Concrete-like Materials Research Articles

Anisotropic damage modelling of biaxial behaviour and rupture of concrete structures

This paper deals with damage induced anisotropy modeling for concrete-like materials. A thermodynamics based constitutive relationship is presented coupling anisotropic damage and elasticity, the main idea of the model being that damage anisotropy is responsible for the dissymmetry tension/compression. A strain written damage criterion is considered (Mazars criterion extended to anisotropy in the initial model). The biaxial behavior of a family of anisotropic damage model is analyzed through the effects of yield surface modifications by the introduction of new equivalent strains.

Modelling of compressive behaviour of concrete-like materials at high strain rate

Uniaxial compression tests are the most common tests for characterizing the strength of concrete-like materials. The dynamic compression strength of concrete-like material is typically obtained by Split Hopkinson Pressure Bar (SHPB) tests. The increase in material strength under dynamic loading is usually attributed to the strain rate effect and modelled with a dynamic increase factor (DIF). However, it was observed by some researchers that the radial inertial confinement caused apparent increase of dynamic strength of concrete-like specimen in SHPB tests. They attributed the material strength increase to this inertial effect, instead of the strain rate effect. In the present study, numerical analyses are performed to investigate the compressive behaviour of concrete-like material at high strain rates. A homogeneous macroscale model and a heterogeneous mesoscale model are developed in the study. In the macroscale model, the material is assumed to be homogeneous and isotropic. In the mesoscale model, the test sample is modelled as a three-phase composite consisting of aggregate, mortar matrix and interfacial transaction zone (ITZ) between the aggregate and the mortar matrix. The aggregate is assumed to be circular and the ITZ is modelled as a thin boundary around the aggregate. In the both models, the materials are assumed to be insensitive to the strain rate first. Therefore, the obtained strength enhancement is only due to the inertial confinement. Strain rate sensitive material properties are then used in the two models in the calculations. Numerical simulations of the concrete samples under compression at different strain rates are carried out. The relative contribution of the inertial effect and the strain rate effect on the compressive strength DIF is examined based on the numerical results. The failure process of concrete specimen is also studied.

Strength and stability of cementless concrete-like materials in air environment

The experiments carried out by checking specimen's long-term strength and examining the composition and microstructure of cured matter in air environment. It was found that strength development of specimens with only HCOSFA took place in two stages: increase during the first month and following continuous drop up to the ending of experiments (60 months). Ettringite ? one of curing products played a major role in this process. It was determined that the addition of low calcium coal fly ash (LCCFA) improved strength and stability of the material. The strength curve of specimens with HCOSFA+LCCFA in atmospheric air had three sections. The first section showed evidence of the curing process and development of strength within the first month. The second section (from one to six months) showed an abrupt decrease in strength. In the third section, starting from the sixth month, strength declined at a slower rate and then stabilises from 24 up to 60 months.

Inverse Analyses in Fracture Mechanics

The present purpose is a survey of some engineering-oriented research results which may be representative of the main issues in the title subject. Some recent or current developments are pointed out in the growing area of fracture mechanics centered on the calibration of cohesive fracture models for quasi-brittle materials, by approaches which combine experimentation, experiment simulation and minimisation of the discrepancy between measured and computed quantities. Specifically, reference is made herein to the following topics in calibration of fracture constitutive models: (a) deterministic characterisation of concrete-like materials by traditional three-point-bending tests (TPBTs), supplemented by optical measurements; (b) wedge-splitting tests (WST) and extended Kalman filter (EKF) for the stochastic estimation of fracture parameters; (c) in situ parameter identification for the local diagnosis of possibly deteriorated concrete dams on the basis of flat-jack tests; (d) fracture properties of ceramic materials and coating-substrate interfaces identified through indentation tests, imprint mapping and inverse analysis in micro-technologies.

Local impact effects of hard missiles on concrete targets

This paper presents the recent progress in formulating and modeling local impact effects in concrete targets struck by hard missiles. New research results in this area are also presented, these being part of the UK nuclear safety program against impact threats on concrete structures in nuclear power stations conducted under the auspices of Magnox Electric. Failure mechanisms are classified based primarily on experimental evidence. First, a collection of empirical formulae to predict the penetration depth, scabbing thickness and perforation thickness is presented in both Imperial and SI units. The current status of various design codes is then summarized. Based on a dimensional analysis, dominant non-dimensional parameters that may influence the local impact effects on concrete targets are obtained and then used to present some of the test data. Various nose shape factors are compared and a unique definition of the nose shape factor is suggested. Analytical models and numerical simulation methods for penetration are summarized. Criticisms are made for the current understanding of the effects of strain rate on the unconfined uniaxial compressive strength of concrete-like materials based on measurements by the split Hopkinson pressure bar technique.

An entropic optimization approach for a parameter identification problem in quasibrittle fracture

The cohesive crack model is a widely used idealization to represent simply and reliably the quasibrittle fracture behavior of concrete-like materials. However, knowledge of the parameters characterizing this model is of prime importance and cannot all be obtained directly from experiments. Typically, recourse is made to some inverse numerical approach. Our particular formulation can be elegantly cast as an instance of a challenging optimization problem known as a mathematical program with equilibrium (or, more precisely in our case, complementarity) constraints (MPEC). The present paper investigates application of an entropic optimization approach to solve the MPEC, and compares its performance with our previously proposed Fischer–Burmeister smoothing scheme. We use actual experimental data for the comparison.

A computational setting of calcium leaching in concrete and its coupling with continuum damage mechanics

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

Time-Dependent Behavior of Cementless Concrete-Like Material Based on Oil Shale Fly Ash Binders in Ambient Air

The time-dependent behavior of cementless concrete-like materials inambient air was assessed by checking long-term strength of laboratoryspecimens on the basis of high calcium oil shale (HCOSFA) binders aswell as X-Ray Diffraction and Scanning Electron Microscopy, studyingcomposition and microstructure of cured binder material. It wasestablished that there are two distinct stages in the strengthdevelopment of specimens containing only HCOSFA as a binder: An increaseof compressive strength for the first month and the continuous dropuntil the 60th month of exposure. In specimens prepared with usingHCOSFA and low calcium coal fly ash (LCCFA) binder, three stages ofstrength change were identified: An increase of compressive strength forthe first month, a sharp drop thereafter until the third to sixth monthfollowed by a gradual loss or stabilization over a period of 60 months.It was resolved that binder hydration results in the formation ofettringite and gypsum together with other compounds. It was found thatettringite is not stable in ambient air and over time the amount ofettringite was diminished. This disintegration resulted in a continuousloss of strength in specimens containing only HCOSFA. The addition ofLCCFA to HCOSFA generated an additional amount of high-strength, stablesecondary CSH in the hardened system. The secondary CSH helped toneutralize consequences of ettringite transformation and improved theperformance of cementless concrete-like materials in ambient air.

Calculation of the tensile and flexural strength of disordered materials using fractional calculus

Aim of the present paper is to show an application of the fractal integral, which was recently introduced in the framework of fractional calculus, to the mechanics of materials with disordered microstructure. Some rules of integration for simple functions performed on generalized Cantor sets have been developed. We believe that these results can be of some interest in the modeling of materials whose microstructure is fractal-like. Part of the paper is devoted, as an example, to show why concrete can be considered such a material. The fractal dimension of the stress carrying material ligament is found. Finally, by the fractal integration rules previously developed, the computation of the tensile and flexural strength for structures made by a concrete-like material is performed and consequent size effects are highlighted.

個別要素法によるコンクリート圧縮破壊解析におけるモール・クーロン条件の及ぼす影響

This paper discusses the effect of Mohr-Coulomb's parameters on the analysis results of concrete-like material failure behavior using the Distinct Element Method. The failure behavior of plane concrete which is model by the particle elements arranged in a couple of plane which are stood parallel on a horizontal plane is analyzed under several constitutive law conditions. Two types Mohr-Coulomb condition are used, and various cohesion parameter and friction angles are combined in some simulation condition. It is pointed out that 5 types failure modes appear in global viewpoint depending on the Mohr-Coulomb condition.

About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test

Split Hopkinson pressure bar (SHPB) technique has been used widely to measure the dynamic strength enhancement of concrete-like materials at high strain-rate between 10 1 and 10 3 s −1. Although SHPB technique has been verified for metallic materials, the validity and accuracy of SHPB results for non-metallic materials have not been thoroughly studied. The present paper examines the application of SHPB to determine the dynamic strength of concrete-like materials whose compressive strength is hydrostatic-stress-dependent. It shows that the apparent dynamic strength enhancement beyond the strain-rate of 10 2 s −1 is strongly influenced by the hydrostatic stress effect due to the lateral inertia confinement in a SHPB test. This apparent dynamic strength enhancement has been wrongly interpreted as strain-rate effect and has been adopted in both dynamic structural design and concrete-like material models for analytical and numerical simulations, which may lead to over-prediction on the dynamic strength of concrete-like materials. The SHPB test is simulated in the present paper using FE method and Drucker–Prager model to investigate how the hydrostatic stress affects the SHPB test results of concrete-like materials. A rate-insensitive material model is used in order to examine this pseudo-strain-rate sensitive phenomenon. A collection of SHPB test results of concrete-like materials are compared with simulation results, which confirms quantitatively that the apparent dynamic strength enhancement of concrete-like materials in a SHPB test is caused by the lateral inertia confinement instead of the strain-rate sensitivity of the tested material.

Influence of damage on the fractal properties of concrete subjected to pure tension

In a previous work [1] the authors showed how to acquire the meso-structural characteristics of undamaged concrete-like materials by a peculiar laser equipment [2]. In order to extend the analysis to damaged disordered materials, a new direct tension test equipment has been developed, that minimizes flexural effects by freely rotating boundary conditions. Increasing levels of damage are obtained, after reaching the peak load, by proceeding along the descending strain-softening curve. After the desired damage level is reached, the load is removed and the specimen is cut to permit the laser acquisition of the most damaged zone. The progressive rarefaction of the effective stress-carrying cross section is described by means of fractal concepts. It is worth noting that both the fractal dimension and the measure of the stress carrying cross section decrease after the peak load, and vanish when the specimen is broken apart.

Direct Tensile Tests on Concretelike Materials: Structural and Constitutive Behaviors

The complete stress-strain and stress-crack opening response of a concretelike material loaded in tension is examined starting from a series of displacement-controlled tests on notched cylinders, whose end sections were prevented from rotating (fixed platens). The test results refer to two very high-strength cementitious composites (tensile strength fc ≈ 160–165 MPa) and one “reference” high-strength concrete (fc ≈ 90 MPa). Their behavior (pseudoelastic up to first cracking and cohesive after crack localization) is analyzed to identify the nonlinear stress-strain and stress-crack opening response and to distinguish it from the structural behavior of the specimens. The ascending branch is modeled by studying the stresses at the notch tip by means of Neuber's approach based on stress concentration factors. As for concrete softening (falling branch), an appropriate cohesive law is introduced. Finally, the structural response associated with progressive cracking is systematically analyzed, and once more, it is shown that the load-displacement relationship obtained in a test is hardly a material property.

Damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications

This paper is concerned with the development of a damage model for concrete materials exhibiting a residual hysteretic behaviour at a fixed level of damage. This feature is obtained by coupling damage mechanics and friction phenomena. In its complete form, the damage variable by means of which the stiffness decrease is obtained in an orthotropic second-order tensor. Its evolution is governed by the tensile part of the strain tensor. The sliding between the crack lips is assumed to have a plasticity-like behaviour with non-linear kinematic hardening. The sliding stress depends on the level of damage. Such a model assumes the evolution of two yield surfaces: a fracture one and a sliding one. If unilateral effects need to be taken into account for cyclic loading analysis (crack closure modelling), the damage evolution remains isotropic. The effectiveness of this model in reproducing a part of damping when subjected to dynamic loading is exemplified through two structural case studies. Copyright © 2000 John Wiley & Sons, Ltd.

Determination of quasibrittle fracture law for cohesive crack models

A basic and necessary ingredient of cohesive crack models, so widely used for numerical quasibrittle fracture simulations, is the softening function which characterizes the property of concrete-like materials. In this paper, a simple procedure to determine the softening parameters for such functions is proposed. In addition to knowledge of the tensile strength—typically obtainable within about 20% from a cylinder splitting strength (Brazilian) test—the only other requirement is knowledge of the load-displacement curve, as would be obtained from a standard three-point bending test. The method is particularly suitable for materials, such as fiber reinforced concrete, which exhibit a long tail in their load-displacement response. Although suitable for identifying both nonlinear and piece-wise linear relations, we illustrate applications of the scheme using a bilinear law.

Three-dimensional fractal analysis of concrete fracture at the meso-level

The fracture process in concrete-like materials cannot be properly modelled in an Euclidean framework, due to its complex morphology at the micro- and meso-level. The inherent flaws interact through a multi-scale process, leading to self-affine fracture surfaces. Moreover, the self-organized network of microcracks displays fractal properties prior to the formation of the final fracture surface. At the same time, due to the presence of pores and voids, the stress-carrying cross section is a rarefied fractal domain, even from the beginning of the loading process. A new experimental equipment has been developed which allows the entire fracture surface, or any plane cross section, to be digitised and analysed. This represents an important progress with respect to the study of one-dimensional profiles. In this paper, the three-dimensional algorithms for evaluating the fractal dimension of invasive surfaces and lacunar sections are described. The invasive fractal character of the fracture surfaces is confirmed. Moreover, the lacunar fractal character of the stress-carrying cross sections, a priori assumed by Carpinteri [A. Carpinteri, Mechanics of Materials 18 (1994) 259–266], is now proven experimentally.

Size-effects induced bifurcation phenomena during multiple cohesive crack propagation

The nonlinear behavior of concrete-like materials in tension is characterised by strain-softening. Phenomena involving the localisation of strain caused by strain softening can be analysed accurately through the so-called “cohesive crack model” which uses the length of the fictitious crack as a control variable. In this approach, the length of the process zone is not fixed and the ratio between this length and the length of the specimen decreases with increasing size-scale. This phenomenon is evident even for small changes in size. It can explain why, in four point shear test, a critical size is observed, below which a secondary crack starts to propagate. This is a size-related phenomenon of bifurcation of equilibrium path, which is predicted by the cohesive crack model and confirmed experimentally. The theoretical results obtained by means of the cohesive crack model involving two cracks are in good agreement with experimental results.

A study on testing techniques for concrete-like materials under compressive impact loading

An analysis of specific experimental problems encountered in the testing of concrete and concrete-like materials under impact loading, using the split Hopkinson pressure bar test (SHPB) or the so-called direct impact Hopkinson bar test (DIHB), is presented in this paper. On the one hand, in data processing, it is shown that recent improvements such as wave dispersion correction and exact time shifting are indispensable to obtain accurate measurements in those tests. On the other hand, the conventional analyses of those two kinds of tests are investigated with the aid of transient numerical simulations. It is concluded that only one of the conventionally used formula offers a good estimate of stress-strain curve for concrete-like materials. It is also illustrated that the usual assumptions of DIHB analysis are not reliable for the concrete-like specimen. An inverse approach is nevertheless possible to give more accurate results.

97/01917 Manufacture of high-strength nonporous concrete-like building materials with the use of hydraulically active brown-coal fly ashes

97/01917 Manufacture of high-strength nonporous concrete-like building materials with the use of hydraulically active brown-coal fly ashes

Crack growth initiation in concrete-like materials in the presence of creep

A numerical procedure that employs the finite element method and the state variables approach is proposed to analyse the critical condition of a crack in an aging viscoelastic body under sustained load. A far field solution proposed by Schapery is used. An example shows how a crack can become critical after some finite time that depends on the characteristics of the concrete.