behaviour of reactive powder concrete columns without

Journal of Advanced Concrete Technology Vol. 6, No. 2, 377-386, June 2008 / Copyright © 2008 Japan Concrete Institute 377

Technical report

Behaviour of Reactive Powder Concrete Columns without Steel Ties Adnan R. Malik1 and Stephen J. Foster2

Received 8 September 2007, accepted 20 February 2008

Abstract In this paper, an experimental and numerical investigation of six steel fibre reinforced reactive powder concrete (RPC) columns with 150 mm square cross sections is reported. The columns were tested in either concentric or eccentric com-pression with varying initial eccentricities. The RPC mix contained 2% (by volume) of 0.2 mm diameter by 13 mm long straight steel fibres with concrete strengths ranging from 140 to 155 MPa. The columns contained either 4% or 7% of longitudinal reinforcement but no tie reinforcement in the test region. Experimental data on the axial load and lateral and axial deformations was obtained for each test, together with the failure mode. All the columns failed in a controlled manner without observing spalling of concrete cover or buckling of the longitudinal reinforcement to well beyond the peak load. The columns were further modelled using the finite element (FE) software DIANA, the results from which reasonably correlate to test data.

1. Introduction

During the past two decades, significant improvements have been made in the physical and mechanical proper-ties of reinforced concrete; high strength concrete (HSC) is now being used in many parts of the world. Many studies have demonstrated the economy of using HSC in columns of high-rise buildings, as well as low and mid rise buildings. It is shown in a number of stud-ies (Cusson and Paultre, 1994; Foster and Attard, 1997; Saatcioglu and Razvi, 1998; Liu et al., 2000) that the failure of HSC columns is usually brittle and is charac-terized by early spalling of the concrete cover (Foster et al., 1998; Foster, 2001). After separation of the cover concrete from the section, the load drops significantly (Saatcioglu and Razvi, 1993; Cusson and Paultre, 1994). Tests by Paultre et al. (1996), Foster and Attard (2001) and Zaina and Foster (2005), amongst others, have shown that the use of steel fibres in the mix design can improve the ductility of HSC columns. RPC is a special concept for high performance concretes, whereby duc-tility is achieved through incorporation of a large con-tent of metallic fibres (Richard and Cheyrezy, 1994). The inclusion of fibres delays the dilation of concrete by acting as crack arresters and, thus, helps indirectly in confinement of concrete under compressive loads.

In this study, six square RPC columns containing two percent by volume of steel fibres are tested under con-centric and eccentric loading. The columns had longitu-dinal reinforcement but no tie reinforcement in the test-ing region. The results of the tests and corresponding

analyses are reported in this paper.

2. Experimental programme

2.1 Test specimens Six fibre reinforced RPC columns of 150 mm square cross-section were constructed. Each end of the columns was haunched to prevent premature failure at the col-umn ends and to allow for eccentric loading to be ap-plied. The longitudinal reinforcement consisted of either eight 12 mm or eight 16 mm diameter hot rolled de-formed (N-grade) bars giving steel reinforcement ratios of 4.0% and 7.1%, respectively. No tie reinforcement was used in the test region in any of the columns. The concrete cover was 15 mm.

The columns are designated as RPC1 to RPC6. The columns RPC1, RPC2 and RPC3 contained eight 16 mm diameter (N16) longitudinal bars and were tested under an initial eccentricity of 20, 8 and 0 mm, respec-tively. The columns RPC4, RPC5 and RPC6 contained eight 12 mm diameter (N12) longitudinal bars and were tested under an initial eccentricity of 20, 8 and 0 mm, respectively. The specimen dimensions, reinforcement arrangements and loading plate arrangement are pre-sented in Fig. 1.

2.2 RPC materials The constituent materials making up the RPC were as follows: 1050 kg/m3 Kandos Type 1 general Portland cement manufactured to AS3972 (1997); 221 kg/m3 of undensified silica fume produced in Western Australia; and 795 kg/m3 of Sydney sand with particle size range between 150 μm and 400 μm. The steel fibres used were 13 mm long by 0.2 mm diameter straight fibres with a tensile strength of 1800 MPa. Glenium 51 super-plasticizer was used to improve the flow of the RPC mix and the water-binder ratio was 0.17.

1Structural Design Engineer, Woolacotts Consulting Engineers, Sydney, Australia. E-mail:[email protected] 2Professor, Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia.

378 A. R. Malik and S. J. Foster / Journal of Advanced Concrete Technology Vol. 6, No. 2, 377-386, 2008

2.3 Concrete mixing and properties All the dry constituents of the RPC were batched by an electronic balance. The dry constituents were then mixed in a horizontal pan concrete mixer for about 10 minutes. Water and superplasticizer were mixed and added gradually until the materials were uniformly mixed. The fibres were introduced last, dispersed uni-formly using a sieve and mixed for a further 10 minutes.

The mixing procedures proved satisfactory in that the dispersion of fibres were found to be uniform and there was no evidence of fibre balling. Flow table tests as per ASTM C230 were undertaken before casting of the specimens to assure that the fibre reinforced concrete mix had achieved a flow of between 160 and 220 mm for the selected mix.

Compression strength tests were undertaken on 200 mm high by 100 mm diameter cylinders with three cylinders tested from each batch. The tensile strength (fdp) was determined using a standard double punch test on 200 mm high by 100 mm diameter cylinders using a pair of 25 mm high by 25 mm diameter rigid circular steel punches on the top and bottom surfaces of the specimens (see Fig. 2). The tensile strength was then determined using the Chen and Yuan (1980) equation. The flexural tensile strengths (fct) were obtained from notched three point bending tests. The specimens used in this test were 100 mm square prisms spanning 400 mm with a notch depth of being 25 mm. The notches were formed by a 3 mm wide saw cut across the full width of the specimen. The specimens were counter balanced to eliminate the effect of the self-weight on the fracture measurement. The notched specimens were controlled using the crack mouth opening displacement (CMOD). The control specimen properties are given in Table 1 where Ec is the Young modulus of elasticity, v is the Poisson’s ratio, fcm is the mean cylinder compressive strength and Gf is the fracture energy. Figure 3 presents a typical stress strain curve obtained from testing a 200 mm high by 100 mm diameter RPC cylinder cast with specimen RPC1. Figure 4 shows a typical graph for load versus CMOD for the RPC mix.

2.4 Steel reinforcement The reinforcement used for the longitudinal steel con-sisted of 12 mm diameter (N12) or 16 mm diameter (N16) bars with a nominal yield strength of 500 MPa. The deformed steel bars were tested for the yield strength fsy (taken as the 0.2% proof stress), modulus of elasticity Es and ultimate tensile strength fsu. The rein-forcing steel properties are presented in Table 2 and the stress-strain curves for the reinforcement used are shown in Fig. 5. 2.5 Fabrication The columns were cast in reusable steel forms and, due to the limited capacity of the concrete mixer, each col-umn was cast separately. To reinforce each haunch, four N12 corner bars were cut to length and shaped to the

200 x 200 x 70 mmhigh strength steelplate

100 x 100 mm highstrength steel pin

Base Plate

e

490

B BN12

AA 650N16 for RPC1, RPC2, RPC3

N12 for RPC4, RPC5, RPC6

300

400

Reinforcement Details

1450

300

(a) Specimen dimensions (in mm) and reinforcement details

(b) Details of loading plates and bearing pins

Fig. 1 Specimen details and loading plate arrangement.

Section B-B

W4 @ 40

150

300

Section A-A

150

150

200

100

25

25

Fig. 2 Experimental setup for double punch tensile strength test.

A. R. Malik and S. J. Foster / Journal of Advanced Concrete Technology Vol. 6, No. 2, 377-386, 2008 379

haunches. Two sizes of 4 mm diameter wire ties (W4) used in the end haunches were fabricated and delivered to the testing laboratory; 120 mm square ties and 270 x 120 mm ties. Additional ties for the transition regions were fabricated and fitted on site. No ties were placed in the central test region of the specimens (see Fig. 1a). The steel cages were tied together and placed in the moulds with 15 mm clear cover to the longitudinal rein-forcement. 2.6 Instrumentation and casting After fabricating the reinforcement cages, 6 mm diame-ter steel lugs, used to measure axial strains in the rein-forcement, were welded onto the corner longitudinal bars. Strains and curvatures at the mid-height of the columns were calculated from the change in displace-ments measured between the lugs using linear variable displacement transducers (LVDTs). An additional LVDT was placed at the mid length of the specimens to meas-ure lateral deflections. The locations of LVDTs used to measure deformation are shown in Fig. 6. 2.7 Testing procedure The columns were tested vertically in a stiff testing frame. For the eccentrically loaded tests, high strength steel pins and bearing plates were placed at the desired eccentricity at each column end to allow free rotation of the ends and to distribute the load (see Fig. 1b). For the concentrically loaded columns, the rotational pins were removed from the test setup.

Testing was undertaken using a closed loop servo-control system. The lateral displacement was used as the control for the eccentrically loaded specimens and the axial displacement, via LVDT1 (see Fig. 6b), for the concentrically loaded specimens. Undertaking this pro-cedure enabled the descending load curves of the RPC columns to be obtained. The test was started under ram displacement control to 40% of the predicted column capacity. This allowed a check on the electronic data acquisition system that was used for recording the data input and to monitor the behaviour of the test control parameter. When all indicators showed that the system was operating within control limits, control was trans-ferred to either the axial strain at a rate of 2 mm/hr for

Table 1 Properties of RPC.

Specimen cmf (MPa)

ν Ec (MPa)

dpf (MPa)

cff (MPa)

Flow (mm)

fG (N/mm)

RPC1 155 0.12 44150 7.8 15.3 195 10.8

RPC2 153 0.09 41670 6.9 35.6 195 32.8

RPC3 154 0.12 41600 7.6 10 210 21.5

RPC4 152 0.10 39920 7.4 18.6 175 12.9

RPC5 140 0.12 40140 7.5 23.2 185 19.1

RPC6 154 0.11 43370 7.7 28 195 22.7

0

20

40

60

80

100

120

140

160

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Axial Strain

Axi

al S

tres

s (M

Pa)

Circumferential strain

Fig. 3 Typical stress strain curve for RPC cylinder.

0

8

16

24

32

40

0 2 4 6 8 10 12CMOD (mm)

Load

(kN

) .

Fig. 4 Typical load versus CMOD for the RPC mix.

Table 2 Properties of reinforcing steel.

Bar diameter (mm)

fsy (MPa)

fsu (MPa)

Es (GPa)

16 552 646 202

12 545 635 199


the concentrically loaded columns or lateral deflection control, at a rate of 10 mm/hr, for eccentrically loaded columns. The testing of the columns is shown in Fig. 7.

3. Test results and observations

The peak loads (Pu), moments at peak load (Mu) and corresponding lateral displacements at the mid height of the specimen (Δmid), axial displacement measured over the full height of the specimen (Δaxial), initial target load eccentricities and the actual initial eccentricities as post evaluated from the LVDTs data are presented in Table 3.

For the eccentrically loaded columns, the failure of the specimens was initiated by crushing of concrete at the extreme compressive fibre at approximately the mid-hight of the specimens. With increasing displace-ment further cracking appeared while existing cracks widened. When the peak load was reached one or more cracks in the critical zone (in compression) widened and, with increasing lateral deflection, tensile cracks were observed. Finally the columns failed by crushing of con-crete.

Figure 8 shows the failure zone and failure type for specimen RPC1 and is typical of the eccentrically loaded columns. During the tests, the sound of popping of fibres pulling out of concrete could be heard. How-ever, no loud noises were heard during the failure of the RPC columns for the eccentrically loaded columns. For the concentrically loaded columns, the initiation of fail-ure was sudden with the appearance of one or two major cracks near the peak load. The cracks widened as the testing continued. The concrete cover region did not spall for any of the tests (eccentric and concentric) and there was no evidence of buckling of the longitudinal reinforcement. The load versus mid-height lateral de-flection diagrams for the eccentrically loaded columns is presented in Fig. 9. In Fig. 10 the curves for load ver-sus axial strain (measured using LVDT1) are plotted for the eccentric and concentrically loaded specimens.

0

150

300

450

600

750

0 0.04 0.08 0.12 0.16 0.2Axial Strain

Axi

al S

tres

s (M

Pa)

N12 bars

(a) N12 deformed bars

0

150

300

450

600

750

0 0.03 0.06 0.09 0.12 0.15 0.18

Axial strain

Axi

al S

tres

s (M

Pa)

N16 bars

(b) N16 deformed bars Fig. 5 Stress-strain curves of reinforcing steel.

600

2 5

AA

Section A-A LVDT1 (used tocontrol the rammovement)

200

LVDT6

200

A A52

1

600

LVDT3

axis ofrotation

LVDT4LVDT5LVDT2

LVDT1

LVDTs 2 and 3LVDTs 4 and 5

LVDT6

e

(a) Eccentrically loaded specimens (b) concentrically loaded specimens

Fig. 6 LVDT locations.


(a) (b) (c)

Fig. 7 Observed behaviour of RPC columns: (a) eccentrically loaded column at the start; (b) during the test and (c) con-centrically loaded column.

Table 3 Peak axial loads and corresponding moments.

Specimen Pu (kN)

Δmid (mm)

Mu (kNm)

Δaxial (mm)

Target Initial eccentricity

(mm)

Eccentricity LVDTs (mm)

RPC1 2772 8.4 79.0 1.60 20 18 RPC2 3791 4 45.5 1.94 8 7 RPC3 3493 # # # 0 - RPC4 2282 7.7 63.2 1.29 20 18 RPC5 3184 4.2 38.8 1.61 8 7 RPC6 2428 - - 2.48 0 -

Note # loss of data from displacement measuring devices due to power failure during testing

(a) Compression side

(b) Tension side

Fig. 8 Failure of specimen RPC1 near completion of test.


The ultimate load Nuo for columns loaded in axial compression can be calculated by the expression:

ssysgcpuo AfAAfN +−= )( (1)

where fcp is the strength of the in-situ concrete, Ag is the gross column cross sectional area, As is the total cross sectional area of steel reinforcement in the column cross section and fsy is the steel yield strength. When only the core of the cross section is considered to be effective, the ultimate load Nc is given by:

ssysccpc AfAAfN +−= )( (2)

where Ac is the column cross sectional area taken as the area bounded by the outer limits of the longitudinal bars. Table 4 compares the experimental results for the con-centrically loaded specimens with the theoretical predic-tions of ultimate load based on Eqs. 1 and 2 with the in-situ strength taken as fcp = 0.9 fcm. The ratio between the theoretical loads considering only the core concrete area and experimental results is greater than 1.0 for column RPC3 with N16 bars and is equal to 0.84 for RPC6 with N12 bars. It is seen that the loads for the concentrically

0

500

1000

1500

2000

2500

3000

3500

4000

0 10 20 30 40 50mid-height lateral displacement (mm)

Axi

al L

oad

(kN

)

RPC1

RPC2

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30mid-height lateral displacement (mm)

Axi

al L

oad

(kN

)

RPC4

RPC5

(a) Specimen with N16 longitudinal reinforcement (b) Specimen with N12 longitudinal reinforcement

Fig. 9 Axial load versus mid-height lateral displacement for eccentrically loaded RPC columns.

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.001 0.002 0.003 0.004 0.005 0.006Axial Strain

Axi

al L

oad

(kN

)

RPC2

RPC5

RPC4 RPC1

0

500

1000

1500

2000

2500

3000

0 0.002 0.004 0.006 0.008 0.01 0.012

Axial Strain

Axi

al L

oad

(kN

)

RPC6

(a) Eccentrically loaded specimens (b) Concentrically loaded specimens

Fig. 10 Axial Load versus axial strain (from LVDT1).

Table 4 Experimental and theoretically predicted ultimate loads for concentrically loaded specimens.

Specimen Nuo (kN) Nc (kN) Exp. (kN) Exp./ Nuo Exp./Nc

RPC3 3783 3191 3493 0.92 1.09

RPC6 3486 2893 2428 0.70 0.84


loaded specimens were lower than the theoretical squash load, and for specimen RPC6, less than the theo-retical strength of the core. During the testing of these specimens, however, significant crushing of the concrete was observed on one side of the specimen before the other, indicating a sizeable applied eccentricity of load-ing. For specimen RPC6, the initial crushing was ob-served to be in one corner or the specimen indicating biaxial loading eccentricity. With these accidental, un-measured, eccentricities, no statements of the squash loading can be made. However, it can still be said that, in each case, no spalling of the cover concrete or buck-ling of the longitudinal reinforcement was observed throughout the test.

In Fig. 11 the load paths for the eccentrically loaded columns are plotted together with the axial force-bending moment interaction diagram. The interaction diagram was obtained by using an elastic-perfectly plas-tic stress-strain model for the concrete with an elastic modulus of 43 GPa, compressive failure strain of 0.005 and with k3 values of 1.0 and 0.9, where k3 is the in-situ strength factor and is given by k3 =fcp/fcm . Figure 11 shows that the peak load is greater than the theoretical model and it is suggested that the fibres provide some confining effects to the section.

4. FE analysis of FR-RPC columns

To compliment the experimental tests, 3D nonlinear FE analyses of the columns were undertaken using the com-puter software DIANA. To reduce computational cost, two-fold symmetry was used so that only quarter of the tested columns were modelled with the boundary condi-tions set to satisfy the symmetry conditions. In the nu-merical simulation, loading was applied by two vertical line loads, P1 applied along the centreline of the speci-men and P2 applied eccentrically to the centreline by 25 mm (Fig. 12). The values of P1 and P2 were adjusted so that their resultant is equivalent to the externally ap-plied experimental load. Geometric non-linearity was taken into account using a total Lagrange formulation.

The FE mesh for the RPC columns tested is shown in Fig. 13. The concrete was modelled by 20-node isoparametric brick elements on a 3x3x3 numerical in-tegration scheme. The reinforcing bars were modelled as embedded reinforcement bars with perfect bond as-sumed between the reinforcement and the concrete. The concrete in the haunched region was modelled as an isotropic elastic material. An elasto-plastic model in conjunction with the Drucker-Prager (D-P) yield locus was used with a tension cut-off (Fig. 14a) for describing the behaviour of concrete. The tensile behaviour of con-crete was modelled using a linear tension softening rela-tionship (Fig. 14b) with the maximum tensile strain (εu) derived from the yield stress of the reinforcement in the square column section. In Fig. 14, fcp and ft are the in-situ compressive and tensile strength of the concrete, respectively. A crack band width h equal to the volume

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 20 40 60 80 100

Moment (kNm)

Axi

al L

oad

(kN

)

RPC2

RPC1

9.03 =k

0.13 =k

(a) Specimen with N16 longitudinal reinforcement

0

500

1000

1500

2000

2500

3000

3500

4000

0 20 40 60 80Moment (kNm)

Axi

al L

oad

(kN

)

RPC4

RPC50.13 =k

9.03 =k

(b) Specimen with N12 longitudinal reinforcement

Fig. 11 Load path for eccentrically loaded RPC columns.

25 mm

Specimen

RPC1, RPC4

RPC2, RPC5

Ratio P1 : P2

0.25 : 1

0.68 : 0.32

P2 P1

725

mm

150 mm

Fig. 12 Numerical simulation of loading for eccentrically loaded columns.


of element V raised to the power of 1/3 (h = V 1/3) was adopted. A smeared fixed-crack model (De Borst and Nauta, 1985; Rots, 1988) was used for modelling the behaviour of the cracked concrete and a shear retention factor of 20% of the uncracked shear stiffness was adopted for the post-cracked state. The material proper-ties used in the FE analyses for the concrete and the reinforcing steel are given in detail in Table 5.

In Fig. 15 the experimental load-deflection behaviour of RPC1, RPC2, RPC4 and RPC5 columns are com-pared with the results of the FE analyses. In all cases, the numerical model is in reasonable agreement with the

measured load-deflection response for the eccentrically loaded columns. It is worth mentioning, however, that a converged numerical solution could not be found for the post-peak softening response for the columns tested and

Fig. 13 FE mesh used for modelling the RPC columns tested.

cracking

crushing

crac

king

fcp

fcp

ft

(a)

σ

εεu

ftε =u

fsyEs

1Ec

(b)

Fig. 14 (a) Concrete failure surface using Drucker-Prager plasticity model in principal stress space with tension cutoff and (b) Linear softening model in tension.

Table 5 Material properties for concrete and steel used in the FE analysis.

Concrete in the haunched region Reinforcing steel

Young’s modulus Ec see Table 1 Yield stress fsy Young’s modulus Es

550 MPa 200 GPa

Poisson’s ratio v see Table 1 Yield criterion Von-Mises

Concrete in square column section

Parameters for concrete plasticity model Parameters for modelling tensile cracking

Yield criterion Drucker-Prager Tension stiffening εu fsy/Es

Friction angle φ in D-P model 37 degrees Shear retention factor β 0.2

Dilation angle ψ in D-P model 17 degrees Threshold angle α 90 degrees

(fixed crack)

Young’s modulus Ec see Table 1 Tensile strength ft = fdp see Table 1


is a limitation of the DIANA model. The concentrically loaded columns were modelled

similarly to the eccentrically loaded columns but with P1 and P2 replaced by an axial pressure applied concen-trically to the specimens. In the experimental program, it was observed that the failure loads for the concentri-cally loaded specimens were lower than the theoretical squash loads (see Table 4). During the testing of these specimens, however, significant crushing of the concrete was observed on one side of the specimen before the

other, indicating bi-axial applied eccentricities of load-ing. With these accidental, unmeasured eccentricities, no statements could be made in regards to the squash load capacity. The load versus axial strains measured from the experiments is compared with FE results in Fig. 16. As expected, the load capacities obtained using DIANA show higher values than obtained from the ex-periments for the concentrically loaded specimens and is consistent with the theoretical expectations. The acci-dental eccentricities in the loading are clearly seen in

0

500

1000

1500

2000

2500

3000

0 2 4 6 8 10 12mid-height lateral deflection (mm)

Axi

al L

oad

(kN

)

ExperimentFE analysis

(a) RPC1 column

0

800

1600

2400

3200

4000

0 1 2 3 4 5mid-height lateral deflection (mm)

Axi

al L

oad

(kN

)


(b) RPC2 column

0

500

1000

1500

2000

2500

0 2 4 6 8mid-height lateral deflection (mm)

Axi

al L

oad

(kN

)


(c) RPC4 column

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6

mid-height lateral deflection (mm)

Axi

al L

oad

(kN

)


(d) RPC5 column

Fig. 15 Comparison of experimental and FE analyses.

0

1000

2000

3000

4000

0 0.002 0.004 0.006 0.008

Strain (ε)

Load

(kN

)

Strain at location 2



3 452

C.L. &

Axis of rotation

FE analysis

(a) RPC3 column

0

900

1800

2700

3600

0 0.001 0.002 0.003 0.004 0.005Strain (ε)

Load

(kN

)




3 452

1

Axis of rotation&

C.L.


FE analysis

(b) RPC6 column

Fig. 16 Comparison of load versus axial strain measurement for the experimental and FE analysis.


the test data.

5. Concluding remarks

Six high strength steel fibre reinforced RPC square col-umns without steel ties were tested in combined com-pression and bending. The tests showed that inclusion of high volumes of steel fibres is an effective way of pre-venting both spalling of the cover concrete and buckling of the longitudinal reinforcement. A considerable reduc-tion or, perhaps, elimination of tie reinforcement for RPC columns might be possible which could lead to an increase the speed of construction with an associated potential reduction in construction costs. More test data, however, is required to fully justify this conclusion.

Using conventional approaches for determining the axial force-bending moment interaction diagram gives conservative results for sections loaded with greater that the minimum loading eccentricity. Due to flaws in the testing set-up for the concentrically loaded specimens, however, no conclusions can be drawn in regards to the squash load capacity.

Acknowledgements This project was supported by Australian Research Council (ARC) Discovery Grant. The support of the ARC is acknowledged with appreciation. References AS 3600, (2001). “Concrete structures code.” Standards

Association of Australia. ASTM C230. “Standard specification for flow table for

use in tests of hydraulic cement.” ASTM International. Chen, W. F. and Yuan, R. L. (1980). “Tensile strength of

concrete: Double-Punch Test.” Journal of the Structural Division, ASCE, 106(ST 8), 1673-1693.

Cusson, D. and Paultre, P. (1994). “High-strength concrete columns confined by rectangular ties.” Journal of Structural Engineering, ASCE, 120(3), 783-804.

De Borst, R. and Nauta, P. (1985). “Non-orthogonal cracks in a smeared finite element model.” Engineering Computations, 2, 35-46.

DIANA-Release 9.1 (2005). TNO Building and

Construction Research, Delft, The Netherlands. Foster, S. J., Liu, J. and Sheikh, S. A. (1998). “Cover

spalling in HSC columns loaded in concentric compression.” ASCE, Journal of Structural Engineering, 124(12), 1431-1437.

Foster, S. J. and Attard, M. M. (1997). “Experimental tests on eccentrically loaded high-strength concrete columns.” ACI Structural Journal, 94(3), 295-303.

Foster, S. J. (2001). “On behavior of HSC columns: cover spalling, steel fibers and ductility.” ACI Structural Journal, 98(4), July-August, 583-589.

Foster, S. J. and Attard, M. M. (2001). “Strength and ductility of fiber-reinforced high-strength concrete columns.” Journal of Structural Engineering, ASCE, 127(1), 28-34.

Liu, J., Foster, S. J. and Attard, M. M. (2000). “Strength of tied HSC columns loaded in concentric compression.” ACI Structural Journal, 97(1), 149-156.

Paultre, P., Khayat, K. H., Langlois, A., Trudel, A. and Cusson, D. (1996). “Structural performance of some special concretes.” Proceedings of the 4th

International Symposium on the Utilization of High Performance Concrete, Paris, France, May, 787-796.

Richard, P. and Cheyrezy, M. H. (1994). “Reactive powder concretes with high ductility and 200-800 MPa compressive strength.” ACI, SP-144(24), San Francisco, CA, 507-518.

Rots, J. G. (1988). “Computational modeling of concrete fracture.” PhD Thesis, Delft University of Technology, The Netherlands.

Saatscioglu, M. and Razvi, S. (1993). “Behaviour of confined high strength concrete columns.” Proceedings CSCE/CPCA, Structural Concrete Conference, May 19-21, Toronto, Ontario, 37-50.

Saatcioglu, M. and Razvi, S. (1998). “High-strength concrete columns with square sections under concentric compression.” Journal of Structural Engineering, ASCE, 124(12), 1438-1447.

Zaina, M. S. and Foster, S. J. (2005). “Testing of concentric and eccentrically loaded fibre-reinforced HSC columns.” UNICIV Report No. R-437, The University of New South Wales, Sydney, Australia.

behaviour of reactive powder concrete columns without

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