Parametric finite element analysis of punching shear behaviour of RC slabs reinforced with bolts

Computers and Structures 228 (2020) 106147

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Parametric finite element analysis of punching shear behaviour of RC slabs reinforced with bolts M. Navarro a, S. Ivorra a,b,⇑, F.B. Varona a a b

Department of Civil Engineering, University of Alicante, San Vicente Del Raspeig, Apartado 99, 03080, Spain Department of Civil Engineering, University of Bristol, Queen’s Building, University Walk, Clifton, Bristol BS8 1TR, United Kingdom

a r t i c l e

i n f o

Article history: Received 28 November 2018 Accepted 2 November 2019

Keywords: Finite element analysis Flat slab Nonlinearity Parametric study Reinforced concrete Shear bolts Structural analysis automatization Structural retrofit

a b s t r a c t Reinforced concrete slabs are an essential part of high-rise structures and are designed to withstand the loads to which they are subjected. However, concrete slabs may fail due to punching shear, which is one of the greatest risks they face. This type of failure, hard to predict, befalls almost instantaneously and may lead to catastrophic consequences. In this paper, ABAQUS is used to analyse a series of non-linear numerical models to simulate the punching shear effect on reinforced bolt-retrofitted concrete flat slabs whose bolts are arranged in three different positions around the support. To start with, an initial calibration of a finite element model was carried out with experimental results reported by Adetifa and Polak. Next, a parametric analysis was performed to determine the influence of the retrofitting geometrical parameters. For this purpose, over two hundred models were created with the help of an automation algorithm programmed in Python. Our parametric study shows that a shear-bolt radial layout may be most adequate for retrofitting slab-to-column connections in which the phenomenon of punching shear is likely to occur. Moreover, the distance between the first pair of bolts and the column’s face is recommended to be approximately five times the diameter of the shear bolts. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction In reinforced concrete slabs, pure punching shear failures occur in a brittle manner, i.e. abruptly and without any warning. Therefore, the consequences of these failures tend to be tragic in most of the cases [1,2]. Fernández-Ruiz et al. [3] refer to a case in which a fire breaking out in a parking building caused the failure of a reinforced concrete (RC) slab next to a support resulting from punching shear. This RC slab failure triggered the complete collapse of the whole frame. Fernández-Ruiz et al. also reported other factors intervening in the collapse: (i) an unexpected load located on the roof, (ii) the lack of transverse reinforcement that significantly limited the final deformation, and (iii) poor calculations which underestimated the punching shear phenomenon. Punching shear resistance is arguably the most critical feature to be considered in a conventional flat or waffle RC slab building structure, and so the problem needs to be examined carefully. The purpose of this study is to examine situations in which new extra loads are added to those calculated in the original RC flat slab design, causing retrofitting to take place due to insufficient reinforcement. ⇑ Corresponding author at: Department of Civil Engineering, University of Alicante, San Vicente Del Raspeig, Apartado 99, 03080, Spain. E-mail addresses: [email protected], [email protected] (S. Ivorra). https://doi.org/10.1016/j.compstruc.2019.106147 0045-7949/Ó 2019 Elsevier Ltd. All rights reserved.

The phenomenon of punching shear has been experimentally studied for a number of years. In the 1990s, Marzouk and Hussein [4], Lips et al. [5] and Gomes and Regan [6] conducted experimental studies of the behaviour of concrete slabs focused on the different mechanical and geometrical parameters which could ultimately lead to punching shear failures. In the early 2000s, Adetifa and Polak [7] tested full scale specimens of column-slab connections to study their punching shear behaviour. The study also included retrofitted specimens. FEM models have been applied to this particular study of punching shear. De Borst and Nauta [8], Cervera et al. [9] and Shehata and Regan [10] may be said to be pioneers in applying FEM to describe the phenomenon of punching shear failure. Polak and Genikomsou [11–13] developed FEM models to simulate RC slab punching shear test results. More recently, Belletti et al. [14] compared the numerical predictions – based on a non-linear finite element model made up of two-dimensional reinforcing layers – with the experimental results and analytical values obtained from the application of different standards. Cavagnis et al. [15] and by Wosatko et al. [16] have also contributed to the field with numerical analyses. Wosatko specifically applied concrete damage plasticity models to the numerical simulation, which Navarro et al. [17] have also recently analysed.

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Notations d Del 0 DI e Ec1 Ecm EQ fcm fs fy Gf Kc w

Scalar stiffness degradation variable Initial elasticity matrix Distance between the support face and the first pair of shear bolts Eccentricity Secant modulus of elasticity of concrete Tangent modulus of elasticity of concrete Spacing between shear bolts Mean compressive strength of concrete Ultimate strength of reinforcing steel Yield strength of reinforcing steel Fracture energy Shape parameter Crack width

Moreover, theoretical and analytical models have been developed. Jiang and Shen [18], Menétrey [19], Muttoni [20] and Marí et al. [21] are worth mentioning. With regards to loading conditions, special loading conditions have been tackled by Micallef et al. [22]. They analysed the dynamic impact on a RC slab numerically. Almeida et al. [23] focused on the reverse horizontal loading, and the vertical load to which RC slabs may be subject to. Leaving aside the references given, not much research has been done on crucial issues like how punching shear failure can be determined by parameters such as (i) reinforcement type, (ii) reinforcement configuration and external retrofitting reinforcement, and (iii) geometrical and mechanical reinforcement ratios. Different authors tackled the problem from different perspectives: Menétrey et al. [24] was one of the first to analyse such parameters as concrete strength, amount of reinforcement, and geometric relationships in an axisymmetric model of a circular column-to-slab connection. Guan [25] dealt with size and location of cracks in relation to the column. In terms of experimental and analytical results, Belleti et al. [14] and other authors have compared them with available analytical models proposed by different standards and regulations. Inácio et al. [26] contended that the mainstream regulations overestimate strength in slabs, especially for high values. Navarro et al. [17] in their parametric approach to RC slabs with no retrofitting, compared some numerical results with Eurocode 2 [27] and Model Code 2010 [28] models. Different strategies undertaken for RC slab retrofitting and so prevent punching shear have been object of research. Polak and others [7,29–31] illustrated both experimentally and numerically the results of steel and FRP shear bolts when used as transverse reinforcement in punching shear failure experiments. Dam and Wight [32] assessed the capacity of orthogonal and radial layouts of shear bolts. El-Salakawy et al. [33], Durucan and Anil [34], Elbakry and Allam [35] and Meisami et al. [36] proposed steel or fibre reinforced polymer (FRP) plates or strips as alternatives. Other techniques, such as thin undulated steel strips acting as top external reinforcement or different bolt layouts in rails and plates [37], have also been deployed. This present study is concerned with a parametrical analysis of RC slab-column connections retrofitted with shear bolts. The parameters include bolt diameter, bolt number, bolt-to-column spacing, bolt-to-bolt spacing, and, more importantly, geometrical layout. After introducing the topic, the second section summarises Adetifa and Polak’s [7] experiments, later to be used to calibrate the proposed numerical model. In the third section, the calibration of

e epl ec ec;lim et r rc rt l

w Ø

Strain Plastic deformation Strain of concrete Ultimate strain of concrete in compression Tensile strain of concrete Normal stress Compressive stress of concrete Tensile stress of concrete Viscosity Dilation angle Nominal diameter of reinforcing bar

the numerical model analysed in ABAQUS [38] is addressed. ABAQUS takes advantage of the available damage plasticity model for concrete [38–40]. Numerical simulations in ABAQUS reduce costs in terms of experimental testing of RC failure analysis [41,42]. The fourth section deals with the parametric study of 243 different models, developed in Python [43]. Finally, in the last section, the most relevant conclusions are drawn and further lines of research are proposed. The novelty of this article resides in the contribution of two main features: a) the development of a parametric study of RC flat slab retrofitting based on non-linear, three-dimensional FEM models, and b) the innovative character of FEM models in terms of code creation and automation. The parametric study consists in comparing three different shear bolt arrangements around a column to compensate for insufficient punching shear reinforcement. The comparison specifically deals with ultimate load and ultimate deflection in column-to-slab connections, whose control perimeter is not limited by the slab’s edges or openings, and the column’s reaction is assumed to have zero eccentricity. Retrofitting consisted of shear bolts drilled around the column. Our parametric analysis identifies the arrangement that is likely to work best for punching shear retrofitting. The study is also felt to serve designers to select the right shear bolt layout for retrofitting slab-to-column connections subject to punching shear.

2. Description of the experimental background The FEM model was calibrated with Adetifa and Polak’s [7] test results, drawn from real-scale models of RC slab-to-column connection. The slabs measured 1800
1800
120 mm, and the column studs, protruding from both the upper and lower faces of the slab, had a height of 150 mm and a cross section of 150
150 mm. Table 1 illustrates the main mechanical properties of concrete, reinforcing steel bars and external reinforcement shear bolts. The longitudinal flat slab reinforcement consisted of two mesh fabrics acting as top and bottom longitudinal/transversal reinforce-

Table 1 Material properties of the slab tested in [7]. Compressive strength of concrete [MPa]

Tensile strength of concrete [MPa]

Yield strength of steel reinforcement [MPa]

Yield strength of steel shear bolts [MPa]

41

2.1

455

381

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ment. In both cases, the size of reinforcing bars was 10 M, (Canadian sizes), with a cross-sectional area of 100 mm2 (nominal diameter  11 mm). The pitches of the meshes were 200 mm in compression and 100 mm in tension. The concrete cover to longitudinal rebar centre was 20 mm. Reinforcement of the column stud consisted of 4–20 M longitudinal bars (cross-sectional area 300 mm2, nominal diameter  20 mm) plus 4- links 8 M in size (cross-sectional area 50 mm2, nominal diameter  8 mm). The column studs had an effective depth of 130 mm. The slab was simply supported along its 4 edges on small neoprene supports, creating 1500-mm spans in the X and Y directions. Adetifa and Polak tested six slab-to-column connections specimens. Specimen SB1 was a slab-to-column connection with no shear bolts which was used for preliminary calibration, [44]. Specimens SB5 and SB6 had openings next to the column and therefore, fell beyond our scope. Specimens SB2, SB3 and SB4 did use shear bolts in increasing number. Specimen SB4 was chosen because it delivered the greatest increase in the ultimate load after strengthening. Prior to tests, external transverse reinforcement shear bolts were fitted in 16 mm diameter holes, drilled around the column studs. As shown in Fig. 1b, specimen SB4 had four rows of bolt pairs per column face, which means that a total of 32 shear bolts were used. During the test, the load kept being transmitted through the column studs until punching shear failure occurred in a brittle manner. The experimental layout was made opposite to that of a real structure. Fig. 1b shows the shape of the crack at failure point, and Fig. 1a illustrates the crack pattern in specimen SB1. This specimen was identical to specimen SB4 except for the external shear bolts. The relationship between the applied load and the vertical displacement of the centre of the column’s lower face was recorded and is illustrated in Fig. 5.

3. Implementation of the slab numerical model

mental tests [7]. To reproduce the test, this quarter of slab was mounted on simple supports, specifically on its two outer edges, and boundary conditions of symmetry were applied to its inner edges (see Figs. 2 and 3). With regards to simulating the behaviour of concrete, ABAQUS provides the Concrete Damage Plasticity model. Previous research [17,48–51] on modelling techniques using damage plasticity models for structural concrete have been successfully validated with experimental results. In these studies, concrete is assumed to display two types of failure mechanisms: cracking and crushing. The model is a revision of Drucker and Prager’s approach [52], which, in turn, assumes Lubliner et al.’s criterion [40] and incorporates Lee and Fenves’ adjustments [39] to address the evolution of both compression strength and tension strength in concrete. Since the main stresses appear in various directions, the stress-strain relationship can be defined through Eq. (1).

r ¼ ð1  dÞDel0 : e  epl




ð1Þ

where d is the scalar stiffness degradation variable, whose values range from zero (undamaged) to one (completely damaged); Del0 the initial elasticity matrix; e the total strain; and epl the plastic deformation. Model Code CEB 2010 [28] provides the constitutive model for concrete in compression and is represented in Fig. 4a, where rc is compression stress, ec strain of concrete, fcm mean concrete compression strength, ec,lim ultimate strain, Ecm tangent elasticity modulus, and Ec1 secant elasticity modulus. For concrete uniaxial behaviour in tension, the basic model is provided by Hillerborg et al.’s fracture energy [53] – Fig. 4b and Fig. 4c – where rt is tensile stress, et concrete strain, w crack width, and Gf fracture energy.

Control Load

z-y symmetry plane Ux=URy=URz=0 Bottom supports Uz=0

3.1. Features of the model A numerical model for finite element analysis (FEA) was implemented in ABAQUS [38] for calibration. This software is capable of simulating the non-linearity of materials, such as steel and concrete. Mirza [45], Obaidat [46], Alfarah et al. [47] and other authors have made use of this software to simulate concrete structures with great accuracy. Because of the symmetry in geometry and loading conditions, only one quarter of the slab-to-column connection has been modelled to reproduce Adetifa and Polak’s experi-

Bottom supports Uz=0 z-x symmetry plane Uy=URx=URz=0

Fig. 2. Geometry and boundary conditions of the model.

Fig. 1. Crack pattern in experimental study [7]: (a) test carried out in a specimen with no shear bolts acting as transverse reinforcement; (b) test carried out in specimen SB4 containing 32 shear bolts.

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Fig. 3. Shear bolt arrangement in the slab model simulating specimen SB4 in [7]. Left: general view of the FEM. Right: diagram showing location and spacing of shear bolts.

Fig. 4. Constitutive behaviour of concrete: (a) in compression, in compliance with Model Code 2010 [28]; (b) in tension before cracking; (c) softening after cracking, according to Hillerborg et al. [53].

For steel reinforcing, the bi-linear model of Eurocode 2 [27] was adopted. Starting with a linear elastic curve, the model reaches the steel yield strength fy and then a second curve follows up to the point the model failed at stress fs, with an ultimate strain of 0.9 times the characteristic ultimate strain. In addition, Von Misses failure criterion was applied for steel. The bolts were assumed to be perfectly elastic as stress never approached their yield strength. Also, the surfaces of concrete and steel were assumed to be perfectly bonded, a common practice in the global analysis of reinforced concrete elements (Genikomsou and Polak [12], and Wosatko et al. [16]). The concrete mesh consisted of 8-node hexahedral elements with reduced integration (C3D8R). The longitudinal and transverse reinforcing mesh fabrics within the RC slab were meshed with 4node reduced-integration shell elements (S4R). Reinforcement bars of the concrete studs protruding from the RC slab were modelled with 2-node truss elements with reduced integration (T3D2). Finally, 3-node quadratic beams in space (B32) were used to model the shear bolts.

In line with the experimental test, a displacement control method was used in the FEM slab model. A constant vertical displacement speed was set for vertical load application. Thus, the convergence problems that would entail a load-control solution were minimized. Table 2 shows the calibrated values taken from the Concrete Damage Plasticity model to tally Adetifa and Polak’s [7] experiments. Table 3 reports the calibrated values for the behaviour of concrete subjected to compression and tension forces. These values, applied to our FEA, are based on our previous work [17] in which a numerical model for RC slab punching shear was accurately calibrated with experimental results from real tests. 3.2. Validation of the calibration for the slab model Fig. 5 and Table 4 show the experimental results from [7], and the load displacement responses from our calibrated finite element analysis (FEA). Fig. 5 illustrates the SB1 (specimen with no shear reinforcement) load deflection curve, the SB4 (specimen with shear

Table 2 Calibrated values for Concrete Damage Plasticity finite element analysis (FEA).

Genikomsou & Polak [12] Current FEA

Dilation angle w

Eccentricity e

Viscosity l

Shape parameter Kc

Max. compression axial/biaxial

40° 36°

0.1 0.1

0 0.00001

1.16 1.16

0.667 0.667

Table 3 Concrete properties associated with constitutive behaviour of concrete in compression and tension.

Genikomsou & Polak [12] Current FEA

Modulus of elasticity of concrete [MPa]

Poisson’s ratio

Fracture energy of concrete [N/mm]

Tensile strength of concrete [MPa]

35,217 35,217

0.2 0.2

0.077 0.105

2.2 2.1

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Fig. 5. Load–deflection responses obtained in the tests by Adetifa and Polak [7], in the FEA by Genikomsou and Polak [12] and in the current FEA with calibrated parameters.

Table 4 Results of punching shear tests reported in [7] and through FEA of the calibrated numerical model for RC slab with shear bolts. With no shear reinforcement

With shear reinforcement

Adetifa and Polak [7], specimen SB1

Adetifa and Polak [7], specimen SB4

Current FEA with calibrated parameters

Ultimate load (kN) 253

Ultimate load (kN) 360

Ultimate load (kN) 361

Associated deflection (mm) 11.9

reinforcement) load deflection curve, Genikomsou and Polak’s FEA results [12] and our results. The values of the parameters of [12] can be found in Tables 2 and 3. These tables show slight differences in general terms. However, note that in Genikomsou and Polak’s FEM model, the slab longitudinal reinforcement –consisting of T3D2 elements for each bar– has been replaced with a continuous mesh introduced in the previous section. The parametric study, which took into account over 200 models, involved modelling the slab longitudinal reinforcement by smeared distribution of the steel mesh fabrics to equal the desired reinforcement ratio. If discrete positions of varied-sized longitudinal-reinforcing bars had been used, the automation process would have become much more complex. Fig. 5 shows that for displacements greater than 10 mm and loads in excess of 250 kN, the FEA calibrated results offer a better agreement with the experiment results than those in [12], readily appreciated in the 25–30 mm interval, just before failure. Overestimation of stiffness in relation to experiment results is known to be recurrent in numerical analysis and may be associated with boundary conditions because in real empirical conditions the restraints are not perfect. Our calibrated model shows that slabto-column connection stiffness for small displacements and loads, in the range of 50–250 kN, is indeed overestimated as is also the case in [12], the displacements of which are even greater for loads in excess of 300 kN. This difference in calibration between the two may be attributed to the viscosity parameter, l, and the setting of a greater value for fracture energy in our calibration. Table 4 illustrates the level of consonance in experiment results between our model and Adetifa and Polak’s: the relative errors in the ultimate load and the associated ultimate displacement are 0.28% and 1.01%, respectively. 3.3. Parametric analysis variables Table 5 shows our source model, which will be systematically modified to generate a series of numerical models exhibiting different reinforcement configurations. The variables taken into account are: bolt diameter, number of bolts in each layout, dis-

Associated deflection (mm) 29.8

Associated deflection (mm) 30.1

Table 5 Values of parameters in the reference model for parametric study. Variable

Initial value

Yield strength of steel (MPa) Concrete compresive strength (MPa) Longitudinal reinforcement ratio Column width/Slab width ratio Column width/Slab thickness ratio Punching shear reinforcement

500 25 1.5% 0.1 1.25 None

tance from the first bolt to the support’s face (DI), bolt-to-bolt spacing (EQ), and shear bolt layout. Table 6 illustrates the three different values or types assigned to each variable. The range of values taken for DI (distance from first bolt to column) and for EQ (bolt-bolt spacing complies with the Eurocode 2 [27] and the Spanish Standard for Structural Concrete EHE-08 [54]. A number of 243 models were devised to study all possible combinations of the five parameters involved in Table 6. Distances DI and EQ are defined as a function of the diameter selected and will influence the final geometrical layout. Identical geometry and number of bolts but different reinforcement diameters will affect the area covered by the retrofitting as shall be seen. Fig. 6 illustrates the different bolt layouts. Every model was subjected to FEA with the control displacement set at a constant vertical speed. The displacement was

Table 6 Values adopted for each variable. Parameter

Value 1

Value 2

Value 3

Bolt diameter (mm) Number of bolt pairs per support’s face First bolt-column distance (mm) Distance bolt-to-bolt (mm) Bolt layout

Ø8 2

Ø12 3

Ø16 4

3.5Ø

5Ø

6.5Ø

5Ø

6.5Ø

8Ø

Double-line

Radial

Diamond

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Fig. 6. Bolt arrangement: 2 bolts at top row, 3 bolts in middle row, 4 bolts at bottom row; double-line layout (left column), radial layout (middle column), diamond layout (right column).

applied to the same point in each model and showed a maximum vertical deflection of 40 mm since a vertical deflection of 20 mm had been detected not to reach the failure point in most cases. A routine was programmed in Python [43] to create the geometrical and mechanical definition of all 243 models. Then, the routine launched the analysis of the models in ABAQUS and retrieved the results afterwards. Tables 7 and 8 show a record of the two most relevant data – ultimate load and its associated ultimate displacement.

3.4. Automating parametrisation analyses Structural engineers, and engineers in general, need to be competent in computer techniques to develop projects [55,56]. Simulation of the mechanical performance of materials requires skills oriented towards the parametrisation of material properties, geometric features and process automation. The latter proves critical in reducing the time required to create FEM models. Automation came as a result of programming in Python [43]. This tool enables the user to program a code for the processes to be controlled step by step in ABAQUS and so deliver FEM models

in every phase – parameterization and automation, analysis, and data collection [57]. There are two possible ways to perform the parametric analysis. One possibility is to create and run each model one after another and to retrieve the results one by one. The link between Python and ABAQUS allows a second alternative in which a series of similar models can be created and analysed. Each batch of models shares the same values for all parameters except one or two. In this way, the code takes control of ABAQUS and sets the creation of the parametrised batch of models, their analysis, and the retrieval of results. Useful as this feature may be, it poses the problem of computational overload, so the user should be careful to set an adequate batch size that does not exceed the processing capabilities of the computer. Since the parametric analysis entailed the management of 243 simulations, we opted for the second procedure which offers a clear advantage of time-saving, reducing the dependence on the user’s participation between tasks to a minimum. ABAQUS [38] provides the user with an immense library of commands written in Python [57], crucial for developing the code and its parameterization and bringing about the automation required. Among the commands, one particular user interface was devised that significantly increased comfort for it enhanced

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Table 7 Ultimate load depending on the geometrical disposition of shear bolts, distances EQ and DI, diameter of bolts and number of pairs of bolts per support’s face.

the intuitive nature of the parametrisation and automation operations.

4. Analysis of the results 4.1. Introduction An Intel Core i7 340 GHZ processor took an average of 4 h per model to make all the calculations. Since the number of FEM models analysed rules out the possibility of including our results in this paper, just a selection of the most remarkable findings are presented. Table 7 shows the ultimate load for each of the 243 models, and Table 8, their ultimate deflection. Note that some radial and diamond layouts designs featuring 16-mm- diameter bolts reached a vertical deflection of 40 mm – the displacement control limit – before failing. Thus, not many conclusive results could be drawn from them. Tables 7 and 8 present the results multi-

dimensionally, illustrating the interrelation among the 5 parameters the study takes into account. The nine columns show the shear bolt diameters and the number of pairs of bolts per support’s face for each geometrical arrangement. The rows show geometrical configuration, distance EQ (bolt-to-bolt spacing), and distance DI (between the first bolt pair to the support’s face). A coloured scale is set to distinguish lower from higher values. In Table 7, the lowest values for ultimate load are coloured in red whilst the highest values for load in green. Thus, the most effective retrofit layout for shear bolts is readily seen to be the diamond configuration featuring 4 pairs of bolts 12 mm in diameter per support’s face (see Fig. 6, bottom row, right column, with a total of 48 bolts). Ductility is associated with ultimate displacement and Table 8 tells us that the diamond configuration featuring shear bolts 12 mm in diameter may not be the most suitable layout for punching shear retrofit despite having the highest value for ultimate load. The radial configuration, however, showing 4 pairs of bolts

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M. Navarro et al. / Computers and Structures 228 (2020) 106147 Table 8 Ultimate displacement (associated to ultimate load), depending on the geometrical disposition of shear bolts, distances EQ and DI, diameter of bolts and number of pairs of bolts per support face.

12 mm in diameter per support’s face, provides middle level–moderate ultimate deflection and a remarkable increase in ultimate load. Especially noteworthy is the design in which (DI) is 5Ø (60 mm) and (EQ) is 6.5Ø (78 mm) because it yields an ultimate load of almost 400 kN and an ultimate displacement in excess of 30 mm. 4.2. Effect of the shear bolt diameter on the retrofit Ultimate load was observed to undergo an average increase of 3.3% when the diameter increased from 8 mm to 12 mm. However, it decreased by 10% when the diameter changed from 12 mm to 16 mm. This behaviour was particularly noticeable in the diamond configuration and is illustrated in Fig. 7a. In this configuration, the load increased by 9% when the diameter changed from 8 mm to 12 mm, but decreased by 13.8% when the diameter went from

12 mm to 16 mm. The linear relationship between bolt diameter and distances DI and EQ leads to designs with fewer shear bolts per area. Therefore, using a large bolt diameter might induce a decrease in ultimate load in spite of increasing the total transverse reinforcement area. On the other hand, Fig. 7b corresponds to a double-line-geometry layout and shows the effect the diameter has on a retrofitting design. This layout consists of 3 pairs of bolts per support’s face, DI = 5Ø and EQ = 8Ø. The unexpected decrease in the ultimate load when using diameters greater than 8 mm could AGAIN be explained by distances DI and EQ which increase alongside the diameter. Consequently, the area affected by the shear bolts falls beyond the control perimeter. As a result, a relatively few 16-mm bolts lie within the control perimeter and are capable of effectively avoiding punching shear failure. Eurocode 2 [27] locates the control perimeter at twice the distance of the effective depth, measured from the perimeter of the column. Model

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Fig. 7. Examples of load-deflection FEA results: (a) diamond layout consisting of 2 pairs of shear bolts, DI = 5Ø and EQ = 6.5Ø; (b) double-line layout consisting of 3 pairs of shear bolts, DI = 5Ø and EQ = 8Ø.

Code 2010 [28] reduces the distance to half the effective depth. Previous research [17] based on our calibration of Adetifa and Polak’s test [7] may lead to conclude that the control perimeter location advanced by Eurocode 2 is roughly valid, at least for this particular geometry. The ultimate displacement was observed to increase an average of 9.4% when the diameter of the shear bolts increased from 8 mm to 12 mm. However, an increase of 25.1% took place in displacement when the diameter increased from 12 mm to 16 mm. Some cases in the double-line geometry, though, showed that an increase in diameter from 8 mm to 12 mm produced a decrease in ultimate displacement (see Fig. 7b). A much more noticeable increase in ultimate displacement can be observed in radial layout – 15% – for the same diameters. If the bolt diameters were changed from 12 mm to 16 mm, the diamond geometry would definitely prove

to be the most sensitive to ultimate displacement, showing an increase of 44.5%. 4.3. Effect of the number of bolts on the retrofit An increase in the number of pairs of bolts per support’s face – from 2 to 3– brought about an average increase of 5.6% in ultimate load. Moreover, if the number of bolts increased from 3 to 4 pairs, the ultimate load would experience an increase of 4.1% in average. The diamond geometry was found to be greatly affected by this variable: an increase of 9.6% in ultimate load when the number of pairs was 3 instead of 2, and of 7.2% when 4 pairs were selected instead of 3. The double-line geometry proved less affected in that the ultimate load showed an increase of less than 2%. Fig. 8 and 8a show the double-line layout for shear bolts of diameters 8 mm and

Fig. 8. Load-deflection response with shear bolts placed in double-line layout: (a) 8 mm diameter bolts, DI = 5Ø and EQ = 6.5Ø; (b) 16 mm diameter bolts, DI = 6.5Ø and EQ = 5Ø.

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16 mm, respectively. In the latter configuration, a thicker diameter implied longer DI and EQ distances, resulting in their spreading beyond the control perimeter, and because of this the addition of more bolts affected neither ultimate load nor ultimate displacement (see Fig. 8b). For the same reason, the effect of the number of 16 mm bolts on the radial and diamond configurations was less than 4.1% (2–3 pairs) and less than 2% (3–4 pairs). Neither in the double-line layout nor in the radial geometry was any significant increase found in the ultimate deflection – less than 1% – if we changed from 2 to 3 pairs of bolts – a negligible reduction of 0.2% was recorded for the diamond configuration. However, a significant reduction in ultimate deflection of 6.9% was noticed in the diamond configuration. The reason is assumed to lie in this typology that has the highest density of bolts per area, which reduces the ultimate displacement while gaining in strength. 4.4. Effect of the distance from the first bolt to the column on the retrofit The distance between the first bolt pair and the column (DI) matters. If increased from 3.5Ø to 5Ø, the models’ ultimate load decreased by an average of 5.1%. Double-line and radial layouts showed a reduction of approximately 6 and 7%, respectively. In the diamond configuration the load was less affected (<3%). If, on the other hand, (DI) became 6.5Ø instead of 5Ø, the ultimate load would decrease by an average of 2.5%. Fig. 9 presents the general trends associated with the models exhibiting a radial geometry with 4 pairs of bolts of 12 mm in diameter per face, and bolt-tobolt spacing EQ = 6.5Ø. As previously seen, a high value of the initial distance (DI) moved the bolts away from the column and consequently, fewer bolts lay within the control perimeter, which reduces the ultimate load capacity. Conversely, if the distance DI increased, the ultimate displacement also increased. The longer the distance DI – from 3.5Ø to 5Ø, the greater the ultimate displacement: 7.7% in double-line, 15.2% in radial, and 20.9% in diamond. However, if DI increased from 5Ø to 6.5Ø, the ultimate displacement increased much less: 1.4% in the double-line layout, and 9.1% in the diamond geometry.

Fig. 10. Load-deflection response of the FEM model with diamond layout, 2 pairs of shear bolts per support face, 8 mm diameter bolts and DI = 6.5Ø.

effect was found to be less apparent. If EQ increased from 5Ø to 6.5Ø, the ultimate load also increased by approximately 1.2%; and a further EQ increase from 6.5Ø to 8Ø yielded no change in the load. However, in the radial geometry, an increase in EQ produced a decrease in the load of about 1%. Fig. 10 shows a model in diamond configuration with 2 pairs of bolts per support face, bolts 8 mm in diameter, and distance DI = 6.5Ø. In summary, the effect of bolt-to-bolt spacing EQ on the ultimate strength seemed to be negligible (less than 2%). Bolt-to-bolt spacing, EQ, also affects the ultimate displacement but in different ways in each layout. In the radial layout, when EQ changed from 5Ø to 6.5Ø, the ultimate displacement increased as much as 8.8%. Moreover, if EQ = 8Ø, the displacement increased by 6.3%. The other layouts were less responsive in that the increase amounted to less than 3.9%.

4.5. Effect of bol-to-bolt spacing on the retrofit 4.6. Effect of the shear bolt layout on the retrofit In double-line and diamond layouts, bolt-to-bolt spacing EQ had the same effect as the distance DI had on the ultimate load, but this

Fig. 9. Load-deflection response of the FEM model with radial disposition, 4 pairs of bolts per support face, 12 mm diameter bolts and EQ = 6.5Ø.

In this section, the standard double-line, radial and diamond configurations are compared. Radial and diamond geometries were more successful than double-line in withstanding the ultimate load in FEM models. In radial and diamond configurations, the increase in ultimate load in contrast to double-line was 12.7% and 13.9%, respectively. Fig. 11 shows load-deflection curves in FEA from models with 3 pairs of 8 mm bolts (Fig. 11a) and with 4 pairs of 16 mm bolts (Fig. 11b). It is observed that (i) with 2 pairs of bolts per support face, radial layouts proved more effective than double-line since its ultimate load increased over 9.6%; (ii) when 3 pairs of bolts were involved, radial and diamond behaved equally well and performed better than double-line, showing an increase in ultimate load of 13.5% (see Fig. 11a); and (iii) with 4 pairs of bolts per support face, diamond showed the best response: 20.9% in average, much greater than in double-line (see Fig. 11b). Performance of radial layouts was better than those of double-line, which is consistent with the conclusions of Dam and Wight [32], though they did not address the diamond layout. Compared with double-line configurations, the diamond did not respond as well to punching shear ductility: diamond layouts showed an average loss of 1.3% with 2 pairs of bolts per support face, and of 10.3% with 4 pairs. Fig. 11a illustrates this trend. Nonetheless, Fig. 11b provides us with an exceptional instance in which the diamond layout showed greater ultimate displacement.

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Fig. 11. Load-deflection response of the FEM models: (a) 3 pairs of shear bolts of Ø8 mm per support face, DI = 5Ø and EQ = 6.5Ø; (b) 4 pairs of bolts of £16 mm, DI = 5Ø and EQ = 6.5Ø.

When radial layouts were compared with double-line geometries, the ultimate displacement was seen to decrease by 1.2% with 2 pairs of bolts, but to increase by an average of 1.8% with 3 pairs, and 3.1% with 4 pairs of bolts.



5. Conclusions FEM models implemented in ABAQUS have served the purpose of studying the performance of different retrofitting layouts for RC slab-to-column connections subjected to punching shear. Key parameters of the FEM models were previously calibrated quantitatively and qualitatively to match the experimental and numerical results offered in scientific literature concerning the topic. A Python programmed code allowed the generation and control of over 240 finite element model analyses in ABAQUS, thus automating a parametric analysis. This analysis studied the effects of different geometrical features on the structural response of retrofitted RC slabs. The main conclusions related to the parametric study are the following:  Bolt-to-column and bolt-to-bolt spacing are arguably proportional to the shear bolt diameter. That means that retrofitting designs using 16-mm-diameter bolts spread further than designs with smaller bolts. This entails that the outer groups of shear bolts, i.e, the furthest from the column, may fall beyond the control perimeter area, thus triggering a decrease in ultimate load capacity compared to designs with smaller bolts.  An increase in number of bolts in any layout generally produces an increase in ultimate load. However, if 16 mm bolts are used, the increase in ultimate load is less significant in radial and diamond configurations, and even detrimental in double-line. It is contended that the answer resides in the number of bolts effectively found within the control perimeter. Since the diamond layout is more densely reinforced, it is thus less affected. The addition of a third pair of bolts per support face did not significantly increase the ultimate displacement. In some cases, the







addition of a fourth pair may surprisingly cause a decrease in the ultimate displacement, especially in the diamond retrofitting geometry. In terms of spacing between the column and the first bolt pair (DI), the models that exhibited greater ultimate load were those whose DI was 5Ø. When DI = 3.5 Ø, the model failed to reach the control perimeter, and when DI = 6.5 Ø, it went beyond. But, as far as the ultimate displacement is concerned, it decreased when DI increased, probably because of the insufficient concentration of transverse reinforcement around the column. Bolt-to-bolt spacing (EQ) seems not to be as decisive as DI for calculating ultimate load. Variations in the ultimate displacement can be explained in terms of variations in DI. Radial and diamond geometries exhibit more pairs of bolts than double-line does. Diamond has the greatest density within the control perimeter of the column. Therefore, when DI decreased, the control perimeter was denser and the ultimate displacement decreased. Furthermore, when DI = 5Ø, the greatest ultimate load was reached, validating our previous conclusions. As for ductility, diamond showed the greatest loss in the ultimate displacement. All in all, radial responded the best since it provided an adequate increase in ultimate load without compromising ultimate displacement, and it even showed a slight gain in ductility for a higher number of shear bolts. Although code management of FE analysis software tools can be complex for its requirements of combined skills and knowledge of Civil Engineering and Computer Engineering, it has proved essential in the development of our models, especially the parametric ones. Even though code programming is timeconsuming, it has allowed us to automate processes, saving a great deal of time in the creation of many of our models.

As a final remark, we firmly believe that the results obtained have paved the way towards future work aimed at systematically finding the optimum design parameters. Some situations beyond the scope of this study are column-to-slab connections close to the slab edges as well as the effect of openings close to the column

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perimeter, which parametrisation.

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require

specific

calibration

and

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors would like to thank the Technical University of Valencia for their collaboration, allowing us to share their ABAQUS license. A special mention needs to be made to Dr. Vicente Albero and Dr. David Pons for their assistance and advice in the application of the capabilities of this software. References [1] Kunz J, Fernández-Ruiz M, Muttoni A. Enhanced safety with post-installed punching shear reinforcement, no. l. London: Taylor & Francis Group; 2008. [2] Foti D. Shear vulnerability of historical reinforced-concrete structures. Int J Archit Herit 2015;9(4):453–67. [3] Fernández-Ruiz M, Muttoni A, Kunz J. Strengthening of flat slabs against punching shear using post-installed shear reinforcement. ACI Struct J 2010;107(4):434–42. [4] Marzouk H, Hussein A. Experimental investigation on the behavior of highstrength concrete slabs. ACI Struct J 1991;88(6):701–13. [5] Lips S, Fernández-Ruiz M, Muttoni A. Experimental investigation on punching strength and deformation capacity of shear-reinforced slabs. ACI Struct J 2012;109(6):889–900. [6] Gomes Ronaldo B, Regan PE. Punching resistance of RC flat slabs with shear reinforcement. J Struct Eng 1999;125(6):684–92. [7] Adetifa B, Polak MA. Retrofit of slab column interior connections using shear bolts. ACI Struct J 2005;102(2):268–74. [8] de Borst R, Nauta P. Non-orthogonal cracks in a smeared finite element model. Eng Comput 1985;2(1):35–46. [9] Cervera M, Hinton E, Hassan O. Nonlinear analysis of reinforced concrete plate and shell structures using 20-noded isoparametric brick elements. Comput Struct 1987;25(6):845–69. [10] Shehata IAEM, Regan PE. Punching in R.C. slabs. J Struct Eng 1989;115 (7):1726–40. [11] Polak MA. Modeling punching shear of reinforced concrete slabs using layered finite elements. ACI Struct J 1998;95(1):71–80. [12] Genikomsou AS, Polak MA. Finite element analysis of a reinforced concrete slab-column connection using ABAQUS. Structures Congress 2014;2014:813–23. [13] Genikomsou A, Polak MA. Damaged plasticity modelling of concrete in finite element analysis of reinforced concrete slabs. Proceedings of the 9th international conference on fracture mechanics of concrete and concrete structures, 2016. [14] Belletti B, Walraven JC, Trapani F. Evaluation of compressive membrane action effects on punching shear resistance of reinforced concrete slabs. Eng Struct 2015;95:25–39. [15] Cavagnis F, Fernández Ruiz M, Muttoni A. Shear failures in reinforced concrete members without transverse reinforcement: An analysis of the critical shear crack development on the basis of test results. Eng Struct 2015;103:157–73. [16] Wosatko A, Pamin J, Polak MA. Application of damage–plasticity models in finite element analysis of punching shear. Comput Struct 2015;151:73–85. [17] Navarro M, Ivorra S, Varona FB. Parametric computational analysis for punching shear in RC slabs. Eng Struct 2018;165:254–63. [18] Jiang D, Shen J. Strength of concrete slabs in punching shear. J Struct Eng 1986;112(12):2578–91. [19] Menétrey P. Synthesis of punching failure in reinforced concrete. Cem Concr Compos 2002;24(6):497–507. [20] Muttoni A. Punching shear strength of reinforced concrete slabs without transverse reinforcement. ACI Struct J 2008;105(4):440–50. [21] Marí A, Cladera A, Oller E, Bairán JM. A punching shear mechanical model for reinforced concrete flat slabs with and without shear reinforcement. Eng Struct 2018;166:413–26. [22] Micallef K, Sagaseta J, Fernández Ruiz M, Muttoni A. Assessing punching shear failure in reinforced concrete flat slabs subjected to localised impact loading. Int J Impact Eng 2014;71:17–33. [23] Almeida AFO, Inácio MMG, Lúcio VJG, Ramos AP. Punching behaviour of RC flat slabs under reversed horizontal cyclic loading. Eng Struct 2016;117:204–19. [24] Menétrey P, Walther R, Zimmermann T, Willam KJ, Regan PE. Simulation of punching failure in reinforced-concrete structures. J Struct Eng 1997;123 (5):652–9.

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