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1.
Concrete cracking in reinforced concrete structures is governed by two mechanisms: the activation of bond forces at the steel–concrete interface and the bridge effects of the reinforcement crossing a macro‐crack. The computational modelling of these two mechanisms, acting at different scales, is the main objective of this paper. The starting point is the analysis of the micro‐mechanisms, leading to an appropriate choice of (measurable) state variables describing the energy state in the surface systems: on the one side the relative displacement between the steel and the concrete, modelling the bond activation; on the other hand, the crack opening governing the bridge effects. These displacement jumps are implemented in the constitutive model using thermodynamics of surfaces of discontinuity. On the computational side, the constitutive model is implemented in a discrete crack approach. A truss element with slip degrees of freedom is developed. This degree of freedom represents the relative displacement due to bond activation. In turn, the bridge effect is numerically taken into account by modifying the post‐cracking behaviour of the contact elements representing discrete concrete cracks crossed by a rebar. First simulation results obtained with this model show a good agreement in crack pattern and steel stress distribution with micro‐mechanical results and experimental results. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Microscopic studies using advanced experimental techniques have provided better insight into the fracture mechanisms in cement‐based materials. A clear understanding of fracture mechanisms is critical for the development of rigorous computational models for analysing fracture. Fracture analysis is usually carried out by finite element method. Accuracy of FE analysis depends upon the choice of mesh and for the predictions to be reliable, discretization errors are to be minimized. In cohesive crack approach, the non‐linearity is limited to the boundary conditions along the geometric discontinuity while the bulk of the material retains its elastic nature. The paper presents a mesh‐adaptive strategy based on ZZ error estimator to model discrete crack propagation in cement‐based materials. Examples of simulations have demonstrated the potential of the mesh‐adaptive technique in modelling the evolution of the localized strain profiles as well as failure of concrete test specimen. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Nathan Benkemoun Hayder Al Khazraji Philippe Poullain Marta Choinska Abdelhafid Khelidj 《国际地质力学数值与分析法杂志》2018,42(3):449-468
In this paper, mesoscale hydromechanical simulations are performed to study (1) fracture features and (2) crack‐gas permeability coupling evolution in the context of the tensile splitting test. The mesostructure is based on a 2‐phase 3‐D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. To take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account microcracking. This mechanical model is cast into the framework of the enhanced finite element method. Concerning the coupling with gas permeability, a double‐porosity method is used to simulate the flow through the cracks and the porosity. The apparent gas permeability is afterwards evaluated by a homogenization method. On the basis of finite element simulations, influence of aggregate size on ultimate crack opening, macroscopic ultimate tensile stress, total dissipated energy, and gas permeability evolution is numerically investigated. Furthermore, gas permeability evolution is also compared with experimental results from the literature. In addition, in the spirit of a sequential multiscale approach, macroscale gas permeability equations are identified from the hydromechanical results coming from the mesoscale computations. These equations lead to a relation between macroscale gas permeability evolution and crack opening. Besides, we show how the aggregate size influences the percolation threshold and that after this threshold, a cubic relation between macroscale gas permeability and crack opening is obtained. 相似文献
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Frédéric Dufour Grégory Legrain Gilles Pijaudier‐Cabot Antonio Huerta 《国际地质力学数值与分析法杂志》2012,36(16):1813-1830
Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one‐dimensional approach for estimating a crack opening from a continuum‐based finite element calculation to two‐dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post‐treatment procedure. The original one‐dimensional problem devised in Dufour et al. [4] is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two‐dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three‐point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (> 40µm). Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
5.
Numerical modelling of concrete cracking requires robust models able to describe opening and propagation of cracks. Structural concrete codes provide practical relations to describe crack openings. However, these empirical methods were developed for specific structures and cannot be used for general applications. Here, a continuous modelling approach based on damage mechanics is used to compute crack openings in a tie‐beam concrete structure. We propose a post‐processing method to extract crack openings from a continuum damage finite element computation. This method can be applied to all continuum damage/plasticity models. The tie‐beam concrete is characterized by a weak stress gradient; this aspect complicates predictions of crack positions and number. A stochastic method is used to take into account the spatial variability in concrete properties and create a spatially correlated random property field. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
In order to apply the mechanical properties (measured on material specimens or laboratory‐sized models) to large structures (such as concrete dams), a non‐linear theory able to predict the size‐scale effect has to be used. One of these theories was first proposed by Hillerborg and co‐workers (fictitious crack model) and is based on the earlier works by Barenblatt and Dugdale for metals (cohesive crack model). It is based on the existence of a fracture process zone (FPZ), where the material undergoes strain softening. The behaviour of the material outside the FPZ is linear elastic. A large number of short‐time laboratory tests were executed, by varying the load, under crack mouth opening displacement control. Since concrete exhibits a time‐dependent behaviour, an interaction between creep and micro‐crack growth occurs in the FPZ. Therefore, different testing conditions can be applied: rupture can be achieved by keeping the load constant before peak value (pre‐peak tests), or after peak value and after an unloading and reloading procedure (post‐peak tests). The crack propagation rate is shown to be small enough to neglect inertial forces and large enough to keep the time‐dependent behaviour of the process zone as dominant compared to the behaviour of the undamaged and viscoelastic zone. Due to the variability in material microstructure from one specimen to another, experimental data show large ranges of scatter. Well established methods in probability theory require sufficient experimental data in order to assume a probability density distribution. The objective of this study is to investigate the ranges of variation of the time response under constant load in simple structural elements associated with pre‐selected variation (fuzziness) in the main material parameters. For situations where the values of the material parameters are of a non‐stochastic nature, the fuzzy set approach to modelling variability has been proposed as a better and more natural approach. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
7.
This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on the smeared approach, identifying as its main drawbacks the observed mesh‐size and mesh‐bias spurious dependence when the method is applied ‘straightly’. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and the strong discontinuity (discrete cracks) approaches are analysed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
Hongyuan Liu Per‐Arne Lindqvist Urban Åkesson Shaoquan Kou Jan‐Eric Lindqvist 《国际地质力学数值与分析法杂志》2012,36(10):1280-1302
Realistic texture‐based modelling methods, that is microstructural modelling and micromechanical modelling, are developed to simulate the rock aggregate breakage properties on the basis of the rock actual microstructure obtained using microscopic observations and image analysis. The breakage properties of three types of rocks, that is Avja, LEP and Vandle taken from three quarries in Sweden, in single aggregate breakage tests and in inter‐aggregate breakage tests are then modelled using the proposed methods. The microstructural modelling directly integrates the microscopic observation, image analysis and numerical simulation together and provides a valuable tool to investigate the mechanical properties of rock aggregates on the basis of their microstructure properties. The micromechanical modelling takes the most important microstructure properties of rock aggregates into consideration and can model the major mechanical properties. Throughout this study, it is concluded that in general, the microstructure properties of rock aggregate work together to affect their mechanical properties, and it is difficult to correlate a single microstructure property with the mechanical properties of rock aggregates. In particular, for the three types of rock Avja, LEP and Vandle in this study, crack size distribution, grain size and grain perimeter (i.e. grain shape and spatial arrangement) show good correlations with the mechanical properties. The crack length and the grain size negatively affect the mechanical properties of Avja, LEP and Vandle, but the perimeter positively influences the mechanical properties. Besides, the modelled rock aggregate breakage properties in both single aggregate and inter‐aggregate tests reveal that the aggregate microstructure, aggregate shape and loading conditions influence the breakage process of rock aggregate in service. For the rock aggregate with the same microstructure, the quadratic shape and good packing dramatically improve its mechanical properties. During services, the aggregate is easiest to be fragmented under point‐to‐point loading condition, and then in the sequence of multiple‐point, point‐to‐plane and plane‐to‐plane loading conditions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
A numerical model capable of performing deformation analysis of a medium containing discontinuity surfaces is presented. The discontinuity can be either a crack, which can be open or closed, or a shear band. The model consists of two separate numerical algorithms, which are coupled together by means of the principle of superposition. In particular, an integral equation scheme based on the theory of dislocations is adopted for modelling the discontinuity, while a finite element discretization is used for the continuous medium. In this paper the discontinuity modelling is illustrated in detail, together with the specific formulation of the principle of superposition adopted, and some simple examples of application are presented. The well-known modelling approach based on Fracture Mechanics theory is also briefly discussed. The two models are compared and some advantages and drawbacks of each are pointed out, comments are made regarding their applicability in the specific case of soil mechanics, and conclusions are drawn as regards the conditions under which one or the other is appropriate. Finally, a full-scale example of deformation analysis using the proposed model is presented. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
12.
A 3D discrete FEM iterative algorithm for solving the water pipe cooling problems of massive concrete structures 
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下载免费PDF全文 Water pipe cooling has been widely used for the temperature control and crack prevention of massive concrete structures such as high dams. Because both under‐cooling and over‐cooling may reduce the efficiency of crack prevention, or even lead to great harm to structures, we need an accurate and robust numerical tool for the prediction of cooling effect. Here, a 3D discrete FEM Iterative Algorithm is introduced, which can simulate the concrete temperature gradient near the pipes, as well as the water temperature rising along the pipes. On the basis of the heat balance between water and concrete, the whole temperature field of the problem can be computed exactly within a few iteration steps. Providing the pipe meshing tool for building the FE model, this algorithm can take account of the water pipe distribution, the variation of water flow, water temperature, and other factors, while the traditional equivalent algorithm based on semi‐theoretical solutions can only solve problems with constant water flow and water temperature. The validation and convergence are proved by comparing the simulated results and analytical solutions of two standard second‐stage cooling problems. Then, a practical concrete block with different cooling schemes is analyzed and the influences of cooling factors are investigated. In the end, detailed guidance for pipe system optimization is provided. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
A computational formulation of discrete simulations of damage and failure in brittle rocks using mathematical programming methods is proposed. The variational formulations are developed in two and three dimensions. These formulations naturally lead to second-order cone programs and can conveniently be solved using off-the-shelf mathematical programming solvers. Pure static formulations are derived so that no artificial damping parameters are required. The rock is represented by rigid blocks, with interfaces between blocks modelled by zero-thickness springs based on the rigid-body–spring network method. A modified Mohr–Coulomb failure criterion is proposed to model the failure of the interfaces. When the interface’ strength limits are reached, a microscopic crack forms and its strength is irreversibly lost. The microscopic elastic properties of the springs are related to the observed elastic behaviour of rocks with the developed empirical equations. The program is first validated with three simple tests. Then, numerical uniaxial and biaxial compression tests and the Brazilian tests are conducted. Furthermore, the proposed approach is employed to study the rock crack propagation and coalescence using cracked Brazilian disc test. The results are in good agreements with reported experimental data, which shows its potential in modelling mechanical behaviour of brittle rocks. 相似文献
14.
This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this paper, we propose an anisotropic plastic damage model for semi-brittle geomaterials based on a discrete thermodynamic approach. The macroscopic plastic deformation is generated by frictional sliding of weakness planes. The evolution of damage is related to growth of such weakness planes. The local frictional sliding in each family of weakness planes is described by a non-associated plastic model taking into account material softening and volumetric dilatancy. The damage evolution is coupled with plastic deformation and modelled by an isotropic damage criterion. The proposed model is applied to modelling mechanical responses of typical sandstone under different loading paths. There is good agreement between numerical predictions and experimental data. Further, the anisotropic distributions of plastic deformation and induced damage are analysed and discussed. 相似文献
17.
Powell-Sabin B-splines, which are based on triangles, are employed to model cohesive crack propagation without a predefined interface. The method removes limitations that adhere to isogeometric analysis regarding discrete crack analysis. Isogeometric analysis requires that the initial mesh be aligned a priori with the final crack path to a certain extent. These restrictions are partly related to the fact that in isogeometric analysis, the crack is introduced in the parameter domain by meshline insertions. Herein, the crack is introduced directly in the physical domain. Because of the use of triangles, remeshing and tracking the real crack path in the physical domain is relatively standard. The method can be implemented in existing finite element programmes in a straightforward manner through the use of Bézier extraction. The accuracy of the approach to model free crack propagation is demonstrated by several numerical examples, including discrete crack modelling in an L-shaped beam and the Nooru-Mohamed tension-shear test. 相似文献
18.
The dry‐stone retaining walls (DSRW) have been tipped as a promising solution for sustainable development. However, before recently, their behavior is relatively obscure. In this study, discrete element method (DEM) approach was applied to simulate the plane strain failure of these walls. A commercial DEM package (PFC2D™) was used throughout this study. The authors used a fully discrete approach; thus, both the wall and the backfill were modeled as discrete elements. The methodology for obtaining the micromechanical parameters was discussed in detail; this includes the three mechanical sub‐systems of DSRWs: wall, backfill and interface. The models were loaded progressively until failure, and then the results were compared with the full‐scale experimental results where the walls were loaded, respectively, with hydrostatic load and backfill. Despite its complexity and its intensive calculation time, DEM model can then be used to validate a more simplified approach. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
19.
This paper is aimed at showing the efficiency of discrete element modelling for the prediction and understanding of drying shrinkage and associated cracking. The discrete element approach used is presented first. Cohesive forces between grains, as well as drying shrinkage deformation, are included in the formulation. A numerical model is then used to simulate drying shrinkage experiments conducted on a fine-grained soil. The numerical simulations agree well with the experimental measurements. When drying shrinkage is constrained at the boundaries, and when moisture gradients develop in the drying soil, the model is able to predict the time of the occurrence of cracking, as well as the crack pattern formed. Finite element simulations and the discrete element approach both predict similar behaviours before cracking occurs. The proposed discrete element approach is highly promising for studying the origins and causes of cracking in soils. 相似文献
20.
Nenad Grujovic Dejan Divac Miroslav Zivkovic Radovan Slavkovic Nikola Milivojevic Vladimir Milivojevic Dragan Rakic 《Acta Geotechnica》2013,8(3):265-278
The mechanical behaviour of a rock mass is described in this paper using a method that combines experimental and numerical techniques. A new discontinuity (joint) constitutive model is proposed based on the non-associative yield law. Constitutive relationships for an anisotropic rock mass are determined by introducing an interaction between sets of discontinuities and the monolith in which they occur. The model is based on the concept that deformation of the monolith and its associated sets of discontinuities are coupled. An experimental investigation of the concrete foundations of the Bogovina Dam on the Crni Timok River in Serbia has been used to verify the presented numerical model. The tests included discontinuity and monolith sample investigations and large-scale field tests. 相似文献