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China Ocean Eng., Vol. 28, No. 1, pp. 115 – 126 © 2014 Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg DOI 10.1007/s13344-014-0009-4, ISSN 0890-5487 Uplift of Symmetrical Anchor Plates by Using Grid-Fixed Reinforced Reinforcement in Cohesionless Soil * Hamed Niroumand 1 and Khairul Anuar Kassim Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Technology Malaysia, Johor 81310, Malaysia (Received 2 November 2012; received revised form 12 May 2013; accepted 23 July 2013) ABSTRACT Uplift response of symmetrical anchor plates with and without grid fixed reinforced (GFR) reinforcement was evaluated in model tests and numerical simulations by Plaxis. Many variations of reinforcement layers were used to reinforce the sandy soil over symmetrical anchor plates. In the current research, different factors such as relative density of sand, embedment ratios, and various GFR parameters including size, number of layers, and the proximity of the layer to the symmetrical anchor plate were investigated in a scale model. The failure mechanism and the associated rupture surface were observed and evaluated. GFR, a tied up system made of fiber reinforcement polymer (FRP) strips and end balls, was connected to the geosynthetic material and anchored into the soil. Test results showed that using GFR reinforcement significantly improved the uplift capacity of anchor plates. It was found that the inclusion of one layer of GFR, which rested directly on the top of the anchor plate, was more effective in enhancing the anchor capacity itself than other methods. It was found that by including GFR the uplift response was improved by 29%. Multi layers of GFR proved more effective in enhancing the uplift capacity than a single GFR reinforcement. This is due to the additional anchorage provided by the GFR at each level of reinforcement. In general, the results show that the uplift capacity of symmetrical anchor plates in loose and dense sand can be significantly increased by the inclusion of GFR. It was also observed that the inclusion of GFR reduced the requirement for a large L/D ratio to achieve the required uplift capacity. The laboratory and numerical analysis results are found to be in agreement in terms of breakout factor and failure mechanism pattern. Key words: grid fixed reinforced (GFR); Plaxis; fiber reinforcement polymer (FRP); uplift response; anchor plate 1. Introduction A foundation system that resists vertical or horizontal uplift loads needs to be considered in the design of many structures. As part of a large effort to improve the performance of foundation systems, the development of guidelines for an anchor system design and installation needs to be focused on. Different structures like transmission towers, tunnels, sea walls, buried pipelines, retaining walls etc. are subjected to considerable uplift forces. In such cases, an absorbing and economical design solution may be obtained through the use of tension members. These elements, which are regarded as anchors, are usually fixed to the structure and embedded in the ground at an effective depth so that they can resist uplifting forces safely. Many researchers have investigated the influence of different parameters on the uplift response of horizontal anchors in sand. Researchers such as Mors (1959), Giffels et al. * This research was partially supported by the research Grant at UTM, Malaysia (GUP Grant), and the project name is "uplift response of symmetrical anchor plates in grid fixed reinforced in cohesionless soil". 1 Corresponding author, Post-doc. E-mail: [email protected]
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China Ocean Eng., Vol. 28, No. 1, pp. 115 – 126 © 2014 Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg DOI 10.1007/s13344-014-0009-4, ISSN 0890-5487

Uplift of Symmetrical Anchor Plates by Using Grid-Fixed Reinforced

Reinforcement in Cohesionless Soil*

Hamed Niroumand1 and Khairul Anuar Kassim

Department of Geotechnical Engineering, Faculty of Civil Engineering,

University of Technology Malaysia, Johor 81310, Malaysia

(Received 2 November 2012; received revised form 12 May 2013; accepted 23 July 2013)

ABSTRACT

Uplift response of symmetrical anchor plates with and without grid fixed reinforced (GFR) reinforcement was

evaluated in model tests and numerical simulations by Plaxis. Many variations of reinforcement layers were used to

reinforce the sandy soil over symmetrical anchor plates. In the current research, different factors such as relative density

of sand, embedment ratios, and various GFR parameters including size, number of layers, and the proximity of the layer

to the symmetrical anchor plate were investigated in a scale model. The failure mechanism and the associated rupture

surface were observed and evaluated. GFR, a tied up system made of fiber reinforcement polymer (FRP) strips and end

balls, was connected to the geosynthetic material and anchored into the soil. Test results showed that using GFR

reinforcement significantly improved the uplift capacity of anchor plates. It was found that the inclusion of one layer of

GFR, which rested directly on the top of the anchor plate, was more effective in enhancing the anchor capacity itself than

other methods. It was found that by including GFR the uplift response was improved by 29%. Multi layers of GFR

proved more effective in enhancing the uplift capacity than a single GFR reinforcement. This is due to the additional

anchorage provided by the GFR at each level of reinforcement. In general, the results show that the uplift capacity of

symmetrical anchor plates in loose and dense sand can be significantly increased by the inclusion of GFR. It was also

observed that the inclusion of GFR reduced the requirement for a large L/D ratio to achieve the required uplift capacity.

The laboratory and numerical analysis results are found to be in agreement in terms of breakout factor and failure

mechanism pattern.

Key words: grid fixed reinforced (GFR); Plaxis; fiber reinforcement polymer (FRP); uplift response; anchor plate

1. Introduction

A foundation system that resists vertical or horizontal uplift loads needs to be considered in the

design of many structures. As part of a large effort to improve the performance of foundation systems,

the development of guidelines for an anchor system design and installation needs to be focused on.

Different structures like transmission towers, tunnels, sea walls, buried pipelines, retaining walls etc.

are subjected to considerable uplift forces. In such cases, an absorbing and economical design solution

may be obtained through the use of tension members. These elements, which are regarded as anchors,

are usually fixed to the structure and embedded in the ground at an effective depth so that they can

resist uplifting forces safely. Many researchers have investigated the influence of different parameters

on the uplift response of horizontal anchors in sand. Researchers such as Mors (1959), Giffels et al.

                                                            * This research was partially supported by the research Grant at UTM, Malaysia (GUP Grant), and the project name is "uplift response

of symmetrical anchor plates in grid fixed reinforced in cohesionless soil". 1 Corresponding author, Post-doc. E-mail: [email protected]

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 116

(1960), Balla (1961), Turner (1962), Ireland (1963), Sutherland (1965), Mariupolskii (1965),

Kananyan (1966), Baker and Konder (1966), Adams and Hayes (1967), Andreadis et al. (1981),

Dickin (1988), Frydman and Shaham (1989), Remesh Babu (1998), Krishna (2000), Frgić et al. (2003),

Merifield and Sloan (2006), Dickin and Laman (2007), Kumar and Bhoi (2008), and Kuzer and Kumar

(2009) were interested in the universal solution especially for an ultimate uplift capacity based on

experimental works in sand. Increasing the use of symmetrical anchor plates to resist uplift response

may be achieved by increasing the size and depth of an anchor or the improvement of soil in which

these anchors are embedded, or both. In restricted situations, increasing the size and depth of an anchor

may not be economical compared with other alternatives. On the other hand, soil improvement can be

attained by the inclusion of soil reinforcement to resist large uplift forces. However, few investigations

on the behavior of horizontal plates in a reinforced soil bed under uplift loads have been reported.

Subbarao et al. (1988) studied the improvement in uplift capacity by using geotextiles as ties to

reinforced concrete model anchors embedded in sand. Selvadurai (1989, 1993) reported significant

enhancement, of the order of 80% to 100%, in the uplift capacity of pipelines embedded in fine and

coarse-grained soil beds reinforced by laying geogrids immediately above the pipeline in an inclined

configuration. Krishnaswamy and Parashar (1992, 1994) studied the uplift behavior of circular plates

and rectangular plates embedded in cohesive and cohesionless soils with or without geosynthetic

reinforcement and reported that the geocomposite reinforcement offered high uplift resistance than

geogrid and geotextile reinforcement. Ilamparuthi and Dickin (2001) investigated the influence of soil

reinforcement on the uplift behavior of model belled piles embedded in sand. A cylindrical gravel-

filled geogrid cell was placed around the enlarged pile base. It was reported that uplift response

increases with the diameter of the geogrid cell, sand density, pile bell diameter, and embedment. El

Sawwaf (2007) investigated the influence of soil reinforcement on the uplift behavior of plate anchors

in slopes. In summary, existing relevant works in the literature are mainly focused on the capacity of

symmetrical anchor plates embedded in non-reinforced soils with a horizontal ground surface.

However, few researches have focused on anchor plates embedded in reinforced soil. On the other

hand, to the knowledge of the authors, hardly any effort has been made so far to evaluate the

performance of a symmetrical anchor plate located in reinforced soil. Therefore, the effect of soil

reinforcement on the stability and rupture surface of the soil and, hence, on the symmetrical anchor

plate capacity is unclear. The current research describes insight into the effect of soil reinforcement on

the response of horizontal symmetrical anchor plates which were embedded adjacent to a soil surface.

The main objectives of this work are to study the optimum number, sizes and the best position of GFR

inclusion for enhancing the ultimate uplift response of a symmetrical anchor plate, as well as the

influence of embedment depth, soil density and breakout factors.

2. Methodology

The cohesionless soil placement is particularly important during uplift tests. Similar cohesionless

soil unit weights were used as a basis for comparing the influence of uplift parameters on the

symmetrical anchor plate capacity. A sand unit weight at a value of 15 kN/m3 was decided for sand in

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 117

loose packing, whereas sand in dense packing was defined as 17 kN/m3. The loose sand condition was

obtained using the sand raining technique. For the sand raining test, a range of sand falling heights

were employed in order to obtain the height required for the desired unit weight. A falling height of

450 mm for loose sand had to be maintained every 30 mm layer to achieve a dry unit weight of 15

kN/m3. For the dense sand, a compaction time of 2 min. per 50 mm layer was required. This

compaction time was expected to give a sand unit weight value of 17 kN/m3. Uplift tests were carried

out in two test boxes covering two separate areas. The first test box was used for failure tests and has

dimensions of 600 mm×250 mm and is 450 mm deep with side glass walls to enable observation of

sand movement and behavior. The second test box was used for uplift tests and has dimensions of 1000

mm ×500 mm and is 1200 mm deep.

3. Material Tests

Several tests were done to determine the properties of sand samples during experimental work.

Table 1 shows the soil properties, and Tables 2 and 3 show the plate and GFR properties.

Table 1 Material properties used in Plaxis

Parameter value Loose packing Dense packing

Cohesion, c (kPa) 0.5 0.5

Residual angle of internal friction (°) 38 44

Angle of dilatancy 8 14

Unit weight, (kN/m3) 15 17

Secant stiffness, E50 (kN/m2) 20000 30000

Initial stiffness, EOED (kN/m2) 20000 30000

Unloading/reloading stiffness, EUR (kN/m2) 60000 90000

Poisson’s ratio 0.2 0.2

Rinter 0.9 0.9

Table 2 GFR Properties

Geosynthetic type GFR

Polymer type FRP

GFR shape Spherical

Apparent diameter 10 mm

Table 3 Steel Plate Properties

Type Steel plates EI 163 kNm²/m EA 3.4105 kN/m

4. Experimental Test

The uplift test was conducted in the geotechnical laboratory at the University of Technology

Malaysia. The main treatment observed during experimental tests is the stress-displacement

relationship during symmetrical anchor plate breakout. The set up for the uplift test steps are described

in the following sections. A schematic experimental set up is shown in Fig. 1. The test boxes contained

cohesionless soil for the embedment pattern. The model’s symmetrical anchor plates were connected to

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 118

a pulling tendon cable for hoisting. A quasi static rate of pullout of approximately 1.5 mm/min was

used for every test. All factors should indicate that data obtained from the test are reliable before being

accepted for analysis. The effect of embedment ratio, plate sizes, sand density, vertical spacing of GFR

layers, GFR layer proximity to plates and number of GFR layers were investigated as illustrated in Fig.

2. Table 4 shows the test summary.

Fig. 1. Schematic of the uplift test. Fig. 2. Schematic of GFR layers in the uplift test.

Table 4 Summary of uplift tests and simulations conducted for various combinations of parameters

Item test Conditions Cohesion less soil types

Anchor plate sizes 50 mm, 75 mm, 100 mm, 200 mm, 300 mm

Non-reinforced

Anchor plate shapes Circular, Square, Srrip Non-reinforced

Sand unit weight Loose and Dense Non-reinforced

Anchor plate’s embedded ratio 1, 2, 3, and 4 Non-reinforced

Number and vertical spacing of GFR layers B/D=12, x/D=0–0.5, u/D=01

GFR-reinforced

GFR layer proximity to the anchor B/D=12, x/D=0–0.5 GFR-reinforced

5. Breakout Factor

The breakout factor was analyzed by use of Meyerhof and Adams’s (1968) equation:

2,L

P f LDD

, (1)

where P is the ultimate uplift load obtained from the test, D is the width of the anchor plate, H is the

embedded depth of the anchor plate, is the dry unit weight, is the internal friction angle, and L/D is

the embedment ratio. The internal friction angle is constant for loose and dense sand in the test.

6. Numerical Simulation

A series of two-dimensional finite element analyses (FEA) on a prototype symmetrical anchor

plate-sand system were performed in order to assess the experimental model tests’ results and find

out deformation’s behavior within the sand body. The analysis was performed under the finite

element program, Plaxis package (professional version 8, Bringkgreve and Vermeer, 1998). Plaxis is

geotechnical software that can analyze soil problems. In general, the initial conditions comprise the

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 119

initial groundwater conditions, the initial geometry configuration, and the initial effective stress state.

The sand layer in this research was dry, so there was no need to enter ground water conditions. The

analysis was done using the Hardening Soil Model (HSM). The geometry of the prototype anchor

plate-box system was supposed to be the same as the experimental model. The same gradient of

model test and steel plate material for the symmetrical anchor plate, GFR, and sand was used in the

prototype research. The software automatically produces 6 or 15 node triangle plane strain elements

for square and rectangular plates and axisymmetry for circular plates in the sand. The grid fixed

reinforced (GFR) were simulated by fixed end anchors. Springs were used as the fixed end anchors,

which simulate the tying of a single point. A fixed end anchor was presented as a rotated “T” (—|)

based on a special angle.

7. Results

A summary of uplift test results is presented in this part for symmetrical anchor plates based on

non-reinforced, and GFR reinforced in the simulation and experimental work. With reference to Fig. 3,

symmetrical anchor plates experience an increase in uplift capacity for every increase of symmetrical

circular anchor plate’s size. These increases are, however, non-linear for loose and dense packing in

sand. Fig. 4 illustrates symmetrical square anchor plates exhibiting non-linear increases for uplift

capacity in the symmetrical anchor plate’s length or diameter when placed in sand in loose packing.

For symmetrical anchor plates in dense packing, Fig. 5 illustrates symmetrical rectangular anchor

plates’ uplift response based on length. The increase in uplift capacity with the symmetrical anchor

plate’s size, regardless of packing conditions, is due to the increased lateral stresses acting on the

symmetrical anchor plates with the depth and increasing contact area between the symmetrical anchor

plates and the embedment media. This can be understood from the formula of the uplift response,

AH , where symmetrical anchor size is one of the parameters. Therefore, an increase of the

symmetrical anchor plate’s size would increase the uplift capacity, as given by Balla’s formula (1961),

AH . From Figs. 4 and 5, a geometric increase of uplift capacity in square and rectangular plates in

both loose and dense packing is evident.

Fig. 3. Variation of uplift capacity Q with symmetrical anchor Fig. 4. Variation of uplift capacity Q with symmetrical anchor plate size D for circular anchor plate at L/D=4 in loose plate size D for square anchor plate at L/D=4 in loose and dense sand. and dense sand.

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 120

As seen from Fig. 6, symmetrical anchor plates in the maximum embedment ratio, L/D=4, have

larger uplift capacities than symmetrical anchor plates in the minimum embedment ratio such as

L/D=1. The increases of breakout factor for symmetrical anchor plates embedded in loose sand

compared with dense sand are illustrated in Fig. 6. These increases are, however, non-linear for loose

and dense packing in sand.

Fig. 5. Variation of uplift capacity Q with symmetrical anchor Fig. 6. Variation of breakout factor Nq with embedment ratio plate size D for rectangular anchor plate at L/D=3 in L/D for symmetrical anchor plates in both loose and loose and dense sand. dense sand packing.

The discussion of uplift capacity of symmetrical anchor plates in reinforced sand involves a

separate analysis of the parameters of number of GFR layers, GFR layer length, GFR layer proximity

to the anchor and vertical spacing of the GFR layers. GFR as one type of geosynthetics was used in

this study. Typical physical and technical properties were obtained from the manufacturer’s data sheet

and are given in Table 1. This is to enable an impartial and focused review of the effect of each

parameter on the symmetrical anchor plate during the uplift test. One of the areas that need to be

considered is the effect of reinforced sand on symmetrical anchor plates. The uplift responses of the

symmetrical anchor plates with or without soil reinforcement (Pu and Po, respectively) were obtained

from the uplift load. Improvement of the symmetrical anchor plate’s capacity due to soil reinforcement

is represented using a non-dimensional factor, called the symmetrical anchor plate capacity ratio (El

Sawwaf, 2007), to assist the comparison of the test results. This factor (ACR) is defined as the ratio of

the symmetrical anchor plate’s ultimate capacity with soil reinforcement, Pu-reinforced, to the ultimate

capacity of symmetrical anchor plate in tests without soil reinforcement, Po. These results are

discussed in the following sections. In this study, GFR length (B) was not kept constant and the

number of GFR layers varied for researches. Figs. 7 and 8 illustrate the performance of the GFR at

various x/D.

With reference to Figs. 9 and 10, tests were performed to study the effect of reinforced sand with

various numbers of GFR inclusions on the behavior of the symmetrical anchor plate located in the

loose and dense sand and at embedment depths of 14. In reinforced tests, GFR layers were placed at

equal vertical spacings of 0.5B, 0.75B, and 1B with the first layer placed on the plate at 0 and 0.5B.

The variations of the symmetrical anchor plate’s capacities with u/D for a number of various GFR

layers are plotted in Figs. 9 and 10. The figures clearly show that the anchor plate’s behavior is largely

improved with soil reinforcement.

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 121

Fig. 7. Variation of ACR with B'/B of GFR layer at x/D=0. Fig. 8. Variation of ACR with B'/B of GFR layer at x/D=0.5.

Fig. 9. Variation of ACR with a number of GFR layers at Fig. 10. Variation of ACR with amount of GFR layers at

x/D=0 and u/D=0.5. x/D=0.5 and u/D=0.5.

Also, it can be seen that the inclusion of GFR layers has a much better result than that of non-

reinforced layers. In fact, the inclusion of multi layers of GFR resting directly on the top of the plate

enhances reinforcement to approximately the same extent as the inclusion of a single layer. Therefore,

it can be concluded that, in terms of symmetrical anchor plate’s capacity, using one GFR layer is

equivalent to, but more economical than, reinforcing the soil itself with several layers.

8. Discussion

This part presents a comparison of theoretical and experimental values for the experimental and

numerical programs conducted. Figs. 1114 illustrate a comparison of theoretical and experimental

values as forwarded by various researchers such as Balla (1961), Meyerhof and Adams (1968), Vesic

(1971), Rowe and Davis (1982), and Murray and Geddes (1987). The difference among these

theoretical predictions lies in the value of the breakout factor in uplift. Balla (1961), Meyerhof and

Adams (1968), Vesic (1971), Rowe and Davis (1982), and Murray and Geddes (1987) proposed

theoretical values based on the curved failure model determined by the method of analytical and

experimental evaluation in non-reinforced sand.

Figs. 11 and 12 illustrate comparisons of theoretical breakout factor values and current results

based on experimental and numerical analysis. The overall trend indicates that, for the series of tests

and models conducted, experimental and numerical values are in close agreement and similar to values

of Balla (1961) for circular plates, Vesic (1971) for square plates and Meyerhof and Adams (1968) for

rectangular plates. For symmetrical anchor plates shown in Figs. 13 and 14, numerical results using

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 122

Plaxis values appear much lower than tested values of breakout factors using laboratory tests and they

appear to be in agreement with values of Balla (1961) for square plates and Meyerhof and Adams

(1968) for circular and rectangular plates. Fig. 11 shows that the breakout factor increases significantly

with the anchor embedment depth for GFR and non-reinforced cases. Breakout factor values from

experimental laboratory testing are in close agreement and similar to values of Balla (1961) for circular

and square plates, and Meyerhof and Adams (1968) for rectangular plates. For symmetrical anchor

plates shown in Figs. 13 and 14, numerical results using Plaxis values appear much lower than tested

values of breakout factors using laboratory tests and they appear to be in agreement with values of

Balla (1961) for circular and square plates and Meyerhof and Adams (1968) for rectangular plates.

Figs. 13a and 14 show that the breakout factor increases significantly with the anchor embedment

depth for GFR and non-reinforced cases.

Fig. 11. Comparison of breakout factor between experimental results and theoretical and numerical predictions

for circular and square anchor plates in loose packing.

Fig. 12. Comparison of breakout factor between experimental results and theoretical and numerical predictions for rectangular anchor plates in loose packing.

Fig. 13. Comparison of breakout factor between experimental results and theoretical and numerical predictions

for circular and square anchor plates in dense packing.

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 123

Fig. 14. Comparison of breakout factor between experimental results and theoretical and numerical predictions for rectangular anchor plates in dense packing.

9. Empirical Relationship for Reinforced Sand by GFR

Based on the results, the variations of non-dimensional uplift responses with embedment ratio are

plotted. The tests are based on loose and dense conditions to derive the behavior of symmetrical anchor

plates (such as square, circular and rectangular plates) in sand using GFR. Tests in loose sand

conditions consist of three parts. The first part employs square plates with side lengths of 50 mm, 75

mm and 100 mm with a number of various GFR layers and various x/D, B' and u/D. While the second

part employs circular plates with various diameters of 50 mm, 75 mm and 100 mm with a number of

various GFR layers and various x/D, B' and u/D. The third part employs rectangular plates with various

diameters of 200 mm and 300 mm with a various number of GFR layers and various x/D, B' and u/D.

Similar tests were made for symmetrical anchor plates in dense conditions.

The empirical relationship for symmetrical square and circular anchor plates of length and

diameter, respectively, of 50 mm, 75 mm and 100 mm and rectangular plates of 200 mm and 300 mm

in loose sand conditions using GFR were developed by combining both non-dimensional uplift

responses to obtain average values. These methods were also adopted for dense conditions. The

relationship between various parameters was plotted for symmetrical anchor plates. The empirical

relationship was developed from test results. A linear regression was employed to obtain a linear

relationship of all data included. In square plates, this enables the following empirical relationship to

be derived:

q 1.98 3 / 0.56 /N L D B D . (2)

For dense sand conditions, similar methods used with loose sand were adopted. Thus the

empirical relationship for square anchor plates in dense sand condition can be expressed as:

6.57 3.45 / 0.49 /q

N L D B D , (3)

where L/D and number of GFR layers (N) give a linear equation by means of linear regression with a

coefficient of regression. As the confidence level has been set at 95% in the analysis, the p-value of

significant variables should be smaller than 0.05. According to the analysis, “embedment ratio” and

“ratio of geogrid width to plate width” have significant impacts on the overall service quality. The

impact of “embedment ratio” is positive and the impact of “ratio of geogrid width to plate width” is

negative. In circular plates, this enables the following empirical relationship to be derived as:

q 2.29 2.85 / 0.52 /N L D B D . (4)

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 124

For the dense sand conditions, similar methods used with loose sand were adopted. Thus

empirical relationships for square anchor plates in dense sand conditions give:

q 6.91 3.30 / 0.45 /N L D B D . (5)

The embedment ratio L/D and number of GFR layers N give a linear equation by means of a

linear regression with a coefficient of regression. As the confidence level has been set at 95% in the

analysis, the p-value of significant variables should be smaller than 0.05. The “embedment ratio” and

“ratio of geogrid width to plate width” have significant impacts on the overall service quality. The

impact of “embedment ratio” is positive and the impact of “ratio of geogrid width to plate width” is

negative. Eqs. (2)–(5) are valid for symmetrical anchor plates in loose and dense sand conditions with

a restriction of / 4L D .

10. Conclusions

Parametric research was conducted to obtain the knowledge on symmetrical anchor plates in loose

and dense soil conditions, such as GFR reinforcement and non-reinforced reinforcement and to

determine the behavior of the symmetrical anchor plates during uplift. Although it is not dedicated to

any specific practical conditions in engineering practice, it is useful to study the various effecting

factors that influence the symmetrical anchor plate’s capacity when subjected to uplift forces. An

analysis of the effect of various parameters has gained a deeper understanding of the behavior of

symmetrical anchor plates in reinforced sand when subjected to uplift loads. The failure shape for

symmetrical anchor plates with embedment ratio / 4L D is cylindrical despite variations in size,

density and reinforcement materials in reinforced sand when subjected to uplift loads. The size and

depth of the anchor plate are important parameters to be taken into consideration when selecting an

appropriate depth to achieve the most economical uplift design. It would therefore be more economical

and rational to increase the uplift capacity of symmetrical anchor plates by simply increasing the

symmetrical anchor plate’s depth, which helps to boost uplift capacity significantly, than by increasing

the symmetrical anchor plate’s size in order to increase the contact area with sand. Selection of the

symmetrical anchor plate’s shape must also be carefully considered to achieve an economical anchor

plate uplift design. Rectangular anchor plates provided a higher uplift response compared with square

or circular anchor plates. A deeply embedded symmetrical rectangular anchor plate proved

substantially more resistant to uplift forces than a symmetrical square or circular anchor plate, due to

the geometric progression in capacity with increase in symmetrical anchor plate’s depth. It is also

important to note that soil packing was found to be the most influential parameter in increasing uplift

capacity. Adequate compaction of soils around the symmetrical anchor plates is an important factor, as

indicated by the tests conducted on soils with relative density. The number and vertical spacing of

GFR layers is an important design factor of symmetrical anchor plates. In fact, the inclusion of multi

layers of GFR resting directly on the top of the plate provides approximately the same effect as the

inclusion of a single layer. However, if multiple layers of GFR reinforcement are required for a

particular design, then the optimum vertical spacing between layers is 0.5B. The outfitted tension trend

in the reinforcement allows the GFR to resist the formed horizontal shear stresses built up in the sand

Hamed Niroumand and Khairul Anuar Kassim / China Ocean Eng., 28(1), 2014, 115 − 126 125

mass inside the loaded zone and move them to stable layers of loose and dense sand leading to a

broader and deeper failure zone. Based on this result, sand GFR interaction not only results in an

increase in the uplift force due to the developed longer failure surface, but also results in an expansion

of the contact zone between the soil and laboratory box. From the detailed analysis given beforehand,

findings of the parametric study can be summarized. Based on the experimental and numerical studies

carried out on symmetrical anchor plates (such as square, circular and rectangular anchor plates) that

were embedded adjacent to an experimental box with two sand densities with or without GFR

reinforcement, the following conclusions can be drawn:

(1) Inclusion of GFR reinforcement in a laboratory test chamber significantly increases the

ultimate uplift resistance of a symmetrical anchor plate embedded in sand.

(2) In cases where design requirements necessitate large uplift resistance, soil reinforcement can

be considered as an economical solution and can be used to obtain the designed symmetrical anchor

plate capacity instead of increasing the embedment depth or anchor size.

(3) In terms of anchor capacity, inclusion of multi layers of GFR over the anchor plate is more

cost effective than sand reinforcement using a single layer.

(4) In terms of symmetrical anchor capacity, the inclusion of multi layers of GFR over the anchor

plate is more effective than soil reinforcement using one layer. In terms of reinforced conditions on

symmetrical anchor plates using multi layers of GFR, the optimal space between GFR layers is 0.5B.

(5) Increased soil density and embedment depth result in greater uplift capacity.

(6) Inclusion of GFR reinforcement in a laboratory chamber significantly increases the uplift force

by developing a longer failure surface, but also results in extending the contact zone between the soil

and laboratory box.

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