Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation

Grassl, Peter; Bažant, Zdeněk P.

doi:10.1061/(asce)0733-9399(2009)135:2(85)

Cited by 81 publications

(53 citation statements)

References 26 publications

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“…The geometrical randomness of discrete models is insufficient to simulate the size effect. To that end, one must include an autocorrelated random field of local strength, with the autocorrelation length equal to the RVE size (Carmeliet and de Borst 1995;Vořechovský and Sadílek 2008;Grassl and Bažant 2009).…”

Section: Review Of Weakest-link Model and Its Nonlocal Extensionmentioning

confidence: 99%

“…Therefore, the RVE must be defined as the smallest volume whose failure causes the failure of the whole structure (Bažant and Pang 2007). Recently, the random particle model indicated that the RVE size is approximately equal to the autocorrelation length of the spatial variation of material strength (Grassl and Bažant 2009). Therefore, RVE strengths can be assumed to be mutually independent.…”

Section: Introductionmentioning

confidence: 99%

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Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Eliáš

Bažant

2012

J. Eng. Mech.

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Engineering structures must be designed for an extremely low failure probability, P f < 10 À6 . To determine the corresponding structural strength, a mechanics-based probability distribution model is required. Recent studies have shown that quasibrittle structures that fail at the macrocrack initiation from a single representative volume element (RVE) can be statistically modeled as a finite chain of RVEs. It has further been demonstrated that, based on atomistic fracture mechanics and a statistical multiscale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted at a point of the probability about 10 À4 to 10 À3 . The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying gradually from the Gaussian distribution modified by a far-left Weibull tail applicable for small-size structures, to the Weibull distribution applicable for large-size structures. Compared with the classical Weibull strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution of the RVE strength makes the computation of the strength distribution of quasibrittle structures inevitably more complicated. This paper presents two methods to facilitate this computation: (1) for structures with a simple stress field, an approximate closed-form expression for the strength distribution based on the Taylor series expansion of the grafted WeibullGaussian distribution; and (2) for structures with a complex stress field, a random RVE placing method based on the centroidal Voronoi tessellation. Numerical examples including three-point and four-point bend beams, and a two-dimensional analysis of the ill-fated Malpasset dam, show that Method 1 agrees well with Method 2 as well as with the previously proposed nonlocal boundary method.

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Section: Review Of Weakest-link Model and Its Nonlocal Extensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Eliáš

Bažant

2012

J. Eng. Mech.

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“…This is an experimentally challenging task, but can be tackled by increasingly realistic numerical models. For example, Van Mier et al [1,17] and Grassl et al [18,19] used discrete lattice model to study the size effect of quasi-brittle materials. Karihaloo et al [20] and Duan et al [6] used the fictitious crack model to investigate the size effect on concrete.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: a size effect study

Wang

Yang

Jivkov

2015

Construction and Building Materials

160

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h i g h l i g h t sSize effect of concrete studied by realistic mesoscale models and Monte Carlo simulations. Key meso-control parameters (aggregate fraction and porosity) considered. Weibull size effect laws of strength obtained considering the key parameters. Equations relating strength and the key parameters obtained. Both aggregate fraction and porosity play significant role. a b s t r a c tSize effect in concrete under tension is studied by Monte Carlo simulations of mesoscale finite element models containing random inclusions (aggregates and pores) with prescribed volume fractions, shapes and size distributions (called meso-structure controls). For a given size and a set of controls, a number of realisations with different spatial distribution of inclusions are simulated to produce statistical data for macroscopic load/stress-strain curves. The complex meso-crack initiation and propagation is captured by pre-inserted cohesive interface elements. The effects of specimen size and meso-structure controls on macroscopic strength and toughness are analysed, and empirical size-effect laws for their dependences are proposed by data regression. It is also shown that the mesoscale porosity affects both strength and toughness and should not be ignored in size effect studies of concrete.

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“…With the development of computer and based on the theory of meso-mechanics, some outstanding researchers as Wrigers [65], Cusatis [66], Bazant [67,68] and Leite [69] established several models to study the problem with meso-mechanics theory and uniformization method. The results well disclosed that the initiation of crack is mostly from the interface between the aggregate and mortar, and the aggregate shape and grading as well as cement mortar strength affect a lot on the concrete strength.…”

Section: The Damage Mechanism Of Dam Concrete and Foundation Rockmentioning

confidence: 99%

Research advance in failure risk and local strength failure for high arch dams

Ren

Liu

2012

Chin. Sci. Bull.

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To develop national economy and use the water resources and hydropower resources sufficiently, a lot of high arch dams, with the height of more than 200 m, have been and will be built in China. Although arch dams have good mechanical behavior, there is still failure possibility due to the huge water pressure and high stress level in dam, complex topographic and geologic conditions, formidable environment and high intensity earthquake. As one of the three main aspects concerning the safety of high arch dam, the study on global destruction, has been elaborated in the literatures, and research advance in the other two aspects, namely the failure risk and local damage of high arch dams, will be reviewed in this paper. In recent years, the failure risk of high arch dams has been investigated, and the model for identifying dam failure risk factors has been established. It is shown that the foundation deterioration and strong earthquake are the major risk sources for high dam failure. With the fault tree method, the failure mode and failure probability of high arch dams are studied, and the principle for determining failure mode and the method of calculating failure probability are proposed. Meanwhile, the determination principle of acceptable risk standard for high arch dam was proposed, and the acceptable risk rate and the acceptable standard value of various risk losses were given. For the local damage of arch dam, it is pointed out that the local damage belongs to the strength failure at material level. The study on local failure mechanism of arch dam is reviewed, based on the theories that from traditional strength theory to damage mechanics and meso-mechanics theory. Aiming at the cracking, the main pattern of local failure of high concrete dam, the research advances in the analysis methods and cracking criteria for smeared crack model and discrete crack model are summarized, and the research findings of preventive measures for local failure are shown. high arch dam, failure risk, local damage, research advance Citation:Ren Q W, Li Q, Liu S. Research advance in failure risk and local strength failure for high arch dams. Chin Sci Bull, 2012Bull, , 57: 46724682, doi: 10.1007 To develop national economy, to save energy and to reduce emission, exploitation and utilization of water resources and hydropower resources are continued in China. At present, the height of arch dams under construction and to be built are of 300 m high level, such as Jinping arch dam (305 m high), Xiaowan arch dam (294.5 m high), Xiluodu arch dam (285.5 m high), and Baihetan arch dam (289 m high). The construction scale and difficulty of these dams are beyond the current design specifications, and there is hardly successful precedential reference. Moreover most of these high arch dams are located in the western region of China, where the topographic and geologic conditions are quite complex, with harsh environment and high seismic intensity as well as frequent geological disasters. In addition the resistance of dam and foundation may be red...

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Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation

Cited by 81 publications

References 26 publications

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation

Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: a size effect study

Research advance in failure risk and local strength failure for high arch dams

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