Several investigations at the building level, following rigorous assessment approaches, suggest that, in most cases, brick wall infills may enhance the performance of RC frames at low-intensity earthquake excitations (increased base shear capacity). Further, at higher intensities, shear-related failures of columns or out-of-plane collapse of damaged infills (especially if they have openings) may lead to premature exhaustion of buildings' structural capacity (i.e., at lower drifts) with respect to the bare structure at different serviceability or ultimate limit states (see, e.g., dynamic experiments in [11] or analytical investigations in [12–14], among others). Wall infills are very crucial to take into account, especially in the damage assessment at serviceability limit states [14]. In any case, an increased uncertainty in building behavior should be considered as the dynamic excitation intensity is increased and/or multiple structural deficiencies are identified.

Innovative repair and strengthening solutions for RC frames with infill walls involved externally applied sprayable ductile fiber-reinforced cementitious composites [15], or fiberreinforced polymer sheets [3,16,17], among others. Koutas et al. [18] tested RC frames infilled with brick walls, strengthened with textile-reinforced mortar. The RC frames were of old-type detailing (with inherent deficiencies). In most of the cases of such RC frames subjected to a constant vertical load and cyclic horizontal loading, the infill walls revealed limited ductility before their retrofitting. Even after their strengthening, the structural behavior and failure mechanism were similar to the as-built infilled frames. However, the retrofitted infilled RC frames exhibited a significant increase in the shear resistance and dissipated energy [19,20]. Again, usually, the accumulation of severe damage occurs for a lateral drift range between 0.5 and 1.5%. Such values for the infill performance limit the potential of the retrofitted RC frames [18]. This early damage accumulation may pose a threat, in some cases, to the targeted ductile behavior of strengthened RC frames with infill walls. For example, detrimental effects may be introduced by the highly uncertain and undesirable infill wall–RC frame interaction. Such effects may include premature shearrelated failure of the columns in contact with the infills, or partial collapse of the infills, among others, or trigger an undesirable soft-story mechanism [21] and even whole-building collapse (if seismically induced overloads or out-of-plane infill collapses occur).

In general, the deterioration of the bond between commonly used cement-based materials at the boundary between the RC frame and the infill, as well as the severe damage accumulation within the fragile brick infills (subjected, mainly in plane, to variably imposed diagonal compressive deformation and suffering diagonal cracks or corner crushes), led to the development of different seismic protection solutions. Marinkovic and Butenweg [22,23] proposed a system to protect the infilled frame against in-plane and outof-plane loads. Specially designed, three-sided elastomer joints at the infill–RC boundary interface were placed with a total thickness of 62.5 mm (25 mm plus 37.5 mm). A bottom elastomer was used as well. The composite frame sustained in-plane and out-of-plane loading, reaching a 3% ultimate drift for in-plane loading. Morandi et al. [6] proposed sliding joints inserted in the masonry at different levels with 30 mm thickness (3 × 30 = 90 mm) and deformable joints at the wall–frame interface (25 mm thickness). Similarly, the seismic protection was remarkable up to a 3% frame drift.

Real-scale shake table experiments are of great significance for the validation of novel seismic protection systems. INMASPOL ("INfills and MASonry structures protected by deformable POLyurethanes in seismic areas"—INMASPOL SERA Horizon 2020 project) involved a real-scale RC frame building subjected to multiple ground excitations on a shake table. The excitation was suitable for the validation of the out-of-plane performance of the OrthoBlock brick wall infills of the structure, protected by innovative seismic joints, as well as for their in-plane response. The joints were made of highly deformable polyurethane (polyurethane flexible joints, PUFJ) of 20 mm thickness. The structure was driven to a high lateral drift of up to 3.7% without base shear degradation and no brick infill collapse. Then, the brick infills were retrofitted with an innovative glass grid, impregnated with high-deformability polyurethane (fiber-reinforced polyurethane, FRPU) and retested (for the experimental validation, see [20,24]). The techniques of seismic joints and externally

bonded fiber grid jackets have already been validated separately in real-scale RC frames subjected to pseudo-static cycles of horizontal top displacements [25]. Different frames with boundary polymer seismic joints on three or four sides were tested with a 20 mm thickness. Further, an infilled frame without seismic joints was retrofitted with a fiber grid jacket impregnated with highly deformable polyurethane. In all cases of the tested frames, the ductility of the composite frames was remarkable, and the corresponding drift ranged from 3.5% to 4.4%. However, during experimental campaigns involving large-scale frames, only a few parameters can be investigated due to the high demand of resources and time. Three-dimensional (3D) finite element (FE) modeling and analyses may help address the effects of critical design parameters (see [26–34], among others).

This paper developed suitable 3D pseudo-dynamic FE models for a real-scale brick infilled frame receiving external fiber grid retrofitting. Further, this study developed suitable 3D FE models of the real-scale RC INMASPOL frame building with innovative polymer seismic joints at the boundary of the infills. The analyses cover the first phase of successive shake table tests as well as the second phase of shake table tests, after retrofitting of the damaged structure with externally bonded fiber grids. The structure sustained a series of scaled modified real earthquake recordings of increasing maximum ground acceleration during tests, in accordance with the dynamic pushover approach. The analyses presented herein concern the inelastic pseudo-dynamic pushover response of the structure through imposed top displacements. Bare structure analysis is also included for comparative investigations. The 3D FE analyses' results compare well with the experimental ones and may provide a unique insight on the variable interaction of the brick infill–RC frame with seismic polymer joints and retrofitting through FRP jacketing. The results help to elucidate the unique features of the interventions that enable the investigated RC framed structures to reveal high top displacement ductility. Suitable combined retrofits are also examined.

#### **2. Brief Presentation of Existing Experimental Results**

#### *2.1. Seismic Protection of Infilled RC Frames with FRP Jackets*

Herein, the experimental results of the real-scale RC frame A2R from the study by [25,35] were considered for the analytical elaborations. The RC frame had plane dimensions of a 270 cm-long beam with extensions of 30 cm on both sides and a height of 245 cm (245 cm to the level of the diaphragm). The columns had cross-section dimensions of 25 × 25 cm, 8Φ16 longitudinal continuous rebars (without lap splices) and Φ10/100 mm closed stirrups (one peripheral and one rhombic per 100 mm). The columns had two top extensions of 30 cm, as well as a common foundation beam with dimensions of 30 × 40 × 355 cm. The top beam had cross-section dimensions of 25 × 25 cm and was reinforced with 8Φ14 longitudinal rebars and Φ10/100 mm closed stirrups (peripheral). The dimensions of the RC frame and the detailing of the internal steel reinforcement are presented in Figure 1a and in Table 1. Specimen A2R included an infill wall with special thermal insulating hollow clay units, KEBE OrthoBlocks K100 (KEBE, Greece), with dimensions of 100/240/250 mm and a weight of about 100 kg/m2 (infill wall with vertical holes in the bricks), built with mortar. The mortar for the building of the walls (with nominal strength class M10) formed 3 mm-thick layers at the head or bed joints as well as at the infill–RC frame interface (no seismic joint). The infill was retrofitted with an external glass grid (of type SikaWrap 350 G Grid, with a real weight of 360 g/m2) impregnated with highly deformable PS (Sika) polymer (fiber-reinforced polyurethane jacket, FRPU, Figure 1b). The corresponding properties are cited in Table 2.

**Figure 1.** (**a**) Dimensions of the RC frame and detailing of the internal steel reinforcement and (**b**) specimen A2R with FRPU jacket on the infill surfaces.

**Table 1.** The dimensions of the RC frame and the detailing of the internal steel reinforcement.

1 To the level of the diaphragm.

1 Cubic strength at 28 days.

The two columns of the frame received a constant concentric axial load of 375 kN each. The horizontal actuator imposed successive pseudo-static cycles of gradually increased displacements at the top beam. More details on the materials used, the experimental setup, the instrumentation and test results of the A2R can be found in [25,35].

#### *2.2. Seismic Protection of Infilled RC Structure with Highly Deformable Joints* 2.2.1. Material Properties

A real-scale fully symmetrical one-story RC structure, consisting of masonry wall infilled RC frames (4 columns and 4 beams with a top slab), was subjected to shake table tests (see also Figure 2). The structure was designed according to current Eurocodes 2 and 8 [36,37]. The plane dimension of the structure was 3.8 × 3.8 m, and it was 3.3 m high. The material properties for the concrete, the reinforcing steel bars, the masonry (made of OrthoBlocks identical to the ones in A2R), the glass fiber grid and the PS polymer in the FRPU composite (FRPU identical to the one in A2R) are cited in Table 2. The structure was protected with 20 mm-thick polyurethane flexible joints (PUFJ) at the infill–RC frame interfaces made of PM polymer (mechanical properties are cited in Table 2). More details on the material properties can be found in [24].

**Figure 2.** Structure significantly damaged after PHASE 1: (**a**) north side—type B infill; (**b**) south side—type B infill; and (**c**) FRPU-strengthened infill of type B after PHASE 1.

#### 2.2.2. Structure Detailing

The frames had floor plan dimensions of 2.7 × 2.7 m—based on the columns' position and a height of 2.5 m (to the top of the slab). The dimensions and longitudinal and transverse reinforcement detailing are cited in Tables 3 and 4, respectively. The beam was hidden inside the slab. The 4 columns supported, on their top, an RC slab that was 200 mm thick. The slab carried carefully anchored steel ingots as additional masses (total 7200 kg) for the tested structure. The slab had a central square opening for access to the inside of the structure. The welded mesh top and bottom reinforcements of the slab are cited in Table 4. An additional slab reinforcement was placed at the perimeter edges and at the edges of the opening. The structure had a special foundation, with holes and hooks for attaching it to the shake table and for lifting and manipulating the structure (Figure 2a).

The infills in the building had a height of 2.3 m. Therefore, the ratio of the vertical (or horizontal) interface joint thickness to the infill wall height was 20/2300 = 0.0087. The infills were 100 mm thick, with holes in the vertical direction (identical to the ones in A2R). Out of the total of four infills, the two pairs of parallel walls had different seismic joint configurations to experimentally investigate the implementation of PUFJ in existing and new buildings. The two parallel infills of type B (Figure 2b) were constructed directly on the RC foundation with a 3 mm-thick mortar bed joint, while there was a PUFJ of 20 mm thickness, produced in situ through injection of polyurethane Sika PM. The polymer was injected between the infill and the RC columns, and between the infill and the RC slab

(three-sided joint). The adhesiveness of Sika PM to brick substrates was determined equal to 0.63 MPa by a pull-off test in [38], followed by an adhesive brick/polymer failure mode. The two parallel infills of type C were constructed on a prefabricated 20 mm-thick PUFJ bottom joint (bonded to the RC foundation beam), while identical prefabricated joints were bonded at the sides and top of the infill (four-sided joint). The adhesiveness of Sika PS to brick substrates (used in FRPU) was determined by a pull-off test in [38] and was equal to 1.48 MPa, followed by an adhesive brick/polymer failure mode. More details on the detailing of the structure can be found in [24].

**Table 3.** Dimensions of structure and of different parts.

**Table 4.** Reinforcement detailing.

#### 2.2.3. Loading Phases

Only PHASE 1 and PHASE 2 were considered for the numerical analysis. The original position of the model was such that both walls of type B were loaded in plane, and both walls of type C were loaded out of plane. In this position (PHASE 1), the structure suffered at least 10 dynamic earthquake runs of increasing maximum acceleration. The structure sustained a top slab relative displacement of 88.9 mm, corresponding to a 3.7% drift during the last run of PHASE 1. The damage to the infills of type B after the last run is depicted in Figure 2a,b. However, it should be noted that during that run, both brick infills of type B (tested in plane), protected by the PUFJ seismic joint, did not exhibit any significant damage up to a 2.5% drift of the structure. Both brick infills of type C (tested out of plane) had no significant damage after the last run of PHASE 1. After the first PHASE, the damaged brick infills of type B received FRPU external strengthening bonded on both sides of the damaged wall using a flexible adhesive of type Sika PS without any special treatment of the infill face and no crack repair (see Figure 2c). Then, three additional runs were performed during PHASE 2 up to a 1.62% drift of the structure. Further excitation during PHASE 2 was avoided in order to secure the integrity of the structure for PHASE 3 of the experiments (not presented herein) as the RC columns had already suffered significant damage. No additional significant damage to the infill walls of type B or to the infill walls of type C or any damage to the FRPU retrofit was observed after PHASE 2.

#### **3. 3D FE Models**

The numerical models were developed, and the material parameters were suitably calibrated based on the experimental parameters, using the Explicit Dynamics framework of the ANSYS Workbench [39] (see also [33,34]).

#### *3.1. Geometry and Elements*

RC members were modeled with solid elements for the concrete and linear elements for the reinforcement. Longitudinal steel bars and steel stirrups for columns, beams and slabs were modeled using the concept of "reinforcement" body interaction, not permitting separate reinforcement behavior. The parts for PUFJs were solid bodies with a 20 mm thickness, surrounding the 3 sides of the brick infill–RC frame interface for the type B infill and the 4 sides for the type C infill. Due to the small thickness of FRPUs, they were modeled as surface bodies to eliminate numerical instabilities and enhance the mesh quality. The body interaction between different components was considered as "bonded". The model used the 8-node reduced integration hexahedral elements. These elements are suitable for dynamic applications including large deformations, large strains, large rotations and complex contact conditions in Explicit Dynamics. Linear 4-node tetrahedron elements are available for use in Explicit Dynamics analysis whenever hexahedral element meshing fails. Figure 3 shows the geometry of the FE models and mesh density.

**Figure 3.** Geometry and mesh of the (**a**) A2R frame and of (**b**) 4-column model of INMASPOL structure.

#### *3.2. Material Models*

The properties of the materials satisfied the experimental properties. PUFJs and glass FRPU were modeled as elastic materials. Concrete was of type RHT concrete, an advanced plasticity model for brittle materials developed by Riedel et al. [40–42]. The failure function for the RHT constitutive model, its fracture surface and the strain softening and damage relations of the model are gathered in Table 5.

σeq is the uniaxial compressive strength; YTXC(p) is the fracture surface; FCAP(P) is a dimensionless cap function which activates the elastic strength surface within the RHT material model at high pressures; R3(θ) is the third invariant dependence term; (F)RATE(i) is the strain rate effect represented through fracture strength with plastic strain rate; *f c* is the cylindrical compressive strength; *AFail*, *NFail* are user-defined parameters; P\* is pressure normalized to *f c* ; *P*∗ *spall* is the normalized hydrodynamic tensile limit; *FRATE* is the rate-dependent enhancement factor in Equation (3); fc and ft are static uniaxial compressive and tensile strengths; ε, ε0 are the static strain rates; α is the compressive strain rate factor; δ is the tensile strain rate factor; Yelastic is the initial elastic surface; Yfail is the failure surface; G is the shear modulus; ηpl is the plastic strain before the failure strength; ηpl(pre-softening) is the total plastic strain, and it can be determined by the secant modulus between the elastic limit surface and the failure surface; D1 and D2 are material constants used to describe the effective strain to fracture as a function of pressure. Damage accumulation can have two effects in the model.

#### *3.3. Boundary Conditions and Loads*

The supports of the columns and infill had a fixed boundary condition. Pseudodynamic analyses of controlled monotonic displacement, imposed at the top of the structure (beam in A2R or at the top slab), were conducted to obtain the inelastic behavior of the A2R frame or of the structure for PHASE 1 and PHASE 2. The pseudo-dynamic pushover approach followed herein utilizes the advanced Explicit Dynamics features and minimizes the analysis time for demanding cyclic or dynamic tests (see also [33,34]).

#### **4. 3D FE Analyses Results**

#### *4.1. A2R Frame*

Figure 4 shows, in black and black-gray curves, the experimental envelope base shear–top displacement curves of A2R for (+) and (−) push, respectively, based on the results reported in [25,35]. The external application of the FRPU jackets on the OrthoBlock infill resulted in a remarkable top displacement ductility of the infilled frame A2R, with a negligible base shear reduction up to a 3.6% drift for push (+) and (−). Table 1 cites the experimental and numerical results of the A2R frame. The parameter used for the comparisons in this study is the absolute divergence (AD), also known as the absolute error (AE), and it is defined in Equation (10).

$$\text{AD} = \frac{|a\_{\text{anal.}} - a\_{\text{exp.}}|}{a\_{\text{exp.}}} \tag{10}$$

where *a* is the compared value (analytical or experimental).

**Figure 4.** Analytical base shear force–displacement curve for A2R, compared against the experimental ones.

The pseudo-dynamic analytical FE red curve coincides with the experimental ones up to 10 mm of top displacement, and then it falls in between the experimental curves for top displacement higher than 35 mm. The analytical maximum base shear is 204.7 kN (between the experimental push (−) and push (+)) at a top displacement of 59.1 mm, which is 9.1% lower than the experimental one. Satisfactory is the prediction of the ultimate base shear as well (Table 6). The divergence at the range of 10–35 mm top displacement may be attributed to the relatively rough modeling of the infill wall as a 3D panel.

**Table 6.** Comparative results for A2R frame.

#### *4.2. INMASPOL Structure*

Based on the FE developments in RC frames and on the characteristics of the IN-MASPOL structure, three numerical models were developed and analyzed. The bare RC structure with no infills (model 1) was analyzed for comparison reasons. The response of analytical model 1 was compared against the response of the brick wall infilled structure with the innovative PUFJs (model 2, INMASPOL structure), as tested in PHASE 1. Then, the damaged brick wall infilled structure received external double-sided glass FRPU jacketing (model 3, corresponding to PHASE 2 shake table tests). The damage in model 3 was implemented by removing the continuous material from the infill walls, based on the observed infill type B wall damage after the end of the experimental PHASE 1 (see Figure 2a). That is, in model 3 the infill had selected 3D finite elements removed to simulate the locally damaged parts of the infill. Such approaches can also be found in the analytical investigation of the residual capacity of buildings with damaged infills or RC members in [43].

Figure 5a presents the diagrams of the experimental top slab accelerations (equivalent to the base shear divided by the excited mass of the structure) versus the relative drift of the top slab (relative top slab–column bottom displacement divided by the respective vertical distance) for each dynamic excitation of the structure on the shake table for PHASE 1, while Figure 5b shows these for PHASE 2. Herein, it should be noted that the results are reported in acceleration–drift terms, as in [20], and can be easily transformed to the equivalent base shear–top displacement terms.

**Figure 5.** *Cont*.

**Figure 5.** Mean slab acceleration (or base shear/mass) versus horizontal drift diagram (**a**) for experimental PHASE 1; (**b**) for experimental PHASE 3; and (**c**) for numerical model 1, model 2 and model 3, against the experimental results of PHASE 1 and PHASE 2.

Figure 5c shows the results obtained from the pushover analyses in terms of top slab acceleration (base shear divided by the excited mass of the structure) versus the drift of the structure (relative top slab–column bottom displacement divided by the respective vertical distance).

The black star marks in Figure 5a,c show the experimental results from the shake table tests for the INMASPOL real-scale RC structure with OrthoBlock infills and PUFJ highly deformable seismic joints. The structure exhibits a ductile top acceleration–drift behavior which is equivalent to a ductile base shear–drift behavior. It reaches a 3.7% drift without degradation of the top acceleration (base shear). Figure 2a suggests there is no collapse of the infills tested in plane or out of plane after a 3.7% drift. Further, Figure 2c shows that the damage in infills of type B could be repaired with emergency FRPU external jackets without any special treatment of the infill (more details can be found in [20,24]).

The red star marks in Figure 5b,c show the experimental results from the shake table tests for the INMASPOL real-scale RC structure with OrthoBlock infills and PUFJ highly deformable seismic joints after the repair with FRPU (PHASE 2). The structure exhibits a rather linear elastic-like top acceleration–drift behavior which is equivalent to a linear elastic base shear–drift behavior. During retesting of the retrofitted structure, the achieved drift was 1.62% without degradation of the top acceleration (base shear). The FRPU maintained the integrity of the damaged infills, and collapse was also avoided in PHASE 2 (more details can be found in [20]). Interestingly, the stiffness of the repaired structure seems relatively increased, owing to the effects of the externally bonded FRPU jackets (more details can be found in [20]).

The abovementioned dynamic experimental results validate the advanced seismic protection provided by the 20 mm-thick PUFJ to the infill and the RC frame. An undesirable interaction is avoided, and the base shear drift behavior is remarkably ductile, while the potential of the structure is higher (tests at higher accelerations were avoided to prevent the structure from collapse and continue with PHASES 2 and 3). Similarly, the results in PHASE 2 validate the advanced retrofit of the infills by the FRPU jackets, and the potential of the structure is again higher.

Figure 5c also includes the FE analysis results for model 1 (triangles), for model 2 (black rhomb) and for model 3 (red rhomb). The developed models 2 and 3 compare well with the experimental results of the PHASE 1 and PHASE 2 tests. For model 2, the INMASPOL structure, in PHASE 1, at the initial stage of the acceleration–drift diagram, the behavior of the structure is elastic, and the experimental (black star marks) and analytical curves (black rhomb marks) coincide. After the stage of yielding of the steel bars of the concrete columns, the analytical curves start to overestimate the experimental points. The analytical acceleration value at a 3.7% drift slightly overestimates the corresponding experimental one. Overestimation of the experimental values by the analyses may be attributed to the higher damage accumulation in the RC columns and in the brick infills of type B during the experiments (the structure suffered a total of 10 earthquake excitations of increasing severity).

At PHASE 2, the analytical model was updated with the observed damage of the brick infill and with the retrofit with the FRPU (see the mesh in Figure 6a). The analytical values of model 3 (red rhomb) slightly overestimate the experimental ones (red star). The model reproduces the FRPU repair effects despite the local brick damage. Figure 6c reveals the engagement of broad infill regions (predamaged regions included) through the interaction with the highly deformable FRPU jacket and the RC frame.

**Figure 6.** *Cont*.

**Figure 6.** (**a**) Mesh of the RC structure, of the damaged brick infill and of the external FRPU retrofit; (**b**) model 2 at the end of PHASE 1; and (**c**) model 3 at the end of PHASE 2.

Furthermore, the advanced FE analyses allow for a comparative investigation of the analytical response of the bare RC structure (model 1) against analytical models 2 and 3. The analyses in Figure 6 show that the bare structure sustains a maximum acceleration of around 0.55 g, while model 2's and model 3's maximum accelerations occurred at the end of PHASE 1 at around 1.63 g and 0.99 g, respectively. Therefore, the infilled structure with seismic protection developed a three times higher maximum acceleration (or base shear) than the bare structure at PHASE 1. The corresponding increase in the initial stiffness was similarly remarkable while maintaining the high displacement ductility (3.7% horizontal drift). At PHASE 2, the retrofitted structure still revealed a higher initial stiffness when compared with the bare structure, while it could develop, at least, around double the maximum acceleration (base shear). The area under the acceleration–drift curve (denoting a measure of the energy dissipation potential) is higher for model 2 (RC structure with infills protected with PUFJ joints) than for model 1 (bare RC structure). Therefore, in the case that the OrthoBlock infill with PUFJ protection is considered in the intervention for a weak bare RC frame, it can ensure a remarkable increase in the elastic stiffness and base shear while providing a desirable ductile P–δ behavior, with a drift as high as 3.7%.

#### *4.3. FRPU Retrofitted INMASPOL Structure with the Addition of Steel Dowels*

The developed 3D FE models allow for the analytical investigation of the FRPU retrofitted INMASPOL structure with additional mild intervention with steel dowels. Only

five steel dowels were used at the top infill–RC beam boundary interface in order to increase the initial stiffness of the damaged structure, based on the approach proposed by Facconi and Minelli [44]. The steel connectors had a diameter of 16 mm and a length of 90 mm and consisted of a smooth-surface round bar made of structural steel having a nominal yield strength of 235 MPa. The distance between the five dowels was 410 mm (horizontal direction), while the middle dowel was placed at the middle of the beam span (no dowels in the vertical interfaces). This detailing avoids the position of the dowels within the corner beam–column regions that will increase their efficiency but will also increase the damage within the brick infill. As it is depicted in model 3, FRPU is efficient enough to maintain the integrity of the corner regions. The anchorage of the steel dowels in the reinforced concrete beam is 40 mm, and in the masonry wall, it is 50 mm. To increase the cohesiveness of the connection and to prevent early-stage damage, the area around dowels in the masonry was modeled with thixotropic mortar, as in [44].

Indeed, Figure 7 shows that at a 0.22% drift, the developed acceleration is 0.135 g for the revised model 3DOW with the additional steel dowels. Model 3 without dowels developed only 0.08 g acceleration (Figure 5c). The increase in the developed acceleration is 68% and reveals the earlier engagement of the infill. After a 0.6% drift, the accelerations for the two models almost coincide. Figure 8 reveals that the proposed dowel detailing leads to damage accumulation around the region within the brick infill in which the dowels are anchored. A vertical mode in controlled damage accumulation within the infill is denoted that coincides with the position of the five dowels. However, the interaction with the FRPU maintains the integrity of the infill. Based on the developed 3D FE models, the structure may receive a suitable combination of retrofits that could manipulate (in this case increase) the engagement of the infill and, correspondingly, the initial stiffness, if required. Further, the damage accumulation may be controlled in order not to lead to degradation in the performance of the structure.

**Figure 7.** Mean slab acceleration (or base shear/mass) versus horizontal drift diagram for the model 3DOW with additional steel dowels.

**Figure 8.** Damage accumulation in model 3DOW at the end of PHASE 2 (upper part).

#### **5. Conclusions**

The developed 3D FE analytical models provide satisfactory predictions of the experimental P–δ response of the RC frame A2R with infills and FRPU jacketing. Similarly, satisfactory are the predictions for the experimental top acceleration–drift response of the INMASPOL structure having seismic protection through PUFJs in PHASE 1 and then retrofitting with FRPU jackets in PHASE 2.

The external application of double-sided FRPU jackets on the OrthoBlock infill resulted in a remarkable top displacement ductility of the infilled RC frame A2R, with a negligible base shear reduction up to a 3.6% drift for push (+) and (−). FRPU jackets with highly deformable polyurethane impregnation resin may maintain an adequate bond with the surrounding RC frame. Further, they maintain an adequate bond with the brick infill substrate. In all cases, FRPU jacketing ensured the integrity of the infill and of the jacket, excluding total or partial collapse of the infill or of smaller parts.

The INMASPOL real-scale RC frame possesses a low base shear capacity and a high ductility to satisfy the aims of the shake table tests: (a) carry enough mass to lead the real-scale infilled structure to in-plane infill failure and allow for the investigation of the infill contribution at high ductility levels and up to failure; (b) suffer specially designed severe excitation for the out-of-plane performance of the infills. The real-scale RC structure with OrthoBlock infills and PUFJ highly deformable seismic joints exhibited a ductile top acceleration–drift behavior (which is equivalent to a ductile base shear–drift behavior) up to a 3.7% drift, without degradation of the top acceleration (base shear). No collapse of the infills tested in plane or out of plane after a 3.7% drift was evidenced. The damage to infills of type B could be repaired with emergency FRPU external jackets without any special treatment of the infill. After its emergency repair with FRPU (PHASE 2), the structure exhibited a rather linear elastic-like top acceleration–drift behavior (equivalent to a linear elastic base shear–drift behavior) up to 1.62%, without degradation of the top acceleration (base shear). The FRPU maintained the integrity of the damaged infills, and collapse was avoided. The abovementioned dynamic experimental results validate the advanced seismic protection provided by the 20 mm-thick PUFJ to the infill and the RC frame. An undesirable interaction was avoided, and the base shear drift behavior was remarkably ductile, while the potential of the structure was expected to be higher (tests at higher accelerations were avoided to prevent the structure from collapse and continue with PHASES 2 and 3). Similarly, the results in PHASE 2 validate the advanced retrofit of the predamaged infills by the FRPU jackets, while the potential of the structure was expected, again, to be higher.

The advanced FE analyses allowed for a comparative investigation of the analytical response of the bare RC structure (model 1) against analytical models 2 and 3. The infilled

structure with seismic protection developed a three times higher maximum acceleration (or base shear) than the bare RC structure at PHASE 1. The corresponding increase in the initial stiffness was similarly remarkable while maintaining the high displacement ductility, with a 3.7% horizontal drift. At PHASE 2, the FRPU retrofitted structure still revealed a higher initial stiffness when compared with the bare structure, while it could develop, at least, around double the maximum acceleration (base shear). Model 3 reproduced the FRPU repair effects despite the local brick damage. Broad infill regions (predamaged inregions cluded) were engaged through the interaction with the highly deformable FRPU jacket and the RC frame through the PUFJ. It seems that FRPU bridged the damaged brick infill areas and, together with the PUFJ, succeeded in causing a beneficial stress redistribution within the infill.

In the case the OrthoBlock infill with PUFJ protection is considered in the intervention for a weak bare RC frame, it can ensure a remarkable increase in the elastic stiffness and base shear while providing a desirable ductile P–δ behavior, with a drift as high as 3.7% (even after multiple earthquake excitations). Simultaneously, for the case under investigation, it prevents in- or out-of-plane collapse of the protected infills. Even if the structure suffers a drift as high as 3.7%, it may receive emergency retrofitting to maintain the integrity of the infill and increase its beneficial contribution to the RC frame.

The realization of a desirable ductile behavior of infilled frames through PUFJs of only 20 mm thickness (only 0.0087 of the height of the infill, compared with alternative proposals with detailing of 65 mm seismic joints or 90 mm sliding joints) and FRPU jacketing is of high importance. PUFJ, due to its high deformability and excellent bonding properties, constitutes a low-volume application (only 20 mm thickness of the joint) with simple detailing (only an interface layer). The application is straightforward in the retrofitting of existing walls (by injection) or in the construction of new walls with the use of prefabricated PUFJs. The polymer cures within hours (see [20]), and therefore it can serve as an emergency measure for retrofitting through injection or in new wall constructions (even with the construction of the prefabricated joints in situ ready to be used). No shear key detailing is required to exclude out-of-plane failure of the infill. The simplicity of the detailing, the low volume and the fast curing, compared with alternative seismic joint solutions such as the abovementioned ones presented in [6,22,23], reveal this solution's feasibility of practical application, economic advantages and fast full protection activation. Similarly, FRPU, due to the high-deformability polyurethane involved, can be applied without any prior treatment of the infill substrate, cures within hours and maintains the bond with the substrate despite extensive infill cracking during loading. Such advantageous alternatives may contribute to building collapse prevention as well as preventing in- and out-of-plane infill collapses. Both are common causes of detrimental human injuries or human loss during severe earthquakes. The developed FE models provided a unique insight on the variable interactions and effects of the innovative interventions and may serve as a solid basis for further analytical investigations such as the utilization of combined retrofits.

**Author Contributions:** Conceptualization, T.R.; investigation, T.R., V.V., T.F. and E.A.; writing review and editing, T.R., V.V., T.F. and E.A.; supervision, T.R.; project administration, T.R.; funding acquisition, T.R., T.F. and E.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning 2014–2020» in the context of the project "Advanced Material Retrofits of Infilled Framed Reinforced Concrete Structures with Predamages Against Collapse" (MIS 5050146).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Assessment of Different Retrofitting Methods on Structural Performance of RC Buildings against Progressive Collapse**

**Barham Haidar Ali 1,\*, Esra Mete Güneyisi 1 and Mohammad Bigonah 2**

**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Progressive collapse refers to the spread of primary local damages within the structure. Following such damages due to removing one or more load-bearing columns, the failure spreads in a chain and causes structural failure. This study represents a report investigating the influence of various retrofitting methods on the progressive collapse resistance of multistorey reinforced concrete (RC) structures. To this end, eight different cases were considered. The first one included a thirteenstory RC moment-resisting frame (bare frame), while the others were frames upgraded with the application of X-brace, diagonal brace, inverted V-brace, the viscous damper in the central bay, viscous damper in two inner bays, viscous damper only in certain stories and carbon fiber reinforced polymer. Moreover, three different column removal scenarios were considered as a column failure at stories one, six, and thirteen of each case study structure. The analysis results indicated that the redistribution of loads after the column's failure and the RC buildings' collapse resistance was increased depending mainly on the type of approach used for upgrading the bare frame.

**Keywords:** column removal; non-linear analysis; progressive collapse; reinforced concrete frame; retrofitting

#### **1. Introduction**

Progressive collapse refers to the spread of primary local damages within the structure (also known as disproportionate collapse) is a high-impact, low-probability event. After the collapse of the Ronan Point Building in London in 1968, the Murrah Federal Building in Oklahoma City in 1995, and the World Trade Center Towers in New York City in 2001, the structural engineers and government organizations became concerned about progressive collapse [1,2]. Because it is hard to describe a potentially hazardous load that causes localized damage to a building, it is common to use the decoupling technique to suppose whether the remaining structure can bridge over the removed components by removing a supporting column or wall. The remaining structures would be subjected to linear static, linear dynamic, non-linear static, and non-linear dynamic analysis [3]. Energy equilibrium [4] or equation of motion can connect dynamic and static performance [5].

Researchers have recently become interested in the effect of secondary components, such as bracing, on progressive collapse performance. The strengthening of reinforced concrete (RC) frame structures against progressive collapse have various challenges: (1) The application of typical strengthening methods for RC frame construction continues to be researched because progressive collapse is a significant deformation behavior; (2) The degree of strengthening against progressive collapse is significant, which could result in "strong beams and weak columns" and have an impact on seismic performance; (3) Anchorage is the primary issue in strengthening reinforced concrete structures against progressive collapse, and dependable and rapid construction anchorage solutions for minimizing progressive collapse strengthening are urgently needed [6].

Retrofitting is not a common practice to make an old system compliant with the new code's rules, as this option is not cost-effective. Alternatively, to ensure a set degree of

**Citation:** Ali, B.H.; Mete Güneyisi, E.; Bigonah, M. Assessment of Different Retrofitting Methods on Structural Performance of RC Buildings against Progressive Collapse. *Appl. Sci.* **2022**, *12*, 1045. https://doi.org/10.3390/ app12031045

Academic Editor: Pier Paolo Rossi

Received: 27 December 2021 Accepted: 5 January 2022 Published: 20 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 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/).

collapse or to avoid the building collapsing entirely, it is advised that retrofit goals for a structure prone to progressive collapse be based on performance-based criteria. Steel braces are often employed to produce lateral stiffness and resist lateral loads in steel buildings [7–9]. Seismic retrofitting with steel bracing for existing RC frames has also received much interest due to the ease of installing steel braces [10–12]. In another study by Bigonah et al. [13], which evaluated the performance of infill types, the results show that adding infill reduces vertical displacement and improves redistribution of forces against progressive collapse. Steel braces impact on the resilience of structures to progressive collapse has recently attracted researchers' attention through two-dimensional numerical models. In addition, they investigated the progressive collapse of 10-storey braced steel frames designed following different seismic intensities and found that the frame with concentric braces is more likely to collapse than the frame with eccentric braces [14]. The effective techniques of modern strengthening methods of RC frames against progressive failure are studied, and the results show that increasing the percentage of rebar reduced vertical displacement [15]. The structural behavior of three-dimensional (3d) 20-storey braced steel frames is investigated and discovered that removing a column at a higher story increases the likelihood of the frame collapsing [16,17]. Another study experimentally investigated the progressive collapse resistance of five one-fourth scaled two-bay by threestory RC frames strengthened by four types of steel bracing [18]. They found that basically, all bracing can improve progressive collapse resistance, with eccentric X braces performing the best. Steel bracing is either designed for seismic design or lateral stability. The steel braces are only situated at one or several defined spans but are continuous in elevation from the first to the thirteenth floor. Costanzo et al. [19] reviewed the design rules and requirements for XCBFS to simplify the design and improve the ductility and waste capacity of the structural system, applying bracing on the roof floor to obtain a structural response with proper distribution of plastic deformation section with height. At the same time, it can be ignored for three-story structures. D'Aniello et al. and Costanzo et al. [20,21] also investigated the effect of beam flexural stiffness on the seismic response of concentric braces. The results show that the higher the stiffness, the lower the drift ratio occurs. As a result, the deformation in the brace is limited under compression. The braces can add progressive collapse resistance if the removed column is positioned in the braced span; otherwise, their contribution is minimal [12,16,17]. This means that steel bracing designed to withstand seismic loads and provide lateral stability may be incapable of enhancing structural robustness. On the other hand, steel bracing is a viable alternative for strengthening existing buildings against progressive collapse, and the best approach to design such braces requires more research.

Similarly, the effectiveness of proposed carbon fiber reinforced polymers (CFRP) and glass fiber reinforced polymers (GFRP) strengthening strategies for improving progressive collapse behavior using a series of flat slab substructures were evaluated [22]. Moreover, the efficiency of ten RC beams employing CFRP anchors and/or U-wraps is studied [23]. Hence, CFRP is used to improve the continuity of RC beams to shift the load carried by the damaged column to an intact zone and therefore control the spread of progressive collapse [24]. They found that beams with discontinuous reinforcement improved by roughly 55 to 60%, while beams with continuous reinforcement improved by 109%.

Compared to other retrofitting methods, such as bracing and CFRP, there have been fewer researches on the influence of viscous dampers retrofitting. Viscous dampers often meant to reduce building vibration caused by wind or earthquakes, are another type of retrofit to improve a structure's resistance to progressive collapse. Kim et al. [23] examined the progressive collapse resistance of structures equipped with viscous dampers, often installed to dampen wind- or earthquake-induced vibration.

In this study, an attempt is made to evaluate the influence of various retrofitting systems on the progressive collapse resistance of a multi-storey RC building. For this purpose, eight different cases were taken into account. The first one contained a thirteenstory RC moment-resisting frame (bare frame) while the others were frames upgraded

with the use of X-brace, diagonal brace, inverted V-brace, the viscous damper in the central bay, the viscous damper in two inner bays, viscous damper only in certain stories and carbon fiber reinforced polymer (CFRP). Besides, three different column removal scenarios were considered as a column failure at stories one, six, and thirteen. Non-linear dynamic analysis was conducted by using a finite element program. Parametric study results for each case were provided by considering the shear, axial, and moment of columns adjacent to the collapsed column. The moment and shear forces for the beam above the collapsed column were also investigated with the story displacements and building performance levels reported after the vertical member's loss. Finally, all the investigated parameters for each case were evaluated and discussed comparatively.

#### **2. Methodology**

#### *2.1. Description of Structural Models*

The structure studied in this research is a 13-story RC building (Figures 1 and 2). The structure is two-dimensional (2D), and it consists of five bays with a 6 m length span. The height of each story is 3.2 m. Dead and live loads are 4 and 2 kN/m2, respectively. The section of the beams for all cases is 500 mm × 350 mm. The column sections from stories 1 to 4, 5 to 9, and 10 to 13 are 600 mm × 600 mm, 500 mm × 500 mm, and 400 mm × 400 mm, respectively. The compressive strength of the concrete is 25 MPa, and the yield strength of the steel bar is 392 MPa according to the specified factory. The structure is designed following the framework of ACI Committee 318 (2014). To evaluate the behavior of the RC buildings against progressive collapse eight different cases were taken into consideration. The first one is RC moment-resisting frame (bare frame), whereas the others are the upgraded frames, namely, X braced frame, diagonally braced frame, inverted V-braced frame, viscously damped frame in the central bay, viscously damped frame in two inner bays, viscously damped frame only in certain story and frame with CFRP. Then, three different column removal scenarios were adopted by considering the failure of the central column at stories one, six, and thirteen. Evaluation and comparison of the structural response of the eight frames against progressive collapse have been conducted. Table 1 defines the cases studied.

**Figure 1.** Plan view of the RC building.

In the case of the frames upgraded with braces, common configurations for concentric bracing systems including inverted-V (chevron)-type, X-type, and diagonal braces were considered. The force-displacement relationship of braces based on the uniaxial phenomenological model, adopted in Federal Emergency Management Agency (FEMA- (356)) [25], in which Δy and Δcr are the yielding and buckling displacements, and Py and Pcr are the tension and compression forces, respectively. The braces are hollow steel tubes, and sections are 2UNP14 and 2UNP13 for stories 1 to 6 and 7 to 13, respectively. The analyzed

structural models are subjected to the loss of the first, sixth and thirteenth-floor center column, in which the structure deforms symmetrically, and the full capacity of bracing is activated. Figure 3 shows the various bracing configurations to be analyzed.

**Figure 2.** Elevation view of the RC building.

**Table 1.** Definitions for the different frames.

**Figure 3.** (**a**) X-braced frame; (**b**) Diagonally braced frame, and (**c**) Inverted V-braced frame.

The diagonal brace or chevron brace is the traditional configuration for viscous dampers. In the case of the frames with viscous dampers, the former one was used. The cases for viscous dampers are viscously damped frame in the central bay, viscously damped frame in two inner bays, and viscously damped frame only in a certain story, as shown in Figure 4. Damper's capacity has been determined according to the study of Cimellaro and Retamales [26].

**Figure 4.** (**a**) Viscously damped frame in the central bay, (**b**) viscously damped frame in two inner bays, and (**c**) Viscously damped frame only in certain stories.

In the studied structure, the effect of viscous damping with 15% damping has been investigated. To determine the required damping of the structure to reach the damping percentage of the target, the stiffness of the whole structure should be determined [26]. First, the triangular pattern of the base shear force and the level of drifts of each story are calculated. Then, with the help of the sheer force of each story and the corresponding drift with the same shear force, the shear stiffness of each story can be obtained. Finally, the total damping coefficient that must be added to the structure to achieve the target damping can be calculated [27].

In the case of the frames upgraded with carbon fiber reinforcement polymer (CFRP), the CFRP is assumed to be warped around the two sides and bottom of beams. The ultimate strength is 3200 MPa, in the longitudinal direction of fibers, and the elastic modulus is 210,000 MPa. The thickness of the CFRP wrap is 1.4 mm. An investigation of the effectiveness of the proposed CFRP strengthening schemes in mitigating the progressive collapse of the structures of this study is made.

The nominal shear strength of an RC section (*Vn*) with CFRP is expressed in Equation (1)[28]:

$$V\_n = V\_\mathbb{C} + V\_\mathbb{S} + V\_f \tag{1}$$

*VC* is the shear strength of the concrete, *VS* is the shear strength of the steel reinforcement, and *Vf* is the shear contribution of the CFRP. The design shear strength, *Vn*, is achieved by multiplying the nominal shear strength by a strength reduction factor for shear, the factor for steel and concrete contribution from (ACI 440.2R-02) [28] is 0.85 [29], and the factor for CFRP contribution is suggested to be 0.70. Equation (2) [28] presents the design shear strength.

$$
\phi V\_n = 0.85(V\_\varepsilon + V\_s) + 0.7V\_f \tag{2}
$$

The expression to compute CFRP contribution is given in Equation (3) [28]. This equation is similar to steel shear reinforcement and is consistent with (ACI 440.2R-02).

$$v\_f = \frac{A\_f \times f\_{f\varepsilon}(\sin\theta + \cos\theta) \times d\_f}{S\_f} \le \left(\frac{2\sqrt{f\varepsilon'} \times b\_w \times d^2}{3} - V\_s\right) \tag{3}$$

#### *2.2. Removal of the Column and Details of the Analysis*

The removal process of the column should be such that the effect of a dynamic effect on the structure is seen due to the shock caused. A method to consider collapse ability in SAP2000 software was used to do this. The number of joints and elements is depicted in Figure 5. To simulate the sudden removal of columns in different scenarios in non-linear analysis, dead and live loads were first applied from 0 to 5 s, and then, they were removed, and the structure response was reviewed after this moment up to 10 s. Figure 6 shows the removal of the inner columns at different story levels. The dynamic amplification factor in the dynamic analysis is not recommended by both guidelines (GSA and UFC). To apply dynamic analysis, prior to column removal, axial force acting is calculated. Then the column is replaced by point loads equivalent to its member forces [1,2,30].

**Figure 5.** Numbering of elements and joints.

**Figure 6.** Column removal scenario in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

#### **3. Results and Discussion**

In this section, the status removing columns are investigated, with the amount of displacement and the redistribution forces after applying the column removal scenario. Non-linear dynamic analysis (NDA) is done for inner column removal in the first, sixth and thirteenth floors, and results are presented here. Four graphs are plotted in SAP2000: vertical displacement vs. time, axial force vs. time, bending moment vs. time, and shear vs. time. Vertical displacement is taken at the point where the column was removed. The beam with maximum axial force and bending moment vs. time is taken for plotting.

All of the examples were subjected to a 2D frame analysis. As illustrated in Figures 7–14, all 2D frame analysis cases showed partial progressive collapse. The collapse zones in the 2D frame analysis were estimated directly after the collapse of beams connected to the removed column. The 2D frame analysis revealed that the collapse spreads to all levels of the structure, indicating that the structure has a high risk of progressive collapse and should be modified, according to the General Service Administration (GSA). In addition, because the main support was removed, the static system of beams became longer, resulting in collapse due to insufficient reinforcing.

**Figure 7.** Hinge formation in the moment-resisting frame (Bare frame) exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 8.** Hinge formation in the X braced frame exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 9.** Hinge formation in the diagonally braced frame exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 10.** Hinge formation in the inverted V-braced frame exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 11.** Hinge formation in the viscously damped frame in central bay exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 12.** Hinge formation in the viscously damped frame in two inner bays exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 13.** Hinge formation in the viscously damped frame only in certain stories exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

**Figure 14.** Hinge formation in the frame with CFRP exposed to column removal in (**a**) story one, (**b**) story six, and (**c**) story thirteen.

#### *3.1. Performance Level of the Frames*

The damage levels of members were analyzed for the non-linear analytic techniques using various performance levels such as immediate occupancy (IO), life safety (LS), and collapse prevention (CP). The performance level of the structure should not exceed collapse prevention according to GSA rules, or structural members will be classified as seriously failed [1]. In all cases, the plastic hinge formation is illustrated in 2D frames.

Figure 7 shows the removal of columns on different stories in a moment-resisting frame (bare frame). After removing the column on the first floor, all the beams in the span were failed at collapse prevention, and the span completely collapsed at all floors above. The removal of the column on floor six caused the beams to fail and reach the life safety point at all floors above, and the structure could not redistribute the forces well. Moreover, removing the column on floor thirteen puts its beam almost in a state of complete collapse. The hinges of the beams in the affected spans reach the failure point (red-colored hinge), as shown in Figure 7 in all the cases of column removal scenario. The failure of one column leads to the collapse of all the members in the affected span.

Steel bracings are used as a remedy to provide resistance against progressive collapse [31]. Although few bracing members fail by buckling in compression, a bracing system can strengthen the building to resist progressive collapse. For example, Figure 8 shows the removal of columns at different stories by adding an X brace. After removing a column and a brace, the function of the beams was out of operational performance.

The plastic hinges generated in the beams meet the acceptability level. The plastic hinge creation occurred on the diagonal braced element inside the collapse range, which is considered compression failure of the brace, as shown in Figure 8a.

In Figure 9, the use of one-way bracing on both sides improved the performance of the whole structure. The plastic hinge did not enter the non-linear area because the structure's chain function was well performed. However, even the performance of the brace did not enter the operational performance levels. As seen in Figure 9a,b, the plastic hinge formation has begun to develop in brace members. As a result, plastic hinges formed in columns and beams and were disseminated over particular building members within the immediate occupancy area. The lateral stiffness is improved as well compared with other braced frames.

In Figure 10, the use of inverted V-bracing in the structure improved the performance of the structure against progressive collapse. Although the column was removed at higher stories, the structure had a better performance, and the concentration of stiffness at the removed point improved the redistribution of forces and the chain performance of the structure. The inverted-braced arrangement increases the constraint level at the beam end, allowing catenary action. The bracing system generated a new load transfer path. The horizontal braces distributed certain gravitational stresses to the surrounding structures then carried to the foundation via the vertical braces. Following compression brace buckling, certain columns buckled before tension braces yielded, culminating in brittle failure modes. When a column adjacent to the braced bay was removed, the constructions with only single-bay braces proved extremely fragile. The progressive collapse can be avoided in this scenario by designing the frame with braces.

In Figure 11, the frame is called a viscously damped frame in the central bay; a viscous damper was used diagonally in a span. The results showed that, as shown in Figure 11a, the plastic hinges in beams on the third and fourth floors reach within range of collapse and that the application of a viscous damper prevented significant oscillation and shock to the structure. In addition, plastic rotation in the beam ends was lowered to below the immediate occupancy state, and plastic hinges were removed in numerous places.

The application of viscous dampers in two inner bays enhanced the structure's tensile performance, whereas the performance of the beams improved when compared to the viscously damped frame in the central bay example, as shown in Figure 12. As shown in Figure 12a,b, the plastic hinge creation in the area of column removal (the connection of beam and column removal) is observed. The plastic hinge formation is more common in the structure's vertical parts.

Figure 13 shows viscously damped frame only in certain stories based on the method of Cimellaro and Retamales [26], the most optimal case in 3 stories was used. The results show that it had little effect on the performance of the structure and the redistribution of forces was not well done and the plastic hinges were out of the collapse prevention.

Figure 14 shows a frame with CFRP, which uses a CFRP layer in all beams. The results showed that the redistribution of forces and tensile performance in the beams was fairly distributed, increased the structure's strength, and improved the chain performance in the beams. Moreover, relatively low cost created the best performance in the whole structure against progressive collapse. The plastic hinge formation disperses mostly on the column, which is in a state of immediate occupancy.

#### *3.2. Frame Displacements Due to Column Loss*

For internal column loss in the first, sixth, and thirteenth stories, the numerical findings from non-linear dynamic calculations up to 10 s are given in Figures 15–17. The maximum permitted ductility and/or rotation limits of beams are verified following GSA. For RC structures, GSA refers to ASCE 41 [32] approval criteria for non-linear analysis to assess the damage on a structure due to a column loss. If beam end rotations in any of the frames investigated herein surpassed the acceptance standards, then it would indicate the maximum permissible ductility of the beam, as specified in [1,32]. It is seen that the maximum displacement is varied around 45 cm for the braced frames, as indicated in Figure 15, due to the rapid inner column loss in story one. When compared to other types of frames, the abrupt columns in the first, sixth and thirteenth stories do not affect the displacement of an X braced frame.

On the other hand, the displacement of X braced, and inverted V-braced frames are often smaller than that of other types of frames. Moreover, as given in Table 2, the momentresistant frame (bare frame) is observed to be failed for all column removal scenarios. The discrepancies in displacement values for the others are varied depending mainly on the strengthening method used.

**Figure 15.** Vertical displacement at column removed position due to column loss in story one.

**Figure 16.** Vertical displacement at column removed position due to column loss in story six.

**Figure 17.** Vertical displacement at column removed position due to column loss in story thirteen.

**Table 2.** Vertical displacement after removing a column in the stories.

Due to the removal of the column on the first story as shown in Table 2, the maximum vertical displacement is related to case 7 and also case 1 is damaged in all floors and the best performance is related to case 3, while in the 6th floor the most Vertical displacement is related to case 7 and the lowest is related to case 3 with a value of −8.63 mm. Therefore, in addition to removing the column on the top floor, there was a breakdown in case 3 in case 7.

#### *3.3. Force Distribution Due to Column Loss in Beams Next to Column Removal*

Bending moment and shear generated by sudden column loss were greater for story one beams than for frames with CFRP (Case 8). This is due to the higher flexural stiffness of the CFRP-framed structure, which captivates more forces. Figures 18 and 19 depict the bending moment and shear on the beam caused by column loss for the first and sixth stories. Bending moments for the bare frame and various retrofitting frames are less than for CFRP framed first and sixth stories, as demonstrated in Figure 19. This is because the joint stiffness of CFRP frames attracts more force. Apart from Case 8, forces are dispersed evenly throughout all levels in all other situations. As a result, having a CFRP framed structure reduces the bending moment demands in a simple jointed beam, increasing the CFRP frame's progressive collapse resistance owing to column loss.

**Figure 18.** Beam behavior after column removal in story one: (**a**) shear and (**b**) moment.

**Figure 19.** Beam behavior after column removal in story one: (**a**) shear and (**b**) moment.

In the first and sixth stories, the beam shear force for the bare frame (Case 1) is less than the other cases (see Figures 18 and 19). This is because the joint stiffness of CFRP frames attracts more force. In other circumstances, pressures are evenly dispersed overall plot levels. As a result, having a CFRP framed structure minimizes the axial force demands in a simple jointed beam, enhancing the CFRP frame's progressive collapse resistance due to column loss. The bending moment value for the viscously damped frame in two inner bays on floor thirteen is more than the bending moment for CFRP framed, as shown in Figure 20. Because of the stiffness, Case 8 performs well against progressive collapse, although there are many moments in the column adjacent to the brace, necessitating the employment of a less rigid brace. Viscous dampers were able to lower bending moment forces and provide effective energy absorption in the circumstances where they were applied.

**Figure 20.** Beam behavior after column removal in story thirteen: (**a**) shear and (**b**) moment.

As shown in Table 3, which was compared with the removal of the column on the first floor in case 8, in beam number 118, the highest shear force is related to case 8, and the lowest is related to case 1; however, in the bending moment model is the highest force in case 8 and the lowest is related to case 3. As Figure 19 shows and values are illustrated in Table 4, after removing the column on the 6th floor, the highest shear force is created in case 8, while the lowest is related to case 3. Therefore, the bending moment force is related to case 3.

**Table 3.** Result force story 1 for element 118.

**Table 4.** Result force story 6 for element 123.

As shown in Figure 20 and tabulated in Table 5, case 8 has the highest shear force, and its lowest shear force is related to case 7 with a value of −2622.87 N. In the case of bending moment, when it is proven after the oscillation, the highest bending moment is related to case 4; however, the lowest is related to case 7 and its value is 20,838.58 N.

**Table 5.** Result force story 13 for element 130.

As shown in Figure 21 and depicted in Table 6, after removing the first-floor column, the results show that the highest axial force in the case of Case 4 is with the −1,009,521 N value, whereas the lowest in case of Case 6 is that of 18,863.2 N in the case of flexural anchor, is the most applied force associated with Case 5 and the lowest in case of Case 7.

As shown in Figure 22 and Table 7, after removing the column in the 6th floor, the maximum axial force created in the column in case 3 is −594,235 N, while in the shear force created in the column, the maximum is related to case 2, and in the case of bending moment, most of it is related to case 2, although it has good performance in some members and has enhances improved the chain performance as well as the forces in the members.

**Figure 21.** Column behavior after column removal in story one: (**a**) axial force, (**b**) shear, and (**c**) moment.

**Figure 22.** Column behavior after column removal in story six: (**a**) axial force, (**b**) shear, and (**c**) moment.

**Table 7.** Result force story 6 for element 58.

In Figure 23 and Table 8, the results show that the maximum bending force generated in Case 2 is 92,318.4 N, while the lowest bending force is in Case 3. The lowest is related to case 3. In the case of shear force, the highest force is related to case 8, and the lowest is 5244.2 N in case 3.

**Figure 23.** Column behavior after column removal in story six: (**a**) axial force, (**b**) shear, and (**c**) moment.

**Table 8.** Result force story 13 for element 65.

#### **4. Conclusions**

In this study, the assessment of different retrofitting approaches on the structural performance of RC buildings against progressive collapse was studied by comparing the eight different cases. The following conclusions are drawn from the results of the analysis:

**Author Contributions:** Conceptualization, B.H.A.; methodology, B.H.A.; software, B.H.A.; validation, M.B and B.H.A.; formal analysis, B.H.A.; investigation, B.H.A. and E.M.G.; resources, B.H.A. and M.B; writing—original draft preparation, B.H.A. and M.B.; writing—review and editing, E.M.G.; visualization, B.H.A.; supervision, E.M.G.; project administration, E.M.G.; funding acquisition, B.H.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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**4. Experimental Evaluation**

The proposed solution identifies context-aware sociability patterns using incremental unsupervised learning. Consequently, applying metrics commonly used to evaluate learning models is challenging because there is no ground truth available to compare results. By considering this, we evaluate the proposed solution's feature to consistently recognize sociability patterns for modeling social routine and behavior changes.

In [20], we performed the following: (i) a comparison of the similarity between the sociability patterns identified with the intervals recognized by Gaussian Mixture Models (GMMs); (ii) an analysis of the contribution of context-aware sociability patterns to understand the monitored individual's social routine. Here, we performed a more in-depth evaluation to recognize the proposed solution ability to identify context-sensitive sociability patterns that model social behavior and detect behavioral changes.


*<IP_ADDRESS> Carbon nanomaterials*

Carbon nanomaterials including graphite, CNT and graphene, have been widely used in fabricating wearable electromechanical sensors. Graphite is a conductor and attracts more and more attentions with development of pencil-on-paper electronics [54]. Graphite flakes in pencil lead is easy to be deposited on paper surface by the physical friction between lead tip and porous cellulose paper. Moreover, structural edges in graphite flakes results in a strain-induced resistance variation of pencil traces, making them suitable for strain sensor. The contact area between graphite flakes increases by compressing the trace and decreases when the tension strain is applied, leading to the decrease or increase of resistance. The wearable strain sensor fabricated with pencil-on-paper shows high GF up to 536.61 [27].

CNT are allotropes of carbon with a cylindrical nanostructure, which possesses excellent electrical conductivity and mechanical properties. It has been demonstrated that a single CNT shows strong structural effect and has a GF higher than 1000. However, wearable electromechanical sensor fabricated with single CNT is difficult and hard to realize mass production. Thus, CNT is usually intermingled into polymer substrates and its excellent conductivity plays an important role in electromechanical sensor construction. Wearable capacitive and piezoresistive electromechanical sensors have all been demonstrated by depositing CNT onto substrate or forming composite with polymers. For the piezoresistive composite sensor, the resistance change is mainly due to the strain-varied intertube tunneling resistance. The maximum GF can be achieved when the concentration of CNT is near the percolation threshold (PH). When the CNT loading is much lower than PH, the distance between adjacent CNTs is larger than their cut-off distance and there is almost no tunneling resistance. On the contrary, when CNT loading is much higher than PH, the CNTs can form dense 3D network and most of CNTs would connect with each other, resulting in a small intertube resistance. In this case, the contact resistance dominates the behavior, which will significantly decrease the GF. For piezoresistive film sensor, the variation of resistance gains almost a tenfold increment compared with nanocomposite type, but its cycle durability is not favorable enough because of unexpected cracks and desquamations. CNTs are also used to form wrinkle structure on a soft substrate via heating of the film or a prestrained substrate and are utilized to fabricate high-performance wearable strain sensor.

Due to outstanding electroconductibility, excellent mechanical properties, great thermal characteristic and optical transmittance, graphene becomes the most promising sensing material for the development of wearable electromechanical sensor [28]. Graphene has been developed as electrode material for capacitive sensor and filler for piezoresistive sensor. A variety of graphene electromechanical sensors with different forms have been demonstrated, including porous foams, flakes, ripples, woven fabrics, and films. For example, the GWF film, which can be fabricated either by CVD or dip coating, consisted of many overlapping microribbons and features a good trade-off between sensitivity and stretchability, making it suitable for wearable strain sensors. It shows fascinating stretchability (a tolerable strain up to 57%) and sensitivity (GF = 416 for 0 < ε < 40%, and GF = 3667 for 48 < ε < 57%) by encapsulating the obtained GWFs in natural rubber latex [29].


**6. Conclusions**

We proposed an auditory card game system that presents the card's contents by sound, towards playing equally with others, regardless of whether they have a visual impairment or not. This is one of the solutions that presents public information of board games. Although this proposal cannot improve the accessibility of all board games, it contributes to expand the range of inclusive board games for the visually impaired. Furthermore, clarifying the impact of element of the system to the players will greatly assist in designing an appropriate board game using the proposed system. The purpose of this paper is to determine whether the game allows for fair competition for people with visual impairments and to clarify the effects of the valuable parameters of the system on the players. In the system evaluation, we developed "Auditory *Uta-Karuta*" and verified the usefulness of this system by having the game played by visually impaired people, sighted people, and sighted people with a blindfold. The purpose of this experiment is to test the applicability of auditory card game system to board games. We found that "Auditory *Uta-Karuta*" has the potential to be played by all players, regardless of whether they have a visual impairment or not. The following experiment was conducted to measure the effect of the design of the audio cue on the player in the proposed system, and several major considerations were obtained.

These results show that it is necessary to design audio cues appropriately due to the characteristic of public information indicated by the components in order to make the auditory card game system effective. In particular, for a board game that requires accurate information presentation for players, such as *Uta-Karuta*, it is considered that playing representational sounds one by one is effective. However, in Section 4, despite the game design described above, the sighted players had an advantage, so it would be effective to adopt a vertical layout that gives an advantage to the visually impaired.

As described above, the results of the experiments in Section 5 can be used to create an appropriate board game design that allows players with different visual states to achieve the same level of game performance. However, the enjoyment of a game depends not only on the winning rate, but also on factors such as strategy and communication. Therefore, further experiments will be needed to construct a board game that is fun for players regardless of whether they have visually impaired or not, with a view to the qualitative factors that may influence the enjoyment of the game. In addition, as mentioned in Section 5.6, the results of this study can even be used for games in which private information is used, and we will

consider applying them to the case of games that include private information in future research. Furthermore, in order to reduce the cost and broaden the range of board games that can be supported, it is necessary to consider not only the iPod touch, but also many other component shapes and types.

**Author Contributions:** Methodology, H.M., N.K., and K.Z.; software, H.M.; investigation, H.M., N.K., and H.E.B.S.; writing—original draft preparation, H.M.; writing—review and editing, N.K., H.E.B.S., and K.Z.; supervision, K.Z.; project administration, K.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by Ethics Review Committee of the University of Faculty of Engineering, Information and Systems, University of Tsukuba (2019R314, 24 May 2019).

**Informed Consent Statement:** Informed consent was obtained from all participants in the study.

**Conflicts of Interest:** The authors declare no conflict of interest.


**3. Carl Brans' "spectator matter"argument**

Brans did his doctoral work at Princeton in the late 1950s. His doctoral supervisor was the noted experimentalist, Robert Dicke. After passing his qualifying exam, Dicke tasked Brans with investigating the question of as the origin of inertia in general relativity, as Dennis Sciama and others had made "Mach's principle" a central question in general relativity several years earlier. When Brans read Einstein's remarks on Machian inertia in Einstein's 1921 comments quoted above, he noted a problem. If gravitational potential energy due to nearby matter contributes to the rest masses of test particles, the Equivalence Principle is violated. This is not a minor problem. The Equivalence Principle is the bedrock of general relativity. The solution to this problem adopted in Brans' graduate school days was the imposition of a "coordinate condition". (A "gauge" solution is/was not available as general relativity is not a gauge theory).

As Brans, responding to several published papers on Mach's principle, later wrote in 1977 [4]:

*Over the years, many and varied expressions of Mach's principle have been proposed, making it one of the most elusive concepts in physics. However, it seems clear that Einstein intended to show that locally measured inertial-mass values are gravitationally coupled to the mass distribution in the universe in his theory. For convenience I repeat the first order geodesic equations given by Einstein to support his argument:*

*[Brans inserted here Einstein's equations displayed above.]*

*… Einstein's claim is that "The inertial mass is proportional to l*ð Þ þ *σ , and therefore increases when ponderable masses approach the test body.*

Brans pointed out that having the masses of local objects, the unit mass test particle in this case, depend on their gravitational potential energies acquired by interaction with spectator matter must be wrong. Were it true, then the electric charge to mass ratios of elementary particles for example would depend on the presence of nearby matter. If this were true, gravity could be discriminated from accelerations without having to check for the presence of spectator matter by going to the window in a small lab and looking out to see if one were on Earth, or in a rocket accelerating at one "gee" in deep outer space– a violation of the Equivalence Principle. From this, Brans inferred that

… *global, i.e., nontidal, gravitational fields are completely invisible in such local standard measurements of inertial mass, contrary to Einstein's claim … Einstein ought to have normalized his local space-time measurements to inertial frames, in which the metric has been transformed approximately to the standard Minkowski values, and for which distant-matter contributions are not present. [Emphasis added.]*

This is the "coordinate condition" required by Brans' work: that the coordinates be compatible with the assumed approximate Minkowski metric applicable in small regions of spacetime. Since the absence of gravity is presupposed for Minkowski spacetime, this amounts to the assumption that the Newtonian potential due to exterior matter in such small regions of spacetime is effectively everywhere/ when equal to zero. That is, the locally measured value of the total Newtonian gravitational potential is universally zero. This certainly makes the localization of gravitational potential energy impossible in general relativity, a now widely accepted fact. And where there is effectively no gravity, there can be no gravitational induction of inertia. Accordingly, it would seem that Brans'spectator matter argument makes Machian gravitationally induced inertia incompatible with general relativity.


**6. Complications**

Acute complications commonly include local features, consisting with dry and moist skin desquamation, vaginitis, cystitis, and proctitis. Management of these complications varies between anti-inflammatory medications and anti-microbial drugs given for prophylaxis.

Brachytherapy side effects are mainly due to neighboring organ toxicity and include vaginitis, cystitis and uterine perforation.

Late complications include vaginal stenosis, recto-vaginal and vesico-vaginal fistula and intestinal perforation.


**4. Conclusions**

This study analyzed the process of manual picking of tea buds and investigated the mechanical functioning and mechanic paths for bionic tea-bud picking. The bionic picking mechanics paths obtained herein can be used to determine the structural design of a lowdamage, fast-picking mechanism to use for tea shoots. The main findings of this study are as follows:

**Author Contributions:** Conceptualization, K.L., Z.W., C.C. and X.Z.; methodology, K.L., Z.W., C.C. and K.Q.; software, K.L. and M.A.; validation, K.L., X.Z. and Z.W.; formal analysis, K.L.; investigation, K.L.; data curation, K.L.; writing—original draft preparation, K.L.; writing—review and editing, K.L., Z.W., C.C. and K.Q.; supervision, K.L. and M.A.; funding acquisition, Z.W. and K.Q. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key R&D Program of China [grant number 2021YFD1601102] and by the National Natural Science Foundation of China [grant number 52105239].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable. **Acknowledgments:** The authors would like to thank Zhengmin Wu from State Key Laboratory of Tea Plant Biology and Utilization for providing equipment and technical support during the experiments. We also thank other colleagues in the laboratory such as Kuan Qin, Xuenchen Zheng, and Minhui An for their help in the experiments.

**Conflicts of Interest:** The authors declare no conflict of interest.


**5. LED Therapy automation using an embedded system integrated with a control software**

The main goal here was to provide a control interface of the therapy between the healthcare professional and the patient, giving them the possibility to monitor the phototherapy ses‐ sions progress and to treat the patient in a simple and effective way.

There are already lots of resources available in the market that use LEDs for skin disease treatment, like skin cancer or even aesthetic purposes, among others. When a new treatment is discovered,the creation of a new essay is necessary and therefore a new productis created. This project proposes a solution for this problem integrating hardware with control software. With the control software acting over the embedded system, it's possible to program new assays for each treatment; acting directly overthe LED's, and dynamically minimizing the costs over new products every time a new treatment is discovered

### **5.1. System overview**

The system is divided into two parts: the embedded system and the control. The embedded system contains a microcontroller, a LED board and an Ethernet Module for communication with the application [12]. The control consists of a database server and an application, as shown in Figure 12.

**Figure 12.** Automation of phototherapy with high brightness LEDs using an embedded system integrated with a soft‐ ware control.

Through the control application, it is possible to register a patient or start a treatment session. The treatments are mapped to the database as essays that determine the variable values for each pathology. The variables are: the colors and the time of firing the LED arrays [25]. The communication between Embedded System and Application control is possible through the Ethernet Protocol [16].

#### **5.2. System model**

The voltage produced on the LED was 3.8V and current of the LEDs around 580mA. The values

**5. LED Therapy automation using an embedded system integrated with a**

The main goal here was to provide a control interface of the therapy between the healthcare professional and the patient, giving them the possibility to monitor the phototherapy ses‐

There are already lots of resources available in the market that use LEDs for skin disease treatment, like skin cancer or even aesthetic purposes, among others. When a new treatment is discovered,the creation of a new essay is necessary and therefore a new productis created. This project proposes a solution for this problem integrating hardware with control software. With the control software acting over the embedded system, it's possible to program new assays for each treatment; acting directly overthe LED's, and dynamically minimizing the costs over new

The system is divided into two parts: the embedded system and the control. The embedded system contains a microcontroller, a LED board and an Ethernet Module for communication with the application [12]. The control consists of a database server and an application, as shown

**Figure 12.** Automation of phototherapy with high brightness LEDs using an embedded system integrated with a soft‐

obtained were close to the simulation and design [11].

products every time a new treatment is discovered

sions progress and to treat the patient in a simple and effective way.

**control software**

242 Advances in Bioengineering

**5.1. System overview**

in Figure 12.

ware control.

In this section the prototype details will be shown, such as: the application operation, embed‐ ded system operation and the database server details [16].

#### *5.2.1. Application*

The control application was written in JAVA language. The application aims to perform the user interface with the proposed system. Through the application the user can perform the following tasks:

The application stores the results of each treatment session.

#### *5.2.2. Embedded system*

The embedded system purpose is to communicate with the application and to execute the treatment over the patient. The embedded system is based on the Atmega328p AVR micro‐ controller present in the Arduino UNO board. It also has a LED board and an Ethernet Module ENC28J60 and resistors. The Figure 13 shows the prototype schematics. The database server aims to store all the patient data and the treatments as well. It's in the database that the LED treatment sequence is also stored. The chosen Data Base Management System (DBMS) was the PostgreSQL version 9, because it doesn't have license costs and it's capable of storing all the needed data [13, 14, 16].

Tree arrays were assembled on a phenolite board with tree blue, yellow and red LED colors. Each array has thirty LEDs of the specified color which are powered by the corresponding Arduino pin and a common ground.

Where, (A) Ethernet ENC28J60 module, (B) Resistors, (C) Arduino UNO and (D) LEDs array.

The LEDs board is composed by three arrays of high brightness LEDs with the following characteristics:

**•** Red array: The red light emitting LED array contains 30 high brightness LEDs of 5mm, with wavelength between 725nm and 730nm. Operates at 3, 3V and 20mA.

**Figure 13.** Prototype schematics.

Figure 14 shows the prototype used in the laboratory.

**Figure 14.** Numerous tests were performed with the prototype before manufacturing the device.


**2. Theoretical Foundations of Agility in Supply Chains**

The literature describes strategic agility as the "ability of management to constantly and rapidly sense and respond to a changing environment by intentionally making strategic

moves and consequently adopting the necessary organizational configuration for successful implementation" (Weber and Tarba, [28] (p. 7)). Therefore, strategic agility examines processes, actions, structures, culture, attributes, skills and relationships designed to ensure the organization remains flexible when it faces uncertainties [28]. This is important as De Groote [29] defines flexibility as a hedge against the diversity of the environment. Additionally, Shukla et al. [30] defined it as the ability to change with little penalty in time effort, cost or performance' across four dimensions: temporal, range, intention and focus. Strategic agility gained prominence as current theoretical approaches such as "strategic planning", "competitive advantage" and "resource-based view" were found inadequate and vague for strategic options in the complex business environment and market disruptions [28,31]. The introduction of the concept of the agile enterprise was driven by the emergence of rapid change in the business environment is accelerating and overtaking the abilities of many organisations to adapt [32]. Thus, as enabling, many organisations gained leverage from the strategic agility concept [33]. From the literature, the main thrust of strategic agility is flexibility notably the capacity of the actors and or entities to rapidly sense and seize opportunities, change direction and avoid collusion or failure [30,34–36]. However, the ability and potency to remain sufficiently agile in order to manage and adjust to change caused by strategic discontinuities, business environments and disruptions remain the main crust of the strategic agility philosophy [37]. Thus, strategic agility examines actions, processes, structures, culture, attributes, skills and relationships designed to ensure the organization, the network or the supply chain remains flexible when it encounters uncertainties [28].

However, does strategic agility provide leverage in supply chains? The thrust of strategic agility's relationships with flexibility throughout an organisation or supply chain implies a perspective of reconfiguring resources in an organization or supply chain for optimum performance [38,39]. Thus, as a competitive strategy component that can be pursued in management scenarios, it is the ability to swiftly change businesses and business processes beyond the normal level of flexibility to effectively manage unpredictable external and internal changes in an organisation or supply chain. Strategic agility, therefore, is seen as a concept with broad scope and has "multidimensional constructs" in supply chains and is generally presented as supply chain agility (SCA) [40]. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 4 of 16

> The literature traces the evolution of the concept of supply chain agility to four main aspects: pathways, criteria, scope and objectives [41]. The early proponents restricted it to customer responsive manner [42], thus limiting the concept to a reactive capability of providing speedy responses to sudden changes in demand, to gain leverage [41]. However, after Li et al. [43] work, the concept has been significantly widened with different adaptations. Do et al. [41] capture this evolution in Figure 1. advantage. Thus, improving competitive metrics such as operational performance indicators (i.e., product innovation, lead time reduction and service quality), and strategic performance indicators (i.e., competitiveness, financial, relational and marketing performance) [51–53]. In addition, the literature incorporates supply chain agility in business continuity [54], and opportunity–seeking in times of turbulence [13,55] to serve as riskmitigating factors [38,56,57].

**Figure 1.** Evolution of Supply Chain Agility Concept (Adapted from Do et al. [41] (p. 739)). **Figure 1.** Evolution of Supply Chain Agility Concept (Adapted from Do et al. [41] (p. 739)).

ductions in land productivity and declining agricultural output."

type of product, and the structure and organization of supply chains."

mestic markets, they might be less affected by international trade disruptions*."*

*2.2. Horticulture Exports Supply Chain Monitoring and Evaluation*

Research on the global COVID-19 pandemic posits that it is expected to have severe

Vos et al. [9] posited that the COVID-19 pandemic will affect food supply chains in three main ways. These are succinctly captured in Van Hoyweghen et al. [13] (p. 424) as:

i. "disruptions in international trade, stemming from an increase in trade costs due to restrictions in international mobility and quarantine measures, or stemming from trade policy measures, such as export taxes and bans, in response to the crisis." ii. "decline in on-farm labour, stemming from workers being unwilling or unable to work due to contamination risk and various containment measures, leading to re-

iii. "decline in productivity and farm output, caused by disruptions in distribution channels and in the provision of capital inputs and services. Effects likely differ with the

In addition, the literature recognises that the size of production and distribution units, the capital intensity of operations, the level of vertical coordination, the length of the chains, and the level of integration in international markets will be impacted differently resulting in supply chains exhibiting different levels of resilience to the effects of COVID-19 pandemic [49,58,59]. These will affect supply chains differently with distinctions in traditional, transitional and modern supply chains. Van Hoyweghen et al. [13] (p. 424) therefore argued that "as traditional and transitional supply chains are less integrated in international markets on the output side and oriented more toward production for do-

We then proceed to review the literature on monitoring and evaluation frameworks for horticultural supply chains to enable the study to evaluate the effects of the global COVID-19 pandemic measures in the Ghanaian horticultural supply chain. There is a need

*2.1. Horticulture Exports Supply Chain and COVID-19 Pandemic*

As a pathway, supply chain agility is now conceptualized to include the physical capability of taking reactive and proactive measures, and the cognitive capability of alertness and quick anticipation and detection of opportunities and sensing turbulence [41]. Golgeci et al. [44] expanded these cognitive capabilities to include market learning and innovation. The criteria perspective of supply chain agility expands the speed criterion for response assessment to change to include flexibility [36,39,43,45–47]. The scope perspective ensues supply chain agility expanded to include all sudden changes both internal and external. Li et al. [43] included the immediate and sudden components of change to the scope and other literature includes uncertain, temporary, abrupt and unexpected changes in the short and immediate term [47–50]. Do et al. [41] assert that this attribute of supply chain agility is more pertinent in scenarios such as the COVID-19 pandemic context. From the dimension of the objectives or the overarching goal of the supply chain, Yusuf et al. [47] emphasize that supply chain agility enables firms to attain leverage and competitive advantage. Thus, improving competitive metrics such as operational performance indicators (i.e., product innovation, lead time reduction and service quality), and strategic performance indicators (i.e., competitiveness, financial, relational and marketing performance) [51–53]. In addition, the literature incorporates supply chain agility in business continuity [54], and opportunity– seeking in times of turbulence [13,55] to serve as risk-mitigating factors [38,56,57].