INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Geo polymer materials are inorganic polymers synthesized by reaction of a strongly alkaline silicate solution and an alumino silicate source. Geo polymer is used as binder to completely replace the ordinary Portland cement in producing Geo polymer concrete(GPC). They possess the advantages of rapid strength gain, elimination of water curing, good mechanical and durability properties and are additional ecofriendly and sustainable alternative to Ordinary Portland Cement (OPC). While substantial research work has been reported on behaviour of reinforced concrete structural elements, similar studies have not been reported on GPCs. This paper describes an experimental and analytical investigation on shear behaviour of reinforced GPC and OPCC beams. The aim is to study the shear behavior of reinforced GPC and OPCC beams. Three GPC mixes and one OPCC mix were considered for the study. All the beams were provided with the same flexural and shear reinforcement and the beams were tested under two point loading with two shear span to depth ratios of 1.5 and 2 for each of the mixes. This paper presents the details of the mix designs of GPC mixes, parameters investigated, preparation of RGPC beams, testing and evaluation of structural behavior with respect to cracking, service load, deflections at various stages and failure modes. Comparison of shear design procedure of beams was made by conventional IS 456 2000 approach and Modified compression field theory. Non linear finite element analysis of beams by 3D modelling of concrete (solid65 element) and discrete modeling of reinforcement (Link8 element) was carried out using ANSYS software. For shear span to depth ratio of 1.5, load shear capacity, load deflection characteristics and failure modes and crack patterns obtained from the experimental and analytical study were compared for both RPCC and RGPCC beams. The results of the study indicate that the performance of RGPC is similar to that of RPCC beams and the ultimate loads are in the same order. The failure modes and crack patterns are also similar.


Introduction
The deterioration of Reinforced Concrete (RC) structures has been a perennial problem due to the corrosive nature of reinforcements embedded in the concrete. Though several recommendations like the use of water proofing admixtures in concrete, impermeable membranes, epoxy coated reinforcements are tried for preventing the corrosion of steel reinforcement, all the attempts are not commercially much viable. The use of noncorrosive reinforcements in the place of steel reinforcements has therefore been focused as an alternative to improve the life span of the concrete structures. Fibre Reinforced Polymer (FRP) reinforcements offer many advantages over steel reinforcements including resistance to electrochemical corrosion, high strength to weight ratio and easy in fabrication and electromagnetic insulating properties. Further more, FRPs are available commercially in the form of sheets or reinforcements. FRP reinforcements are made of two components namely, fibres and matrix. The matrix is usually a thermoset resin such as vinyl ester or epoxy, while the fibres are carbon, aramid or glass fibres. The use of GFRP reinforcements, in lieu of conventional steel reinforcements requires better understanding under different parametric

Behaviour of Concrete under Fatigue Loading
Fatigue is a permanent internal structural (micro cracking) change in a material subjected to fluctuating stresses or strains, if the loading exceeds a certain limit. Fatigue failure of materials normally occurs at a stress level much lower than the static stress because of repeated stress or deformation, and in most cases it appears in an abrupt brittle fracture pattern. Pavements, bridges and other structures supporting oscillating machinery are included in this category. Fatigue fracture of concrete is characterized by considerably large micro cracking and strains when compared to fracture of concrete under static loading. The degree of fatigue damage can be measured by the magnitude of elastic and residual (plastic) deflection, crack widths and strains at various levels along the thickness of the specimen. In fatigue test, the number of cycles applied on the slabs up to their failure is noted and a graph is drawn between stresses versus numbers of cycles applied (SN curve). In the present study, two types of repeated loading schemes such as constant amplitude fatigue loading (scheme I) and accelerated fatigue loading with variable amplitude (scheme II) are adopted. Generally, bridge structures are seldom subjected to constant amplitude repeated loading during their life time, but considering the variability in the load amplitudes, constant load amplitude is being normally considered (Ferreira 2001, KaeHwan Kwak 2001, Benmokrane 2007).
The constant amplitude loading has been actuated between a minimum load and a peak load i.e. 10% and 80% of the nominal ultimate static strength of the control slab at a rate of 4 Hz to acquire the load cycles of constant amplitude. The minimum load level is set to prevent any impact during cyclic loading and the maximum load is fixed so as to accelerate the speed of testing. The loading range is same for all the specimens and it is chosen to be approximately symmetrical around the service load and to enable the slab specimen failure within the reasonable time. The accelerated fatigue loading with variable amplitude (scheme II) is done to assess the effect of cyclic loading at lower peak load levels. The minimum load is fixed as 2 kN and different percentages (20%, 40%, 60% and 80%) of the peak loads of the corresponding slabs are selected as variable maximum loads. For all the specimens, 10,000 number of cycles is applied for each and every percentage of load at a frequency of 4 Hz. and is continued till the slab completely fails.

Concrete
The concrete mix is designed for relatively higher strength due to the high strength possessed by fibre reinforcements. All the slab specimens are cast using normal weight concrete of

Testing programme
The Testing programme is classified into three categories: 1. Sixteen slabs are subjected to static or monotonic type of loading; 2. Sixteen slabs are subjected to constant amplitude of fatigue loading; 3. Seven slabs are subjected to variable amplitude of fatigue loading scheme.

Experimental set up for Static loading condition
The length and width of all slabs are 2400 mm and 600 mm respectively. The clear span of 2200 mm is kept constant for all the specimens. A clear concrete cover of 20 mm is adopted for the longitudinal reinforcements. Load frame of capacity 50 tonnes is used for testing all slab specimens. All slabs are instrumented with a Linear Variable Differential Transformer (LVDT range 0100mm) at mid span and at onethird points to monitor vertical deflections. The static load on the slabs is applied with the help of hydraulic jack having 25 tones capacity and measured with a proving ring. Demec gauge pellets are pasted at the topmost compression fibre, at the middle of the slab and at the level of reinforcements of slab to observe the displacements. The load is applied at an increment of 2 kN. The crack widths are measured using crack width detection microscope. The static test results are presented in Table 3. The experimental test set up for static loading is shown in figures 2 and 3.

Experimental set up for constant amplitude of fatigue loading condition
To simulate the traffic loading, two types of repeated loading have been tried in this study. First set of slabs (sixteen in numbers) are subjected to constant amplitude of fatigue loading scheme. Slabs are kept on the loading frame. A 20mm thick neoprene sheet is used between the steel plate and the concrete surface to avoid local effect. A clear span of 2200mm is adopted between the supports. A 50 kN capacity with 250mm stroke actuator monitored by computer is programmed to apply fatigue loads on the slab. A data acquisition system is used to monitor and acquire all strain readings with the help of strain gauges and LVDTs for both the static and repeated loadings. Demec gauges are also used to observe the displacements on a pre defined positions i.e on the brass pellets. The minimum load level is set at 2 kN to prevent any impact due to repeated loading and also to represent the effect of superimposed loads on a bridge like pavement and insulation (Kumaran 2002, kumaran, 2003Viyaprakash 2004, Rashid 2005. The maximum load level is set at 80% of ultimate static load of  Table 4. Figure 4 shows the test set up for the same.

Experimental set up for variable amplitude of fatigue loading condition
The second set of slabs (sixteen numbers) are subjected to constant amplitude of fatigue loading scheme. The experimental set up for variable amplitude of fatigue loading condition is similar to constant amplitude of fatigue loading condition. The variable loading scheme is applied by selecting 2 kN as minimum load for all the slabs and different percentages of their ultimate loads (i.e. 20%, 40%, 60%, and 80%) as maximum loads to assess the effect of cycling at lower peak load levels (Sobhy Masoud 2001). Each and every fatigue loading steps is applied for 10,000 cycles at a frequency of 4 Hz till the failure of the slabs. The degree of fatigue damage can be evaluated by the magnitudes of strains in reinforcement, crack width, elastic deflection and residual (plastic) deflection. The magnitude of residual deflections is the energy dissipation of the slab which is considered as a proper measure to estimate the degree of damage. The deflections, crack widths, crack propagation, crack patterns, modes of failure and number of cycles up to failure are measured at the end of each repeated loading step. The results of slabs under variable amplitude of fatigue loading scheme are presented in Table.5 and 6.

Analytical Study
In this study, a nonlinear finite element model consisting of full size oneway concrete slab is considered. Material modelling for concrete is done based on the compressive and tensile behaviour and the degradation properties of concrete due to cracking and crushing using shell elements. GFRP reinforcements are modelled as layers which exhibits uniaxial response. A perfect plastic and strain hardening plastic approaches are used to model the compressive and tensile behaviours of concrete. Figure 5 shows the finite element representation of full size RC one way slab. The effect of finite element mesh is also considered in this study and the results are compared.

Compressive behaviour of concrete
The non linear behaviour of concrete is inelastic. A perfect plastic and strain hardening plasticity approaches are used to model the compression behaviour of concrete. A dual criterion for yielding and crushing in terms of stresses and strains is considered (Ferreira 2001).

Tensile behaviour of concrete
The response of concrete under tensile stresses is assumed to be linear elastic until the fracture surface is reached. This type of fracture or cracking is governed by a maximum tensile stress criterion. Cracks are expected to form in planes perpendicular to the direction of maximum tensile stress, as soon as it reaches a specified concrete tensile strength. In this study, concrete is assumed to be an isotropic material before cracking and the concrete becomes orthotropic after cracking, with a material axis oriented along the directions of cracking. Figure 2 shows the finite element representation of full size RC one way slab simply supported along two opposite edges and free along other two. The slabs are rectangular in plan and spanned 2400mm with two variable thicknesses of 100mm and 120 mm. They are reinforced with mesh type of reinforcements with three different types of steel/ GFRP ratios of 0.65%, 0.82% and 1.15% in longitudinal directions. Concentrated loading is applied at one third points. The entire thickness of slab is divided into ten concrete layers of equal thickness, out of which one layer is steel/GFRP. In each layer, 144 slab elements are considered in the basic analysis and totally 1440 elements in the entire slab. In order to investigate the effect of finite elements mesh size on the results a 144 and a 288 elements are considered in each layer in the finite element modelling of the slab and the results are compared. The material properties of the specimen are summarized in Table 2.

Interpretation of the Results
The results of the experimental study are depicted in the form of graphs as shown in Figures 6 23.

Repeated loading results
The degree of fatigue damage is determined by the magnitudes of strains in reinforcement, crack widths, elastic deflections and plastic (residual) deflections (KaeHwan Kwak 2001, Yost 2001). The magnitude of residual deflections is related to the energy dissipation of the slab and the same is considered in this study as an accurate measure to estimate the degree of damage. Based on this study, it is observed that with the increase in the number of load cycles, the corresponding ultimate deflection, number of cracks and the width of the cracks increase. These measurements differ considerably according to the types of reinforcements used in this study.  r slab. Also, by increasing the grade of concrete from 20 N/mm 2 to 30 N/mm 2 , the fatigue performance of similar type of slabs increases by 1.33 times. It is also noted that the magnitude of damage accumulated to the slab reinforced with steel reinforcements is higher than GFRP reinforced ones. Among all the GFRP reinforced slabs, sand coated GFRP reinforced slabs exhibits the lowest residual deflection and the greatest stiffness. Sand coated GFRP reinforced slabs proved its excellent fatigue performance over the slabs reinforced with other types of reinforcements. Under the variable amplitude scheme of loading, the load was applied at different loading steps by choosing a constant minimum and varying maximum loads and each load steps are repeatedly applied for about ten thousand times. It is observed that most of the slabs exhibited equal or nearer values of ultimate deflection and crack width that have been experienced in the slabs subjected to static loading. The test results (residual and ultimate deflections and crack widths) are lesser than the results obtained from the constant amplitude scheme of loading. The experimental results of the constant and variable amplitude repeated loadings are shown in Table. 4, 5 and 6. SN curves are drawn for constant amplitude loadings and are depicted in Figure 16. From the fatigue test results, it is found that GFRP reinforced concrete slabs have failed at 6075% of the static ultimate load. The equation regarding the relation between the operational stresses applied and the number of cycles is shown as follows.
where, A and B are experimental constants derived from the test values, Y operational stress applied, N is the fatigue life of slabs in terms of number of load cycles. From the above study, the relation between fatigue strength (which is the percentage ratio of fatigue loading and static ultimate loading ) and fatigue life are depicted in Fig. 7. Eqn. 2 is obtained from the regression analysis. 15 where ( 783 .

Crack growths and modes of failure
Cracks appear at the bottom surfaces of concrete slabs whenever the tensile stresses exceed the modulus of rupture of concrete. The first crack appears at the middle of the slab and develops slowly across the width of the slab. The second crack forms at the right support of the slab and subsequently at the left support of the slab. Further development of cracks occurs, on increasing the application of load under static type of loading and on increasing the number of load cycles under the fatigue type of loading at constant amplitude and variable amplitude. All the slabs experience flexural type of failure. At ultimate load GFRP reinforced slabs experience concrete crushing followed by the rupture of GFRP reinforcements. Steel reinforced slabs show the flexural type of failure by the yielding of steel which is then followed by crushing of concrete. The ultimate load carrying capacity of GFRP reinforced slabs is increased and the corresponding deflections, strains and crack width are reduced by increasing the thickness, grade of concrete, reinforcement ratio of the slabs. GFRP reinforced concrete slabs experience better performance and longer fatigue life when compared with those slabs reinforced with steel. This is mainly attributed due to the equal values of the modulus of elasticity for GFRP reinforcements and concrete in addition to the linearelastic behaviour of GFRP reinforcements. From the experimental results it is observed that sand coated GFRP reinforced slabs have showed better fatigue performance than the other reinforced slabs.

Finite element analysis observations
Based on Finite Element Analytical study, it is observed that the effect of tension stiffening and mesh size of the element are almost identical and agreeable very well with the experimental results. But in contrast, the solution without the effect of mesh size of the element significantly overestimates the slab deflection.  Figure 6: Load Vs Deflection for 100mm thick slab reinforced with different types of Reinforcements The results of the latter case reveal that the crack band width extends over the entire element and model becomes much more flexible than the real structure. In order to improve the accuracy of the results, a much finer mesh is tried out. It has also been observed that neglect of the effect of strain softening of concrete results in lesser deflection consequently higher stiffness than the actual slab. Figure 19 compares the analytical load deflection relation with the experimental data. It is found that the predictions of the proposed model are in good accordance with the experimental data.

Conclusions
A total number of thirty eight one way concrete slabs, (out of which eleven are reinforced with conventional steel reinforcements and twenty nine are reinforced with Glass Fibre Reinforced Polymer (GFRP) reinforcements) are studied. A rigorous analytical and experimental studies on the behaviour of conventional and GFRP reinforced concrete one way slab under static and repeated loading are investigated by considering reinforcement 567 ratios, grade of concrete, thickness of slab and type of GFRP reinforcements. GFRP slabs are investigated for static and repeated loading (with constant and viable amplitude loading). Finite element analysis is also performed to study the effect of different parameters on the flexural capacity of slabs. All the slabs experience flexural type of failure. At ultimate load, GFRP reinforced slabs experience concrete crushing followed by the rupture of GFRP reinforcements. As the ultimate load carrying capacity of GFRP reinforced slabs is increased, the corresponding deflections, strains and crack width are reduced by increasing the thickness, grade of concrete, reinforcement ratio of the slabs. GFRP reinforced concrete slabs experiences better performance under repeated loading than those slabs reinforced with steel. It is due to the fact that the onset of permanent deformations is delayed due to the higher stains in the GFRP specimens than the conventionally reinforced slabs. This is mainly attributed due to the equal values of the modulus of elasticity for GFRP reinforcements and concrete in addition to the linearelastic behaviour of GFRP reinforcements. From the experimental results it is observed that sand coated GFRP reinforced slabs have shown better fatigue performance than the other reinforced slabs. Based on this study, it is found that a good agreement exists between the analytical and experimental results.