Failure mechanism criterion for multiaxial strength of concrete after exposure to normal and high temperatures
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 aswhere 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 follow
The variation of failure locus on the deviatoric plane is defined as the following form of Willam–Warnke [15].where 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).
References (44)
- et al.
3D lattice type fracture model for concrete
Eng. Fract. Mech.
(2003) - et al.
Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials
Int. J. Solids Struct.
(2009) - et al.
Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: a 3D study
Int. J. Solids Struct.
(2010) - et al.
3D meso-scale fracture modelling and validation of concrete based on in-situ X-ray computed tomography images using damage plasticity model
Int. J. Solids Struct.
(2015) - et al.
A plastic-damage model for concrete
Int. J. Solids Struct.
(1989) - et al.
An elasto-plastic damage model for plain concrete subjected to high temperatures
Eng. Struct.
(2002) - et al.
An elasto-plastic damage model for reinforced concrete with minimum number of material parameters
Comput. Struct.
(2004) - et al.
Damage-plastic model for concrete failure
Int. J. Solids Struct.
(2006) - et al.
A plastic-damage model for concrete in fire: applications in structural fire engineering
Fire Saf. J.
(2015) - et al.
A plastic-fracture model for concrete
Int. J. Solids Struct.
(1982)
Mechanical properties of concrete at high temperature – a review
Constr. Build. Mater.
Study on concrete at high temperature in China – an overview
Fire Saf. J.
Multiaxial tensile–compressive strengths and failure criterion of plain high-performance concrete before and after high temperatures
Constr. Build. Mater.
Triaxial strength and failure criterion of plain high-strength and high-performance concrete before and after high temperatures
Cem. Concr. Res.
Experimental study of strength and deformation of plain concrete under biaxial compression after freezing and thawing cycles
Cem. Concr. Res.
Triaxial compressive strength of air-entrained concrete after freeze-thaw cycles
Cold Reg. Sci. Technol.
Experimental study on strength and deformation of plain concrete under triaxial compression after freeze-thaw cycles
Build. Environ.
Triaxial T-C-C behavior of air-entrained concrete after freeze-thaw cycles
Cold Reg. Sci. Technol.
Dynamic multiaxial strength and failure criterion of dam concrete
Constr. Build. Mater.
Strength characteristics and failure criterion of plain recycled aggregate concrete under triaxial stress states
Constr. Build. Mater.
Micro-macro fracture relationships and acoustic emissions in concrete
Constr. Build. Mater.
Triaxial compressive behavior of UHPCC and applications in the projectile impact analyses
Constr. Build. Mater.
Cited by (11)
A fatigue life prediction method of cement-stabilized aggregates considering the effect of stress state
2023, Construction and Building MaterialsNonlinear strain energy based (NSEB) criterion for quasi-brittle materials under multiaxial stress states
2023, Construction and Building MaterialsExperimental study on the free expansion deformation of concrete during the cooling process after being heated to high temperature
2022, Construction and Building MaterialsCitation Excerpt :The structural load-bearing capacity was also reduced. Further, the safety of people and property will be seriously threatened [1,2]. Concrete is widely used in practical projects.
Investigation on the free expansive deformation of concrete during the heating process
2021, Construction and Building MaterialsCitation Excerpt :In addition, the inconsistency in the internal and external temperatures of concrete results in the development of cracks at weak links inside concrete, which further weakens the cohesive force among the various components in concrete. Then the bearing capacity of the concrete member exposed to fire would be reduced [1–4]. Concrete is a heterogeneous material dominantly composed of cement paste, coarse and fine aggregate, and pores.
Effect of heating rate on the free expansion deformation of concrete during the heating process
2021, Journal of Building EngineeringTri-axial compressive properties of high-performance fiber-reinforced cementitious composites after exposure to high temperatures
2018, Construction and Building MaterialsCitation Excerpt :On a unit scale base, the weight factors of the total materials cost, 28-day tensile strength, 28-day tensile ductility, and 28-day compressive strength were 0.3, 0.2, 0.3, and 0.2, respectively. The optimum mixture was then used to investigate the effect of confining pressure [38–43] and loading rate [46] on tri-axial compressive properties. The uniaxial tensile and compressive properties of the mixtures were reported in a previous study [44].