Retraction Retraction: Finite element analysis of two-way hollow core

This research provides informationabout the finite element analysis of the structural behavior of an innovative new type of two-wayhollow reinforced concrete (RC) slabs of twoway plastic piping system under the effects of concentratedpunching repeated loads. This new type of two-way hollow slab could be constructedbyreplacing part of the concrete volume by a continuous network of two-way plastic piping systemsto cutportion of the dead loads by reducing the self-weight of the createdslabsas well as offering networks of voids inside the RC slab which could be valuable for passing utility lines. The reliability of elements forms, material characteristics,types of constantsand the convergence study of the proposed finite element model of the new type of two-way hollow RC slabswas confirmed by the outcomes of the numerical study and the experimental results using five different parametric studies. The proposedFE modeshowed satisfactoryaccuracy with a maximum varianceratio of about 0.11in comparison with the ultimate loading capacity of the experimental behavior. The results weredemonstratingthe efficiency of the new methodology of producing two-way hollow RC slabs using the two-way piping system by reducing the self-weight by about 24% with maintaining about 79% of the total strength. Moreover, the reduction in the strength could be eliminated by locating the networks of plastic pipes out of the locations of the maximum stresses, adding micro steel fiber, using high strength concrete or increasing the reinforcement ratio.


Introduction
Today, one of the requirements of constructing different types of reinforced concrete buildingsis providing largespaces with a minimum number of columns.Increasing the clear spacing could lead to several issues such as increasing the slab depth, increasing the self-weightand causing higher cost. A number ofchoices are offered in practice such asusing RC slabs of higher depth, prestressing the reinforcement or replacing RC solid slab by RC hollow slab. The first option of using deeper RC slabs provides higher stiffness that canlead to satisfying the requirements of the serviceability. Unfortunately, using thicker RC slabs could lead to severalissues, including producing heavierslabs, which requires bigger structuralmembers (foundations and columns)along with effecting the clear height of floors. The second mentioned option (using prestressed units)also has several issues, includingthe necessities of highly trained staff and expensive equipment. In contrast, the third option IOP Publishing doi:10.1088/1757-899X/1145/1/012051 2 of using hollow RCslab systems, which usually produced by replacing a portion of the volume of the solid concrete by styro-foam blocks, plastic molds or polystyrene blocks, could provide lower selfweight, thinner columns, smaller foundations, less construction material and lower time of construction [1,2].
Over the last decades, several types of research were conducted on the structural behavior of hollow RC slab. It has been reported that increasing the hollowness ratio of hollow-core slab led to reducing the ultimate shear strength along with decreasing theductility [3].Replacing a portion of the solid concrete by hollow steel pipes increased the ultimate capacity and improving the slab toughness by reducing the deflection [4]. It also was shown that using both cubes and spheres that were made from recycled polypropylene, in fabrication RC hollow slabsled to similar ultimate capacity [5]. Furthermore, the mechanical performance of the hollow-core RC slab was significantly improved by increasing the thickness [6,7]. The structural performance of hollow-core RC slab has been proved to be improved by using shear reinforcement [8].
Engineers have been concerned in investigating the structuralbehavior of two types of RC hollow slabsincludingone-way hollow RC slabs (such as hollow-core slabs) and biaxial voided RC slab systems (such as styro-foam,Airdeck,BubbleDeck, U-boot, and cobiax). Those systems of RC hollow slab could be used only in dropping the self-weight of RC slabs. In contrast, the suggested new category of two-way hollow RC slab decreases the self-weight of RC slabs and providing continues networks of voids inside the RC slabs that could be used in passing utility. Thepresent paper providesvaluableinformation regarding the finite element analysis of the structural behavior of the new system of two-way hollow RC slab using ABAQUS/Standard 2017.

Materials
Traditional Portland cement, fine aggregates, coarse aggregates and superplasticizer (Sika ViscoCrete® 5930-L) were used in producing concrete mixtures. Moreover, silica fume was used in producing self-compacting high strength mixtures, and limestone was used in manufacture normal strength self-compacting mixtures. Also, fiber reinforced concrete was produced using micro steel fibers. Steel rebar (∅6 and ∅4) of diameter (6 mm and 4 mm, respectively) were used as (main and secondary reinforcement, respectively) in producing both the bottom and top layers of reinforcement, respectively. Finally, the two-way piping systems were fabricated using plastic pipes and plastic fittings, as shown in Fig. 1.

Figure 1.
Using two-way plastic piping systemsinassembling two-way hollow RC slabs.

Testing parameters
The structural behavior of eightRC slabs (two reference solid RC slabs and six two-way hollow RC slabs of different parameterswith dimensions of (80 ×880 × 880 mm)wasevaluated under the effects of concentrated punching repeated loads (CPRL). The influences of five variables were evaluated in this study,including the following:  Fig. 2(B, A, and C, respectively).

Details of reinforcement
All RC concrete slabs were reinforced by a bottom layer of 6∅6@150 cm c/c and a top layer of 6∅4@150cm c/cin two orthogonal directionsexcluding two-way hollow RC slab C65.F0.H16.D32.R2.Au.Lcof 16% of voids that hada bottom layer of 12∅6@75cm c/c and a top layer of 6∅4@150 cm c/cin two orthogonaldirections. A clear uniformcover of 1 cm was used for RCslabs.

Supporting and loading conditions
The supporting systemwas designed to provide a simply supporting condition by utilizingfour solid steel circular shafts of diameter (20 mm) that setting on arigid I-section steel frame, as presented in Fig. 3. As demonstrated in Fig. 3, the concentrated punching repeated load (CPRL) was applied to theRC slabs using a steel plate of dimensions (100 × 100 × 10 mm).The concentrated punching repeated load was applied overfive phaseswitha set of ten intervals with an increment of about 20% of the expected ultimate loading capacity. Finally,steel C-clamps were utilizedto prevent the uplifting of the corners.

Finite element model of two-way hollow slab
Nonlinear FEAwas performed to analyze the mechanical behavior of two-way hollow RC slabs under the effects of concentrated punching repeated load using an advanced three dimensional FEengineering computer program (ABAQUS/Standard 2017) and as follows:

Convergence study
The suitable mesh of two-way hollow RC slab model was conducted by performing a convergence study by assessing the effects of using different mech size ranging from (100 mm to 15 mm) on the ultimate carrying capacity. The convergence study showed insignificant influences on the load vs. carrying capacity for mesh size ranging between 15 mm and 30 mm. As a result, anelement side of 20 mm was used in this research, as presented in Fig. 4.

Assembly of parts
Assembling the two-way hollowRC slab model required five parts,including RC slab, solid steel shafts for supports, a bearing steel plate for loads andrebarfor reinforcement.3-D linear truss(T3D2), which could be define as 2-node element, was assigned for meshing the rebar whilea linear hexahedral elements (C3D8R, solid brick element), which could be defined as a 8-node linear brick, was assigned for meshing both of two-way hollow RC slabs, steel bearing plate andsolid steel shafts.

Interaction
Two types of constraints were considered in this study, includingan embedded constrain forthe reinforcing rebar (Fig. 5(A)) andthe surrounding concrete along with a tie constraint for both of thesupporting shafts (Fig. 5(B)) and the bearing plate withthe surrounding concrete (Fig. 5(C)).

Tie Constraint
Embedded Region Tie Constraint (A) (B) (C) Figure 5. Details of the constraint

Supporting and loading conditions
In this study, the supporting conditions were applied in two parts. The first was representing the simply supporting condition that wasachieved through applying displacement constrained at the solid steel shafts while the other part of the constrain was accomplished through using spring elements at the RC slab corners to prevent the uplifting of the corners, as shown in Fig.6(A and B, respectively).The punching repeated load was assainedby applying uniform pressure on the bearing steel plate (as shown in Fig. 6(C)).

Results and discussion
Typical behavior of three main levels was experiencedduring the test oftwo-way hollow RC slabs under the effects of concentrated punching repeated loads. First of all, a linearrelationship (elastic range) was experienced between loads vs. deflection curves from zero loadings until crack initiation. After crack imitation (elastic-plastic level) that happened at a load level ranging from 25.8% to 38.8% of the ultimate loading capacity, more cracks were initiated and propagated following diagonal paths towards the four edges due to increasing the magnitude or the number of cycles of CPRL. In this level of loading, a linear relationshipwithdifferent slopes was distinguishedinload-deflection curves. Also, cracks widthwasraised and moved to the corners of the RC slabs. The finale stage (plastic stage) was spotted witha higher level of loading with significant reduction in the stiffness.A test was terminated at thefailure of RC slabs, which could be experienced as a punching shear failure. The laboratoryresultsexposed that about 21% reduction in ultimate loading capacity was reported due to using two-way plastic piping systems in the production of two-way hollow RC slabs with hollowness ratio as high as 24% [8]. The research outcomes also proved the effectiveness of using a higher ratio of the reinforcement, adding micro steel fiber,allocating two-way plastic piping systems far from the area of maximum stresses or using high strength concrete to eliminating the decline that happens in the mechanical behavior of two-way hollow RC slabs [8].
Asatisfactory agreement was observed between the 3-D nonlinear finite element analysisand the mechanical behavior of the two-way hollow RC slabs that conducted by the laboratory work. Fig. 7, presented a comparative study between the deflection shapeof the FE models and the experimental models ofC65.F0.H16.D32.R1.Au.Lc two-way hollow RC slab as an attempt to verify the adequacy of the proposed FE model. TheFE analysis also stated that loads that corresponding to the first crack and the ultimate level were higher than the experimentalloads by about (14% and 11%, respectively) except for C65.F0.H24.D40.R1.Au.Lcthat had lower ultimate loading capacity byabout 4.5%. Besides, the ultimate central deflection of FE analysis was lower than the experimental deflection by about 15% except for C35.F0.H0.D0.R1.A0.Lcthat showed higher deflection by about 4.5%.Moreover, a stiffer behavior was observed by the models of finite element method, as demonstrated in Fig. 8 and Table 1.

Conclusions
This research was preparedfor conducting the mechanical behaviorof two-wayhollow RC slabsof twoway piping systems, which could be made-up by networks of plastic pipes and fittings,under the effects of concentrated punching repeated loads using ABAQUS/Standard 2017. EightRC slabs of dimensions (80× 880 × 880 mm) were tested in this research. Main findings include: 1) Usingtwo-way piping systems of about 24% of voids in producing two-way hollow RCslabs could lead to reducing the self-weight of RC solid slab with keeping about 79% of theoriginal ultimate strength along with providing useful networks of voids that could be used for passing utility lines.
2) The reductionin the strength of two-way hollow RC slabs could be eliminated by different options, including adding micro steel fiber, distributing two-way plastic piping systemsfar from the position of maximum stresses, increasing the ratio of the main reinforcement or using high strength concrete.
3) Conducting the structural performance of two-way hollow RC slabs under the effects of CPRL bynonlinear FEAshowed satisfactoryoutcomesin comparison with the experimental results with a maximum difference in the ultimate loading capacity,cracking loads and central deflection byabout (11%, 14% and 15%, respectively).