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Modeling and analysis of the shear capacity of adhesive anchors

post-installed into uncracked concrete

Mehmet Gesog

˘lu

a,

⇑

, Esra Mete Güneyisi

a

, Erhan Güneyisi

a

, Muhammet Enes Yılmaz

a

,

Kasım Mermerdasß

b

a

Gaziantep University, Civil Engineering Department, 27310 Gaziantep, Turkey

b

Hasan Kalyoncu University, Civil Engineering Department, 27410 Gaziantep, Turkey

article info

Article history:

Received 16 January 2013

Received in revised form 18 November 2013

Accepted 9 January 2014

Available online 17 January 2014

Keywords:

A. Metal–matrix composites (MMCs)

B. Adhesion

B. Strength

C. Analytical modeling

abstract

This paper reports the results of an analytical study to predict the edge breakout shear capacity of single

adhesive anchors post-installed into uncracked hardened concrete. For this purpose, an experimental

database for the adhesive anchors compiled by the ACI Committee 355 was obtained and utilized to con-

struct training and test sets so as to derive the closed-form solution by means of gene expression pro-

gramming (GEP). The independent variables used for development of the prediction model were

anchor diameter, type of anchor, edge distance, embedment depth, clear clearance of the anchor, type

of chemical adhesive, method of injection of the chemical, and compressive strength of the concrete.

The generated prediction model yielded correlation coefﬁcients of 0.98 and 0.92 for training and testing

data sets, respectively. Moreover, the performance of the proposed model was compared with the exist-

ing models proposed by American Concrete Institute (ACI) and Prestressed/Precast Concrete Institute

(PCI). The analyses showed that the proposed GEP model provided much more accurate estimation of

the observed values as compared to the other models.

Ó2014 Elsevier Ltd. All rights reserved.

1. Introduction

Anchorages to concrete include cast-in-place and post-installed

anchors. Post-installed anchors are either mechanical or adhesive

(bonded) anchors [1]. As a result of advancement in high strength

bonding agent technology, using adhesive anchors have soared

considerably [2]. An adhesive anchor can be deﬁned as a reinforc-

ing bar or a threaded rod inserted into a drilled hole in hardened

concrete with a structural adhesive acting as a bonding agent be-

tween the concrete and the anchor steel [3]. The hole is ﬁlled with

the adhesive that bonds the steel to the concrete. Currently

available structural adhesives can be classiﬁed as several types of

thermosetting plastics including epoxies, polyesters, vinylesters

as well as a few hybrids of organic and inorganic binders [4]. Adhe-

sive anchors have three possible failure mechanisms: yield and

fracture of failure anchor steel, formation of an adhesive cone,

accompanied by pullout of an adhesive core; and pullout of

adhesive core [5].

In the literature, there have been elaborate studies regarding

the mechanical behavior of post installed anchors [1–9]. Gesog

˘lu

et al. [6] examined the behavior of such anchors in normal and

high-strength concretes with and without steel ﬁber reinforce-

ment. They stated that the maximum capacity of the anchors

increased with increasing the concrete strength. They also revealed

that the use of steel ﬁbers in concrete did not importantly affect

the pullout capacity of the anchors but the failure type altered

from cone to pullout. Fujikake et al. [9] carried out an experimental

study to investigate the behavior of the adhesive anchors subject to

rapid pullout loading. They reported that the dynamic ultimate

pullout resistance increased with the loading rate. In the study of

Cook and Konz [4], the factors affecting the bond strength of the

polymer based adhesive anchors were investigated. The ﬁndings

of this study demonstrated that the reliable prediction of adhesive

anchor performance was only practical by extensive product and

condition speciﬁc testing.

The studies regarding the modeling shear capacity of the anchor

bolts has not yet found adequate attention in the literature. Lee

et al. [10] carried out an experimental study on shear behavior of

headed anchors with large diameters and deep embedments. They

compared the experimental shear capacities with those computed

from existing formulas proposed by ACI 349 and ACI 318 design

codes. They concluded that the existing methods yielded less shear

capacities for the specimens dealt with the study. Bickel and Shaik

[11] compared the prediction of performance of the model speci-

ﬁed in PCI Design Handbook and CCD model from ACI 318-02,

for shear capacity of the headed and adhesive anchors. They re-

ported that PCI Design Handbook method and CCD method, with

proper adjustments, can be used for predicting the shear capacities

of adhesive anchors with similar accuracy.

1359-8368/$ - see front matter Ó2014 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.compositesb.2014.01.015

⇑

Corresponding author. Tel.: +90 342 3172404; fax: +90 342 3601107.

E-mail address: mgesoglu@gantep.edu.tr (M. Gesog

˘lu).

Composites: Part B 60 (2014) 716–724

Contents lists available at ScienceDirect

Composites: Part B

journal homepage: www.elsevier.com/locate/compositesb

In the prediction models, various parameters are used for

estimating the shear capacity of the adhesive anchors. Compres-

sive strength of the concrete and edge distance parallel to the

loading direction are included in all of the shear capacity predic-

tion models. The models proposed by ACI 349 and ACI 318 (CCD

model) also contain anchor diameter and embedment depths.

However, type of anchor bolt (rebar or threaded rod), type of

chemical adhesive, method of injection and clear clearance of the

drilled hole are not taken into account when computing the shear

or pullout capacities of the post installed anchors. For example, the

hole diameter is typically 10 or 25 percent larger than the inserted

anchor bolt or bar diameter [3]. Therefore, the effect of clear clear-

ance can be considered as a factor inﬂuencing the mechanical

behavior of anchor.

This study aims at providing a handful tool for prediction of the

edge breakout shear capacity of post-installed anchors with a rea-

sonable degree of accuracy. For the purpose of explicit formula-

tions for the shear capacity of the single adhesive anchors, the

worldwide database compiled by the ACI Committee 355 was

employed. A total of 98 adhesive single anchor tests were selected

regarding shear load testing in uncracked concrete. Soft computing

technique of genetic programming was applied for constructing

the model proposed in this study. Moreover, the derived model

was compared with the existing formulas given in ACI 318, ACI

349 and Prestressed/Precast Concrete Institute (PCI) as well as

Modiﬁed CCD method proposed by Hoffman [12].

2. Estimating edge breakout shear capacity of a single anchor as

speciﬁed in current design codes

In order to estimate the concrete edge breakout strength of an-

chor bolts under shear loading various relations have been pro-

posed in the literature as given in Eqs. (1)–(8) [11–18]. The ACI

shear resistance formula assumes the concrete failure surface to

be a semicone of height equal to edge distance and a contact incli-

nation angle of 45°with respect to the contact edge [13]. The shear

resistance of anchor bolt is calculated on the basis of the tensile

strength of the concrete acting over the projected area of the sem-

icone surface. According to ACI 349-97 [14], the design shear

strength is given by the formula below (Eq. (1) in U.S. customary

units). Ueda et al. [13] presented the same relation in SI units

(Eq. (2)). The concrete capacity design method is based on K-meth-

od developed by University of Stuttgart (Germany) in the late

1980s [11]. For ACI 349-06 [15], the value of k=7 was valid for

cracked concrete while the tests selected herein were performed

in uncracked concrete. Assuming a ratio of uncracked to cracked

strength of 1.4, a value k=9.8 (k=71.4) was utilized for the

evaluation of predicted capacities [10]. In ACI 349-06, edge break-

out shear capacity of bolt was presented by Eq. (3) [15]. The mod-

els based on Concrete Capacity Design (CCD) [16,17] and Modiﬁed

CCD [12] were given in Eqs (4)–(6). The capacity of a single anchor

in uncracked structural member under shear loading toward the

free edge is also described in Precast/Prestressed Concrete Institute

(PCI) Design Handbook (ﬁfth edition) [18]. Eqs. (7) and (8) of PCI

method are given in US customary and SI units below.

ACI 349-97 (in U.S. customary units) [14]:

V

U

¼2

p

c

2

1

ﬃﬃﬃﬃ

f

0

c

qðlbÞð1Þ

SI equivalent of this formula [13]:

V

U

¼0:522c

2

1

ﬃﬃﬃﬃ

f

0

c

qðNÞð2Þ

ACI 349-06 (in U.S. customary units) [15]:

V

U

¼9:8ðl=d

0

Þ

0:2

ﬃﬃﬃﬃﬃ

d

0

pﬃﬃﬃﬃ

f

0

c

qc

1:5

1

ðlbÞð3Þ

Concrete Capacity Design (CCD method) (in U.S. customary units)

[16,17]:

V

U

¼13ðl=d

0

Þ

0:2

ﬃﬃﬃﬃﬃ

d

0

pﬃﬃﬃﬃ

f

0

c

qc

1:5

1

ðlbÞð4Þ

SI equivalent of this formula [11]:

V

U

¼1:1ðl=d

0

Þ

0:2

ﬃﬃﬃﬃﬃ

d

0

pﬃﬃﬃﬃﬃ

f

0

cc

qc

1:5

1

ðNÞð5Þ

Modiﬁed CCD method (in SI units) [12]:

V

U

¼3d

0:1ðh

ef

=c

1

Þ

0

h

0:1ðd

0

=c

1

Þ

0:2

ef

ﬃﬃﬃﬃﬃ

f

0

cc

qc

1:5

1

ðNÞð6Þ

PCI method (in U.S. customary units) [18]:

V

U

¼12:5c

1:5

1

ﬃﬃﬃﬃ

f

0

c

qðlbÞð7Þ

SI equivalent of this formula [18]:

V

U

¼5:2c

1:5

1

ﬃﬃﬃﬃ

f

0

c

qðNÞð8Þ

where V

U

is the ultimate shear capacity of an adhesive anchor in un-

cracked concrete (lb for the equation in U.S. customary units N for

the equation in S.I. unit); f

0

c

is concrete compressive strength (psi

for the equations in U.S. customary units MPa for the equations in

S.I. unit) to be veriﬁed using cylinders; f

0

cc

is concrete compressive

strength (MPa) to be veriﬁed using 200 mm cubes; h

ef

is embed-

ment depth (mm); d

o

is diameter of anchor (in. for the equations

in U.S. customary units mm for the equations in S.I. unit); lis load

bearing length of anchor (in. for the equations in U.S. customary

units mm for the equations in S.I. unit); and c

1

is anchor edge

distance (in. for the equations in U.S. customary units mm for the

equations in S.I. unit).

3. An overview of genetic programming (GP) and gene

expression programming (GEP)

A genetic algorithm (GA) is a search technique that has been

used in computing for ﬁnding precise or approximate solutions

to optimize or search problems. Genetic algorithms can be catego-

rized as global search heuristics. They are a particular class of evo-

lutionary computation. The techniques used by GA are inspired by

evolutionary biology such as; inheritance, mutation, selection,

crossover (recombination).

Genetic programming (GP), proposed by Koza [19] is essentially

an application of genetic algorithms to computer programs. GP has

been applied successfully to solve discrete, non-differentiable,

combinatory, and general nonlinear engineering optimization

problems [20]. It is an evolutionary algorithm based methodology

inspired by biological evolution to ﬁnd computer that performs a

task deﬁned by a user. Therefore, it is a machine learning technique

used to construct a population of computer programs according to

Fig. 1. Schematic presentation of typical post installed single adhesive anchor

under shear loading.

M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724 717

a ﬁtness landscape determined by a program’s ability to perform a

given computational task. Similar to GA, the GP needs only the

problem to be deﬁned. Then, the program searches for a solution in

a problem-independent manner [19,21].

Table 1

Training data base used for development of the prediction model.

Sample

no

Independent variables (X

i

) Dependent

variable (Y)

X

1

: Diameter

(mm)

X

2

: Type of

injection

*

X

3

: Chemical

type

**

X

4

: Anchor

type

***

X

5

: Embedment

depth (mm)

X

6

: Clear

clearance (mm)

X

7

:fc

(MPa)

X

8

: Edge

distance (mm)

Shear capacity

(kN)

1 12.70 1 1 1 114 1.04 23.52 114.30 42

2 12.70 1 1 1 114 1.04 23.52 114.30 35

3 15.88 1 1 1 144 1.98 23.52 133.35 67

4 15.88 1 1 1 144 1.98 23.52 133.35 76

5 19.05 1 1 1 171 2.10 23.52 171.45 86

6 19.05 1 1 1 171 2.10 23.52 171.45 94

7 22.23 1 1 1 199 2.06 23.52 200.03 139

8 22.23 1 1 1 199 2.06 23.52 200.03 122

9 25.40 1 1 1 226 2.15 23.65 228.60 189

10 12.70 1 1 1 115 1.04 40.89 114.30 49

11 15.88 1 1 1 144 1.98 40.89 142.88 79

12 15.88 1 1 1 144 1.98 40.89 142.88 71

13 19.05 1 1 1 173 2.07 40.89 171.45 112

14 22.23 1 1 1 199 2.06 40.89 200.03 149

15 22.23 1 1 1 199 2.06 40.89 200.03 138

16 9.53 1 1 1 86 1.08 23.52 38.10 6

17 9.53 1 1 1 86 1.08 23.52 38.10 6

18 15.88 1 1 1 86 1.98 23.65 63.50 16

19 15.88 1 1 1 86 1.98 23.65 63.50 15

20 9.53 1 1 1 86 0.79 13.48 85.73 19

21 12.70 1 1 1 114 0.79 13.48 85.73 36

22 12.70 1 1 1 117 0.79 13.48 85.73 42

23 15.88 1 1 1 117 1.59 13.48 142.88 60

24 15.88 1 1 1 117 1.59 13.48 142.88 57

25 19.05 1 1 1 169 1.59 13.48 171.45 64

26 19.05 1 1 1 168 1.59 13.48 171.45 65

27 19.05 1 1 1 175 1.59 13.48 171.45 72

28 19.05 1 1 1 173 1.59 13.48 171.45 72

29 22.23 1 1 1 201 4.76 13.48 200.03 103

30 25.40 1 1 1 225 1.59 13.28 228.60 107

31 25.40 1 1 1 230 1.59 13.28 228.60 114

32 12.70 0 1 0 113 1.59 31.57 107.95 54

33 15.88 0 1 0 133 1.59 31.57 127.00 69

34 15.88 0 1 0 135 1.59 31.57 127.00 57

35 19.05 0 1 0 178 1.59 31.57 155.58 87

36 19.05 0 1 0 168 1.59 31.57 155.58 90

37 22.23 0 1 0 164 3.18 31.57 168.28 120

38 22.23 0 1 0 165 3.18 31.57 168.28 100

39 25.40 0 1 0 210 3.18 31.57 203.20 145

40 25.40 0 1 0 208 3.18 31.57 203.20 151

41 12.70 0 1 0 103 1.59 13.13 107.95 38

42 12.70 0 1 0 114 1.59 13.13 107.95 38

43 15.88 0 1 0 133 1.59 13.13 127.00 44

44 15.88 0 1 0 127 1.59 13.13 127.00 49

45 19.05 0 1 0 162 1.59 13.13 171.45 78

46 19.05 0 1 0 175 1.59 13.13 171.45 65

47 22.23 0 1 0 165 3.18 13.34 177.80 75

48 22.23 0 1 0 175 3.18 13.34 177.80 87

49 25.40 0 1 0 203 3.18 13.34 203.20 126

50 25.40 0 1 0 187 3.18 13.34 203.20 103

51 8.00 0 0 1 80 1.00 15.00 40.00 9

52 8.00 0 0 1 80 1.00 43.00 40.00 12

53 10.00 0 0 1 90 1.00 43.00 45.00 17

54 12.00 0 0 1 110 1.00 15.00 55.00 19

55 16.00 0 0 1 125 1.00 16.00 62.50 24

56 16.00 0 0 1 125 1.00 16.00 125.00 53

57 20.00 0 0 1 170 2.50 16.00 85.00 44

58 20.00 0 0 1 170 2.50 16.00 170.00 70

59 24.00 0 0 1 210 2.00 16.00 262.50 115

60 24.00 0 0 1 210 2.00 28.00 105.00 62

61 12.00 0 0 1 110 1.00 14.00 55.00 45

62 12.00 0 0 1 110 1.00 14.00 165.00 68

63 12.00 0 0 1 110 1.00 36.00 110.00 106

64 12.00 0 0 1 110 1.00 36.00 137.50 106

*

1 for cartridge injection, 0 for glass capsule.

**

1 for epoxy and 0 for unsaturated polyester.

***

1 for steel rebar, 0 for threaded bars.

718 M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724

Gene expression programming (GEP) is a natural development

of genetic algorithms and genetic programming. GEP, introduced

by Ferreira [22], is a natural development of GP. GEP evolves com-

puter programs of different sizes and shapes encoded in linear

chromosomes of ﬁxed-length. Its algorithm begins with the

random generation of the ﬁxed-length chromosomes of each indi-

vidual for the initial population. Then, the chromosomes are

expressed and the ﬁtness of each individual is evaluated based

on the quality of the solution it represents [23].

4. Construction of the prediction model

When loaded in shear, anchor’s adhesive layer bears on the

concrete. With enough force this will cause the edge of the con-

crete to break out [11].Fig. 1 shows a typical edge breakout failure

of a single adhesive anchor. The test setup generally consists of a

loading frame, loading plate, jack assembly, and load cell. The load

is applied to the anchor under force control in increasing percent-

ages of the estimated capacity (such as 5%, 10%, 20%, and so forth to

failure) with loading frames oriented parallel to the concrete

surface of each specimen. Load is continuously and very slowly

increased to avoid abrupt failure. The clear distance between the

supports is arranged to allow for unrestricted formation of a con-

crete breakout. Moreover, in some of these experimental studies

the displacement of the anchor in the direction of load at the level

of concrete top surface and axial strains in the anchor bolt are

observed as well as the failure load [10].

The models given in the design codes basically depend on the

compressive strength of the concrete and edge distance. Some

models also consider embedment depth and diameter of the

anchor bolt. However, clearance distance (see Fig. 1), type of the

anchor, type of adhesive and method of injection have not yet been

considered in the formulation of shear capacity of the anchor. For

this, anchor diameter, type of anchor (threaded bar or rebar), edge

distance, embedment depth, clear clearance of the anchor, type of

chemical adhesive (epoxy or unsaturated polyester), method of

injection of the chemical (glass capsule or cartridge injection),

and compressive strength of the concrete with the experimental

results of shear capacity of the anchors were arranged to obtain

a data set.

The adhesive anchors dealt with this study are steel anchors

either threaded rod or deformed bar inserted into a drilled hole

in normal strength concrete. A structural adhesive was utilized to

achieve proper bonding between the concrete and anchor. For

adhesive anchors, the diameter of the drilled hole is typically not

larger than 1.5 times the diameter of the steel element [1]. Adhe-

sive anchors are available in glass capsules or in injection systems

using organic or inorganic compounds. The adhesives utilized in

this study are epoxy and unsaturated polyester. For example,

test-1 in Table 1 has the following experimental parameters: steel

rebar of 12.70 mm diameter was post installed into a concrete

Table 2

Testing data base used for evaluating the performance of the prediction model.

Sample

no

Independent variables (X

i

) Dependent

variable (Y)

X

1

: Diameter

(mm)

X

2

: Type of

injection

*

X

3

: Chemical

type

**

X

4

: Anchor

type

***

X

5

: Embedment

depth (mm)

X

6

: Clear

clearance (mm)

X

7

:fc

(MPa)

X

8

: Edge

distance (mm)

Shear capacity

(kN)

1 9.53 1 1 1 85.73 1.08 23.52 85.73 26

2 12.70 1 1 1 114.30 1.04 23.52 114.30 41

3 15.88 1 1 1 143.94 1.98 23.52 133.35 77

4 19.05 1 1 1 171.45 2.10 23.52 171.45 91

5 25.40 1 1 1 226.49 2.15 23.65 228.60 170

6 25.40 1 1 1 226.49 2.15 23.65 228.60 149

7 15.88 1 1 1 143.94 1.98 40.89 142.88 78

8 19.05 1 1 1 172.52 2.07 40.89 171.45 105

9 9.53 1 1 1 85.73 1.08 23.52 38.10 8

10 15.88 1 1 1 85.73 1.98 23.65 63.50 16

11 12.70 1 1 1 117.37 0.79 13.48 85.73 41

12 15.88 1 1 1 114.33 1.59 13.48 142.88 59

13 19.05 1 1 1 170.92 1.59 13.48 171.45 83

14 22.23 1 1 1 206.45 4.76 13.48 200.03 93

15 22.23 1 1 1 200.05 4.76 13.48 200.03 92

16 25.40 1 1 1 226.70 1.59 13.28 228.60 116

17 15.88 0 1 0 133.35 1.59 31.57 127.00 71

18 19.05 0 1 0 168.28 1.59 31.57 155.58 96

19 22.23 0 1 0 168.28 3.18 31.57 168.28 128

20 25.40 0 1 0 206.38 3.18 31.57 203.20 126

21 12.70 0 1 0 106.38 1.59 13.13 107.95 41

22 15.88 0 1 0 142.88 1.59 13.13 127.00 48

23 19.05 0 1 0 155.58 1.59 13.13 171.45 78

24 22.23 0 1 0 177.80 3.18 13.34 177.80 83

25 25.40 0 1 0 177.80 3.18 13.34 203.20 98

26 10.00 0 0 1 90.00 1.00 15.00 45.00 14

27 10.00 0 0 1 90.00 1.00 15.00 67.50 19

28 12.00 0 0 1 110.00 1.00 43.00 55.00 27

29 16.00 0 0 1 125.00 1.00 36.00 62.50 37

30 20.00 0 0 1 170.00 2.50 36.00 85.00 63

31 24.00 0 0 1 210.00 2.00 16.00 105.00 51

32 12.00 0 0 1 110.00 1.00 14.00 110.00 57

33 12.00 0 0 1 110.00 1.00 38.00 55.00 60

34 12.00 0 0 1 110.00 1.00 38.00 110.00 91

*

1 for cartridge injection, 0 for glass capsule.

**

1 for epoxy and 0 for unsaturated polyester.

***

1 for steel rebar, 0 for threaded bars.

M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724 719

having a compressive strength of 23.52 MPa using cartridge

injection system in which epoxy being the bonding agent.

The derivation of a genetic-programming-based explicit formu-

lation is accomplished by means of the training data containing

input and output variables. Besides, in order to examine and test

the performance of the developed model, a supplementary data

set containing the same number and sequence of input and output

variables is used. Therefore, in the current study, the ensemble of

available experimental data was arbitrarily divided into two parts

to obtain the training and testing databases. Approximately 2/3 of

the total data samples were used as the training set while the rest

was employed as the testing set, as shown in Tables 1 and 2,

respectively. Thus, a total of 64 and 34 samples from training

and testing sets, respectively were utilized in constructing the

model.

A software, named GeneXproTools.4.0 was employed for

derivation the mathematical model presented in Eq. (9). The mod-

els developed by GEP in its native language can be automatically

parsed into visually appealing expression trees, permitting a quick-

er and more complete comprehension of their mathematical/logi-

cal intricacies. Fig. 2 demonstrates the expression tree for the

terms used in the formulation of the GEP model which has the

Fig. 2. Expression tree for the GEP model [d

0

: Anchor diameter (mm), d

1

: Injection type (1 for cartridge injection, 0 for glass capsule), d

2

: Chemical type (1 for epoxy and 0 for

unsaturated polyester), d

3

: Type of anchor (1 for steel rebar, 0 for threaded bars), d

4

: Embedment depth (mm), d

5

: Clear clearance (mm), d

6

: Concrete compressive strength

(MPa), d

7

: Edge distance (mm) c

0

and c

1

: constants (c

0

=7.08139 for Sub-ET3, c

0

= 5.801483 for Sub-ET4, c

0

= 5.138702 for Sub-ET5, c

0

=6.909272 for Sub-ET6,

c

1

=6.227142 for Sub-ET1, c

1

= 3.883179 for Sub-ET3, c

1

= 8.091003 for Sub-ET5)].

720 M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724

parameters given in Table 3. As seen in Table 3 that various math-

ematical operations were included to provide a reliable model.

V

U

¼V

1

V

2

V

3

V

4

V

5

V

6

ð9Þ

V

1

¼ln ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

6:227142 þX

8

X

3

X

6

þtanðX

4

1

Þ

3

q

2

ð9aÞ

V

2

¼ln ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

X

2

7

þX

1

qÞ

sin

2

ðX

7

Þ

þX

1

3

s

2

6

43

7

5ð9bÞ

Table 3

GEP parameters used for the proposed model.

P1 Function set +, ,

,/,p, ^, ln, exp, sin, tan

P2 Number of generation 940,695

P3 Chromosomes 40

P4 Head size 10

P5 Linking function Multiplication

P6 Number of genes 6

P7 Mutation rate 0.044

P8 Inversion rate 0.1

P9 One-point recombination rate 0.3

P10 Two-point recombination rate 0.3

P11 Gene recombination rate 0.1

P12 Gene transposition rate 0.1

Fig. 3. Performance of the proposed GEP model: (a) train set and (b) test set.

Fig. 4. Predicted shear capacity values from ACI 349-97.

Fig. 5. Predicted shear capacity values from ACI 349-06.

Fig. 6. Predicted shear capacity values from CCD method.

Fig. 7. Predicted shear capacity values from modiﬁed CCD method.

M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724 721

V

3

¼ln½X

7

sin½ðX

5

þ3:883179Þ

3

þtanð7:08139 X

5

Þ ð9cÞ

V

4

¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

X

7

þX

6

½tanðsin X

7

ÞX

4

þ5:801483

6

qð9dÞ

V

5

¼ln½lnðX

1

tanðX

8

þ8:091003 X

4

Þtanð5:138702

X

1

ÞÞ ð9eÞ

V

6

¼½lnðﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

tanðln X

8

Þþð6:909272Þ

X

2

þX

8

þX

4

3

qÞ

3

ð9fÞ

where V

U

is the ultimate shear capacity of adhesive anchor in un-

cracked concrete (kN); X

1

: Anchor diameter (mm); X

2

: Injection

type (1 for cartridge injection, 0 for glass capsule); X

3

: Chemical

type (1 for epoxy and 0 for unsaturated polyester); X

4

: Type of an-

chor (1 for steel rebar, 0 for threaded bars); X

5

: Embedment depth

(mm); X

6

: Clear clearance (mm), X

7

: Concrete compressive strength

(MPa), and X

8

: Edge distance (mm).

5. Performance of the prediction model

Performance of the proposed GEP prediction model in Eq. (9)

was depicted in Fig. 3 for both train and testing data sets. More-

over, the correlations between experimental and predicted shear

capacities for the existing models were also given in Figs. 4–8 for

the entire data. Fig. 3 revealed that a high estimation accuracy

was accomplished for both training and testing data sets. The cor-

relation coefﬁcient of training set was 0.98 while that of testing

was 0.92. It is seen in Fig. 6 that despite having lower R

2

value,

CCD method presented similar trend as GEP model. As a result of

uniform scatter of the data, the correlation coefﬁcients calculated

for the other models also appeared to be very close to each other.

However, the shear capacities computed from ACI 349-97, ACI 349-

06, and PCI models underpredicted the actual values while

Modiﬁed CCD method provided overprediction. Some statistical

parameters were also given in Table 4 for comparing the tendency

of the distribution of the predicted values. The proposed GEP

model had the lowest errors such that MAPE (mean absolute

percentage error) was about 10 and 14% for the train and test sets,

respectively. However, when the existing models in the literature

were considered, MAPE ranged from 19% to 66%, depending on

the prediction capability of the model. Therefore, this absolute

error of the proposed GEP model seemed to be fairly reasonable

when the noisy nature of the experimental results of adhesive an-

chors was taken into account [24,25]. Of all the existing formulas,

CCD method appeared to be the most reliable one attributed to its

relatively lower prediction error.

Figs. 9–12 indicate the variations of the normalized shear

capacity found by dividing the predicted over experimental values,

versus compressive strength of the concrete, edge distance, diam-

eter of anchor and embedment depth of the anchor, respectively.

Since compressive strength of the concrete and edge distance are

the fundamental factors as being available in all of the prediction

models, Figs. 9 and 10 contained all of the prediction models dealt

with this study. Nevertheless, in Figs. 11 and 12, ACI 349-97 and

Fig. 8. Predicted shear capacity values from PCI method.

Table 4

Statistical parameters of the proposed model as well as existing ones.

Parameters GEP model CCD model Modiﬁed CCD model ACI 349-97 ACI 349-06 PCI model

Training data set Testing data set

Mean Square Error (MSE) 36.9 168.7 261.3 3858.9 556.7 1051.5 1327.6

Mean absolute percent error (MAPE) 10.0 14.2 18.9 66.0 33.0 42.2 41.5

Root Mean Square Error (RMSE) 6.1 13.0 16.2 62.1 23.6 32.4 36.4

Correlation coefﬁcient (R

2

) 0.98 0.92 0.88 0.89 0.87 0.88 0.89

Fig. 9. Prediction performance of the GEP, CCD, modiﬁed CCD, ACI 349-97, ACI 349-

06, and PCI models for different concrete compressive strengths.

Fig. 10. Prediction performance of the GEP, CCD, modiﬁed CCD, ACI 349-97, ACI

349-06, and PCI models for different edge distances.

722 M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724

PCI formulas are excluded because they do not include the diame-

ter and embedment depth of the anchor (Eqs. (2) and (8)). It can be

seen from the ﬁgures that CCD method and proposed GEP model

revealed a very close trend in terms of prediction performance.

For example, considering the overall 98 normalized values, 60

points for GEP model and 38 points for CCD model fell between

±10% limits while 10, 5, 3 and only 1, point were observed for

ACI 349-97, modiﬁed CCD, PCI, and ACI 349-06 models, respec-

tively. Modiﬁed CCD model gave the highest normalized values

for all of the factors considered. The range of the normalized values

for modiﬁed CCD model was observed to be 0.50-2.67. However,

the range for the proposed GEP model was 0.45-1.69. The lowest

upper limit for the normalized values was observed for both ACI

349-06 and PCI models as 0.91. As seen in Figs. 9 and 10, these

two models exhibited similar trend in underpredicting the shear

capacities for a given compressive strength and edge distance.

Fig. 9 showed that the normalized values tend to approach to

almost 1 for the compressive strengths of 24–32 MPa whereas

beyond that a divergence was obtained. Tendency of clustering

the data was observed for the highest edge distance in Fig. 10,

for the highest diameter in Fig. 11, and for the highest embedment

depth in Fig. 12. In the study of Gesog

˘lu and Güneyisi [25], predic-

tion models were developed to estimate the pullout capacity of

adhesive anchors through soft computing methods. They also re-

ported that the prediction capability of the proposed models and

the CCD method were increased for deeper embedment depth

and larger diameter anchors. It can be seen from Figs. 9–12 that

the normalized shear capacity results tend to be divergent as the

compressive strength of concrete, the diameter of anchor, the

embedment length and the edge distance decrease. In the study

of Bickel and Shaik [11] it was stated that the shear capacity exhib-

its lesser increase in strength with concrete compressive strength.

Moreover, the predicted shear capacity values were scattered for

lower embedment depth and edge distances. This situation may

be attributed to the number of experimental data used for deriva-

tion of the models. The higher the number of data, the more robust

and repeatable the derived model. For example, in the proposed

GEP model, few number of data for the anchors having bar diame-

ter less than 12 mm generated both underestimation and overesti-

mation performance. However, due to the fact that most of the

anchors have bar diameter of higher than 12 mm, the predicted

results for such anchors fell between ±10% of the actual results.

6. Conclusions

Based on the analyses presented above, the following conclu-

sions may be drawn:

Breakout shear capacity prediction model was developed by

genetic programming considering the chemical characteristics

and method of the placing of the adhesive anchors. The model

provided reasonable predicted values with signiﬁcantly high

accuracy. The empirical formulation was generated through

gene expression programming (GEP) with correlation coefﬁ-

cient of 0.98.

Although the database for testing were not utilized for training,

a high level of estimation was obtained for both training and

testing data sets associated with low mean absolute percentage

of error and high coefﬁcients of correlation. This indicates the

generalization capability of the developed model.

The proposed model was compared with the existing formulas

available in ACI 349-97, ACI 349-06, ACI 318-08 (CCD method),

PCI-98 design handbook as well as the model proposed by Hoff-

man [12], namely, modiﬁed CCD method. The statistical analy-

sis revealed that the proposed GEP model had relatively lower

errors than the others. The closest prediction tendency to the

GEP model was demonstrated by CCD method.

Normalization of the predicted values was performed to evalu-

ate the performance of the existing and proposed prediction

models. It was observed that ACI 349-97, ACI 349-06, PCI

method, and CCD method underpredicted while modiﬁed CCD

method overpredicted the shear capacity. The values obtained

from PCI model, ACI 349-97 and ACI 349-06 models appeared

to be close to each other. However, the values obtained from

GEP model were observed to be more uniform and much closer

to the actual results.

Acknowledgement

The authors would like to thank to Professor Ashour for provid-

ing the database of adhesive anchors. Professor Cook maintains

this database on behalf of the ACI Committee 355.

References

[1] Eligehausen R, Cook RA, Appl J. Behavior and design of adhesive bonded

anchors. ACI Struct J 2006;103(6):822–32.

[2] McVay MC, Cook RA, Krishnamurthy K. Pullout simulation of post-installed

chemically bonded anchors. J Struct Eng 1996;122(9):1016–24.

[3] Cook RA, Kunz J, Fuchs W, Konz RC. Behavior and design of single adhesive

anchors under tensile load in uncracked concrete. ACI Struct J 1998;95(1):

9–26.

[4] Cook RA, Konz RC. Factors inﬂuencing bond strength of adhesive anchors. ACI

Struct J 2001;98(1):76–86.

Fig. 11. Prediction performance of the GEP, CCD, modiﬁed CCD, and ACI 349-06

models for different anchor diameters.

Fig. 12. Prediction performance of the GEP, CCD, modiﬁed CCD, and ACI 349-06

models for different embedment depths.

M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724 723

[5] Cook RA. Behavior of chemically bonded anchors. J Struct Eng 1993;119(9):

2744–62.

[6] Gesog

˘lu M, Özturan T, Özel M, Güneyisi E. Tensile behavior of post-installed

anchors in plain and steel ﬁber reinforced normal-and high-strength concretes.

ACI Struct J 2005;102(2):224–31.

[7] Cook RA, Doerr GT, Klingner RE. Bond stress model for design of adhesive

anchors. ACI Struct J 1993;90(5):514–24.

[8] Higgins CC, Klingner RE. Effects of environmental exposure on the performance

of cast-in-place and retroﬁt anchors in concrete. ACI Struct J 1998;95(5):

506–17.

[9] Fujikake K, Nakayama J, Sato H, Mindess S, Ishibashi T. Chemically bonded

anchors subjected to rapid pullout loading. ACI Mater J 2003;100(3):246–52.

[10] Lee NH, Park KR, Suh YP. Shear behavior of headed anchors with large

diameters and deep embedments. ACI Struct J 2010;107(2):146–56.

[11] Bickel TS, Shaik FA. Shear strength of adhesive anchors. PCI J 2002:92–102.

[12] Hofmann J. Tragverhalten und Bemessung von Befestigungen am Bauteilrand

unter Querlasten mit beliebigem Winkel zur Bauteilkante (Load- Bearing

Behaviour and Design of Fasteners Close to an Edge under Shear Loading with

an Arbitrary Angle to the Edge), PhD thesis, Institut für Werkstoffe im

Bauwesen, Universität Stuttgart, 2004. p. 235 (in German).

[13] Ueda T, Kitipornchai S, Ling K. Experimental investigation of anchor bolts

under shear. J Struct Eng 1990;116(910–92):1.

[14] ACI Committee 349. Code Requirements for Nuclear Safety-Related Concrete

Structures and Commentary (ACI 349-97). Farmington Hills, MI: American

Concrete Institute; 1997. p. 123.

[15] ACI Committee 349. Code Requirements for Nuclear Safety-Related Concrete

Structures and Commentary (ACI 349-06). Farmington Hills, MI: American

Concrete Institute; 2007. p. 153.

[16] ACI Committee 318. Building Code Requirements for Structural Concrete (ACI

318-05) and Commentary (318R-08). Farmington Hills, MI: American Concrete

Institute; 2008. p. 467.

[17] Fuchs W, Eligehausen R, Breen JE. Concrete Capacity Design (CCD) approach for

fastening to concrete. ACI Struct J 1995;92:73–94.

[18] PCI Design Handbook. Precast-Prestressed Concrete. 5th ed. Chicago: Precast-

Prestressed Concrete Institute; 1998.

[19] Koza JR. Genetic programming: On the programming of computers by means

of natural selection. MIT Press; 1992.

[20] Goldberg D. Genetic algorithms in search, optimization and machine

learning. MA: Addison-Welsley; 1989.

[21] Zadeh LA. Soft computing and fuzzy logic. IEEE Software 1994;11(6):48–56.

[22] Ferreira C. Gene expression programming: a new adaptive algorithm for

solving problems. Complex Syst 2001;13(2):87–129.

[23] Özbay E, Gesog

˘lu M, Güneyisi E. Empirical modeling of fresh and hardened

properties of self-compacting concretes by genetic programming. Constr Build

Mater 2008;22:1831–40.

[24] Sakla SSS, Ashour AF. Prediction of tensile capacity of single adhesive anchors

using neural networks. Comput Struct 2005;83:1792–803.

[25] Gesog

˘lu M, Güneyisi E. Prediction of load-carrying capacity of adhesive

anchors by soft computing techniques. Mater Struct 2007;40:939–51.

724 M. Gesog

˘lu et al. / Composites: Part B 60 (2014) 716–724