Shear Response of Reinforced Concrete Beams Containing Recycled Coarse Aggregate under 45° Biaxial Loading: Experimental Testing and Finite Element Analysis

2.1 Geometry and materials

Eight reinforced concrete beam specimens were fabricated and tested to evaluate the combined influence of cross-sectional geometry and RCA content on biaxial shear behavior. The beams were divided into two groups according to cross-sectional shape: square and rectangular, with four specimens in each group. The square beams had cross-sectional dimensions of 250 × 250 mm, whereas the rectangular beams measured 150 × 350 mm, as shown in Figure 1.

Figure 1. Longitudinal and transverse reinforcement details of the tested reinforced concrete (RC) beams with cross-sections 1-1 and 2-2

All beams were cast with a total length of 1500 mm and tested under simply supported conditions over a clear span of 1300 mm, with a support width of 100 mm at each end. Steel bearing plates were placed at the supports and at the loading point to ensure uniform load transfer and to prevent local crushing of concrete. The load was applied at midspan along a 45° orientation relative to the principal section axes to induce biaxial shear action. The adopted span-to-depth ratios and boundary conditions were selected to promote shear-dominated behavior representative of short reinforced concrete beams subjected to combined shear actions [1].

Four concrete mixtures were prepared by partially replacing natural coarse aggregate with RCA at replacement levels of 0%, 30%, 50%, and 75% by mass. Ordinary Portland Cement complying with the Iraqi Specification No. 5/1984 and ASTM C150 requirements was used throughout the experimental program. All concrete mixtures were prepared with a constant water-to-cement ratio (w/c) of 0.43. Natural river sand was used as fine aggregate, while conventional river gravel was used as natural coarse aggregate. The RCA was obtained by crushing previously tested concrete specimens collected from the structural laboratory. Before mixing, the recycled aggregate was cleaned, sieved, and used in an air-dried condition. Both natural and RCAs had a nominal maximum size of 20 mm, and the aggregate grading complied with the standard limits, as illustrated in Figure 2.

Figure 2. Grading curve of the used coarse aggregate compared with the standard upper and lower grading limits

A high-range water-reducing admixture (Sika® ViscoCrete®-905) conforming to ASTM C494 was used to improve concrete workability, particularly for mixtures containing RCA. All beam specimens were cast and cured under similar laboratory conditions. After casting, the specimens were demolded after 24 hours and cured in water until the testing age of 28 days.

Compressive strength was determined at 28 days using six 150 mm cube specimens for each mixture. The resulting average compressive strengths corresponding to each replacement ratio are reported in Table 1. For each RCA level, one square beam and one rectangular beam were cast to investigate the influence of cross-sectional geometry and RCA replacement ratio on the structural response of the tested beams.

Table 1. Mechanical properties of concrete mixtures with different recycled coarse aggregate (RCA) replacement ratios at 28 days

All specimens were reinforced with eight longitudinal deformed bars distributed along the perimeter of the beam cross-section and enclosed by a nominal concrete cover of 25 mm, as illustrated in Figure 1. Bar diameters of 12 mm and 16 mm were used in the square and rectangular beams, respectively, in accordance with the dimensions and structural configuration of each beam group. No transverse reinforcement was provided within the shear span to avoid additional shear contribution from stirrups and to ensure that failure was governed by concrete shear resistance [2]. To maintain the position of longitudinal reinforcement during casting, two closed 10 mm stirrups were placed only near each support region. This detailing ensured that all beams remained shear-critical and failed within the span under biaxial shear loading.

2.2 Test setup, measurement devices, and loading conditions

The reinforced concrete beam specimens were tested under simply supported conditions to investigate their structural response under biaxial shear loading. To produce the required loading inclination, each beam was rotated about its longitudinal axis so that the applied load acted at an angle of 45° relative to the vertical axis.

Inclined steel supports were installed at both ends to maintain the specified orientation during testing. A steel load-transfer block was positioned at midspan to ensure that the applied load was aligned with the inclination of the supports and passed through the shear center of the beam section in Figure 3.

Figure 3. Experimental setup showing the inclined support, loading plate, load cell, and linear variable differential transformer (LVDT) used during the biaxial loading test

All specimens were tested after 28 days of curing. Before testing, the beam surfaces were cleaned and painted to facilitate clear observation of crack initiation and propagation. Loading was applied monotonically under load-control mode in increments of 5 kN until failure occurred.

The applied load was measured using a calibrated load cell, and the readings were recorded through a data acquisition system. Vertical deflection at the bottom of midspan was monitored using a linear variable differential transformer (LVDT) to capture the overall load–deflection response. Shear deformation within the shear span was measured using mechanical strain gauges (Demec points) with a gauge length of 50 mm. Three pairs of Demec points were installed at a 45° orientation within the shear span to represent the principal shear directions. Electrical strain gauges were attached to the longitudinal reinforcement to measure strains in the extreme tension and compression bars during loading.

During testing, the loads corresponding to first-crack load (P_cr) and ultimate load (P_u) were recorded. Crack initiation and propagation were continuously monitored, and the failure mode of each specimen was carefully documented.

For clarity, a simplified specimen designation system was adopted. The label “RE” refers to rectangular beams, and “SQ” denotes square beams, followed by the RCA replacement ratio. Accordingly, the specimens were designated as RE-0, RE-30, RE-50, RE-75, and SQ-0, SQ-30, SQ-50, SQ-75.

4.1 Finite element model

A three-dimensional finite element model was developed using ABAQUS to simulate the structural behavior of the tested reinforced concrete beams, as shown in Figure 9. The nonlinear analysis was performed using the static general procedure with displacement-controlled loading to ensure stable convergence during the post-peak response [26].

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Figure 9. Finite element model of the reinforced concrete beam in ABAQUS

Concrete was modelled using eight-node linear brick elements with reduced integration (C3D8R), which are widely used for nonlinear analysis of reinforced concrete members due to their computational efficiency and capability to capture cracking and crushing behavior [26, 27].

The reinforcing bars were represented using two-node truss elements (T3D2), which are suitable for modeling axial force transfer in reinforcing steel [27, 28].

The interaction between concrete and reinforcing bars was defined using the embedded region technique, assuming a perfect bond between steel and surrounding concrete. Although this assumption does not explicitly account for local bond-slip effects, the adopted modelling approach provided satisfactory agreement with the experimental response of the tested beams in terms of overall structural behavior and failure mode. This approach allows the reinforcement to share the displacement field of the host concrete elements without explicitly defining the bond interaction between steel and concrete.

To simulate the experimental loading conditions, steel loading and support plates were modelled to ensure a uniform distribution of the applied displacement and to avoid unrealistic stress concentrations at the contact regions [26]. A structured mesh was generated for the concrete domain with an average element size of approximately 20 mm, providing a balance between computational efficiency and solution accuracy [27].

4.2 Material properties

The material properties adopted in the numerical model were based on the experimental results obtained from the tested concrete mixtures. Four concrete mixes corresponding to RCA replacement ratios of 0%, 30%, 50%, and 75% were considered, and the measured compressive and split tensile strengths were used to define the concrete behavior in the model. The nonlinear behavior of concrete was simulated using the Concrete Damaged Plasticity (CDP) model in ABAQUS. The compressive and tensile responses were defined using stress–strain relationships for concrete in compression and tension derived from the experimentally measured compressive strength, split tensile strength, and modulus of elasticity of the tested concrete mixtures. Established empirical formulations reported in the literature were adopted to represent the nonlinear behavior of concrete. In addition, the corresponding compression and tension damage parameters were incorporated to account for stiffness degradation associated with concrete cracking and crushing [28, 29]. The reinforcing steel was modelled using an elastic–perfectly plastic constitutive law, assuming linear elastic behavior up to the yield stress followed by a perfectly plastic response [26]. In addition, the reinforcement layout in the numerical model was defined to match the experimental specimens, including the number of bars, their diameters, and their distribution within the beam cross-section.

The main parameters defining the CDP model are summarized in Table 3 [27].

Table 3. Concrete Damaged Plasticity (CDP) parameters

4.3 Boundary conditions

The boundary conditions adopted in the numerical model were defined to reproduce the experimental test setup as closely as possible. The beams were modelled under simply supported conditions, consistent with the laboratory tests. Steel plates were introduced at the loading and support regions and assigned elastic steel properties to ensure a uniform distribution of stresses and to avoid unrealistic stress concentrations at the contact zones [26].

The interaction between the concrete beam and the steel plates was modelled using a surface-to-surface contact approach, allowing a more realistic representation of the interface behavior. This formulation enables proper load transfer while accounting for friction and possible separation between the contacting surfaces [26, 28, 30].

The external load was applied at the midspan of the beam using displacement control through the loading plate, allowing the nonlinear response of the beam to be captured up to failure [2].

4.4 Mesh sensitivity

Meshing refers to the discretization of the numerical model into a finite number of elements to approximate the structural response. The accuracy and stability of the finite element analysis are influenced by the adopted mesh density; therefore, selecting an appropriate mesh size is important for achieving stable and accurate numerical results [30, 31].

In this study, a mesh sensitivity study was conducted using element sizes of 15 mm, 20 mm, and 25 mm to evaluate the influence of mesh refinement on the numerical response. Based on the obtained results, an element size of 20 mm was selected, as it provided a good balance between numerical accuracy and computational efficiency. Further mesh refinement did not lead to significant changes in the global response of the beams [30]. The mesh sensitivity assessment in the present study was primarily focused on the global structural response and load–deflection behavior of the beams.

4.5 Numerical results

4.5.1 Numerical load capacity and load–deflection behavior

The load-carrying capacity of the beams was evaluated in terms of the P_cr and P_u obtained from the finite element analysis. These results are summarized in Table 4 and compared with the experimental findings to assess the accuracy of the numerical model and its ability to capture the shear behavior of recycled aggregate concrete beams under biaxial loading.

Table 4. Comparison of load capacities obtained from experimental tests and finite element analysis

The comparison between the numerical and experimental results presented in Table 4 indicates that the finite element model provides a reasonable prediction of both the cracking load and P_u for all beam specimens. For the cracking load, the numerical-to-experimental ratios ranged approximately between 0.84 and 0.95, showing that the model generally tends to slightly underestimate the cracking load, particularly at higher RCA replacement levels. This behavior may be associated with the sensitivity of crack initiation to local material heterogeneity and tensile properties, which are difficult to capture precisely in numerical simulations. In terms of P_u, the numerical predictions showed good agreement with the experimental results, with ratios ranging between 0.88 and 1.13. The model demonstrated a consistent ability to capture the shear capacity of both square and rectangular beams.

Overall, the results indicate that the developed finite element model is capable of reasonably predicting the load-carrying capacity of recycled aggregate concrete beams, particularly in terms of P_u response.

The load–deflection curves shown in Figure 10 and Figure 11 illustrate the general behavior of the rectangular and square beams obtained from both experimental and numerical results. In general, the response can be divided into three main stages. In the first stage, a nearly linear relationship is observed, representing the elastic behavior before cracking. This is followed by a nonlinear stage initiated by the formation of the first-cracks, where a gradual reduction in stiffness occurs. The final stage corresponds to the approach to P_u, where deflection increases with a reduced rate of load increment until failure.

A good agreement in the overall shape and response stages can be observed between the numerical and experimental curves for both beam types. Although slight differences in deflection values exist, the general trend and progression of the curves indicate that the finite element model is capable of capturing the structural behavior with reasonable accuracy. The comparison between the numerical and experimental results was primarily focused on the overall structural response and global load–deflection behavior rather than detailed local crack width and crack spacing prediction.

4.5.2 Numerical crack patterns

The tensile damage contours (DAMAGET) predicted by the finite element model are presented in Figure 12 for all beam specimens. In the ABAQUS simulations, the DAMAGET variable was used as an indicator of tensile damage development and probable crack localization zones within the concrete. The results suggest that tensile damage initiated near the bottom tension region of the beams and progressively localized along inclined paths toward the loading region, indicating the likely formation of dominant diagonal cracking zones.

The predicted tensile damage localization patterns showed good agreement with the experimental observations presented in Figure 4, where similar diagonal shear cracking regions were observed extending between the support and loading zones. Although the numerical results do not directly represent physical crack widths or exact crack trajectories, they provide a reasonable indication of the regions where cracking is likely to develop under the applied loading conditions.

Furthermore, the numerical results indicated that increasing the RCA replacement ratio was generally associated with a wider and more continuous tensile damage zone, which may reflect the lower stiffness and tensile strength characteristics of recycled aggregate concrete. Despite these variations, the overall failure mode remained similar for both rectangular and square beams, indicating that the finite element model was able to reasonably capture the dominant shear failure mechanism observed experimentally. This behavior was characterized by progressive localization of tensile damage along inclined paths with limited deformation prior to failure, which is consistent with a shear-dominated brittle response.

In addition, the distribution of maximum principal plastic strain (PE, Max. Principal), as shown in Figure 13, provided further indication of strain localization within the shear span. The concentration of plastic strain along inclined bands supports the observed shear transfer mechanism and identifies regions susceptible to crack development, without directly representing actual crack widths or crack openings.