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Engineer ing Fracture ~e~fiunies Vol. 35. NO. l/2/3, pp. 261-268, 1990 0013-7944po s3.00 + 0.00Printed in Great Britain. Pergamon Press pk.

FIBER-REINFORCED CONCRETE UNDERBIAXIAL COMPRESSION

W. S. YIN,? ERIC C. M. SU,$ M. A. MANSUR$ and THOMAS T. C. HSUIItDepartment of Civil Engineering, University of Houston, Houston, Texas, U.S.A.,iWalter P. Moore & Associates, Houston, Texas, U.S.A.,$Department of Civil Engineering, National University of Singapore, Singapore,//Department of Civil En~n~~ng, University of Houston, Houston, Texas, U.S.A.

Abstract-Fiber-reinforced concrete is tested under biaxial compression. Test results show that theaddition of steel fibers increases the strength, stiffness and ductility of concrete.

TESTS HAVE shown that the tensile and flexural strengths of concrete can be substantially increasedby the addition of closely spaced fibers[ 11. This can be explained by the fact that concrete containsnumerous flaws and microcracks[2] and the propagation of these microcracks can be arrested bythe fibers. Encouraged by the evidence of improvement in tensile properties, much research hasbeen done on the uniaxial and flexural behavior. In contrast, studies of fiber concrete incompression are less frequent because experiments show that the incorporation of fibers in concretehas very little effect on its uniaxial compressive strength[3-51. This paper, however, describes aseries of biaxial compression tests on fiber concrete and demonstrates that the addition of steelfibers does have a significant beneficial effect on the strength, stiffness and ductility.

EXPERIMENTAL STUDYTest program

Fiber-reinforced and plain concrete plates of size 6 x 6 x 1.5 in. (15.2 x 15.2 x 3.8 cm) weresubjected to biaxial compression. Four principal biaxial compression stress ratios of a,/~, = 0(uniaxial compression), 0.2, 0.5 and 1.0 were selected. The principal stresses were expressed as5, > 5* > 53, algebraically. The lengths of fibers studied were 3/4 and 1 in. (19 and 25 mm). Thepercentages of volume were 1.0 and 2.0% for l-in. (25 mm) fibers, and 1.0% for 3/4-in. (19 mm)fibers. At least two specimens were tested for each stress ratio. All specimens were loaded underthe ASTM loading rate (approximately 2000 psi/min or 14 MPa/min). For uniaxial tests, specimenswere loaded in the direction ~~ndicular to the direction of casting. For biaxial tests, the majorstresses were loaded in the direction perpendicular to the direction of casting.Test specimens

The concrete test specimens were made of Type III Portland cement. The mix proportion was1: 2.16: 1.88 by weight for cement, sand and coarse aggregate, respectively. The water-cement ratiowas 0.6 and the maximum size of aggregate was 3/8 in. (0.95 cm). The coarse aggregate consistedof quartz and flint, with some feldspar. The carbon steel fibers were smooth, straight-slit type, witha cross-section of 0.01 x 0.022 in. (0.25 x 0.56 mm). The average tensile strength of steel fibers was60 ksi (414 MPa). The mixing was done in a 5 cu.-ft. (0.14 cu.-m) rotary drum mixer, while the fiberswere gradually sprinkled into the drum by hand. After all the fibers were added, mixing continuedfor about one minute. Three 6 x 6 x 20 in. (15 x 15 x 50-cm) steel molds were used for casting,with the 20-in. (50-cm) dimension horizontal.The plate specimens were cut from the 6 x 6 x 20-in. (15 x 15 x 50-cm) concrete blocks by aprecision diamond saw. The concrete blocks were stored in a water tank in the moist room at 78F

tResearch Assistant, fEngineer, @enior Lecturer, /iProfessor.EFM 35--l,+--~ 261

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262 W. S. YIN et al.(26C) and 100% relative humidity until sawing at one week before testing. After sawing, theconcrete specimens were coated with two thin layers of sealant to prevent the evaporation of water.The specimens were tested at the ages between 44 and 168 days.Test fa~iiities

The specimens were tested in a specially designed biaxial test machine, as shown in Fig. 1. Theload was supplied by a 220-kip (978kN) capacity hydraulic actuator, mounted on top of the testingframe. This downward load passed through a load cell and a spherical bearing hinge, and was thenresolved into a pair of forces by a load bifurcation mechanism.Brush-loading platens, rather than solid platens, were used to minimize the frictionalconfinement of the test specimens by the loading platens. These brush platens reduced the frictionalstresses to about 0.33% of the applied stresses, and the load carried by the concrete was foundto be 99.3% of the applied load. As such, a well-defined biaxial stress state was assured.

Deformations in the three principal axes were each measured by a pair of capacitance-type transducers. Details of the test facilities and the experimental procedures were as thosereported in[6].

RESULTSUltimate strength

The ultimate strength data are summarized in the form of biaxial stress envelopes, as shownin Fig. 2, All the stresses are converted into 90-day strength, and then nondimensionalized by theuniaxial compressive plate strength of plain concrete, fcp, tested at the ASTM loading rate(2000 psi/min or 13.8 MPa/min). The average compressive plate strength of plain concrete (S,,) is-5460 psi (-37.6 MPa) at the age of 90 days. The average cylinder strength at 90 days is- 6100 psi (-42 MPa). Each test point in Fig. 2 is the average of two specimens.

The effect of the addition of fibers is quite different in uniaxial and biaxial compressions. Fiberconcrete, in general, possesses higher strength than plain concrete in biaxial compression. Theincrease is up to 35% for l-in. fiber length, 2% volume ratio and stress ratio of az/a3 = 0.2. Incontrast, the increase of strength due to the addition of steel fibers is negligible in uniaxialcompression.

Figure 2 also shows that the biaxial compressive strength increases as the length of the fiberincreases from 314 in. to 1 in. For the same fiber length of 1 in., the increase in volume percentageof fibers from 1 to 2% has little effect on the biaxial compressive strength.

- c2f,p1.8 1.8 X4 1.2 1.0 0.8 0.6 0.4 0.2 0 0

0.8 I0.8 ~3

fOP.0

Fig. 2. Biaxial strength envelopes.

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Fiber-reinforced concrete under biaxial compression 263

Fig. 1. Biaxial compression test facility

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264 W. S. YIN et al.

(a 1Uniaxial compression, 02 /cr3 = 0

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Fiber-reinforced concrete under biaxial compression 265

(a) Uniaxial compression, u2 /CT~ = 0

(b) Biaxial compression, 02 /cl3 = I .OFig. 4

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Fiber-reinforced concrete under biaxial compression 267Failure modes

Figure 3(a and b) show pictures of typical failure patterns of fiber concrete subjected touniaxial and biaxial compressions. It can be seen that fiber concrete, in general, possesses shear-typefailure. In uniaxial compression testing, fracture occurs by the formation of multiple shear planeswhich make an angle of 20-40 with the cl rr3 plane (Fig. 3a). Under biaxial compression, fractureoccurs by the formation of a single shear plane perpendicular to the gl o3 plane, and inclined atan angle of approximately 18 with respect to the loading (azo3) plane (Fig. 3b).In contrast, failure of plain concrete occurs by tensile splitting (Fig. 4a and b). Under uni-axial compression, the formation of cracks is in the direction of loading and perpendicular tothe plane of a test specimen (Fig. 4a). Under biaxial compression, fracture surface occursalong a plane parallel to the plane of the test specimen (Fig. 4b). In both types of failure, tensilesplitting occurs along the fracture surface(s) perpendicular to the direction of the maximumtensile strain. Apparently, the addition of fibers effectively prevented the tensile splitting failurepattern (Fig. 4b) from happening, thus changing the failure pattern into the shear-slip type(Fig. 3b).DeformationFigure 5 shows a typical relationship of normalized stress to total strain for fiber concreteunder biaxial loadings, fq is the uniaxial plate strength of plain concrete at the age when thespecimen is tested. The principal strains, 6 , cl and c3, are in the direction of the principal stresses,ol, c2 and c3, respectively. Figure 5 shows the effect of fiber content on the stress-strainrelationships under biaxial loading (a2/a3 = 1.0). In the near-linear range, the addition of steelfibers increases the stiffness of concrete in the two principal compression directions (e2 and c3), aswell as in the out-of-plane expanding direction, 6,. Thus, the steel fibers not only stiffen thespecimen in the loaded direction, but also reinforce the specimen in the unloaded expandingdirection. This observation may partially explain why the biaxial strength of fiber concrete is higherthan that of plain concrete.Figure 5 also shows that the failure strains in all three directions (q, c2 and c3) doincrease with increasing fiber content. In other words, the addition of fiber does increasethe ductility of concrete. Incidentally, the small difference in the two principal compressionstrains (t2 > c3) is attributed to the anisotropy characteristics associated with the direction ofcasting[7,8].

Fiber Content- 0%----3/4.-t%-.- ,._,((

Tenrile V Compr~rrlve0 I I I I I1000 0 -2000 -400Strain in Microstrain

Fig. 5. Stress-strain relationships under biaxial compression.

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268 W. S. YIN er al.DISCUSSION

The significant increase of biaxial strength, due to the addition of fibers, may be explainedby the change of the stress state in the specimens. The steel fibers will reinforce the specimen inthe unloaded or out-of-plane direction. This is equivalent to a certain amount of compressive forceapplying in the unloaded direction. In other words, a triaxial stress state is generated. Van Mier[S]has performed extensive tests on the triaxial compression of concrete. He observed that the strengthof plain concrete under a stress state of cr, a2: a) = -0.05: - 0.2 : - 1.0 is 47% higher than thatunder a stress state of a, :a2 : aj = 0: - 0.2 : - 1 O. That is, for a biaxial stress ratio of a,/a, = 0.2,a small out-of-plane stress of a, = -0.05 a3 would cause a very large (47%) increase of strength.By analogy, a 35% increase in biaxial compressive strength of fiber concrete reported herein (l-in.fiber length and 1% volume ratio) should be equivalent to an out-of-plane stress of only about3.5% of the major stress, a3. This small magnitude of stress could conceivably be supplied passivelyby the steel fibers.

CONCLUSIONS1. The biaxial strength of fiber concrete is greater than that of plain concrete. A maximumincrease of approximately 35% is achieved in the case of l-in. fiber length, 2% volume ratio, and

a stress ratio of a,/a, = 0.2. For uniaxial compression, the increase of the strength, due to the steelfibers, is negligible.2. The biaxial compression strength increases as the length of fiber increases from 3/4 in. to1 in. For the same fiber length of 1 in. the increase in volume percentage from 1 to 2% has littleeffect.3. For plain concrete subjected to biaxial and uniaxial compression, failure occurs bytensile-splitting or cleavage failure. For fiber concrete subjected to biaxial compression, failureoccurs by shear.

4. Under uniaxial compression, the addition of steel fibers into plain concrete does not changethe stiffness. Under biaxial compression, however, the addition of steel fibers increases the stiffnessof concrete in the major principal stress direction, as well as in the direction of the principal tensilestrain.

REFERENCESItIPI

;:;151161171181

American Concrete Institute Committee 544, Report No. 544.1R-82, State-of-the-art report on fiber reinforcedconcrete. Concr. Int. Des. Consrr. 4, 9-30 (1982).T. T. C. Hsu, F. 0. Slate, G. M. Sturman and G. Winter, Microcracking of plain concrete and the shape of thestress-strain curve. J. Am. Concr. hr. 60, 209-224 (1963).S. P. Shah and B. V. Rangan, Fiber reinforced concrete properties. J. Am. Concr. I nst. 68, 126135 (1971).G. R. Williamson, The effect of steel fiber on the compressive strength of concrete. SP-44, American Concrete Institute,Detroit, 195-207, (1974).W. F. Chen and J. L. Carson, Stress-strain properties of random wire reinforced concrete. J. Am. Concr. I nst. 68,933-936. (1971).E. C. M. Su and T. T. C. Hsu, A fatigue test machine for the biaxial compression of concrete. J. Test Eval. ASTM,16, 549-554 (1988).B. P. Hughes and J. E. Ash, Anisotropy and failure criteria for concrete. Muter. Srruct. RILEM, 3, 371-374 (1970).J. G. M. Van Mier, Strain-softening of concrete under multiaxial loading conditions. Ph.D. Dissertation, EindhovenUniversity of Technology, Netherlands (Nov., 1984).

(Received for publication 16 November 1988)