Failure Analysis of Polypropylene Fiber Reinforced Concrete Two ‐ Way Slabs Subjected to Static and Impact Load Induced by Free Falling Mass

The impact resistance of concrete is considered as poor due to a relatively energy dissipating characteristics and tensile strength. Therefore, this paper investigates the feasibility of using polypropylene fibers PF to enhance punching shear capacity of reinforced concrete RC two‐way slabs subjected to drop‐weight impacts. The evaluated parameters included two slab thickness 70 mm and 90 mm , five different PF per‐ centages 0%, 0.3%, 0.6%, 0.9%, and 1.2% , and two impact load height 1.2 m and 2.4 m . The tested slabs divided into three groups: not subjected to impact load, subjected to im‐ pact load at a height of 1.2 m, and subjected to impact load at a height of 2.4 m, resulting in a total of 25 slabs. The behavior of each two‐way RC slab was evaluated in terms of the crack patterns, ultimate punching shear capacity. The present ex‐ perimental data can be used for further assessment of the performance of PF reinforced concretes two‐way slabs as well as providing a well‐documented dataset related to the impact‐resistant applications which is presently limited within the literature. The results showed that adding the PF at a dosage of 0.3 to 1.2% by volume of concrete and increas‐ ing the slab thickness from 70 mm to 90 mm leads to consid‐ erable enhancement in the overall structural behavior of the slabs and their resistance to impact loading. Interestingly, the degradation in the ultimate punching capacity of the slabs subjected to impact load at a height of 1.2 and 2.4 m is 30.5% and 34.6%, respectively. Finally, an empirical model was pro‐ posed for predicting the punching shear capacity of RC two‐ way slabs based on reliable experimental results available in literature


INTRODUCTION
The response of reinforced concrete RC elements subjected to impact load is a hot topic in the previous published research work and still needs more elaboration in order to understand their complex behavior.This hot topic is very important especially in the area of RC nuclear facilities or military fortification structures that are used in high-hazard or high-threat applications as well as in the structures that are designed to resist the accidental impact loading due to falling rock and ship or vehicle collisions with offshore facilities, bridges, and buildings.Therefore, an extensive work should be undertaken in an attempt to develop a design procedure for post impact resistant and to improve the behavior of RC elements subjected to impact loads.Up to now, the developing of empirical provisions for estimating the damage and structural capacity under specific impact loading is the most focused topic of the majority of the impact loading related research Kennedy 1976, Vimal et al. 2017, Wei et al. 2013, Chen and May 2009 .Furthermore, more of the research work has been exclusively focused on slab and wall mechanism of localized damage such as impactor penetration, concrete scabbing, and impactor perforation Chang-Geun et al. 2015, Duc-Kien and Seung-Eock 2014, Shujian et al. 2016 .In addition, little effort is focused on the energy dissipation due to damage growth at localized location and global deformations in terms of axial, shear and bending deformations of RC flat slabs under impact loading Duc-Kien and Seung-Eock 2017 .Nowadays two-way RC flat slabs can be consider as the superlative solution for residential, commercial, and office buildings because of the efficient and economical issues such as easy installation of electrical and mechanical infrastructures, the greatly simpler and reduced formwork, and faster site operations as well as the easier and versatility space partitioning.Moreover, the punching failure can be considered as a complex behavior in design of the RC two-way flat slab.In addition, the punching failure is typically brittle and considered as ultimate load capacity of two-way RC slabs and can cause a sudden collapses of the entire structure Lorena et al. 2016 .The bent-up bars, closed stirrups, post-installed shear reinforcement or shear studs techniques as well as high strength concrete are used to increase the punching shear capacity of RC two-way flat slabs Micael et al. 2015 .Recently, utilization of fiber reinforced concrete FRC has emerged as a practical approach for enhancing the performance of RC elements under impact loading.Numerous studies have shown FRC elements containing conventional steel reinforcing bars demonstrate superior resistances to global impact behavior than local damage mechanism development and, as a result, acquire enhanced energy absorption capabilities under impact loading with respect to RC elements Ong et al. 1997, Kurihashi et al. 2006, Zhang et al. 2007 .In addition, FRC is used to increase the punching shear capacity and the deformation capacity of RC flat slabs due to the capability of fibers in the bridging after the creation of the cracks Cheng and Parra-Montesinos 2010 , Maya et al. 2012 .Current design code provisions ACI 318-14 2014 , Fédération Internationale du Béton-Vol. 1 2010a , Fédération Internationale du Béton-Vol.2 2010b , JSCE 2007 for punching shear had been proposed for normal weight concrete structures and their appliance to for FRC flat slab is not constantly straightforward especially for empirical design formula.Over the last decades, several stipulated empirical models for punching shear of FRC flat slab have been proposed by taking into account the contribution of tensile and compressive strength at the critical section of the punching shear as well as the pull out strength and quantity of fibers Choi et al. 2007, Higashiyama et al. 2011, ASTM 2004 .Base d on the previous literature review, the punching shear strength of the RC two-way flat slabs after impact load is omitted.Therefore, this paper presents the methodology and conclusions from an experimental program undertaken to study the effect of impact load on the punching shear behavior of RC and polypropylene fiber reinforced PFR concrete two-way slabs.Highlighting was placed on assessing the effect of slab thicknesses, fiber volume fractions, and freely dropped weight heights on the RC two-way flat slab behavior in terms of ultimate load capacity, deflection profile, toughness or energy absorption as well as mode of failure.In an effort to fully detain the post impact behaviors of the tested RC slabs, the test data collected were used to propose an analytical formula that can estimate the pre impact and post impact punching shear capacity of RC flat two-way slabs with and without PFR.The experimental program included testing twenty eight two-way reinforced concrete slabs as simply supported system with equal clear length and width of 1.0 m as shown in Figure 1.The investigated parameters include the slab thicknesses, h s 7 cm and 9 cm , fiber volume fractions, V f 0%, 0.3%, 0.6%, 0.9%, and 1.2% , and freely drop weight 10 cm in diameter and weighs 7 kg heights, h I 1.2 m and 2.4 m .The slabs were reinforced with seven steel bars with a diameter of 5 mm in each direction which is equivalent to steel reinforcement ratios of 0.0018 and 0.0025 for the 9 cm and 8 cm slabs according to the ACI 318-14 Code 2014 .A dropped mass height of 1.2 m and 2.4 m produces impact velocity of 4.85 m/s and 6.86 m/s, respectively, as well as kinetic energy of 82.32 J and 164.64 J, respectively.
Figure 1: Tested slabs layout and setup details all dimensions in mm .

Concrete Mixture
The mixture ingredients include Type I ordinary cement 375 kg/m 3 , local coarse aggregate 916 kg/m 3 , local fine aggregate 700 kg/m 3 , and silica sand 64 kg/m 3 .The specific gravities for the coarse and fine aggregates were 2.5 and 2.6, respectively.Polypropylene fibers with a monofilament configuration were used with a length of 19 mm, tensile strength of 165 MPa, specific gravity of 0.91, excellent alkali resistance, ability in decreasing drying and plastic shrinkage, ability in increasing impact resistance of young concrete, ability to reinforced concrete by acting mechanically with multidimensional fiber network coated with mortar.All the ingredients were mixed consistently and then the fibers were feeding manually to ensure the uniform distribution of fibers in the concrete mixture as shown in Figure 2. Then the concrete is placed in the wooden molds, vibrating them, straightening the top of the concrete specimen, de-molding the specimens for 24 hours after casting, and placing the specimens in lime-saturated water for 28 days for curing.The RC two-way slabs were tested firstly under impact load A steel ball of 7 kg mass with adjustable heights of 1.2 m to 2.4 m is allowed to fall freely through 150 mm in diameter hollow tube member placed vertically to stick the top surface of the tested two way slabs at the center by using a special design setup consists of steel members with I-section joined together to provide a horizontal platform to give simply supported condition for the two way slab as shown in Figure 1 Stage 1 .Then, all slabs were loaded up to failure using a hydraulic jack centrally positioned at the top of the slab as shown in Figure 1 Stage 2 .The reference slabs that have not subjected to impact load were just loaded up to failure Stage 2 .A square steel plate with a thickness of 50 mm and a side length of 200 mm was used to simulate the a column with 200 mm sides as shown in Figure 1.The applied load was measured by using load cell and three linear variable differential transformers LVDT were placed at specific location to measure the deflection profile of the tested slabs as shown in Figure 1.

Concrete Strength Results
Figure 3 shows the stress-strain diagrams for the concrete with different fiber volume fractions as well as the compressive strength, splitting tensile strength, and modulus of elasticity.Inspection of Figure 3 reveals that the slope of the stress-strain curve is linear up young's modules of elasticity to about 30-40% of the ultimate compressive strength, after that the curves become non-linear due to the initiation of the micro cracks at the paste-aggregate interface.The ultimate stress occurred after the formulation of the large crack within the concrete.Also, Figure 3 shows that the maximum compressive strength f ' c , splitting tensile strength f r , and young's modules of elasticity E c increased with the increase of the increasing of polypropylene content according to ASTM-C39, ASTM C496, and ASTM-C469 ASTM 2004 , respectively.The results also show that the polypropylene fibers had higher effect on the tensile strength and dynamic modules of elasticity than the compressive strength.Based on the experimental results, all tested slabs were failed in the punching shear mode and flexural cracks started from the loading steel plate and extended until the edges of the tested slab.Punching shear mode or failure was brittle failure which occurred near the loading steel plate compression face or top surface at the ultimate failure load, followed by the development of a punching shear failure cone at the tensile face Bottom surface .Figures 4-6 show the typical punching shear failure on the compression face and tensile face.Inspection of Figure 4 reveals that the 90 mm slab thickness had a remarkable impact on the flexural cracks and punching shear cone than 70 mm slab thickness by decreasing the number of the flexural cracks Tensile face and small punching shear cone.Also, Figure 5 shows that slabs subjected to impact had more flexural cracks and large punching shear cone than slabs not subjected to impact.In addition, Figure 6 shows the increasing of fiber volume decreased the number of flexural crack and the size of punching shear cone because the fibers contribution in the resisting of the applied forces until the fibers were pulled out from the concrete.Additionally, the occupation of fibers in stretching the failed bottom surface tension face of the slab away from the loading steel plate thus increased their punching shear capacity.Table 1 and Figure 7 show the summarized results and the effect of fiber volume percentage and impact load on punching shear load of the tested slabs.Inspection of Figure 7 reveals that the ultimate punching shear capacity of control slab slabs not subjected to impact generally increases and the degradation in slab strength due to impact load decreases with the increasing fiber volume percentage.Adding PFR in 0.3 to 1.2% by volume fraction increased the ultimate punching capacity with respect to slab without PFR by about 5 to 22%, respectively.While, the slab thickness h s 90 mm has a strong impact on the ultimate punching shear capacity with an enhancement of 35% with respect to slab with a thickness of 70 mm.In addition, the impact load at a height of 1.2 m and 2.4 m created degradation in the ultimate punching shear capacity of 30.5% and 34.6%, respectively, as well as the efficiency of fiber in absorbing of impact load or decreasing the ultimate load capacity degradation 30.5% to 16.1% is increased with the increasing of PFR percentage.c shows the effect of the impact load, slab thickness, and fiber volume on the load displacement behavior, stiffness, and toughness.The stiffness is defined as the slope of the part between the initiation of the first crack reaching the tensile strength of the concrete and the load at which the displacement equal to 3 mm and the toughness is defined as the area under the load displacement behavior.The load displacement behavior can be divided into two stages based on the crack growth and the shape of the load-displacement behavior as shown in Figure 8 d .In the first stage zero loading to load at which the displacement equal to 3 mm , the behavior is approximately elastic liner before the initiation of the first crack which is located at the center of slab and close to the loading steel plate which is caused a reduction in the stiffness of the curve.Then, in the second stage, the stiffness was reduced suddenly, followed by the development of the punching shear cone.Inspection of Figure 8 a reveals that the impact load at a height of 1.2 m and 2.4 m caused a reduction of 3.8% and 4.2%, respectively, in stiffness and 5.5% and 7.5%, respectively, in toughness with respect to control slab no impact load .While, the slab thickness h s 90 mm has a helpful strong impact on the stiffness and toughness with an enhancement of 151% and 127%, respectively, with respect to slab with a thickness of 70 mm as shown in Figure 8 b .In addition, Figure 8 c shows that the stiffness and toughness generally increase 30% to 128% and 22% to 86% , respectively, with the increasing fiber volume percentage 0.3% to 1.2% because adding PFR assist to delay and resist the formulation and expanding of cracks, thus slab stiffness and toughness are enhanced.3.4 Deflection Profile Assessment of the displacement profile of the tested slabs provides further information quantitative measure on the topic of the effect of tested parameters Figure 9 on the global structural behavior that is not directly obvious from studying of the load-displacement behavior and ultimate midpoint displacement.Figure 9 a-c shows the effect of the impact load, slab thickness, and fiber volume on the displacement profile.While Figure 9 d shows the displacement profile at different load value A: point between zero load and the load at which the displacement equal to 3 mm; B: point at displacement equal to 3 mm; C: point between the B and failure point; and D: point at failure at ultimate punching load capacity.Inspection of Figure 9 a reveals that the impact load at a height of 2.4 m had the highest displacement profile specifically at the mid-point comparing with impact load at a height of 1.2 m.This conclusion is observed the same in the mode of failure where that slabs subjected to impact at a height of 2.4 had more flexural cracks and large punching shear cone than slabs subjected to impact at a height of 1.2 m.While the displacement at the quarter-point is almost equal for both impact heights.In addition the slab thickness had the same effect on the displacement profile midpoint and quarter-point as the impact load and decreased with the increasing of the slab thickness as shown in Figure 9 b .In comparing all of the displacement profile showed in Figure 9 c , it can be seen that the PFR were successful in justifying the growth of localized failures in terms of number of flexural crack and the size of the punching shear cone, the PFR slabs exhibited displacement profile in which displacement were more consistently distributed and, as a result, were able to achieve larger displacement profile at failure.

EMPIRICAL MODEL
4.1 Punching Shear Model for Two-Way RC Slabs Subjected to Impact Load Prediction of punching shear strength in RC two-way slabs with different slab thicknesses, fiber volume fractions, and freely drop weight heights Impact load is fundamental in order to propose structural design procedures for structures subjected to impact load.Thus, an empirical model was proposed to predict the punching shear strength of two-way RC slabs subjected to impact load as a function of tested parameters.Most models founded in the literature and design codes base their verifications on a critical section to find the punching shear strength of non-impacted RC slabs without shear reinforcement Lorena et al. 2016, Micael et al. 2015, Ong et al. 1997, Kurihashi et al. 2006, Zhang et al. 2007  1 where V R is the punching shear capacity of two-way slabs at critical section located at d/2 from the face of the square or circular column.d is the effective depth of the slab, f′c is the concrete compressive strength at 28 days, and b o is the perimeter of the critical section.Based on the above equation, Eq. 2 can be used to describe the punching shear capacity of RC two-way slabs subjected to impact with some modifications as following: where α and β is a factor accounting for fiber volume fraction and impact load effects, respectively.Based on the regression analysis of the RC two-way slabs not subjected to impact load β 1 Figure 10 , Eq. 3 presents the relationship between the fiber volume fraction and α factor.where V f is the fiber volume fraction percentage.Based on the regression analysis of the RC two-way slabs subjected to impact load at a height of 1.2 and 2.4 m which is equivalent to a kinetic energy KE of 82.32 J and 164.64 J, respectively, Figure 11 , Eq. 4 and 5 presents the relationship between the fiber volume fraction and β factor, respectively.Thus the punching shear strength of the RC two-way slabs subjected to impact can be defined by the following equations

 
Note: where fsp is the indirect cylinder tensile strength of fiber reinforced concrete, τb 4.15 MPa is the average fiber-matrix interfacial bond stress, αf is a factor depending of the fiber geometry, lf is the length of the fiber, df is the diameter of the fiber, Vf is the volume of the fiber, d is the effective depth of the slab, e is the column side length, ρ is the steel reinforcement ratio, and f'c is the concrete compressive strength at 28 days  To find the predictability and the accuracy of the proposed model in Eq. 6 , it was compared with the punching shear models which are the most valid and accurate model for proposed model Narayanan and Darwish 1987 ; Shaaban and Gesund 1994 ;Harajli et al. 1995 ;Higashiyama et al. 2011 as shown in Table 2.The average value predicted/tested , coefficient of variation and correlation coefficient for punching shear capacity predicted by using various theoretical models are shown in Table 3. Inspection of Table 3 reveals that the predicted value Shaaban andGesund 1994 andHarajli et al. 1995 is closed to the tested value with an average value predicted/tested of 1.049 and 1.063, respectively, as well as the correlation coefficients are more than 0.95 which reflects that the behavior of the test data are well described by these models.Also, Narayanan and Darwish 1987 have an acceptable predicted/tested of 1.123.While, Higashiyama et al. 2011 is overestimated the punching shear capacity with an average value of 1.397.Figure 12 shows the tested punching shear strength versus predicted of existing models.Inspection of Figure 12 a-d reveals that the theoretical models are overestimated the punching shear strength of the tested slabs with higher R 2 more than 90%.In addition, Figure 12 f shows that the proposed model provides the highest number of predictions of predicted/tested in the intervals 0.98-1.02and the Higashiyama et al. 2011 have the lowest number of predictions of predicted/tested in the intervals 1.28-1.49 .

Predictability of the Proposed Model
The proposed model is checked against published experimental results by predicting the punching shear strength as shown in Table 4.In addition, the average value predicted/tested , coefficient of variation and correlation coefficient for the experimental results presented by Theodorakopoulos and Swamy 1993, Alexander and Simmonds 1992, Swamy and Ali 1982, Harajli et al. 1995, Narayanan and Darwish 1987, and Higashiyama et al. 2011 are summarized in Table 4. Inspection of Table 4 reveals that the average prediction error ranged from 2% for Theodorakopoulos and Swamy 1993 to 37% for Narayanan and Darwish 1987 , where the average value and the Correlation Coefficient for all the experimental results was approximately equal 87% and 94%, respectively, which shows that the proposed model has a good prospective to predict punching shear strength 5 CONCLUSIONS Based on the results and observations, the following conclusions are drawn: 1.The increasing in slab thickness had a notable effect on the flexural cracks and punching shear cone by decreasing the number of the flexural cracks Tensile face and the size of punching shear cone while the increasing in impact load and the fiber volume are increased the number of the number of flexural cracks and the size of punching shear cone.2. The increasing in slab thickness of 28% had an enhancement of the ultimate punching shear capacity of 35% and the adding PFR in 0.3 to 1.2% by volume fraction enhanced the ultimate punching capacity with 5 to 22% while the impact load at a height of 1.2 m and 2.4 m created degradation in the ultimate punching shear capacity of 30.5% and 34.6%.3. The impact load caused a reduction of less than 10% in stiffness and toughness of the tested slabs but the slab thickness enhanced the stiffness and toughness with an enhancement of 151% and 127%, respectively, as well as the stiffness and toughness increased 30% to 128% and 22% to 86% , respectively, with the increasing fiber volume percentage of 0.3% to 1.2%.4. The PFR slabs exhibited displacement profile in which displacement were more consistently distributed and, as a result, were able to achieve larger displacement profile at failure. 5.The proposed empirical model was in good agreement with theoretical models experimental results available in literature in predicting the ultimate punching shear capacity of two way slabs not subjected to impact.

Figure 2 :
Figure 2: Mixing procedure of the tested two way slab 2.3 Test Setup and Instrumentation

Figure 3 :
Figure 3: Stress-strain diagrams and mechanical properties of concrete / c f : compressive strength, r f :

Figure 4 :
Figure 4: Effect of slab thickness on crack patterns

Figure 7 :
Figure 7: Effect of fiber volume percentage and impact load on punching shear load

Figure 8 :
Figure 8: Typical load versus displacement curves 3.3 Load Deflection Behavior Figure 8 a-c shows the effect of the impact load, slab thickness, and fiber volume on the load displacement behavior, stiffness, and toughness.The stiffness is defined as the slope of the part between the initiation of the first crack reaching the tensile strength of the concrete and the load at

Figure 10 :
Figure 10: Relationships between fiber volume fraction percentage Vf and α factor for RC two way slabs not subjected impcat load

Figure 11 :
Figure 11: Relationships between fiber volume fraction percentage Vf and β factor for RC two way slabs subjected impcat load

Figure 12 :
Figure 12: Tested punching shear strength versus predicted of existing models Model1: Narayanan and Darwish 1987 ; Model2: Shaaban and Gesund 1994 ; Model3: Harajli et al. 1995 ; Model4: Higashiyama et al. 2011 ; Model5: Present Study Failure Analysis of Polypropylene Fiber Reinforced Concrete Two-Way Slabs Subjected to Static and Impact Load Induced by Free Falling Mass

Table 1 :
Specimens' Details and Test Results Note: Toughness is defined as the area under the load versus deflection curve

Table 2 :
Existing Punching Shear Strength Models

Table 3 :
Predicted to test punching shear strength

Table 4 :
Literature Experimental data and punching shear strength prediction