Experimental and Analytical Investigation of the Load-Bearing Capacity of 3D Printed Concrete – Concrete E-Learning Platform

Link zur deutschen Version: Experimentelle und analytische Untersuchung der Tragfähigkeit von 3D-gedrucktem Beton

In recent years, 3D printed concrete (3DPC) has primarily been used for non-structural applications, such as formworks for complex geometries or hybrid components, rather than as a load-bearing material. The primary limitation arises from the lack of well-established mechanical models and a structural design basis, caused by uncertainties related to the layered nature of 3DPC and the challenges of reinforcement integration. In fact, due to the layered structure caused by the printing process, 3DPC exhibits anisotropic behaviour: the strength and failure modes thus depend not only on the concrete matrix but also on the quality of the bond between adjacent layers. Consequently, design rules developed for conventional concrete cannot always be directly applied to 3DPC. To enable the structural use of 3DPC, it is therefore essential to develop reliable testing methods and failure criteria, which is a fundamental step towards defining the load-bearing capacity of printed concrete and establishing a consistent design framework. To better understand how 3DPC performs under different loading conditions, we present in the following two test methodologies developed at ETH Zürich: the modified slant shear test and the direct tensile test on reinforced 3D printed concrete ties.

Modified Slant Shear Test

The first type of test presented is a modification of the slant shear test, which is commonly used for conventional concrete to study the interfacial bond strength between concrete cast at different times, or concrete and a repair material (e.g., adhesives). In this test, according to EN 12615:1999, a prism with an interface plane inclined at an angle of $\alpha$ = 60° to the horizontal is loaded under uniaxial compression to assess the shear transfer capacity along that interface.

In the context of 3DPC, the Modified Slant Shear Test (MSST), accounting for the anisotropy introduced by the layered structure, was employed to determine the 3DPC strength, and the main governing parameters such as the compressive strength of the concrete matrix, the cohesion, and the friction angle of the concrete layer interface. A total of 45 specimens were tested at 7, 14, and 28 days after printing. Each specimen consisted of a 3DPC prism 400 mm high with a 100 × 100 mm² square cross-section, printed with different layer inclinations ( $\alpha$ = 0°, 30°, 60°, 75°, and 90°) to the horizontal, see Figure 1a. In addition, to simulate a realistic interruption during the printing process, a 30-minute cold joint was introduced approximately at mid-height of each specimen. When the fabrication of the specimen is completed, the specimen can be placed in the testing machine. The test setup of the MSST for 3DPC is illustrated in Figure 1a, and essentially consists of a uniaxial compression test performed on 3DPC prisms.

Figure 1b also shows the stress distribution on both the horizontal and inclined sections of the specimens under a vertical compressive force ( $F$ ). $\sigma_v$ represents the vertical stress (normal stress on a horizontal plane), while $\sigma_n$ and $\tau_{tn}$ denote, respectively, the normal and shear stresses acting on the interface plane between printed layers, inclined at an angle $\alpha$ to the horizontal. These stresses can be calculated as:

(1) $\begin{equation*}\sigma_v=\frac{F}{A}\qquad\qquad \sigma_n=\sigma_v \cos^2\alpha \qquad\qquad \tau_{tn}=\sigma_v\sin\alpha\cos\alpha \end{equation*}$

where $A$ is the effective horizontal area.

Figure 1 – 3DPC specimen: (a) Test setup of the Modified Slant Shear Test (MSST) for 3DPC, and (b) definition of layer inclination $\alpha$ and stresses acting on the layer plane [1].

Depending on the layer inclination, two distinct failure modes were observed: (i) matrix failure, and (ii) layer interface failure. Specimens printed with layer inclinations of 0°, 30°, and 90° exhibited matrix failure, similar to conventional concrete (Figure 2a, b, and e). However, the anisotropy caused by the printing process may result in premature layer interface failures occurring at the cold joint in specimens with layer inclinations of 60° and 75° (Figure 2c and d). The specimens that failed in the layer interface exhibited a reduced strength of about 10%–20% compared to those that exhibited matrix failures.

Figure 2: Typical failure modes for different layer inclinations [1].

Based on these results, a general Mohr’s envelope was proposed to characterise the load-bearing capacity of 3DPC elements, including the influence of the layer joints. The model combines the modified Coulomb yield condition for the concrete matrix with a Coulomb failure criterion of the layer joints.

Accordingly, the modified Coulomb yield condition of the concrete matrix is derived from (i) the average of the peak compressive stress ( $\sigma_v=f_c$ ) in the specimens exhibiting matrix failure ( $\alpha$ = 0°, 30°, and 90°), (ii) the tensile strength of the concrete matrix $f_{ct}$ , and (iii) the angle of friction $\varphi_c$ and cohesion $c_c$ of the matrix, with the corresponding Mohr’s circles given by:

(2) $\begin{equation*}\left(\sigma-f_{ct} +\frac{c_c-f_{ct}\tan\varphi_c}{\tan\left(\frac{\pi}{4}-\frac{\varphi_c}{2} \right)}\right)^2 +\tau^2 = \left(\frac{c_c-f_{ct}\tan\varphi_c}{\tan\left(\frac{\pi}{4}-\frac{\varphi_c}{2} \right)}\right)^2 \end{equation*}$

On the other hand, the Coulomb failure criterion of the layer joints was derived (by using linear regression) from the stress states ( $\sigma_n$ and $\tau_{tn}$ ) in the joint at the peak load of the specimens exhibiting layer interface failures ( $\alpha$ =60° and 75°), that is

(3) $\begin{equation*}\tau_{tn} = c_i - \sigma_n\tan(\varphi_i) \end{equation*}$

where $\varphi_i$ and $c_i$ are the angle of friction and cohesion of the interface, respectively.

Figure 3 illustrates the resulting general Mohr’s envelopes for 3DPC (boundary of the shaded areas) under plane stress conditions with cold joints. In this representation, the modified Coulomb yield condition of the concrete matrix is intersected by the Coulomb failure criterion in Points A and B, which correspond to the critical angles ( $\alpha_{crA}$ and $\alpha_{crB}$ ). These angles mark the transition between the two distinct failure modes. Therefore, layer interface failure governs in the MSST when the layer inclination lies within the critical range $\alpha_{crA}<\alpha<\alpha_{crB}$ . For flatter ( $\alpha<\alpha_{crA}$ ) or steeper ( $\alpha>\alpha_{crB}$ ) layer orientations, matrix failure is expected instead. In these latter cases, the compressive strength $f_c$ of the concrete matrix is reached under uniaxial compression, as observed in the MSST. Conversely, for intermediate inclinations within the critical range ( $\alpha_{crA}<\alpha<\alpha_{crB}$ ) the layer interface fails earlier, resulting in a reduced peak compressive stress, lower than $f_c$ . Based on the strength and failure modes observed in the MSST for the different layer interface inclinations, the general Mohr’s envelope of the 3DPC can thus be obtained.

Figure 3: Mohr’s envelope as failure criterion for 3DPC [1].

The critical layer inclinations were identified as $\alpha_{crA}$ = 60° and $\alpha_{crB}$ = 75°, with an interface friction angle of approximately $\varphi_i$ = 46°. As a final remark, the 3DPC reached its full compressive strength — approximately 60 to 80 MPa — within 14 days after printing, and achieved about 80 % of that strength (55 to 65 MPa) after 7 days.

These findings demonstrate that the MSST can effectively capture the anisotropic behaviour of 3D-printed concrete and provide a practical basis for developing mechanical models and safety factors for its future structural use. Further research will explore the influence of longer printing interruptions and expand the experimental dataset to refine the proposed failure envelope. More detailed explanations about the experimental results and analytical model can be found in [1].

Direct Tensile Tests on Reinforced 3D Printed Concrete Ties

For the 3DPC to safely carry tension, the 3DPC elements must incorporate reinforcement. Specifically, transverse reinforcement is placed between layers during fabrication, and longitudinal bars are in grouted channels within the printed shell. Complementary to the MSST results, we therefore investigated the tensile behaviour of reinforced 3DPC ties. While the tensile response of conventional reinforced concrete is well described by the Tension Chord Model (TCM), its applicability to reinforced 3D printed concrete (R3DPC) remains uncertain. This knowledge gap was addressed through a pilot experimental campaign focused on the tensile performance of 3DPC elements. The study examined the influence of various parameters, including the reinforcement ratio, local cross-sectional variations caused by the surface texture of the printed layers, and the presence of stirrups, on the force transfer between the materials forming the reinforced 3DPC (R3DPC) ties as well as on the development of the crack pattern. The ultimate goal of this investigation was to provide a foundation for mechanically consistent models that can support the structural analysis and design of 3DPC elements in future research.

First of all, the tensile behaviour and crack formation of R3DPC ties — consisting of a longitudinal steel bar embedded in grout and enclosed by a 3DPC shell — can be described analytically through the equilibrium of forces in an idealised tension chord, both before and immediately after cracking (see Figure 4). Crack formation provides valuable insight into how the tensile forces are transferred through the grout core from the steel bar to the 3DPC shell. Cracking may initiate in either the 3DPC shell or in the grout, depending on their tensile strength and elastic modulus. If the applied stress continues to increase after the first material cracks, the second material may crack either after a further load increase or simultaneously. This results in four possible cracking sequences (see Table 1): (a1) the 3DPC cracks first while the grout remains uncracked; (a2) 3DPC and grout crack simultaneously under an axial cracking load ( $N_{cr}$ ) governed by 3DPC stresses; (b1) the grout cracks first while the 3DPC remains uncracked; and (b2) grout and 3DPC crack simultaneously under an axial cracking load ( $N_{cr}$ ) governed by grout stresses. Assuming linear-elastic behaviour and a rigid bond before cracking — i.e., equal strain ( $\varepsilon$ ) in the steel, grout, and 3DPC — the total axial load before cracking ( $N$ ) can be expressed as the sum of the axial force contributions of each material: $N = N_c+ N_g+ N_s$ , where subscripts $c$ , $g$ , and $s$ denote the 3DPC, grout, and steel, respectively. Table 1 summarises the cracking criteria, the first ( $N_{cr,1}$ ) and second ( $N_{cr,2}$ ) cracking loads, the corresponding stresses in grout ( $\sigma_g$ ) and 3DPC ( $\sigma_c$ ) after the first crack, and the minimum reinforcement ratio ( $\rho_{s,\text{min}}$ ) required to prevent brittle failure.

3DPC is expected to crack first when $f_{gt}\geq n_g f_{ct}$ (Scenarios a1 and a2), otherwise, grout cracks first (Scenarios b1 and b2). Assuming $n_g=1$ (a reasonable estimation), the cracking criteria derived by imposing that the grout tensile stress exceeds its tensile strength (grout cracks immediately after 3DPC) is reported in Table 1 under Scenario (a2). Since the grout ratio ( $\rho_g$ ) is typically small, its tensile strength would have to be several times higher than that of 3DPC to prevent cracking at the same location. In practice, as a result, scenario (a1) rarely governs. Therefore, under realistic configurations:

if the 3DPC cracks first, the grout will crack simultaneously at the same position, as stresses in the grout are highest where the shell cracks (scenario a2);
if the grout cracks first, the 3DPC may remain uncracked briefly (Scenario b1), but will soon crack at the same location due to the stress concentrations developing in that region.

Figure 4: Differential tension chord element: (a) cross-section; (b) applied axial loads and bond shear stresses acting on each material [2].

Table 1: Cracking development criteria, axial cracking loads of the first and second material, grout and 3DPC stresses at cracks and minimum reinforcement ratio [2].

Each R3DPC tie consisted of a conventional B500B steel bar embedded in grout and enclosed by a 3DPC shell. The specimens were 1.8 m long, including 1.44 m of R3DPC with a 140 mm circular cross-section and 180 mm protruding bar at each end. The grout core had a diameter of 60 mm, while the 3DPC shell comprised 8 mm thick, 40 mm wide printed layers (Figure 5b). To investigate the influence of reinforcement ratio, three specimens with different rebar diameters of Ø10, Ø12, and Ø14 mm were used, corresponding to ratios of 0.51%, 0.73%, and 1.00%. In addition, two specimens with an Ø12 mm rebar diameter were prepared with smoothed (ground) surfaces to aid in the interpretation of results and assess the effect of printed surface texture on Digital Image Correlation (DIC) measurements. Regarding transverse reinforcement, four specimens had no stirrups, while one included stirrups spaced at 240 mm. Figure 5c summarises the experimental campaign, including the specimen designation with the test type (TC = tension chord), number (1–5), rebar diameter (D10, D12, D14), surface treatment (NG = not ground, G = ground), and shear reinforcement (S = stirrups). Figure 5d also shows the test setup of the direct tensile test on R3DPC ties. The specimens were placed in a vertical position and subjected to an axial tensile load with deformation control at the ends.In this specific case study, the material properties indicate behaviour consistent with Scenario (b1): the grout is expected to crack first ( $f_{gt}< n_g f_{ct}$ ), while the 3DPC shell should initially remain uncracked (Table 1). The axial load required to crack the 3DPC is ≈30% higher than that for the grout. These theoretical results were further proven with the experimental campaign consisting of the five R3DPC tension ties, which were tested to failure under tensile force.

Figure 5: R3DPC Specimens: (a) Production overview, (b) dimensions, (c) specimen nomenclature, and (d) test setup [2].

Moreover, the specimens were instrumented with Digital Image Correlation (DIC) and Distributed Fibre Optic Sensing (DFOS). DIC enabled the continuous measurement of displacement and strain fields on the surface of the 3D-printed shell, while DFOS provided quasi-continuous strain measurements along the reinforcing bars by means of integrated optical fibres, which facilitates the investigation of the interaction between the reinforcement and the surrounding grout.

Figure 6 shows the experimental results in terms of the load–deformation behaviour, the average strain development along the specimen length (top T and bottom B in Figure 6), and the crack pattern. Specimen TC1_D10_NG is excluded from the analysis as its reinforcement ratio $\rho$ was below the minimum $\rho_\text{min}$ , leading to yielding before crack stabilisation. This configuration was not intentionally selected and reflects practical limitations, including the limited size of R3DPC ties, uncertainty in 3DPC tensile strength, and low capacity of Ø10 mm bar. In general, the following main consideration can be drawn:

As in conventional reinforced concrete, the reinforcement ratio influences crack development: higher ratios lead to smaller crack spacing and help prevent yielding at crack initiation (as happened for specimen TC2_D12_NG). Insufficient reinforcement results in few or no visible cracks, reducing deformation capacity (see average strain for specimen TC2_D12_NG).
The load–deformation response of the R3DPC ties showed a clear tension-stiffening effect, evidenced by the shift between the curves of the reinforced specimens (continuous black curve in Figure 6) and the bare steel bar (dashed grey curve in Figure 6).
Stirrups acted as local weak points, reducing the effective cross-section and triggering cracks at their locations, which prevented the formation of a constant crack load (see specimen TC4_D12_G_S).
Surface texture affected cracking behaviour: ground specimens developed regular cracks at nearly constant load levels (see specimen TC3_D12_G), while non-ground ones cracked irregularly and lacked a clear plateau in the force–deformation curve (see specimen TC5_D14_NG).
Correlated DIC and DFOS measurements confirmed an effective tensile force transfer from steel to grout and 3DPC, with cracks forming at the same location and almost simultaneously in both materials. Analytical results also support this observation, showing that after grout cracking, the 3DPC may remain briefly uncracked; however, 3DPC rapidly cracks at the same position due to stress concentration. Reliable DIC data were also obtained from non-ground specimens, confirming that the printed surface texture did not compromise measurement accuracy.

Figure 6: Load-deformation behaviour, average strain development along the specimen, and crack pattern: (a) TC2_D12_NG, (b) TC3_D12_G, (c) TC4_D12_G_S, and (d) TC5_D14_NG [2].

These findings suggest that the Tension Chord Model (TCM) can be extended to 3D-printed concrete (3DPC). More detailed explanations about the experimental results can be found in [2]. Nonetheless, further testing is required, as five specimens are insufficient for full validation. More experiments are coming soon. For any questions, feel free to reach out to Lucia Licciardello.

Lucia Licciardello

Referenzen

Licciardello L., Giraldo-Soto A., Kaufmann W., Metelli G. Determining the strength of 3D printed concrete with the modified slant shear test. Structural Concrete 2025;26:2467–86. https://doi.org/10.1002/suco.202400238.
Licciardello L., Meillasson H., Giraldo-Soto A., Kaufmann W. Direct tensile tests on Reinforced 3D Printed Concrete ties, 4^th fib Young Symposium 2025, Naples.