Historia de la IU

The damage progress in the HPFRC and BC specimens throughout the loading history is shown in Table 6. The HPFRC specimens, particularly Specimen S1, exhibited enhanced damage tolerance compared with the geometri-cally identical plain concrete Specimen BC. Both HPFRC columns behaved elastically up to a drift ratio of approxi-mately 1.3% (nominal ductility μ = 1.5 based on first yielding of Specimen BC). The actual ductility of the tested HPFRC columns μa is, therefore, two-thirds that of the BC column.

The HPFRC specimens developed relatively similar damage states as the reference BC specimen, but at higher displace-ment levels. For example, damage observed in Specimens S1 and S2 at 3.9% drift ratio (μ = 4.5) was smaller than that in Specimen BC, as seen in Table 6. Large portions of the BC column cover had already spalled off at this

displace-ment level, while the HPFRC columns sustained relatively minor damage with no spalling despite experiencing rela-tively large flexural cracks.

At a nominal ductility level of 6.25 (5.4% drift), the spiral reinforcement in the S1 column fractured at an approximate height of 150 mm (6 in.) above the column base. This spiral fracture resulted in longitudinal bar buckling and significant concrete cover spalling and core degradation in the subse-quent displacement cycles. All the continuous longitudinal bars in Specimen S1 underwent buckling and fractured by the end of the cycle, corresponding to a nominal ductility level of 12.5 (10.7% drift). The dowels in Specimen S1 did not buckle or fracture. Specimen S2, on the other hand, experienced longitudinal bar buckling and spiral fracture at two locations, followed by fracture of two continuous longi-tudinal reinforcement bars during the cycle at a nominal ductility demand level of 6.25 (5.4% drift). The BC specimen did not experience spiral fracture, bar buckling, or longitu-dinal reinforcing bar fracture because the spiral spacing was half that provided in the HPFRC specimens, and the column was only cycled up to a nominal ductility level of 4.5 (3.9%

drift) because it was subsequently tested under monotoni-cally increased axial load.⁶ The maximum displacement ductility level attained during the test of Specimens S1 and S2 without substantial loss of gravity load-carrying capacity was 12.5 and 6.25, respectively (10.7 and 5.4% drift ratio).

Tests of Specimens S1 and S2 were terminated after several of the longitudinal bars fractured, compromising the safety of the test setup.

The length of the plastic deformation zone Lp in Specimen S1 was approximately 450 mm (18 in.) at the end of the test, which is slightly larger than the column diameter. Inelastic deformations in Specimen S1 first developed at approx-imately 350 mm (14 in.) from the base, and propagated upwards as well as down towards the base of the column.

Table 4—Fiber-reinforced concrete mixture quantities

Item Value

w/c 0.45

Coarse aggregate weight (9.5 mm [3/8 in.]

maximum size) 602 kg/m³ (1324 lb/yd³) Top sand weight 551 kg/m³ (1212 lb/yd³) Blend sand weight 194 kg/m³ (426 lb/yd³) Total fine aggregate weight 745 kg/m³ (1638 lb/yd³)

Cement 324 kg/m³ (712 lb/yd³) High-range water-reducing admixture 621 mL/m³ (21 oz/yd³) Water 145 kg/m³ (320 lb/yd³) Fibers 88 kg/m³ (194 lb/yd³) Note: Specified 28-day compressive strength: 34.5 MPa (5.0 ksi); slump: 140 mm (5.5 in.); 1 yd³ = 0.765 m³; 1 lb = 0.45 kg.

Table 5—Average values of HPFRC mechanical properties

Parameter 11 days 28 days 49 days 60 days

Regular concrete

33.0 MPa (4.78 ksi) 41.9 MPa (6.07 ksi) 42.1 MPa (6.11 ksi) 41.9 MPa (6.08 ksi)

HPFRC compressive strength

fcFRC′ 37.0 MPa (5.37 ksi) 46.7 MPa (6.77 ksi) 47.1 MPa^* (6.83 ksi) 47.3 MPa^* (6.86 ksi) HPFRC elastic modulus E_c-FRC 22.9 GPa^* (3323 ksi) 28.9 GPa^* (4190 ksi) 29.2 GPa^* (4227 ksi) 29.3 GPa^* (4246 ksi)

HPFRC first peak flexural

strength f₁ — 5.44 MPa (0.79 ksi) 6.67 MPa (0.97 ksi) 6.37 MPa (0.92 ksi)

HPFRC absolute peak flexural

strength f — 6.69 MPa (0.97 ksi) 7.10 MPa (1.03 ksi) 7.58 MPa (1.10 ksi)

HPFRC residual flexural strength at L/600 deflection

f_res,L/600

— 6.37 MPa (0.92 ksi) 6.49 MPa (0.94 ksi) 7.29 MPa (1.06 ksi)

HPFRC residual flexural strength at L/150 deflection

fres,L/150

— 4.69 MPa (0.68 ksi) 5.58 MPa (0.81 ksi) 5.38 MPa (0.78 ksi)

*Obtained indirectly from linear interpolation of test results performed on other days.

Table 6—Comparison of damage progress in HPFRC and BC specimens

S1: HPFRC S2: HPFRC BC: Plain concrete

State of column specimens at nominal ductility demand of 1.5 (1.3% drift)

State of column specimens at nominal ductility demand of 2.0 (1.7% drift)

State of column specimens at nominal ductility demand of 3.0 (2.6% drift)

State of column specimens at nominal ductility demand of 4.5 (3.9% drift)

State of column specimens at nominal ductility demand of 6.25 (5.4% drift)

Test terminated.

State of column specimens at nominal ductility demand of 8.0 (6.9% drift)

Test terminated.

State of column specimens at nominal ductility demand of 12.5 (10.7% drift)

The S2 column, on the other hand, developed a primary crack at a height of 250 mm (10 in.) above the foundation at the cutoff point of the dowel bars, resulting in a concentra-tion of deformaconcentra-tion and damage in that region with limited spreading of the plastic deformation zone towards the base of the column. The extent of the BC column plastic defor-mation zone was estimated at 300 mm (12 in.), equivalent to 3/4 of the column diameter.⁶

Force-displacement response

The force-deformation response of the HPFRC and BC specimens is shown in Fig. 4. Only the primary cycles corre-sponding to the nominal ductility level of 1 and higher are shown. The deformation axis is expressed in terms of resul-tant drift ratio (displacement of the column top divided by the distance between the top of the column base to the actu-ator axes). The force axis is expressed in terms of resultant shear stress (Fig. 4(a)) and shear stress ratio (Fig. 4(b)). The resultant shear stress was calculated as the resultant shear force applied by the two actuators divided by the effective area in shear, defined by Caltrans SDC⁸ as 0.8 times the gross area of the column. The shear stress ratio was obtained by dividing the total shear force in the column by the assumed nominal shear strength provided by the transverse steel rein-forcement at yielding V_s, calculated according to Caltrans SDC⁸ as follows

V A f D

s s

= v yh ′

(1)

where A_v = (π/2)A_b is the area of shear reinforcement, Ab is the area of the spiral reinforcement, f_yh is the corre-sponding yield strength, D′ is the cross-sectional dimension of confined concrete core measured between the centerline of the spiral, and s is the spiral pitch.

Figure 4 shows a three-fold increase in shear stress ratio demand in the HPFRC specimens compared with the BC specimen due to: 1) half as much transverse reinforcement in the HPRFC columns than in the BC column; and 2) dowels in the plastic hinge region of the HPRFC specimens that added flexural resistance and moved up the plastic hinge region, increasing the shear demand at flexural yielding.

From Fig. 4, it can be seen that even though the shear demand on the HPFRC specimens increased significantly

and the amount of transverse reinforcement was reduced by half compared with that in the BC specimen, the HPFRC specimens maintained a stable hysteretic behavior governed by flexure throughout the entire loading history. The degra-dation of lateral resistance with the progression of damage in the HPFRC specimens, which initiated at a nominal displacement ductility of 6.25 (5.4% drift), was governed by the loss of flexural capacity (concrete crushing, bar buckling, and finally bar fracture), and not by shear-related cracking or damage. Sliding of the column along the cold joint at the column-foundation interface or significant shear distortions of the column plastic hinge zone were not observed.

A conventional shear force versus nominal displacement ductility envelope, derived by plotting the peak lateral force at each nominal displacement ductility level imposed, is shown in Fig. 5(a). This plot was computed using the peak resultant force of the specimens in the x- and y-directions, to reconcile the differences in the response produced by the circular load pattern. Both HPFRC specimens remained in the elastic response range up to a nominal ductility demand of 1.5 (based on first yielding of Specimen BC). The peak applied force remained generally constant between nominal ductility levels of 1 and 4.5 for the BC column, and between 1.5 and 6.25 for the HPFRC columns. The S1 column was slightly stronger than the S2 column.

The secant lateral stiffness of the specimens, computed using the resultant peak force and corresponding displace-ment value attained during each new primary cycle, is shown in Fig. 5(b). The cracked elastic stiffness of the two HPFRC specimens was comparable, and higher than that of Specimen BC. However, the stiffness degradation rate for Specimen BC was somewhat lower than that for the HPFRC specimens up to nominal displacement ductility of 4.5. This is likely due to the use of twice as much transverse reinforce-ment (and tighter spiral spacing) in Specimen BC.

Column plastic hinge deformations

Measurements of cross section rotation relative to the column base about the x- and y-axes were obtained at four levels along the height of the column (0.375D_col, 0.75D_col, 1.125D_col, and 4.5D_col above the column base). From these rotations, average curvatures for each segment between two adjacent rotation measurements were calculated to eval-uate the spread of inelastic deformations along the column Fig. 4—Force-deformation response of HPFRC and BC specimens: (a) total shear stress versus total drift; and (b) shear stress ratio versus total drift.

height. Profiles of these curvatures for all three specimens are shown in Fig. 6.

The significant difference in the length of the plastic deformation zones among these three specimens, discussed previously and evident in Fig. 6, shows that it is possible to design and detail the longitudinal reinforcement of an HPFRC column to achieve a highly desirable spreading of plastic deformation. In particular, the addition of dowel rein-forcement elevated the center of the plastic hinge zone from the column base, thus providing more space for its spreading.

Debonding of the dowel reinforcement (thus avoiding termi-nation of dowels within the plastic hinge) in the column of Specimen S1 allowed for very effective spreading of bar yielding along the column height and formation of several flexural cracks in the plastic hinge region. The less successful detail used in Specimen S2, on the other hand, shows that there are significant unexplored opportunities to develop improved designs to ensure adequate spread of yielding in

HPFRC plastic hinges. It should be noted, however, that increased curvature demands were imposed on the HPRFC specimens for a given displacement level, compared with those imposed on the BC specimen, due to the upward shift of the plastic deformation region.

Bond stress

In both HPFRC specimens, the bonded region of dowel reinforcement started at 250 mm (10 in.) above the founda-tion. Strain gauge measurements along the dowel reinforce-ment recorded peak strain values exceeding the steel yield strain at a height of 100 mm (4 in.) above the foundation or 150 mm (6 in.) from the bar termination point, resulting in a length Ld as small as 150 mm (6 in.) or 12 bar diameters required to develop the yield strength of the No. 4 dowel bars. The peak average bond stress up to first yielding of the reinforcement in the HPFRC specimens was determined based on force equilibrium between the resultant force from Fig. 5—(a) Shear force-displacement envelope; and (b) lateral stiffness degradation versus nominal displacement ductility (or drift) demand.

Fig. 6—Curvature profiles from experiments for: (a) S1; (b) S2; and (c) BC.

an average uniform bond stress ub acting on the surface of the dowel reinforcement along a length measured from the bar termination point to the section at which first yielding occurred, and the yield strength of the bar. It is important to note that dowel bar yielding occurred after substan-tial cracking occurred around the cover of the HPFRC specimens. The resulting peak average bond stress ub was 10.2 MPa (1.5 ksi), which can be rewritten in terms of the unconfined HPFRC compressive strength results obtained from cylinder tests, fc′,FRC = 47.3 MPa (6.86 ksi). The degra-dation of bond stress with increasing bar inelastic strains could not be evaluated due to lack of data. Thus, the peak bond stress for reinforcing bar strains not exceeding the yield strain was approximately ub,max = 1 5. f_{c FRC}′_, , MPa (ub,max = 18 f_{c FRC}′_, , psi). This value is significantly higher than bond strengths reported in the literature for regular concrete¹⁶ of 1.0√fc′, MPa (12√fc′, psi) and 0.5√fc′, MPa (6√fc′, psi) for deformed bars at slip values smaller and larger than the slip measured at bar yield strain, respectively. These measure-ments thus indicate that reinforcement development lengths in HPFRC columns could be shorter than those in conven-tional concrete columns. Similar conclusions were estab-lished in recent studies.⁹ Conservative development lengths for conventional concrete, however, should be used for HPFRC until more test data on the subject become available.

CALIBRATED HPFRC COLUMN MODELS