Dynamic Penetration of a Flying Wing Anchor in Sand in Relation to Floating Offshore Wind Turbines

A new concept called the Flying Wing Anchor was recently proposed that consists of a kite-shaped plate anchor that is installed by free-fall penetration, and then rotates into a position that is near normal to the mooring line. Understanding the free-fall penetration behavior and initial embedment depth is critical to assessing the feasibility of the anchor in sandy soils. Small-scale 1g model tests were performed to investigate the dynamic penetration behavior of the anchor both in dry and saturated sand. Simple numerical models were also developed to model the dynamic penetration under drained and undrained conditions. The results indicated that dynamic penetration is likely an undrained process and the key factor controlling the embedment is the undrained strength and strain rate effects. Considering an undrained loading it may be possible for the Flying Wind Anchor to achieve embedment depths of up to 3 times the anchor height in loose sands.


CHAPTER 1: INTRODUCTION
Chapter 1 introduces into the topic of Flying Wing Anchors (patent pending) and gives background of this research. Further, the statement of the problem and the objectives of this study will be introduced.

INTRODUCTION AND BACKGROUND
Global energy consumption is constantly increasing. Modern societies, politics and economy are facing the problem of how to satisfy the need for a permanent and sustainable energy supply. One possible solution is to increase offshore wind energy production. Studies by Musial & Butterfield (2004) have shown that the overall offshore wind energy resources of the United States are 908,000 MW.
While offshore wind turbines in shallow water depth are already widely distributed in Europe, there is still a lack of deep-water solutions due to technical and economic issues as well as practical experience. Nevertheless, wind power in general has developed itself as a major source of renewable energy. Furthermore, onshore wind farms have satisfied the large demand for electricity in the United States and Europe (Matha et al., 2009). Studies by Musial & Butterfield (2004) have shown that only 10 % of the US offshore wind energy resources are located in shallow waters, up to 30 m in depth. The larger part, 90%, of the US offshore wind energy resources is located in deep water with depths of more than 30 m. For New England the overall offshore wind energy resources are 220,500 MW, where almost 95% are located in deep water.
The general difficulties of offshore wind turbines are high investment costs, higher capital and maintenance costs, as well as the different environmental conditions at sea such as more corrosion from salt water, additional loads from waves and ice and obviously higher construction cost. These difficulties require a long planning phase including environmental, engineering, feasibility and site-specific studies (Breton and Moe, 2009).
Currently the majority of wind farms in the world 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 fixed-bottom structures are placed on a foundation in the seabed and are, therefore, limited to water depths of about 30 m. Therefore, there is a need to develop new technologies for deep-water foundations, because fixed-bottom systems, such as lattice-jacket and tripods are not practical in greater water depths (Butterfield et al., 2007). Floating options are being investigated for such cases for which the load would be carried by the buoyancy force. In this regard, experience developed in the offshore oil and gas industry in countries like Norway, the US and UK could be highly valuable (Breton and Moe, 2009).

Figure 1: Progression of Expected Wind Turbine Evolution to Deeper Water (Musial & Butterfield, 2004)
A new "green" anchor concept called the Flying Wing Anchor (patent pending) was proposed by Gilbert and Bradshaw (2012) for floating offshore wind platforms. The Flying Wing Anchor is a combination of a torpedo pile anchor and a plate anchor. The anchor is lowered into the water by a long chain or cable and dropped from above the sea floor with its nose facing down thereby penetrating vertically the soil like a torpedo anchor. By increasing the mooring line tension the anchor moves along a specific trajectory until it reaches the expected soil depth at a certain orientation like a plate anchor ( Figure 2). The Flying Wing Anchor is a new concept that needs further research. However, preliminary analyses and model tests executed by University of Texas and University of Rhode Island show promise for this concept. The anchor has the potential to be used in many different applications, such as foundation for offshore wind turbines, floating bridges and renewable energy power plants for waves. Although the concept seems feasible, a fundamental understanding of the soil-structure interaction that considers the orders-of-magnitude range of shear rates during free-fall penetration, line pre-tensioning and environmental loading in practice needs to be further investigated.
Research on the Flying Wing Anchor in clays is currently being performed at the University of Texas (UT), University College Dublin (UCD), and Queens University Belfast (QUB). UT is performing 1g model testing of the anchor in clay soils along with analytical modeling of the anchor kinematics. UCD is performing detailed numerical analyses of the anchor capacity in clay. QUB is investigating the strength of clays at very high rates of strain that might be achieved during free-fall penetration.
Research on the Flying Wing Anchor in sands is ongoing at the University of Rhode Island. The research approach has been to look at the three phases of anchor installation and service loading including (1) free-fall penetration, (2) trajectory, and (3) capacity.
Studies of anchor capacity were initiated by Dietrich (2014) and trajectory is currently being investigated by Sivarajah (2015). This thesis focuses on the free-fall penetration aspects of the Flying Wing Anchor in sand.

STATEMENT OF THE PROBLEM
Although dynamically penetrating anchors in general have been studied in clay, there is very little information available to support the feasibility of installing dynamically penetrating anchors in sand. Based on the literature, dynamic penetration has been studied mainly for torpedo-type anchors in calcareous sands. There is essentially no data on the dynamic penetration of plate-shaped anchors in sands in general.

OBJECTIVES OF THIS STUDY
The objective of this study is to investigate and analyze the behavior of a new anchor concept called the Flying Wing Anchor under free-fall penetration in sand. This will be accomplished through a combination of 1g model experiments and numerical modeling.

CHAPTER 2: LITERATURE REVIEW
This chapter summarizes the existing literature related to dynamically penetrating anchors in sands.

DEEP PENETRATING ANCHORS AND TORPEDO PILES
Some research has already been done on dynamically penetrating anchors. One example is the Deep Penetrating Anchors (DPA) first introduced by Lieng et al. (1999). DPAs are rocket-shaped anchors, which when released from a specified height above the seabed, free-fall through the water and penetrate the ocean floor.
In the category of DPAs, Medeiros (2001) first introduced the concept of "Torpedo" piles. This anchor system consists of a pipe pile filled with scrap chain and concrete, close ended with a cone tip and is installed by free fall from a vessel. Medeiros (2002) tested the penetration of torpedo piles in sands in Brazil. To evaluate the torpedo pile penetration, computer programs were developed using the finite difference method and a viscoelasticplastic model to simulate the pile/soil interaction. Calculating the impact velocity and the maximum height from which to drop the torpedo, a computer program with hydrodynamic analysis was developed. days. In pull out tests, the medium soil resistance was about 800 kN and after 10 days the piles failed with loads between 2000 to 2200 kN.
The authors further summarize that torpedo piles are less sensitive to increasing water depth than conventional concepts, because special subsea equipment or large support vessels are not required. Richardson et al. (2005) carried out research where they analyzed the behavior of DPAs in calcareous sand through a series of centrifuge model tests (see Figure 4). As a model anchor, Richardson et al. (2005) used a 1:200 scale model, fabricated from brass and designed in accordance with the Type I Torpedo Anchor reported by Medeiros (2001).
The purpose of their research was to predict embedment depth from the impact velocity. (1) Where is the vertical pullout capacity, is the submerged anchor weight, is the bearing capacity factor, ′ is the vertical effective stress, is the projected area of the anchor, is the ratio of shaft friction to effective overburden stress and ℎ is the shaft area of the anchor.
In addition to the vertical pullout capacity formula, Richardson et al. (2005) also found expressions for the static resistance force .
Furthermore, the equation of motion for anchors were introduced.
where is the anchor mass and is a rate dependent term to account for velocity dependence of the soil resistance terms. is further defined as: Where is a constant, is the anchor velocity and is the reference penetration velocity at which the static resistance was measured (1 mm/s). A finite difference approach was used to solve Equation 3. Richardson et al. (2005) stated that the bearing capacity factor as well as the ratio β in calcareous sand is somewhat uncertain, therefore the β has been applied to fit the measured static pullout capacity data. The authors used values of 32 and 35 with β values of 0.42 and 0.3. The average value of = 0.006, which are 0.6% per log cycle.
Overall, Richardson et al. (2005) indicated that the DPA has potential as an anchoring system in calcareous sediments. Additionally, with the given formulas it is possible to predict the embedment in calcareous sand from the static resistance profile. Embedment Where and 0 are shear stress and yield shear stress, ̇ is the shear strain rate, 0 is the yield shear strain rate, is the consistency index, is the power-law and 0 is the yield viscosity that is defined as the yield shear stress over the yield shear strain rate. At the tip of the shaft, an ad hoc increase is assumed. This increase is defined as is the yield shear stress specified at the tip, is the static undrained shear strength of the soil, is the end-bearing factor. and are the penetrator frontal area and projected area of the tip on the plane parallel to the penetrator longitudinal axis.
The CFD procedure gave promising results in predicting the embedment depth in both a laboratory and full-scale torpedo anchor installation tests in clays. In the CFD procedure, there is no further need to assume the anchor effective mass, internal drag force and side adhesion factor as the case in the analytical approach. Additionally, it provides estimates of the pressure and shear distributions on the soil-anchor interface and in the soil.
Where is the net total downward force, is the external driving force (e.g. rocket motor), is the penetrator buoyant weight, is the nose or tip bearing resistance, is the side friction or adhesion and ℎ is the fluid drag force. Figure 5 shows the forces acting on the penetrator before and after contact with the seafloor. The tip resistance can be determined as Where ( ) is the soil undrained shear strength at a depth 0.35 below , averaged over ℎ increment of penetration, ̇ is the strain rate factor, is the end area of penetrator and is a dimensionless nose resistance factor, which is determined by the following formula.
The soil undrained shear strength is determined from the following equation based on the work of Seed and Lee (1967): Where is the critical confining stress, and ф is a bearing factor. The critical confining stress is estimated with the formula: Where is the fractional relative density calculated by the following equation: The bearing factor is determined by: The side friction is determined with Where is the soil undrained shear strength averaged over the length of the penetrator in contact with the soil, is the side soil contact area of the penetrator, is the soil sensitivity.
Where * is the maximum strain rate factor, ̇ is the empirical strain rate coefficient, is the velocity at a certain depth, 0 is the empirical strain rate constant, is the undrained shear strength and is the equivalent diameter of penetrator.
The fluid drag force is acting while moving through water, hence, it is further assumed that this force is also existing when the object is penetrating into the soil. This force is calculated by the following formula: Where is the dimensionless fluid drag coefficient, which is the same as that in seawater, is the mass density of the soil, the "fluid" being accelerated and is the penetrator velocity after penetrating the ith layer.
The inertial force is defined as the following: Where M is the penetrator mass and the ratio is describing the instantaneous change in velocity. In the following, the ratio should be replaced by (2Δv)/(2Δz). The double increments are used to minimize deviations in the prediction.

= ( )
The new velocity increment for (i+1)th increment is given by: For the incremental calculation, the velocity at i=1 needs to be defined as Where .5 , .5 , .5 , .5 , ℎ.5 are initial estimates of the respective force values based on conditions at mid-depth in the first layer of penetration.

DYNAMICALLY EMBEDDED PLATE ANCHORS
The concept of Dynamically Embedded Plate Anchors (DEPLA) has been developed from the concept of Suction Embedded Plate Anchors (SEPLA). SEPLAs have been developed as an efficient anchoring system. This system combines the advantages of suction caissons, where the penetration depth and geographical location is known and vertically loaded plate anchors, which have a high geotechnical efficiency and low installation costs (Wilde et al., 2001). The concept was exclusively applied in clays.
The SEPLA consists basically of two parts, a suction caisson and a plate anchor, which is slotted vertically into its base. The suction caisson embeds the plate anchor and penetrates it into the seabed under self-weight. The water is pumped out of the interior of the caisson until it reaches the design embedment depth. In the following, the anchor mooring line is then disconnected from the caisson and the pump flow is reversed, which results in water being forced back into the caisson, causing the caisson to move upwards.
In the meantime, the plate anchor is left in place at the designed depth. The mooring line, which is attached to the plate anchor is then tensioned causing the plate anchor rotation in the ground to an orientation that is similar to the direction of the loading. (Gaudin et al., 2006) The installation process is also shown in Figure 6. With the increasing water depth, anchor installations become more time consuming and complex, which results in higher costs of construction. Due to the fact that no external energy source is needed, the DEPLA provides a more economical and sustainable solution than the SEPLA.
The anchor installation follows a similar approach like the SEPLA. A major difference is the DEPLA flukes and sleeves which will be relesed in the ground while the DEPLA follower will be pulled out and used for further anchor installations. Another difference is that the anchor will be dropped from a certain height over the seabed. Therefore, the anchor is penetrating through water and later soil. times the length of the DEPLA follower. The majority of the test data was about 1.9 to 2.1 times the follower length, which shows respectively agreement with reported field test data of 1.9 to 2.4 times the anchor length for an anchor with a weight of 79 tons which is dynamically installed (Lieng et al., 2010).

CHAPTER 3: PHYSICAL MODELING METHODOLOGY
This chapter provides information on the methods used to perform small-scale physical modeling at 1g. The test anchors, test soil, static penetration tests, and dynamic penetration tests are described.

TEST ANCHORS
The test anchor geometry was obtained from the University of Texas. The anchor was designed to remain hydrodynamically stable during free-fall through the water column.
The anchor had the following dimensions: -Height of 105.9 mm -Width of 127 mm -Thickness of 12.7 mm The geometry is shown in Figure 8.  The anchor could either be used with just a short rod, which should be simulating basically just the weight of the anchor or with the attached rod, which gives the possibility to add weight to the anchor ( Figure 12). The length of the rod was designed in that way that a potential penetration under laboratory conditions would not exceed the length of the rod. In other words, the anchor would potentially stop before reaching the full length of the rod. The small rod had a weight of 16.7 grams (0.037 lb); the large rod, seen in Figure 12, and the added weight summed up to 1.067 kg (2.354 lb). The total length of the anchor and rod is 39.4 cm (15.5 in).

TEST SOIL
Important for this study was the accurate determination of the soil and its properties. The soil used for the tests was obtained from Westerly, Rhode Island. The grain size distribution ( Figure 13) suggests that the soil is uniform with sizes ranging from 0.2 -1 mm and no fines.  The static penetration tests were performed in a 0.9 m x 1.2 m x 2.4 m test tank and the in-place unit weight was determined by placing the cups of known volume at different heights within the tank. The average unit weight of the sample was 14.69 kN/m2. The relative density calculated with the following formula: The values are the dry unit weights from the test sample. and are taken from Table 1.

TEST TANK
The test tank for static penetration tests was developed and was used before by the University of Rhode Island and had the following inside dimensions:  (DAQ) was used to process the data. All these instruments are described in the following section.
A string potentiometer, often called a string pot, is a transducer which can detect and measure the linear position of an object. It is basically a long spool of nylon line attached to a transducer, which transforms the extent of the nylon cable into an electronic signal.
The string pot we used was an SP2-50 with a full stroke range of 1.27m (50 in) from the company Celesco ( Figure 15).

Figure 15: Celesco String Potentiometer mounted on the frame
A load cell is a transducer which creates an electronic signal if a force, either tension or compression, is applied to it. The magnitude of the electronic signal is directly proportional to the applied force. In other words, the higher the force that is applied, the higher the signal that will be recognized by the Data Acquisition Tool (DAT). The load cell we used was a piezoelectric load cell SBA-500LB from the company Omega ( Figure   16).

Figure 16: Load Cell Omega SBA-500LB
All sensor data was recorded using a Data Acquisition System (Figure 17). Through a data acquisition system, it is possible to record a signal from an external device (in this research: String pot and load cell). The signal in mV or V will be recorded and saved into an excel sheet. This excel sheet then contains the raw data which were recorded by the external devices. Later, this raw data can be used to process data and draw graphs. In addition to that, the Data Acquisition Tool we used had a power supply, which could provide small units with electricity. The Data Acquisition Tool was carefully chosen to fulfill both the requirements on precision of the data procession and the compatibility with the used devices. The Omega IstruNet 100 with a InstruNet 200 controller unit seem to fulfill these requirements best.

SOIL PREPARATION
It was crucial for this research to have a uniform sand sample at a desired relative density. To achieve similar soil properties the concept of the pluviator was used. A portable pluviator developed by Dave and Dasaka (2012) and used by Gade et al. (2013) and Dietrich (2014) was seen to meet the requirements best (see Figure 18).

Figure 18: Details of Portable travelling pluviator assembly (Dave and Dasaka, 2012)
The concept of the portable pluviator was calibrated by varying drop height (50.8 mm to 190.5 mm) and the number of installed sieves to achieve a relative density of about 23 %.
It was found out previously by Dietrich (2014)

TEST SET UP AND PROCEDURES
The test set up consisted of the test tank and a big frame over the test tank to mount equipment, such a as string potentiometer and a load cell. The dimensions of the test tank made it possible to run four tests at different positions without preparing a new sample. A schematic diagram is presented in Figure 19.

Figure 19: Schematic Diagram of Test Set Up for Static Penetration Tests
long rod and a load cell is screwed into the rod. The load cell is on the other side connected to a little rod on which weights could be added. This little rod is further connected to a long cable. The long cable is part of a winch which is attached to the ground. While the winch is releasing the cable the anchor with weight and load cell is going down and therefore the load cell is reading an increasing compression force. The anchor penetrates statically driven by the weight of anchor and added weight into the ground. This test was performed until a depth of around 2 -3 anchor fluke length was reached.

Figure 20: Picture of Test Set Up for Static Penetration Test
A string potentiometer, described earlier, gives the extent of the cable and the data acquisition tool is giving the time. Therefore, it could be clearly seen at which point of time the string pot had which extent. A line can be drawn, showing which penetration at what point of time was achieved. Furthermore, this is especially crucial when comparing the sharpened anchor shape and the normal anchor shape.
In addition to that, the load being applied on the anchor was recorded by the load cell.
This signal, which was sent by the load cell, could then be processed by the Data Acquisition Tool. Later the recorded data from the Data Acquisition Tool, which consisted of data from the string pot as well as the load cell, could be combined, which results in a force displacement relationship.

TEST TANK
The dynamic penetration test tank consisted of steel and was put on wheels which allowed it to be moved inside and outside, which was crucial for the high speed tests, which we ran in an outside environment. Furthermore, the test tank had the following The test tank was used for previous tests by the University of Rhode Island and was manufactured from steel, which made it possible to saturate the whole sample and simulate a saturated sand sample. Furthermore, the test tank can be dried after saturating it.

SOIL PREPARATION
For the dry tests, the soil preparation was executed the same way as in the static penetration tests, which were described earlier. For the saturated sand sample, the tube was filled up to a height of 5 cm first, following the sand was pluviated first through the air and then through water. Great attention was paid to maintain a water level between 4 and 6 cm above the soil surface. This procedure was continued until the final volume of sand was reached. The water was maintained at a level of 4 to 6 cm above the soil surface. The soil sample rested for about two hours, then the water which remained over the soil surface was sucked from above till the water column over the soil column had dissipated.
For the saturated sand, the average total unit weight for the saturated sample was between

Figure 22: Test Set Up in Bliss Hall for dynamic penetration tests
In process of the research, a second test set up was developed. The test set up was basically moved outside to obtain a higher height by letting the anchor drop from the third story of an adjacent building.

Figure 23: Test Set Up outside of Bliss Hall
The concept shown in Figure 23 is similar to the one inside the basement of Bliss Hall. In this case, the anchor was also attached to a nylon line, which was attached to a clamp inside the building. The height from the soil surface to the position of the anchor at the height of the third story of the building was 11 meters. The nylon line was burned the same way as in the inside test. Figure 24 shows a picture of the upper test set up, at the location where the anchor was attached, at the third story of Bliss Hall.

Figure 24: Test Set Up for the outside Tests. View on anchor and pulley CHAPTER 4: PHYSICAL MODELING RESULTS AND DISCUSSION
This chapter presents the results and discussion of both the static and dynamic penetration tests described in Chapter 3. Figure 25 shows the applied load over the depth in the soil. Tests 1 and 2 had a blunt edge and Test 3 and 4 had a sharp edge (see also Chapter 3). In general, it can be said that Tests 1,2 and 4 behave in a similar way, while Test 3 seems to be off. In Test 3 the anchor tilted highly during penetration which highly affected the load cell and string pot readings. Test 3 was therefore excluded and retested by Test 4 which shows more likely what could be expected in terms of shape of the curve. Generally, Test 1,2 and 4 are penetrating under its own weight added by a constant force of around 15 N (read by load cell) to a depth of 30 mm (1.18 inches). After that, the curves are increasing more and from Figure 25 there appear to be significant differences between sharp and blunt edge, which will described in the following.

Figure 25: Depth vs. Load Cell Readings for the Static Penetration Tests
The blunt edge curves of Test 1 and 2 increase evenly after the first 30 mm where they appear rather constant. Furthermore, it can be stated that the curves of 1 and 2 are very similar in shape. At the greatest extent, both curves are off by around 20 N, which equals 5% using 380 N as a base. This underlines that both tests can display the behavior of the blunt edge anchor very well. As stated earlier, the anchors initially penetrate to a depth of  The sharp edge curve (Test 4) also increases evenly after the first 30 mm with a constant force of around 15 N. The inclination can be described as linear and steady. An exponential increase at the beginning cannot be seen. At 140 N a depth of 150 mm is reached. The incline is shrinking slightly and hardly visible and remains at a steady increase until it reaches the final position at 300 mm in depth with a force of 335 N.
A difference between the sharp edge and the blunt edge is obvious. The bearing resistance is smaller and the applied force is less than for the blunt edge anchor at the same depth. The difference of the lines of sharp edge and blunt edge constantly increase until the final depth at 300 mm. The difference in the bearing stress is 35 kN/m2 at the max at final depth. Concluding, it can be stated that the sharp edge anchor is penetrating the soil more smoothly while the blunt edge anchor is displacing more soil due to the shape and, therefore, a higher applied load is necessary to reach the final depth of 300 mm.
Since the static push tests measure bearing capacity but also a small amount of side friction, a theoretical approach was taken in order to calculate the side resistance.
Therefore 0 was calculated with the formula, which is presented below: It has further been assumed that 1.5 * 0 is equal to , which is within the values from Conduto (2001) for driven piles. The friction angle in the test tank was assumed to be approximately 37 degrees based on triaxial data in Dietrich (2014). In addition to that, the horizontal stresses were calculated over the depth. The horizontal stress was calculated.
With the horizontal stress the bearing stress could be calculated with the formula = / Where represents the measured toe force subtracted by the theoretical friction which was calculated with the horizontal stresses and is the bearing area. The ratio of shaft resistance and toe resistance was calculated and revealed that this ratio was only 2.8% on average for the blunt edge and 3.4% for the sharp edge anchor.
The bearing stress is plotted in Figure 26 for the three tests, which are two blunt edge and one sharp edge anchor.   Figure 26 shows a steady increase of the bearing stress over the depth. The curves can be described as linear with a slight parabolic shape.
In this research, the bearing stress was only calculated from the point of the anchor being fully embedded. The reason for this is that limitations in the measurement equipment and the uncontrolled behavior of the soil in terms of dilation cannot be seen as reliable.
With the measured data and the theoretical calculations the "true" bearing capacity factor could be calculated. The bearing capacity factor is important for implementing it into the analytical model for predicting the embedment depth. It describes a factor which displays a relation from the bearing resistance and the depth and effective stress. The bearing capacity factor is calculated by the following formula: Where is the bearing stress at a certain depth and describes the effective stress of the soil.

Figure 27: Depth vs. Bearing Capacity Factor Nq for the static push test
The bearing capacity over the depth is plotted in Figure 27. Moreover, the first 105 mm are excluded in the calculation due to questionable reliability. The reason for this is that the Nq values being calculated vary extremely in the first 20 mm of penetration depth. This is mainly due to resolution of the instruments.
This figure shows that the bearing capacity factor has a minimum of 48 and a max of 60 for the blunt edge anchor and a minimum of 39 and a max of 47 for the blunt edge anchor.
The bearing capacity factor Nq has also been studied in the bearing capacity theory by Meyerhof (1951 deep foundations regarding Meyerhof (1951) was 300. These values are significantly higher than the measured bearing capacity values.

DYNAMIC PENETRATION TESTS
The dynamic penetration tests were executed to understand the dynamic penetration behavior. Moreover, it was important to understand, which changes in the test set up and constants influence the penetration depth of the anchor. The following section will show, describe and explain the results from the dynamic penetration tests.
During the research, variables were identified. These were mainly the fall height, the shape of the anchor, either blunt or sharp edge shape, and the soil conditions, either saturated or dry condition. In addition to that, another variable was adding weight to the anchor, which is increasing the weight of anchor without changing its shape. (See Chapter 3 for more information and test set up description).

DYNAMIC PENETRATION TESTS IN DRY SAND
The dynamic penetration tests under dry conditions were executed for blunt and sharp edge anchors, with and without adding weight and one test from two different heights.
The following table displays the tests that were executed under dry soil conditions. The results in Table 3 show that the penetration depth (14.6cm) of a sharp edge anchor is slightly higher than the penetration depth of a blunt edge anchor (13.3 cm). In addition to that the penetration depth of a blunt edge anchor with double the speed resulted only in a slightly higher penetration depth (16.2cm). A significant difference between the blunt and sharp edge anchor was the penetration angle, which describes the angle at which the anchor was found after penetration. The penetration angle of the blunt edge anchor was on average 4 degrees, while the angle from the sharp edge anchor was on average 19 degrees. The test results suggest that the sharp edge anchor promotes tilting during the flight. The blunt and sharped edge anchors at an impact velocity of 7.3 m/s penetrate between 1.23 to 1.39 times their fluke length. The impact velocity of anchors with added weight, represented in Tests 3.1 and 4.1, was the same for both anchor types. Interestingly, while in the tests without adding weight the shape made a slight difference, the penetration depth is now the same with 0.28m or 2.6 times the anchor length for both anchor types (see chart). What this data shows, is that the anchor shape does not play an important role in terms of the same added weight. The penetration depth of both anchors is similar. The penetration angle, which has been significantly different from blunt to sharp edge anchors in the tests without added weight, does not play an important factor anymore and is similar as well (4 degree penetration angle vs. 5 degree penetration angle).
The penetration depths for the dry tests in general were varying between 1.23 and 2.6 times the anchor length. It seems that the penetration angle plays an important role in the tests without added weight, while in the tests with added weight there is no difference in the penetration angle and embedment depths for the two anchor shapes.

DYNAMIC PENETRATION TESTS IN SATURATED SAND
This section describes the results of two tests, both under saturated soil conditions. The difference of both tests is in the total anchor weight. The penetration of the anchor in a saturated sample can generally be described as low. Table 4 shows the impact velocity over the penetration depth of these tests. In both cases, the immediate penetration angle at the time of penetration was at around 4 degrees. At the point of impact, the anchor remains at that angle for a little bit, but then falls to one side and did not stay in the direction of penetration (see Figures 29 and 30).

ANALYSIS OF THE DRAINAGE CONDITIONS DURING DYNAMIC PENETRATION
Soils can experience either drained or undrained conditions, depending on the rate of loading and the permeability of the soil. Coarse grained material, such as sands and gravels, can generally be described as drained, because of a high permeability. A low permeability soil such as silts and clays can be described as undrained.
Dry sand is obviously acting under drained conditions. Under saturated conditions, the question is, whether the soil is experiencing drained, partially drained or undrained conditions. To determine the drainage conditions, procedures which we know from Cone Penetration Tests (CPT) can be applied. Drainage conditions during penetration have already been analyzed for CPT in literature by Finnie and Randolph (1994). The authors came up with an equation which could determine whether a soil is experiencing undrained, drained or partially drained conditions under penetration.
Where the dimensionless penetration rate V is calculated with the cone penetration rate , the cone diameter , and the coefficient of consolidation for lateral drainage.
According to a number of researchers (Finnie and Randolph, 1994, Chung et al., 2006, Kim et al., 2008, the transition from fully undrained to partially drained conditions occurs when ≈ 10.  For this research and its tests, the findings have been applied for the saturated sands. As a cone penetration rate the impact velocity of the anchor was taken, which was 7.3 m/s, for the cone diameter , the thickness of the anchor of 1.27 cm (0.5 inch) was taken.
The coefficient of lateral drainage ℎ was as calculated as a function of the coefficient of the vertical drainage, which is shown in the following: For simplicity reasons, the ratio of ℎ was taken as 1, which resulted in ℎ = . The coefficient of vertical drainage was determined with the equation by Ranjan and Rao (2007).

= (29)
Where is the permeability index, is the coefficient of volume compressibility and is the specific weight of water. A typical value for a loose sand for the coefficient of volume compressebility was 1 * 10 −4 −1 from Domenico and Mifflin (1965).
For the permeability index a value of 5.

DISCUSSION ON THE EXISTENCE OF BOUNDARY CONDITIONS
The effects of boundary conditions come into place due to the close distance of the penetrating anchor to the container wall. During penetration the influence zone of the penetrating anchor extends from the sand into the wall and therefore into the steel. Steel has a higher density and therefore also the strength of the soil is higher.
In literature Bolton et al. (1999) and Phillips & Valsangkar (1987) studied the effects in CPT tests in sands. They both tested the ratio S/B for sands, where S is the distance of the centre of the CPT test from the nearest container wall and B is the diameter of the cone. It was found that for a circular container, there is no significant deviation in Q, for both S/B = 11 and S/B = 22 (Bolton et al., 1999). Also Phillips & Valsangkar (1987), which have studied this ratio as well, recommend to maintain a ratio S/B > 10.

SUMMARY
Based on 1g model tests in dry and saturated sand the following summary points can be made:  The penetration of the sharp edge anchor is higher than the blunt edge anchor for tests without adding weight to the anchor weight.
 The penetration of the sharp edge anchor is the same as the blunt edge anchor for tests with adding weight to the anchor weight. Furthermore, the final penetration angle was the same for both anchor shapes.
 The penetration depth in dry conditions is higher than the penetration depth in saturated conditions.  It has been determined that anchors in dry conditions are penetrating under drained conditions while anchors in saturated conditions are penetrating under undrained conditions.

CHAPTER 5: NUMERICAL MODELING
Chapter 5 describes the development of two predictive numerical models that represent the drained tests under dry conditions based on the publication of Richardson et al. (2005) and for the undrained tests under saturated conditions based on the Handbook for Marine Geotechnical Engineering. Both of these approaches are described in Chapter 2 sections Richardson et al. (2005) and NAVFAC (2011).
The drained model, which was developed by Richardson et al. (2005), was applied to torpedo piles and a tri plate anchor developed by Dr. Aaron Bradshaw and Joseph Giampa. This model was extended in this thesis to predict the embedment for the kite shaped anchor as will be explained in the following sections.
The model is programmed in MATLAB, which is a multi-paradigm numerical computing environment that allows for matrix manipulations, plotting of functions and data, and implementation of algorithms.

MODELING DRAINED CONDITIONS IN DRY SAND
As mentioned above, the existing model has been used in previous research on torpedo piles and the triangular plates to predict the embedment as a function of velocity.
Unfortunately Richardson et al. (2005) does not comment on whether they are dealing with drained or undrained conditions. This is the reason why it is assumed that they dealt with drained conditions. Therefore, this approach will be used for predicting the behavior of anchors in dry sand for drained conditions.

DEVELOPMENT OF THE MODEL
The publication and its formulas were already described in Chapter 2, but will be repeated here. Richardson et al. (2005) determined the static resistance force as: Furthermore, the embedment depth formula was introduced.
where is the anchor mass and is a rate dependent term to account for velocity dependence of the soil resistance terms. is further defined as: Where is a constant, is the anchor velocity and is the reference penetration velocity at which the static resistance was measured. Richardson et al. (2005) does not mention if they are dealing with drained, partially drained or undrained conditions. Equation 31 was solved using the finite difference method by substituting ̇ and ̈ with the following expressions Substituting equations 33 and 34 into equation 31 and rearranging yields.
Solving equation 35 for −1 yields, this results in the following equation: Assuming now a uniform and homogenous deposit, the only parameter for a torpedo pile that changes during the process of penetrating are , the projected area, , the diameter and obviously also the depth . In this case, the increased while the torpedo pile and especially its tip was fully penetrating into the soil. After that the value stays constant.
Also the diameter is increasing within the tip and after that staying constant over the length of the pile. The variable is increasing with the increase in depth.
This model was fully programmed in MATLAB (Full Code in Appendix). Over the full length of the pile the same projected area and diameter was assumed. The full code of this model is attached in the appendix. Equation 36 is basically programmed with a for-loop where a number of elements, or basically how often the loop will be performed, is defined. Within this for-loop each embedment depth is calculated at a certain point following the for-loop with the formula described earlier. After that, the new velocity is calculated with the following formula: After calculating embedment depth and velocity of the specific point the for-loop and therefore the if-loop starts again and continues until the final embedment depth is reached.
The model was then modified to match the requirements of a different shape and different soil specific parameters. The projected area was programmed as constant over the full length. Moreover, the shaft area ℎ was applied to the actual are and the projected area was seen as constant over the full depth. In addition, the value as well as the value which are constants in the formula, were applied for the soil and anchor specifications. For the values, the test results from the static push tests which were described in Chapter 4 can be used. The value, which is the ratio of shaft friction to effective overburden stress, was also calculated from the corrected values described in Chapter 4. With the beta method which is known from deep foundation engineering, beta is calculated with the following formula: Where can be calculated as 1.5 * 0 for piles (Conduto, 2001) and the interface friction angle is 2 3 ⁄ ′ . 0 is defined as 1 − sin ′ . An average beta of 0.28 was found over the full penetration depth.
The constants and the application for the kite shape were then programmed in the model.
These were mainly parameters which describe the shape of the anchor, like length, width and thickness. Also, the weight of the anchor and the soil properties were applied. In addition to anchor shape parameters, the length from the edge to the greatest width was measured and defined. The rate dependent term , which was applied in the publication from Richardson et al. (2005), was seen to be not applicable for dry tests. Sands do not seem to experience high strain rate effects in dry sands. Strain rate effects are believed to be negligible in dry sands. (e.g. Casagrande andShanon, 1949, Sathialingam andKutter, 1988) Therefore, the λ was assumed to be 0 in the calculation.

Figure 31: Anchor divided into Sections (I, II, III)
The if-loop which had only two cases in the existing model was extended to one extra case. The cases can be described as the following: -The first case describes the depth from the edge to the greatest extent of the width (Area I in Figure 31) -The second case describes the depth from the greatest extend of the width to the edge on the other side (Area II in Figure 31) -The third case describes the fully embedded anchor (Area III in Figure 31) Therefore, the anchor is basically divided into two big parts. The first is up to the depth where the width reaches a maximum and the other one is until the end of the anchor is reached.
Summarizing, the following simplifications were made -The projected area is constant over the full length (including Area I) -The bearing capacity factor being constant over the full length -The ratio of shaft friction to effective overburden stress β was assumed to be 0.28 As stated earlier the bearing capacity factor was calculated with the static penetration test.
For the blunt edge the minimum Nq was 48, the max Nq was 60; therefore two different analysis for the max and the min case will be executed. Same will be for the sharp edge anchor with a minimum Nq of 39 and a maximum Nq of 46. The results of this sensitivity analysis are shown in the following.

SIMULATION OF THE MODEL TESTS
The result of the model is given in figure 32 as an example for a blunt edge anchor with a bearing capacity factor of 48. The model predicts the embedment depth as a function of velocity and shows therefore the change of velocity within the ground.  The predicted results can definitely be described as close to the actual measured results.
The model is slightly over-predicting the embedment depth, except for the blunt edge with adding weight. For the blunt edge, a bearing capacity factor should probably be closer to a value of 48 (min). Especially, the tests with a blunt edge anchor with adding weight seem to be more reliable. For the sharp edge anchor a bearing capacity factor of 46 (max) seem to have the best fit. This factor is generally over predicting the embedment depth but it can be considered as little comparing to lower bearing capacity factors.
What this table also shows, is that the bearing capacity factor has an important impact on the embedment depth, while the side friction as stated earlier, is only responsible for around 3 % of the total resistance. In other words, the anchor is mainly experiencing bearing resistance. This explains why the bearing capacity factor plays this important role.
The presented measured and predicted data encourage a discussion and explanation of the soil behavior under dry conditions. Rapid loading tests have been made on dry sands and are reported in literature, with the result that the strain rate effect in dry sands is small or neglible. (e.g. Casagrande and Shannon, 1948) Although the behavior was studied later, rarely information is available on the change of friction angle during loading. Whitman (1970) reported that the friction angle for the tested sands first decreases as the strain rate increases beyond the required time to failure of 5 min. Later the trend reverses and a slight increase in strength is reported. Although the author questioned his results and indicated systematical errors as the explanation, Sathalingam and Kutter (1988) supported the findings by explaining this behavior with similar findings on bearing capacity reported by Vesic et al. (1965). The tests on bearing capacity show first a decrease in bearing capacity and as the loading velocity increases a gradual increase is reported.

MODELING UNDRAINED CONDITIONS IN SATURATED SAND
The model predicting the embedment depth of an anchor under saturated conditions will be described in the following section. The approach, which was used, was developed by the Handbook for Marine Geotechnical Engineering (2011), referred to as NAVFAC (2011). The authors assume an undrained soil condition, which means that the pore water in the soil does not have time to flow, and excess pore pressure are developed based on the soils' tendency for volume change (NAVFAC, 2011).
Therefore, this approach will be used for predicting the behavior of scaled anchors in saturated sand for undrained conditions, as well as predicting the anchor behavior for the full scale.

DEVELOPMENT OF THE MODEL
The publication NAVFAC (2011) and its formulas were already described in Chapter 2, but will be repeated here. The authors developed an embedment prediction model for penetrating objects into the seabed under undrained conditions. Different forces acting on the penetrating object are introduced. These are shown in the formula below. A positive force describes a downward and a negative force describes a resisting or upward force.
Where is the net total downward force, is the external driving force (e.g. rocket motor), is the penetrator buoyant weight, is the nose or tip bearing resistance, is the side friction or adhesion and ℎ is the fluid drag force.
The tip resistance can be determined as Where ( ) is the soil undrained shear strength at a depth 0.35 below , averaged over ℎ increment of penetration, ̇ is the strain rate factor, is the end area of penetrator and is a dimensionless nose resistance factor, which is determined by the following formula.
The soil undrained shear strength is determined with Where is the critical confining stress, and ф is a bearing factor.
The side friction is determined with Where is the soil undrained shear strength averaged over the length of the penetrator in contact with the soil, is the side soil contact area of the penetrator, is the soil sensitivity. In cohesionless soils, such as sands, we usually do not deal with issues of sensitivity. In this context, it makes therefore sense to think of a substitute of this parameter for sands.
Where * is the maximum strain rate factor, ̇ is the empirical strain rate coefficient, is the velocity at a certain depth, 0 is the empirical strain rate constant, is the undrained shear strength and is the equivalent diameter of penetrator.
The authors also include a fluid drag force in their equation. This formula seems to be reasonable, while the object is moving through the water. The authors assume that this force will continue as it moves through the soil. This force is calculated by the following formula: Where is the dimensionless fluid drag coefficient, which is the same as that in seawater, is the mass density of the soil, the "fluid" being accelerated and is the penetrator velocity after penetrating the ith layer.
It is somehow questionable, whether this force should be included while the anchor is penetrating through the soil, especially since the other forces are already including parameters accounting for drag forces in the soil. From a theoretical point of view, this force should be included for the area which will be above the soil surface at the point of initial penetration. Including and excluding this term in later calculation, it was seen that this term does not have a big impact on the penetration depth. In the following, this term should, therefore, be neglected.
The goal is it now to rearrange the equation towards −1 . Eventually, this results in the following equation. Due to simplicity the substitutions of ̇ are not written in this formula.
What the equation indicates is the ̇ and are dependent on the velocity, or specifically on the embedment depth over the increment of time ∆ .
With the equation, the embedment depth +1 in every point can be calculated and, therefore, the velocity can also be calculated with the following formula: Similar to the drained model, the constants and the application of the kite shape were programmed in the undrained model. These were mainly parameters which describe the shape of the anchor, like length, width and thickness. Also the weight of the anchor was applied.
In the MATLAB model equation 50 is basically programmed with a so called for-loop where a number of elements, or basically how often the loop will be performed, is defined. Within this for-loop the model is calculating each embedment depth at a certain point.
The if-loop is as well as the if loop for the drained model divided into three different cases. The cases are analog to the ones of the drained model: Besides the changing area, which is crucial for accounting for the side friction, the model implies further features which will be explained in the following: The buyout weight which is the anchor dry weight subtracted by the buyout force, is changing over the depth. Furthermore, the dimensionless nose resistance factor, is calculated for every increment in time and is therefore also applied to every embedment depth and velocity.
The same applies for the strain rate factor ̇, which consists of three parameter values: -̇ (the empirical strain rate coefficient) - * (the maximum strain rate factor) -0 (the empirical strain rate constant) These values were determined from the chart presented in NAVFAC (2011). For objects where excess penetration is of primary concern, the value for * is 2, for ̇ is 1915.2 N/m2 and 0 is 1.0.
The undrained shear strength seemed to be a difficult property to measure. When sands are sheared during a dynamic penetration event, the pore water pressure does not have time to flow, and failure occurs when either the sand grains are crushed or cavitation of the pore water occurs. Dealing with this problem, Seed and Lee (1967) developed methods to predict the undrained shear strength from drained data. Result of this is the calculation of the undrained shear strength with the following formula: To determine the critical confining stress and the fractional relative density equations 12 In addition to that, it was assumed that shearing of the sample results in only dilative behavior and no strain softening has occurred. In this case the residual load is the same as the undrained shear strength . Usually, the relation can be described as Where varies between 0 and 1. (see also Yoshemi et al., 1999)

SIMULATION OF THE MODEL TESTS
The result of the model is given in figure 33, as the velocity over embedment depth for a blunt edge anchor without adding weight as an example for an undrained shear strength of 15 kPA.  Table 6 compares the predicted and actual measured results at different undrained shear strengths for the blunt edge anchor with and without adding weight. As a second reference, undrained shear strength of a value of 15 kPa had a good agreement with the measured data. While the model in this case is slightly overpredicting the embedment depth of just the anchor, the anchor with adding weight is almost on point the same value. This shows clearly that the undrained shear strength, which is a difficult parameter to estimate, has a crucial effect on predicting the embedment depth and the reliability of the model.
Saturated sand under rapid loading is highly influenced by volume change tendency in shear. Under static or slow loading, loose sands tend to compress and dense sands tend to dilate. (Omidvar et al., 2012) Dilation results in a decreasing pore water pressure and increasing effective stress, while contraction results in an increasing pore water pressure and decreasing effective stress. Under rapid loading, loose saturated sands tend to dilate. Whitman (1970) reported an increase in the soil of 200% at low to moderate confining pressures. If the decrease in pore water pressure is high enough, the pore water will cavitate.
The described behavior can be displayed in the presented tests. The saturated sand sample built up high strength. The sand sample, tended to dilate with the effect of decreasing pore water pressure and increasing strength. Comparing the embedment depth from the blunt edge anchor under dry and saturated soil conditions, a difference of factor 3 is reported. This agrees with Whitman (1970). In this context it is not sure if cavitation occurs, which would limit the pore water pressure to -1 atm.

PREDICTIONS FOR THE FULL SCALE ANCHOR
As discussed earlier, the sand was seen to experience dilation during the penetration of the anchor. This behavior can be assumed as long as the confining pressures are assumed to be low. Dilation occurs as long as the effective stress paths increase and , so the If the soil in the prototype is contractive due to the higher confining pressures, the peak undrained shear strength will be higher than 15 kPa. The strength in the prototype was therefore modeled using the equations proposed by Seed and Lee (1967) that resulted in an undrained shear strength of 302 kPa.
The results of the model are shown in Table 8. The impact velocities of 7.5 m/s, 13 m/s and 24 m/s were carefully chosen to match with the impact velocities which were published for torpedo piles, mainly by Richardson et al. (2005) and Madeiras (2002 In the full scale tests the importance of the correct estimation or better determination of the undrained shear strength is obvious. Although the reported test data is within the ranges given by the undrained model, these ranges are huge and, therefore, do encourage further study. Future research should, therefore, focus on analyzing strain rate effects of saturated sands as well as better predication models of undrained shear strength and undrained shear strength at the critical state.

CHAPTER 6: CONCLUSIONS
The topic of this thesis was the investigation of the penetration behavior of the "Flying Wing Anchor" (patent pending). The penetration behavior of objects in sand have already been studied previously. The literature review is displaying relevant literature in this field, along with physical tests and first prediction models for the embedment depth.
The goal of this thesis, to investigate and analyze the behavior under dynamic penetration in sand, was accomplished through a combination of 1g model experiments and numerical modeling. The physical tests led to the following findings:  The penetration of sharp edge anchors is higher than the blunt edge anchor for tests without adding weight to the anchor weight.
 The penetration of the sharp edge anchors is the same as the blunt edge anchor for tests with adding weight to the anchor weight. Furthermore, the final penetration angle was the same for both anchor shapes.
 The penetration depth in dry conditions is higher than the penetration depth in saturated conditions. Anchor.
The feasibility of the concept has been shown by prediction depths of approximately up to 3 times the fluke lengths for impact velocities of 24 m/s which were achieved in physical field tests (see Madeiras, 2002).
This research further underlines the effect of contraction and dilation of saturated soils.
Especially, the effect of dilation with decrease in pore water pressure and increase in effective stress for the saturated tests of saturated sand samples can be well seen from the findings of this research.
Further research is encouraged in the soil behavior of saturated sands under rapid loading.
Although more recently research has been touching this topic, the change in pore water pressure is still unknown, especially for dense sand. (Omidvar et al., 2012) Evaluating more data would help to understand and predict the effect of saturation on rapid loading better.