elements is essentially based on two load transfer methods, as outlined by Liew et al. (2019) [5]. In the first case, the modules are designed with a wired system of column-beam carriers, most often made of steel or mixed concrete-steel, allowing for internal layout flexibility and reducing module weight, which facilitates lifting and transportation. However, the connections between the steel modules require regular maintenance and complicate thermal and acoustic insulation [6,7,8].

In the second case, the module is made up of a system of load-bearing concrete walls. From a structural point of view, the choice of load-bearing concrete walls gives great rigidity and stability to the structure. However, this system needs to be improved by working mainly on the lightening of the modules, as the weight constraint leads to the production of modules with a short span (about 6 m), as observed by Liew et al. (2019) [5]. Great advances of this concept have been demonstrated in the construction of two residential towers in Singapore Clement Capony [2]. These high buildings, with 40 floors, are made of 1899 modules, weighing from 23 tons to 31 tons. The main geometrical characteristics of the modules are being 5 to 8 m long, 2 to 3.4 m wide, and 3 m high, with a wall thickness of 8 cm. This second method used load-bearing concrete walls, providing greater rigidity and enhanced acoustic insulation, but necessitating module weight reduction, as their span is limited to approximately 6 m. In this context, it is crucial to develop solutions that balance flexibility and lightweight design while maintaining structural performance and which do not suffer from the previously mentioned limitations (module size). In this article, a 3D volumetric system with the assembly of six plane elements made of steel fiber-reinforced concrete (SFRC) is proposed. This study aims to validate this new concept. This paper is structured into three main parts. First, the mechanical properties of the SFRC material used in this concept were evaluated through different experiments and simulations. Then, the mechanical characteristics, such as the stiffness, load-bearing capacity, and ductility, of the structural elements constituting the module were assessed experimentally, and their response, obtained through the conducted tests, was reproduced numerically. The structural behavior of SFRC in the context of residential modular construction remains insufficiently explored in the literature. SFRC is widely acknowledged for its ability to replace conventional shear reinforcement. However, at high fiber dosages, it can also reduce the need for traditional reinforcement, offering further design flexibility. Finally, the transportation process, which is critical due to the potential risk of inducing structural damages, cracks, or failure, was also investigated. There is also a lack of studies considering shocks and vibrations during module transportation and the possible induced damages of these. Ultimately, a two-story (R + 1) house was constructed, thus demonstrating the full relevance of this new concept.

2. Modular Unit Definition

Each 3D volumetric module is assembled with six flat elements, including four SFRC walls and two SFRC slabs assembled by metal bolting (Figure 1). An epoxy adhesive is used to ensure watertightness.

Each constitutive element of the module (panels and slabs) is stiffened or ribbed (with orthogonal stiffeners) and was obtained by pouring SFRC on a thermal and acoustic insulating layer, which serves as a lost formwork, integrated from the start (Figure 2). The insulation was then directly performed at the industry manufacturing stage, thus avoiding the need for a subsequent installation step once the building is constructed. The prefabricated prefinished volumetric construction (PPVC) here developed allows for a better treatment of thermal and sound insulation, as discussed in [2,9].

After seven days of maturation, these elements are assembled on the manufacturing site, to obtain a so-called 3D volume element which is a constituent cellular element of the modular house (Figure 3). Each cellular element is then fully finished, including the installation of electrical and plumbing systems, as well as the application of interior finishes. Finally, 60 days after manufacturing, these cellular elements are transported to be assembled on site (Figure 4).

The SFRC allowed the production of 5 cm thick walls and 7 cm thick slabs, leading to a significant reduction in material consumption and a decrease in module weight compared to conventional concrete versions. The largest module, 10 m × 3.95 m × 3.12 m, which complies with transportation requirements (Figure 1), weighs 35 tons when fully finished and furnished.

The concrete formulated reduces CO₂ emissions by around 30%, thanks to the use of CEM III instead of CEM I, primarily due to its lower clinker content, the main source of CO₂ in cement production. Clinker requires high-temperature processing (around 1450 °C), which generates significant carbon emissions. In contrast, CEM III incorporates 35% to 65% ground granulated blast furnace slag, a by-product of the steel industry that does not require additional thermal treatment. This substitution not only reduces the carbon footprint of concrete but also contributes to the valorization of industrial waste, aligning with sustainable construction practices. Finally, the use of CEM III cement, combined with material savings (concrete and steel) of approximately 35%, achieved through the reduced thickness of structural elements and the elimination of traditional shear reinforcement, significantly lowers the carbon footprint of the current modular concept. In addition, prefabrication and on-site optimization (including reduced construction time, the use of thermal insulation as permanent formwork, concreting operations, material waste, and transportation) contribute a further 5 to 10% reduction. Altogether, these strategies lead to a total estimated reduction in CO₂ emissions of 55 to 60% compared to a conventional reinforced concrete house built with CEM I cement.

3. Mechanical Characterization of SFRC Material

First, the mechanical properties of the SFRC used in this new concept were evaluated. According to G. Chen et al. (2021) [10], the minimum dosage to avoid brittle failure is 20 kg/m³. The more hooks the fiber has, the better its anchorage in the concrete, which improves the residual strength. In addition, increasing the fiber aspect ratio (l/d) increases the residual strength, but not significantly compared to the fiber content. The use of steel fibers in a concrete structure subjected to bending or shear stresses improves the post-cracking regime by inhibiting crack propagation. This allows the load-bearing capacity of the structure after cracking to be enhanced or even maintained, thus ensuring a large ductility. The collapse load is relative to the fiber content, the size of the structure, and the test conditions [11,12,13,14,15,16]. Several studies, such as those by Vivas et al. (2020) [17], G. Chen et al. (2021) [10] and Zhang et al. (2019) [18], have been able to observe that the presence of fibers does not significantly modify the strength associated with the crack initiation but increases the residual strength in proportion to the fiber content. Apart from the fiber content, there is also the wall effect, the orientation of the fibers, and the scale effect, which significantly impacts the post-cracking resistance [19]. The wall effect influences the distribution of the fibers when the specimens are manufactured in “U” molds. In the process of concrete flow, the fibers tend to have a random flow at the beginning of placement. As the flow propagates between the two side walls of the formwork, the fibers are placed parallel to the walls [20]. Fiber distribution has a significant influence on the reproducibility of mechanical test results. Parameters such as the height, width, and length of the formwork, as well as the casting method, strongly influence how fibers are dispersed within the concrete. These factors further complicate the prediction and control of fiber orientation and distribution. However, Zhao et al. (2021) [20] observed that the viscosity and flow resistance of fresh concrete significantly affect the ability of fibers to align with the flow. In particular, lower viscosity facilitates better alignment of fibers along the flow direction. For small specimens, the fibers are oriented preferentially on the surface of the mold, thus constituting a beneficial effect. Khan et al. (2023) [21] investigated the influence of fiber content and casting position on the mechanical performance of SFRC slabs. Their results revealed that, for the same steel fiber volume fraction (0.5% or 1.0%), slabs cast from the center exhibited a significantly higher load-bearing capacity compared to those cast from a corner (by approximately 17.2% for 0.5% fiber content and up to 40% for 1.0%). This highlights the critical role of casting strategy, as it directly affects the spatial distribution of fibers and thereby the structural efficiency of the slab. More recently, Abedi et al. (2025) [22] confirmed that the rheological behavior and mix design have a greater impact on fiber distribution than the casting procedure itself. Their findings suggest that employing self-compacting concrete (SCC) and a two-point casting strategy, from opposite ends of the formwork, results in a more homogeneous fiber dispersion. In contrast, single-point casting tends to increase the risk of fiber clustering, segregation, and significant local variations in fiber content, particularly for steel fibers. Other researchers [23,24,25] have proposed alternative methods for the choice of geometry and dimensions of samples in order to take into account the anisotropy in the distribution and orientation of the fibers and to minimize this wall effect. These methods include the use of circular panels and slabs with deeper thickness rather than the usual 15 cm × 15 cm × 60 cm prismatic specimens. This allows for a more realistic representation of the behavior of fiber-reinforced concrete under real conditions and takes into account differences in the toughness and residual capacity of the structure. However, the transition from small specimen tests to a larger scale requires some precautions. Indeed, Michels et al. (2012) [25] compared the cracking energy absorption capacity between 150 mm × 150 mm × 600 mm specimens tested in four-point bending and round plates with a diameter of 2.34 m and a thickness of 20-40 mm, all made of steel fiber reinforced concrete (LF = 50 mm and DF = 1.3 mm), for a dosage of 100 kg/m³. They found a decrease in fracture energy for large-scale elements. Therefore, they suggest introducing a geometric factor into the design procedure of the large-scale elements when using strength values from laboratory-scale studies.

Here, the concrete produced in the concrete plant on the industrial site includes 80 kg/m³ (volumetric fraction Vsf = 1%) of Bekaert 3D 65/35 metal fibers (Figure 5) and 300 g/m³ (Vppf = 0.33%) of polypropylene fibers (PB Eurofiber Ref. 506 20/6 Φ = 19.8 μm, length L = 6.0 mm), used to reduce the spalling of concrete at high temperature [26].

The dynamic modulus of elasticity is determined by a non-destructive technique, it also serves as an indicator of the drying of the specimens and to evaluate the drying of structural elements. Cylindrical specimens of 11 cm × 22 cm are tested under compression according to the EN 12390-3 [27] and splitting tension according to the EN 12390-6 [28]; the quasi-static elastic modulus is also characterized during compression tests. The energy corresponding to crack propagation in SFRC plays a determinant role; its characterization is generally conducted on notched prismatic samples. Finazzi et al. (2014) [11] studied the effect of the depth of the notch made on the prisms. The authors analyzed two sizes of notch depth (25 mm and 45 mm) on 150 mm × 150 mm × 600 mm prisms. They found that the deeper the notch, the less scattered the results were in the post-cracking phase. The effect of specimen size was studied by Nguyen et al. (2013) [29]. The authors performed four-point bending tests on three types of specimens without notches (50 mm × 50 mm× 150 mm, 100 mm × 100 mm × 300 mm and 150 mm × 150 mm × 450 mm) and concluded that there is a clear size effect on the flexural strength of the test specimens. The flexural strength and energy absorption capacity decrease as the specimen thickness increases. However, a greater number of cracks are found on large specimens, with a wider crack spacing. In the case of notched prisms, the size effect is still present but less significant. Here, the fracture energy G_f of the fiber-reinforced concrete was determined using flexural tests carried out on 15 cm × 15 cm × 60 cm notched prisms and also on 7 cm × 7 cm × 28 cm prisms. The height of the latter being more representative of the slab elements. This allows us to observe the sensitivity of the fracture energy Gf as a function of the specimen scale.

3.1. Three-Point Bending on 7 cm × 7 cm × 28 cm Prismatic Specimens

Three-point bending tests were carried out on 7 cm × 7 cm × 28 cm prisms, according to EN 12390-5 [30] (Figure 6), at 8 days and 54 days of concrete curing. The tests were conducted at different curing stages of the specimens, allowing the identification of strength thresholds corresponding to module assembly (7–8 days) and transportation (54–60 days). Two types of tests are carried out, either a force control (51.3 N/s) or a displacement control (3 mm/min). In both cases, the data acquisition frequency is set at 20 Hz.

Figure 7 shows the load–displacement curves for twelve 7 cm × 7 cm × 28 cm prisms tested. The curves of the first four prisms tested for 8 days show quite similar evolutions, with an ultimate load corresponding to an ultimate stress between 11.41 MPa and 12.65 MPa, i.e., a difference of 1.24 MPa (10%). The ultimate stress at 54 days is between 9.79 MPa and 13.50 MPa (

Table 1. Summary of test results for 7 cm × 7 cm × 28 cm prismatic specimens.

Test Specimens	Curing	Dynamic Modulus	Loading Speed	Cracking Resistance ft	Average Cracking Resistance Ftm	Standard Deviation	Maximum Strength	Ultimate Resistance
	days	GPa		MPa	MPa		kN	MPa
P1	8	33.80	51.3 N/s	7.18	7.21	0.08	12.08	11.41
P2		32.85	3 mm/min	7.31			14.06	12.65
P3		32.51	51.3 N/s	7.12			13.09	12.35
P4		33.15	3 mm/min	7.23			13.23	12.53
P5	54	31.76	51.3 N/s	6.88	7.79	0.86	11.08	10.00
P6		32.92	3 mm/min	8.47			13.49	12.07
P7		32.09	3 mm/min	8.90			10.97	9.79
P8		32.98	51.3 N/s	6.71			14.09	13.50
P9		31.64	3 mm/min	7.82			11.21	10.38
P10		32.20	3 mm/min	7.95			12.11	11.48

), with a greater dispersion of the behavior in the post-cracking phase. The cracking stress is between 6.71 MPa and 8.90 MPa, i.e., a difference of 2.19 MPa (25%). This stress corresponds to the tensile limit of the concrete cementitious matrix before the fibers begin to work. The average stress from the tensile tests on cylindrical specimens is 7.68 MPa. This value is within the range of the crack onset values of the three-point flexural tests. The behavior after crack initiation depends on the anchorage of the fibers in the cement matrix and on the fiber content and orientation in the crack section. The observation of the fracture facies (Figure 8) of the different specimens shows a dispersion of the distribution of fibers. This explains the larger deviations of the load/crack opening curves in the post-cracking phase (Figure 7).

3.2. Three-Point Bending on Prismatic Specimens of 15 cm × 15 cm × 60 cm

Six 15 cm × 15 cm × 60 cm prisms, kept in ambient drying under the same ambient conditions as the structures produced in the plant, were tested at 40 days under three-point bending (Figure 9). According to the EN 14651 [31] recommendations, the prisms are notched (5 mm wide and 25 ± 1 mm deep) 48 h before testing. The first four prisms were notched with the notch perpendicular to the surface corresponding to the formwork bottom (notch position No. 1 for specimens Gf1 to Gf4) and the other two prisms were notched on the surface corresponding to the formwork base (notch position No. 2 for specimens Gf5 and Gf6). An extensometer placed between the two edges of the notch measures the edge spacing and transcribes it into the crack opening (distance from the two opposite edges of the notch called crack mouth opening displacement (CMOD). According to the EN 14651 [31], the loading is obtained through a displacement control applied to the center section of the prism via a steel cylinder with a load speed of 0.05 mm/min until the CMOD crack opening reaches 0.1 mm. The speed is then gradually increased to 0.2 mm/min and is kept constant. The test is stopped when the CMOD crack opening reaches 4.2 mm.

The force–CMOD curves of the prisms are similar, except that of prism No. 2, which has a lower curve in the post-cracking phase. This difference is probably related to a manufacturing defect or a poor distribution of fibers. In addition, the load-CMOD curves of the notched prisms at the bottom of the formwork have an almost identical evolution (Figure 10). By superimposing the force–CMOD curves obtained for all the tests, we noted a better behavior of the prisms with notches at the bottom of the formwork (position No. 2). These curves are slightly higher than those obtained on the notched prisms in position No. 1. This seems to confirm an increase in the fibers at the bottom of the formwork by settling.

Prism No. 2 has the lowest flexural tensile stress of 5.79 MPa compared to other prisms with the same notched position (No. 1) which have a closer flexural tensile strength (an average of 6.68 MPa). In addition, apart from prism No. 2, prisms with notches at the bottom of the formwork have a tensile stress higher than that of prisms with notches in position No. 1 of about 5%. The cracking stresses measured by bending on notched specimens of 15 cm × 15 cm × 60 cm (6.64 MPa on average) is lower than that measured by 3-point bending of 7 cm × 7 cm × 28 cm specimens (7.79 MPa on average) without notches. This last value is close to the tensile stress obtained by splitting tensile tests of cylinders (7.68 MPa on average). Specimens with a notch at the bottom of the formwork have a higher number of fibers than in the case of the notch made on the face perpendicular to the bottom of the formwork (Figure 11). We also observed that smaller specimens (7 cm × 7 cm × 28 cm) exhibited higher flexural strength and deformation energy compared to thicker ones (15 cm × 15 cm × 60 cm), consistent with previous findings reported by Nguyen et al. (2013) [29].

This explains the better resistance to crack opening and propagation (

Table 2. Summary of Gf characterization results.

Notch Position	Test Specimens	Cracking Resistance (MPa)	* FR.1 (MPa)	* FR.2 (MPa)	* FR.3 (MPa)	* FR.4 (MPa)	Maximum Strength (MPa)
	Reference	LOP	CMOD1	CMOD2	CMOD3	CMOD4	Ftmax
No. 1 (The notch is located on one of the lateral faces of the specimen, perpendicular to formwork bottom)	Gf1	6.47	11.81	10.23	8.65	7.33	11.82
	Gf2	5.79	8.61	7.46	6.23	4.80	8.78
	Gf3	6.68	11.85	11.04	9.64	8.40	12.05
	Gf4	6.85	11.70	11.58	10.27	9.50	12.32
No. 2 (notch is located at the base of the specimen)	Gf5	7.04	12.49	11.86	10.98	9.44	12.52
	Gf6	7.03	11.93	11.66	10.62	9.09	12.21
Average		6.64	11.40	10.64	9.40	8.09	11.62

* FR. j: tensile strength by residual bending. LOP: proportionality limit/flexural tensile strength.

).

4. Mechanical Characterization of the 3D Module Constitutive Slabs: Experiments

The use of SFRC aims to significantly reduce conventional reinforcements and save manufacturing time. Several studies have shown that metallic fibers can replace shear reinforcement (stirrups) [14,32,33,34,35]. In the case of thin slabs, although they are more sensitive to bending loads due to their low bending stiffness, they allow a greater deformation capacity partly due to the presence of fibers but also to significant deflection and rotation capacity. Considering 8 cm thick slabs containing a fiber volume of 0.5%, Khaloo and Afshari (2005) [36] found that adding fibers improves energy absorption (twelve times higher than that of an ordinary concrete slab). However, in a contradictory way, if we compare a SFRC slab with a non-fiber-reinforced concrete slab under bending, the study by Colombo et al. (2023) [37] (test on 12 cm thick slab 3 m long and 0.6 m wide) demonstrated that increasing fiber content does not lead to an increase in the performance class, mainly due to fiber distribution which remains the key parameter to control. Furthermore, they also demonstrated that the use of steel fibers in combination with a minimal conventional reinforcement makes it possible to achieve a similar bearing capacity to that provided by conventional reinforced concrete (RC) beams. But the ductility remains higher for RC than when using SFRC alone or in combination with low steel rebar reinforcement. Therefore, they proposed to use a minimum longitudinal steel bar reinforcement when using SFRC to avoid any loss of ductility.

This part focuses on the mechanical characterization of planar elements intended for the new concept of 3D volumetric modular construction here considered. These elements, made of SFRC with high volume of metallic fibers, are reinforced with stiffeners (ribbed) to improve bending rigidity but do not include shear reinforcement.

A total of six non-ribbed slabs, three 128 cm × 68 cm × 7 cm and three 68 cm × 30 cm × 7 cm (length × width × thickness) are cast and tested under three-point bending. Two 395 cm × 128 cm × 7 cm stiffened slabs, representative of the real module slabs, are also tested in four-point bending.

4.1. Unstiffened Slab

Three-point bending tests are carried out on SFRC slabs (three 128 cm × 68 cm × 7 cm slabs and three 68 cm × 30 cm × 7 cm slabs). For the 128 cm × 68 cm × 7 cm slabs, they are each supported by two steel cylinders 50 mm in diameter and 124 cm apart (Figure 12). The loading is applied using a rigid steel cylinder (diameter 40 mm) positioned on the centerline of the slab. A layer of sand 1–2 mm thick is placed on the slab at the load line to compensate surface imperfections and allow a continuous linear smooth diffusion of the stress. In addition to a displacement sensor linked to the hydraulic jack, four other displacement sensors are placed under the slab. Figure 12 and Figure 13 illustrate the LVDT positions. The minimal distance of L3, L4, and L5 transducers from the nearest border of the slab is 1.5 cm. For the tests on the 68 cm × 30 cm × 7 cm panels, a single sensor is placed in the middle part of the bottom surface of the slab.

The loading is carried out using a 120 kN Walter-bai servo-valve hydraulic machine, under displacement control with a speed of 0.008 mm/s (0.48 mm/min). The acquisition frequency is set at 10 Hz.

The cracking stresses for slabs are similar (8.07 MPa for the 128 cm × 68 cm × 7 cm slab and 8.23 MPa for the 68 cm × 30 cm × 7 cm slab). It is recalled here that the average tensile strength obtained by splitting tensile test on an 11 cm × 22 cm cylinder is 7.68 MPa, and 7.79 MPa for flexural tensile test on 7 cm × 7 cm × 28 cm specimens (without notching), while for 15 cm × 15 cm × 60 cm prisms (with notch) it is worth 6.64 MPa. The tensile strength, which corresponds to the beginning of cracking obtained on the slabs, is very close to that associated with the three-point bending and splitting tensile tests (without notching). The effect of notching on 15 cm × 15 cm × 60 cm specimens induces a lower tensile strength compared to the other tests. The ultimate loads of the tested slabs, on the other hand, show greater variability. For 128 cm × 68 cm × 7 cm slabs, the ultimate load varies from 17.10 kN to 21.45 kN, and for 68 cm × 30 cm × 7 cm it varies from 15.08 kN to 20.17 kN (

Table 3. Results of unstiffened panels tests.

References		Cracking				Failure
No. Slab	Dimensions (cm)	Load (kN)	Cracking Stress (MPa)	Average Stress (MPa)	Standard Deviation	Maximal Load (kN)	Maximum Stress (MPa)	Average Stress (MPa)	Standard Deviation
1	128 × 68 × 7	14.20	7.90	8.07	0.15	17.10	9.53	10.65	1.23
2		14.70	8.20			21.45	11.97
3		14.50	8.10			18.70	10.46
S1	68 × 30 × 7	12.23	7.99	8.23	0.16	15.08	9.85	11.68	1.22
S2		12.95	8.46			18.41	12.02
S3		12.60	8.23			20.17	13.17

). This difference is explained by the random distribution of fibers in the concrete. A high ductility (20 mm deflection for large slabs and 7 mm for small slabs) is observed (Figure 14). The ductility can reach higher values, but the loading was deliberately stopped to avoid the total rupture of the slab which could damage the displacement sensors. The slabs therefore show a significant deformation capacity thanks, in part, to the presence of fibers but also to the fact that thin slabs show large displacements and rotations before their collapse.

The failure modes of the two slab configurations are similar, characterized by a large crack at mid-span (Figure 15 and Figure 16). Longitudinal micro-cracks are also observed near the central crack on both sides. These cracks run through the slab width and are visible on both sides of its thickness. However, these cracks close as soon as the crack opening is concentrated on the central crack. The post-peak phase of the curve essentially reflects the opening of the central crack.

4.2. Stiffened Slab

Two stiffened slabs, 3.95 m long, 1.28 m wide, and 70 mm thick in the off-stiffeners areas representative of the modular concept (see Figure 17) were tested under four-point bending (Figure 18) at CSTB (Scientific and Technical Centre for Building) [38]. The stiffeners, 80 mm wide and 60 mm deep, increase the rigidity and bearing capacity under bending of the slab. They also ensure the holding of the thermal and sound insulation layer and will serve afterwards as a support to fix the wall covering. A perimeter stiffener, a heel of 190 mm long and 130 mm thick, all around the slab, reinforce its ends and corresponds to the support area. The span between supports is 3.75 m.

The two slabs are made from the same cast concrete. Their constituent material has an average tensile strength by splitting of 6.03 MPa, a compressive strength of 50.01 MPa, and an average modulus of elasticity of 27.2 GPa.

Three 15 cm × 15 cm × 60 cm prisms notched in accordance with the EN 14651 [31] were tested under three-point bending; the results are shown Figure 19. The value of the flexural tensile strength at the beginning of crack is 4.0 MPa and the maximum residual stresses achieved in the ultimate state are 8.2 MPa, 7.8 MPa, and 5.7 MPa, respectively, for the G2-Gf1, G2-Gf2, and G2-Gf3 prisms. The G2-Gf3 test gives a lower rupture strength; the deviation from the other two tests is due to a lower distribution of the fibers in the concrete. The tensile strength and fracture energy of the material are lower compared to those of non-stiffened slabs.

The shape of the load–deflection curves (Figure 20) show that the tests are reproducible, although test No. 2 gives a lower curve compared to test No. 1. The explanation for this discrepancy on the beginning of cracking and on the ultimate load, comes from a dissymmetry of the loading that has been observed during the test. The slab did not rest on the support along its entire width, which led to premature cracking. The load associated with the beginning of cracking is 10.70 kN and 13.89 kN, a deviation of 30% (

Table 4. Results of stiffened panels tests.

References		Cracking				Failure
No. Slab	Dimensions (cm)	Load (kN)	Cracking Stress (MPa)	Average Stress (MPa)	Standard Deviation	Maximal Load (kN)	Maximum Stress (MPa)	Average Stress (MPa)	Standard Deviation
1	395 × 128 × 7	10.70	6.39	7.35	1.35	17.61	10.53	11.32	1.12
2		13.89	8.30			20.28	12.12

). For the breaking loads, 17.61 kN (test 1) and 20.28 kN (test 2), the difference is smaller, about 15%. The average value of the ultimate load is 18.945 kN, corresponding to an average cracking stress of 11.32 MPa. Significant ductility was observed for both tests, which is essentially due to the metal fibers. The fiber-driven scatter significantly affects the reproducibility of results, both in the material tests and structural tests. In our previous observations, a noticeable variability was found in the flexural responses of both 7 cm × 7 cm × 28 cm prisms and notched 15 cm × 15 cm × 60 cm specimens. At the structural scale, similar divergence in behavior was also observed. In practice, self-compacting concrete helps reduce such variability, the casting method remains a key factor influencing fiber orientation and distribution, which is difficult to control in practice.

The four-point bending test shows a constant and maximum moment distribution between the two load points, so there are several flexural cracks that cross the slab with a relatively regular pitch between adjacent cracks, about 10 cm. This distance is considered a characteristic length, the test corresponding to a 4-point bending guaranteeing a constant moment zone of 1250 mm. However, after the peak load, the fracture is mainly concentrated on a single crack located in line of load (Figure 21).

5. Finite Element Modeling

A numerical model was developed, and its accuracy was demonstrated by its ability to predict the mechanical response of the slabs tested in bending. The variability of the post-peak behaviors observed during the SFRC material tests leads us to set different laws of post-peak behavior. The relevance of the calibration is evaluated by modeling different cases of fiber-reinforced concrete structures where failure under bending was obtained.

5.1. Discretization: Choice of Element Type

To properly represent the cracking and its propagation through the thickness, the structure is modeled with volumetric elements. In Abaqus code, linear or quadratic solid elements can be chosen. To reduce the computation time, linear elements are used. Two types of elements are considered: C3D8R (8-node linear brick, reduced integration with hourglass control) and C3D8I (8-node linear brick, incompatible modes). Figure 22 shows the modeling of the 7 cm × 7 cm × 28 cm prism.

First, the mesh convergency was checked through the elastic simulations, this leads to a mesh size of 10 mm. Then, the relevance of the element used was also gauged by considering the stress analysis. The numerical calculated stress is compared to the analytical solution in the case of the three-point bending of a 7 cm × 7 cm × 28 cm elastic SFRC.

This shows the best performance in terms of stress is given by the C3D8I elements compared to the C3D8R element.

To model the non-linear behavior of the concrete material, the “Concrete Damage Plasticity” (CDP) model in Abaqus is used. This model has been validated for reinforced concrete [39,40] and can also be applied to SFRC [41,42]. This model allows us to have a behavior coupling plasticity and damage; however, in our case, we only consider the parameters associated with the plastic part of the concrete. The CDP model employs a non-associated flow rule, meaning that the plastic flow direction does not coincide with the gradient of the yield surface. In the case of SFRC, the presence of steel fibers enhances strain hardening and increases the material’s capacity for plastic deformation. To account for this in the CDP model, the dilation angle can be slightly increased to better capture the additional ductility provided by the fibers. This angle governs the direction of plastic flow in the CDP formulation. However, it is not a direct physical property but a model parameter that must be calibrated based on experimental results. Its influence on simulation outcomes is significant; an excessively low angle may underestimate ductility, while an overly high angle can lead to an overestimation of crack openings and energy dissipation. The value of the expansion angle parameter is set at 37°, as recommended in the literature for conventional concrete [15,38,39,40]. It should be emphasized that the dilation angle adopted in this study is calibrated for the specific fiber dosage investigated. Since fiber content has a strong influence on the post-cracking behavior of SFRC, particularly in terms of ductility, this parameter may need to be adjusted accordingly when different fiber dosages are used.

5.2. Three-Point Bending Tests for Prisms of 7 cm × 7 cm × 28 cm

The tensile behavior law in the numerical model was first calibrated using the experimental results from the bending tests of the 7 cm × 7 cm × 28 cm prisms. First, the test specimen shown in Figure 23 was selected, exhibiting a cracking stress of 7.82 MPa and an ultimate stress of 10.38 MPa. However, according to the MC2010 [43] and other studies [34,44,45,46], the direct tensile stress, is lower than the bending tensile stress. Then, the uniaxial tensile stress introduced into the model is 6.5 MPa, 17% lower than the experimental value, within the recommended approach value range.

The other characteristics retained in the model are the elastic modulus E = 35 GPa, the Poisson’s ratio μ = 0.2, and the compressive stress ${\mathrm{f}}_{\mathrm{c}}$ = 64 MPa.

The tensile law is approximated by considering two phases. The first phase corresponds to the linear behavior until the appearance of the first crack as for the conventional concrete. The second phase corresponds to the post-cracking regime. For conventional concrete, the post-cracking phase can be illustrated by following the evolution of the cracking energy calculated from the Gf formula prescribed by the Model Code 1990 [47] (see Figure 24):

$${\mathrm{G}}_{\mathrm{f}}={\mathrm{G}}_{\mathrm{f}0}{\left({\displaystyle \frac{{\mathrm{f}}_{\mathrm{c}\mathrm{m}}}{10}}\right)}^{0.7}\mathrm{i}\mathrm{f} {\mathrm{f}}_{\mathrm{c}\mathrm{m}}\le 80\mathrm{M}\mathrm{P}\mathrm{a}$$

(1)

where ${\mathrm{G}}_{\mathrm{f}0}=\left(0.00005{\mathrm{d}}_{\mathrm{m}\mathrm{a}\mathrm{x}}^2-0.0005{\mathrm{d}}_{\mathrm{m}\mathrm{a}\mathrm{x}}+0.026\right)$ with ${\mathrm{d}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum aggregate size (12 mm).

In the post-cracking regime of SFRC, two phases can be distinguished, an ascending or hardening phase of the load and a softening phase reflecting the opening of the crack. The calibration of the direct tensile law of SFRC is obtained by iteration to have a final load/deflection curve similar to the experimental test. From the uniaxial tensile strength obtained by readjusting the cracking stress of fiber-reinforced concrete during a bending test, 6.5 MPa marks the beginning of cracking, followed by a stress drop to 3.56 MPa. Then the load rises slightly, marking the recovery of the fiber force during cracking and a final softening phase of the curve up to the ultimate limit state at 2 MPa. (Figure 25b).

Two calculation methods, the implicit and the explicit, are then used and compared. The comparison of the load/CMOD curve between experimental test and calculation is presented in Figure 25c. The two methods provide similar load/deflection curves. The explicit method gives a lower force associated with the onset of cracking than the implicit method. No displacement sensor has been placed at the bottom of the specimen; therefore, the deflection measurement is only given by the displacement of the loading jack. This explains the difference in stiffness between the simulation and the test in the elastic phase. If we observe the plastic deformation at mid-span (Figure 26), the crack appears on the tensile side of the specimen, then it propagates step by step upwards according to the depth of the beam; at the same time, the amplitude of the plastic deformation increases on and near the bottom face, reflecting an increase in the crack opening. This was also observed during the test.

In the experimental analysis of the three-point bending on six 7 cm × 7 cm × 28 cm prisms, the lowest ultimate stress value is 9.79 MPa (P7) and the maximum stress is 13.50 MPa (P8). Two tensile laws are calibrated, respectively, with the P9 prism test, which has a maximum stress of 10.38 MPa, and the P8 prism test, which has the highest maximum stress, i.e., 13.50 MPa. The two calibrated tensile laws are shown in Figure 27, giving load/deflection curves similar to those obtained for the three-point flexural test.

5.3. Three-Point Bending of Prisms 15 cm × 15 cm × 60 cm

Generally, the tensile law used for the calculation of SFRC structures is established from bending tests on 15 cm × 15 cm × 60 cm notched prisms. However, in this study, the results of these tests are used to verify the relevance of the calibrated law from the tests conducted on 7 cm × 7 cm × 28 cm unnotched specimens (Figure 28). The resulting crack load versus opening curves (CMOD) are shown in Figure 29. Law 2 closely matches the high curves of the tests carried out while slightly increasing the ultimate load. Law 1 gives an intermediate curve between the maximum curve and the minimum curve. The two laws correctly reproduce the initial stiffness. The obtained results concerning the modeling of the 15 cm × 15 cm × 60 cm notched specimens tested, show the relevance of the law based on the bending tests of 7 cm × 7 cm × 28 cm specimens. In the following part, the same laws are used to simulate the behavior of the thin slabs under bending.

5.4. Three-Point Bending on Slabs of 68 cm × 30 cm × 7 cm and 128 cm × 68 cm × 7 cm

Two slabs of 68 cm × 30 cm × 7 cm and 128 cm × 68 cm × 7 cm are modeled using the two laws (low and high law) for each case. The small slab is fully meshed, but for the large slab, only half is modeled (Figure 30) to limit the computation time. For both cases, the discretization is performed with C3D8I elements with a mesh size of 10 mm.

The numerical calculation reproduces the initiation of the non-linear behavior (Figure 31). The beginning of plasticity in the simulation traduces the cracking of the concrete; the ultimate load is also suitably reproduced (law 1 corresponds to the case of low load and law 2 corresponds to the case of the larger load). The non-linear behavior observed numerically before reaching the maximum load and until the beginning of the post-peak behavior fits quite well with the experimental curves. The results show a sensitivity to the choice of the tensile law.

Considering the collapse mode, slabs without stiffeners display a bending failure mode dominated mainly by one central crack. For the large slab, the crack propagation is shown in P5 and P6 of Figure 32. The onset of cracking is indicated by the appearance of three cracks in the slab center. Then, the cracking energy is mainly concentrated on the central crack that crosses the entire width of the slab. The other cracks adjacent to this central crack continue to develop across the entire width of the slab. Finally, there are a total of five cracks that cross the slab on the tensile face (Figure 33a). These cracks have a characteristic length (spacing between cracks) equivalent to six elements, i.e., 60 mm. For the CDP model, the crack spacing can vary depending on the mesh size. For the small slab with a length of 68 cm, the numerical model shows three longitudinal cracks with a characteristic shorter length of 40 mm (Figure 33b).

As the load increases, the energy is concentrated on the central crack and the deformation of the neighboring cracks decreases. Figure 34 allows us to analyze the maximum plastic deformation of the element corresponding to the crack zones for the large slab of 128 cm length. From the beginning of cracking, the cracking energy is concentrated only on the central crack (point P1 of the load/deflection curve). Then we observe the appearance of neighboring cracks next to the central crack, but the cracking energy remains essentially on the central crack. Before the ultimate load, the plastic deformation of the center crack is 5.03 times, 5.10 times, and 9.31 times greater than those of the secondary cracks at points P3, P4, P5, respectively. In the post-peak phase, for example at point P6, only the central crack widens with a greater plastic deformation than those of the secondary cracks (19 times larger). By observing the total deformation in the longitudinal direction, the secondary crack closes after the post-peak (Figure 35).

In other words, the neighboring cracks are closed while the central crack widens. This point also confirms what has been observed experimentally. The failure mode of the slab under three-point bending shows a single-crack-type fracture mechanism with a cracking energy corresponding only to a single central crack.

5.5. Four-Point Bending of a Representative Stiffened Slab

A four-point bending test was conducted on a representative ribbed or stiffened slab of 395 cm × 128 cm × 7 cm and the simulation of this test is here considered. According to the symmetry planes in this case, only a quarter of the slab is modeled (Figure 36) to allow a shorter calculation time. The mesh considers solid C3D8I elements of a size of 10 mm. Loading is applied to two stiffeners, as shown in Figure 17.

The tensile law is based on the three-point bending test of the 15 cm × 15 cm × 60 cm prisms shown in Figure 19. The lowest curve obtained for the G2-Gf3 specimen (cracking stress 4 MPa and fracture stress 5.7 MPa) is used for the law calibration. The calibrated tensile law and the test/calculation comparison for this test on a 15 cm × 15 cm × 60 cm prism are presented in Figure 37.

The result of the numerical simulation of the stiffened slab test, considering the tensile law retained following the wedging, is compared with the two experimental tests in Figure 38. The numerical simulation reproduces the initial stiffness. The beginning of cracking and the evolution of the stiffness in the non-linear phase obtained for the N1 slab confirms again the relevance of the numerical model used. However, the ultimate load obtained numerically (24.35 kN) is greater than the experimental one (20.28 kN for the N1 panel), with a deviation of +17%. To explain this difference, the numerical SFRC slab behavior is analyzed at several equilibrium points of the load–deflection curve, before and after the post-peak, in Figure 38b.

The first crack, detected at point P1, appears under the applied load line (Figure 39 and Figure 40). Then, several cracks were noticed between the two load points P2 and P3, as seen in Figure 38b. Beyond the P2 point and until P4 point, cracks appeared between the load point and the support but with low plastic strain. After the peak load (point P4), in the post-peak regime, the plastic strain is mainly concentrated on a single crack at the mid-span (point P5). Multi-cracks appear in the non-linear phase and the load gradually increases until the ultimate load. For the numerical model, the material is assumed to be homogeneous, whereas in the test, the distribution of the fibers is not completely uniform. So, during crack propagation, if a crack propagates into an area with less fibers, failure may occur earlier than expected. This explains a lower failure load for the experiment test compared to that of the numerical simulation.

6. Transport of SFRC Module

Transportation can be a critical weak point in the concrete modular construction process, as decelerations and vibrations during module movement may introduce damages and compromise structural integrity. To assess these effects, measurements of the dynamic loads generated during the transportation of 3D modules were conducted. Accelerometer transducers enable the measurement of forces and movements experienced by the modules during truck transport.

6.1. Measurement During the Lifting Phase

The module studied is equipped with two triaxial accelerometers. The first one is positioned on a small wall and the second on the upper slab. These accelerometers are connected to an on-board data-logger; the measurement acquisition frequency is 9.6 KHz. The vibration analysis of the module consists of impacting the module using a shock hammer to measure the responses of the two triaxial accelerometers glued to the module (Figure 41). The first natural frequency characterized is of the order of 2.4 Hz, the next frequencies are 24 Hz, then 38.4 Hz, and finally 74 Hz.

6.2. Measurement During Transport

The module is transported by truck (Figure 42); the journey time is about 30 min. The maximum speed measured is Vmax = 60 km/h, obtained using the “Speedometer V2024.3” software on a mobile phone.

A tri-axis accelerometer (A2X, A2Y, A2Z) is glued to the top panel, with the X direction towards the lateral side of the truck, the Y axis towards the truck’s direction of movement, and the Z axis towards the ground. The three components of the maximum acceleration vector measured on the high panel are 0.1282 g, 0.4188 g, and 0.3881 g (Figure 43). A second dual-axis accelerometer (A3Y and A3Z) is glued directly to the truck bed on which the module rests. Similarly, the Y axis is in the direction of the truck’s movement and the Z axis towards the ground. The maximum acceleration measured on the chassis is 0.6234 g and 1.593 g in the Y and Z direction, respectively, (Figure 44). The vertical acceleration peak (Z) measured on the truck is approximately 2.6 times higher than the longitudinal acceleration peak (Y). Innella et al. (2020) [49] also observed in their study that vertical accelerations are more critical than lateral and longitudinal accelerations in the same order of magnitude, a value between 1.3 and 4.6 times higher. In addition to the effect of acceleration direction, the authors also analyzed the influence of accelerometer location, truck speed, and road roughness. The results show that acceleration intensity increases with speed. Accelerometers positioned near the tires recorded the highest acceleration levels. At a speed below 40 km/h, the acceleration measured at the front of the truck was 0.11 g, compared to 0.36 g at the rear. Between 41 and 60 km/h, the acceleration increased slightly to 0.12 g at the front and 0.40 g at the rear. The maximum acceleration generated by the truck was 0.43 g, while the peak acceleration transmitted to the transported module was 0.15 g in the vertical direction (downward). In our study, the average truck speed was approximately 60 km/h and the peak vertical acceleration recorded (towards the ground) was significantly higher, reaching 1.593 g, substantially above the levels reported by Innella et al. (2020) [49]. Several factors could explain this difference. The first is the weight of the transported modules; while the modules studied by Innella et al. (2020) [49] were lightweight steel frames weighing around 17 tons, our SFRC modules weigh approximately 35 tons. Other contributing factors include the transport distance, road conditions, driving behavior, truck type, the lifting system used, and the truck’s suspension system.

The two signals measured on the truck chassis and on the high slab are superimposed on the same graph (Figure 45 for the Z direction and Figure 46 for the Y direction). Despite a large amplitude of the acceleration on the chassis (1.593 g in the Z direction and 0.485 g in the Y direction), the accelerations transferred to the module on the high panel are much lower (0.3345 g in the Z direction and 0.095 g in the Y direction).

Although these acceleration peaks were substantial (

Table 5. Accelerations measured on the module versus those recorded on the truck.

Axis and Direction	Time (Seconds)	On truck (A3)	On the Top Slab of the Module (A2)	[A3 − A2/A3] (%)
Y, truck’s movement and	T = 1482.95 s	−0.3056 g	−0.0191 g	93.7
	T = 1482.96 s	0.4850 g	0.0120 g	97.5
	T = 1482.97 s	−0.3776 g	−0.0950 g	74.8
	T = 1482.99 s	0.1676 g	0.0409 g	75.6
Z, towards the ground	T = 1482.95 s	−1.3640 g	−0.1282 g	90.6
	T = 1482.96 s	1.5930 g	0.0676 g	95.7
	T = 1482.97 s	−1.1820 g	−0.1360 g	88.5
	T = 1482.99 s	0.5272 g	0.3345 g	36.5

), the stresses associated with truck transport, as well as the installation of the modules on site, did not generate any damage to the modules. This analysis was carried out on several modules of different sizes transported on various road sections. In all cases, no damage is observed, for temporal distributions of accelerations close to those presented.

7. Conclusions and Perspectives

This study investigates a new concept of 3D modular structure in SFRC. It demonstrates the structural and logistical feasibility of a thin SFRC modular system with low carbon impact (through the use of CEM III cement and reduction in conventional reinforcement). It provides an experimental reference and a consistent modeling strategy, from SFRC material characterization to structural elements. The elementary cell is made up of surface elements (two slabs and four walls). To lighten the module for transport, the ribbed slabs and stiffened walls are thin, i.e., 5 cm for the walls and 7 cm for the slabs.

• The tests conducted on SFRC with 80 kg/m³ of steel fibers demonstrated that 7 cm thick slabs were able to withstand transport stresses and flexural loads without conventional reinforcement. In practice, 1 m³ of SFRC with a fiber content of 80 kg/m³ costs approximately 1.5 times more than conventional RC with minimum reinforcement, typically between 20 and 40 kg/m³ (as in the case of slabs). However, the use of SFRC enables a significant reduction, about 65% in our case, of the total concrete volume required.
• Moreover, the considered stiffeners increase the flexural rigidity of these elements. These low thicknesses, as well as the use of a CEM III binder, reduce the carbon footprint. In long term, SFRC is known for its high durability, particularly in humid, aggressive, or crack-prone environments. The steel fibers used in this study are galvanized, making them less susceptible to corrosion issues. Flexural tests performed at 54 days indicated that the mechanical performance of the SFRC continues to improve significantly beyond the conventional 28 days used for ordinary concrete. Ongoing investigations are conducted to better assess long-term creep performance, and further insights will be reported in future work.

SFRC material behavior was analyzed through three-point bending tests conducted on 7 cm × 7 cm × 28 cm specimens without notching and 15 cm × 15 cm × 60 cm specimens with notching. The results showed that the ultimate load and post-peak behavior are highly variable depending on the distribution of the fibers in the concrete. These tests were used to set a calibrated CDP material law of the SFRC. This law made it possible to correctly simulate the bending tests on 15 cm × 15 cm × 60 cm notched prismatic specimens. Flexural tests performed on thin SFRC ribbed slabs demonstrated ductile behavior. Their numerical simulation with Abaqus, using C3D8I and the calibrated CDP model, corroborate the experimental finding. The initial stiffness, crack initiation, crack propagation, and the hardening role of the fibers that bridge the crack opening are correctly reproduced. However, the final fracture occurs earlier in the experimental test than for the numerical calculation. A non-homogeneous distribution of the fibers along the cracked plane is suspected.

To fully validate the concept of a 3D modular structure, its truck transport phase is also studied. All the loading history, and mainly the peaks deceleration and/or acceleration induced by the truck transport, are directly characterized by instrumenting the module and the truck with accelerometers. The module remains intact, although significant peaks of deceleration are noticed. The maximum acceleration measured on the truck chassis is 0.623 g in the Y horizontal direction and 1.593 g in the Z vertical direction.

Currently, the proposed construction method has been validated for a single-story structure. Future developments will focus on assessing its applicability to multi-story configurations.

As part of the study of this modular construction concept, several test campaigns were carried out on the stiffened wall under compression or shear load, as well as on the slab–wall and wall–wall connections. These test campaigns and their numerical simulations will be discussed in a future publication.