MICROPLANE MODEL FOR RECYCLED AGGREGATE CONCRETE

Transcription

1 MICROPLAE MOEL FOR RECYCLE AGGREGATE COCRETE Jiain LI (1 2) Jianzhuang XIAO (2) and Jian HUAG (3) (1) Institute for Structural Concrete Graz University of Technology Austria (2) epartment of Building Engineering Tongji University P.R China (3) Guangdong Institute of Building Science P.R China Astract This paper presents an innovative constitutive model for recycled aggregate concrete sujected to compression and tension. The model was formulated through the extension of a newly developed material model for normal (or natural aggregate) concrete called M4L and formulated using the microplane theory. The model parameters in model M4L were evaluated according to the test data for concrete with different amounts of recycled (coarse) aggregate. The model for recycled aggregate concrete was formulated y making the normal stress oundary and some key parameters in the deviatoric stress oundaries in model M4L dependent on the recycled aggregate amount. Through such a way the influence of recycled aggregate on the nonlinear material ehaviour of concrete oth in compression and tension can e well captured. The model is further verified with other test data in the literature. umerical results indicate that the model developed in this paper is ale to sufficiently depict the inelastic ehaviour of recycled aggregate concrete including the change of Poisson s ratio with the stress level as well as the volume change. 1. ITROUCTIO The mechanical ehaviour of recycled aggregate concrete i.e. concrete incorporating recycled aggregates (crushed waste concrete) is different from that of normal (or natural aggregate) concrete. umerous tests have shown that the increase of recycled aggregate may result in the degradation of the concrete strength and stiffness although the negative effect is usually minor when the amount of the recycled aggregate is less than 20%. However experiments at the structural level on reinforced eams columns or slas and frames made of recycled aggregate concrete indicate that this kind of concrete is suitale for use as structural concrete in spite of the relative weak properties. Moreover some uilding projects with recycled aggregate concrete have een successfully performed in several countries such as Germany Japan and China. The stress-strain ehaviour of recycled aggregate concrete is necessary for the structural analysis and design of structures made with this material. Several experiments on the influence of the recycled aggregate on the stress-strain ehaviour of concrete in uniaxial 542

2 compression and tension have een carried out [ ]. In these tests the amount of recycled aggregate represents the mass percentage of the recycled aggregate in the whole coarse aggregate. According to the test findings the most important characteristics for the stress-strain curve of recycled aggregate concrete can e summarized as follows: The amount of recycled aggregate concrete has a remarkale influence on the stress-strain curve. However the shape of the stress strain curve for recycled concrete in oth compression and tension is similar to that of normal concrete irrespective of the recycled aggregate amount [1 4]; With the increase of the recycled aggregate the curvature for the ascending ranch the stress-strain curve increases progressively increases as a result of the reduction in the modulus of elasticity [1]; The strain at peak stress under compression increases with the amount of recycled aggregate. With 100% recycled aggregate a 20% increase has een found [1 2]. The lateral dilation with recycled concrete is relatively smaller in comparison with normal concrete [3]; The steepness of the descending ranch for the stress-strain curve in compression decreases as the recycled aggregate content increases [1]. To etter understand the structural response of recycled aggregate concrete structures towards rational structural design only empirical equations for the stress-strain curves e.g. in [1 4] are not enough; instead a sophisticated constitutive model is required. In this paper an innovative material model for recycled aggregate concrete is proposed which is formulated through the extension a newly developed microplane model for normal concrete y the first author [5] y considering the influence of the amount of recycled aggregate. 2. MICROPLAE THEORY 2.1 Theoretical framework The microplane theory [6] developed y Prof. Bazant at orthwestern University is more and more recognized as a powerful approach for descriing the inelastic ehaviour of quasi-rittle materials such as concrete. In this framework the nonlinear ehaviour of the material is represented y simple relations etween stress and strain components on planes of various orientations called microplane. A microplane is an aritrary plane which cuts through the material at a point and is defined y its normal unit vector n see Figure 1(a). To define the strain components on the microplane the kinematic constraint is used. The microstrains are otained through the projections of the macrostrain tensor on the microplane. The normal strain ε on the microplane is given as: ij ij ε = ε (1) To etter characterize the shear strain it is defined in two orthogonal directions M and L. ε M = M ijε ij L Lijε ij ε = (2) The magnitude of the shear strain is given y ε = ε + ε (3) T 2 M 2 L 543

3 The normal strain is further split into volumetric ( ε ) and deviatoric ( ε ) parts. ε = ε + ε (4) The strain components on a microplane are shown in Figure 1(). The microstresses on each microplane are determined from predefined stress-strain relations for a generic microplane. The macrostress tensor at a material point is then otained through comining the contriutions of all the microplanes y using the principle of virtual work. (a) Microplanes at a material point [7] () Strain components on a microplane Figure 1: Fundamentals on microplane theory 2.2 Microplane model M4L for normal concrete A novel microplane model for normal concrete called model M4L has een recently developed at Leipzig University y Li [5]. This model is an improved version of the model M4 y Bazant and his co-workers [7]. Model M4L enhances M4 oth in constitutive formulation and numerical algorithm. In this model the nonlinear ehaviour of concrete is descried through microstress-microstrain oundaries (or microstrain dependent yield limits) which in fact follows the same approach as in model M4. The stress oundary is an empirical concept which represents the limit of elastic microstrain for the microstress. Inside the oundaries the material response is assumed to e linear elastic. If the microstress value exceeds the associated oundary the stress is dropped at a constant strain to the oundary. 544

4 In model M4L altogether 5 microstress oundaries were introduced to simulate the inelastic ehaviour of concrete under different stress states. They include a normal stress oundaryσ a compressive deviatoric stress oundaryσ and a tensile deviatoric stress oundaryσ oundary + a shear stress oundary σ T as well as a compressive volumetric stress σ. The formulation and description of each oundary is given in Tale 1. The model consists of two material parameters : modulus of elasticity E and Poisson s ratio v. In addition a total of another 31 microplane parameters are used in model M4L to define the microstress oundaries for each microplane including k 1 -k 4 and c 1 -c 27. The role of each individual parameter can e found in Li [5]. umerious experiences have shown that the c parameters (c 1 -c 27 ) can e fixed for almost all normal concretes while the k parameters (k 1 -k 4 ) have to e adjusted according to the concrete properties. The reference values for c 1 -c 27 are given in [5]. umerical results indicate that model M4L is very efficient in capturing many kinds of inealstic ehaviour for concrete under various stress states. For details see [5]. Tale 1: Formulation and role of stress oundaries in model M4L Boundary σ ε ε σ ε ε + σ ε ε σ T σ ε Formulation with escription σ ε c Characterizes tensile cracking σ / f Simulates compressive softening 1 σ / f Controls lateral dilation in compression 1 σ c Characterizes friction and slip Simulates hydrostatic compression 3. EXTESIO OF MOEL M4L FOR RECYCLE AGGREGATE COCRETE To examine the suitaility of model M4L for simulating the stress-strain ehaviour of concrete containing various amounts of recycled aggregate the test data y Xiao et al. [1] for uniaxial compression and Xiao and Lan [4] for uniaxial tension are used. umerical experiments indicate that in fact model M4L is capale of descriing the nonlinear ehaviour of concrete with recycled aggregate provided that oth the k and c parameters are adjusted. However such a method inevitaly complicates the matter since different set of parameters has to e calirated for concrete with different amount of recycled aggregate. In this paper the aforementioned prolem is solved through making the microstress oundary dependent on the amount of recycled aggregate while keep the model parameters the same as that for normal concrete. The amount of recycled aggregate is denoted as r ( 0 r 1 ). 3.1 Modification of model M4L As mentioned aove the normal stress oundary simulates the tensile fracture and cracking ehaviour of the material. Since experiments have shown that the recycled aggregate 545

5 has a remarkale influence on the tensile ehaviour of concrete [4] thus the normal oundary should e affected y the recycled aggregate content. In this paper the following normal stress oundary is developed for recycled aggregate concrete. σ = σ f( r) M4L f ( r ) = exp( a r 1 ) The compressive and tensile deviatoric stress oundaries represent the failure surface of concrete under pure deviatoric deformation which simulates the axial crushing and the lateral expansion respectively. The test data shows the amount of recycled aggregate concrete influences the uniaxial compression ehaviour consideraly oth in the longitudinal and the lateral direction [1 3]. Keep this in mind the deviatoric stress oundaries should e also made to reflect the influence of the amount of recycled aggregate. However some trial numerical experiments show that the aove idea can lead to some inconsistent results. A etter way is to make the key parameters involved in the deviatoric stress oundaries dependent on the amount of recycled aggregate concrete. As descried in [5] the parameter c 5 in the tensile deviatoric stress oundary and c 7 in oth two deviatoric stress oundaries controls the lateral ehaviour and the slope of the descending ranch respectively. In this study the following equations are assumed for the aove two parameters in the model for recycled aggregate concrete c = c α ( ) c = c β( ) (7) 5 r 5 M4L 7 r 7 M4L 1 α ( r) = 1+ a2r β( r) = (8) 1+ a3r The shear and compressive volumetric oundary have less effect on the uniaxial compression and tension ehaviour. These two oundaries remain the same as in model M4L. In the aove equations the parameters a 1 a 2 and a 3 can e identified through inverse calirations. (5) (6) 546

6 (a) r=0% () r=30% (c) r=50% (d) r=100% Figure 2: Concrete in uniaxial compression: Test data [1] and model predictions 3.2 umerical caliration with test data With the guidance of the test data in [1 4] inverse calculations have een performed to determine the aove parameters. In these calculations the elastic modulus and the Poisson s ratio are input according to the test data. The adjustale microplane parameters are determined according to the test data on normal concrete. Through a large amount of trial-and-error calirations the parameters a 1 a 2 and a 3 in Equations (6) and (8) have een determined as: a 1 = a 2 = a 3 =1.454 A comparison of the test data and the model predictions is shown in Figures 2 and 3. One can see that the model developed in this paper is capale of simulating the ehaviour of concrete oth in compression and tension with different amount of recycled aggregate in a sufficient way. 547

7 (a) r=0% () r=30% (c) r=50% (d) r=100% Figure 3: Concrete in uniaxial tension: Test data [4] and model predictions 4. UMERICAL ERFICATIO OF THE MOEL To further check the aility of the model developed aove more verification is required. However test data for concrete containing different content of recycled aggregate loaded in uniaxial compression or tension are not very sufficient especially for the lateral and volumetric properties. ue to this reason in this paper only the experimental findings of Ajdukiewicz and Kliszczewicz [3] for concrete with 100% recycled aggregate are used to validate the model. In this calculation the two material parameters in the model i.e. E and v were taken as the experimental values E=3.18x10 4 MPa v =0.18. The parameters k 1 -k 4 are identified through fitting the test data for normal concrete. The three new parameters a 1 -a 3 are kept the same as aove. The numerical results are illustrated in Figure 4. Figure 4(a) shows a comparison ewteen the experimental and numerical predicted stress-strain ehavior. It can e seen that the model reproduction is very close to the test result oth for the peak stress and the deformation. Figure 4 () and 4(c) present the numerical simulations for the variation of the Poisson s ratio and the volume change with stress level. It is evident that the model correctly reproduces the test oservations. 548

8 (a) Stress-strain curve () ariation of Poisson s ratio (c) olume change Figure 4: Comparison of test data [3] and model predictions for uniaxial compression 5. COCLUSIOS This paper descries the development and verification of a microplane model for recycled aggregate concrete considering the influence of the recycled aggregate amount. The model is ased on a recently developed microplane model for normal concrete and formulated through adding a nonlinear function of the amount of recycled aggregate to the normal stress oundary in model M4L and making the key parameters controlling the compressive softening and the lateral expansion varies with the recycled aggregate content. umerical results indicate that the model can sufficiently capture the inelastic ehaviour of recycled aggregate concrete in compression and tension. It might e noted that a correct reproduction for the lateral deformation of recycled aggregate concrete is also ale to achieved with the model. ACKOWLEGEMETS This work was finished under the support of a series of research projects from FG (German Science Foundation) granted to Leipzig University and Graz University of Technology as well as a project from Chinese Educational Bureau granted to Tongji University. These fiancé supports are highly acknowledged. REFERECES [1] Xiao J. Li J. and Zhang Ch. 'Mechanical properties of recycled aggregate under uniaxial loadings' Cem. Concr. Res. 35 (6) (2005)

9 [2] Rühl M. and Atkinson G. 'The influence of recycled aggregate concrete on the stress strain relation of concrete' armstadt Concrete. 14 (1999). [3] Ajdukiewicz A.B. and Kliszczewicz A.T. 'Comparative tests of eams and columns made of recycled aggregate concrete and natural aggregate concrete' J. Adv. Concr.Tech. 5 (2) (2007) [4] Xiao J.and Lan Y. 'Investigation on the tensile ehaviour of recycled aggregate concrete' Chin. J.Build. Mater. 9 (2) (2006) [5] Li J. 'evelopment and validation of a novel material model for concrete on asis of microplane theory' Ph thesis Leipzig University Germany [6] Bazant Z.P. and Prat P.C. 'Microplane model for rittle-plastic material. I: Theory' J. Eng. Mech. 114 (10) (2000) [7] Bazant Z.P. Caner F.C. Carol I. Adley M.. and Akers S.A. 'Microplane model for concrete. I: formulation with work-conjugate deviatoric stress' J. Eng. Mech. 126 (9) (2000)