Modelling crack propagation in concrete structures with a two scale approach

A simplified computational technique based on a refined global–local method is applied to the failure analysis of concrete structures. The technique distinguishes the scale of the structure, modelled with large size finite elements, from the scale at which material non‐linearity occurs due to progressive cracking and macro‐crack propagation. The finite element solution is split into two parts: a linear elastic analysis on a coarse mesh over the entire structure and a non‐linear analysis over a small part of the structure where a dense finite element grid is employed. In the non‐linear calculation, a non‐local damage model is implemented. These two computations are coupled with the help of an iterative scheme. The size and location of the region where a non‐linear analysis is performed, is adapted to follow the development of the damage zone. Numerical examples of mode I fracture of concrete specimens with straight and curved cracks are presented. Copyright © 2003 John Wiley & Sons, Ltd.     

A mesoscopic model for the behaviour of concrete under high confinement

When impact loaded, concrete is submitted to high triaxial stresses. The experimental response of concrete under quasi‐static triaxial compression is studied using a triaxial press capable of applying a mean pressure greater than 1 GPa on cylindrical samples measuring 7 cm in diameter and 14 cm high. A numerical analysis of these previous experiments is performed herein at a mesoscopic scale. Concrete is modelled as a biphasic material consisting of a mortar (cement paste and fine aggregates) and roughly spherical aggregates (with a diameter exceeding 2 mm) whose characteristics are applied on a regular cubic finite element mesh. A damage‐plasticity model is then used to model the behaviour of mortar. An identification of model parameters on mortar samples and the subsequent comparison between numerical and experimental tests will be presented for hydrostatic and triaxial compression. Copyright © 2009 John Wiley & Sons, Ltd.     

A practical method to estimate crack openings in concrete structures

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.     

Coupled damage and plasticity modelling in transient dynamic analysis of concrete

In a concrete structure subjected to an explosion, for example a concrete slab, the material is subjected to various states of stress which lead to many modes of rupture. Closer to the explosive, a state of strong hydrostatic compression is observed. This state of stress produces an irreversible compaction of the material. Away from the zone of explosion, confinement decreases and the material undergoes compression with a state of stress, which is slightly triaxial. Finally, the compression wave can be reflected on a free surface and becomes a tensile wave, which by interaction with the compression wave, produces scabbing. We present, in this paper, a model aimed at describing these three failure modes. It is based on visco‐plasticity and rate dependent damage in which a homogenization method is used in order to include the variation of the material porosity due to compaction. The model predictions are compared with several experiments performed on the same concrete. Computations of split Hopkinson tests on confined concrete, a tensile test with scabbing, and an explosion on a concrete slab are presented. Copyright © 2001 John Wiley & Sons, Ltd.     

A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

A coupled damage–plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification

The development of a coupled damage‐plasticity constitutive model for concrete is presented. Emphasis is put on thermodynamic admissibility, rigour and consistency both in the formulation of the model, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the model can be derived from two specified energy potentials, following procedures established beforehand. Based on this framework, a constitutive model featuring full coupling between damage and plasticity in both tension and compression is developed. Tensile and compressive responses of the material are captured using two separate damage criteria, and a yield criterion with a multiple hardening rule. A crucial part of this study is the identification of model parameters, with these all being shown to be identifiable and computable based on standard tests on concrete. Behaviour of the model is assessed against experimental data on concrete. Copyright © 2007 John Wiley & Sons, Ltd.     

An original semi‐discrete approach to assess gas conductivity of concrete structures

For civil engineering structures with a tightness role, structural permeability is a key issue. In this context, this paper presents a new proposition of a numerical modelling of leakage rate through a cracked concrete structure undergoing mode I cracking. The mechanical state of the material, considered in the framework of continuum mechanics based on finite element modelling, is described by means of the stress‐based nonlocal damage model which takes into account the stress state and provides realistic local mechanical fields. A semi‐discrete method based on the strong discontinuity approach to estimate crack opening is then considered in the post‐treatment phase. Using a Poiseuille's like relation, the coupling between the mechanical state of the material and its dry gas conductivity is performed. For validation purposes, an original experimental campaign is conducted on a dry concrete disc loaded in a splitting setup. During the loading, gas conductivity and digital image correlation analysis are performed. The comparison with the 3D experimental mechanical global response highlights the performance of the mechanical model. The comparison between crack openings measured by digital image correlation and estimated by the strong discontinuity method shows a good agreement. Finally, the results of the semi‐discrete approach coupled with the gas conductivity compared with experimental data show a good estimation of the structural conductivity. Consequently, if the mechanical problem is well modelled at the global scale, then the proposed approach provides good estimation of gas conductivity. Copyright © 2016 John Wiley & Sons, Ltd.     

Continuum large cracking in a rate‐dependent plastic–damage model for cyclic‐loaded concrete structures

Formulation and algorithmic treatment of a rate‐dependent plastic–damage model modified to capture large tensile cracking in cyclic‐loaded concrete structures are presented in detail for a three‐dimensional implementation. The plastic–damage model proposed by Lee and Fenves in 1998 was founded based on isotropic damaged elasticity in combination with isotropic multi‐hardening plasticity to simulate cracking and crushing of concrete under cyclic or dynamic loadings. In order that the model can capture large crack opening displacements, which are inevitable in plain concrete structures, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic–damage variable controlling the evolution of tensile damage is larger than a critical value. In such a condition, the crack opening/closing mechanism becomes similar to discrete cracking. The consistent tangent operator required to accelerate convergence rate is also formulated for the large cracking state including viscoplasticity. The validation and performance of the modified algorithm implemented in a special finite element program is exemplified through several single‐element tests as well as three structural applications. The last example examines the model in the seismic fracture analysis of Koyna dam as a benchmark problem and the resulting crack profile is compared with the available experiment. The numerical experimentations well demonstrate that the developed model whose modification is necessary to properly simulate the cyclic behavior of plain concrete subjected to large tensile strains is robust and reasonably accurate. Copyright © 2012 John Wiley & Sons, Ltd.     

Anisotropic model of damage for geomaterials and concrete

A damage model for geomaterials and concrete is proposed. This model expresses the anisotropic character induced by the degradation of material. The law of behavior obtained by differentiation of the free energy shows the dissymmetry effect observed in traction–compression loading and the residual strains caused by the damage. The present approach requires the identification of a reduced number of parameters having a clear physical significance. An application to the case of the uniaxial traction–compression loading shows a good adequacy with the experimental observations. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of continuous and discontinuous constitutive models to simulate concrete behaviour under mixed‐mode failure conditions

The paper presents detailed FE simulation results of concrete elements under mixed‐mode failure conditions according to the so‐called shear‐tension test by Nooru‐Mohamed, characterized by curved cracks. A continuous and discontinuous numerical two‐dimensional approach was used. In order to describe the concrete's behaviour within continuum mechanics, two different constitutive models were used. First, an elasto‐plastic model with isotropic hardening and softening was assumed. In a compression regime, a Drucker–Prager criterion with a non‐associated flow rule was used. In turn, in a tensile regime, a Rankine criterion with an associated flow rule was adopted. Second, an isotropic damage constitutive model was applied with a single scalar damage parameter and different definitions of the equivalent strain. Both constitutive laws were enriched by a characteristic length of micro‐structure to capture properly strain localization. As an alternative approach, the extended finite element method was used. Our results were compared with the experimental ones and with results of other FE simulations reported in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical modeling of the elastoplastic damage behavior of dry and saturated concrete targets subjected to rigid projectile penetration

The objective of the present paper is to present a numerical study on the penetration performance of concrete targets with 2 different water contents. Numerical analysis has been performed by using the finite element code Abaqus/Explicit, in which a coupled elastoplastic damage model has been developed for saturated/unsaturated concrete under a wide range of confining pressures. The performance of proposed model has been firstly verified by simulating the triaxial compression tests and penetration tests realized with saturated/dry concretes. Comparisons of available experimental results and numerical simulations show that the proposed model is able to reproduce satisfactorily the mechanical behavior of saturated and dry concretes. A higher failure stress and a more important pores closing are generally obtained in dry concrete samples with respect to saturated ones. Furthermore, the main observed patterns of penetration test realized with saturated concrete targets are also satisfactorily simulated by the numerical results. Therefore, the proposed model is used to numerically predict the penetration performance of dry concrete target, and the penetration performance of dry/saturated concrete target is discussed. We observe that in dry concrete target, the penetration of projectile is strongly declined, and a smaller damage zone is created. The numerical predictions and discussions can help engineers to enhance their understandings on the influence of hydraulic conditions on structural vulnerability of concrete structures subjected to near‐field detonations or impacts.     

Simulation of damage–permeability coupling for mortar under dynamic loads

The results reported in this paper deal with the simulation of damage in cohesive geomaterials such as rocks or concrete subjected to dynamic loads. The practical objective is to stimulate the production of tight gas reservoirs with a technique that is an alternative to hydraulic fracturing. The principle is that when subjected to dynamic loads, cohesive materials such as concrete, rocks or ceramics exhibit distributed micro‐cracking as opposed to localised cracking observed under static loads. Hence, a low permeability rock containing gas trapped into occluded pores can be fragmented with the help of dynamic loads, and gas can be extracted in a much more efficient way compared with hydraulic fracturing, where only large macro cracks are formed with very few connections between occluded pores. At the stage of laboratory development of this technique, compressive underwater shock waves have been used to increase the intrinsic permeability of concrete specimens. In a previous study, pressure waves generated by pulsed arc electrohydraulic discharges in water were used in order to induce micro‐cracking and an increase of average permeability of concrete hollow cylinders subjected to confinement stresses (equivalent to geostatic stresses). We discuss here a 3‐D anisotropic constitutive model aimed at describing the dynamic response of these specimens. It is based on rate‐dependent continuum damage constitutive relations. Crack closure effects and damage‐induced anisotropy are included in the model. The directional growth of damage is related to the directional growth of material intrinsic permeability. Numerical simulations of damage induced by shock waves show good agreement with the experiments for various confinement levels of the specimens. Copyright © 2013 John Wiley & Sons, Ltd.     

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage‐embedded discontinuity model

This paper deals with numerical modeling of dynamic failure phenomena in rate‐sensitive quasi‐brittle materials, such as rocks, with initial microcrack populations. To this end, a continuum viscodamage‐embedded discontinuity model is developed and tested in full 3D setting. The model describes the pre‐peak nonlinear and rate‐sensitive hardening response of the material behavior, representing the fracture‐process zone creation, by a rate‐dependent continuum damage model. The post‐peak response, involving the macrocrack creation accompanied by exponential softening, is formulated by using an embedded displacement discontinuity model. The finite element implementation of this model relies upon the linear tetrahedral element, which seems appropriate for explicit dynamic analyses involving stress wave propagation. The problems of crack locking and spreading typical of embedded discontinuity models are addressed in this paper. A combination of two remedies, the inclusion of viscosity in the spirit of Wang's viscoplastic consistency approach and introduction of isotropic damaging into the embedded discontinuity model, is shown to be effective in the present explicit dynamics setting. The model performance is illustrated by several numerical simulations. In particular, the dynamic Brazilian disc test and the Kalthoff–Winkler experiment show that the present model provides realistic predictions with the correct failure modes and rate‐dependent tensile strengths of rock at different loading rates. The ability of initial embedded discontinuity populations to model the initial microcrack populations in rocks is also successfully tested. Copyright © 2016 John Wiley & Sons, Ltd.     

面板堆石坝垂直缝破坏下三维渗流场有限元模拟

采用改进节点虚流量法求解无压稳定渗流场,并引入无厚度的裂缝模型对破坏的垂直缝渗流行为进行模拟,得到面板堆石坝裂缝渗流问题的有限元分析方法,并编制Fortran程序。以某混凝土面板堆石坝为例,计算了面板单一垂直缝破坏和多条垂直缝破坏条件下的三维渗流场,得到不同条件下渗流场的水头分布、浸润线以及渗漏量,系统分析了面板堆石坝在垂直缝破坏条件下的稳定渗流场规律和特点。结果表明,该方法能对渗流逸出点和浸润线进行准确定位,还能很好地模拟面板垂直缝破坏对坝区渗流场的影响,可以为面板堆石坝的接缝设计提供参考。     

Experimental and numerical study of the damage process in RC beam-column sub-assemblages during a progressive collapse scenario

In the present paper, the collapse resistance of reinforced concrete (RC) beam-column sub-assemblages subjected to a middle column removal scenario is investigated on the basis of experimental tests and numerical calculations. For the experimental programme, three one-third scale substructures are designed with two types of longitudinal steel rebar to observe the influence of rebar detailing on the global structural behaviour. The structure under consideration is composed of a two-bay beam, and a middle column lies on two sliding-pin connections to prevent a catenary action mechanism. A digital image correlation (DIC) technique was employed with the experiments to observe the growth of cracks. In addition, numerical simulations using the finite element method (FEM) were also done. The Denoual-Forquin-Hild (DFH) anisotropic damage model is used to simulate the behaviour of the concrete, whereas a plasticity model is used for the steel rebars. The numerical simulations are compared with experimental data in terms of structural yield strength, change in stiffness and crack propagation, and better agreement is observed when a weakening of the concrete due to beam stirrups is taken into account.     

Simulation of localization failure with strain‐gradient‐enhanced damage mechanics

Strain gradient implies an important characteristic in localized damage deformation, which can be observed in the softening state of brittle materials, and strain gradients constitute the basic behaviours of localization failure area of the materials. The most important point in strain gradient is its damaging function including an internal length scale, which can be used to express the scale effects of mechanical responses of brittle rock mass. By extending the strain gradient theory and introducing an intrinsic material length scale into the constitutive law, the authors develop an isotropic damage model as well as a micro‐crack‐based anisotropic damage model for rock‐like materials in this paper. The proposed models were used to simulate the damage localization under uniaxial tension and plain strain compression, respectively. The simulated results well illustrated the potential of these models in dealing with the well‐known mesh‐sensitivity problem in FEM. In the computation, elements with C₁ continuity have been implemented to incorporate the proposed models for failure localization. When regular rectangle elements are encountered, the coupling between finite difference method (FDM) and conventional finite element method (FEM) is used to avoid large modification to the existing FEM code, and to obtain relatively higher efficiency and reasonably good accuracy. Application of the anisotropic model to the 3D‐non‐linear FEM analysis of Ertan arch dam has been conducted and the results of its numerical simulation coincide well with those from the failure behaviours obtained by Ertan geophysical model test. In this paper, new applications of gradient theories and models for a feasible approach to simulate localized damage in brittle materials are presented. Copyright © 2002 John Wiley & Sons, Ltd.