LOCALIZED FRACTURE LENGTH AND FRACTURE ENERGY OF CONCRETE IN COMPRESSION ABSTRACT

Transcription

1 LOCALIZED FRACTURE LENGTH AND FRACTURE ENERGY OF CONCRETE IN COMPRESSION Torsak LERTSRISAKULRAT *, Ken WATANABE *, Maki MATSUO * and Junichiro NIWA * ABSTRACT The distribution of local vertical strains inside concrete specimens subjected to uniaxial compression has been measured to examine the failure mechanism and localization effects. Test results show that, when localization in uniaxial compression occurred, i.e., the localized fracture length is found to be dependent only on the size of the cross-section. Whereas the height-depth ratio and the cross-section shape are found to have less effects on Lp. The fracture energy in compression has been found to be constant for the same properties of concrete. KEYWORDS: fracture mechanics, localization effects, size effects, fracture energy in compression, localized compressive fracture length. INTRODUCTION It is now generally accepted that tensile failure of concrete is localized to a limited zone. Many researchers have studied the localization behavior in tension and useful results have been obtained []. The localized behavior in tension is modeled by stress-crack width relationship based on the tensile fracture energy (GF). A uniaxial description of the properties is sufficiently realistic, because no major lateral deformations take place. On the other hand, material models for compressive failure of concrete are normally based on a uniaxial compressive stress-strain curve obtained from tests, where uniform deformation of the concrete specimens is assumed. This assumption is reasonable for the ascending branch of the stress-strain curve, but not necessarily accurate for the descending branch. As it was found that the deformation after the peak stress is localized to certain zones [], so descending branch of the stress-strain curve becomes size dependent as the measured strain depends on the gage length and position of the gage. Though many studies were carried out [3] [], the localization behavior and fracture zone of concrete in compression have not yet been clarified. The compressive failure is more complex than tensile failure, as it is always accompanied by significant lateral deformations. The lateral deformations are mainly caused by splitting cracks, which form and expand during the failure process. In addition to these cracks, localized shear bands may also form. Thus, the fracture process in compression is not only determined by localized cracks, as in tension, but in a realistic manner both the local and the continuum components of compressive softening have to be taken into account. It is necessary to study the behaviors of concrete under compression by considering also the localization of cracks and fracture energy of concrete in compression, in order that the more accurate post-peak behavior of concrete can be analyzed. In this paper, by considering the parameters of height-depth ratio, cross-section shape and size of specimen, the localized compressive fracture length and fracture energy in compression of concrete under uniaxial compressive stress have been determined based on the experimental results. The concretes having * Department of Civil Engineering, Faculty of Engineering, Tokyo Institute of Technology

2 cylindrical compressive strength ranged from 0 to 50 N/ with the maximum size of aggregate of 0 were used in the tests. In all tests, the high early strength cement was used.. EXPERIMENT The experiment was conducted to examine the effects of the geometrical parameters of specimen such as height-depth ratio, cross-section size and shape on the failure of specimens relating to the localized compressive fracture length and compressive fracture energy. The details of the experimental program are listed in Table. Specimen Prism Cylinder Table Experimental program * Cross- section m m Height Designation 800 PS PS0-0 PS ** PR ** PR0-0 ** PR PS0-0 PS0-0 PS C C0-0 C C0-0 C0-0 C0-0 *Average cylinder compressive strength at 7 days for all case is 5 N/ with the maximum size of aggregate 0. **In case of PR0, D = was used. All specimens were cast by using the same mix proportion of concrete with the average cylindrical compressive strength at 7 days of 5 N/ and the maximum size of aggregate 0. The tops of specimens were capped by cement paste to ensure the smooth horizontal surface while loaded. Specimens were demolded after one day and were cured in water for 7 to 8 days before tested. The compressive strength tests of concrete cylinder taken from the same batch of specimen were also conducted. The technique of measuring local strain inside concrete specimen by embedding a deformed acrylic resin square bar studied by Nakamura and Higai [3] was found effective and was adopted in this experiment. The acrylic resin square bar with cross-section of 00, was first deformed by furrowing half cylinder-shaped gutters along the opposite sides of the acrylic bar in order to ensure the good bond between the bar and concrete, as shown in Fig. (a). Then, the deformed bar was attached by strain gages and installed vertically at the position coincident with the specimen axis before casting of concrete. The strain gages were attached to the bar vertically to measure the longitudinal local strain at the interval of 0 (or 0 in case of height specimen). The overall deformation of the specimen was also measured externally by the use of deflection gages set between loading plates while specimen was loaded in the testing machine. The reduction of the friction between concrete specimen and loading platen interfaces was done by placing friction-reducing pads set which consists of two teflon sheets inserted by silicon grease. The data were recorded through the data logger. The installation of strain gages and the test set up is illustrated in Figure. The post-peak load-deformation curves were captured by the one directional repeated loading in the stress descending range. The initiation and the propagation of cracks were also visually observed.

3 Strain gage Gutter (a) Acrylic bar with strain gages (b) Installation of acrylic bar (c) Loading set up Figure The installation of strain gages and the test set up 3. RESULTS AND CONSIDERATIONS 3. TEST RESULTS From the test results, the overall load-deformation curves in dimensionless form, together with the distribution of the local vertical strain along the specimen axis are plotted as an example shown in the Figure for PS0-SERIES specimen. maxand o represent the stress at the maximum resistance and the corresponding strain, respectively. All test results are suarized as shown in Table. /max PS0-SERIES / 0 Figure Typical results from the tests (PS0-SERIES) As mentioned above, the attempt to reduce the friction between specimen and loading platens was done by using friction-reducing pads. The test results show that the ratios of the maximum stress of specimen to its cylindrical compressive strength, max/fc, fall within the range of 63 to 8 percent, when, which means the friction was effectively removed by the friction-reducing pads. In the case of =, the average of σmax/fc is The reason why this low value is obtained is because specimens failed in splitting failure mode, which is explained in details in the next section. 3. CRACKING PATTERN Measured Strain 6.36 kn.59 kn 0.30 kn kn kn 9.57 kn kn 6.6 kn Strain Distribution (at different loading level) Localized Failure Zone Unloading Zone ( Intact Zone)

4 Table Suary of test results Specimen Section A C H m ax N/ f c N/ max / f c % f t N/ L p A curve kn- PS0-80 PS0-0 PS0-0 0, ,0, PRISM PR0-80 PR0-0 PR0-0 0, PS0-0 PS0-0 PS0-0 0, CYLINDER C0-80 C0-0 C0-0 C0-0 C0-0 C0-0 3,6 7, , * * Result not available. From the observation of the occurrence of cracks on tested specimens, it can be seen that, for short specimen, =, specimens were failed by splitting from the top to the bottom of specimen and the observed value of localized compressive fracture length, Lp, are, almost all cases, equal to H. As for the longer specimens, = and, lots of small visual vertical cracks were observed over some regions when the maximum resistance was reached. At the final state, in the post-peak region at 0.Pmax, the small cracks were coalesced forming a large crack band. That means the localization occurred just in the case of, hence the later sections discussing about Lp and GFc will refer to only the results of specimens having. It can also be clearly seen from the cracking pattern of specimens at the final state shown in Figure 3. = = = Figure 3 Cracking patterns of tested specimens (PS0-SERIES) 3.3 COMPRESSIVE FRACTURE LENGTH, Lp It can be seen from the stress-strain curve of each gage embedded inside the same specimen, as shown in Figure, that the failure localized in some parts of the specimen. In this case, i.e. PS0-0, the failure occurred from the top of specimen down to approximately 80, whereas the bottom part showed unloading behavior. Based on the local stress-strain curve obtained, the localized compressive fracture length of each specimen was determined and suarized as shown in Table. The effects of each

5 experimental parameter are discussed as the followings: () Height-depth ratio Figure shows that, for the same cross-section specimens, the variation of of specimen causes almost no change to Lp. In other words, the change in height of specimen has no effects on Lp. () Cross-section size and shape From Figure, it can be further observed that, regardless of the results of =, the shape of specimens, i.e. square, rectangular and circular, has small effect on Lp. Nevertheless the higher values of Lp are observed when the cross-sectional area of specimens becomes larger. (3) Formulation of Lp As it was found that the height of specimen and shape of specimen have virtually small effects on Lp, while the size of the cross-section of specimen exhibits remarkable effect on Lp. Therefore, the relationship between cross-section size and Lp has been considered in terms of the equivalent width, D *, which is the square root of the area of the cross section, AC. Figure 5 (a) shows that almost constant value of Lp/D * equal to.5 was obtained. 300 P, N 50 Pmax Lp, 50 A curve 50 0 PS0 C0 PR0 PS0 C Pmax dmax d, Figure The variation of Lp with the, size and shape of specimens Figure 6 Area under load-deformation curve Lp/D * PS0 C0 PR0 PS0 C0 Average =.50 Standard Deviation = 0.9 L p L p =.5D * AC,cm (a) Experimental results (b) Proposed formulation Figure 5 Relation of Lp and equivalent width of the specimen

6 Finally, the following relation can be proposed, Lp = H.5D * ; < () =.5 D * ; () where, D * = Ac, or, as depicted in Figure 5 (b). It should be noted that the proposed relation is obtained within the range of compressive strength 0-50 N/ and the maximum size of aggregate is FRACTURE ENERGY IN COMPRESSION, GFc In this research, fracture energy in compression, GFc, is calculated by dividing the area under load-deformation curve up to 0.Pmax, i.e. Acurve (Figure 6), by the fracture volume, Vp. The fracture volume is calculated by Lp times the cross-sectional area, AC. Considering Figure 7, it is found that, regardless of the volume of specimen, Vc, the value of GFc divided by fc are almost constant with the average value of 3.0 and the coefficient of variation of 3%. Therefore, when the localization in compression occurs, the following relation can be obtained, GFc = 3.0 fc (3) where, the unit of GFc and fc are N/. Figure 7 Relationship of GFc/fc and concrete volume. CONCLUSIONS The test results show that the localization in compression occurred when the specimen of was loaded under uniaxial compression. It can also be further observed that, in case of the localization occurred, the, height and cross-section shape of specimen have no significant effects on Lp while the size of the cross-section is found to play an important role on Lp. The relation of Lp equal to.5 times of the equivalent section width has been proposed. Furthermore, it is found that the fracture energy in compression is not dependent on the geometry of the specimens but found to be constant when concrete with the same properties was used. REFERENCES. Bažant, Z. P. and Oh, B. H., Crack Band Theory for Fracture of Concrete, Materials and Structures, Vol.6, No.93, 983, pp Santiago, S. D. and Hilsdorf, H. K., Fracture Mechanisms of Concrete under Compressive Loads, Cement and Concrete Research, Vol. 3, 973, pp Nakamura, H. and Higai, T., Compressive Fracture Energy and Fracture Zone Length of Concrete, JCI-C5E Seminar on Post-Peak Behavior of RC Structures Subjected to Seismic Loads, Vol., Oct. 999, pp Markeset, G., Failure of Concrete under Compressive Strain Gradients, Dr.Eng. thesis, 993:0, Norwegian Institute of Technology, Trondheim, 993.