Danish Test (Lok-Strength)

In 1962, Kierkegaard-Hansen3_{initiated a research program to determine the optimum geometry for the}

pullout test so that it could be performed in the field with simple equipment and so that there would be a high correlation between ultimate pullout load and compressive strength. The results of his work led to the widely used test system known as the LOK-TEST. Kierkegaard-Hansen’s work is reviewed in detail because it is useful to understand the reasoning used to establish the values of the embedment depth, insert head diameter, and bearing ring diameter for this test system.

According to Kierkegaard-Hansen, the embedment depth should be sufficient to assure that more than the outermost “skin” of the concrete is tested and that some coarse aggregates is included within the failure cone. This would favor deep embedment. With increasing embedment, however, the force required to pullout the insert would increase, leading to bulky testing equipment and increasing the damage to the structure. Based on these factors, an embedment depth of 25 mm (1 in.) was chosen arbitrarily.

Kierkegaard-Hansen performed a series of pilot tests to establish the optimum diameters for the insert head and bearing ring. Figure 3.5 shows the test configuration used in these pilot tests. Because a suitable tension loading system did not exist, a laboratory compression testing machine was used to apply the load. The insert was extracted by applying a compressive load to the bottom of the embedded disk, as shown in Figure 3.5. In this configuration, the pullout test can also be considered a punching-type test. The Danish word for punching is lokning. Hence, Kierkegaard-Hansen called the quantity measured by the test the “lok-strength” rather than the pullout strength.

*_{By today’s standards, a coefficient of variation of 8.4% for the strength of laboratory-prepared cylinders would}

In the first series of tests, the head diameter was varied from 20 to 40 mm (0.79 to 1.57 in.). For these tests, a large-diameter bearing ring was used so that the failure cone formed within the ring. He observed that the failure surface was not the idealized conic frustum shown in Figure 3.1. Instead, the extracted fragment was “trumpet-shaped”; i.e., the inclination of the fracture surface, with respect to the load direction, increased with increasing distance from the insert. It was found that the pullout strength increased about 1% for each 1 mm increase in diameter. The insert head diameter was chosen arbitrarily to be 25 mm (1 in.).

The next series of pilot tests examined the relationship between compressive strength and ultimate pullout load. A bearing ring with a diameter of 130 mm (5.1 in.) was used. For this large diameter, failure occurred within the bearing ring, and the test was analogous to the earlier tests of Volf and Tremper. The compressive strength ranged from about 10 to 45 MPa (1500 to 6500 psi). In agreement with Tremper, Kierkegaard-Hansen found that the relationship between ultimate pullout load and compressive strength was nonlinear, and he stated:3

It follows from this that the stress field in the rupture surface cannot be equal to the stress field occurring during crushing of cylinders.

The relationship had a shape similar to that of tensile strength vs. compressive strength. It was concluded that, for a large bearing ring, the pullout strength is likely to be related to the concrete tensile strength. Because of the nonlinear relationship, test sensitivity decreased with increasing strength of concrete; i.e., large changes in compressive strength resulted in small changes in pullout strength (see Figure 3.4). Thus, Kierkegaard-Hansen decided to examine the effects of reducing the bearing ring diameter. Here is where the modern pullout test improved upon the earlier tests of Volf and Tremper.

As the ring diameter decreases, the fracture surface area decreases. It was reasoned that the ultimate pullout load would also decrease unless the presence of the ring alters the state of stress, in which case it could increase. Hence, in the next series of pilot tests, Kierkegaard-Hansen examined the relationship between ring diameter and ultimate pullout load. The ring diameter was varied between 130 and 50 mm (5.1 and 2.0 in.). He found that the ultimate pullout load increased gradually as the diameter decreased from 130 mm (5.1 in.) to about 80 mm (3.1 in.). As the diameter was reduced further, the ultimate pullout load increased rapidly. After these pilot tests were completed, a loading apparatus was developed for applying a tensile load to the insert as depicted in Figure 3.1.

The new loading apparatus was used to examine further the relationship between bearing ring diameter and pullout strength. For the next series of tests, the pullout strength was expressed as a stress by dividing the ultimate pullout load by the area of the idealized conic frustum defined by the embedment depth,

FIGURE 3.4 Compressive strength and pullout force results reported by Tremper.2

0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 Gravel Aggregate Crushed Stone LogC = 0.000248 P + 2.743 C = 1.09 P – 370

Compressive Strength (psi)

insert head diameter, and bearing ring diameter. For reasons not clearly stated, Kierkegaard-Hansen concluded that the optimum bearing ring diameter should be 55 mm (2.2 in.).*

After establishing the dimensions of the pullout test, Kierkegaard-Hansen studied the relationship between ultimate pullout load and compressive strength. The results of these studies are discussed in a subsequent section.

In 1970, Kierkegaard-Hansen obtained a U.S. patent**_{for “A Method for Testing the Strength of Cast}

Structures, Particularly Concrete Structures,” which described a pullout testing device composed of an embedded disk (called a “piston” in the patent), a pull rod, and a bearing ring. Specific dimensions of the test system were not given except that the apex angle of the conic frustum should be “at least about 60$.”

3.2.4 U.S. Test by Richards

In the early 1970s, Richards of the United States obtained a U.S. patent***_{on a pullout test system similar}

to Kierkegaard-Hansen’s. One of the differences was that Richards’ insert (described as a “shank” in the patent) consisted of an enlarged head that was integral with the insert shaft (see Figure 3.1). The patent did not recommend an apex angle for the idealized conic frustum.

Rutenbeck4_{was the first to report the results of work based on Richards’ ideas. In these early studies,}

the insert shaft was made from 19-mm (3/4 in.) threaded steel rod, and the insert head was formed by a steel washer brazed to a nut screwed onto the rod. The insert head diameter (d) was 57 mm (2.25 in.), the depth of embedment (h) was 53 mm (2.08 in.), and the bearing ring diameter (D) was 127 mm (5 in.). The apex angle for this configuration was 67$. A similar insert was used in evaluations by Malhotra.5,6

Richards’ early test configuration produced a conic frustum with a surface area of about 18,320 mm2

(28.4 in.2_{), which is about five times greater than the surface area of Kierkegaard-Hansen’s system. The}

author believes that Richards chose this size so that the conic surface area would be approximately equal to the cross-sectional area of a 152 = 305-mm (6 = 12-in.) cylinder. Because of the large dimensions, the test equipment was bulky and not suited for field applications.

FIGURE 3.5 Testing configuration for pilot tests by Kierkegaard-Hansen. (Adapted from Reference 3.)

*_{For a ring diameter of 55 mm, the correlation between ultimate pullout load and compressive strength was such}

that the pullout load expressed in kilonewtons was about the same number as the compressive strength of the concrete expressed in MPa. Thus, if the ultimate pullout load was 20 kN, the compressive strength would be about 20 MPa. (Note that in Figure 3.4 there is similar numerical relationship between pullout load (in lb) and compressive strength (in psi) at the lower strength range.)

**_{U.S. patent 3,541,845, November 24,1970.} ***_{U.S. patent 3,595,072, July 27, 1971.}

Reaction Force Variable Disk Cylindrical Specimen 25 mm Reaction Force Punching Force 25 mm

In 1977, Richards7_{reported on a smaller, machine-produced insert with a head diameter and embed-}

ment depth of 30 mm (1.18 in.). The bearing ring diameter was 70 mm (2.75 in.), thereby preserving a 67$ apex angle. Richards’ new configuration has a fracture surface that is about 50% greater than that of Kierkegaard-Hansen. These two pullout test configurations are compared in Figure 3.6. The shaft of Richards’ insert is integral with the head. The pullout force is applied through a rod screwed into the shaft. On the other hand, Kierkegaard-Hansen’s insert has a removable shaft, and a high strength pull- rod is screwed into the head for load application.