Elsevier

Construction and Building Materials

Volume 125, 30 October 2016, Pages 105-118
Construction and Building Materials

Failure mechanism criterion for multiaxial strength of concrete after exposure to normal and high temperatures

https://doi.org/10.1016/j.conbuildmat.2016.08.029Get rights and content

Highlights

  • Failure mechanism criterion is proposed based on experimental phenomenon and micro/meso-mechanism of concrete failure.

  • Material parameters in the failure mechanism criterion are confirmed and validated.

  • Failure mechanism criterion can predict the multiaxial strength of NSC and HSC after exposure to NHTs.

Abstract

Failure mechanism criterion is proposed based on comprehensive analysis of experimental phenomenon and micro/meso-mechanism of concrete failure. The failure mechanism criterion can successfully predict the multiaxial strength of normal-strength concrete (NSC) and high-strength concrete (HSC) in other studies. The newly proposed failure mechanism criterion is further developed to include temperature dependences and a cubic function is adopted to describe the relationship between material constants and temperature in the failure mechanism criterion. Then, the temperature dependent failure mechanism criterion is applied to predict the multiaxial strength of NSC and HSC after exposure to normal and high temperatures (NHTs). Good agreement is observed between the predicted values and experiment results from other studies. For the purpose of comparison, the mean error of the failure mechanism criterion is calculated and compared with that predicted by Seow–Swaddiwudhipong criterion, Songs criterion and He–Song criterion. The calculation indicates that the mean errors of the failure mechanism criterion, Seow–Swaddiwudhipong criterion, Songs criterion and He–Song criterion are 4.18%, 7.65%, 12.66% and 16.32%, respectively. This suggests that the failure mechanism criterion can give a more reliable prediction for engineering applications.

Introduction

Prediction of multiaxial strength for concrete is one of the most important issues in analysis and design of concrete structures. Several concrete failure criteria derived from different physical and phenomenological foundations have been developed including micro/meso-mechanically motivated fracture criteria [1], [2], [3], [4], [5], [6] and the plastic-damage theory [7], [8], [9], [10], [11], [12], [13]. Although these physics based models are more proper to characterize micro/meso-structure and evolution of plastic strain and damage for concrete, it became very difficult to determine several parameters in these physics based models due to the strong coupling of them and some of them have to be determined by stochastic methods. These drawbacks restrict the engineering applications of the physically motivated failure criteria. For engineering applications, several empirical criteria are developed to predict the concrete failure [14], [15], [16], [17], [18], [19], [20]. In spite of high accuracy, empirical criteria are unable to capture the failure mechanism in concrete because of lack of physical and phenomenological foundations.

The multiaxial strength of concrete is not only dependent on loading conditions, but also on temperature. Many research works [21], [22] have been carried out to investigate the strength and deformation of concrete after exposure to normal and high temperatures (NHTs). However, these researches are limited to uniaxial loading. The multiaxial strength of concrete has not been comprehensively investigated until the different loading experiments were carried out by Zhang [23] and He–Song [24], [25], [26]. These experiments included true triaxial test, biaxial test and axisymmetric test for normal-strength concrete (NSC) and high-strength concrete (HSC) after exposure to NHTs, respectively. The test results provided clues to multiaxial strength of concrete after exposure to NHTs. Meanwhile, three empirical criteria [23], [25], [26] were proposed to evaluate part of these test results, which are not enough to reveal the multiaxial strength of concrete after exposure to NHTs. In this investigation, experimental phenomenon and micro/meso-mechanism are comprehensively analyzed for failure of concrete under different loading conditions. These factors are combined to develop a failure mechanism criterion. Then, the temperature effects on the failure behavior of NSC and HSC is introduced into the failure mechanism criterion. The failure mechanism criterion is also used to construct the failure loci of NSC and HSC to validate their performance on prediction of the deviatoric stress invariant to failure.

Section snippets

Definition of stress state

Cartesian coordinate system (σ1, σ2, σ3) and Haigh–Westergaard coordinate system (ξ, ρ, θ) have been developed to describe the stress state, as shown in Fig. 1. From the geometrical construction, the ξ, ρ and θ can are expressed with σ1, σ2 and σ3 asξ=|OO|=13(σ1+σ2+σ3)ρ=|OP|=13(σ1-σ2)2+(σ1-σ3)2+(σ2-σ3)212θ=tan-13(σ2-σ3)(2σ1-σ2-σ3)where ξ, ρ and θ are hydrostatic stress invariant, deviatoric stress invariant and deviatoric polar angle, respectively. In this paper, tensile stresses are taken to

Analysis of experimental phenomenon and micro/meso-mechanism of concrete failure

Multiaxial experiments of concrete conducted by Zhang [23], He and Song [24], [25], [26], Shang and Song [27], [28], Shang et al. [29], Shang [30], Shi et al. [31] and He and Zhang [32] show that one or more macro-failure planes, which are parallel to the orientation of σ2, have been observed, as illustrated in Fig. 2. For convenience, one equivalent-failure plane is introduced to accommodate this failure mode in concrete block, as shown in Fig. 3. The normal stress σeq and shear stress τeq

Validation of the failure mechanism criterion

The tension and compression meridians of NSC and HSC are taken by Seow and Swaddiwudhipong [18] as followξfcu=a2ρtfcu2+a1ρtfcu+a0θ=0ξfcu=b2ρcfcu2+b1ρcfcu+b0θ=π/3

The variation of failure locus on the deviatoric plane is defined as the following form of Willam–Warnke [15].ρ(ξ,θ)=2ρc(ρc2-ρt2)cosθ+ρc(2ρt-ρc)4(ρc2-ρt2)cos2θ+5ρt2-4ρtρc1/24(ρc2-ρt2)cos2θ+(2ρt-ρc)2where a2 = −0.1597, a1 = −1.455, b2 = −0.1746, b1 = −0.788 and a0 = b0 = 0.1732 are determined by Seow and Swaddiwudhipong for NSC and HSC. By

Temperature dependent the failure mechanism criterion for concrete

Multiaxial strength of two concrete types is investigated by Zhang [23] and He–Song [24], [25], [26] under different loading conditions after exposure to NHTs. These concretes types are NSC [23] and HSC [24], [25], [26] and test results are tabulated in Table A.2, Table A.3. Three empirical criteria are proposed to describe part of these test results [23], [25], [26]. The types of tension and compression meridians of three empirical criteria are the same as Seow–Swaddiwudhipong criterion [Eq.

Conclusions

In this paper, failure mechanism criterion is proposed based on comprehensive analysis of experimental phenomenon and micro/meso-mechanism of concrete failure. The following conclusions can be drawn

  • 1.

    Determination of material parameters indicates that a, b and c in failure mechanism criterion can be assumed constants at d1eq = 0 for concrete, while the study of material parameters shows that the failure mechanism criterion is non-convex at d1eq = 0. However, to the best of our knowledge, most of

Acknowledgment

The authors gratefully acknowledge funding from the National Natural Science Foundation of China (Grant Nos. 50971098, 51271138).

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