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Mechanical behavior of confined polymer concrete
CEMENT and CONCRETE RESEARCH. Vol. 22, pp. 621-630, 1992. Printed in the USA. 0008-8846/92. $5.00+00. Copyright © 1992 Pergamon Press Ltd.
MECHANICAL BEHAVIOR OF CONFINED POLYMER CONCRETE
S. Wei, S. T. Mau, and C. Vipulanandan Department of Civil And Environmental Engineering University of Houston Houston TX 77204-4791 U.S.A. (Refereed) (Received July 23, 1991)
ABSTRACT In order to broaden the application of polymer concrete, the mechanical behavior of a polyester-based polymer concrete is investigated. The focus of the study is the compressive stress-strain relationship under lateral confinement. A total of 18 cylindrical specimens of 9-inch length and 3-inch diameter were tested under monotonic axial compression. The lateral confinement was provided in a passive way by aluminum rings uniformly spaced in a central confined zone of the test specimen. The degree of confinement was varied from specimen to specimen by changing the thickness of the rings. Test results indicate that the lateral confinement enhances the compressive strength in proportion to the confining stress and improves the post-peak behavior. An empirical formula is suggested to predict the compressive strength of the polymer concrete under lateral confinement. A simple equation for the compressive stress and strain relationship is also developed. Introduction In recent years, the applications of polymer concrete have been broadened from one for surface repair of existing structures to that as a main construction material for nonstructural as well as structural elements. Latest applications include railway ties and bulky machine bases (1). In such applications, the suitability of polymer concrete as the construction material is often verified by the direct testing of the prototype. The results are only valid for a given geometry, and a given loading condition and cannot be generalized for other applications. Fundamental studies on the mechanical properties of polymer concrete, necessary for general applications, are limited to uniaxial compression and flexural strength only (2-4). Thus, further studies on the strength of polymer concrete under more complex stress conditions are needed. The polymer concrete is also known for its brittle failure under uniaxial compression, where its load-carrying capacity reduces drastically after the peak strength is achieved. This is an undesirable feature from the point of view of the ultimate strength design philosophy for most civil engineering structures. In the construction of structures with cement concrete, such brittle behavior under compression is prevented by providing lateral confinement to the concrete in the form of spiral steels or lateral steel ties. The improvement of post-peak behavior under lateral confinement is most successful for regular strength cement concrete and expansive cement concrete 621
622
s. Wei et al.
Vol. 22, No. 4
(4-7) but less successful for high strength cement concrete (8). It is of practical interest, therefore, to explore the behavior of polymer concrete under confinement. The present study is directed towards providing qualitative and quantitative information on the effect of lateral conf'mement on the compressive strength and post-peak behavior of a polymer concrete. A series of cylinder tests on a polyester-based polymer concrete is performed. The results are analyzed and summarized for potential applications. $~¢imen Design and Preparation The polymer concrete used in this research was polyester-based. The composition of the polymer concrete was chosen among several studied in a previous research and was the one with the highest compressive strength (9). The following table summarizes the composition. TABLE 1 Composition of a Polyester-Based Polymer Concrete Constituents Relative Weight Matrix-Polyester Resin 14% Initiator-MEKPO 1.5%* Promoter-Cobalt Napthenate 0.3%* Aggregate-Blasting Sand 86% Note: MEKPO=Methyl Ethyl Ketone Peroxide; *by weight of resin The blasting sand consisted of five grades of equal weight ranging from D10 (10% by weight are smaller) = 0.12 m m to 0.75 mm and D60 =0.17 m m to 1.50 mm. The compressive strength of the polymer concrete was expected to be close to 9,000 psi (62 MPa). The specimens were solid cylinders with a length-to-diameter ratio of 3:1. This ratio was selected, as opposed to the standard concrete cylinder ratio of 2:1, to secure a zone in the middle of the length of the specimen that was relatively uniformly stressed and confined. The nominal length and diameter of the test specimens were 9 inches (229 mm) and 3 inches (76 mm), respectively. The polymer concrete cylinders were cast in aluminum tubes with wall thickness of 0.225 inches (5.7 mm) and a nominal strength of 40 ksi (275 MPa). The aluminum tubes were machined to ensure a uniform circular cross-section. The tubes were also used later as confining rings. Before casting the polymer concrete, grease was applied to the inside wall of the tube to reduce bonding. The polymer concrete was mixed and cast by compacting with a steel rod in three to five lifts. The polymer concrete was cured at room temperature (about 20°C) for 24 hours followed by 24 hours in oven at 80° C. This curing condition was established as an optimal one (3). The cured polymer concrete was pushed out of the aluminum mold. The average diameter of the polymer concrete cylinder was 3.077 inches (78 mm) and the average unit weight was 126 lb/ft3(19.8 kN/m3).
STRAIN GAGE (~) ( ~ EXTENSOMETERS V 0.125 1.350
),200~_____
0.050
)
6.000
1,350 0.125
FIG. 1. Specimen Dimensions in inches (25.4 mm)
Vol. 22, No. 4
POLYMERCONCRETE,CONFINEMENT.STRENGTH
623
The polymer concrete cylinders were confined by aluminum rings, as shown in Figure 1. The rings, instead of a single tube, were used for confinement so that better estimate of the confining stress can be made because the rings were assumed to be stressed only circumferentially. This eliminates the bi-axial stress complication in a confining tube. After considering other alternatives, it was decided that the spacing and the height of the rings be kept constant for all specimens, only the wall thickness of the ring be varied to provide varied degree of confinement. Twenty-four rings, each with a height of 0.2 inches (5.08 mm), were placed in the middle 6-inch (152 mm) portion of the polymer concrete cylinder with a uniform spacing of 0.05 inches (1.27 ram). At the two ends, rings of 1.35 inches (34.29 turn) high were placed to provide higher confinement to prevent premature failure in the end zones. The thickness of the rings was varied from 0.03 inches (0.76 ram) to 0.11 inches (2.79 ram) in 0.01 inch (0.25 mm) increment. For each specimen the thickness of the ring was the same. The rings were machined from the same aluminum tube used as mold in preparing the polymer concrete cylinder. The aluminum tube was machined to the desired thickness and then cut transversely into rings. The rings were then bonded to the polymer concrete cylinders with epoxy. Before testing, ends of the polymer concrete specimens were treated in one of two ways. In the first series ends of 10 specimens were ground to parallel plane surfaces to ensure better contact to the test platens. In the second series 8 specimens were capped with sulfur compound according to ASTM C617. Confinin~ Rine Characterization In addition to tesdng of the confined polymer concrete, the stress-strain relationship of the confining aluminum were quantified experimentally. The aluminum rings were subjected to internal pressure as a result of the interaction between the ring and the confined polymer concrete. The best quantification would be a relation between the internal pressure and the circumferential strain. A direct test on the ring under internal pressure was not done, however, because of the lack of proper equipments. Instead, a direct tension test was performed on longitudinal strips cut from the aluminum tube. In doing so, it was assumed that the longitudinal behavior was close to the circumferential behavior. In making the rings of different thicknesses, the aluminum tubes were machined from outside to the desired thickness and cut transversely into rings. Thus, rings of different thicknesses came from different parts in the radial direction of the tube and may have different strengths. To account for the possible variation of tensile strength due to this effect and other effects of machining, tension coupon tests were performed on aluminum strips of 0.03, 0.07 and 0.11 inches 50000
(a)
(b)
40000 I |
~30000 II Ii
20000 [] II
10000
I
0
1 STRAIN(%) 2
0 STRAIN (%) 2 FIG. 2. (a)Stress-Strain Curves for 0.07-in. Coupons, (b) Averaged Stress-Strain Curves for 0.03, 0.07, and 0.11-in. Coupons
3
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thickness, machined the same way as the rings. These strips were 9 inches long with a 4 inches long and 0.4 inches wide central part of uniform cross-section. The longitudinal strain was measured using a 2-inch gage length clip-on extensometer. For each thickness, three strips were tested and the results averaged. It was observed that the tensile behavior can be represented approximately by an elasto-perfect plastic relationship within a strain of 0.03, and the thinner the specimen the lower the yield strength. Figure 2 shows the longitudinal stress-swain curves for the 0.07-inch thick specimen and the average curves for the cases tested. Through a simple interpolation, it is found that the yield strength in psi may be represented for different thicknesses between 0.03 and 0.11 inches by Oy = 37,800 + 51,100 t, where t is the thickness in inch. The strength variation within this range of interest is about 10%. Also the Young's modulus was calculated to be 10xl0~ psi (68,900 MPa) with a 9% coefficient of variation. These elasto-plastic relations were used later to calculate the confining stresses in the rings. Instrumentation and Testing Procedure Two 2-inch (50.8 mm) gage extensometers were attached 180-degree apart to the rings in the middle portion of the specimens to measure the longitudinal strains in the confined region, Figure 1. Two 30-ram strain gages,180-degree apart, were pasted on a central ring to measure the circumferential strains. For unconfined polymer concrete specimens the extensometers and the strain gages were attached to the polymer concrete specimen. An LVDT was used to measure the distance between the loading platens to provide feedback for the control of the loading. The specimens were loaded in a 400 kips (1,779 kN) capacity Tinius Olson Universal Testing Machine. The loading was displacement-controlled at a strain rate of 0.0005/min. The readings were taken at discrete intervals and fed into an HP3497 data acquisition unit and processed in an HP85 computer. All the specimens were preloaded once or twice to approximately 20 to 30% of the unconfined strength of polymer concrete. The uncapped specimens were loaded with a fixed platen while the capped specimens were loaded with a swivel head to allow self-adjustment of the platen. In both cases, minor adjustment for the centering of the specimens was performed during the preloading process to minimize the difference between the longitudinal strains obtained from the two extensometers. Generally readings were taken at approximate equal force intervals of either 5 kips or 10 kips during loading and equal strain intervals of 0.05-0.15% near the peak load region and during unloading. The test was stopped when one of the rings broke. Obseryations from the Tests Despite the efforts to minimize bending effects, the two extensometers seldom gave nearly identical longitudinal strain readings even for the capped specimens. The strain gage readings of the circumferential strain at a middle ring were also different to some degree. Shown in Figure 3 are four samples of the two pairs of extensometer readings from capped (COO and C06) and uncapped 0tOO and U06) specimens with or without confinement. It is seen that the capping does seem to reduce the difference in the longitudinal readings. This may be explained by the better distribution of stress at the contact surfaces between the specimen and the loading platens for the capped specimens. Other factors, such as the inherent inhomogeneity, localized internal damages at higher level of loading and imperfect contact between the tings and the polymer concrete, may all contribute to the deviation from a perfect concentric loading condition. In subsequent presentations, the average of each pair of reading is used to represent the longitudinal or the circumferential strain. These averaged readings are also assumed to represent the strains in the polymer concrete even though they were obtained from gages attached to the rings. The pertinent data for the 18 cases are summarized in Table 2. The specimen number starts with a letter C for capped specimens or a letter U for uncapped specimens, followed by two digits
Vol. 22, No. 4
POLYMERCONCRETE,CONFINEMENT,STRENGTH
80
625
120
U00
U06 100
6O
~
00
Q
qlO0
00 Oe Oe 00 Oe 00 00 Cl
~40 © ~J 20
0
O0 O0 O0
80
•
oO#
O0 Oe
60
go°
40 20
J
0
COO
o oQeto,k~,o$. 60
O0 O0 OD 13D aid Q Q
~4o <
20
0
00
I00
•
80
0
C06 ee~ °m~l°q~D
/
60 40
el
Ooo~
20
r 0.0
0
I
i
I
0.5
1.0
1.5
2.0
STRAIN (%)
0
I
I
I
I
2
3
STRAIN (%)
FIG. 3. Comparisons of Two Axial Swain Measurements
TABLE 2 Summary of Test Results Specimen Number UOO
go psi
0.77
8,598 COO C03
U04
1.20
C04
1.24
C05
1.54
C07
1.53
C08
il.45 1.40
14T921
15,459
C09
1.55
14T666 15,002
u09
1.43
13~885 14,814
U08
1.40
13r137
C06
UIO U11
1.17
13r468
U07
1.24
12,190 12,876
U06
1.23
11,463 12,109
U05
0.78
8r988 11r019
U03
%
1.76
15T917 16T603 16,966
1.95 2.00 1.81
psi 0 0 614 614 829 829 1TO50 1,050 IT276 lt276 1T507 1T507 lr744 1~744 1T986 1~986 2r233 2,485
aoo
EO. EOO
1.56
1.28
0.072 1.58
1.28
1.61
1.41
1.52 1.461
1.79
1.54
1.86
1.63
1.99
1.66
0.168 0.203
1.79 2.29
1.80
0.142 0.175
1.88
1.74
0.117 0.149
1.99
1.72
0.092 0.122
2.00
1.57
0.068 0.097
1.59
1.36 1.50
0.OO0
1.00
1.00
1.77 1.93 1.97
0.000
1.00
1.00
O'CO ~OO
0.194 0.231
2.50 2.60 2.35
0.221 0.260 0.289
0 •
626
S. Wei et al.
Vol. 22, No. 4
20000
• ~ : " :
O9
15000
'".
10000
'
""
"
:
•
•
'
,
*
.
.
,
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0810
05
5000
0
I
i
I
I
1
2
3
4
STRAIN
I
0
(%)
1
1
I
I
2
3
4
STRAIN(%)
FIG. 4. Axial Stress-Strain Curves for Uncapped (Dotted) and Capped (Solid) Specimens
indicating the thickness of the confining ring in hundredth of inches. The unconfined specimens are denoted as COO and U00. The stresses and strains are denoted by o and e, respectively. The confining stress is denoted by ~ with a subscript "c". The peak stress and the corresponding strain (referred to as peak strain later) and confining stress are all signified by a single "o" in the subscripts. The double subscript "oo" denotes peak stress or strain for the unconfined specimens. The stress-strain curves for the uncapped and the capped specimens are plotted in Figure 4 in pairs except for the cases of U10 and U l l , where no capped specimens were tested. The unconfined cases of UOO and COO are plotted in both parts of Figure 4 to provide easy comparison for the confined test results. The effect of capping on the testing result can be observed form these plots. While the capped specimens tests should produce higher strengths, the difference in the two unconfined tests is 5% while the differences in all the other cases are less than 3%. Thus the uncapped test data are still considered useful. From these curves it may be concluded that there are two significant effects of confinement: 1) the compressive strength is enhanced by the confinement, and 2) the post-peak descending branch of the curves become flatter as confinement increases. The effect of confinement on the shape of the longitudinal stress-strain curve can be seen clearer by plotting the normalized stress-strain curves as shown in Figure 5. The curves may be separated into two groups according to their post peak behavior: one with ring thickness below 0.05 inches and the other with ring thickness above 0.06 inches. Within each group the post peak slope may have variations not consistent with the amount of lateral confinement due to experimental uncertainties, but there is no doubt that the latter group has a flatter slope than the former. The actual degree of confinement can be deduced from the circumferential strain readings by fu'st calculating the stress in the ring, oo, and then converting it to an effective radial confining stress (~c = 1.6act/D, where t and D are the thickness of the ring and the diameter of the polymer concrete cylinder, respectively• This formula of conversion is based on the assumption of a uniform confining stress within the polymer concrete. The same assumption was found to be very accurate in assessing the confining stress of spirally reinforced concrete columns (10). Shown in Figure 6 are four pairs of confining and compressive stress curves. It is observed that the confining stress rises with the compression until the rings yield. In all cases the polymer concrete
Vol.22, No.4
POLYMERCONCRETE,CONFINEMENT,STRENGTH
627
1.2
1.0 •........4.,.,.,~!r??a.,a...." •'
•
X\
U06-U11
~ ~(/
U00-U05
0.8 I,,I.1
""'~:::~d:,-.
"'",
C00-C05
C06-C09
m~ r~
~
0.6
<
0Z 0.4
0.2
o.o 1
2
0
1
2
NORMALIZEDSTRAIN
NORMALIZEDSTRAIN FIG. 5. Normalized Axial Stress-Swain Ctu-ves
reaches its peak strength after the ring yields. The maximum confining stress for each case is listed in Table 2. After the test, some of the specimens were cut open longitudinally to expose the internal surfaces. In all cases, no macrocracks were found in the confined zone by visual inspection, although the last compressive load was already on the descending branch of the load-deformation curve. A few specimens were loaded beyond the first breaking of ring to the successive breaking of rings and eventually to a fracture failure of the whole specimen. The mode of failure was either of a crushing type happened in the middle of the cylinder where three to four rings had broken, or 20000
15000
~'~10000
U03
,.U._.~..
/~
1
3
C03 ......._
5000 . . . . . . . . . . . . . . . . . . .
........... ....... ~ 0
0
1
~ 2
3
.....
. ..........................
.
,
.............. Lw .
4
0
1
2
.c...°...9....
-
I I
3
STRAIN(%) FIG. 6. STRAIN(%) Confining Stress (Dotted) and Axial Stress (Solid) vs. Axial Strain
4
5
628
S. Wei et al.
Vol. 22, No. 4
of a shear type with a clear surface shearing through the polymer concrete and the rings at an angle of approximately 30 to 40 degrees from the longitudinal axis. The former mode of failure is similar to the one observed in well confined regular strength cement concrete columns (11). The latter failure is similar to that found in tests of high strength cement concrete columns confined by spirals (8) or tubes (12). Stress-Strain Characterization From the test curves shown in Figure 4, the peak stress and peak strain as defined earlier for each test can be identified and listed in Table 2. Also listed are the confining stress at peak. This is also the maximum confining stress for all cases. Although the confining stress gradually increases to the maximum value during the tests, the maximum values are representative of the degree of confinement. Thus, it is not surprising that the increase of the peak stress is related to the maximum confining stress. To find this correlation quantitatively, the peak stresses are first normalized with respect to the peak stress of the unconfined specimens as shown in Table 2. The confining stress is also normalized with respect to the same peak stress. When the normalized peak stresses are plotted against the normalized confining stress, Figure 7, it becomes obvious that a simple linear relationship may be assumed
2.2
=
3.0
2.0
o
2.6'
o
J
1.8 2.2-
,J
o9a-
1.6 13 1.42
o2-"
~'~ 1.8-
e
o
°J ''j
..o" s
oO
P" 1.2,
1.4
J d s ,r
1.0
.
.
.
.
.
!
"
'
"
"
'
0.1
O.
I
0.2
"
"
"
"
1.0
'
O.
FIG. 7.
I
.0
0.1
012
0.3
OCt)/(YOO
Correlation between Maximum Confining Stress and Peak Stress or Strain
Oo
Oc -
0oo
I + a--
(I)
0oo
The parameter ct was estimated to be 3.5 by the least square method. A similar relationship may be established for the normalized peak strain, Table 2, e.o _
e-oo
1 +[3 Oc
(2)
~roo
The parameter 13was estimated to be 5.5. As can be seen from Figure 7, the scatter of data from the linear relationship is larger in the case of peak strain. This may be attributed in part to the greater uncertainties in identifying the peak swain, as the peak stress region is characterized by a small change in stress corresponding to a large change in strain.
Vol. 22. No. 4
POLYMER CONCRETE, CONFINEMENT, STRENGTH
629
To further characterize the stress-strain relationship of polymer concrete under confinement, it is desirable to have an expression for the complete compression curve. Equations (1) and (2) may be used to estimate the peak stress and the peak strain for a given polymer concrete with a given confining stress. The peak stress and the peak strain defines a point on the compression curve. The form of the compression curve for confined polymer concrete may be borrowed from a recently developed model for unconfined polymer concrete (3) E G Go
(3)
(1-p-q)+q(e-)+p(&)s eo
eo
where s= (1-q)/p and p and q are two parameters controlling the shape of the curve. These two parameters are determined by least-square fitting Eq. (3) to the normalized stress-strain curves of the eighteen tests grouped according to the confining stress. Then the dependence of the two parameters on the confining stress is estimated by the following empirical formulas p = 4.5 ac
.0.2
(4)
Goo
q=-4.0
¢~c +0.8
(5)
Goo
where p is limited to be greater than 0.2 and q smaller than 0.4• Using Equations (1) through (5), some of the test curves are reproduced and compared with the measured curves as shown in Figure 8. In view of the simplicity of the suggested formulas, the agreement is very good.
20000
15000
;"
10000
08
5000
0
i
I
i
I
I
I
I
I
1
2
3
4
1
2
3
4
STRAIN(%)
STRAIN (%)
5
FIG, 8. Comparison of Calculated (Solid) and Measured Stress-Strain Curves (Dotted) Conclusions Through the experimental study of the mechanical behavior of polyester-based polymer concrete under axial compression and lateral confinement, it may be concluded that the effects of
630
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conf'mement are to enhance the compressive strength and improve the post-peak behavior. The amount of enhanced compressive strength is linearly proportional to the amount of confining stress. The compressive stress-strain relationship may be expressed by a simple two-parameter equation. A set of formulas with empirically determined constants is shown to reproduce the experimental sTress-strain curves accurately. References 1. 2. 3. 4.
D. Fowler, ACI, SP 116. 129 (1989). ACI Committee 548, Report, ACI, (1986). C. Vipulanandan and E. Paul, Materials, ACI, 87,241 (1990). C. Vipulanandan, N. Dharmarajan and E. Ching, Materials and Structures, RILEM, Paris, 21,268 (1988). 5. R.B. Knowles and R Park, J. Structural Div., ASCE, 95, 2565 (1969). 6. Z. Liu and S. Goel, J. Structural Engrg., ASCE, 1|4, 1488 (1988). 7. V.V. Bertero and S. E. Moustafa, J. Structural Div., ASCE, 9_.fi,2267 (1970). 8. R.L. Carrasquillo, A. H. Nilson and F. O. Slate, ACI, 78. 171 (1981). 9. S. Mebarkia and C. Vipulanandan, J. Materials in Civil Engineering, ASCE, to appear (1992). 10. B. Chen and S. T. Mau, J. Structural Engrg., ASCE,116. 2842 (1990). I 1. J. VaUenas, V. V. Bertero and E. P. Popov, Report UCB/EERC-77/13 (1977). 12. H. G. L. Prion and J. Boehme, Proceedings, 4th Intl. Colloquium, Structural Stability Research Council, 439 (1989).
MECHANICAL BEHAVIOR OF CONFINED POLYMER CONCRETE
S. Wei, S. T. Mau, and C. Vipulanandan Department of Civil And Environmental Engineering University of Houston Houston TX 77204-4791 U.S.A. (Refereed) (Received July 23, 1991)
ABSTRACT In order to broaden the application of polymer concrete, the mechanical behavior of a polyester-based polymer concrete is investigated. The focus of the study is the compressive stress-strain relationship under lateral confinement. A total of 18 cylindrical specimens of 9-inch length and 3-inch diameter were tested under monotonic axial compression. The lateral confinement was provided in a passive way by aluminum rings uniformly spaced in a central confined zone of the test specimen. The degree of confinement was varied from specimen to specimen by changing the thickness of the rings. Test results indicate that the lateral confinement enhances the compressive strength in proportion to the confining stress and improves the post-peak behavior. An empirical formula is suggested to predict the compressive strength of the polymer concrete under lateral confinement. A simple equation for the compressive stress and strain relationship is also developed. Introduction In recent years, the applications of polymer concrete have been broadened from one for surface repair of existing structures to that as a main construction material for nonstructural as well as structural elements. Latest applications include railway ties and bulky machine bases (1). In such applications, the suitability of polymer concrete as the construction material is often verified by the direct testing of the prototype. The results are only valid for a given geometry, and a given loading condition and cannot be generalized for other applications. Fundamental studies on the mechanical properties of polymer concrete, necessary for general applications, are limited to uniaxial compression and flexural strength only (2-4). Thus, further studies on the strength of polymer concrete under more complex stress conditions are needed. The polymer concrete is also known for its brittle failure under uniaxial compression, where its load-carrying capacity reduces drastically after the peak strength is achieved. This is an undesirable feature from the point of view of the ultimate strength design philosophy for most civil engineering structures. In the construction of structures with cement concrete, such brittle behavior under compression is prevented by providing lateral confinement to the concrete in the form of spiral steels or lateral steel ties. The improvement of post-peak behavior under lateral confinement is most successful for regular strength cement concrete and expansive cement concrete 621
622
s. Wei et al.
Vol. 22, No. 4
(4-7) but less successful for high strength cement concrete (8). It is of practical interest, therefore, to explore the behavior of polymer concrete under confinement. The present study is directed towards providing qualitative and quantitative information on the effect of lateral conf'mement on the compressive strength and post-peak behavior of a polymer concrete. A series of cylinder tests on a polyester-based polymer concrete is performed. The results are analyzed and summarized for potential applications. $~¢imen Design and Preparation The polymer concrete used in this research was polyester-based. The composition of the polymer concrete was chosen among several studied in a previous research and was the one with the highest compressive strength (9). The following table summarizes the composition. TABLE 1 Composition of a Polyester-Based Polymer Concrete Constituents Relative Weight Matrix-Polyester Resin 14% Initiator-MEKPO 1.5%* Promoter-Cobalt Napthenate 0.3%* Aggregate-Blasting Sand 86% Note: MEKPO=Methyl Ethyl Ketone Peroxide; *by weight of resin The blasting sand consisted of five grades of equal weight ranging from D10 (10% by weight are smaller) = 0.12 m m to 0.75 mm and D60 =0.17 m m to 1.50 mm. The compressive strength of the polymer concrete was expected to be close to 9,000 psi (62 MPa). The specimens were solid cylinders with a length-to-diameter ratio of 3:1. This ratio was selected, as opposed to the standard concrete cylinder ratio of 2:1, to secure a zone in the middle of the length of the specimen that was relatively uniformly stressed and confined. The nominal length and diameter of the test specimens were 9 inches (229 mm) and 3 inches (76 mm), respectively. The polymer concrete cylinders were cast in aluminum tubes with wall thickness of 0.225 inches (5.7 mm) and a nominal strength of 40 ksi (275 MPa). The aluminum tubes were machined to ensure a uniform circular cross-section. The tubes were also used later as confining rings. Before casting the polymer concrete, grease was applied to the inside wall of the tube to reduce bonding. The polymer concrete was mixed and cast by compacting with a steel rod in three to five lifts. The polymer concrete was cured at room temperature (about 20°C) for 24 hours followed by 24 hours in oven at 80° C. This curing condition was established as an optimal one (3). The cured polymer concrete was pushed out of the aluminum mold. The average diameter of the polymer concrete cylinder was 3.077 inches (78 mm) and the average unit weight was 126 lb/ft3(19.8 kN/m3).
STRAIN GAGE (~) ( ~ EXTENSOMETERS V 0.125 1.350
),200~_____
0.050
)
6.000
1,350 0.125
FIG. 1. Specimen Dimensions in inches (25.4 mm)
Vol. 22, No. 4
POLYMERCONCRETE,CONFINEMENT.STRENGTH
623
The polymer concrete cylinders were confined by aluminum rings, as shown in Figure 1. The rings, instead of a single tube, were used for confinement so that better estimate of the confining stress can be made because the rings were assumed to be stressed only circumferentially. This eliminates the bi-axial stress complication in a confining tube. After considering other alternatives, it was decided that the spacing and the height of the rings be kept constant for all specimens, only the wall thickness of the ring be varied to provide varied degree of confinement. Twenty-four rings, each with a height of 0.2 inches (5.08 mm), were placed in the middle 6-inch (152 mm) portion of the polymer concrete cylinder with a uniform spacing of 0.05 inches (1.27 ram). At the two ends, rings of 1.35 inches (34.29 turn) high were placed to provide higher confinement to prevent premature failure in the end zones. The thickness of the rings was varied from 0.03 inches (0.76 ram) to 0.11 inches (2.79 ram) in 0.01 inch (0.25 mm) increment. For each specimen the thickness of the ring was the same. The rings were machined from the same aluminum tube used as mold in preparing the polymer concrete cylinder. The aluminum tube was machined to the desired thickness and then cut transversely into rings. The rings were then bonded to the polymer concrete cylinders with epoxy. Before testing, ends of the polymer concrete specimens were treated in one of two ways. In the first series ends of 10 specimens were ground to parallel plane surfaces to ensure better contact to the test platens. In the second series 8 specimens were capped with sulfur compound according to ASTM C617. Confinin~ Rine Characterization In addition to tesdng of the confined polymer concrete, the stress-strain relationship of the confining aluminum were quantified experimentally. The aluminum rings were subjected to internal pressure as a result of the interaction between the ring and the confined polymer concrete. The best quantification would be a relation between the internal pressure and the circumferential strain. A direct test on the ring under internal pressure was not done, however, because of the lack of proper equipments. Instead, a direct tension test was performed on longitudinal strips cut from the aluminum tube. In doing so, it was assumed that the longitudinal behavior was close to the circumferential behavior. In making the rings of different thicknesses, the aluminum tubes were machined from outside to the desired thickness and cut transversely into rings. Thus, rings of different thicknesses came from different parts in the radial direction of the tube and may have different strengths. To account for the possible variation of tensile strength due to this effect and other effects of machining, tension coupon tests were performed on aluminum strips of 0.03, 0.07 and 0.11 inches 50000
(a)
(b)
40000 I |
~30000 II Ii
20000 [] II
10000
I
0
1 STRAIN(%) 2
0 STRAIN (%) 2 FIG. 2. (a)Stress-Strain Curves for 0.07-in. Coupons, (b) Averaged Stress-Strain Curves for 0.03, 0.07, and 0.11-in. Coupons
3
624
S. Wei et al.
Vol. 22, No. 4
thickness, machined the same way as the rings. These strips were 9 inches long with a 4 inches long and 0.4 inches wide central part of uniform cross-section. The longitudinal strain was measured using a 2-inch gage length clip-on extensometer. For each thickness, three strips were tested and the results averaged. It was observed that the tensile behavior can be represented approximately by an elasto-perfect plastic relationship within a strain of 0.03, and the thinner the specimen the lower the yield strength. Figure 2 shows the longitudinal stress-swain curves for the 0.07-inch thick specimen and the average curves for the cases tested. Through a simple interpolation, it is found that the yield strength in psi may be represented for different thicknesses between 0.03 and 0.11 inches by Oy = 37,800 + 51,100 t, where t is the thickness in inch. The strength variation within this range of interest is about 10%. Also the Young's modulus was calculated to be 10xl0~ psi (68,900 MPa) with a 9% coefficient of variation. These elasto-plastic relations were used later to calculate the confining stresses in the rings. Instrumentation and Testing Procedure Two 2-inch (50.8 mm) gage extensometers were attached 180-degree apart to the rings in the middle portion of the specimens to measure the longitudinal strains in the confined region, Figure 1. Two 30-ram strain gages,180-degree apart, were pasted on a central ring to measure the circumferential strains. For unconfined polymer concrete specimens the extensometers and the strain gages were attached to the polymer concrete specimen. An LVDT was used to measure the distance between the loading platens to provide feedback for the control of the loading. The specimens were loaded in a 400 kips (1,779 kN) capacity Tinius Olson Universal Testing Machine. The loading was displacement-controlled at a strain rate of 0.0005/min. The readings were taken at discrete intervals and fed into an HP3497 data acquisition unit and processed in an HP85 computer. All the specimens were preloaded once or twice to approximately 20 to 30% of the unconfined strength of polymer concrete. The uncapped specimens were loaded with a fixed platen while the capped specimens were loaded with a swivel head to allow self-adjustment of the platen. In both cases, minor adjustment for the centering of the specimens was performed during the preloading process to minimize the difference between the longitudinal strains obtained from the two extensometers. Generally readings were taken at approximate equal force intervals of either 5 kips or 10 kips during loading and equal strain intervals of 0.05-0.15% near the peak load region and during unloading. The test was stopped when one of the rings broke. Obseryations from the Tests Despite the efforts to minimize bending effects, the two extensometers seldom gave nearly identical longitudinal strain readings even for the capped specimens. The strain gage readings of the circumferential strain at a middle ring were also different to some degree. Shown in Figure 3 are four samples of the two pairs of extensometer readings from capped (COO and C06) and uncapped 0tOO and U06) specimens with or without confinement. It is seen that the capping does seem to reduce the difference in the longitudinal readings. This may be explained by the better distribution of stress at the contact surfaces between the specimen and the loading platens for the capped specimens. Other factors, such as the inherent inhomogeneity, localized internal damages at higher level of loading and imperfect contact between the tings and the polymer concrete, may all contribute to the deviation from a perfect concentric loading condition. In subsequent presentations, the average of each pair of reading is used to represent the longitudinal or the circumferential strain. These averaged readings are also assumed to represent the strains in the polymer concrete even though they were obtained from gages attached to the rings. The pertinent data for the 18 cases are summarized in Table 2. The specimen number starts with a letter C for capped specimens or a letter U for uncapped specimens, followed by two digits
Vol. 22, No. 4
POLYMERCONCRETE,CONFINEMENT,STRENGTH
80
625
120
U00
U06 100
6O
~
00
Q
qlO0
00 Oe Oe 00 Oe 00 00 Cl
~40 © ~J 20
0
O0 O0 O0
80
•
oO#
O0 Oe
60
go°
40 20
J
0
COO
o oQeto,k~,o$. 60
O0 O0 OD 13D aid Q Q
~4o <
20
0
00
I00
•
80
0
C06 ee~ °m~l°q~D
/
60 40
el
Ooo~
20
r 0.0
0
I
i
I
0.5
1.0
1.5
2.0
STRAIN (%)
0
I
I
I
I
2
3
STRAIN (%)
FIG. 3. Comparisons of Two Axial Swain Measurements
TABLE 2 Summary of Test Results Specimen Number UOO
go psi
0.77
8,598 COO C03
U04
1.20
C04
1.24
C05
1.54
C07
1.53
C08
il.45 1.40
14T921
15,459
C09
1.55
14T666 15,002
u09
1.43
13~885 14,814
U08
1.40
13r137
C06
UIO U11
1.17
13r468
U07
1.24
12,190 12,876
U06
1.23
11,463 12,109
U05
0.78
8r988 11r019
U03
%
1.76
15T917 16T603 16,966
1.95 2.00 1.81
psi 0 0 614 614 829 829 1TO50 1,050 IT276 lt276 1T507 1T507 lr744 1~744 1T986 1~986 2r233 2,485
aoo
EO. EOO
1.56
1.28
0.072 1.58
1.28
1.61
1.41
1.52 1.461
1.79
1.54
1.86
1.63
1.99
1.66
0.168 0.203
1.79 2.29
1.80
0.142 0.175
1.88
1.74
0.117 0.149
1.99
1.72
0.092 0.122
2.00
1.57
0.068 0.097
1.59
1.36 1.50
0.OO0
1.00
1.00
1.77 1.93 1.97
0.000
1.00
1.00
O'CO ~OO
0.194 0.231
2.50 2.60 2.35
0.221 0.260 0.289
0 •
626
S. Wei et al.
Vol. 22, No. 4
20000
• ~ : " :
O9
15000
'".
10000
'
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"
:
•
•
'
,
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.
.
,
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0810
05
5000
0
I
i
I
I
1
2
3
4
STRAIN
I
0
(%)
1
1
I
I
2
3
4
STRAIN(%)
FIG. 4. Axial Stress-Strain Curves for Uncapped (Dotted) and Capped (Solid) Specimens
indicating the thickness of the confining ring in hundredth of inches. The unconfined specimens are denoted as COO and U00. The stresses and strains are denoted by o and e, respectively. The confining stress is denoted by ~ with a subscript "c". The peak stress and the corresponding strain (referred to as peak strain later) and confining stress are all signified by a single "o" in the subscripts. The double subscript "oo" denotes peak stress or strain for the unconfined specimens. The stress-strain curves for the uncapped and the capped specimens are plotted in Figure 4 in pairs except for the cases of U10 and U l l , where no capped specimens were tested. The unconfined cases of UOO and COO are plotted in both parts of Figure 4 to provide easy comparison for the confined test results. The effect of capping on the testing result can be observed form these plots. While the capped specimens tests should produce higher strengths, the difference in the two unconfined tests is 5% while the differences in all the other cases are less than 3%. Thus the uncapped test data are still considered useful. From these curves it may be concluded that there are two significant effects of confinement: 1) the compressive strength is enhanced by the confinement, and 2) the post-peak descending branch of the curves become flatter as confinement increases. The effect of confinement on the shape of the longitudinal stress-strain curve can be seen clearer by plotting the normalized stress-strain curves as shown in Figure 5. The curves may be separated into two groups according to their post peak behavior: one with ring thickness below 0.05 inches and the other with ring thickness above 0.06 inches. Within each group the post peak slope may have variations not consistent with the amount of lateral confinement due to experimental uncertainties, but there is no doubt that the latter group has a flatter slope than the former. The actual degree of confinement can be deduced from the circumferential strain readings by fu'st calculating the stress in the ring, oo, and then converting it to an effective radial confining stress (~c = 1.6act/D, where t and D are the thickness of the ring and the diameter of the polymer concrete cylinder, respectively• This formula of conversion is based on the assumption of a uniform confining stress within the polymer concrete. The same assumption was found to be very accurate in assessing the confining stress of spirally reinforced concrete columns (10). Shown in Figure 6 are four pairs of confining and compressive stress curves. It is observed that the confining stress rises with the compression until the rings yield. In all cases the polymer concrete
Vol.22, No.4
POLYMERCONCRETE,CONFINEMENT,STRENGTH
627
1.2
1.0 •........4.,.,.,~!r??a.,a...." •'
•
X\
U06-U11
~ ~(/
U00-U05
0.8 I,,I.1
""'~:::~d:,-.
"'",
C00-C05
C06-C09
m~ r~
~
0.6
<
0Z 0.4
0.2
o.o 1
2
0
1
2
NORMALIZEDSTRAIN
NORMALIZEDSTRAIN FIG. 5. Normalized Axial Stress-Swain Ctu-ves
reaches its peak strength after the ring yields. The maximum confining stress for each case is listed in Table 2. After the test, some of the specimens were cut open longitudinally to expose the internal surfaces. In all cases, no macrocracks were found in the confined zone by visual inspection, although the last compressive load was already on the descending branch of the load-deformation curve. A few specimens were loaded beyond the first breaking of ring to the successive breaking of rings and eventually to a fracture failure of the whole specimen. The mode of failure was either of a crushing type happened in the middle of the cylinder where three to four rings had broken, or 20000
15000
~'~10000
U03
,.U._.~..
/~
1
3
C03 ......._
5000 . . . . . . . . . . . . . . . . . . .
........... ....... ~ 0
0
1
~ 2
3
.....
. ..........................
.
,
.............. Lw .
4
0
1
2
.c...°...9....
-
I I
3
STRAIN(%) FIG. 6. STRAIN(%) Confining Stress (Dotted) and Axial Stress (Solid) vs. Axial Strain
4
5
628
S. Wei et al.
Vol. 22, No. 4
of a shear type with a clear surface shearing through the polymer concrete and the rings at an angle of approximately 30 to 40 degrees from the longitudinal axis. The former mode of failure is similar to the one observed in well confined regular strength cement concrete columns (11). The latter failure is similar to that found in tests of high strength cement concrete columns confined by spirals (8) or tubes (12). Stress-Strain Characterization From the test curves shown in Figure 4, the peak stress and peak strain as defined earlier for each test can be identified and listed in Table 2. Also listed are the confining stress at peak. This is also the maximum confining stress for all cases. Although the confining stress gradually increases to the maximum value during the tests, the maximum values are representative of the degree of confinement. Thus, it is not surprising that the increase of the peak stress is related to the maximum confining stress. To find this correlation quantitatively, the peak stresses are first normalized with respect to the peak stress of the unconfined specimens as shown in Table 2. The confining stress is also normalized with respect to the same peak stress. When the normalized peak stresses are plotted against the normalized confining stress, Figure 7, it becomes obvious that a simple linear relationship may be assumed
2.2
=
3.0
2.0
o
2.6'
o
J
1.8 2.2-
,J
o9a-
1.6 13 1.42
o2-"
~'~ 1.8-
e
o
°J ''j
..o" s
oO
P" 1.2,
1.4
J d s ,r
1.0
.
.
.
.
.
!
"
'
"
"
'
0.1
O.
I
0.2
"
"
"
"
1.0
'
O.
FIG. 7.
I
.0
0.1
012
0.3
OCt)/(YOO
Correlation between Maximum Confining Stress and Peak Stress or Strain
Oo
Oc -
0oo
I + a--
(I)
0oo
The parameter ct was estimated to be 3.5 by the least square method. A similar relationship may be established for the normalized peak strain, Table 2, e.o _
e-oo
1 +[3 Oc
(2)
~roo
The parameter 13was estimated to be 5.5. As can be seen from Figure 7, the scatter of data from the linear relationship is larger in the case of peak strain. This may be attributed in part to the greater uncertainties in identifying the peak swain, as the peak stress region is characterized by a small change in stress corresponding to a large change in strain.
Vol. 22. No. 4
POLYMER CONCRETE, CONFINEMENT, STRENGTH
629
To further characterize the stress-strain relationship of polymer concrete under confinement, it is desirable to have an expression for the complete compression curve. Equations (1) and (2) may be used to estimate the peak stress and the peak strain for a given polymer concrete with a given confining stress. The peak stress and the peak strain defines a point on the compression curve. The form of the compression curve for confined polymer concrete may be borrowed from a recently developed model for unconfined polymer concrete (3) E G Go
(3)
(1-p-q)+q(e-)+p(&)s eo
eo
where s= (1-q)/p and p and q are two parameters controlling the shape of the curve. These two parameters are determined by least-square fitting Eq. (3) to the normalized stress-strain curves of the eighteen tests grouped according to the confining stress. Then the dependence of the two parameters on the confining stress is estimated by the following empirical formulas p = 4.5 ac
.0.2
(4)
Goo
q=-4.0
¢~c +0.8
(5)
Goo
where p is limited to be greater than 0.2 and q smaller than 0.4• Using Equations (1) through (5), some of the test curves are reproduced and compared with the measured curves as shown in Figure 8. In view of the simplicity of the suggested formulas, the agreement is very good.
20000
15000
;"
10000
08
5000
0
i
I
i
I
I
I
I
I
1
2
3
4
1
2
3
4
STRAIN(%)
STRAIN (%)
5
FIG, 8. Comparison of Calculated (Solid) and Measured Stress-Strain Curves (Dotted) Conclusions Through the experimental study of the mechanical behavior of polyester-based polymer concrete under axial compression and lateral confinement, it may be concluded that the effects of
630
S. Wei et al.
Vol. 22, No. 4
conf'mement are to enhance the compressive strength and improve the post-peak behavior. The amount of enhanced compressive strength is linearly proportional to the amount of confining stress. The compressive stress-strain relationship may be expressed by a simple two-parameter equation. A set of formulas with empirically determined constants is shown to reproduce the experimental sTress-strain curves accurately. References 1. 2. 3. 4.
D. Fowler, ACI, SP 116. 129 (1989). ACI Committee 548, Report, ACI, (1986). C. Vipulanandan and E. Paul, Materials, ACI, 87,241 (1990). C. Vipulanandan, N. Dharmarajan and E. Ching, Materials and Structures, RILEM, Paris, 21,268 (1988). 5. R.B. Knowles and R Park, J. Structural Div., ASCE, 95, 2565 (1969). 6. Z. Liu and S. Goel, J. Structural Engrg., ASCE, 1|4, 1488 (1988). 7. V.V. Bertero and S. E. Moustafa, J. Structural Div., ASCE, 9_.fi,2267 (1970). 8. R.L. Carrasquillo, A. H. Nilson and F. O. Slate, ACI, 78. 171 (1981). 9. S. Mebarkia and C. Vipulanandan, J. Materials in Civil Engineering, ASCE, to appear (1992). 10. B. Chen and S. T. Mau, J. Structural Engrg., ASCE,116. 2842 (1990). I 1. J. VaUenas, V. V. Bertero and E. P. Popov, Report UCB/EERC-77/13 (1977). 12. H. G. L. Prion and J. Boehme, Proceedings, 4th Intl. Colloquium, Structural Stability Research Council, 439 (1989).