EVALUATION OF THEORETICAL CAPACITY MODELS FOR PLATE ANCHORS IN SAND IN RELATION TO FLOATING OFFSHORE WIND TURBINES

Increasing emission of carbon dioxide from combustion of fossil fuels its effect on the earth’s climate has led to increased research into renewable, clean energy solutions. Wind energy has been used as an alternative energy source for hundreds of years, however current research proposes the deployment of offshore wind farms in the deep waters of the oceans. A major challenge of deploying offshore wind farms is to safely and economically fix the wind turbines by means of anchors in the seabed. The objective of this study is to evaluate whether different anchoring concepts are suitable for securing floating offshore wind turbines in sandy soil conditions. For this purpose, an extensive literature review has been carried out to identify existing anchor capacity prediction models for three different anchor types. A 1-g model laboratory program was then developed and pullout tests using different anchor shapes in sand were performed. The laboratory testing program included pullout tests on shallow, vertically loaded square plate anchors, inclined square plate anchors, and drag embedment anchors in sands. For this purpose a testing facility (1.2 m width, 2.4m length and 0.9m height) was developed and a total of 11 pullout tests were carried out. The sand samples were prepared at a relative density of 22% and the tested depths varied from 0.15 m to 0.45 m. Tests results show an increase in capacity with increasing inclination angles. A comparison of the obtained test results and predicted capacities were used to evaluate the existing models. Best fit models were identified and loads derived from a state-of-the-art wind turbine were used to assess the feasibility of the proposed anchors to secure the 5-MW turbine. The results suggest that the examined anchor types are theoretically capable of mobilizing allowable capacities larger than the acting forces. The feasibility of anchor installation at the required embedment depths has to be proven in future research.

wind farms is to safely and economically fix the wind turbines by means of anchors in the seabed.
The objective of this study is to evaluate whether different anchoring concepts are suitable for securing floating offshore wind turbines in sandy soil conditions. For this purpose, an extensive literature review has been carried out to identify existing anchor capacity prediction models for three different anchor types. A 1-g model laboratory program was then developed and pullout tests using different anchor shapes in sand were performed.
The laboratory testing program included pullout tests on shallow, vertically loaded square plate anchors, inclined square plate anchors, and drag embedment anchors in sands. For this purpose a testing facility (1.2 m width, 2.4m length and 0.9m height) was developed and a total of 11 pullout tests were carried out. The sand samples were prepared at a relative density of 22% and the tested depths varied from 0.15 m to 0.45 m. Tests results show an increase in capacity with increasing inclination angles.
A comparison of the obtained test results and predicted capacities were used to evaluate the existing models. Best fit models were identified and loads derived from a state-of-the-art wind turbine were used to assess the feasibility of the proposed anchors to secure the 5-MW turbine. The results suggest that the examined anchor types are theoretically capable of mobilizing allowable capacities larger than the acting forces. The feasibility of anchor installation at the required embedment depths has to be proven in future research. iv

ACKNOWLEDGMENTS
This past year has been one of the most interesting years, both personally and professional and would not have been possible without the help of so many people on so many levels.   Merifield, 2006) Hanna et al. (1988) Neubecker and Randolph (1996)) ..... 35 Figure 13-Failure surface assumed (adapted from: Meyerhof and Adams, 1996) ... 40

Overview of Mooring Systems for Offshore Floating Structures
Offshore wind energy is a major focus of wind energy research and deployment both in Europe and in the United States. As the need for energy exponentially increases a steady desire for new energy resources exists . Although the concept of wind energy as a source of green energy was introduced in the 1970's (Heronemus, 1972), it was not until the 1990's that extensive research studies were carried out. While offshore wind turbines in shallow water depth are already widely distributed, there still is a lack in deepwater solutions due to technical and economical issues. Nevertheless wind power has established itself as a major source of non-polluting renewable energy and onshore wind farms have helped meet the large demand for electricity in the United States and Europe .
Currently the majority of wind farms are located either in shallow water or onshore.
Shallow water depths allow the manufacturers to use conventional land-based turbines with upgraded electrical and corrosion control systems. These fixedbottom structures are placed on a foundation in the seabed and are therefore limited to water depths of about 30 m. Unlike the waters surrounding most northern European countries, waters along the U.S. east coast are often deeper and there is pressure to move proposed wind farms out of the viewshed of the public.
The result is that many offshore wind farms on the U.S. east coast are likely to be in 2 water depths greater than 30 m. Greater water depths lead to more severe loading conditions that make conventional anchoring systems extremely difficult and expensive . Fixed-bottom systems, such as monopoles, lattice-jacket, and tripods, are not practical in greater water depths and therefore new anchoring systems have to be developed that can withstand the wind, wave, and tidal forces (Butterfield et al., 2007).
A major concern with offshore wind energy is whether it is practical to provide renewable energy at low and competitive costs compared to traditional energy resources (Snyder and Kaiser, 2009). Several studies analyzing costs of offshore wind turbines (OWT) have been carried out (e.g. Hensel et al., 2012) and a comprehensive analysis of offshore floating wind turbines can be found in Vasilakos (2011), Jonkman andBuhl (2007) and Breton and Moe (2009).
Only about 10% of the potential offshore wind resources available in the United States are in shallow water while the remaining ones are located in deeper water depths. Recent studies have indicated that for the New England States within a range of 40-90 kilometers off the coast, energy resources up to 166,300 MW are available in deep water. The potential of deepwater solutions can be emphasized when taking into account that only about 2,700 MW are available in shallow water.
It is estimated that, in total, about 900 GW of wind potential is accessible in areas between 10 km and 100 km off the coast of the United States. In total, the offshore 3 wind resource potential is higher than the current U.S. electrical capacity .
It is not unreasonable to assume that the U.S. offshore wind industry will inevitably move towards deepwater floating platforms. Moving further offshore means not only an increase in water depth but also an increase in the uncertainties of the ocean conditions especially in the Atlantic Ocean. In contrast to the well defined wind, wave, tide, and current conditions in the North and Baltic Sea these conditions are less known in the Atlantic, particularly in the case of extreme events such as hurricanes and nor'easters Aubeny et al., 2001).
The feasibility of floating structures has already been proven by the offshore oil and gas (O&G) industry for decades. Floating structures have been constructed in water depths up to 2,400 m. It is anticipated that the offshore wind industry will go through a similar development. In both industries the first developments were located relatively close to the shore in shallow water (Schneider and Senders, 2010).
However it remains to be proven that the technology for floating wind platforms can be transferred to the offshore wind industry. The experience gained in the O&G industry can be used as a guideline but significant differences in loading conditions, soil properties, and foundation types must be considered.
In order to support a floating offshore platform, there are primarily three different designs being used in the O&G industry right now  1. A ballasted deep-drafted spar buoy; 2. An unballasted tension leg platform;

A drafted barge.
For this thesis, floating production storage and offloading structures have been excluded because of their lack of application for offshore wind energy facilities.
The three concepts are displayed in Figure 1. The difference between these concepts lies in the way they try to achieve stability and resistance against the applied forces. The drafted barge generates stability by using the distributed buoyancy of the platform. The idea of the ballasted deep-drafted spar buoy is to create stability by hanging weights below a centrally installed buoyancy tank. This tank creates a righting moment and high inertial resistance. The tension leg platform (TLP) solely relies on the stability created by the line tension (Butterfield et al., 2005). A TLP provides the most stable form of floating platforms and with increasing numbers of tendons the stability can increase even more. Large parts of platforms anchored with vertical moorings usually are submerged and thus not exposed to wave loadings. In general, TLP anchors need to withstand larger moorings forces than an anchor in a catenary mooring system . There are different alternatives on how to anchor floating structures to the seabed depending on the type of floating platform. The most common mooring systems in the O&G industry are catenary moorings, taut-leg moorings, and vertical tension legs . Catenary mooring systems are usually used with ballast stabilized buoys or buoyancy stabilized barges. The tension leg platforms meanwhile use taut, semi-taut leg or vertical mooring systems (Jonkman, 2007). There are multiple possibilities of the types of mooring cables used, such as chains, steel, or synthetic fibers.

6
Catenary systems have been used for a long time to secure floating structures. They were named after the curve the mooring line forms between the floating platform and the seabed because of its flexible structure. Due to this bending, the mooring touches the seabed before it reaches the anchor and the angle of the anchor chain and mudline is close to zero. This results in almost entirely horizontal forces on the anchor. It is not uncommon for catenary mooring systems to have large footprints and to be anchored in the seabed at a radial distance close to the water depth . The scope of a mooring system, defined as the ratio of the total length of the mooring components to the water depth, can be as high as 5 for catenary mooring systems.
As the water depths increase, the heavy weight of anchor chains can become a limiting parameter in deep water applications. Thus taut or semi-taut moorings with smaller scopes become a more desirable solution in deeper water. Another advantage of the taut or semi-taut moorings is the smaller footprint that they require (Butterfield et al., 2005).
The main difference between taut moorings and catenary mooring for the geotechnical anchor system is the angle at which the mooring enters the seafloor. In taut moorings the line usually arrives at an angle between 30 and 45 degrees relative to the horizontal at the seabed, and the anchor has to withstand horizontal and vertical forces .
Tension-leg platforms are usually anchored with vertical moorings that arrive at an angle close to 90 degrees and will result in mainly vertical forces. The steeper the angle between mudline and floating platform is, the shorter and lighter the anchor line will be .
The different moorings systems are displayed in Figure 1 with a vertical mooring line system in Figure 1b and a caternary mooring system on the right and left hand side (Figures 1a and 1c).
There are numerous variations of anchors available today to use with both canetary and taut mooring systems. The load capacity of an anchor-system always depends on the seabed soil conditions. These conditions vary for each site so usually the anchor will specifically be designed for the conditions found (Musial et al., 2004a).
The typical anchor of a catenary mooring system is the drag embedment anchor (DEA). Inclined plate anchors can be used for taut-leg and semi taut-leg systems and vertically loaded plate anchors are usually used with vertical moorings. Plate anchors, in contrast to pile anchors for example, achieve their capacities from a combination of bearing and friction and not solely from friction on the sides. This results in significant higher anchor efficiencies and plate anchors are less susceptible to friction fatigue failure that might occur when using pile anchors. Therefore this study subsequently focuses on plate anchors.
The design of DEAs is dominated by empirical design charts and equations published by a variety of authors (NCEL, 1987;NAVFAC, 2012). The values used in these curves 8 were developed from actual test data and extrapolated to fit a wide range of soil conditions and anchor sizes. Most of the design charts and equations published by manufacturers for vertical and inclined anchors are for clay conditions and usually based on empirical results as well (Vryhof Anchors, 2010).

Statement of the Problem
The pullout capacity of each anchor depends on the individual soil conditions at the site. The standard design procedures using empirical models might be insufficient, as these models do not take any soil specific parameters into consideration.
Theoretical models have also been developed to predict the pullout capacity of a vertical loaded anchor and a few models cover inclined anchors. Using soil specific models might be desirable as they include the effects of the actual soil profile of the site more accurately and therefore could be a better choice to precisely predict the anchor capacity.

Objective of the study
The objective of this study is to analyze and evaluate existing theoretical and empirical capacity prediction models for vertically loaded and inclined plate anchors in sand. A best fit model for each anchor type will be chosen. The feasibility of vertically loaded anchors and inclined anchors to be used to secure floating offshore wind turbines in deep water is assessed.

Scope of the Study
To meet the objective of this study, small-scale, 1g anchor pullout tests are performed on local beach sand. The tests include the testing of a squared plate drag embedment anchor, vertically loaded plate anchor, and inclined plate anchor. An analytical study, using published models, is also performed in order to evaluate which model fits the experimental results best. The chosen model is then used to assess the feasibility of plate anchors to secure floating platforms, by designing the anchor accordingly to actual loads, derived from a standard 5-MW offshore wind turbine. This turbine and the resulting loads have been proposed and developed by the NREL and therefore represent a realistic approach (Jonkman et al., 2009;Sclavounos et al., 2010).

Introduction
The focus of this study is on the evaluation of proposed theoretical capacity models for inclined and vertically loaded plate anchors. To accomplish that, the study will be carried out in two sections. The first part will consist of a laboratory testing program and the second section will contain an analytical study of different theoretical anchor capacity models.
The experimental program consists of a series of different pullout tests. These tests will include strict vertically loaded anchors, inclined anchors, and drag embedment anchors. The anchors will be placed at different embedment depths and the mobilized resistance will be measured.
The analytical study will include a comparison of the predicted and measured capacities of a drag embedded anchor, a vertical loaded anchor, and an inclined anchor. Different theories will be used to predict the capacities and a parametric study will be carried out to analyze different parameters and settings. In order to compare the near-normally loaded anchor with the conventional drag embedment anchor the anchors will be simulated having the same fluke area and anchor weight for each setting. As a simplification, the drag embedment anchor is assumed to have a squared fluke area. Real loads for a typical floating wind turbine will be used to design the anchors according to a realistic loading condition.

11
The following chapter will provide a theoretical review of important considerations, such as sample preparation and scaling issues for 1g tests, and anchor capacity prediction models. This literature review does not claim to be complete but is used to understand the state of knowledge on relevant work.

Sample preparation at large scale
The preparation of sand specimens for laboratory testing can be generally achieved with several methods. Butterfield and Andrawes (1970) distinguish between two groups: (1) Methods where the density is adjusted after the deposition (e.g. shoveling, tamping and vibrating) (2) Methods where the density is adjusted during deposition (e.g. wet and dry pluviation).
The pluviation method, or raining of sand through the air, is today widely used in different forms and by various researchers. Some of the advantages of this method are the ability to achieve higher dry densities, minimal particle crushing, reduced segregation, and better repeatability (Okamoto and Fityus, 2006). Compared with other sample preparation methods, pluviation through air can be performed with greater flexibility in less time than other methods. It not only results in homogeneous samples with a desired relative density but also enables to simulate a soil fabric that is similar to the soil fabric found in natural deposits formed by sedimentation (Okamoto and Fityus, 2006).
This technique also allows samples to be prepared in different layers and to place instruments, testing equipment, or density caps at desired depths in the process of 13 pluviation (Gade et al., 2013). This is a big advantage compared to the other methods given the importance of preparing undisturbed sand specimens.
Several studies have shown that the deposition rate (i.e. in kg/m 2 /min) has the greatest effect on relative density. Greater deposition rates yield samples with lower densities. Other parameters such as diffuser sieve size, fall distance between diffuser sieves, and number of sieves used in a diffuser, have shown to have only minor contributions to the relative density (Rad and Tumay, 1987). The effect of the fall height on the relative density has been discussed controversially in the literature. Vaid and Negussy (1984) found out that the influence of the fall height on the relative density seems to be most important for fall heights smaller than 50 cm. Gade et al. (2013) proposed the usage of a portable pluviator developed by Dave and Dasaka (2012). Figure 2 shows the suggested setup with the proposed dimensions. The pluviator is based on concurrently controlling the number of sieves installed, drop height (referring to the distance between the last sieve and the top of the soil layer), and deposition rate depending on the desired relative density. One of the main advantages of this setup is the good accessibility and mobility when preparing large scale laboratory tests. The authors concluded that the relative density of the samples increases with an increase in drop height. Relative densities also decrease with increasing deposit rates and numbers of sieves for any particular drop height used. The maximum and minimum relative densities obtained in that study are respectively 41% and 100%.
14 A pluviator developed by Purdue University consists of a system of shutter plates and diffuser sieves with a diameter of 2 m. The pluviator is hung on a steel gantry above a soil tank with the same inside diameter. A mechanical hoist is used to adjust the height and keep a consistent drop height. Holes to control the deposition rate are drilled in the top of the pluviator and two sieves beneath the top part are used to evenly distribute and rain the sand. This pluviator has been used to prepare 15 samples with relative densities ranging from 38% to 91% depending on the setup (Prezzi, 2009). Tufenkjian et al. (2010) and Giampa (2014) used a pluviator developed by NAVFAC to create a uniform sand bed. The pluviator consisted of a frame, hopper, internal distribution drum, dispensing tray, drive wheels, and an electric motor. It was mounted on top of a trench and four guide wheels allowed it to traverse the length of the trench while depositing sand. With this setup three configurations control the relative density of the trench: (1) drop height, (2) opening size, and (3) the angle of deposition. It has been shown that with the right combination of those three variables relative densities between 10% and 88% can be achieved.

Scaling effects in 1g experiments
Physical modeling of various problems has been performed for many years in geotechnical research. Physical modeling has been used to test theories that need to be proven by field tests or to validate numerical models. However, field testing at full scale is often impossible due to high costs, time consumption, and the lack of full scale facilities. Large scale test results are also often difficult to interpret and compare due to the variability of soil conditions, layering, and inhomogeneity in insitu soils (Kirsch, 2009). For these reasons, testing is often performed on small scale models that represent the actual structure or prototype at some scale. They can be used to identify the behavior of the soil, its interaction with existing structures, or modeling the construction process.
Soil response is controlled by the effective stress within the soil mass. This applies especially for granular soils that at a given relative density and stress level behave in either a contractive or dilative manner. Thus when using small scale models, the results have to be evaluated carefully and scaling laws and scaling effects have to be taken into consideration (Yan and Byrne, 1989).
A distinction is usually made between model tests conducted at 1g-conditions and centrifuge tests conducted at ng-conditions. According to scaling laws, the centrifuge model will represent the prototype at a scale: where n= geometric scaling factor and B p and B m are the prototype and model dimensions, respectively.
The stresses acting in a model scaled in this way will be identical with the stresses of the prototype, but the displacements anticipated in the prototype will be larger than those of the model by the scaling factor n = N (Yan and Byrne, 1989).
A centrifuge test uses the rotation of a centrifuge to increase gravitational forces on the model, so that stresses in the model are the same as stresses occurring in the prototype. A model is build with a scale 1/n from the assumed prototype and is tested under an "n" times bigger gravity field. The typical radius of a centrifuge is between 0.2 and 10 meters. Due to the radial acceleration and increase in gravity on the model, the self-weight of the soil is scaled up. This results in a stress distribution with depth comparable or equal to the stress distribution in the prototype.
Therefore the stress dependent soil characteristics can be reproduced correctly (Kirsch, 2009).
Although centrifuge testing is seen as the most favorable method for small scale testing, limitations exist. Since the acceleration depends on the distance of the soil to the centre of the centrifuge, the mass forces are not equal over the height of the model. However, the main drawbacks are the high costs of centrifuge testing, the long preparation time, and the need for specially trained personnel to run these tests (Laudahn, 2005).

18
An alternate to centrifuge testing is 1g scale model tests. If a soil is being tested under conditions of normal gravity, simply scaling to the ratio of geometric size is not sufficient. Yan and Byrne (1989) presented a method to overcome this insufficiency by employing a high hydraulic gradient within the soil. This has the effect of creating a high body force and therefore stress levels are created that are close to field conditions. By applying seepage through the sample basically the same principle is applied as in the centrifuge test, namely an increase in the vertical effective stress. When using this principle certain scaling rules have to be applied. If a downward hydraulic gradient (i) is used in a model, the effective unit weight of the soil will be increased by a seepage force of magnitude iγ w where γ m = effective unit weight of the soil in the model i = applied hydraulic gradient γ w = unit weight of water γ' = buoyant unit weight of the soil.
The ratio of the unit weight of the model and the prototype is denoted with the unit weight factor N and is defined as where γ p = effective unit weight of the soil of the prototype.
Depending on the groundwater conditions in the prototype this could be total or buoyant unit weight.
Alternatively, tests at 1g conditions can be scaled by linking stress and strain to changes in void ratio or density of the soil following the change of stress.
The effect of a change in soil volume caused by a change in shear stress was linked by Casagrande (1936). Casagrande introduced the expression "critical void ratio" which is defined as the void ratio at which deformations continuously occur without changing the principal stress difference (Holtz et al., 2011). Typically loose sands (high void ratio) contract and dense sands (low void ratio) dilate when sheared.
Contractive behavior describes a reduction in volume and an increase in density when being sheared under drained conditions. Dilative behavior describes an increase in volume and decrease in density during drained shear. This means that the volume change behavior of a soil subjected to shear is controlled not by the void ratio alone, but rather the void ratio in relation to the critical void ratio (Fellenius and Altaee, 1994). Roscoe et al. (1958)  Fellenius and Altaee (1994) introduced a concept that uses the steady state as a reference state for physical modeling. The concept takes advantage of the uniqueness of the state for each soil and the relative ease of experimentally reaching the state. Figure 3 shows the steady state line for three drained compressions tests, tested at different initial void ratios and different initial mean stresses. P represents the prototype situation and samples M1 and M2 represent smalls scale model situations. The vertical distance from the samples to the steady state line is named "upsilon parameter" by Fellenius and Altaee (1994), "e-prime" by Roscoe and Poorooshasb (1963) and "the sate parameter" by Been & Jefferies (2002). Sample 21 M1 was prepared to have the same vertical distance or upsilon parameter to the steady state line as sample P, while sample M2 had the same void ratio as sample P.
The consolidation stress for samples M1 and M2 were the same and the stress for sample P was much higher.

Figure 3-Steady state line (Fellenius and Altaee, 1994)
When analyzing the Mohr circles shown in Figure 4 for these tests one can see that sample M2 would exhibit a higher friction angle than sample M1 and P; the two samples with the same upsilon parameter. Fellenius and Altaee (1994) also proved that testing at the same upsilon parameter not only results in the same friction angle but also reflects the entire behavior of the soil. Hence the volumetric strain vs.
axial strain behavior of sample M1 and P are identical.
22 Therefore only a small scale model with the same upsilon parameter, in this case sample M1, truly represents the prototype conditions. Thus the behavior of the sample M2 cannot correctly been used to analyze the prototype behavior.
Still there are some drawbacks to the theory proposed by Fellenius and Altaee (1994). One of the key points is the knowledge of the initial void ratio and mean stress for the prototype. These values can easily be determined for laboratory tests but are hard to determine for in-situ tests (Fellenius and Altaee, 1994). Houlsby (1991) found out that the dilatancy angle effects volume changes of soil as well as the apparent strengths. This means a model needs to be prepared in such a way that the soil peak friction angle and dilatancy angle are the same for the model and the prototype and therefore the soil behaves the same way. This can be achieved by preparing the test sample in a looser state. Figure 6 shows curves of different relative density as a function of friction angle (φ) and effective stress (p').
This shows that for the particular soil and geometric scaling factor a friction angle of 43 degrees at a prototype relative density of 75% correspond to a relative density of 38% for the model (Leblanc et al., 2010).
However this concept also has certain limitations. First, the sample cannot be prepared looser than the maximum void ratio and thus certain prototype conditions cannot be modeled. Secondly, the sample must not be prepared in a denser conditions that the minimum void ratio of the prototype soil.
25 Considering these limitations, it is clear that proper scaling is an important part of 1g testing. When using the results of a small scale test model to predict the prototype behavior, it is important to apply the according scaling relations to calculate stresses, strains and displacements. If the scaling issue is not addressed, the results of 1g tests cannot be used to predict prototype behavior.

Anchor Capacity Models
At the present day there are a variety of anchors commercially available. They can generally be divided into gravity anchors and embedded anchors. Gravity, or surface, anchors generate their capacity by their self-weight and the friction between its base and the seabed. Because of limitation in size and therefore capacity, gravity anchors are restricted to shallow water depths. Embedded anchors can be used in deeper water and are able to generate larger holding capacities. In practice, three different types of embedment anchors have generally been accepted: driven or drilled and grouted piles, suction caissons, and plate anchors .
The major difference of the three anchor types is the way these anchors achieve The pullout capacity of different plate anchors will be discussed in detail in the following chapter and various prediction models will be analyzed. This study focuses on shallow plate anchors, including drag embedment, vertically, and inclined loaded anchors.

Drag Embedment Anchors
One of the most used forms of anchors for floating structures is the drag embedment anchor (DEA). Its use with floating platforms has been well documented for some time (Schneider and Senders, 2010). Most of the common anchors share similar features that are illustrated in Figure 7.
The anchor usually consists of a shank, which is used to direct the line load to the anchor and one or more flukes to dig the anchor into the seabed and create bearing capacity through the mobilized soil wedge. One vital part of the anchor system is the attachment of the chain or wire to the anchor at the tip of the fluke. Usually a relatively small part of the chain is below the soil surface while the larger part is in the water. Since the self weight of the chain is dragging the chain towards the seabed, the chain arrives at an angle close to zero at the anchor-chain connection.

29
This is a desirable feature of the anchor system as the anchor is used to mainly withstand horizontal forces in catenary mooring systems (NAVFAC, 2012). The angle between fluke and shank, β, plays an important role in the design considerations to achieve maximum penetration depth. Depending on the soil condition at each site the angle is adjusted. Different studies showed that an angle around 50° for clay-like soil conditions and 30° for sands seems to be optimal. The penetration depths vary on the material. To achieve penetration, the anchor is placed on the seabed and embedded by applying horizontal tension forces to the attached chain. The anchor penetrates the soil until it reaches equilibrium and therefore its final position (Miedema et al., 2005). This ultimate penetration depth depends on the type of mooring line, anchor size, and soil conditions at the installation site. Typical penetration depths are between one and five fluke lengths.   Thorne, 1998) Due to complexities in shape and uncertainty concerning the variables affecting the performance, the capacity of DEAs is often extrapolated from empirical databases.
In efforts to aid in the design steps, the Naval Civil Engineering Laboratory (NCEL) developed a first series of figures and tables in 1987. These curves provide a holding capacity for DEA depending on the anchor weight and specific anchor type chosen. Figure 9 shows an example of anchor capacity curves for sand. The manual proposes a specific procedure in order to use these standard values properly. As a first step the ultimate horizontal holding capacity of the desired anchor has to be determined. This is done by calculating the maximum design horizontal load and multiplying this by a factor of safety proposed by NCEL. Next, an anchor that satisfies the needs has to be chosen. A convenient way to determine the ultimate holding capacity is to make use of the relationship between anchor efficiency and anchor weight, the simple efficiency ratio method.
where T M is the ultimate holding capacity, e is the anchor efficiency and W A is the weight of the anchor. The anchor efficiency is defined as the ratio between the ultimate holding capacity divided by the weight of the anchor (NAVFAC, 2012). To use this method several assumptions have to be made. As a first assumption, the anchor efficiency is assumed to be constant for a specific soil type over a range of anchor sizes and weights. Secondly, the anchor is installed properly and safely, and thirdly, the necessary embedment depth and embedment distance in order to develop the maximum capacity is reached. As these assumptions sometimes prove Anchor weight (kips) Fluke angles set for sand conditions 32 not to be true, this method may over-predict holding capacities, especially as tests have showed that a constant relationship between anchor efficiencies and anchor weight is untrue. The efficiency tended to decrease with increasing anchor weights.
Nevertheless this method is still widely used because of its simplicity and its history of usage (NAVFAC, 2012).
To account for the nonlinear relationship between anchor weight increase and capacity NAVFAC (2012) where m, b are dimensionless soil and anchor dependent parameters and W a is the weight of the anchor.
Values for parameters m and b are found using field test data and are given in the manual. This relationship proved to be valid for anchor weighing 200 lb or more.  (Neubecker and Randolph, 1996a;Neubecker and Randolph, 1996b). They investigate the static and kinematic behavior of drag anchors in sand. In order to predict the static holding capacity, a limit equilibrium approach is used.
The method is a modification of a more simplistic approach proposed by Le Lievre and Tabatabaee (1981). The theories differ in the way the failure wedge is assumed.
Contradictory to Le Lievre and Tabatabaee's suggestion, Neubecker and Randolph assume three dimensional failure wedge which resembles a more realistic failure mode. This is again an idealized failure mode.

35
There are only two unknown forces in the soil wedge force polygon. These are the fluke force, F f , and the soil reaction, R. They can be calculated by applying vertical and horizontal force equilibrium.
When considering the anchor force polygon individually again only two forces are left unknown, which are the force on the back of the fluke, F fb , and the chain tension, T a . They also can be calculated using force equilibrium.

36
The weight of the soil plays a main part in this analysis and it adds a major contribution in the development of pullout capacity. The correct prediction of the weight of the soil appears to be the most difficult part since the anchor could already mobilize the maximum holding capacity before it is fully embedded (Monaco, May 2013).
Due to the high uncertainty in the design of DEAs it is general practice to design the anchor as the "weaker link" of a mooring system. This means that the anchor is

Vertically loaded plate anchors
The following section summarizes different installation methods of plate anchors and describes already proposed models to predict the vertical uplift capacity of square plate anchors in cohesionless, dry sands. Generally plate anchors are embedded using pile driving techniques or suction pile followers, while drag-in plate anchors are today only theoretically possible due to accuracy issues in positioning the anchor. When the driving method is used, the plate anchor is driven into the sand by a follower. These followers could be hydraulic hammers or, if the underwater situation does not allow a hammer to be used, suction followers (SEPLA). SEPLAs have been used in clays for the O&G industry but the use of such a suction follower in sand is still being researched. The follower ensures that the desired embedment depth and position of the plate anchor is reached but is removed before the mooring line is loaded and therefore can be reused. Another possible option to achieve anchor penetration is the use of the jetting technology. A pulsating supply of water at the anchor tip is used to loosen soil and allow the anchor to penetrate. This is specifically used in very dense sands to assist penetration. This technique can also be used to develop sufficient soil densities around the anchor after the placement (NAVFAC, 2012;.
As most of the prediction models have been developed by different researchers in different years, various definitions have been used to characterize capacity. For 38 numerical convenience, ultimate anchor capacities will be presented in a standardized form of a dimensionless breakout factor N γ , where N γ is defined as: where Q u is the ultimate pullout capacity, γ is the unit weight of the soil, A is the area of the anchor and H is the embedment depth of the anchor.
A good overview of different capacity models for vertically loaded anchors is given by Merifield (2006) and is displayed in Table 2. The models of interest are those that present solutions for square and rectangular anchors. These are in particular Meyerhof and Adams (1968), Murray and Geddes (1987), Sarac (1989), and Merifield et al. (2006).
Meyerhof and Adams (1968) presented a limit equilibrium solution to predict the pullout capacity of strip, horizontal and rectangular plate anchors. Based on tests carried out by the authors simplifying assumptions were made. The failure surface was assumed to be inclined and shaped like a truncated cone and will reach the soil surface for shallow depths. The failure surface is illustrated in Figure 13.  with respect to the vertical, where φ' is the effective friction angle of the sand. The first solution was found for strip and continuous footings and then modified for use in sands and clays for both circular and rectangular footings. It was found that the passive earth force was governing the pullout resistance. To find the corresponding passive earth pressure coefficients, the theory of Caquot and Kerisel (1949) was used. A theoretical shape factor (s) is introduced to extend the theory from strip footings to square and rectangular plates and to account for the differences in shapes. For shallow depths s can be calculated with: where s is the shape factor, m is a coefficient depending on the friction angle, H is the embedment depth, and B is the plate width.
The pullout capacity for the model proposed by Meyerhof and Adams (1968) can be calculated with: where N γ is the breakout factor, s is the shape factor, K u is a theoretical uplift coefficient, φ' is the effective friction angle, H is the embedment depth, and B is the plate width.
Murray and Geddes (1987) developed a limit analysis approach to create an envelope for the predicted capacities. Contrary to limit equilibrium approaches, a limit analysis method does not provide an exact prediction but deliver a bounded solution. Upper bound solutions usually over-predict capacity and by obeying the associated flow rule (θ= φ' =ψ) are searching for a failure mechanism that is as close as a bound as possible to the ultimate uplift resistance. The lower bound solution is merely defined as the soil block located vertically above the anchor base. Murray & Geddes (1987) conclude that the most appropriate failure boundary consists of a straight-line failure plane inclined at the friction angle φ to the vertical at the edges of the plates. The failure surface is illustrated in Figure 14. The upper bound solution can be found using the following equation: where N γ is the breakout factor, H is the embedment depth, B is the plate width, and φ is the friction angle.
A limit equilibrium solution for circular and square anchor slabs is presented by Sarac (1989) in form of a design chart. The breakout factor can be determined depending on the ratio of embedment depth to plate width (H/B) and friction angle.

43
The author assumes, based on experimental tests, the failure surface to be shaped like a convex curve that met the soil surface at an angle of 2 ' 45   . A logarithmic spiral failure plane is proposed by the author to approximately display the real rupture line. The solution to the limit equilibrium approach is found using a finite difference method and the stresses on the rupture line are calculated with Bereyancev's theory of complete limit equilibrium. Figure 15 shows the failure geometry.  Merifield et al. (2006) points out that very few rigorous numerical analyses have been performed to determine the pullout capacity of anchors in sand. To close this 44 gap, the authors present a three-dimensional lower-bound limit analysis solution.
Developing a lower-bound solution, the authors expect the soil to still be in equilibrium. The associated flow rule is used, assuming the friction and dilatancy angle to be equal. Using the research software SNAC a finite analysis is carried to estimate the capacity of circular anchors utilizing axisymmetrical elements. The results, dimensionless breakout factors, were presented as a function of friction angle and the ratio of embedment depth to plate width, in the form of charts. 45

Inclined plate anchors
In this section, the pullout capacity of inclined anchors in cohesionless soil will be examined. Various theories and models have been published that use empirical relationships to predict anchor capacities or consider circular and strip anchor geometries. Some of these include Murray and Geddes (1989), Ghaly (1997), Choudhury and Subba Rao (2005), Ghosh (2010). As this study focuses on theoretical models for square anchors, these models are not part of this study. For a more detailed literature review on vertical and horizontal plate anchors see Das (2013) and Hanna et al. (1988).
The considered problem geometry is shown in Figure 16. The shallow plate anchor is inclined at an angle α relative to the horizontal at an embedment depth H measured from the soil surface to the bottom of the plate and a width of the anchor plate B.
46 Figure 16-Anchor geometry used (adapted from: Meyerhof (1973) In this study a number of existing numerical and laboratory studies that address the inclined capacity of anchors in cohesionless soils have been analyzed. In particular the research carried out by Meyerhof (1973), Hanna et al. (1988), and Goel et al. (2006) demonstrated to be of interest and the corresponding models have been used in a parametric study. Meyerhof (1973) extended a previous theory of vertical uplift capacity of anchors published by Meyerhof and Adams (1968) to inclined anchors and piles under axial load. Depending on the depth of embedment two different failure mechanisms can be differentiated: 47 1: The failure surface of shallow anchors will reach the ground level and will be considered as a general shear failure; 2: For greater embedment depths a local shear failure will occur close to the anchor.
For loose sands, Meyerhof states that at a ratio of embedment depth to anchor width of 4 the failure mode changes from a general shear type of failure to a local shear type.
The theory is based on active and passive earth pressure theory and the ultimate pullout capacity can be interpreted as the difference in active and passive earth pressure above and below the anchor plate. When the anchor reaches failure, the mobilized soil wedge is assumed to be in the shape of a truncated pyramid.
In order to calculate the ultimate holding capacity in form of the dimensionless breakout factor N γ for inclined plate anchors, the following equation is proposed: where N γ is the breakout factor, K b is a net earth pressure coefficients, s is a shape factor, H is the embedment depth, B is the plate width, and α is the inclination angle with respect to the vertical.
The uplift coefficients used are obtained from the earth pressure coefficients for an inclined wall (Caquot and Kerisel, 1949). The value of K b increases for a given friction angle φ with increasing load inclination α. A maximum value is reached at an inclination of α equals 90 degrees with respect to the vertical which corresponds to horizontal pull. A minimum value of K b represents vertical uplift (α equals zero degrees). Meyerhof presents a chart, which displays the variations of the uplift coefficients for shallow strip anchors, deep strip anchors, and deep square anchors.
To account for shallow square anchors, the uplift coefficient, K b , for shallow strip anchors is used and a shape factor (s) is introduced. The shape factor can be found in Meyerhof and Adams (1968) and in Equation 7. The coefficient K c can be neglected in this work since the focus is on cohesionless, dry sands. Hanna et al. (1988) developed a theoretical model to estimate ultimate holding capacities of an inclined shallow strip anchor using limit equilibrium analysis.
Despite the fact that strip anchors are not part of this study, Hanna et al. (1988) is included as the authors compare their theory to square anchor laboratory test. The theory is proposed for inclination angles α ranging from zero to 60 degrees. It is assumed that at an inclination larger than 60 degrees the failure mechanism is closer to a failure mechanism proposed for vertical retaining walls. Figure 17 shows the failure planes assumed by Hanna et al. (1988).
In this method the failure planes are assumed to be parallel to the anchor chain and therefore in line with the pullout force. This assumption is used as a simplification of the problem but does not reflect the actual failure plane. Along the assumed failure planes, two passive forces will act inclined at an angle δ. To account for the simplification, δ is an angle smaller than the peak friction angle φ. The angle δ also 49 depends on the inclination angle of the anchor α and on the embedment depth as only the end points of the plate anchor are located on the actual failure surface. The forces P 1 and P 2 can be determined using passive earth pressure theory and passive earth pressure coefficients (Caquot andKerisel, 1949 andSokolovskii, 1965).
Depending on the ratio angle of mobilized shearing resistance and peak friction angle, δ/φ, a reduction factor is applied. This reduction factor accounts for the oversimplification of the assumed failure surface. A generalized solution for this problem is presented in the study and as a simplified result a punching uplift coefficient is introduced. The punching uplift coefficient K s depends on friction angle of the soil φ, inclination of the anchor α, and embedment depth. The variation of 50 this coefficient is presented for ease in design charts. Introducing this coefficient to the previous equation Hanna et al. (1988) concluded: where N γ is the breakout factor, α is the inclination angle of the anchor, K s is the punching uplift coefficient, L 1 and L 2 are the length of the assumed failure planes, B is the plate width, and H is the embedment depth.
The authors conclude that the anchor capacity increases with increasing inclination angle α and with increasing embedment depth H. Experimental tests carried out by the authors support this conclusion. Goel et al. (2006) proposed a theory to predict breakout resistances for inclined circular anchors for deep and shallow conditions using a limit equilibrium solution.
This theory is also included because the authors compare their theoretical approach to laboratory results for inclined square anchors. The geometry used is the same used by Meyerhof (1973) and shown in Figure 16. A solution is found analyzing an elemental length of anchor cable at a certain depth. The pressures on that cable are calculated using an elliptical horizontal section and earth pressure theory for lateral pressures and uplift respectively. This resistance is assumed to be symmetrical for the elliptical periphery. A coefficient I i is introduced by the authors. This coefficient accounts for the unit resistance at any point in the ground and depends on the angle on inclination α, the coefficient of lateral earth pressure used in the analysis, 51 and the position of this one point with respect to its position on the cable. When integrated over the embedment length of the anchor cable the following equation is found (Goel et al., 2006): where N γ is the breakout factor, D is the diameter of the plate anchor, K is the coefficient of lateral earth pressure, α is the inclination angle of the anchor, I i is a coefficient for unit resistance.
An overview over different failure patterns for shallow inclined anchors is presented by Ghaly (1997). A differentiation between four major failure surfaces is presented in the reference. Only two proposed failure surfaces correspond to failure surfaces for square or rectangular anchors. One surface is shaped like a truncated pyramid, identical to Meyerhof's (1973) proposal. The second surface is a pattern of a straight line -log spiral -straight line, proposed by Wang and Wu (1980). The other two surfaces are proposed for circular anchors.

LABORATORY TESTING PROGRAM
As described at the beginning of Chapter 2, a laboratory testing program was developed to perform model tests on drag embedment and inclined embedment anchors. This chapter presents a summary of results for the element testing (e.g. sieve analysis, maximum and minimum density, specific gravity and drained triaxial tests) carried out on the sand used for this investigation. A detailed description of the 1g model testing facilities built for the project at the University of Rhode Island is also presented. Results from the pullout tests performed on the anchors are discussed. The results of these tests will be used for the analytical study presented in Chapter 4.

Soil Properties
This section presents a brief discussion and results of the tests performed to characterize the beach sand from Rhode Island used in this investigation. These tests include classification tests, isotropically consolidated drained triaxial compression tests, determination of the critical state line

Soil properties
The sand used for this study was obtained from a local Rhode Island beach. Figure   18 shows the grain size distribution for the sand. The gradation curve presented in this figure shows the sample exhibits a fairly uniform gradation with grain sizes ranging from 0.2 to 1 mm and no fines. According to the Unified Soil Classification System (ASTM D 2488-00), the soil classifies as poorly graded sand.
Minimum and maximum dry unit weight of the sand was determined according to the procedure described in the ASTM D 4254 (Method C) and ASTM D 4253 (Method 1A). The soil properties are summarized in Table 3.

Shear Strength of the Rhode Island Beach Sand
In order to determine the shear strength properties of the sand (i.e. effective internal friction angle, φ'), a series of monotonic isotropically consolidated drained triaxial tests were carried out on reconstituted specimens. Samples were sheared at various confining stresses (30, 50, 100 kPa) and a Mohr Failure Envelope was developed for the soil in question.
The following subsections describe the methodology used for triaxial testing.

Sample Preparation:
In this study, samples were prepared in three different states: very loose (Dr≈ 15%), loose (Dr≈ 30%), and medium dense (Dr≈ 55%) using the dry pluviation method. The samples were placed in layers by pouring the sand into the mold using a funnel.
Depending on the desired relative density, different opening sizes were used. A smaller opening size resulted in a higher relative density. Denser samples were additionally tapped with a small hammer after every other lift. The drop height was kept constant during sample preparation to ensure homogenous samples.
Once the sample was in the mold within the membrane, the porous stone and top cap were placed and the triaxial chamber was assembled. The chamber was filled with distilled water and a small vacuum was applied to the sample to ensure sample stability. Samples were flushed with CO 2 to substitute the air in the pores and then inundated with deaired water, through the bottom and top cap. This flushing of CO 2 56 and deaired water helped achieve saturation. Table 4 shows a summary of the dimensions of the samples, density and void ratio.  (2) shear. During the consolidation phase, an isotropic pressure was applied to specimen until the desired vertical effective stress was reached. During the shear phase, in addition to the vertical effective stress, a deviator stress is applied to the specimen until failure. For these tests, samples were sheared at a strain rate of 0.5% / min up to a maximum axial strain of 20%. Failure was defined as maximum deviator stress. Friction angles were calculated using Equation (13) where q f is the shear stress at failure and p' f is the mean effective confining pressure at failure. The results of the triaxial tests are presented in Table 5. Figures 19 shows volumetric strain vs. axial strain behavior and Figure 20 shows deviatoric stress vs. axial strain behavior for different relative densities respectively. Figure 21 shows a Mohr Coulomb circle with the corresponding failure envelope for the dense specimen. The calculations include corrections for the area and for piston friction.

Critical state friction angle
Critical state friction angles can be obtained by means of drained triaxial tests or a simplified procedure developed by Santamarina and Cho (2001). Both procedures were carried out in this study and will be discussed briefly. Santamarina and Cho (2001) proposed that the critical state friction angle can be found using a graduated cylinder. Sand was poured in a cylinder filled with water.
The cylinder was then tilted and slowly brought back to its initial position. The angle of repose in the middle region of the slope is the critical state friction angle. This procedure was repeated ten times and an average was taken. The results are summarized in Table 6.  (13) with the values σ 1 σ 3 corresponding to the point where the change in axial strain is equal to zero.   Bolton (1986) studied the relationship between strength and dilatancy of sands. He presents an empirical correlation to calculate dilatancy angles. The dilatancy angle is a function of peak friction angle, critical state friction angle, relative density, mean effective stress, and two fitting parameters. Peak friction angles for triaxial strain can be determined using:

Bolton's stress dilatancy relationship
where φ' peak is the effective peak friction angle, φ' cs is the effective critical state friction angle, p' is the mean effective stress, and Q and R are fitting parameters.
Q and R can be found by performing a linear regression using the data obtained in the triaxial tests and the average critical state friction angle calculated using the approach developed by Salgado et al. (2000). The confining pressures expected in the model tests are in the range of 1 to 4 kN / m 3 while the lowest confining pressures in the triaxial tests were 30 kN/ m 3 . For this reason the relationship described above is assumed to be also true for smaller stresses and extrapolated to the smaller stress levels occurring in the model.
The best fit line is represented in Figure 24 with Q= 10.46 and R=-1.89 (r 2 =0.988).

Figure 24-Determination of Bolton's parameters for the sand used in this study
The angle of dilation, ψ, can be calculated when rearranging Equation 14 to the following: where ψ is the dilatancy angle.

66
The just described relationship was used to prepare the soil samples for the study. 67

1g Model anchor tests
The following chapter describes the experimental testing program and the smallscale pullout tests carried out at the University of Rhode Island to model the breakout behavior of shallow square plate anchors in sand. The main focus was to represent the in-situ conditions in the best way possible and to perform repeatable and comparable anchor pullout tests. It was ensured that the prepared samples represented the desired in-situ conditions.

Model Test Experimental Setup
Two test tanks were set up to perform pullout tests on small scale anchors. The equipment consisted of a gantry crane, a winch and pulley system, load cells, string potentiometers, a data acquisition system, and the different miniature anchors. The completed tests included drag embedment, inclined and vertically loaded plate anchor tests.
The testing tanks used in this study were designed and built at the University of Rhode Island. The inside dimensions of the tank were 1219 mm wide, 2413 mm long, and 914 mm high. The bottom and sides were made out of plywood and reinforced by wooden beams. Two identical boxes were set up alongside one another but tests were only performed in one box. The second box was meanwhile used as a storage box for the used sand.
The overhead crane was set up in a way that the pluviator could be adjusted laterally and vertically while preparing the sample. The frame also allowed inclining the loading chain and anchors at any desired angle. The winch was placed and fixed on the floor and the steel cable was connected with a pulley system to the frame. A schematic diagram of the experimental setup is presented in Figure 25.

Figure 25-Schematic test setup
Model anchors were fabricated from steel. Tables 8 and 9 give an overview of the anchor properties. The plates were assumed to be rigid enough to not bend for the expected loading conditions. A steel chain was connected to the anchor and embedded in the sand to simulate the anchor chain. Figures 26 and 27

Sample preparation
The preparation of a uniform and repeatable sand bed with a desired relative density was required in this study. In order to achieve this, three different pluviation methods were tried in this study. The portable pluviator proposed by Gade et al. (2013) proved to meet the requirements best and was therefore used in this study.
The pluviator is described in detail in Chapter 2.
One of the main selection criteria was the desired relative density. For this purpose the pluviator was calibrated by varying the drop height (50.8 mm to 190.5 mm) and alternating the number of installed sieves. A drop height of 152.4 mm and two 6.35 mm sieves resulted in a desired relative density of about 23%.
Six tests samples were prepared with relative densities ranging from 18-24%. The average unit weight for the six tests was 14.84 kN / m 3 . The height of soil placed in the box was 609.6 mm for each box and a total of 11 anchor tests were performed.
To ensure a homogenous sample, the drop height was adjusted every 50.8 mm and the pluviator was moved laterally throughout the box using the steel frame. The test anchors were placed at different embedment depths during the pluviation. For the placing of the anchors, possible boundary issues were considered and it was ensured that boundary effects were minimized. An advantage of the portable pluviator was the anchors could be put into place without disturbing the soil around and above it.

74
Minicone penetrometer tests (mCPT) were performed for each box at six different locations. The locations were carefully chosen to minimize possible boundary effects from box edges and to eliminate soil disturbance for the anchors. The miniature cone had a tip area of 1 cm 2 and was pushed in the sand using the pulley system and weights stacked on the cone to simulate a downward force. The cone was calibrated beforehand using the Geocomp® system. A known load was applied to the cone and the corresponding reading was recorded. A relationship between the applied weight and recorded values was then established and used throughout the tests for the cone.
A correlation between tip resistance and relative density was used to determine the density at each location and an average was taken for the whole box. The equation was proposed by Kulhawy and Mayne (1990) and is as follows: where D R is the relative density, Q c is a compressibility factor, OCR is the overconsolidation ratio, q c is the measured tip resistance, σ v is the overburden stress, and pa is the atmosphere pressure (100 kPa).
Typical tip resistance and sleeve friction profiles with depth are presented in Figure   28 and 29, respectively. Figure 30 shows a typical result of the relative density with depths and Table 10 summarizes all collected data.

75
Additionally, density was measured directly during the pluviation using caps of a known volume. While pluviating a layer of soil the caps were filled and weighed.
Densities were then calculated using the known volume of the caps and the measured weight of the soil. Figure 31 shows a typical result of the relative density with depths and Table 11 summarizes all data. Both density readings showed comparable results. For the following calculations the density readings obtained from the density caps were used.     Relative Density, Dr (%)

Anchor Pullout tests
The anchor pullout tests were performed using an electrical winch connected to a pulley system on the steel frame. The anchors were pulled at a constant rate of 5 cm / s, which was controlled by the pulley system and the winch speed. The acting forces and resulting displacements were measured as described before.       The results show that the pullout capacity increases with an increase in the embedment ratio. This is consistent with the existing theories as the pullout capacity is a combination of the mobilized soil wedge and the friction on the sides of the wedge. Also, the capacity increases with an increase in inclination angle. This is due to the larger soil wedge mobilized in inclined tests. The needed displacements corresponding to the peak capacity for inclined anchors are larger and in the range of 30-70 mm. Furthermore, the post peak softening behavior of the inclined anchors were not as distinctive but for both anchor types the mechanism was catastrophic.
Two different sized plate anchors (152mm and 304mm) were tested at the same H/B ratio to study scaling effects in the test tank. For the vertical pullout tests basically no difference in breakout factors between the anchors can be observed as the larger plate's breakout factor was 9% higher than the breakout factor of the small plate. Different sized anchors were also used in the inclined pullout tests. For these tests, the smaller plate recorded a 36% higher breakout factor. In total the results suggest that the size of the anchor does not affect the results.
The drag embedment anchor tests exhibited larger pullout capacities than plate anchors. On the contrary no distinctive peak was observed with drag anchors. This is due to the fact that the failure for drag embedment anchor is not a catastrophic failure. Even after the initial movement the anchor is still dragged horizontally through the soil and resistance is mobilized. The load-displacement curves also show this behavior. After a peak is reached almost no strain softening behavior can be observed. The recorded displacements for drag embedment anchors were larger than the displacements for plate anchors.

84
The recorded pullout test results are used in the following analytical program to evaluate existing prediction models and to assess their accuracy with regard to the specific soil conditions used in this study. In order to fully describe the behavior of the different anchor types, tests in denser conditions should be performed; however this is beyond the scope of this study. 85

ANALYTICAL PROGRAM
The following chapter presents a summary of the analytical study carried out for this investigation. First, a parametric study was performed to study the effects of inclination angle, H/B ratios, and friction angles on the predicted capacity of inclined square plate anchors. Second, a variety of anchor capacity prediction models, described in Chapter 2, were used to estimate breakout resistance factors for the anchor tests presented in Chapter 3. A comparison between the experimental results and the model predictions led to a choice of a single model that is used in a later part of this chapter to model the anchoring of a floating platform using real loads derived from a 5-MW offshore wind turbine.

Parametric Study of Analytical Models for Inclined Anchors
The use of taut, semi-taut mooring or vertical mooring system instead of catenary mooring system can be favorable in deep and ultra-deepwater. This is mainly due to the high weight of the anchor chain in the catenary system at large depths and uncertainty in the positioning of drag embedment anchors in the soil. Because of this, the use of plate anchors in semi-taut mooring systems seems promising. In semi-taut mooring systems the anchor has to withstand both vertical and horizontal mooring forces. To achieve this, the anchor is penetrated in the soil and then pulled until its final position is achieved as described in Chapter 2.3.3 .

86
Three analytical models, described in Chapter 2, are used to investigate the influence of load inclination and embedment depth on the breakout capacity for inclined square plate anchors. These models include Meyerhof (1973), Hanna et al. (1988), and Goel et al. (2006). Three different sand conditions, with friction angles ranging from φ= 30, 40, 50 degrees, are used to investigate a broad range of sands.
The inclination angle, α, of the anchor is taken with respect to the vertical, and H/B is the ratio of embedment depth to fluke width. The results are presented in terms of the dimensionless breakout factor, N γ ,

Effect of inclination angle
Generally, the breakout capacity increases with increasing inclination angle. An inclination of zero degrees corresponds with vertical uplift and 90 degrees means horizontal pull. Hanna et al. (1988) limit their theory to an angle of 60 degrees because in their observations greater inclination angles change the failure mechanism. Meyerhof (1973) and Goel et al. (2006) are modeled to inclination angles of 75 degrees. This range captures the typical mooring angles being used in practice up to this date. For this investigation the H/B ratio is fixed to 2.

Meyerhof (1973)
As described in Chapter 2, Meyerhof proposed the following breakout factor: In this form the breakout factor is not very sensitive to the inclination angle. This might be due to the small changes in the uplift coefficient K b , utilized in the model to account for changes in inclination angle. Dense sands show an increase in capacity of 20% when comparing vertical uplift and an inclination of 60 degrees, while in case of very low friction angles the breakout capacity even decreases with increasing inclination angles. This behavior is illustrated in Figure 35.
The breakout factor was described by Hanna et al. (1988) as: Figure 36 shows the breakout factor as a function of inclination angle for friction angles of 30, 40, and 50 degrees. Similar to the Meyerhof (1973) approach, the Hanna et al. (1988) breakout factor is insensitive to inclination angle and friction angle for inclination angles less than 40 degrees. The breakout factor ranges from approximately 2 for inclination factors less than 40 degrees to 5-9 for an inclination factor of 60 degrees. Goel et al. (2006) The breakout factor was described by Goel et al. (2006) as: The variation of this breakout factor as a function of inclination angle for friction angles of 30, 40, and 50 degrees is shown in Figure 37. These breakout factors increase both with increasing inclination angle and friction angle. The dense sand showed an increase of capacity of almost 450% over the course of the variation of α.
Contrary to the other two methods notable increases in capacity for small inclination angles (α ≤ 40°) can be seen. It is observed that for any friction angle, the breakout factor shows a continuous increase with an increasing inclination angle.

Evaluation of models
In this section the different theoretical models are compared with the pullout test results described in Chapter 3. The comparison is made using the dimensionless breakout factor.

Drag embedment anchors
The theoretical model used to predict the capacity of a drag embedment anchor for this study was developed by Neubecker and Randolph (1996). As described before,  Table 15.  The tests were limited to a ratio of embedment depth over fluke width of 1.5. This ratio is recognized as the maximum penetration depth in practice for sandy soil conditions and drag anchors. Due to the high uncertainties described before and the lack of test results, the applicability of the model as a design standard for drag embedment anchors remains uncertain.

Vertically loaded plate anchors
In this section the results of the vertical pullout test results are compared to the known models for vertically loaded plate anchors. The results of each model and the corresponding plots will be presented first, followed by a discussion for each model.
The models are individually evaluated and the model representing the experimental results most accurately is identified.

Meyerhof and Adams (1968)
The limit equilibrium approach developed by Meyerhof and Adams (1968) has been compared to the experimental results and shows an over-prediction on average of capacity of 144% with a coefficient of variation of 0.24. Figure 43 shows the experimental test results plotted against the proposed theory and Figure 44 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 16.  99 Murray and Geddes (1987) The limit analysis method presented by Murray and Geddes (1987) is an upper bound solution. It over-predicts breakout factor on average by 100% with a coefficient of variation of 0.23. Figure 45 shows the experimental test results plotted against the proposed theory and Figure 46 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 17.  Bias H/B Sarac (1989) The limit equilibrium solution by Sarac (1989) over-predicts capacity by 83% on average with a coefficient of variation of 0.2. Figure 47 shows the experimental test results plotted against the proposed theory and Figure 48 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 18.  Bias H/B Merifield et al. (2006) The solution presented by Merifield et al. (2006) uses a limit analysis approach to predict the capacity and a lower bound solution is developed by the authors. The model showed to over-predict capacity by 155% on average with a coefficient of variation of 0.14. Figure 49 shows the experimental test results plotted against the proposed theory and Figure 50 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 19.  Meyerhof and Adams assume the average angle of the failure surface to be φ'/3 with the vertical. Using the peak friction angle of the experimental tests; this results in inclination angles ~1 5°. The lateral earth pressure coefficient is assumed to be between 1 and 2. This might over-estimate the stresses and the use of K 0 conditions might be more appropriate.
In the model presented by Sarac, a log spiral failure surface is assumed that meets the ground surface at an angle of 45-φ'/2. Using the peak friction angle of the experimental tests, this results in inclination angles ~2 0°. The earth pressures used are only described briefly and their effect on capacity remains unclear.
The limit analysis methods used in this study utilize the associated flow rule where the dilatancy angle is assumed to be equal to the friction angle and to the inclination angle of the failure wedge (θ= φ' =ψ). As a result the assumed failure wedges are oversized and the corresponding models over-predict capacities. The over-prediction of Murray and Geddes solution is consistent with their theory, as the limit analysis gives an upper bound solution and should therefore over-predict. Merifield et al. (2006) presented a lower bound solution and ought to under-predict the capacity. The results indicate that this is not the case and the solution may not be lower bound as it over-predicts breakout factors for all embedment depths.

106
The described models over-predicted the measured capacity on average by 120%.
For this reason a new model was derived based off a model presented by White et al. (2008) for strip anchors and circular pipes.
where γ' is the buoyant unit weight, H is the embedment depth, B is the plate width, ψ is the dilatancy angle, φ is the friction angle, Q u is the pullout capacity, and F1 and F2 are uplift coefficients, K 0 is the coefficient of lateral earth pressure at-rest.
The re-derived solution over-predicts capacity by 27% on average with a coefficient of variation of 0.14. This is an excellent agreement of theoretical values and experimental results. For this reason this method is chosen as the best fit for the experimental values. Figure 52 shows the experimental test results plotted against 109 the proposed theory and Figure 53 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 20.

Inclined plate anchors
Three models for predicting the breakout capacity for inclined plate anchors were compared to the experimental results from this study: Meyerhof (1973), Hanna et al. (1988), and Goel et al. (2006). The performance of each model is described separately followed by a discussion of the results.
On average, the breakout capacities were 36% higher than the experimental results with a coefficient of variation of 0.2. Figure 54 shows the experimental test results plotted against the proposed theory and Figure 55 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 21.  In contrast to the other limit equilibrium solutions for inclined plate anchors, the model developed by Hanna et al. (1999) under-predicts capacity. The predictions were 5% lower than the experimental results on average with a coefficient of variation of 0.2 for this study. Figure 56 shows the experimental test results plotted against the proposed theory and Figure 57 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 22.  Bias H/B Goel et al. (2006) Similarly to the solutions of Meyerhof, the limit equilibrium solution presented by Goel et al. (2006) over-predicts capacity by 33% on average with a coefficient of variation of 0.14. Figure 58 shows the experimental test results plotted against the proposed theory and Figure 59 the calculated bias. A summary of theoretical predictions and experimental results is given in Table 23.  117

Discussion
All three presented models were, in the first place, developed to predict breakout factors for strip anchors. The model presented by Meyerhof can, according to the author, be used for square anchor plates as well. For this reason a shape factor is introduced as described in Chapter 2.3.3. The other two models do not include shape factors to account for different shapes such as square plates. Therefore the results obtained from Hanna et al. (1988) and Goel et al. (2006) must be interpreted with caution. The reason why they are still included in this study is that the authors compare their models themselves to square anchors in their publications. Meyerhof (1973) Meyerhof's (1973) approach seem to match the experimental results and thus it appears that the assumptions capture the behavior of inclined anchors. The models derived for strip anchors were neglected even though they showed a smaller bias developed for square anchors in the first place and therefore assume different failure mechanisms. For this reason this model has been chosen as the best fit for inclined anchors in sand. Table 24 provides an overview of every analyzed model and each calculated bias and coefficient of variation.

Design Analysis
This section is used to demonstrate that plate anchors theoretically can be used to secure offshore wind platforms. A study on the feasibility of floating platforms carried out by  provides an estimation of the anchors loads from an offshore wind platform. For standardization reasons a 5-MW wind turbine developed at NREL was used (Jonkman et al., 2009). Two different floating concepts with different mooring systems are discussed in the analysis: (1) the NREL wind turbine with a tension leg platform and (2) a dutch developed tri-floater concept with a comparable power output. The NREL concept uses vertical tendons to connect the platform to six anchors in the seafloor. These anchors are designed to carry a vertical tension force of 4700 kN. For the dutch concept a system of six anchors in a catenary mooring system is designed. These anchor forces are significantly smaller than the loads in the vertical mooring system as these anchors are only used to restrain platform movement and the heavy anchor chain is taking considerable loads as well. The mooring lines are pre-tensioned at 300 kN for the dutch study (Bulder et al., December 2002). Sclavounos et al. (2010) presented a study on motion resistant floating wind turbines supporting 3-5 MW offshore wind turbines. Two different concepts are presented in their study: (1) is similar to the NREL concept as it also uses a tension leg platform with a vertical mooring system and (2) a taut leg buoy concept using a semi-taut mooring system. The difference between buoyancy effects of the 120 platform and weight of the turbine and structure is equal to the uplift capacity of the anchors. To compare the results the 5-MW wind turbine is used to calculate the corresponding capacities. For the tension leg platform the cumulative capacity is equal to 20,000 kN and for the buoy the capacity is 25,000 kN. In both cases a mooring system with six anchors is considered. The floating structures and mooring systems are shown in Figure 60 with the TLB on the left and the TLP on the right hand side. These two studies can be seen as examples on the magnitude of the loads acting on floating offshore platforms. In general a load analysis needs to be carried out for each design project individually as many variables depend on the site (i.e. wind loads, wave heights, current loads) (Matha, 2009;Tong, 1998;Myhr et al., 2011).

121
The models that best fit the experimental results from this study are used to determine the minimum anchor dimensions for the loads for drag embedment anchors, vertically loaded anchors, and inclined anchors. For vertically loaded anchors it showed that the re-derived model of White et al. (2006)  A similar calculation has been carried out for the inclined anchors used in a semitaut mooring system. Sclavounos et al. (2010) estimated the forces to be 4200 kN per anchor, using a six anchor mooring system. Again, three different anchor dimensions are presented in Table 27 and 28 for each soil condition. The capacity of the inclined anchors is, as expected, generally higher than the capacity of the vertically loaded anchors. The used factor of safety represents the common practice and is recommended by anchor manufacturers. meters below the seabed in clay. The proposed anchor dimensions include larger plate areas (25m 2 ) with smaller embedment depths, medium size plate areas (15m 2 ), and small plate areas (5m 2 ) with large embedment depths. None of the proposed anchors exceed the already realized anchor dimensions or embedment depths and with reasonable fluke areas no H/B ratios larger than 7 are needed to mobilize pullout capacities satisfying the demands. Considering this, the use of plate anchors to secure floating offshore wind turbines is technically feasible.
Optimization in the design process will require a cost-benefit analysis of the amount of used steel for the anchor and the installation costs (and feasibility) of the anchor for deeper embedment depths.

Summary
In this thesis different anchoring systems associated with floating offshore platforms for wind turbines have been examined. The need for renewable and clean energy Different theoretical models to predict holding capacities, based solely on soil parameters, have been published over the years for anchors that possibly can be used to stabilize the floating platforms. An accurate capacity prediction is a crucial aspect in designing offshore anchors with respect to the safety and serviceability of these floating structures. The first objective of this thesis was to analyze and evaluate the existing theoretical capacity prediction models for vertical and inclined plate anchors in sand. The second objective was to identify a best fit model for both 125 anchor types and use this model to assess the technical feasibility of these anchors to secure floating offshore wind turbines in deep water.
An extensive literature review was carried out which included the following topics: sample preparation at large scale, scaling issues in 1g model tests and different anchor shapes. A laboratory testing program involving 1g model pullout tests was performed. Bolton's stress dilatancy concept was used to design the experiment to obtain the same constitutive response in the test tank and prototype. The sand prepared in the test tanks was therefore prepared at lower relative densities than the corresponding prototype (approximately 22% compared with 30% in the prototype) to give it the same volume change characteristics (contractive vs. dilative) as the prototype despite the very different stress conditions.
For the preparation of the samples different pluviators were analyzed. A pluviating concept was chosen that allowed to place both the soil in layers and the anchors at the desired depths without disturbing the soil around or above it. Hand readings and a miniature cone penetrometer were used to ensure the samples were homogeneous. The readings of the miniature cone were correlated to relative densities and a soil profile was developed for each test. Six soil samples were prepared and three different anchor types were tested for a total of 11 tests. The test results were then compared and evaluated to theoretical prediction models.

Conclusions
The following conclusions can be made:  It is possible to model prototype conditions in a lab when scaling issues are considered properly. The test tank needs to be prepared in a looser state with lower stress levels to achieve the same constitutive response and friction angle in the prototype and model.
 Neubecker and Randolph's (1996) model to predict capacity of a drag embedment anchor in sand compared promisingly with the laboratory model test results. However the development of models to predict the kinematics of these anchors in sand is still ongoing and it is not possible to predict the final embedment depth and orientation beforehand, yet. This, combined with various variables and assumptions incorporated in the model, makes the model highly uncertain and inapplicable for a safe anchor design.
 The presented models to predict the holding capacity of vertically loaded anchors entirely over-predict capacity even though different failure mechanisms are assumed. The upper bound theory of Murray and Geddes (1987) is expected to over-predict capacity, as it is the upper part of a capacity envelope. The second limit analysis method, presented by Merifield et al. (2006), also over-predicts but was inconsistent with their theory of being a lower bound solution. The two examined limit equilibrium models by Meyerhof and Adams (1968) and Sarac (1989) also over-predict capacities, possibly by using earth pressure coefficients higher than the actual pressures.
 The re-derived model by White et al. (2008) for vertical uplift showed an excellent agreement between experimental and analytical values. It is also the only model that takes the dilatancy angle into consideration when predicting the holding capacity. As it is most precise, it is recommended to be used for vertically loaded anchors.
 For shallow square plate inclined anchors the only model available was a limit equilibrium method presented by Meyerhof (1973). It showed good agreement between the recorded and predicted values. The two other models assessed were developed for strip anchors and did not include a shape factor to account for a square form.
 It was shown that plate anchors generally can be used to secure the applied loads on a floating offshore platform in deep water just from a capacity point of view. The embedment depths needed to mobilize the desired holding capacities have already been realized in clay.

Recommendations for future research
To completely capture the behavior of plate anchors in sand tests more tests need to be carried out. Due to time restrains and technical limitations the testing for this study was limited to H/B ratios of 3. Usually a change in failure mechanism is expected to happen at an H/B ratio greater than 5 and therefore it should be aimed to fill this gap. Also, this study was conducted on very loose sands that represent the lower end of the soil spectrum. A test series on dense sand could provide valuable inside into the behavior of plate anchors in these conditions and finalize the laboratory studies of holding capacities.
Since the behavior of anchors in the process of installation is still researched, a model accounting for different anchor geometries would be useful as they might change. All models are derived for square, circular, rectangular or strip anchor geometries. As it is still unclear to the present day which geometry would be optimal for soil penetration, a model accounting for different anchors shapes would be needed.
Another key point is the kinematic behavior of a plate anchor during embedment.
Different installation methods have already been used including jetting and driving but a promising new approach might be to use the self-weight of the anchor to freefall penetrate the soil. Previous studies on ultimate embedment depth concentrated on clay-like soil conditions and the ultimate embedment depths in sands remain 129 unknown. An experimental database needs to be developed to verify the theoretical embedment depths required.
It might be an interesting concept to investigate the expended energy in conventional anchor design, manufacture, and installation and compare it to the energy needed for the new anchor concepts. The energy saving potential could be a decisive criterion for the future of offshore wind platforms.