**1. Introduction**

The beam-column joint is a sensitive and crucial part of a structure, where a failure in it can cause the sudden collapse of a building [1]. It is the most seismically vulnerable component in a structure that is typically designed for gravity loads [2]. Recently, extensive research has been on the behavior of reinforced concrete (RC) beam-column joints brought under monotonic loading [3–5]. It was found that many beam-column joints designed with the concept of strong column weak beam concept undergo severe shear force during a seismic event causing joint failure [6].

Shear failures are brittle and more vulnerable causing the catastrophic collapse of structures. To achieve ductile design, ductile material or appropriate reinforcement should be used to improve shear capacity. The latter technique is mostly done by providing stirrups and ties in beams and columns, respectively, with appropriate spacing for good bonding between concrete and reinforcement [7]. Shear capacity can also be enhanced by following various techniques. De Corte and Boel [8] examined the use of rectangular spiral reinforcement (RSR) by testing RC beams under continuous four-point test and results showed increased shear capacity. Yang, Kim [9] explored the effectiveness of Spiral type wire rope as a shear reinforcement by testing three two-span reinforced concrete T-beams in the four-point test under static loading conditions, and results demonstrated increased

**Citation:** Nafees, A.; Javed, M.F.; Musarat, M.A.; Ali, M.; Aslam, F.; Vatin, N.I. FE Modelling and Analysis of Beam Column Joint Using Reactive Powder Concrete. *Crystals* **2021**, *11*, 1372. https://doi.org/10.3390/ cryst11111372

Academic Editor: José L. García

Received: 20 September 2021 Accepted: 8 November 2021 Published: 11 November 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

ductility and controlled crack width. Similarly, Al-Nasra and Asha [10] utilized swimmer bars as transverse reinforcement with three types of connection (weld, bolt, and U-link bolt), and results depicted that it is a convenient method for improving shear strength, ductility, and controlling crack width. Another research by Ghobarah and Said [11] suggested different retrofitting and reinforcing techniques for improving shear resistance of beam-column joints by using concrete jacketing, bolted steel plates, and corrugated steel sheets, etc. [12]. Moreover, Gencoglu and Mobasher [13] concentrated on the use of external steel plates on each side of the column face by bolting it through epoxy bonding and steel angles welded to the plates and the joint region inflamed with concrete fillet in a two-way beam column slab system to provide additional strength to structure against different loadings. As the columns were prefabricated, these approaches were extremely beneficial in terms of construction time. All these methods were very effective in enhancing the shear strength of a beam-column joint, but such techniques are neither cost-effective nor time-efficient.

Reactive powder concrete (RPC) exhibiting strain hardening processes can be utilized to improve beam-column joint strength. During the 1990s, ultra high strength performance mortar known as reactive powder concrete was developed having the compressive strength of 200 MPa [14]. The RPC concept was first developed in 1990 by P. Richard and M. Cheyrezy [15]. It was first utilized in 1997 for the construction of the Sherbrooke bridge in Canada [16]. RPC provides many advanced and high strength and ductility properties in comparison to conventional concrete [17]. RPC constituents include cement, sand, silica fumes, quartz powder, superplasticizers, and steel fibers (optional) [18]. The compressive strength of the RPC used in high prestressed bridge girders is more than 200 MPa while its flexural strength is 50 MPa with high workability. Moreover, it possesses strong ductility and energy absorption characteristics [19]. These properties of RPC make it a significant material. Therefore, RPC is widely used in the construction industry for the construction of different structures like prestressed girders, sewer pipes, blast resistance structures, and high-pressure pipes [20]. Experimental investigation on RPC showed significant improvement in the strength, ductility, strain capacity, and energy dissipation of structures. Furthermore, during the uniaxial compression test, RPC sustained a significant amount of load after initial cracking [21]. The presence of silica fumes and fine particles in the material provides pozzolanic characteristics, agitating the hydration reaction and increasing strength [14]. RPC sometimes shows brittle behavior due to its ultra-high strength. This can be mitigated by adding steel fibers. RPC is gaining momentum and recently has been used in a number of construction fields including bridge erection, mining engineering and high-rise buildings [22,23].

RPC can be used for retrofitting structures. Al-Jubory [24] evaluated the bond strength and durability of RPC using as a repairing material. The addition of silica fume and quartz powder to RPC improved temperature resistance and rendered the structure impermeable. Furthermore, employing RPC as a retrofitting material increased the structure's compressive and flexural strength by more than 12%. It was observed that the abrasion coefficient of RPC was 7.58% more than ordinary concrete. Results indicated no drastic declination for RPC which proved it to be more durable than reinforced concrete.

The experimental study was employed on reinforced RPC (having 1% and 2%) with and without steel fibers. On both of these samples, several strength tests were performed, including compressive strength, tensile strength, and flexural strength. It was discovered that the inclusion of steel fibers increases compressive strength, flexural strength, and split tensile strength by more than 10%. Compressive strength for samples without and with reinforcement was 50–67 MPa and 74.5 MPa, respectively. Low values indicated the presence of higher calcium aluminate content. Experimental results showed that RPC has 250 times greater durability and 200% more compressive strength and 150% more flexural strength than conventional and high strength mortar (HSM). Furthermore, RPC has an abrasion coefficient that is eight times that of normal and four times that of HSM. Freeze and thaw cycles have less effect on RPC which makes it more durable. All these factors lead RPC to be one of the best retrofitting materials [25].

RPC has improved material usage in the concrete industry by providing economic benefits and builds considerably strong, efficient, and durable structures. Experimental research on RPC is conducted by many researchers, however, there is little study on modeling of RPC beam-column joints. This research focused on the numerical modeling of RPC beam-column joint besides experimental work. Numerical modeling provided complete diagnoses about the cause and extent of damage to the structures. Moreover, it is an efficient technique, and it is gaining momentum as it is not only cost-effective but also time efficient. The numerical modeling of the beam-column joint was done using ABAQUS software which is capable of simulating the nonlinear behavior and gives more realistic results in comparison to other software. The experimental results obtained were validated against the numerical results. research on RPC is conducted by many researchers, however, there is little study on modeling of RPC beam-column joints. This research focused on the numerical modeling of RPC beam-column joint besides experimental work. Numerical modeling provided complete diagnoses about the cause and extent of damage to the structures. Moreover, it is an efficient technique, and it is gaining momentum as it is not only cost-effective but also time efficient. The numerical modeling of the beam-column joint was done using ABAQUS software which is capable of simulating the nonlinear behavior and gives more realistic results in comparison to other software. The experimental results obtained were validated against the numerical results. **2. Experimental Investigation** 

abrasion coefficient that is eight times that of normal and four times that of HSM. Freeze and thaw cycles have less effect on RPC which makes it more durable. All these factors

RPC has improved material usage in the concrete industry by providing economic benefits and builds considerably strong, efficient, and durable structures. Experimental

### **2. Experimental Investigation** otonic loading for the determination of tensile strength of beam-column joints. Two out

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lead RPC to be one of the best retrofitting materials [25].

Four triangular frames as shown in Figure 1 were cast and tested under simple monotonic loading for the determination of tensile strength of beam-column joints. Two out of four frames consisted of conventional concrete. RPC was used in the beam-column joint in the remaining two frames. of four frames consisted of conventional concrete. RPC was used in the beam-column joint in the remaining two frames.

Four triangular frames as shown in Figure 1 were cast and tested under simple mon-

**Figure 1.** Triangular frames of 2<sup>0</sup> × 2 0 .

**Figure 1.** Triangular frames of 2′ × 2′. The cross-section and long section details of specimens are shown in Figures 1 and 2. Column and beam dimensions are 4′′ × 4′′ × 24′′ and 4′′ × 6′′ × 24′′, respectively, with a cover of 0.5′′ from all sides. All the frames were brought under a monotonic loading machine for testing. During the application of load, roller support was provided to the beam and the column was kept fixed. Sensors were installed both at the joints and the beam ends. The cross-section and long section details of specimens are shown in Figures 1 and 2. Column and beam dimensions are 4<sup>00</sup> × 4 <sup>00</sup> × 24<sup>00</sup> and 4<sup>00</sup> × 6 <sup>00</sup> × 2400, respectively, with a cover of 0.500 from all sides. All the frames were brought under a monotonic loading machine for testing. During the application of load, roller support was provided to the beam and the column was kept fixed. Sensors were installed both at the joints and the beam ends. *Crystals* **2021**, *11*, x FOR PEER REVIEW 4 of 22

Constituents of RPC are shown in Table 1. RPC mix requires a higher cement quantity

low sodium oxide and low calcium aluminate content [27–30]. Reinforcement of grade 60 (60 ksi) was used in the specimens. RPC specimens in this study were made with low C3A Portland cement Type V complying with ASTM C150-2. Silica fume was utilized as an auxiliary binder. This was done as RPC requires a pozzolanic substance containing microparticles to reduce small voids in the paste. It also contributed to enhancing the strength and durability properties of the mix as a result of improved dense packing. According to ASTM C 494, a superplasticizer was used to recompense for the decreased water/cement ratio [31]. In the end, quartz mineral was employed to produce high-performance RPC. As the attributes of RPCs not only depend mainly on the order in which the components are inserted into the combination, but also on the speed and length of the process of mixing [32–34]. Approximately 7 min of gradual mixing of dry materials made out of silica fume, Portland cement, and quartz. The superplasticizer was added to water and the whole combination from the superplasticizer with water was added to the components immediately. The blend was then mixed up at around 10 min of progressively escalating speed. Beam column joint for two out of the four frames were left (4 inches for beam and 6 inches for column) for RPC concrete as shown in Figure 3. Joints were cast using RPC concrete monolithically with the conventional concrete as shown in Figure 4. The burlap curing method was adopted. In this method, the triangular specimens were kept under a burlap that was kept wet. Both controlled conventional concrete and RPC specimens were brought under a monotonic loading machine having a capacity of 200 tons as depicted in Figures 5 and 6. In monotonic load testing, the load is steadily escalated at a constant rate, with no reversals from test start to ultimate fracture. Casting and testing of RPC frames

**Figure 2.** Cross-section and reinforcement detailing of beam and column. **Figure 2.** Cross-section and reinforcement detailing of beam and column.

are shown in Figures 3–6.

**Table 1.** Mix design of RPC.

**Silica** 

**Fume Quartz Fine Aggre-**

**gate** 

1 0.25 0.4 1.1 0.17 0.03 0.015

**W/C Ratio**  **Steel** 

**Fibers Superplasticizers** 

**Ordinary Portland Cement** 

Constituents of RPC are shown in Table 1. RPC mix requires a higher cement quantity as compared to conventional concrete. The quality of cement is also of immense significance in this case [26]. Previous studies have employed high-performance cement with a low sodium oxide and low calcium aluminate content [27–30]. Reinforcement of grade 60 (60 ksi) was used in the specimens. RPC specimens in this study were made with low C3A Portland cement Type V complying with ASTM C150-2. Silica fume was utilized as an auxiliary binder. This was done as RPC requires a pozzolanic substance containing microparticles to reduce small voids in the paste. It also contributed to enhancing the strength and durability properties of the mix as a result of improved dense packing. According to ASTM C 494, a superplasticizer was used to recompense for the decreased water/cement ratio [31]. In the end, quartz mineral was employed to produce highperformance RPC. As the attributes of RPCs not only depend mainly on the order in which the components are inserted into the combination, but also on the speed and length of the process of mixing [32–34]. Approximately 7 min of gradual mixing of dry materials made out of silica fume, Portland cement, and quartz. The superplasticizer was added to water and the whole combination from the superplasticizer with water was added to the components immediately. The blend was then mixed up at around 10 min of progressively escalating speed. Beam column joint for two out of the four frames were left (4 inches for beam and 6 inches for column) for RPC concrete as shown in Figure 3. Joints were cast using RPC concrete monolithically with the conventional concrete as shown in Figure 4. The burlap curing method was adopted. In this method, the triangular specimens were kept under a burlap that was kept wet. Both controlled conventional concrete and RPC specimens were brought under a monotonic loading machine having a capacity of 200 tons as depicted in Figures 5 and 6. In monotonic load testing, the load is steadily escalated at a constant rate, with no reversals from test start to ultimate fracture. Casting and testing of RPC frames are shown in Figures 3–6.

**Table 1.** Mix design of RPC.


**Figure 3.** Joint left for RPC. **Figure 3.** Joint left for RPC.

**Figure 4.** Joint filled with RPC concrete.

**Figure 5.** Load setup for specimens.

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**Figure 4.** Joint filled with RPC concrete. **Figure 4.** Joint filled with RPC concrete. **Figure 4.** Joint filled with RPC concrete.

**Figure 3.** Joint left for RPC.

**Figure 3.** Joint left for RPC.

**Figure 5.** Load setup for specimens. **Figure 5. Figure 5.**  Load setup for specimens. Load setup for specimens.

**Figure 6.** RPC specimens before application of load. **Figure 6.** RPC specimens before application of load.

tional concrete samples.

As seen in Figures 7–10, shear cracking was the primary cause of failure in all the specimens. The distribution of cracks in the RPC sample was distributed uniformly due to the presence of steel fibers. As no coarse aggregates were involved in the case of RPC specimens, beam-column joint resulted in decreased stiffness as discussed in the results As seen in Figures 7–10, shear cracking was the primary cause of failure in all the specimens. The distribution of cracks in the RPC sample was distributed uniformly due to the presence of steel fibers. As no coarse aggregates were involved in the case of RPC specimens, beam-column joint resulted in decreased stiffness as discussed in the results

section of the article. RPC resulted in an increase of 10–15 percent of the tensile strength

**Figure 7.** Failure of the conventional concrete specimen (CC\_S1) after application of load.

section of the article. RPC resulted in an increase of 10–15 percent of the tensile strength (the ability of a material to stretch when pulled apart) as compared to controlled conventional concrete samples. section of the article. RPC resulted in an increase of 10–15 percent of the tensile strength (the ability of a material to stretch when pulled apart) as compared to controlled conventional concrete samples.

As seen in Figures 7–10, shear cracking was the primary cause of failure in all the specimens. The distribution of cracks in the RPC sample was distributed uniformly due to the presence of steel fibers. As no coarse aggregates were involved in the case of RPC specimens, beam-column joint resulted in decreased stiffness as discussed in the results

*Crystals* **2021**, *11*, x FOR PEER REVIEW 6 of 22

**Figure 6.** RPC specimens before application of load.

**Figure 7.** Failure of the conventional concrete specimen (CC\_S1) after application of load. **Figure 7.** Failure of the conventional concrete specimen (CC\_S1) after application of load.

**Figure 8.** Failure of the conventional concrete specimen (CC\_S2) after application of load. **Figure 8.** Failure of the conventional concrete specimen (CC\_S2) after application of load.

**Figure 9.** Failure of RPC specimen (RPC\_S1) after application of load.

**Figure 8.** Failure of the conventional concrete specimen (CC\_S2) after application of load.

**Figure 9.** Failure of RPC specimen (RPC\_S1) after application of load. **Figure 9.** Failure of RPC specimen (RPC\_S1) after application of load.

**Figure 10.** Failure of RPC specimen (RPC\_S2) after application of load. **Figure 10.** Failure of RPC specimen (RPC\_S2) after application of load.

Table 2 shows the values of experimental results. Strength (*fc*'), Elastic modulus (*Ec*), maximum load, and displacement for all the specimens were studied. RPC specimens reached ultimate strength at a later stage and have shown higher *Ec*. Moreover, the load taken by RPC specimens was greater in comparison to controlled concrete specimens. Table 2 shows the values of experimental results. Strength (*fc*'), Elastic modulus (*Ec*), maximum load, and displacement for all the specimens were studied. RPC specimens reached ultimate strength at a later stage and have shown higher *Ec*. Moreover, the load taken by RPC specimens was greater in comparison to controlled concrete specimens.

> **Max Load in Experimental (N)**

Recently, numerical modeling has been increasingly adopted to simulate the damaging effect of structures. These numerical models can predict the failure events by analysis of nonlinear behavior such as buckling, large displacements, cracking, and inter-surface contacts. Finite element analysis (FEA) model-based software ABAQUS was used to model and to simulate and determine the response of RPC in improving the shear strength deformation of vulnerable beam-column joint. Different parameters for linear and nonlinear analysis were taken from experimental work of shear strength-deformation improve-

The finite element method (FEM) is the most widely used in numerical simulation of structures [35]. Finite element models have the potential to solve a wide range of complex

CC\_S1 21.03 27,497.88 15,500 35.98 CC\_S2 21.03 27,497.88 13,330 46.28 RPC\_S1 45.24 37,433.67 18,000 40.15 RPC\_S2 45.24 37,433.67 16,020 43.33

**Max Displacement Experimental (mm)** 

ment of vulnerable beam-column connection using RPC.

*3.1. Finite Element Modeling of Nonlinear Behavior of Beam-Column Joint* 

**Specimens** *fc***' (MPa)** *Ec* **(MPa)** 

**3. Modelling** 

3.1.1. Finite Element Method


**Table 2.** Experimental results.

### **3. Modelling**

Recently, numerical modeling has been increasingly adopted to simulate the damaging effect of structures. These numerical models can predict the failure events by analysis of nonlinear behavior such as buckling, large displacements, cracking, and inter-surface contacts. Finite element analysis (FEA) model-based software ABAQUS was used to model and to simulate and determine the response of RPC in improving the shear strength deformation of vulnerable beam-column joint. Different parameters for linear and nonlinear analysis were taken from experimental work of shear strength-deformation improvement of vulnerable beam-column connection using RPC.
