1. - 4555 -
Simplified Approach for Estimating the
Entire Load Profile of Fully Grouted
Anchor Bolt by Strain Measurement
Near Loaded End
Subin Desar*
Doctoral candidate
China Three Gorges University, Yichang, Hubei 443002, China
*Corresponding author e-mail: subin@ctgu.edu.cn
Dr. Li Jian Lin
Professor
China Three Gorges University, Yichang, Hubei 443002, China
Dr. Deng Hua Feng
Professor
China Three Gorges University, Yichang, Hubei 443002, China
Dr. Sun Xu Shu
Associate Professor
China Three Gorges University, Yichang, Hubei 443002, China
ABSTRACT
The load carrying capacity of the anchor bolt depends upon many factors like strengths of rock, grout,
anchor bolt, their interfaces, anchor bolt rib geometry etc. Though there are some formulations for the
anchor bolt load capacity, in many cases variables of the analytical formulas need to be determined
from the lab test. It is general practice to obtain data from as many possible points to get the entire load
profile along the anchor bolt during the pullout test. In this paper, a simplified procedure is presented
for obtaining the entire load profile of fully grouted anchor bolt, using the data read from two points
near the loaded end.
KEYWORDS: Pullout test; Load profile; Fully grouted anchor bolt; Strain measurement
INTRODUCTION
Anchor bolt has been used in varieties of civil engineering works including tunneling, mining,
stabilizing slopes, erecting steel structures etc. Many studies have been conducted in this field to
understand the load transfer mechanism of anchor bolt. Anchor bolt embedded inside the grout
transfer the internal forces due to the bonding mechanism between anchor, grout and surrounding
rock or concrete.

2. Vol. 21 [2016], Bund. 14 4556
In general, the shear strength of an interface comprises three components: adhesion, mechanical
interlock and friction. These forces depend on strength of materials used, strength of their interfaces
and the rib geometry [2]. Materials used in the anchor bolt system vary from one condition to another.
Materials like grout and anchor bolt are controllable up to certain extent but the peripheral rock
cannot be changed in general. Farmer [4] derived a theoretical formulation which works for certain
types of rock while for others types especially for soft rock, modifications are needed due to large
deformation. The grout around the anchor bolt is under confinement during loading process.
Properties of grout in confinement cannot be evaluated directly from the lab test data obtained during
unconfined state. In the dense to very dense confinement stage the compressive strength of grout
ranges between 200 MPa to 800 MPa [1] demanding the sophisticated equipment for evaluation. In
1999, Li & Stillborg [6] proposed an analytical model for different kinds of rock bolt including fully
grouted rock bolts. The analytical formulation representing the elastic zone, partially decoupled zone
and completely decoupled zone was derived by the authors. The derivation was based on the material
properties, bolt diameter, the maximum influence diameter and friction between the materials in
interface of the anchor bolt system. Although material properties could be determined separately, the
procedure of determining the maximum influence diameter was not clear. Maximum influence
diameter is one of the crucial components in the formulation as it is the reflection of the combination
of material properties and interfaces’ strength. Kilic et al. [5] conducted the laboratory experiment to
find the effect of bar shape on the pull-out capacity of fully grouted rock bolt. The result showed that
when the number of rib was one, the load carrying capacity was in the range of 40 to 48 KN. This
indicated that the stress range was greater than 200 MPa in the grout which was in direct contact with
anchor rib, while UCS of the grout was just around 24 MPa. Moosavi et al. [8] found that the capacity
of anchor bolt system further increases by increase in confining pressure. The effect of confining
pressure and rib configuration was also studied by Cao et al. [2] but the formulation works well only
in the high confining pressure range. Ma et al. [7] formulated an analytical model of fully grouted
rock bolts subjected to tensile load. The study proposed some coefficients for the anchor bolt system.
These coefficients depends upon rock bolting system characteristics like bolt profile, mechanical
properties of material, rock confinements etc., demanding the laboratory test for accuracy.
To understand the plastic nature of the grout Changxing et al.[3] conducted the study on the crack
pattern of the grout. The result indicated that the inclined cracks are forms first and then the
horizontal cracks during the pullout test. These researches indicate that anchor bolt system consists of
wide varieties of parameters including rib geometry, material properties and interface strength. The
analytical formulations till date cannot represent all of these parameters satisfactorily. So, there is
need to conduct lab test for accurate determination of load profile. This paper presents a procedure
that utilizes two points’ data for deriving the load profile of fully grouted anchor bolt.
THEORETICAL BACKGROUND
Fully grouted anchor bolt system consists of anchor bolt, grout and surrounding rock or concrete.
The strength parameters of all the materials are reflected in the pullout capacity of the bolt. To
understand the load profile of anchor bolt system, the load profile presented by Li & Stillborg [6] is
shown in Figure 1. It can be seen that when the load is in low range, the load profile follows the
exponential pattern. As the load increases load pattern no more follows the exponential trend but
becomes concave downward and finally becomes (literally) linear. Consider a point between 0 to
0.5m in the Figure 1. Once the pullout force is applied on the anchor bolt, at the low load level the
data of exponential curve can be obtained. As the load increases, the data of concave downward curve
can be obtained. Similarly, the entire further data trend could be obtained within this region as the
pullout load progresses forward. The hypothesis of this research is that if data between two close

3. Vol. 21 [2016], Bund. 14 4557
points are recorded during pullout test at short intervals of time then the pattern of the load profile
could be determined from the recorded data.
To explain this, let us assume a pullout load of P is applied along the anchor bolt as shown in
Figure 2. Let 1,2,3…(n-1), n are the points where data are recorded. These points are on equal
interval L/(n-1) along the entire length (L). R1, R2, R3…..Rn-1, Rn are the data reading on points
1,2,3….(n-1), n respectively. Now if pullout load is increased on the anchor bolt the strain readings at
the points also increase. At certain pullout load P+DP the stress reading of point 2 would be R1. At
this moment the reading of point 3 would be R2, reading of point 4 would be R3 and so on. In this
way, if the data are further recorded in close interval of time, data pattern could be found from the
loaded end to unloaded end.
Figure 1: Axial load along a fully grouted rock bolt at different levels of applied load [3]
Figure 2: Schematic representation of anchor bolt pullout load along bolt axis

4. Vol. 21 [2016], Bund. 14 4558
PULL OUT TEST
First, the anchor bolts were cut as per experiment’s requirement. From the author’s experience it
was known that attaching strain gauge strip on the surface of the anchor bolt would not work properly
as it would be damaged during the pull out test due the friction from grout. To avoid this situation, a
channel of size 8mmx 8mm was made on the surface of 25 mm diameter anchor bolt which is shown
in Figure 3. Care was taken to avoid the damage of any ribs. Damaging the rib would cause non-
uniform bonding of grout and anchor bolt, affecting the result of the experiment. Channel was made
throughout whole length for maintaining the homogeneity of the system along the bolt length. Super
glue was used to glue the strain gauge strip in the channel. Strain gauges were attached in more than
two points so that the result from two points could be verified from others. Two points were properly
chosen near the loaded end (Table 2- Gauge 3 and Gauge 4; Table 5, 425mm and 450mm distance).
Two points were chosen with the consideration that it would represent the mechanical interlocking of
the anchor bolt properly, for which the spacing was maintained at the multiple of rib spacing. Though
theoretically the interlocking of ribs are not considered to be concentrated at the discrete points, in
reality the interlocking are discrete in itself due to the presence of discrete ribs. Hence it was believed
that if the spacing was not multiple of rib spacing it may not represent the mechanical interlocking
properly. So, the spacing of two points was chosen 25mm which was double of rib spacing. The
channel was then covered with water proof glue to prevent the strain gauge strip from water during
grouting (Figure 4). Two types of grout were chosen for the experiment, though the surrounding
concrete (Artificial rock) was kept same for both. The parameters of the materials are shown in Table
1. Manual hydraulic jack was used for pullout test, though the strain was recorded using electronic
strain gauge recording device. The strain gauge recording device could record the data at the interval
of 1 second. The pullout load was kept below 0.5KN/s as it was believed that more data would give
better result. Photograph showing the pullout test arrangement is shown in Figure 5.
Figure 3: Strain gauge strips attached in channel of size 8mm x 8mm on 25 mm dia bar
Figure 4: Bar after covering the channel with water proof glue

5. Vol. 21 [2016], Bund. 14 4559
Figure 5: Pullout test arrangement
Table 1: Material parameters
Material Size (mm) Embedded
Length(mm)
E (MPa) UCS(MPa) Shear strength
(MPa)
Anchor bolt 25mm dia 500 2 e5
Grout 1 40mm dia 500 1.22 e4 6+0.3 3+0.4
Grout 2 40mm dia 500 2.12 e4 18.1+0.4 8.4+0.3
Concrete/
Artificial rock
250 x 250 500 1.51 e4 9.3+0.4 4.3+0.6
RESULTS AND DISCUSSION
The recorded data for anchor bolt with grout 1 is shown in Appendix A. It should be noted that
pullout load was applied manually by hydraulic jack. Practically, it was observed that when the jack
arm was pushed down the strain values increased and when the arm was lifted up for next push, the
strain value decreased little bit. So, there was little fluctuation in strain values which is due to the
internal adjustment and redistribution of stress as the anchor bolt was pullout. That is to say that the
displacement of anchor bolt towards loaded end releases the stress.
To show the data analysis procedure, it would be easy if limited amount of data are used. The
data reading at certain interval is tabulated in Table 2 and graphically presented in Figure 6. The data
obtained are consistent to each other as their increasing and decreasing trend are consistent. From
Table 2, the strain value at gauge 4 is 799.8 m strains when the strain value at gauge 3 is 781.8 m
strains. It means, at the distance beyond (398-373)m or 25mm from gauge 4, the strain value is 781.8
m strains. Then the strain value at gauge 3, corresponding to strain value 781.8 m strains at gauge 4
can be found by linear interpolation between the given values in Table 2 by Eqn. 1;
Let x1 = 799.8, x2 = 700.5, y1 = 781.8, y2 = 649.6, x = 781.8
)( 1
12
12
1 xx
xx
yy
yy −
−
−
+= (1)
y = 758

6. Vol. 21 [2016], Bund. 14 4560
Similarly, the strain value at gauge 3 corresponding to strain value 758 m strains at gauge 4 can be
computed. The Interpolated values at an equal interval of 25mm are shown in Table 3.The
corresponding values calculated from large data (Appendix A) are given in Table 4 and is plotted in
Figure 7. In Figure 7, data from four gauges are those data which were obtained experimentally from
the gauges placed at four points along the anchor bolt (Refer Appendix A) at maximum pullout load.
Two points’ limited but distributed data refers to the data read by gauges 3 and 4(Table 2), which
were selected from the large data in Appendix A, nearly at the regular interval covering whole range
of data. Large data are those data which were read by gauges 3 and 4 at an interval of 1 second (in
Appendix A) during pullout test. The result shows the data reading from two point’s well represents
the load profile of the anchor bolt along the bolt axis.
Similarly, the distributed strain reading at different gauges for the specimen with grout 2 is shown
in Table 5. The curve obtained from two point data is shown in Fig 8.
Table 2: Distributed strain reading at different gauges selected from large data in Appendix
A (m strains)-Specimen with grout 1
Gauge 1 at 45mm from
unloaded end
Gauge 2 at 273mm from
unloaded end
Gauge 3 at 373mm from
unloaded end
Gauge 4 at 398mm from
unloaded end
136.3 583.1 781.8 799.8
65.2 434.7 649.6 700.5
36.2 323.2 535.6 598.6
22.3 251.2 438 501.4
12.3 184.6 342 400.3
4.4 124.4 249.9 299.4
-0.2 71.6 163.1 201.1
-2.3 24.4 81.2 100.2
-2.8 0.4 35.9 51.9
Figure 6: Strain distribution along 500 mm the bolt profile at different loading conditions -
Specimen with grout 1

7. Vol. 21 [2016], Bund. 14 4561
Table 3: Calculated (Interpolated) strain values using limited data from Table 2-Specimen
with grout 1
Distance from unloaded end (mm) Strain value at gauge 4, m strains Strain values at gauge 3, m strains
398 800 782
373 782 758
348 758 726
323 726 683
298 683 631
273 631 571
248 571 508
223 508 445
198 445 384
173 384 327
148 327 275
123 275 229
98 229 188
73 188 152
48 152 123
23 123 100
Table 4: Calculated (Interpolated) strain values using large data from Appendix A-Specimen
with grout 1
Distance from unloaded end (mm) Strain value at gauge 4, m strains Strain values at gauge 3, m strains
398 800 782
373 782 757
348 757 719
323 719 669
298 669 612
273 612 551
248 551 486
223 486 422
198 422 362
173 362 306
148 306 257
123 257 213
98 213 174
73 174 141
48 141 114
23 114 93

8. Vol. 21 [2016], Bund. 14 4562
Figure 7: Anchor bolt load profile showing the comparison among curve obtained by data
from four gauges, interpolated from two points’ limited but distributed data and interpolated
from two points’ large data for 500 mm anchor bolt-Specimen with grout 1.
Table 5: Distributed strain reading at different gauges selected from large data in specimen
with grout 2
Gauge distance from unloaded end (mm)
187 300 350 405 425 450
Strain in m strain
338.5 916.9 1361.5 1702.7 1823.6 2335.3
237.9 756.5 1194.1 1582.3 1788.5 2009.4
144.1 524.3 921.3 1333.5 1532.4 1796.6
94.8 375.7 739 1186.8 1366.2 1601
54.1 254.7 576.2 1038.9 1198 1404.6
21.6 148.5 408.1 881.2 1022.3 1204.5
6.2 87.6 280.8 724 848.6 1004.8
0 47.2 186.8 590.6 701.3 833.9
0
100
200
300
400
500
600
700
800
900
0 100 200 300 400 500
mstrains
Distance along anchor bolt (mm)
Data from four
gauges
Interpolated
from two points'
limited but
distributed data
Interpolated
from two points'
large data

9. Vol. 21 [2016], Bund. 14 4563
Figure 8: Anchor bolt load profile showing the comparison among curve obtained by data
from four gauges, interpolated from two points’ limited but distributed data and interpolated
from two points’ large data for 500 mm anchor bolt-Specimen with grout 2.
COMPARISON WITH OTHER LITERATURE
This method can also be verified from the load profile curve data given by Farmer [4] for 500mm
resin anchor in limestone. Two points were chosen at the distance of 100mm and 110mm. At those
points the strain values were read. It should be noted that the PDF file with load profile graph was
first loaded in AUTOCAD drawing to check the accuracy of the orthogonal axes. Little
discrepancy was found and common base was adopted for the reading. Then, using the similar
procedure described earlier, the load profile curve was derived and compared with the gauge
readings in Fig 9. The comparison is presented in Fig 10. It can be seen that the theoretical and actual
curves agree well with each other.
Figure 9: Load displacement and strain distribution of 500mm resin anchors in limestone.[4]
0
500
1000
1500
2000
2500
0 100 200 300 400 500
strain,mstrain
Bolt axis, mm
Curve from Limited
Distributed Data
Real Data
From Large data

10. Vol. 21 [2016], Bund. 14 4564
Figure 10: Comparison of Farmer’s curve and two point’s data curve for 500mm resin
anchors in limestone.
CONCLUSION
The comparison among the curves shows that the load profile of fully and homogenously grouted
anchor bolt can be obtained from data recorded at two points near the loaded end, if recorded in
regular interval of time during loading. This proves that the assumed hypothesis is true.
This method provides easy way to evaluate the bolt load profile in long anchor bolt and can be
used to check the consistency of the obtained data along the bolt. So, it would save time, effort and
material during the pullout test for obtaining the bolt load profile.
ACKNOWLEDGEMENT
This research was funded by National Natural Science Foundation of China (Grant Nos 51309141
and 51479102) and Public Welfare Industry Special Fund of Ministry of Water Resources for
Scientific Research Projects of China (Grant No.201401029).
REFERENCES
[1] Barley AD. Properties of Anchor grouts in a confined state. Ground anchorages and
anchored structures. Proceedings of the international conference organized by the
institute of civil engineers and held in London, UK, 1997, p.13-22, ISBN 0-7277-2607-
2.
[2] Cao C, Ren T, Cook C, Cao Y. Analytical approach in optimizing selection of rebar bolts
in preventing rock bolting failure. J Rock Mech& Min Sci 2014;72:16-25.
[3] Changxing Z, Xu C, Youdong M, Xulin L. Modeling of grout crack of rock bolt grouted
system. J Min Sci and Tech 2015; 25:73-77.
0
100
200
300
400
500
600
700
0 100 200 300 400 500
Strain,mstrains
Bore hole length(mm)
Farmer's
curve
Curve from
two points
data

11. Vol. 21 [2016], Bund. 14 4565
[4] Farmer IW. Stress Distribution along a Resin Grouted Rock Anchor. J Rock Mech Min
Sci&Geomech 1975;12:347-351.
[5] Kilic A, Yasar E, Atis CD. Effect of bar shape on the pull-out capacity of fully grouted
rock bolts. J Tun Underground Space Tech 2003;18:1-6.
[6] Li C, Stillborg B. Analytical models for rock bolts. J Rock Mech& Min Sci 1999;
36:1013-1029.
[7] Ma S, Nemcik J, Aziz N. An analytical model of fully grouted rock bolts subjected to
tensile load. J Constr and Build Mat 2013;49: 519-526.
[8] Moosavi M, Jafari A, Khosravi A. Bond of cement grouted reinforcing bars under
constant radial pressure.JCem& Concrete Comp 2005;27: 103-109.
The complete data set is given in this document file:
Paper 2016.0440 Appendix
Editor’s note.
This paper may be referred to, in other articles, as:
Subin Desar, Dr. Li Jian Lin, Dr. Deng Hua Feng, and Dr. Sun Xu Shu:
“Simplified Approach for Estimating the Entire Load Profile of Fully Grouted
Anchor Bolt by Strain Measurement Near Loaded End” Electronic Journal of
Geotechnical Engineering, 2016 (21.14), pp 4555-4565. Available at
ejge.com.
© 2016 ejge