A REVIEW ON THE PULLOUT CAPACITY OF AN ANCHOR BLOCK EMBEDDED IN COHESIONLESS SOIL

Abstract

In geotechnical engineering practices, vertical anchor blocks are considered as a robust structural measure to counter the exerted pullout forces from the retaining structure and to maintain the overall stability of it. Several theoretical models are available in the literature to estimate the pullout capacity of the vertical anchor in cohesionless soil. This paper aims to estimate the accuracy and reliability of those theoretical models by comparing the predicted pullout capacity with the experimental results available in the literature. For this purpose, a rigorous literature review is carried out to compile the experimental studies conducted on vertical anchor blocks. A comparative assessment among the theoretical prediction models to assess the pullout capacity is done based on six statistical parameters: Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), McFadden’s pseudo R-square, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Nash-Sutcliffe model efficiency coefficient. These comparisons reveal the relative strength and weakness of each theoretical model. Thus, it will help the engineers to take an informed decision before adopting any theoretical model for design purposes.

Full text

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
A REVIEW ON THE PULLOUT CAPACITY OF AN ANCHOR BLOCK
EMBEDDED IN COHESIONLESS SOIL
M.E. Chowdhury1*, S. Sakib2
1Lecturer, Institute of Water and Flood Management (IWFM), Bangladesh University of Engineering and Technology (BUET),
Dhaka, Bangladesh, email: enayetchowdhury@iwfm.buet.ac.bd
2Graduate Research Assistant, The University of Texas at Arlington, Texas, USA, email: shadman.sakib@mavs.uta.edu
*Corresponding author
Abstract
In geotechnical engineering practices, vertical anchor blocks are considered as a robust structural measure to
counter the exerted pullout forces from the retaining structure and to maintain the overall stability of it. Several
theoretical models are available in the literature to estimate the pullout capacity of the vertical anchor in
cohesionless soil. This paper aims to estimate the accuracy and reliability of those theoretical models by
comparing the predicted pullout capacity with the experimental results available in the literature. For this purpose,
a rigorous literature review is carried out to compile the experimental studies conducted on vertical anchor blocks.
A comparative assessment among the theoretical prediction models to assess the pullout capacity is done based
on six statistical parameters: Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE),
McFadden’s pseudo R-square, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and
Nash-Sutcliffe model efficiency coefficient. These comparisons reveal the relative strength and weakness of each
theoretical model. Thus, it will help the engineers to take an informed decision before adopting any theoretical
model for design purposes.
Keywords
Vertical anchor blocks, Pullout capacity, Cohesionless soil
1. Introduction
Anchor installment is a widely-used soil reinforcement measure. Its design and construction are basically focused
on resisting outwardly directed imposed loads on the structure’s foundation. Several analyses have been done to
determine anchor plates’ capacity [1, 5, 10, 13, 14, 19, 24, 27, 28, 36, 37, 40, 42]. Compared to a relatively greater
number of researches on anchor plates, anchor blocks have drawn attention to a few. The behavior of anchor block
has been studied by a number of researchers [8, 18, 29, 34]. Empirical approximations have been a key feature of
current design practices. It is because of a large number of researches performed in the past is based on laboratory
or field experiments. Vertical anchor block has been an almost unexperimented field in terms of theoretical and
numerical analyses [11]. However, the effect of ground water table on the ultimate pullout loads of anchors has
been rarely studied. Summarizing the frequently used anchor design practices is the prime objective of this study.
Through this attempt, a rigorous discussion on the past studies on anchor blocks in addition to related potential
research approaches on it in future will be established. In this study, an apposite summary of pertinent researches
will be distinctly discussed based on experimental, theoretical and numerical studies. There is no endeavor to
propose an entire bibliography of all the relevant works of literature; it is rather intended to summarize the
researches with the closest relevance to the anchor block design. Currently, available pullout prediction models
will be discussed in a comparative approach with one another based on some statistical measures.
2. Previous experimental investigations
2.1 Investigations on anchor plates
Previous studies on anchor plates are illustrated in Table 1 and Table 2. Researchers’ predilection towards
experimental studies on anchor plates is quite noticeable in the post-2000 era. Within the last few years, the pattern
of anchor failure situated at various depths from the ground surface has been studied by Chowdhary and Dash
(2016). A noteworthy thing is where most of the researchers avoided the study of deep anchors, Akinmusuru
(1978), and Dickin and King (1997) focused their study on shallow, intermediate and deep anchors’ behavior.
Frictional angle effect on a wide range (29.5°-46.1°) was studied. Smith (1962) and Ovesen (1981) were found to
conduct field testing among the other researchers presented in Table 1. The maximum H/B (1-13) ratio was used
by Dickin and Leung (1983, 1985). Centrifuge testing was used in three studies: Ovesen (1981), Dickin and

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
Leung (1983, 1985), Dickin and King (1997). Most of the studies were conducted on strip, rectangular or square
shape of the anchor, where Das (1975) and Akinmusuru (1978) conducted experiments on the circular shape of
anchors. It indicates that post-1980 researchers were not that much concerned about circular anchor plates.
2.2 Investigations on anchor blocks
Experimental studies on anchor blocks were limited in comparison to researches on anchor plates. Duncan and
Mokwa (2001), Naser (2006) and Khan et al. (2017) conducted their researches on anchor blocks (Table 3). The
field test was done only by Duncan and Mokwa (2001); the other two pieces of research were conducted in the
chamber. The maximum embedment ratio (H/B) is 3.2 among all three researches which indicate the anchor blocks
Table 2 Laboratory model tests and field tests on vertical anchor plate in cohesionless soil
Source
Type of testing
Anchor shape
Anchor
size (mm)
Friction
angle (°)
H/B
Heuckel (1959)
Chamber
Square
75-200
34
2
Smith (1962)
Field
Rectangular; L/B = 1.25, 5
915
38.5
1–4.5
Neely et al. (1973)
Chamber
Square; rectangular
50.8
38.5
1–5
Das (1975)
Chamber
Square; circular
38–76
34
1–5
Das and Seely (1975)
Chamber
Square; rectangular; L/B = 1,3,5
51
34
1–4
Akinmusuru (1978)
Chamber
Strip; rectangular; square;
circular; L/B = 2, 10
50
24; 35
1–10
Ovesen (1981)
Centrifuge; field
Square
20
29.5–37.7
1–3.39
Rowe and Devis (1982)
Sand Chamber
Square; rectangular; L/B = 1–
8.75
51
32
1-8
Dickin and Leung (1983,
1985)
Centrifuge
chamber
Square; rectangular; strip
25; 50
41a
1–8; 1–
13
Hoshiya and Mandal
(1984)
Sand chamber
Square; rectangular; L/B = 2, 4, 6
25.4
29.5
1–6
Murray and Geddes (1989)
Sand chamber
Square; rectangular; L/B = 1–10
50.8
43.6, dense
1–8
Dickin and King (1997)
Centrifuge
Rectangular; L/B = 7.8
25
37.3–46.1
1–12
Chowdhary and Dash
(2016)
Sand chamber
Square
100
32–39
1–9
aMobilized plane strain friction angle, φ′mp
Table 1 Pertinent studies on anchors in cohesionless soil
Methods
Sources
Classification based
on anchor geometry
Anchor Plates
Heuckel (1959), Smith (1962), Neely et al. (1973), Das (1975), Das and
Seely (1975), Akinmusuru (1978), Ovesen (1981), Rowe and Devis
(1982), Dickin and Leung (1983, 1985), Hoshiya and Mandal (1984),
Murray and Geddes (1989), Dickin and King (1997), Chowdhary and
Dash (2016)
Anchor Blocks
Duncan and Mokwa (2001), Naser (2006), Khan et al. (2017)
Classification based on
Investigation Types
Theoretical
Investigations
Ovesen and Stromann (1972), NAVFAC DM 7.02 (U.S. Navy, 1986),
BS 8006 (1995), Ghaly (1997), Bowles (1997), Naser (2006),
Jadid et al. (2017)
Numerical
Investigations
Rowe and Davis (1982), Hanna et al. (1988),
Murray and Geddes (1989), Basudhar and Singh (1994), Merifield and
Sloan (2006), Bhattacharya and Kumar (2011), Hanna et al. (2011),
Bhattacharya and Kumar (2014), Bhattacharya and Roy (2016)

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
were placed at shallow depth. Therefore, there is a large scope for the researchers to conduct experiments on
anchor behavior at intermediate and deep depths.
3. Previous theoretical investigations
In common, similar theoretical approaches are adopted for calculating the pullout capacity of vertical anchor plates
and anchor blocks [12]. Simple analytical approaches such as limit equilibrium and limit analysis were used in
previous theoretical studies of anchors in sand. On the contrary, limit analysis approach, developed by Drucker et
al. (1952), has two theorems: 1) Upper bound theorem and 2) Lower bound theorem. Determination of the ultimate
resistance of anchors in the sand through a quasi-empirical method was proposed by Ovesen and Stromann (1972).
According to NAVFAC DM 7.02 (1986), the anchor blocks should be placed outside the surface making an angle
equal to the angle of friction of backfill soil. BS 8006 (1995) emphasizes on using passive resistance coefficient
to calculate the pullout resistance of an anchor block. Passive earth pressure against short structures is relatively
higher than the predicted one by conventional Rankine and Coulomb theories which is not negligible [38]. Hansen
(1966) developed a method for correcting the results of conventional pressure theories for shape (or 3-D) effects.
For short anchors, the ultimate resistance should be multiplied by a coefficient (M) to account for 3-D effects.
However, the experimental studies by Khan et al. (2017) indicated that this coefficient is always less than 4. Ghaly
(1997) used the results of 104 laboratory tests, 15 centrifugal tests, and 9 field tests to propose an empirical
correlation. Bowles (1997) proposed a general equation to determine the horizontal pullout resistance of anchor.
Naser (2006) analyzed the pullout capacity of an anchor block using limit equilibrium approach. Jadid et al. (2017)
derived an equation where the ultimate pullout capacity for an anchor block with the dimension’s height, width,
thickness, and the depth of embedment below soil surface was calculated. They also developed charts for other
shapes of block.
4. Previous numerical investigations
In spite of the presence of numerous studies on experimental results, comparatively a reduced amount of numerical
analyses has been conducted in order to determine anchors’ pullout capacity in cohesionless soil (Merifield and
Sloan, 2006). A summary of some important previous numerical studies post-1980 on vertical anchors is provided
in Table 4. Observation of Table 4 reveals that most of the numerical studies on anchors focused on strip case and
no researches were found to report numerical studies on anchor blocks. Most recently, Bhattacharya and Kumar
(2011) investigated the effect of vertical spacing of anchor plates and anchor roughness on the pullout capacity of
vertical anchors using lower bound finite element analysis. Hanna and Rahman (2011) using limit analysis showed
that the stress-strain condition in a sand mass during and after the installation of an anchor plate, over-
consolidation ratio have a significant effect on the pullout capacity. Again, using numerical lower bound limit
analysis in combination with linear programming, Bhattacharya and Roy (2016) showed that pullout capacity
increases continuously with the decrease in normalized width. Thus, the concepts of anchor plate analyses may
provide significant insight into understanding the behavior of anchor block failure mechanism.
5. Discussions
Table 1 Laboratory model tests and field test on vertical anchor block in cohesionless soil
Source
Type of
Testing
Anchor Block
Shape
Anchor Block
size (mm)
Friction
angle (°)
H/B
Exclusive test condition
Duncan
and Mokwa
(2001)
Field
Rectangular;
L/B = 1.7
1100 x 1900 x 900
50
1
Blocks placed flush with
the ground surface using
two backfill materials
Naser
(2006)
Chamber
Square
150 x 150 x 150
43.5
2
Blocks’ pullout capacity
in saturated condition
Khan et al.
(2017)
Chamber
Square
150 x 150 x 75
37.2- 44.8
3.2
Blocks placed at different
distances from the
yielding retaining wall

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
Only 7 test results (Table 5) were found in the literature to establish the most suitable method for an anchor block.
However, this comparison between the experimental results and theoretical predictions gives us an opportunity to
gain some useful information about the suitability of the theoretical methods in different conditions. For example,
when compared to the pullout capacity reported by Duncan and Mokwa (2001), the methods proposed by
NAVFAC DM 7.02 (1986), BS 8006 (1995), Ghaly (1997) gave an error of more than 50% (Table 5). Duncan
and Mokwa (2001) measured anchor block bearing against compacted gravel backfill near the ground surface.
Naser (2006) performed one laboratory test on 100% saturated sandy soil to observe the effect of degree of
saturation on pullout resistance of anchor. When compared to the pullout capacity observed by Naser (2006), the
methods proposed by Ovesen and Stromann (1972), NAVFAC DM 7.02 (1986) and BS 8006 (1995) gave an error
of more than 50%. The remaining 5 test results were conducted on poorly graded unsaturated sand. Each of the
method discussed here, except Jadid et al. (2017), gives an error of more than 50% for at least twice (Table 5).
Ovesen and Stromann (1972) considered the friction between wall and soil during upward movement of the
passive wedge. Bhattachyarya and Kumar (2014), Kumar and Sahoo (2012) showed numerically that
consideration of wall friction angle contributes favorably to pullout capacity. Again, anchor block moves together
with the passive wedge resulting in no shear displacement between the wall and passive wedge (Duncan and
Mokwa 2001). Thus, Ovesen and Stromann (1972) overestimated the test results in most of the cases. BS 8006
(1995) also significantly overestimated the test results in six out of seven cases. BS 8006 (1995) assumes that the
pullout resistance of anchor is four times the passive resistance of the soil. Whereas, experimental studies by Khan
et al. (2017) indicated this coefficient is always less than four. In other circumstances, Bowles (1997) method
underestimated each test results by a significant margin. Conventional earth pressure theories, assuming identical
cross section along the length of a structure was used in Bowles’s (1997) analysis. But such an assumption might
be suitable for heavy strip anchors. More importantly, the influence of different side conditions of the small
structure was omitted during the development of the theory, which is by far the single most important drawback.
As such, conventional theories provide a lower estimate of the pullout capacity. This is consistent with the findings
of Hanna et al. (2011) and Bilgin (2012). Ghaly’s (1997) empirical equation underestimated test results by more
than 50% (Table 5) for relatively denser soil on two occasions. The results of 104 laboratory tests, 15 centrifugal
tests, and 9 field tests were used to propose this empirical correlation. Unit weight and internal friction angle of
soil ranged from 14 to 16 kN/m3 and 34° to 38.5° respectively. It is expected that excess deviation from the range
of test parameters used to derive the empirical correlation might be the possible source of errors.
Table 4 Numerical studies on vertical anchors in cohesionless soil
This is probably the reason for the highest error corresponding to the test results of Duncan and Mokwa (2001),
where unit weight and internal friction angle of soil were 21.2 kN/m3 and 50° respectively. On the other hand,
Naser (2006) utilized the passive resistance coefficient proposed by Hansen (1966) to estimate the pullout capacity
of an anchor block. This coefficient is defined as the ratio of actual pullout resistance to the corresponding passive
resistance from Rankine theory acting in front of the anchor block.
Source
Analysis method
Anchor
shape
Anchor
roughness
Friction
angle (°)
H/B
Rowe and Davis
(1982)
Elasto–plastic finite element
Strip
Smooth
0–45
1–8
Hanna et al. (1988)
Limit equilibrium
Strip;
inclined
Smooth
All
All
Murray and Geddes
(1989)
Limit analysis – upper
bound
Strip;
inclined
Rough;
smooth
43.6
1–8
Basudhar and
Singh (1994)
Limit analysis – lower
bound
Strip
Rough;
smooth
32; 35; 38
1–5
Merifield and Sloan
(2006)
Limit analysis – upper and
lower bound
Strip
Rough;
smooth
20–40
1–10
Bhattacharya and
Kumar (2011)
Limit analysis – lower
bound
Strip
Rough;
smooth
25–40
1–7
Hanna et al. (2011)
Limit analysis
Strip
Rough
30–45
1–9
Bhattacharya and
Kumar (2014)
Limit analysis – lower
bound
Strip;
inclined
Rough;
smooth
30–40
3–10
Bhattacharya and
Roy (2016)
Limit analysis – lower
bound
Strip
Rough;
smooth
30–40
2–7

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
Table 5 Comparison of theoretical predictions of pullout capacity with experimental results for vertical anchor block
Authors
Exp.
results
Ovesen and
Stromann (1972)
NAVFAC DM
7.02 (1986)
BS 8006 (1995)
Ghaly
(1997)
Bowles
(1997)
Naser
(2006)
Jadid et al.
(2017)
Pu
(kN)
Pu
(kN)
% error
Pu
(kN)
% error
Pu
(kN)
% error
Pu
(kN)
%
error
Pu
(kN)
% error
Pu
(kN)
% error
Pu
(kN)
% error
Duncan
and Mokwa
(2001)
410.0
427.0
4.1
768.0
87.3
735.0
79.2
190.0
-53.6
233.0
-43.2
297.0
-27.6
396.0
-3.4
1.3
1.9
46.1
1.8
38.5
1.9
46.2
1.0
-23.1
0.6
-53.8
1.3
0.0
1.2
-7.7
Naser
(2006)
2.3
2.0
-13.0
2.0
-13.0
2.2
-4.3
1.1
-52.2
0.7
-69.6
1.5
-34.8
1.4
-39.1
0.71
1.5
114.3
1.1
57.1
1.2
71.4
0.6
-14.3
0.4
-42.9
0.8
14.3
0.7
0.0
Khan et al.
(2017)
1.9
2.2
15.8
1.5
-21.1
2.2
15.8
2.1
10.5
0.6
-68.4
1.8
-5.3
1.1
-42.1
2.1
3.1
47.6
3.0
42.9
3.1
47.6
1.8
-14.3
0.9
-57.1
3.6
71.4
1.7
-10.5
2.3
3.5
52.2
3.8
65.2
3.6
56.5
1.9
-17.4
1.0
-56.5
4.4
91.3
2.0
-13.0
1Pullout resistance at 100% saturated condition
Table 6 Cumulative frequency distribution of the available pullout capacity prediction models
Absolute
% error
Ovesen and
Stromann (1972)
NAVFAC DM 7.02
(1986)
BS 8006
(1995)
Ghaly
(1997)
Bowles
(1997)
Naser
(2006)
Jadid et al. (2017)
Freq-
ency
Cum.
Freq-
Ency
Freq-
ency
Cum.
Freq-
ency
Freq-
Ency
Cum.
Freq-
ency
Freq-
Ency
Cum.
Freq-
ency
Freq-
ency
Cum.
Freq-
ency
Freq-
ency
Cum.
Freq-
ency
Freq-
ency
Cum.
Freq-
ency
0-10
1
1
0
0
1
1
0
0
0
0
2
2
3
3
10-20
2
3
1
1
1
2
4
4
0
0
1
3
2
5
20-30
0
3
1
2
0
2
1
5
0
0
1
4
0
5
30-40
0
3
1
3
0
2
0
5
0
0
1
5
1
6
40-50
2
5
1
4
2
4
0
5
2
2
0
5
1
7
>50
2
7
3
7
3
7
2
7
5
7
2
7
0
7

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
Table 7 Goodness of fits for different methods
From experimental investigation, Khan et al. (2017) observed significant discrepancy between experimental
results and predictions of passive resistance coefficient using Hansen (1966) model. From a statistical point of
view, Jadid et al. (2017) give an absolute error in the range, 0 to 15% in 5 out of 7 cases. For the remaining cases,
it underestimates the actual results by 30% to 45%. Table 7 shows that Jadid et al. (2017) gives the best result in
all six goodness of fits. BS 8006 (1995) method is comparatively better than other methods except Jadid et al.
(2017), as it produces the best result after Jadid et al. (2017) according to Root Mean Square Error (RMSE),
McFadden’s Pseudo R-square, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).
6. Conclusions
After comparing the data obtained from the experimental investigations and from the different theoretical methods,
the following principal conclusions are made.
• Jadid et al. (2017) method seemed to predict the pullout capcity of an anchor block more accurately than
any other methods according to different six statistical goodness of fits since their method was devised
exclusively for an anchor block. In addition, the water table correction is also properly accounted for in
this method. BS 8006 (1995) comes second to Jadid et al. (2017) in terms of predicting the pullout capacity
of anchor block according to four different statistical parameters.
• The accuracy of the Ghaly’s (1997) empirical method was found to be satisfactory with the experimental
studies for sandy soil. Due to its simplicity and computational efficiency, it can be used for a rough
estimation of the pullout capacity of an anchor block.
• Bowles’s (1997) method considered plain strain condition to develop his theory which is the case for strip
anchor. Thus, it is probably not suitable for an anchor block where the different end condions due to 3-D
effect needs to be considered.
• Ovesen and Stromann’s (1972) method can be used when the anchor is heavy (e.g., strip anchor) which
causes the development of friction between wall and soil.
Goodness
of
Fits
Ovesen and
Stromann
(1972)
NAVFAC
DM
7.02
(1986)
BS 8006
(1995)
Ghaly
(1997)
Bowels
(1997)
Naser
(2006)
Jadid et al.
(2017)
Mean
Absolute
Percentage
Error
(MAPE)
41.9
46.4
45.9
26.5
55.9
35
16.5*
Root Mean
Square
Error
(RMSE)
0.523
0.461
0.369
0.949
0.386
1.612
0.361*
McFadden's
Pseudo
R-square
0.99999042
0.9999926
0.9999952
0.9999685
0.9999948
0.999909
0.9999954*
Akaike
Information
Criterion
(AIC)
14.4
12.7
9.6
22.8
10.2
30.2
9.2*
Bayesian
Information
Criterion
(BIC)
14.3
12.5
9.4
22.6
10.02
30.04
9.1*
Nash-
Sutcliffe
Model
Efficiency
Co-efficient
0.998
0.103
0.261
0.661
0.781
0.911
0.999*

Proceedings of the 5th International Conference on Advances in Civil Engineering (ICACE 2020)
4-6 March 2021, CUET, Chattogram-4349, Bangladesh
Imam, Rahman and Pal (eds.)
Rigorous experimental, theoretical, and numerical studies should be conducted focusing anchor blocks, as the
present state of the art does not warrant the use of anchor plate theories to analyse anchor block behaviour.
Sufficient field observations are required to develop confidence among the users about the suitability of different
methods mentioned in this paper. The authors hope that this paper will be useful to all those dealing with civil
engineering projects and research works on the anchored retaining wall. This article will also be helpful to those
who are involved in the development of standards for the determination of horizontal pullout capacity of an anchor
block embedded in cohesionless soil.
7. Acknowledgement
We thank Mr Azmayeen Rafat Shahriar, graduate student in the North Carolina State University, Raleigh, United
States, Mr Rowshon Jadid, graduate teaching and research assistant in the North Carolina State University,
Raleigh, United States, and Mr Tanvir Imtiaz, research assistant in the University of Texas at Arlington, United
States, for their valuable inputs throughout this research work.
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