Strength Relationship

The term strength relationship is used for the relationship between pullout strength and compressive strength of concrete that is obtained by regression analysis of test data. In the review of the early pullout test developed in the former Soviet Union, Skramtajew1_{reported that for concrete with cube strengths}

between 1.5 and 10.5 MPa (200 to 1500 psi) there was a constant ratio between pullout load and cube strength. On the other hand, Tremper2_{showed that, over a wide range of concrete strength, the relation-}

ship between pullout load and compressive strength was nonlinear and may be affected by the type of aggregate (Figure 3.4). Recall that these early tests did not involve a bearing ring.

To improve the correlation between pullout strength and compressive strength, Kierkegaard-Hansen3

introduced a bearing ring and concluded from his tests that: “There is nothing to indicate that the relationship between the two strength measurements is nonlinear.” Kierkegaard-Hansen found, however, that the relationship was linear but not proportional, i.e., the straight line had a nonzero intercept. In addition, he found that the relationship depended on the maximum size of the coarse aggregate. He suggested the following strength relationships for his lok-strength system:

P = 5.10 + 0.806C (16 mm maximum aggregate size) (3.5)

P = 9.48 + 0.829C (32 mm maximum aggregate size) (3.6) where

P = ultimate pullout load (kN)

C = cylinder compressive strength of concrete (MPa)

Thus, for equal cylinder compressive strength, concrete with a larger coarse aggregate will have a greater ultimate pullout load.

The manufacturer33_{of the widely used LOK-TEST system originally proposed the following strength}

relationship for all concrete with aggregate sizes up to 32 mm (1 1/4 in.):

P = 5 + 0.8C (3.7)

Bickley24_{reported, however, that correlation testing performed at six test sites, using the same LOK-TEST}

system, resulted in straight lines that differed from Equation 3.7. Table 3.3 summarizes the best-fit values of the slopes and intercepts obtained by Bickley. The table shows that there are positive and negative intercepts and that some of the slopes are significantly greater than the recommended value of 0.8 kN/ MPa. It was shown that, in general, Equation 3.7 is a “conservative” relationship, i.e., for a given pullout load Equation 3.7 estimates a lower compressive strength than the straight lines in Table 3.3.

The lack of agreement among the strength relationships obtained with the same test system, and the illogical result of a nonzero intercept, has caused skepticism among potential users of the pullout test method. This section demonstrates that, for a given test system, there is not a unique strength relationship applicable to all concrete. Also, it is shown that the correlation for a particular combination of materials and test system is not necessarily linear. The discussion is limited to relationships between ultimate pullout load and cylinder compressive strength.

First, the shape of the strength relationship is investigated. Figure 3.20A shows correlation data obtained using concrete made with 19-mm (3/4 in.) crushed limestone.27_{The pullout test system had a}

70$ apex angle and a 25-mm (1 in.) embedment depth. Rather than using a linear relationship, consider a power function as follows:

C = _P` _(3.8)

By taking the logarithms of both sides, Equation 3.8 is transformed to

log(C) = log(_) + ` log(P) (3.9)

Thus, by plotting the logarithm of compressive strength vs. the logarithm of pullout load, the power function is transformed into a straight line. The best-fit values of _ and can be obtained by linear regression analysis using the transformed data.*_{The best-fit power function for the data in Figure 3.20A is}

TABLE 3.3 Linear Strength

Relationships by Bickley24_{with LOK-TEST}

System (P = a + bC) Strength Range (MPa) Intercept a (kN) Slope b (kN/MPa) 7.1–38.3 12.7–28.8 9.7–44.4 5.9–32.5 13.7–34.4 8.8–25.2 <0.9 <2.0 2.4 1.7 <2.0 2.7 0.88 1.05 0.85 0.81 1.06 0.89

FIGURE 3.20 Strength relationships for concrete made with crushed limestone:27_{(A) power function relationship}

and (B) straight line relationships for different strength ranges.

*_{Linear regression analysis of the transformed data is preferred when the coefficient of variation of the dependent}

variable (concrete strength in this case) is constant.27

0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN) C = 1.6 P0.88 A 0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN)

C =5.2 + 0.83 P C = 3.8 + 0.87 P

C = 1.6P0.86 _(3.10)

The power function fits the data quite well and the shape is nearly a straight line over the range covered by the data.

Now, examine what happens if a linear relationship is assumed having the equation:

C = a + bP (3.11)

If all points are considered, the best-fit straight line is

C = 3.8 + 0.87P (3.12)

If we consider only the six points for compressive strengths above 20 MPa (2900 psi), the best-fit straight line is

C = 5.2 + 0.83P (3.13)

It is seen that the two straight lines in Figure 3.20C are practically the same for compressive strength above 20 MPa. The point of this exercise is to illustrate that, if the true strength relationship is nonlinear and it is approximated with a straight line, the slope and intercept of the straight line depend on the strength range covered by the correlation data.

Next, consider correlation data for the same test system but for concrete made with 19-mm (3/4 in.) river gravel.27_{The data are shown in Figure 3.21A and the best-fit power function is}

C = 1.07P1.02 _(3.14)

The power function looks very much like a straight line. In this case, the exponent is greater than 1, and the curvature of the strength relationship is opposite to that shown in Figure 3.20A. Figure 3.21B shows the best-fit straight lines for all the data and for only the six data points above 20 MPa (2900 psi). Again, the equations of the straight lines are different but the strength relationships are similar for the data above 20 MPa. Also, note that because of the different curvature, the values of the intercepts are negative. Thus, if the true strength relationship is slightly nonlinear and if the curvature can depend on the type of aggregate, one can explain why Bickley24 _{reported different linear relationships for the same}

pullout test system.

The manufacturer33_{of the LOK-TEST system later proposed the following relationship, which differs}

from Equation 3.7, for concrete with compressive strengths between 3 and 25 MPa (400 and 3600 psi):

P = 1.0 + 0.96C (3.15)

Because the strength relationship is used to estimate compressive strength based on the measured pullout load, it is preferable to treat compressive strength as the dependent variable. Thus, the relationships for the LOK-TEST system are as follows:

C = <1.0 + 1.04P (for 3 MPa < C < 25 MPa) (3.16)

C = <6.3 + 1.25 P (for C * 25 MPa) (3.17) These two straight lines are shown in Figure 3.22A. For purposes of illustration, eight evenly spaced points were chosen along this bilinear strength relationship, as shown in Figure 3.22B. A best-fit power function was fitted to the points, and the equation of the function is as follows:

C = 0.6P1.14 _(3.18)

Figure 3.23 shows correlation data reported by Khoo29 _{for pullout tests and tests of corresponding}

cores. The pullout configuration had an apex angle of 70$ and the embedment depth was 25 mm (1 in.). The concrete was made with 20-mm (0.8 in.) maximum size crushed granite, and the compressive strength ranged between 10 and 40 MPa (1500 and 5800 psi). The best-fit straight-line relationship for the data, as determined by this author, is

C = -1.11 + 1.19P (3.19)

while the best-fit power function is

C = 1.12P1.00 _(3.20)

Because the exponent of the power function is equal to 1, the power function is actually a straight line passing through the origin. The intercept in Equation 3.19 is not statistically significant, and, for the range of strength considered, the compressive strength of the cores is proportional to the pullout load.

Finally, let us examine the effects of test geometry and aggregate type on the strength relationship.

Figure 3.24A shows the reported27_{power-function relationships for two pullout test configurations: one}

had an apex angle of 54$ and the other an angle of 70$. The embedment depth and insert head diameter were 25 mm (1 in.), and the concrete was made with 19-mm 3/4-in.) river gravel. The exponents for the two curves are close to 1 so both relationships are very close to linear. As shown in Table 3.1, the repeatability of the two test configurations was found to be similar. As was discussed by Stone and Giza,20

because the slope of the relationship for the 54$ pullout configuration is lower than for the 70$

FIGURE 3.21 Strength relationships for concrete made with river gravel:27_{(A) power function and relationship}

(B) straight line relationships for different strength ranges.

0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN) C = 1.07 P1.02 A 0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN)

C = –2.2 + 1.21 P C = –0.8 + 1.16 P

configuration, the relationship for the 54$ configuration would result in slightly less uncertainty in the estimated compressive strength.

Figure 3.24B compares power-function relationships for different types of aggregates using the 70$ pullout test configuration.27_{The relationships were found to be statistically different. Note that for}

compressive strengths above 20 MPa (3000 psi), the concrete with crushed limestone resulted in much greater pullout loads. Thus, there is evidence that the aggregate type can affect the strength relationship.

FIGURE 3.22 (A) Bilinear strength relationship proposed for LOK-TEST system.33 _{(B) Power function approxima-}

tion of the two lines.

FIGURE 3.23 Correlation data by Khoo29_{and best fit linear and power function relationships.}

0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80

Compressive Strength (MPa)

Pullout Load (kN) C = –6.3 + 1.25 P A C = –1.0 + 1.04 P 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80

Compressive Streength (MPa)

Pullout Load (kN)

C = 0.65 P 1.14

Points from bilinear relationship B 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40

Compressive Strength (MPa)

Pullout Load (kN)

C = 1.12 P 1.00

3.4.3 Summary

This section has reviewed available information on the within-test variability (repeatability) and the strength relationship of the pullout test. Over a wide range of concrete strength, the standard deviation of the ultimate pullout loads, for repeated tests in the same concrete, increases with increasing strength. Hence the coefficient of variation is the appropriate statistic to describe repeatability. A significant amount of repeatability data have been published, and it appears that the average value of the coefficient of variation for the pullout test is about 8%. The size and type of the coarse aggregate, however, affect the coefficient of variation, and the repeatability for a given concrete mixture can be higher or lower than 8%. Considerable correlation data have been published for the commercially available LOK-TEST system, which uses a 62$ apex angle and a 25 mm embedment depth. The majority of the empirically determined relationships have been reported to be straight lines with nonzero intercepts. It has been explained that these linear relationships are approximations to inherently nonlinear relationships. For this reason, the slopes and intercepts depend on the strength ranges used in developing the correlation data. It has been proposed that a power function is a superior equation for analyzing correlation data. The coefficients of the power function are readily determined by linear regression analysis of the logarithms of pullout and compressive strength data. As demonstrated by examples, the power function can accommodate various degrees of nonlinearity.

Some of the early studies indicated that, for a given test system, the strength relationship is influenced by the maximum aggregate size. More recent results show that the type of aggregate also has an effect. Thus, for the most reliable estimates of in-place strength, a strength relationship should be developed for the specific concrete mixture to be used in construction.28_{The next section discusses methods for}

developing correlation data.

FIGURE 3.24 Strength relationships as affected by (A) apex angle and (B) aggregate type.27

0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN) 70$ 54$ A h = 25 mm 19 mm River Gravel 0 10 20 30 40 50 0 10 20 30 40 50

Compressive Strength (MPa)

Pullout Load (kN) Crushed Limestone Lightweight Apex Angle = 70$ B River Gravel

3.5 Applications

The pullout test has been adopted as a standard test method in many parts of the world, including North America, and its successful use on large construction projects has been reported.24,34,35_{This section reviews}

the evolution of the current ASTM (American Society for Testing and Materials) standard governing the pullout test, and discusses some of the practical aspects for implementing the method and interpreting test results.

3.5.1 Standards

The first standard for the pullout test was established in Denmark in 1977,33_{and the method is recognized}

for the acceptance of concrete in structures. In North America, ASTM adopted a tentative test method in 1978, which was subsequently revised and issued as a standard in 1982. The ASTM standard does not limit the test configuration to a specific geometry. The following compares some of the geometrical requirements in the 1978 tentative method with those in the 1982 ASTM standard:

The 1982 standard set the embedment depth equal to the insert head diameter, d, thereby limiting the range of possible apex angles from 53$ to 70$. The 1987 revision of the ASTM standard made no changes to the allowable test configurations.36

The ASTM standard allows three procedures for placement of cast-in-place pullout inserts: 1. Attached to the surface of formwork prior to concrete placement

2. Attached to formwork with special hardware to enable testing deep within the concrete (refer to

Figure 3.7A)

3. Placed into the surface of freshly placed concrete

In the third procedure, inserts are placed manually into the top surface of the fresh concrete. Special inserts with a “cup” or a plastic plate are used to provide a smooth surface for proper seating of the bearing ring. Manual placement requires care to assure that the concrete around the insert is properly consolidated and surface air voids are minimized. In general, manually placed inserts result in higher variability24,37_{and are not recommended unless absolutely necessary. In all cases, the clear spacing between}

the inserts and the edges of the member should be at least four times the insert head diameter. Also, each insert should be placed so that reinforcing steel does not interfere with the eventual fracture surface when the insert is pulled out.

The number of required pullout tests in the field was a controversial subject during the development of the ASTM standard. The 1978 tentative method had no requirement. The 1982 standard stated that a “minimum of three pullout tests shall comprise a test result,” and Note 6 stated: “Often it will be desirable to provide more than three individual pullout inserts in a given placement.” In 1987, the section on the number of tests was expanded to the following:

When pullout test results are used to assess the in-place strength in order to allow the start of critical operations, such as formwork removal or application of post tensioning, at least five individual pullout tests shall be performed for a given placement for every 115 m3_{(150 yd}3_{), or fraction thereof, or for}

every 470 m2_{(5000 ft}2_{), or a fraction thereof, of the surface area of one face in the case of slabs or walls.}

A note to this requirement stated: “Inserts shall be located in those portions of the structure that are critical in terms of exposure conditions and structural requirements.” In addition, the following statement was also added to the 1987 standard:

ASTM C 900-78T ASTM C 900-82 Embedment depth 1.0d to 1.2d 1.0d

Bearing ring 2.0d to 2.4d 2.0d to 2.4d Apex angle 45$ to 70$ 53$ to 70$

When planning pullout tests and analyzing test results, consideration should be given to the normally expected decrease of concrete strength with increasing height within a given concrete placement in a structural element.

This so-called top-to-bottom effect is well documented.38<41 _{Standards and codes, however, have not}

addressed the significance of the effect; therefore, there are no guidelines on how to deal with such variability. The important point is that when high variability is obtained from pullout tests performed at different elevations within a structural element, it should not be interpreted to mean that the pullout test is unreliable. Engineering judgment is required in selecting the test locations and in interpreting the results.

The 1978 and 1982 versions of the ASTM test method allowed the option of reporting the pullout strength as a stress, obtained by dividing the ultimate pullout load by the area of the idealized conic frustum. There were criticisms that the calculation was not meaningful because the pullout force is inclined to the surface of the frustum. In 1987, the procedure was changed to allow the calculation of a nominal normal stress as given by the previous Equation 3.2. As was discussed, the normal stress distribution on the idealized conic frustum is nonuniform. Therefore, this calculated normal stress is fictitious and should be used only for comparing results of different pullout test configurations. In the 1999 revision of ASTM C 900, the equations for computing nominal stresses on the surface of the idealized frustum were moved to a nonmandatory appendix. The reason was that stress calculations are rarely used in practice and are not essential to the test method.

The ASTM standard has the following statement regarding the relationships between pullout strength and other strength tests:

Such strength relationships depend on the configuration of the embedded insert, bearing ring dimen- sions, depth of embedment, and the level of strength development in that concrete. Prior to use, these relationships must be established for each system and new combination of concreting materials. Aside from assuring a strength relationship that is applicable to the particular combinations of equip- ment and materials, this requirement also forces testing agencies to become familiar with the details of pullout testing procedures prior to using the test equipment at the project site.

Before 2001, ASTM C900 required that the pullout test be completed within 90 to 150 s. Most standard test methods that measure strength properties of concrete require loading at a specified stress rate. Thus, in 2001, the test method was revised so that the nominal normal stress on the assumed conic frustum (see Equation 3.2) was required to increases at a rate from 40 to 100 kPa/s (5.8 to 14.5 psi/s). To assist users of the most common testing configuration, a table was provided that showed the acceptable range of time to complete the test depending on the expected ultimate pullout load.

3.5.2 Strength Relationship

The development of the strength relationship applicable to the specific construction project is a critical step in implementing the pullout test. Unfortunately, no standard procedures exist to obtain correlation data, although American Concrete Institute (ACI) 228.1R provides recommendations.28

Historically, various techniques have been used to acquire companion pullout strength and compressive strength data. Kierkegaard-Hansen3_{placed pullout inserts in the bottoms of standard cylindrical speci-}

mens. A pullout test was performed on the cylinder, and then the same cylinder was capped and tested for compressive strength. If the pullout test was stopped just beyond the point of maximum load, the pullout cone was not extracted, and it was shown that the cylinder could be tested in compression without significant effect on the compressive strength. Bickley24_{also provided data showing negligible effects of}

this procedure on compressive strength. Such a procedure is possible because, during a standard com- pression test, the ends of the cylinder are subjected to confining stresses8_{that prevent premature failure}

of the cylinder due to the damage incurred during the pullout test. However, it was found that, as concrete strength increased, radial cracking occurred at the end of the cylinder outside of the bearing ring, and this reduced the ultimate pullout load.3,24_{Later studies confirmed that, for concrete with compressive}

strengths above 40 MPa (5800 psi), pullout tests in 150-mm (6-in.) diameter cylinders resulted in lower strengths than pullout tests on larger specimens that did not experience radial cracking. For this reason and because there is a limit to the size of the pullout test configuration than can be used on the bottom of a cylinder, this approach is not recommended.

An alternative to placing inserts in standard cylinders is to place them in slabs and cast companion standard cylinders. At designated ages, replicate pullout tests are performed on the slab and replicate cylinders are tested in compression. A drawback to this approach is the need to assure that the pullout tests and compression tests are performed at the same maturity. Because of their different masses and shapes, the slab and cylinders are not likely to experience the same temperature history during the critical early ages, when strength changes rapidly with age and is strongly dependent on temperature history.42

Failure to account for possible maturity differences can lead to inaccurate strength relationships. Either

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