Column of strength - predicting failure behaviour
Azrul Mutalib and Hong Hao from The University of Western Australia show how pressure-impulse diagrams for fibrereinforced polymer-strengthened concrete columns can be used to predict failure behaviour.
Since the early 1990s, fibre-reinforced polymer (FRP) composites have been widely used to strengthen existing concrete and other structures in resisting blast and impact loads. It has been proven that FRP strengthening is highly effective in preventing injuries from explosive bombs, but despite a number of studies that demonstrate the effectiveness of FRP strengthening, there is still a lack of information that quantifies the blast resistance capacities of reinforced concrete (RC) columns with various FRP strengthening measures.
Pressure-impulse (P-I) curves are commonly used to quantify the structural capacities in resisting blast loadings. They are of peak blast pressure (P) and impulse (I) with the structural damage levels. We will show the empirical formulae to predict pressure asymptote (PO) and impulsive asymptote (IO) of P-I diagrams for RC columns strengthened with FRP. The derived P-I diagrams can be used to correlate the increase in structural capacities in resisting blast loadings with respect to the FRP strength, number of layers or thickness of FRP and FRP configurations.
A P-I diagram is one of the simplest methods for describing a structure’s response to an applied explosive load. It is a graphic representation of the damage threshold of a structure when a dynamic load is applied to it. The damage threshold is based on distinct levels that are usually independent of the structure’s response history. The P-I diagrams are used to correlate the blast load to the corresponding damage. These diagrams incorporate both the magnitude and duration of blast loading and can be readily used for a quick damage assessment of structures in different blast scenarios.
The P-I diagram developed in this article corresponds to the defined damage index, D, which is based on the residual axial load-carrying capacity since the primary function of a column is to carry the vertical loads. The damage indexes are defined as – D = 0-0.2 low damage, 0.2-0.5 medium damage, 0.5-0.8 high damage and 0.8-1 collapse. Where D can be calculated as –
In which P Residual is the residual axial load-carrying capacity of the damaged RC column and PDesign is the maximum axial load-carrying capacity of the undamaged RC column. Figure 1 shows typical P-I diagrams with PO and IO of different D. As seen above and to the right of the curve, the damage level of the structure component is exceeded, and that below and to the left the damage level is lower.
Rectangular RC columns are commonly used in low- to medium-rise buildings. The RC column can be retrofitted using FRP composite wraps with unidirectional fabrics of strips in the longitudinal and hoop directions. The hoop wrap is most useful to increase the shear resistance and ductility capacity, as well as providing confinement to the concrete, while the longitudinal fibre strip is added to increase the column bending capacities. The other benefit is that the FRP sheet offers protection from fragment damage. Figure 2 shows the rectangular RC columns strengthened by FRP wrap and longitudinal strips.
Safety in numbers
Intensive numerical simulations have been carried out to calculate the dynamic response and damage of RC columns of different material properties and dimensions, strengthened with FRPs of different thickness and layers of strips and wraps subjected to blast loads of different peak pressures and impulses. The numerical models have been verified by comparing the field test and analysis results by other researchers with the numerical simulation results. The FRP parameters considered in the simulations include the FRP wrap and strip strength, fwrap and fstrip in MPa and thicknesses twrap in millimetres. The RC column parameters considered are concrete strength fcu in MPa, column height H, column width b, column depth d, all in millimetres and the longitudinal and transverse reinforcement ratio, ρ and ρs, respectively. Figure 3 shows the RC column details.
Previous studies, as well as the present numerical results, indicate that the P-I diagram for RC columns can be expressed as –
where PO and IO are the pressure and impulse asymptotes respectively. Therefore, the P-I diagram can be easily constructed once PO and IO are obtained. The PO and IO at different damage levels can be calculated using the formulae given in equation (3)-(14).
for nonretrofitted RC columns, while for FRP strengthened RC columns,
It should be noted that the derivation of the above formulae is based on the reinforcement steel strength of 550MPa. If the reinforcement strength is not 550MPa, the equivalent longitudinal and transverse steel area Ase, defined below, should be used when calculating the respective reinforcement ratio –
Constructed P-I diagrams
Using the same dimension of column, Figures 4-6 show examples of the constructed P-I diagrams for unstrengthened RC columns, strengthened RC columns with FRP wrap and strengthened RC columns with FRP wrap and strips, respectively.
The P-I diagrams can be used to assess the performance of RC columns under various blasting scenarios. With intensive numerical simulations, the empirical formulae are derived to predict PO and IO for constructing P-I diagrams of RC columns of different dimensions and material properties, with or without FRP strengthening measures.
Azrul Mutalib and Professor Hong Hao, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia. Tel: +61 (08) 6488 6000. Email: firstname.lastname@example.org and email@example.com