11
ORIGINAL PAPER Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand Adel Hanna Adolfo Foriero Tahar Ayadat Received: 27 June 2013 / Accepted: 26 February 2014 Ó Indian Geotechnical Society 2014 Abstract Experimental and analytical investigations on the pull-out capacity of inclined shallow strip plate anchors in sand were conducted. Experimentally, a prototype set-up was developed to measure the pull-out load and displace- ment of anchor plates in dense sand and further to depict the failure mechanism of the anchor and the soil mass. Analytically, the concept of the plastic limit equilibrium method of analysis was used to develop the analytical model that would utilize the failure mechanism observed during the present experimental investigation. In this investigation, the effect of dilatancy for dense sand, plate flexibility, and shape factor were examined. After validat- ing the developed theory with the present experimental results and the available data in the literature, the analytical model was used to develop data for a wide range of anchor inclination/soil/geometry conditions. Design procedure is recommended for the use of practicing engineers. Keywords Pull-out capacity Shallow anchors Inclined anchor Experimental investigation Failure mechanism Limit equilibrium method of analysis Sand Geotechnical engineering Introduction Quite often, foundations are designed to resist pullout forces; for example guyed transmission towers, penstock anchor blocks, airport hangars, wind loads on tall struc- tures, hydrostatic uplift due to flooding, earthquake, ice forces, impact from ships on shore structures, to name a few. These types of foundations rely heavily on the mobilized passive earth pressures of soils as the main source for resisting these loading conditions. The pullout capacity of earth anchors has been investi- gated by several researchers; these include: circular plate anchors [12, 15, 18], square and rectangular plate anchors [10, 11, 15, 21], strip and slab anchors [3, 14, 15], and screw anchors [47, 9]. Experimental Investigation Figure 1 presents a sketch the case under investigation. The set-up comprised of an instrumented plate anchor con- nected to a rod and the loading system, and Plexiglas tank, which allows observation during loading and tracing the rupture mechanism of the anchor/soil mass at failure. The inside dimensions of the tank were 150, 1200 and 1000 mm in width, length and height, respectively. Fig- ure 2 presents a schematic diagram of the experimental set- up used in this investigation. Sand placing technique was developed and calibrated in the laboratory for consistency and reproducibility of the desired unit weight of the sand in the testing tank. The test commenced with the placement of the anchor in the testing tank and then spreading the sand from a predetermined height. Once the tank was full, the loading system was connected to a rigid frame, capable of applying a pullout A. Hanna (&) T. Ayadat Department of Building, Civil and Environmental Engineering, Concordia University, 1455 DeMaisonneuve Blvd, West Montreal, QC H3G 1M8, Canada e-mail: [email protected]; [email protected] T. Ayadat e-mail: [email protected] A. Foriero Department of Civil Engineering, Faculty of Science and Engineering, University of Laval, Quebec, QC G1K 7P4, Canada e-mail: [email protected] 123 Indian Geotech J DOI 10.1007/s40098-014-0113-7

Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

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Page 1: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

ORIGINAL PAPER

Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

Adel Hanna • Adolfo Foriero • Tahar Ayadat

Received: 27 June 2013 / Accepted: 26 February 2014

� Indian Geotechnical Society 2014

Abstract Experimental and analytical investigations on

the pull-out capacity of inclined shallow strip plate anchors

in sand were conducted. Experimentally, a prototype set-up

was developed to measure the pull-out load and displace-

ment of anchor plates in dense sand and further to depict

the failure mechanism of the anchor and the soil mass.

Analytically, the concept of the plastic limit equilibrium

method of analysis was used to develop the analytical

model that would utilize the failure mechanism observed

during the present experimental investigation. In this

investigation, the effect of dilatancy for dense sand, plate

flexibility, and shape factor were examined. After validat-

ing the developed theory with the present experimental

results and the available data in the literature, the analytical

model was used to develop data for a wide range of anchor

inclination/soil/geometry conditions. Design procedure is

recommended for the use of practicing engineers.

Keywords Pull-out capacity � Shallow anchors �Inclined anchor � Experimental investigation �Failure mechanism � Limit equilibrium method of analysis �Sand � Geotechnical engineering

Introduction

Quite often, foundations are designed to resist pullout

forces; for example guyed transmission towers, penstock

anchor blocks, airport hangars, wind loads on tall struc-

tures, hydrostatic uplift due to flooding, earthquake, ice

forces, impact from ships on shore structures, to name a

few. These types of foundations rely heavily on the

mobilized passive earth pressures of soils as the main

source for resisting these loading conditions.

The pullout capacity of earth anchors has been investi-

gated by several researchers; these include: circular plate

anchors [12, 15, 18], square and rectangular plate anchors

[10, 11, 15, 21], strip and slab anchors [3, 14, 15], and

screw anchors [4–7, 9].

Experimental Investigation

Figure 1 presents a sketch the case under investigation. The

set-up comprised of an instrumented plate anchor con-

nected to a rod and the loading system, and Plexiglas tank,

which allows observation during loading and tracing the

rupture mechanism of the anchor/soil mass at failure. The

inside dimensions of the tank were 150, 1200 and

1000 mm in width, length and height, respectively. Fig-

ure 2 presents a schematic diagram of the experimental set-

up used in this investigation.

Sand placing technique was developed and calibrated in

the laboratory for consistency and reproducibility of the

desired unit weight of the sand in the testing tank. The test

commenced with the placement of the anchor in the testing

tank and then spreading the sand from a predetermined

height. Once the tank was full, the loading system was

connected to a rigid frame, capable of applying a pullout

A. Hanna (&) � T. Ayadat

Department of Building, Civil and Environmental Engineering,

Concordia University, 1455 DeMaisonneuve Blvd, West

Montreal, QC H3G 1M8, Canada

e-mail: [email protected]; [email protected]

T. Ayadat

e-mail: [email protected]

A. Foriero

Department of Civil Engineering, Faculty of Science and

Engineering, University of Laval, Quebec, QC G1K 7P4, Canada

e-mail: [email protected]

123

Indian Geotech J

DOI 10.1007/s40098-014-0113-7

Page 2: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

load up to 2,500 N through a guiding hole, at any desired

anchor inclination. The pull-out load was applied through a

motorized screw jack with a 75 mm maximum travel,

mounted on a steel plate bolted onto the testing frame. The

combination of a gear shift, a gear reducer and an elec-

tronic speed-controlled device provided the screw jack

with a loading and unloading speed varying from 2.5 to

25 mm/min.

The model anchor was made of a square aluminium

plate 150 mm 9 150 mm. Pressure transducers were

placed flush on the surface facing the sand, in circular

openings cut out of the plate. The transducers were to

measure the earth pressure on the anchor plate during pull-

out loading and accordingly, the pressure distribution on

the plate. The plate was covered with sandpaper to ensure

that the surface characteristics of the plate remained con-

sistent during testing. A hollow steel rod, 25 mm outer

diameter was rigidly connected to the center of the plate

and the loading system, which house the wires connecting

the transducers to the data acquisition system.

The sand used in the investigation is known commer-

cially as ‘‘Morie Sand’’, which is classified as medium sand

with a uniformity coefficient of 1.45. The sand was tested

at a relative density of 63.3 % (dry unit weight

cd = 16.7 kN/m3), which correspond to an angle of

shearing resistance of u = 41.2�, which was obtained from

the test results on direct shear test. Table 1 summarizes the

physical properties of the sand.

Test Results

Table 2 summarizes the testing program and the measured

ultimate pullout load. Figure 3 presents typical test results in

the form of pullout load versus axial displacement. It can be

noted that the pullout capacity increases with the increase of

the inclination angle a of the rod with the vertical, up to a value

of 90�, at which the plate functions as a retaining wall. Fur-

thermore, the pullout capacity Qu increases with the increase

of the ratio H1

B

� �or H2

B

� �: In this investigation, the pullout

capacity Qu was determined from the load–displacement

curve, as the point at which the curve exhibits a peak value or

at the point beyond which the displacement continues to

increase without any increase in the pullout load.

Figure 4 presents test results in the form of the pullout

capacity Qu versus Uf. It can be noted that the pullout

capacity Qu increases with the increase of the angle of

inclination a. This behaviour confirms the finding of Ghaly

and Clemence [4] for shallow and deep inclined anchors in

Sand

H1

H2

H

Q

α

B

Fig. 1 Single plate anchor in sand

1.22m

1.016m

0.61m

Spacing 76mmHoles 14.3mm dia.

Channel section

Steel wire

Rod

LoadCell

Spacing 51mmHoles 14.3mm dia.

ChannelSection

Sand

Anchor

Fig. 2 Schematic diagram of

the experimental setup

Indian Geotech J

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Page 3: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

sand. Based on the result of the present experimental

investigation, the following relationship was proposed:

Qu ¼ 63 � e0:1Uf : ð1ÞFigure 5 presents test results in the form of the passive

earth pressure distribution on the plate as deduced from the

transducers’ readings for an inclination angle a equal 60�

with the vertical. It can be noted as expected that the

bottom edge of the plate is always subjected to higher

pressure compared to the top edge, and accordingly the

failure mechanism starts at the bottom edge of the anchor

and propagates upwards until it reaches the ground level.

This finding confirms our observations during the present

experimental program. Furthermore, it was noted that the

Fig. 3 Pullout load versus axial

displacement (H2/B = 3)

Table 1 Properties of sand

Specific

gravity, Gs

Uniformity

coefficient, Cu

Curvature

coefficient, Cc

Void ratio Grain diameter

Maximum, emax Minimum, emin D10 D30 D60

2.66 1.45 1.24 0.815 0.590 0.82 1.10 1.19

Table 2 Experimental results:

ultimate pullout load (Qu) for

different inclination angles and

the H1/B ratio (u = 41.2�)

Inclination

angle, a (�)

H2/B B (mm) Ultimate pullout

load, Qu (N)

H2/B B (mm) Ultimate pullout

load, Qu (N)

0 2 152.5 255.52 3.25 101.5 235.56

30 289.52 261.12

45 483.24 440.72

60 839.98 783.99

90 1,513.89 1,534.99

0 3 152.5 403.53 4.75 101.5 392.13

30 456.08 461.95

45 771.36 760.91

60 1,176.06 1,435.04

90 2,397.79 –

0 4 152.5 630.16 6.25 101.5 570.61

30 787.07 687.92

45 1,260.77 1,178.04

60 2,334.03 2,278.79

90 – –

Indian Geotech J

123

Page 4: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

rupture surface was roughly a truncated conical shape,

which is further deflated at an increase in the angle of

inclination of the anchor. A similar observation was

reported by Frydman and Shaham [3], for the cases of

a = 30�, 45� and 60� (H2/B B6).

Theoretical Model

The observed rupture surface for inclined anchors sub-

jected to pullout load was idealized by two planes; the first

plane is parallel to the anchor rod and includes the bottom

edge of the plate, while the second is a plane making an

angle b, with the ground surface and includes the top edge

of the plate (Fig. 6). The angle b depends on the inclination

angle (a) of the anchor and the angle of shearing resistance

(u) of the sand having a maximum value of p2þ a:

In developing the theoretical model, it was assumed that

the anchor’s plate to be thin and rigid (so that its deformation

was negligible), and during testing it was in full contact with

the surrounding sand. Furthermore, the frictions between the

sand and the tie-rod and the plate surfaces were small enough

to be neglected; in addition, the anchor system was weight-

less for the purpose of evaluating the pullout capacity of the

anchor. The sand was assumed to be homogeneous, isotropic

and behaves as a rigid perfectly-plastic material.

Fig. 4 Pullout capacity versus

displacement at failure

Fig. 5 Distribution of passive earth pressure on the plate edges at

different anchor displacements (a = 60� and H2/B = 3) Fig. 6 Assumed failure surface for the present theory

Indian Geotech J

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Page 5: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

The average mobilized angle of shearing resistance on

the assumed failure plane was taken as dm, where dmB u[8]. The forces acting on the assumed failure surfaces were

the total passive earth force pressures P1 and P2 inclined at

an average angle dm (Fig. 6). Therefore, for a strip anchor

plate of length H, inclined at an angle a, the ultimate

pullout load can be given as:

Qu ¼ QP1Zþ QP2Z

þ QWZ; ð2Þ

where

QP1Z¼ P1 sin dm; ð3Þ

QP2Z¼ P2 cos dm þ b� að Þ; ð4Þ

QWZ¼ W cos a; ð5Þ

where Qu is the ultimate pullout load of the anchor and W is

the weight of the wedge within the failure planes.

Substituting the values of P1, P2 and W in Eqs. (3)–(5),

respectively, the following equation can be obtained:

QP1Z¼ 1

2Kp

0

1 � c � L21 � sin dm; ð6Þ

QP2Z¼ 1

2Kp

0

2 � c � L22 � cos dm þ b� að Þ; ð7Þ

QWZ¼ c

�H1

cos a� B

4þ H � B

4þ H2 sin 2a

4þ H2

B

4cos a

þH � ðcos aÞ2 B

4þ H2

2 cot b2

�cos a: ð8Þ

Substituting Eqs. (6)–(8) in Eq. (2), thus:

Qu ¼1

2R1 � Kp1 � c � L2

1 � sin dm þ1

2R2 � Kp2 � c � L2

2�

cos dm þ b� að Þ

þ c

�H1

cos a� B

4þ H � B

4þ H2 sin 2a

4þ H2

B

4cos a

þH � ðcos aÞ2 B

4þ H2

2 cot b2

�cos a; ð9Þ

where c is the unit weight of sand

H1 ¼ H � cos aþ B

2� sin a; ð10Þ

H2 ¼ H � cos a� B

2� sin a; ð11Þ

L1 ¼H1

cos a; ð12Þ

L2 ¼H2

sin b; ð13Þ

Kp1 and Kp2 are the coefficients of passive earth pressure

which correspond to the angle of shearing resistance u (dm/

u = 1) and walls inclined at angles -a and ?h,

respectively.

R1 and R2 are the reduction factors which depend on the

ratio dm

u :

The parameters R1, R2, Kp1 and Kp2 were taken from the

Tables of Caquot and Kerisel [2].

Equation (9) can be written in the following form:

qu ¼Qu

B¼ 1

2c � B � Nc þ c � D � Nq; ð14Þ

Where D = H�cosa Nc and Nq are the pullout capacity

factors, representing the contribution of c and q (q = c�D),

respectively, where:

Nc ¼ R1 � Kp1 �L2

1

B2� sin dm þ R2 � Kp2 �

L22

B2

� cos dm þ b� að Þ; ð15Þ

Nq ¼H1

4H � cos aþ 1

4þ H � sin 2a

4 � B þ H2

4H� cos aþ ðcos aÞ2

4

þ H22 cot b

2H � B :

ð16Þ

It can be noted that the ultimate pull-out load Qu of an

inclined anchor in sand depends on the values of the angles

b and dm.

The ultimate pullout load of the anchor given by Eq. (9)

was minimized with respect to the angle b using MAT-

LAB. The derivation oQu

ob ¼ 0 was then solved numerically

using the method of Newton–Raphson for different

anchor’s geometry (H and B), angle of shearing resistance

of the sand (u), angle of anchor inclination (a), and average

of locally mobilized angle of shearing resistance (dm). The

analysis showed that the minimum values of the computed

Qu, for all iterations, were found to correspond to the angle

b given by

b ¼ p2þ a� dm: ð17Þ

The locally mobilized angle of shearing resistance (dz) on

the assumed failure plane varied from a maximum value of

(u) at the anchor’s toe, where both the assumed and actual

failure planes coincided to a minimum value at ground

level [8]. The results of the present experimental investi-

gation were substituted in the left-hand side of Eq. (9), and

Eqs. (6)–(8) were used to evaluate the right hand side. This

procedure continued by trial and error until the two sides of

Eq. (9) agreed. A computer program was coded to conduct

the aforementioned calculation. Based on the results

obtained, it is of interest to note that the ratio dm/u is

independent of the ratio H2/B.

Based on the results obtained, it is of interest to note that

the ratio dm/u is independent of the ratio H2/B; further-

more, the relationship between dm/u and the inclination

angle a was found to be exponential with an average

coefficient of determination R2 higher than 0.96. The ratio

Indian Geotech J

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Page 6: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

Table 3 Values of the parameters a and b for different values of the angle of shearing (u)

u (�) 20 25 30 35 40 45

a 0.436 0.322 0.252 0.177 0.118 0.079

b 0.277 0.441 0.544 0.781 1.055 1.343

Table 4 Pullout capacity factor Nc

a (�) u (�) H/B

1 2 3 4 5 6

10 20 0.06 0.21 0.46 0.81 1.25 1.80

25 0.07 0.28 0.60 1.06 1.64 2.34

30 0.10 0.38 0.84 1.46 2.27 3.25

35 0.13 0.48 1.05 1.84 2.84 4.07

40 0.15 0.56 1.23 2.15 3.33 4.77

45 0.16 0.58 1.28 2.24 3.47 4.97

20 20 0.08 0.26 0.54 0.94 1.44 2.06

25 0.11 0.37 0.79 1.37 2.11 3.00

30 0.17 0.57 1.22 2.11 3.24 4.61

35 0.24 0.83 1.76 3.04 4.67 6.64

40 0.33 1.13 2.41 4.16 6.38 9.08

45 0.42 1.41 3.01 5.20 7.98 11.36

30 20 0.09 0.28 0.58 0.98 1.50 2.12

25 0.14 0.45 0.93 1.58 2.40 3.39

30 0.24 0.75 1.54 2.62 3.99 5.64

35 0.38 1.21 2.50 4.26 6.47 9.15

40 0.60 1.90 3.92 6.67 10.14 14.34

45 0.89 2.81 5.80 9.87 15.01 21.22

40 20 0.10 0.29 0.58 0.96 1.45 2.03

25 0.17 0.51 1.01 1.69 2.54 3.57

30 0.31 0.91 1.83 3.05 4.58 6.43

35 0.58 1.69 3.38 5.64 8.48 11.90

40 1.06 3.09 6.17 10.31 15.50 21.75

45 1.93 5.61 11.21 18.72 28.15 39.50

50 20 0.11 0.28 0.54 0.89 1.31 1.82

25 0.21 0.56 1.07 1.75 2.59 3.61

30 0.42 1.11 2.12 3.47 5.14 7.15

35 0.92 2.43 4.67 7.63 11.31 15.72

40 2.09 5.54 10.62 17.35 25.72 35.74

45 5.19 13.74 26.36 43.06 63.83 88.68

60 20 0.12 0.27 0.49 0.78 1.14 1.56

25 0.27 0.64 1.16 1.84 2.67 3.66

30 0.62 1.46 2.65 4.19 6.10 8.35

35 1.81 4.27 7.76 12.30 17.88 24.49

40 6.10 14.39 26.18 41.48 60.27 82.58

45 26.69 62.95 114.54 181.46 263.71 361.28

Indian Geotech J

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Page 7: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

dm/u was then expressed in terms of the angle a by the

following equation:

dm

u¼ a � eb tan a; ð18Þ

where a and b are the parameters, which depend on the

angle of shearing resistance (u) of sand (Table 4).

Moreover, the following expressions were deduced for a

and b:

a ¼ �0:36Lnðtan uÞ þ 0:06; ð19Þb ¼ 1:69 � tan u� 0:37: ð20Þ

The deduced values of Nc and Nq are given in Tables 3 and 4,

and in graphical form in Figs. 7 and 8, respectively. It can be

noted that the value of Nc is highly influenced by the angle of

shearing resistance u, notably for high values of a, while, the

influence is less visible for the ratio H2/B. However, the

factor Nq is not affected by the angle u notably for H2/B B 3,

while it is influenced by the ratio H2/B.

Comparisons between the theoretical values of the

present investigation and the data available in the literature

are presented in Tables 5 and 6, where good agreement can

be noted (Table 7).

0

5

10

15

20

25

30

35

40

45

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Ratio H2 /B

Fac

tor

φ = 20°φ = 25° φ = 30°φ = 35°φ = 40°φ = 45°

Fig. 7 Factor Nc versus the

ratio H2/B for different angle of

shearing resistance, u (angle of

inclination, a = 40�)

1.17

1.22

1.27

1.32

1.37

1.42

1.47

1.52

3 3.5 4 4.5 5 5.5 6

Ratio H2 /B

Fac

tor

Nq

α = 10°α = 20°α = 30°α = 40°α = 50°α = 60°

Fig. 8 Factor Nq versus the

ratio H2/B for different angle of

shearing resistance, a (angle of

inclination, u = 35�)

Indian Geotech J

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Page 8: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

Design Procedure

The following procedure is recommended to predict the

ultimate pullout load of single inclined shallow anchors in

sand:

(1) Given the height (H) and the base diameter or width

(B) of the anchor, calculate the embedment depth (H2)

and then the depth ratio H2

B: The anchor is considered

to be shallow if its embedment depth ratio C6.

(2) Knowing the inclination of the anchor (a) and the

angle of shearing resistance of the sand (u), estimate

the value of the average mobilized shearing resistance

on the failure planes (dm) using Eq. (19).

Table 5 Pullout capacity factor Nq

a (�) u (�) H/B

1 2 3 4 5 6

10 20 1.07 1.14 1.22 1.30 1.38 1.46

25 1.06 1.14 1.21 1.28 1.36 1.43

30 1.06 1.13 1.20 1.27 1.34 1.42

35 1.05 1.11 1.17 1.23 1.29 1.36

40 1.04 1.09 1.14 1.19 1.24 1.28

45 1.03 1.07 1.11 1.15 1.19 1.23

20 20 1.05 1.13 1.21 1.29 1.37 1.45

25 1.05 1.13 1.21 1.29 1.36 1.44

30 1.05 1.13 1.20 1.28 1.36 1.43

35 1.05 1.11 1.18 1.25 1.32 1.39

40 1.04 1.10 1.15 1.21 1.27 1.33

45 1.03 1.08 1.13 1.18 1.23 1.28

30 20 1.04 1.12 1.20 1.28 1.36 1.44

25 1.04 1.12 1.20 1.28 1.37 1.45

30 1.04 1.12 1.20 1.28 1.37 1.45

35 1.04 1.11 1.19 1.27 1.35 1.42

40 1.04 1.10 1.17 1.24 1.31 1.38

45 1.03 1.09 1.15 1.22 1.28 1.34

40 20 1.03 1.10 1.19 1.27 1.35 1.43

25 1.03 1.11 1.19 1.28 1.37 1.46

30 1.03 1.11 1.20 1.29 1.38 1.47

35 1.03 1.11 1.20 1.29 1.38 1.47

40 1.03 1.11 1.19 1.28 1.36 1.45

45 1.03 1.10 1.19 1.27 1.35 1.43

50 20 1.01 1.08 1.16 1.25 1.33 1.42

25 1.02 1.09 1.18 1.27 1.36 1.46

30 1.02 1.10 1.19 1.29 1.38 1.48

35 1.02 1.10 1.20 1.31 1.41 1.51

40 1.02 1.11 1.21 1.32 1.43 1.53

45 1.02 1.11 1.22 1.33 1.45 1.56

60 20 1.00 1.06 1.13 1.21 1.30 1.38

25 1.00 1.06 1.15 1.25 1.35 1.44

30 1.00 1.07 1.17 1.27 1.37 1.48

35 1.00 1.08 1.19 1.31 1.43 1.55

40 1.00 1.09 1.22 1.35 1.49 1.62

45 1.00 1.10 1.25 1.40 1.55 1.71

Indian Geotech J

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Page 9: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

Table 6 Comparison between

present experimental and

predicted results

Inclination

angle, a (�)

H2/B B (mm) Pullout capacity factor, Nq

Present experimental

results

Predicted

(proposed model)

0 2 152.5 1.23 1.34

30 2.86 3.02

45 3.22 3.55

60 4.46 4.89

0 3 152.5 1.68 1.87

30 3.51 3.88

45 4.09 4.56

60 6.37 6.79

0 4 152.5 2.08 2.67

30 4.31 4.86

45 5.26 5.91

60 8.14 8.88

0 3.25 101.5 1.81 2.05

30 3.74 4.13

45 4.42 4.87

60 6.98 7.43

0 4.75 101.5 2.87 3.32

30 5.12 5.74

45 6.13 6.87

60 9.04 9.67

0 6.25 101.5 3.73 4.16

30 7.86 8.34

45 10.11 10.77

60 18.56 19.24

Table 7 Comparison between predicted results and some experimental data reported in literature

References Inclination

angle, a (�)

H2/B Angle of shear

resistance, u (�)

Testing conditions

Measured Predicted* Test condition

Harvey and Burley [12]

(Circular plate anchor)

15

30

30

30

45

4.3

3.9

4.5

5.2

3.2

40 23

18.7

22.6

25.5

15.2

20.1

15.6

20.3

22.6

12.3

L

A

B

O

R

A

T

O

R

Y

Meyerhof [15]

(Circular plate anchor)

20

30

40

3

6

6

43 15.7

30.2

34.6

14.9

29.3

33.4

Tran-Vo-Nhiem and Biarez [19]

(Strip anchor)

50

70

3

3

26 5

7

5.8

7.8

Ghaly and Clemence [4]

(Screw anchor)

15

30

15

30

15

4

8

4

8

4

31

31

36

36

42

16.2

31.4

28.4

52.9

55.7

14.3

28.3

25.1

46.1

50.1

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Page 10: Pullout Capacity of Inclined Shallow Single Anchor Plate in Sand

(3) Calculate the value of b, in terms of a and dm, from

Eq. (16).

(4) Determine the values of Nc and Nq using Eqs. (14)

and (15) or from Tables 3 and 4, respectively.

(5) Knowing the unit weight of sand (c), estimate the

pullout capacity of the anchor (Qu) using Eq. (13).

(6) Determine the displacement at failure (Uf) using

Eq. (1).

Conclusions

Experimental and theoretical investigations on the ultimate

pullout load of shallow inclined strip anchors in sand were

conducted. Based on the results obtained, the following

conclusions were drawn:

(1) The relationship of pullout capacity (Pu) versus

displacement at failure (Uf) for shallow inclined

anchors installed at different soil/geometry/loading

conditions can be represented by a unique relationship.

(2) The displacement at failure (Uf) for shallow inclined

anchors installed in sand increases with the increasing

of the inclination of anchors.

(3) An empirical relationship was proposed between the

average mobilized angle of shear resistance along the

assumed failure planes (dm) and the angles of

inclination (a) and the peak of shear resistance (u).

(4) A reasonable agreement was noted between the results

produced by the predicted values and the present

experimental results and those available in the literature.

(5) Design procedure were presented for practical

purposes.

Acknowledgments The financial support from the Natural Science

and Engineering Research Council of Canada (NSERC) and Con-

cordia University are acknowledged.

References

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Table 7 continued

References Inclination

angle, a (�)

H2/B Angle of shear

resistance, u (�)

Testing conditions

Measured Predicted* Test condition

Kananyan [13]

(Circular plate anchor)

10

20

2.5

2.5

7.1

12.3

6.3

10.8

F

I

E

L

D

32

Adams and Klym [1]

(Multi-helix anchor)

0

0

6

8

35

45

46

70

40

60

Trofimenkov and Mariupolskii [20]

(Screw anchor)

45

45

6

6

30

35

20

40

14.2

29.7

Radhakrishna [16]

(Screw anchor)

40

40

17.0

16.5

35

35

47

55

42.6

47.6

Robinson and Taylor [17]

(Screw anchor)

10 12.7 30 21 16.8

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mast and tower foundations. In: Proceedings of the 6th

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neering, vol 2. Universite of Toronto Press, Toronto, pp 328–332

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Young RN, Selig ET (eds) Proceedings, application of plasticity

and generalized stress–strain in geotechnical engineering. ASCE,

Reston, VA, pp 291–307

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