Refined approach for modelling strength enhancement of FRP-confined concrete
Introduction
The application of Fibre Reinforced Polymer (FRP) composites is recognized to be an effective design technique in the construction industry for concrete members due to their high strength-weight ratio. An important application of FRP composites is when used as a confining material for concrete columns, where effective strength and ductility enhancements are necessary to overcome extreme actions from earthquake loads for new or existing constructions. A large number of experimental and analytical investigations were conducted on the FRP-confined concrete, part of which involved conducting over 200 experimental studies that resulted in the development of over 85 axial stress-strain models. The majority of these studies were focused on the behaviour of FRP-confined concrete which resulted in proposing models that can be classified into two categories: (a) design oriented models [1], [2], [3], [4], [5], [6], [7], [8] and (b) analysis based models [9], [10], [11]. In the first category, closed-form equations were proposed based on direct interpretation of the experimental results; while in the second category, an incremental numerical procedure was employed to develop stress-strain curves for FRP-confined concrete composite sections.
The influence of concrete strength and confinement level on the axial compressive strength of FRP-confined concrete has been reported by numerous researchers for FRP-wrapped jackets [12], [13], [14], [15], [16], [17], [18], [19], [20] and others reported for FRP tube-encased concrete [21], [22], [23]. In addition, various formats of Peak Strength Expressions (PSE) were developed reflecting the relationship between the strength enhancement ratio (confined concrete strength/unconfined concrete strength, f′cc/f′c) and the confinement ratio (confining pressure/unconfined concrete strength, fl/f′c), which can be directly applied for estimating the improved confinement strength (f′cc). It should be noted however, that the deviation in formulating such relationships are a result of the various ranges of concrete strength and confinement level arrangements set for a particular investigation. From a comparative investigation into the influence of normal, high and ultra-high concrete strength on the confined strength, Vincent and Ozbakkaloglu [21] showed experimentally that the confined axial strength and strain of FRP-confined concrete decreases as the concrete strength increases. While on the other hand, as illustrated by numerous other developed PSEs, the increase in the amount of confinement results in an increase in both of the ultimate strength and stain of FRP-confined concrete.
Noticeably, there is a great number of studies conducted over the past two decades that provides good understanding for the behaviour of FRP-confined concrete in circular sections. However, the majority of these studies are attentive on refining proposed models for reflecting the behaviour of a considered range of concrete strength or confinement level. Thus, their accuracy is greatly limited to the size and parametric range of the test data used in the model development. Subsequently, in the current state of knowledge, most of the available PSE models are not accurately reflecting the individual effects of the concrete strength (f′c) and the confining pressure (fl) on the FRP-confined concrete strength (f′cc).
This paper is aimed at examining the individual effects of f′c and fl parameters on the FRP-confined strength by investigating the existing models in a different graphing format as reported in Section 2. A 3-dimensioal graphing presentation (surface plot) developed from 927 experimental data surveyed from the literature is presented in Section 3 which demonstrated the nonlinear relationship between the confinement parameters. In Section 4, a two dimensional Gauss fitting formulation process is presented for proposing a refined PSE which is recognized to accurately model the individual effects of f′c and fl. The proposed strength enhancement model was experimentally evaluated and its performance was compared with existing models selected from the literature and was found to offer the most reliable results for predicting FRP-confined concrete strength enhancements.
Section snippets
Compressive strength prediction of FRP confined concrete
Several attempts have been made to determine the confined concrete compressive strength (f′cc) as a function of the unconfined concrete strength (f′c) and confining pressure (fl) which can in turn be estimated using Eq. (1).where ffrp is the ultimate tensile strength of FRP material, t is the total thickness of the FRP jacket and d is the diameter of the confined concrete core.
One of the first, well-known equations that can analytically model the strength of an actively confined
Three dimensional graph presentation for strength enhancement
The 2-dimesional presentation of the SER models demonstrated in Fig. 1a, Fig. 1b (directly relating f′c and fl to f′cc) are limited in their ability to express the individual influence of the confinement level (fl) and the concrete strength (f′c) on the anticipated strength enhancement. For example, a 0.5 CR can be applicable for various arrangements of fl and f′c (i.e. fl = 15 MPa and f′c = 30 MPa, fl = 20 MPa and f′c = 40 MPa or fl = 25 MPa and f′c = 50 MPa), for such arrangement a single strength enhancement
Surface function model for predicting SER
The refined experimental-based contour chart (Fig. 4) is further investigated in this section for attaining an adoptable fitting surface function in order to formulate a refined analytical model which is anticipated to account further for the nonlinear relationships between the confining properties fl, f′c and f′cc.
Utilizing Originlab software, the two-dimensional Gauss function of Eq. (5) is utilized for fitting the experimental-based surface chart.where A, B
Experimental evaluation for the effectiveness of FRP confinement with increasing the concrete strength and confinement levels
As part of this paper’s generic aim in formulating a refined model for predicting the strength of FRP-confined concrete cylinders as a function of f′c and fl, an experimental investigation was undertaken by the authors [129] to evaluate the confinement enhancement with increasing the concrete strength and/or the confinement level of the FRP components. Three types of concrete mixes and one cement-mortar based cylindrical specimens were prepared and tested to achieve comparatively different
Conclusion
This paper presents an investigation for the individual effect of the confinement parameters including unconfined concrete strength and confining pressure on the strength of FRP-confined concrete cylinders. As an attempt to model such effects, a surface fitting function was utilized for developing a refined peak strength expression. Based on the observations reported and discussed in this paper, the following conclusions can be drawn:
- 1.
Numerous peak strength expressions are proposed in the
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