Interface parameters between strengthened flat slab and concrete overlay

. This article aims to the comparison of different parameters for defining the interface characteristics between flat slab without transverse reinforcement and reinforced concrete overlay in non-linear analysis. The input parameters for the interface are stiffness, tensile strength, friction coefficient and cohesion. These coefficients represent uncertainties in non-linear modelling. Non-linear model was developed in ATENA 3D software and simulates punching shear of flat slab without shear reinforcement strengthened by concrete overlay. Two types of interfaces are considered: without reinforcement crossing the interface and with shear reinforcement crossing the interface. Parametric study shows, how different values of interface parameters influence the final punching shear capacity of representative model. Numerical models will be used as a prediction for experimental results of specimens.


Introduction
In order to overcome the effect of punching shear at connection zone between flat slab and column, the specific type of strengthening is able to enhance the punching shear resistance.The increase in shear resistance of flat slab could be achieved by several strengthening methods.Presented research is focused on enhancing punching shear capacity of flat slab by concrete overlay.The non-linear analytical model presented in this study was created in Atena 3D software and it is based on real experimental fragment of flat slab.
The results from the experimental investigation will be used to calibrate a non-linear model, specifically the input parameters.

Non-linear analytical model
Atena 3D software provides good corelation between results of analytical model and experimental results, when parameters are appropriately chosen.The major uncertainties of a model represent the number of brick or tetra elements through the depth of the flat slab element, concrete material definition, and interface parameters.

Meshing
Parametric study was carried out by Kadlec and Cervenka (2015) [1], according to a number of brick elements through the slab depth.Non-linear models from this parametric study were calibrated with results obtained from experimental tests.Similar parametric study was carried out by Kormošová (2020) [2], where number of elements and type of loading were compared.Reliable results were achieved by using minimum four, better five elements through the slab depth.
Non-linear model presented in this study was created in respect with findings described above.According to flat slab and overlay thickness, the mesh type was applied as brick with absolute size of 30 mm.

Concrete properties
The concrete material is based on fracture-plastic constitutive model.To define interface parameters, the calculation of interface fracture energy is needed.Fracture energy according to Model Code 1990 [3] can be calculated through compressive strength as shown in Equation (1).Dominant value of compressive strength represents the weakest concrete at concreteconcrete interface.

Interface parameters
Interface between the flat slab and concrete overlay is represented by an element with zero thickness, defined only by the contact area between the two layers of specimens.Important interface parameters are normal and tangential stiffness, tensile strength, cohesion, and friction coefficient.Cohesion was calculated considering the Mohr-Coulomb failure criterion in the interface (Figure 1).3D interface is defined as an open or close one.The open 3D interface allows the realistic behaviour of the interface with full separation of surfaces, while close 3D interface allows mobilization of stresses.The failure criterion is replaced by an ellipsoid in tension.Ellipsoid intersects the axis of normal stress at value of ft and the axis of tangent stress at a value of c (cohesion) [4].The cohesion coefficient is not provided in known design procedures, but the cohesion bond strength can be calculated for rough surface as 1.5-2.5 N/mm 2 and for a very rough one as 2.5-3.5 N/mm 2 [5].Considering a parametric study of M.E.Mohamad (2014) [5], the theoretical cohesion coefficient and friction coefficient can be empirically determined through peak height of the roughness of interface.Friction coefficient was considered as 0.9 to 1.5 according to Model Code 2010 provisions [6].
For simplification, both normal and tangential stiffnesses (KNN, KTT, respectively) are considered by the exact values as it is also recommended by the software developers.As Hugo Fernandes stated in his dissertation thesis [7], acceptable results were obtained, when stiffness was calculated according to Model Code 1990 provisions.Equations ( 2) and ( 3) represent calculation values used in this study.
where:  t,i is an interface tensile capacity,  F,i interface fracture energy,  t,Conc tensile strength of the weakest concrete in interface,  F,WeakConc fracture energy of the weakest concrete in interface.

Description of non-linear model
Analysed specimens represent the 1/4 of the experimental flat slab of size of 2.5 x 2.5 m.The original non-strengthened flat slab (marked as M0) was 180 mm thick and its effective depth was 134 mm.Cylindrical compressive strength of concrete element was assumed 25 MPa, the slab was reinforced by longitudinal steel bars of diameter of 16 mm, with spacing of 100 mm in two perpendicular directions x and y.The original flat slab element is supported by circular support, which represents column of diameter of 250 mm.Square elements of 50 x 50 mm in width are simulating supports and their position was set on lines of contra-flexure, in which zero bending moments are assumed.Supports serve also as monitoring points, in which the maximum normal force will be monitored.
First set of analysed specimens (marked as M1) imitate strengthening by concrete overlay without shear connectors.Element of concrete overlay also represents the 1/4 of experimental strengthened flat slab strengthened by concrete overlay of size of 2 x 2 m and of 60 mm in thickness.Cylindrical compressive strength of this concrete element representing the concrete overlay was of 30 MPa.The element of concrete overlay was reinforced by the main longitudinal steel bars of diameter of 10 mm, with spacing of 100 mm in two perpendicular directions x and y.To achieve the minimum concrete cover to reinforcement with higher reinforcement ratio, steel bars were doubled.To create non-linear fragment marked as M1f Atena 3D default settings [4] of interface concrete-concrete were used and according to low friction coefficient, delamination in interface in early iteration was expected.
Second analysed specimen (marked as M2b) imitates strengthening by concrete overlay with shear connectors, modelled as reinforcement with shear heads.Characteristics of elements were the same as described above.Shear connectors were represented by reinforced steel bars intersecting concrete-concrete interface, with diameters of 10 mm.Definition of interface was the same as for M1b, therefore similar values were achieved in experimental studies abroad.One modelled fragment marked as MP represents strengthened flat slab by concrete overlay, where interface concrete-concrete was considered as perfect connection.Both concrete and reinforcement characteristics were taken over previously mentioned models.
Load was applied by deformation gradually increasing in 0.1 mm steps on the circular column element and whole analysis was iterated by Newton-Raphson method in 80 analysis steps.

Results from the NLFEA modelling
The resistance of the flat slab fragment was determined by failure of the flat slab.Failure mode of the flat slab was signalized by a sharp drop in force at the constant deformation as it can be observed from the following diagrams (Figure 3, Figure 4).Original fragment of flat slab (M0) achieved higher deflection in failure mode as all the strengthened fragments (Figure 3a).Behaviour of fragment M1f was similar to fragment M0 and it was caused by partial delamination from the beginning of the loading process.When full delamination was achieved, the resistance of the flat slab was exceeded, which led to failure.From the beginning of the loading process, the concrete overlay behave as separate element and negatively influenced original flat slab by its weight.Different interface parameters in fragment M1a-1e did not change the results of loading force, neither deflection and results are quite similar, even when minimum friction according to maximum cohesion coefficient were used.Figure 3b compares two models M1b and M2b with the same interface parameters, and the only difference in using shear connectors in fragment M2b.Fragment M2b achieved higher resistance as fragment M1b.It is an object of discussion which peak of the diagram represents failure.At first drop of the peak, shear connectors are able to stabilize concrete overlay from delamination.Fragment reports increasement in both loading force and deflection of the flat slab.Observation of diagram in Figure 3b, can lead to question, if it is possible achieve higher load force with higher deflection by using shear force (M2b), when comparing to perfect connection (MP).The major difference between each model is obtained by observing individual results from principal strains and deformation.Principal strain in fragment M1b just before failure indicates for bending failure (Figure 4a).After the delamination of concrete-concrete interface, brittle failure by punching shear appears (Figure 4b).Separate behaviour of the concrete overlay can be observed from Figure 5. From the beginning of loading process, cracks are concentrated along concrete-concrete interface.The behaviour of original flat slab does not depend on the influence of concrete overlay even when reaching failure mode (Figure 5a).Concrete overlay did not significantly contribute to punching shear capacity of the original flat slab.First set of fragments namely from M1a to M1e reach very similar or the exact values of punching shear capacity and also deflection.However, deformation in some load steps before failure could remind delamination, but software did not notice the loss of cohesion.Figure 6 shows this phenomenon at the moment when loading force reaches the punching shear capacity of original slab, which represents 65 percent of punching shear capacity of modelled fragment M2b.
Results from this parametric study will serve as calibration models to experimental study of tested flat slabs.This work was supported by the Scientific Grant Agency VEGA under the contract No. VEGA 1/0310/22.

Fig. 1 .
Fig. 1.Failure surface according to Mohr-Coulomb [4].where: c is the cohesion of the interface concrete-concrete, ft interface tensile stress,  angle of friction,  interface tangential stress,  interface normal stress.