CONFIDENTIAL Antonius Pieter van Gurp Repository version ...

DEVELOPMENT OF A PLOUGH PULLING FORCE MODEL FOR SUBMARINE

NARROW SHAPED PLOUGHS

CONFIDENTIAL

Antonius Pieter van Gurp

Repository version – October 8, 2014

Delft University of Technology

Section of Dredging Engineering

i

DEVELOPMENT OF A PLOUGH PULLING FORCE MODEL FOR SUBMARINE

NARROW SHAPED PLOUGHS

Author:

A.P. van Gurp

Thesis Committee:

Prof. dr. ir. C. van Rhee Delft University of Technology

Dr. ir. S.A. Miedema Delft University of Technology

Dr. ir. D.J.M. Ngan-Tillard Delft University of Technology

Ir. L. van Baalen VolkerWessels Boskalis Marine Solutions

Ing. M. Biesheuvel Koninklijke Boskalis Westminster N.V.

Under the authority of:

Delft University of Technology

VolkerWessels Boskalis Marine Solutions

Koninklijke Boskalis Westminster N.V.

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ABSTRACT

Development of a plough pulling force model for submarine narrow

shaped ploughs

Antonius Pieter van Gurp

Delft University of Technology, 2014

iv

Offshore cable burial is often performed with submarine narrow shaped ploughs. Available

submarine narrow shaped ploughs have different geometries and the influence of several

variables in the design of these ploughs was analysed during this thesis. This was done to develop

a plough pulling force model for generic narrow shaped plough geometries in clay soil

conditions. Additionally, the specific geometric shape of the Sea Stallion 4 plough was analysed

as this plough is used by VolkerWessels Boskalis Marine Solutions and no satisfactory model for

predicting the required pulling forces in clay was available.

The following variables in the geometries of the narrow shaped ploughs were analysed: adhesion

area, ploughing angle, tip shape and additional cutting teeth. In addition to these geometric

variables the influences by ploughing depth and ploughing velocity were also analysed.

First, a literature study was performed in order to identify analytical models already available for

submarine narrow shaped ploughs and models from other branches that probably could be used to

predict the required ploughing forces for narrow shaped ploughs. The following theories and

models were reviewed: submarine plough models, ultimate bearing capacity models, narrow tine

models and strain-rate dependency models. Concurrently with the literature study, orientating

experiments were performed in order to gain insight in the force magnitudes occurring in small

scale experiments and in order to gain insight in the influence by size, length and tip of the

analysed geometries.

Knowledge gained by the literature study and orientating experiments was used to develop a more

advanced experimental setup, in which all selected variables were analysed. Results from the

experiments were compared to predictions made by the analytical models.

From this comparison, it was concluded that an adapted ultimate bearing capacity theory is most

appropriate to predict the required ploughing forces.

As the more advanced experimental setup, the results gained with this setup and the conclusions

of the research are confidential, the repository version of the report does not contain these parts.

Share area

Teeth

Tip shape

Ploughing angle

Velocity

Depth

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TABLE OF CONTENT

Nomenclature ...........................................................................................................ix

List of Tables......................................................................................................... xiii

List of Figures ......................................................................................................... xv

List of Graphs .........................................................................................................xix

PART I: INTRODUCTION ................................................................................................. 1

1. INTRODUCTION .......................................................................................................... 2

1.1 VolkerWessels Boskalis Marine Solutions ..................................................... 2

1.2 Koninklijke Boskalis Westminster N.V. ......................................................... 2

1.3 Background for the research assignment ......................................................... 3

1.4 Main research objective ................................................................................... 3

1.5 Sub- research objectives .................................................................................. 3

1.6 Research plan .................................................................................................. 4

1.7 Boundary conditions and limitations ............................................................... 4

1.8 Report structure ............................................................................................... 5

2. INTRODUCTION TO CABLE PROTECTION .................................................................... 6

2.1 Necessity for cable protection ......................................................................... 6

2.2 Protection of subsea cables .............................................................................. 6

2.3 Burial Protection Index ................................................................................... 6

2.4 Cable burial methods ....................................................................................... 8

2.5 Specifications of the Sea Stallion 4 plough ..................................................... 9

3. MATERIAL PROPERTIES OF SOIL ............................................................................... 10

3.1 Porosity (Soil)................................................................................................ 10

3.2 Void ratio (soil) ............................................................................................. 10

3.3 Density (soil) ................................................................................................. 10

3.4 Unit weight (soil)........................................................................................... 11

3.5 Degree of saturation (soil) ............................................................................. 11

3.6 Moisture content (soil) .................................................................................. 12

3.7 Atterberg limits (clay) ................................................................................... 12

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3.8 Mohr circle (soil) ........................................................................................... 15

3.9 Mohr-coulomb failure criterion (soil) ........................................................... 16

3.10 Adhesion (clay) ............................................................................................. 17

3.11 Soil classification (soil) ................................................................................. 18

3.12 Clay minerals (clay) ...................................................................................... 18

3.13 Soil structure of clay (clay) ........................................................................... 19

PART II: LITERATURE STUDY ..................................................................................... 21

4. INTRODUCTION LITERATURE STUDY ........................................................................ 22

5. ULTIMATE BEARING CAPACITY THEORY ................................................................. 24

5.1 Ultimate bearing capacity .............................................................................. 24

5.2 Meyerhof (1951)............................................................................................ 26

5.3 Cutting force during ploughing ..................................................................... 27

5.4 Applicability of the model ............................................................................. 28

6. SOIL FAILURE FOR NARROW TILLAGE TOOLS........................................................... 29

6.1 Hettiaratchi & Reece (1967) .......................................................................... 29

6.2 Godwin & Spoor (1977) ................................................................................ 32

6.3 McKyes & Ali (1977) .................................................................................... 36

6.4 Grisso et al. (1980) and Perumpral et al. (1983) ........................................... 38

6.5 Advantages and disadvantages of the narrow tine models ............................ 39

7. SUBSEA PLOUGH MODELS ........................................................................................ 40

7.1 Reece and Grinsted (1986) ............................................................................ 40

7.2 Internal model................................................................................................ 42

7.3 Additional adhesion ....................................................................................... 44

8. TIP SHAPE INFLUENCE .............................................................................................. 45

9. STRAIN-RATE DEPENDENT BEHAVIOUR OF CLAY .................................................... 47

9.1 Strain-rate during ploughing (1) .................................................................... 47

9.2 Influence of the velocity on the undrained shear strength ............................. 48

10. THE BASE PLOUGH PULLING FORCE MODEL ............................................................. 49

PART III: THE PRELIMINARY EXPERIMENTS .......................................................... 51

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11. THE PRELIMINARY EXPERIMENTAL SETUP ............................................................... 52

11.1 Design of the preliminary experimental setup ............................................... 52

11.2 Different profiles analysed during the experiments ...................................... 53

11.3 Preparations for the preliminary experiments ............................................... 55

11.4 Experimental procedure ................................................................................ 56

11.5 After the experiments .................................................................................... 57

11.6 Test report ..................................................................................................... 58

12. THE RESULTS OF THE PRELIMINARY EXPERIMENTS ................................................. 59

12.1 The base prediction model ............................................................................ 59

12.2 Repeatbility of the experiments ..................................................................... 60

12.3 Length influence ............................................................................................ 60

12.4 Size influence ................................................................................................ 61

12.5 Tip shape influence ....................................................................................... 62

12.6 Influence of the joints between the blocks .................................................... 65

12.7 Experiment with a block of natural clay ........................................................ 65

13. VALIDATION OF THE BASE PREDICTION MODEL ...................................................... 67

14. CONCLUSIONS OF THE ORIANTATING EXPERIMENTS ............................................... 69

BIBLIOGRAPHY .................................................................................................................. 71

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NOMENCLATURE

Ploughing angle °

Adhesion factor -

( ) Ploughing angle influence factor -

( ) Depth influence factor -

Tip shape influence factor -

Adhesion Pa

Area of the heel m2

Area of the share m2

Area of the skids m2

Adhesion area m2

Rupture angle from the direction of travel °

Ploughing width m

Width of the foundation m

Cohesion Pa

Soil-metal adhesion Pa

Coefficient for ploughing in sand -

Coefficient for ploughing in sand -

Coefficient for ploughing in clay -

Coefficient for ploughing in clay -

Coefficient for the skids on clay -

Coefficient for the skids on sand -

Ploughing depth m

Effective depth m

Critical depth -

Depth factor for cohesion by Brinch Hansen -

Depth factor for surcharge by Brinch Hansen -

Depth factor for unit weight by Brinch Hansen -

Depth factor for cohesion at infinite depth -

Depth of the foundation m

External friction angle °

Void ratio -

Cutting force N

Friction force by the heel N

Friction force by the share N

Friction force by the skids N

Vertical force N

Horizontal or draught force N

x

Vertical or lift force N

Gravitational constant m/s2

Liquidity index %

Plasticity index %

Critical aspect ratio -

Dimensionless coefficient for plough geometry -



Inclination factor -

Dimensionless coefficient for adhesion-cohesion ratio -

Dimensionless coefficient for surcharge -

Dimensionless coefficient for unit weight -

The logarithmic strain rate dependency coefficient -

Length of the foundation m

Adhesion length of the ploughing profile m

Depth exponent = 2.5-3.0 -

The exponential strain rate dependency coefficient -

Rupture distance ratio -

Mass of solids kg

Mass of the soil kg

Mass of water kg

Depth exponent = 1.5-2.0 -

Porosity -

Dimensionless coefficient for cohesion -

Dimensionless coefficient for surcharge -

Dimensionless coefficient for unit weight -

Internal friction angle °

In-situ density kg/m3

Density of solids kg/m3

Submerged soil density kg/m3

Density of the soil kg/m3

Density of water kg/m3

Average ultimate bearing capacity pressure Pa

Total force on the tool N

Forward failure force N

Sidewards failure force N

Surcharge pressure Pa

Ultimate bearing capacity pressure Pa

xi

Rupture distance from tool to crescent m

First principle stress Pa

Second principle stress Pa

Normal principle stress Pa

Degree of saturation -

Undrained shear strength Pa

Undrained shear strength measured by a CPT Pa

( ) Undrained shear strength at ploughing velocity Pa

Dynamic undrained shear strength Pa

Reference undrained shear strength Pa

Undrained shear strength (yield stress) Pa

Shape factor for cohesion -

Shape factor for cohesion (only one “end effect”) -

Shape factor for surcharge -

Shape factor for unit weight -

Shear strength Pa

Shear strength at failure Pa

Ploughing velocity m/s

Velocity of the CPT measurements m/s

Reference velocity m/s

Volume of pores m3

Volume of solids m3

Volume of soil m3

Volume of water m3

Moisture content %

Effective width of the tool m

Liquid limit %

Plastic limit %

Submerged weight of the plough kg

Weight of soil N

Unit weight N/m3

Ploughing depth m

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LIST OF TABLES

Table 2-1: General specifications of the Sea Stallion 4 plough....................................................... 9

Table 3-1: Bulk densities and unit weight ..................................................................................... 11

Table 3-2: Typical moisture contents ............................................................................................ 12

Table 3-3: Soil classification according to the British Standard Soil Classification System ........ 18

Table 6-1: The common used symbols and definitions in the narrow tillage tool models ............ 29

Table 6-2: Table for calculating the effective width and depth ..................................................... 31

Table 11-1: Profiles used in the preliminary experiments ............................................................. 54

Table 12-1: The Nc coefficients for various tip shapes (w/d ratio of 1:6) ..................................... 64

Table 14-1: The Nc coefficients for various tip shapes (w/d ratio of 1:6) ..................................... 69

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LIST OF FIGURES

Figure 1.1: Main analysed ploughing variables............................................................................... 3

Figure 2.1: Burial Protection Index for various soil conditions (Mole et al, 1997)......................... 7

Figure 2.2: Mechanical trencher (VBMS) ....................................................................................... 8

Figure 2.3: Jetting sledge (VBMS) .................................................................................................. 8

Figure 2.4: V-Shaped plough (Ecosse) ............................................................................................ 8

Figure 2.5: Narrow shaped plough (VBMS) ................................................................................... 8

Figure 2.6: The geometry of the Sea Stallion 4 plough (VBMS) .................................................... 9

Figure 3.1: Atterberg limits (Barnes, 2010) .................................................................................. 13

Figure 3.2: Plasticity chart (Barnes, 2010) .................................................................................... 14

Figure 3.3: Stresses on a soil element ........................................................................................... 15

Figure 3.4: Mohr-Coulomb failure ................................................................................................ 16

Figure 3.5: Undrained failure ........................................................................................................ 17

Figure 3.6: Adhesion factors for driven piles (Tomlinson, 1970) ................................................. 18

Figure 4.1: Overview literature study ............................................................................................ 23

Figure 5.1: Strip foundation .......................................................................................................... 24

Figure 5.2: Influence of depth on sliding surfaces ........................................................................ 25

Figure 5.3: Plastic zones in a deep foundation of purely cohesive material (Meyerhof, 1951) .... 26

Figure 6.1: Forward failure (Hettiaratchi & Reece, 1967) ............................................................ 30

Figure 6.2: Sidewards failure (Hettiaratchi & Reece, 1967) ......................................................... 30

Figure 6.3: Conceptual mechanism of soil failure (Godwin & Spoor, 1977) ................................ 32

Figure 6.4: Crescent failure geometry (Godwin & Spoor, 1977) .................................................. 33

Figure 6.5: 3D view crescent failure (Godwin & Spoor) .............................................................. 34

Figure 6.6: Side view crescent failure (Godwin & Spoor) ............................................................ 34

Figure 6.7: Dimensionless N factors for lateral failure (Godwin & Spoor, 1977) ........................ 35

Figure 6.8: Proposed soil failure (McKyes & Ali, 1977) .............................................................. 36

Figure 6.9: Forces on the soil segments (McKyes & Ali, 1977) ................................................... 36

Figure 7.1: Soil cutting by straight blades (Reece & Grinsted, 1986) ........................................... 41

xvi

Figure 8.1: The formation of compacted cores in front of various cutting interfaces (Zelenin,

1950) .............................................................................................................................................. 45

Figure 8.2: The four different cutting interfaces used in the experiments a): 45° Triangular (T4),

b): Elliptical (T3), c): Flat (T2) and d) 90° Triangular (T1) (Sharifat, 1999) ................................ 45

Figure 8.3: The used energy by the four different tools at a soil moisture content of 11.2%, a

Cone index of 300 kPa and speeds of 10, 15, 20 and 25 km/hr (Sharifat, 1999) .......................... 46

Figure 8.4: The used energy by the four different tools at a soil moisture content of 15.1%, a

Cone index of 300 kPa and speeds of 10, 15, 20 and 25 km/hr (Sharifat, 1999) .......................... 46

Figure 9.1: The shear planes during failure ................................................................................... 47

Figure 10.1: Parameters used in the base prediction model .......................................................... 50

Figure 11.1: Sketch of the preliminary experimental setup ........................................................... 53

Figure 11.2: Profile shapes analysed in the preliminary experiments ........................................... 54

Figure 11.3: The setup to push the box into the clay ..................................................................... 55

Figure 11.4: The box pushed halfway into the clay blocks ........................................................... 55

Figure 11.5: Pushing the profile through the clay ......................................................................... 55

Figure 11.6: Clay after the starting hole is made ........................................................................... 55

Figure 11.7: Preparations for marking ........................................................................................... 56

Figure 11.8: Clay box after marking ............................................................................................. 56

Figure 11.9: The complete experimental setup ............................................................................. 56

Figure 11.10: The clay box into the experimental setup ............................................................... 56

Figure 11.11: Setup to measure the trenched surface .................................................................... 57

Figure 11.12: The height profile of the trenched surface .............................................................. 57

Figure 11.13: The field vane ......................................................................................................... 57

Figure 11.14: The measuring locations ......................................................................................... 57

Figure 11.15: Lay-out of the test report ......................................................................................... 58

Figure 12.1: Overview of the variables and influences analysed with the results of the preliminary

experiments ................................................................................................................................... 59

Figure 12.2: Deformation profile flat frontal shape ...................................................................... 64

Figure 12.3: Deformation profile circular frontal shape ................................................................ 64

Figure 12.4: Deformation profile sharp frontal shape ................................................................... 64

xvii

Figure 12.5: Deformation profile frontal edge of 45° ................................................................... 64

xix

LIST OF GRAPHS

Graph 12.1: Repeatability (su = +/- 33 kPa, vavg = +/- 2.5 mm/s) .................................................. 60

Graph 12.2: Length influence (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/- 2.5 mm/s) ............... 60

Graph 12.3: Size influence (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/- 2.5 mm/s) ................... 61

Graph 12.4: Tip influence, cylinder compared to blunt (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg =

+/ 2.5 mm/s) .................................................................................................................................. 62

Graph 12.5: Tip influence, 90° and 45° sharp edged tip compared to blunt ................................. 63

Graph 12.6: Graph showing the influence of the joints between the clay blocks ......................... 65

Graph 13.1: Overview measured and predicted forces (su = +/- 33 kPa, αa = 0.34, vavg = +/- 2.5

mm/s) ............................................................................................................................................. 67

Graph 13.2: Relation between measured and predicted forces (su = +/- 33 kPa, αa = 0.34, vavg = +/-

2.5 mm/s) ....................................................................................................................................... 67

PART I: INTRODUCTION

1



2

1. INTRODUCTION

This thesis research has been performed under the authority of VolkerWessels Boskalis Marine

Solutions (VBMS) and Koninklijke Boskalis Westminster N.V. During the development of the exact

research objectives it appeared that both VBMS and Boskalis had an interest in the research topic

making a multi company thesis research possible.

1.1 VOLKERWESSELS BOSKALIS MARINE SOLUTIONS

VolkerWessels Boskalis Marine Solutions established a trusted and experienced position as an

international submarine power cable installation contractor, specialised in the intertidal and offshore

markets.

The company was established in 2007 by Visser & Smit Hanab, under the name of Visser and Smit

Marine Contracting (VSMC). Onward establishment the company served as an independent company

within the VolkerWessels group until the year 2013. In that year VolkerWessels and Royal Boskalis

Westminster N.V. decided to combine their forces in the field of offshore cable installation by the

establishment of a 50/50% joint venture in the company. As a result the name of the company was

changed to VolkerWessels Boskalis Marine Solutions in September 2014.

Typical clients of VBMS are electrical power companies, grid operators and companies in the oil and

gas industry. The company provides a full package for installation of cables. Activities executed by

VBMS are:

Installation and burial of export cables

Installation and burial of inter array cables

Inspection, Repair and Maintenance of cables

Construction of land- & outfalls

Construction of offshore cable crossings

1.2 KONINKLIJKE BOSKALIS WESTMINSTER N.V.

Royal Boskalis Westminster N.V. is a leading global maritime services company operating in the

dredging, inland infra, towage, salvage and offshore sectors.

Traditionally Boskalis was a dredging company but with the acquisitions of Smit International,

Fairmount and Dockwise it became also active in towage, salvage and transport and heavy lifting.

After these acquisitions Boskalis is able to provide total solution packages for the major maritime and

offshore challenges.

Main clients of Boskalis are; companies active in the oil and gas industry, port authorities, global and

local governments, shipping companies, international project developers, insurance companies and

mining companies.


3

1.3 BACKGROUND FOR THE RESEARCH ASSIGNMENT

VBMS uses multiple vessels and tools to execute subsea power cable installation projects. One of

these tools is the Sea Stallion 4 plough, a narrow shaped plough. This plough is capable of burying

submarine power cables up to 3m below the seabed in order to protect them against human and

environmental impacts such as anchors, fishing gear, current and wave action, etc. The Sea Stallion 4

plough features a unique design and has a robust chassis that can withstand continuous tow forces up

to 120 tons.

There are several manufacturers of narrow shaped ploughs, defined as ploughs with a small width-

over-depth ratio. Most of these manufacturers have their own basic geometric design. This raises

questions on the influence of variables in the design of these ploughs on the required pulling force.

The influence of these variables is related to the local soil conditions, for which there is in this

research a special interest to clay soils. Once the influence of the selected variables in the design of

narrow shaped ploughs is known this knowledge can be used to develop and optimised design of the

Sea Stallion 4 plough for ploughing in clay soils.

1.4 MAIN RESEARCH OBJECTIVE

This thesis project aims to create an empirical plough pulling force model by assessing available

theories and models in combination with performing lab experiments examining the influence of

selected variables, during ploughing in clay.

Selected main variables analysed and tested in this thesis research are; adhesion/share area, ploughing

angle, ploughing depth, tip shape, additional cutting teeth and ploughing velocity. All these variables

are visualised in Figure 1.1.

Figure 1.1: Main analysed ploughing variables

1.5 SUB- RESEARCH OBJECTIVES

Along with the main research objective there are several sub- research objectives:

Determine which model from literature is most suitable for predicting the required pulling forces

for ploughing with narrow shaped ploughs in clay.

Design and construct an experimental setup.

Perform experiments with the experimental setup.

Share area

Teeth

Tip shape

Ploughing angle

Velocity

Depth


4

Create a plough pulling force prediction model.

Develop an optimised design of the Sea Stallion 4 plough, for ploughing in clay.

1.6 RESEARCH PLAN

First, a literature study is performed to study the applicability of already available force prediction

models for narrow shaped ploughs. Concurrently, preliminary experiments are performed in order to

gain insight in magnitudes of the pulling forces occurring during small scale experiments. Once the

literature study is completed and the preliminary experiments are evaluated a main experimental setup

is designed and constructed. In this main experimental setup, the influence of the selected variables is

analysed. The results of these experiments are compared to the results of the models from the literature

study, in order to identify the model most appropriate for predicting the required pulling forces of

narrow shaped ploughs. At last the knowledge gained from the experiments is used to develop an

optimised design of the Sea Stallion 4 plough.

1.7 BOUNDARY CONDITIONS AND LIMITATIONS

The number of experiments to be performed is limited due to the availability of time. This implies not

all parameters influencing the pulling force can be analysed and tested. The variables during

ploughing selected to be analysed and tested in this research are; adhesion/share area, ploughing angle,

ploughing depth, tip shape, additional cutting teeth and ploughing velocity.

The reasons to select these variables are:

Adhesion/share area: the adhesive force along the side/share of the plough is assumed to be one

of the main force components occurring during ploughing with narrow shaped ploughs in clay.

Ploughing angle: it is often questioned which ploughing angle is most efficient, especially for

ploughing angles between 90° and 150°.

Ploughing depth: different cutting processes are assumed to occur at different depths. At the

surface of the clay crescent failure is expected whereas at lower depths sidewards failure is

expected. The relative influence of the failure modes is changing with cutting depth making it

interesting to identify the influence of the ploughing depth.

Tip shape: the tip shape influences the flow pattern of the soil along the plough, and one would

expect the ploughing force is decreasing with increasing sharpness of the tip.

Additional cutting teeth: the Sea Stallion 4 plough of VBMS is equipped with teeth and it is

therefore in their interest to understand the influence of these teeth on the ploughing forces, in

order to create a plough force prediction model suitable for predicting the required ploughing

forces of the Sea stallion 4 plough.

Ploughing velocity: proving the influence of the ploughing velocity on the required ploughing

forces is limited.

Remaining variables like for example; ploughing width, soil type, teeth shape, teeth angle and clearing

angle below the teeth are not analysed.


5

Among the different geometries selected to be tested in the experiments sometimes two or more

variables are changed simultaneously as a result of changing only one of the geometrical variables.

This makes it difficult to appoint the exact variable being the origin of a certain difference in the

required pulling force. The different experimental geometries are therefore selected such that the

influences of the selected variables can be distinguished separately as much as possible.

This thesis research should be seen as an encompassing research in which a lot of variables are

reviewed and analysed, and which can be used to appoint the variables and influences to which more

in-depth research should be carried out.

1.8 REPORT STRUCTURE

This repository version of the report is divided in three main parts. The first part is an introductory part

and contains an introduction to cable protection and the material properties of soil. The second part of

the report contains the literature study. In the first chapter of this part an overview of the available

models is given after which the ultimate bearing capacity theory, narrow tine models and subsea

plough models are reviewed in separate chapters. The influences by tip shape and ploughing velocity

are also reviewed in separate chapters. The third part of this report is dedicated to the preliminary

experiments. This part discusses the design of the experimental setup after which the results of the

experiments are analysed. The last parts of the research report are excluded from this repository

version as it contained confidential data and information.


6

2. INTRODUCTION TO CABLE PROTECTION

This chapter discusses the necessity for subsea cable burial along with commonly used protection

techniques. The burial depth of submarine cables often depends on the requirements stated by clients.

A commonly used method to gain an indication of the required burial depth is the Burial Protection

Index (BPI) which is elaborated in this chapter.

2.1 NECESSITY FOR CABLE PROTECTION

Recent years showed a massive demand for subsea power cables due to the fast development of

offshore renewable energy. Offshore power generators are connected to transformer platforms by

infield cables and these transformer platforms are in turn connected to shore by export cables. All

these cables do need protection to threats since they are too important to be damaged. A list of main

threats to subsea power cables is given below.

Natural threats:

Submarine landslides

Sediment mobility

Seismic activity

Iceberg scour

Human threats:

Fishing activities

Anchoring

Dredging

Dropping objects

2.2 PROTECTION OF SUBSEA CABLES

There are two primary methods used for protection of submarine cables; internal armouring and burial.

A third less commonly used method is protection by rock dumping or placing flexible concrete

mattresses on top of a cable. Costs for this protection method are generally high and therefore only

used for short areas of particular concern, such as crossing and remedial work locations.

Protection by burial is generally considered to be the most practical and reliable method. Cable burial

is often referred to as “trenching” and can be done in different sequences. During ‘pre-trenching’ the

trench is created before a cable is installed whereas during ‘post-trenching’ the trench is created

underneath an already laid cable. During ‘simultaneous laying and burial’ a cable is buried during

lying. A submarine narrow shaped plough typically uses this last burial method.

2.3 BURIAL PROTECTION INDEX

In the eighties cable burial became common practice. A burial depth of 60 cm was often adopted

without assessing level of threat and strength of the soil. Recently, target burial depths have become

more related to possible threats and strength of the soil.


7

Mole et al. (1997) developed the ‘Burial Protection Index’ (BPI) in an attempt to qualify a relationship

between protection level, soil type and burial depth. Although the BPI is not accepted as industry

standard it is still a very useful tool to indicate the relation between soil type, protection level and

burial depth. Allan (1998); For the burial protection index to work properly it is necessary to identify

with greater confidence the depth to which threats are likely to penetrate into the seabed and the risk

of exposure of the cable with regard to their probability. It is proposed that this is done on the

following basis although this should be adjusted to suit local conditions including method of trenching

and nature of any backfill soil:

BPI = 1 Depth of burial consistent with protecting a cable from normal fishing gear only. Would be

appropriate to water depths greater then say 50 to 100m, where anchoring of ships is

unlikely.

BPI = 2 Depth of burial will give protection from vessels with anchors up to approximately 2

tonnes. This may be adequate for normal fishing activity, but would not be adequate for

larger ships (e.g. Tankers, large container ships)

BPI = 3 Depth of burial sufficient to protect from anchors of all but the largest ships. Suitable for

anchorages with adjustments made to suit known ship/anchor sizes.

The relation between different protection levels, burial depths and soil types is shown in Figure 2.1.

Figure 2.1: Burial Protection Index for various soil conditions (Mole et al, 1997)


8

2.4 CABLE BURIAL METHODS

Protection of cables by burial/trenching can be executed by three main trenching methods:

Mechanical cutting Soil is cut away mechanically by a cutting chain or cutting disc

Jetting Soil is fluidised by water released under medium pressure and high flow

rates so that a cable can sink into the soil

Soil is cut away by water released under high pressure and low flow rates

Ploughing Soil is cut/opened by a passive tool forming a trench

This research is focussing on cable burial by ploughing and therefore only this trenching method is

further reviewed. During ploughing a passive tool is pulled through soil, which in turn is pushing

away this soil, in order to create a trench. Most often used plough types are V-shaped ploughs (Figure

2.4) and narrow shaped ploughs (Figure 2.5), who both owe their name to their shape. V-shaped

ploughs are often used to create trenches for burial of pipelines whereas narrow shaped ploughs are

often used to create trenches for cable burial. Burial by narrow shaped ploughs works well in soft soils

but problems have appeared during projects in stiff clays and dense sands, where the pulling force

became too high (>150 Ton). When these situations occurred the burial depth was temporarily

decreased to be able to pull the plough through these difficult parts of soil.

Figure 2.2: Mechanical trencher (VBMS)

Figure 2.3: Jetting sledge (VBMS)

Figure 2.4: V-Shaped plough (Ecosse)

Figure 2.5: Narrow shaped plough (VBMS)

http://www.google.nl/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=cZ4-AtPFXHDBKM&tbnid=qFnUrq-TZti0vM:&ved=0CAUQjRw&url=http://www.dredgingtoday.com/2013/03/28/boskalis-new-trenchformer-the-netherlands/&ei=FxmLUuiAHa3Y0QXXkYD4CQ&bvm=bv.56643336,d.d2k&psig=AFQjCNHVFEu4lFM1tWgeztb1T-9syvvorA&ust=1384934020916422


9

2.5 SPECIFICATIONS OF THE SEA STALLION 4 PLOUGH

The Sea Stallion 4 cable plough, owned and operated by VBMS is designed by IHC Engineering

Business Ltd, for the aggressive burial of power cables in shallow waters. Sketches showing the

geometry of the Sea Stallion 4 plough are given in Figure 2.6.

Figure 2.6: The geometry of the Sea Stallion 4 plough (VBMS)

General specifications of the Sea Stallion 4 plough are collected in Table 2-1.

Table 2-1: General specifications of the Sea Stallion 4 plough

Burial depth 0 - 3 m

Maximum cable size Ø 280 mm

Cable bending radius Minimum 3.6m

Design strength Sustained pull force: 120 Ton

Peak load: 150 Ton

Operating water depth Minimum: Beach conditions

Maximum: 100 m

Length (overall) 13.9 m

Width (overall) 5.2 m

Height (overall) 4.3 m

Weight in air 32 Ton

The Sea Stallion 4 plough operated by VBMS has a proven track record in various kind of soil

conditions, like e.g. sands, silts, clays and layered combinations of these. In easy soil conditions like

soft clays and loose sands ploughing velocities up to 360 m/hr were reached whereas in difficult soil

conditions like hard clays and very dense sands ploughing velocities up to 100m/hr, or even less, were

reached.


10

3. MATERIAL PROPERTIES OF SOIL

In this chapter the most common parameters to describe the properties and behaviour of clay soils are

described and explained.

3.1 POROSITY (SOIL)

Soils usually consist of particles, water and air. In soil mechanics the space between particles is known

as pores. There are several ways to express the amount of pore space. The most common parameter

describing this amount is porosity, which is defined as:

Eq. 3-1

Porosity [-]

Volume of pores [m3]

Volume of the soil [m3]

For most soils the porosity (n) is in between 0.30 and 0.45. A smaller porosity corresponds with a

denser soil.

3.2 VOID RATIO (SOIL)

A second way in which the amount of pore space can be expressed is void ratio. It is the ratio between

the volume of pores and the volume of particles.

Eq. 3-2

Void ratio [-]


Volume of solids [m3]

3.3 DENSITY (SOIL)

Density of a substance is given by the mass per unit volume of that substance.

Eq. 3-3

Density of the soil [kg/ m3]

Mass of the soil [kg]

Volume of the soil [m3]


11

The in-situ density of a fully saturated soil can be calculated according:

( ) ( ( )) Eq. 3-4

Density in-situ [kg/m3]

Density of water [kg/m3]

Density of solids [kg/m3]

An overview of typical bulk density values for different types of soils is given in Table 3-1.

3.4 UNIT WEIGHT (SOIL)

Unit weight is defined as the weight per unit volume:

Eq. 3-5

Unit weight [N/m3]

Weight of the soil [N]

Gravitational constant [m/s2]

An overview of typical unit weight values for different types of soils is given in Table 3-1.

Table 3-1: Bulk densities and unit weight

Soil type Bulk density [kg/m3] Unit weight [kN/m

3]

Sand and gravel 1.600 – 2.200 16 – 22

Silt 1.600 – 2.000 16 – 20

Soft clay 1.700 – 2.000 17 – 20

Stiff clay 1.900 – 2.300 19 – 23

Peat 1.000 – 1.400 10 – 14

Weak intact rock 2.000 – 2.300 20 – 23

Weak rock 1.800 – 2.100 18 – 21

Hard intact rock 2.400 – 2.700 24 – 27

Hard rock 1.900 – 2.200 19 – 22

3.5 DEGREE OF SATURATION (SOIL)

Pores of soil may contain water and/or air. To describe the ratio between these two, the degree of

saturation is introduced as:

Eq. 3-6


12

Degrees of saturation [-]

Volume of water [m3]


In offshore and near beach conditions of ploughing operations, clay is often assumed to be fully

saturated. This is important to note since it ensures there is no air present inside the clay.

3.6 MOISTURE CONTENT (SOIL)

The moisture content, or water content, is the ratio between the mass of water to the mass of solid

particles and is a valuable indicator for the state of a soil and its behaviour.

Eq. 3-7

Moisture content [%]

Mass of water [kg]

Mass of solids [kg]

Some typical values of moisture content are given in Table 3-2.

Table 3-2: Typical moisture contents

Soil Types Moisture content [%]

Moist sand 5 – 15

‘Wet’ sand 15 – 25

Moist silt 10 – 20

‘Wet’ silt 20 – 30

Normally consolidated clay – low plasticity 20 – 40

Normally consolidated clay – high plasticity 50 – 90

Overconsolidated clay – low plasticity 10 – 20

Overconsolidated clay – high plasticity 20 – 40

Organic clay 50 – 200

Extremely high plasticity clay 100 – 200

Peats 100 - > 1000

3.7 ATTERBERG LIMITS (CLAY)

Atterberg limits are used to describe the nature of a fine-grained soil. Depending on the moisture

content of the soil, it may appear in four states: solid, semi-solid, plastic and liquid. In each of these

four states the behaviour of the soil is different and so are its properties.


13

As the moisture content of plastic clay increases, the clay becomes softer and stickier, until it cannot

retain its shape anymore. This point is called the liquid limit above which the clay is classified to be in

liquid state and below to be in plastic state. If the moisture content of a plastic clay is however

decreasing, the clay becomes stiffer until there is insufficient moisture to provide cohesiveness. The

clay then becomes friable, and cracks or breaks up easily when remoulded. This point is referred to as

the plastic limit, above which the clay is classified as plastic and below as semi-solid or semi-plastic

solid. Below the plastic limit the moisture content can decrease even further until physicochemical

forces between particles do not permit them to move any closer and the clay is in a solid state. The

limit at which the clay is classified to be solid is the shrinkage limit. An overview of the Atterberg

limits is shown in Figure 3.1.

Figure 3.1: Atterberg limits (Barnes, 2010)

3.7.1. PLASTICITY INDEX

Plasticity index is a parameter to denote the degree of plasticity of a soil and is defined as:

Eq. 3-8

Plasticity index [%]

Liquid limit [%]

Plastic limit [%]

A high plasticity index indicates a high compressibility and thus a large capacity of volume change

due to loading or unloading.


14

3.7.2. LIQUIDITY INDEX

Liquidity index is an indicator for the position of the moisture content in relation to the Atterberg

limits. The liquidity index is defined as:

Eq. 3-9

Liquidity index [%]

3.7.3. PLASTICITY CHART

The Atterberg limits can be used to distinguish different types of clays and silts by using a plasticity

chart (see Figure 3.2).

Figure 3.2: Plasticity chart (Barnes, 2010)

Line ‘A’ in this plasticity chart is given by:

( ) Eq. 3-10

Line ‘B’ or line ‘U’ in this plasticity chart is given by:

( ) Eq. 3-11

Generally, clay soils lie above the A-Line whereas silts and organic soils lie below this line.


15

3.8 MOHR CIRCLE (SOIL)

The stress state in any infinitesimal point of a soil can be described using two principle stresses that

are acting perpendicular to each other, and . This stress state can also be described using a

normal stress and a shear stress working on a plane making an angle α with the principle stresses,

as shown in Figure 3.3.

Figure 3.3: Stresses on a soil element

The normal stress and shear stress can be written in terms of principle stresses and making

use of force equilibrium in the infinitesimal point. For creating the force equilibrium equations it

should be considered that the surfaces of the triangle are not equal. If surface B-C is considered to be

unity, surface A-B is given by ( ), and surface A-C is given by ( ). Creating the force

equilibrium equations for the stress state given in Figure 3.3 results in:

( ) ( ) ( ) Eq. 3-12

( ) ( ) ( ) Eq. 3-13

Simplifying these equations results in:

(

) (

) ( ) Eq. 3-14

(

) ( ) Eq. 3-15

Squaring and subsequently summing up these equations results in a circle equation by which the stress

state in the infinitesimal point can be visualised:

( (

))

(

)

Eq. 3-16

This circle equation is known as the Mohr circle.

α

σ2

σ1

τ

σN

A B

C


16

3.9 MOHR-COULOMB FAILURE CRITERION (SOIL)

The Mohr-Coulomb failure criterion represents a linear envelope that is obtained from circular plots of

the shear strength versus the applied normal stress. Once several failure conditions under different

stress states are known, they can be visualised using their Mohr circles in order to determine the

failure line of the Mohr-Coulomb failure criterion, as is shown in Figure 3.4.

cφ

τ

σ σ1 σ1 σ2 σ2

Failure line

Figure 3.4: Mohr-Coulomb failure

The failure line of the Mohr-Coulomb failure criterion is represented by:

( ) Eq. 3-17

Shear strength at failure [Pa]

Normal stress [Pa]

Cohesion [Pa]

Internal friction angle [°]

3.9.1. UNDRAINED SOIL FAILURE (SOIL)

During undrained failure a load is applied so quickly to the clay, that there is no expelling of water out

of the pores of the clay. This means that the applied load is taken by the water in the pores instead of

by the grains of the clay. As a result the effective strength of the clay is independent of the applied

load. The Mohr circles of various undrained failure conditions can be drawn in one figure (see Figure

3.5). In this figure the resulting failure line is nearly horizontal from which can be concluded the angle

of internal friction is close to zero. Consequently it is often referred to as the failure principle,

or a material that is behaving frictionless. According to the Mohr-Coulomb failure criterion it can be

concluded the maximum allowable shear strength (undrained shear strength) is independent of the

applied load and equal to half the compressive strength of the material.


17

Figure 3.5: Undrained failure

The effective strength of clay in undrained failure is often referred to as the undrained shear strength,

(although the terms undrained cohesive strength or cohesion are sometimes also used):

(

)

Eq. 3-18

Undrained shear strength [Pa]

Compressive strength [Pa]

3.10 ADHESION (CLAY)

According to Myers (1991) measured adhesion can be described by: “The state in which two bodies

are hold together by intimate interfacial contact in such a way that mechanical force or work can be

applied across the interface without causing the bodies to separate” The value of adhesion is often

related to the value of the undrained shear strength via the adhesion factor:

Eq. 3-19

Adhesion factor [-]

Researchers in the field of pile foundations found the adhesion factor was decreasing with increasing

undrained shear strength. The adhesion factors for driven piles are according to Tomlinson (1977)

given by Figure 3.6. It is not recommended to use these factors directly for ploughing, as the process

of driving piles is different form the ploughing process. The figure gives however an indication of the

adhesion factors and it shows the adhesion factor is decreasing with increasing undrained shear

strengths.

Su

τ

σ σ1 σ1σ2 σ2

Failure line

Cu


18

Figure 3.6: Adhesion factors for driven piles (Tomlinson, 1970)

3.11 SOIL CLASSIFICATION (SOIL)

Generally soils can be divided in several main groups.. The division of these groups is often based on

the particle size of the grains, and according to the British Standard Soil Classification System the

classification can be made according to Table 3-3.

Table 3-3: Soil classification according to the British Standard Soil Classification System

Name of the soil separate Diameter limits (mm)

Boulders >200

Cobbles 60-200

Gravel 2-60

Sand 0.06-2

Silt 0.002-0.06

Clay Less than 0.002

3.12 CLAY MINERALS (CLAY)

Clay particles are often referred to as particles smaller than 2μm, while not all particles smaller than

2μm are clay particles and not all clay particles are finer than 2μm. To identify a clay particles one

should look into the chemical composition of particles.

Characteristics of clay minerals are; (1) a small particle size, (2) a flat platy shape, (3) a net negative

electrical charge and (4) a very large specific surface which interacts with pore water. Therefore clay

particles have the ability to attract and bind pore water, whereas non-clay particles cannot (Nobel,

2013).


19

3.13 SOIL STRUCTURE OF CLAY (CLAY)

Clay mineral particles are very small and only visible with a microscope. Soils, in which clay particles

predominate, have cohesion, plasticity and a low permeability. Clay soils have very complex

microstructures which are affected by the type of clay minerals and their amounts, the proportion of

silt and sand, the deposition environment and the chemical nature of the pore water.

The macrostructure of clay soils can be seen by eye and generally consist of features that are

originating from deposition like inclusions, partings, laminations and varves and features produced

after deposition like fissures, joints, cracks, and root holes.

To understand the behaviour of a clay (shear strength, compressibility, consolidation, permeability,

shrinkage, etc) one should look into the nature of the microstructure of the soil. The openness of this

microstructure is given by the moisture content, which is a parameter represent the structural nature of

the clay when fully saturated. The liquidity index is used to represent the structural state of the clay, as

it compares the moisture content of the clay to the plastic and liquid limits.


20

PART II: LITERATURE STUDY

21



22

4. INTRODUCTION LITERATURE STUDY

The main variables during ploughing reviewed in the literature study are;

Adhesion/share area

Ploughing depth

Ploughing angle

Additional cutting teeth

Tip shape

Ploughing velocity

Analytical theories available and applicable for prediction of required cutting forces during ploughing,

or the influence of one of the given variables, are discussed in separate chapters. The theories and

models being reviewed are: the ultimate bearing capacity theory, the narrow tine models, the subsea

plough models, the tip shape influence, and the strain-rate dependent behaviour of clay.

The first theory reviewed is the ultimate bearing capacity theory originating from engineering of

foundations. The strip or foundation area used in this theory can be rotated to vertical to represent the

frontal area of the narrow shaped plough and to calculate the required cutting force by the plough.

Additionally an adhesive force accounting for the adhesion along the side/share area of the plough can

be added to this cutting force in order to predict the required ploughing forces.

The second group of models being reviewed are the narrow tine models, which are originating from

the agricultural industry. The geometries of the narrow shaped ploughs are more or less similar to

these of the narrow tines, making it interesting to analyse the usability of these models.

The last group of models being reviewed are the subsea plough models which are developed in the

eighties of the last century. These models are highly empirical and do have empirical coefficients for

each plough shape in combination with certain soil conditions. Due to this high empirical content they

are not preferred to be used in the plough pulling force model of the narrow shaped ploughs.

Last decades showed an increase in the use of numerical tools for the modelling of soil tillage

processes. Commonly used numerical methods are Finite Element Methods (FEM) and Discrete

Element Methods (DEM). The usability of these methods can be reviewed making numerical models

for the plough geometries to be analysed in the main experimental setup. It would however require too

much time to familiarise with the software using these methods and to develop the numerical models

of the various plough geometries to be analysed in the main experiments.

Only analytical models are reviewed in the literature study, in order to keep the plough pulling force

model as simple as possible. The analytical models predicting the required ploughing force, the

influence by the tip shape, and the influence by ploughing velocity are reviewed separately. No

models are available predicting the influence of certain tip shapes on the required pulling force, but

research by Sharifat (1999) showed the required pulling force by sharp tip shapes was lower compared

to blunt tip shapes. The influence of the ploughing velocity on the required ploughing force is


23

originating from the strain-rate dependent behaviour of clay. Various researchers developed models

accounting for this behaviour on the undrained shear strength of the clay, using exponential or

logarithmic functions.

A visual overview of the literature study is given in Figure 4.1.

Figure 4.1: Overview literature study

Analytical model

Emperical subsea plough models

Theoretical models

Reece & Grinsted (1986)

Internal model

Additional adhesion

Ultimate bearing capacity theory

Narrow tine models

Soil property models

Tip shape influenceStrain-rate

dependency models

Logaritmic model

Exponential modelBrinch Hansen

(1961)Hettiaratchi & Reece (1966)

Godwin & Spoor (1977)

McKyes & Ali (1977)

Grisso et al. (1980) and Perumpral

et al. (1983)

Meyerhof (1951)

Literature study

Numerical models

Finite element modeling

Dicrete element modeling


24

5. ULTIMATE BEARING CAPACITY THEORY

This chapter describes the ultimate bearing capacity theory used for foundation designs. The strip or

foundation area used in this theory can be rotated to vertical to represent the frontal area of the narrow

shaped plough and to calculate the required cutting force by the plough.

5.1 ULTIMATE BEARING CAPACITY

Terzaghi (1943) was the first to present a comprehensive theory for evaluating the ultimate bearing

capacity of a rough shallow foundation. Terzaghi suggested that for an infinity long strip failing in

general shear, the failure surfaces in the soil are similar to that of Figure 5.1.

I

IIIII

Active Rankine zone

Prandtl zone

Passive Rankine zone

Overburden pressureqult

Figure 5.1: Strip foundation

The first zone of this figure is the active Rankine zone which is pushed downwards by the load and

which is pushing the second zone sidewards. In the active Rankine zone it is supposed that the vertical

stress will be larger than the horizontal stress which in turn is assumed to be equal to the applied load.

The second zone is known as the Prantl zone which is pushed sidewards by the Rankine zone and

which is pushing the third zone both sidewards and upwards. This third zone is known as the passive

Rankine zone in which it is supposed that the horizontal stress is larger than the vertical stress, which

in turn is assumed to be equal to the surcharge load.

During failure, movement of these zones will mobilise the full shear strength of the soil over the slip

surfaces. The shear strength of soil is obtained from the Mohr-Coulomb shear strength parameters c

and ϕ in combination with effective stresses in soil. These effective stresses are in turn depending on

the self-weight of the soil and the surcharge pressure acting around the applied load. The ultimate

bearing capacity given by a combination of these influences is according to Terzaghi (1943) given by:

Eq. 5-1

Cohesion [Pa]

Surcharge pressure [Pa]

Unit weight [N/m3]


25

Width of the foundation [m]

The bearing capacity factors , and are depending on the internal friction angle and can be

found in Appendix A.

5.1.1. SHAPE FACTORS

Equation 5-1 is only valid for infinite long strips where shearing is assumed to take place in a two-

dimensional plane. For rectangular foundations shearing will however also occur at the short ends of

the rectangle, producing “end effects”. In order to account for this “end effects” shape factors are

added to equation 5-1:

Eq. 5-2

The shape factors for rectangles with a width B and a length L are according to Brinch Hansen (1970)

given by:

Eq. 5-3

Eq. 5-4

Eq. 5-5

To calculate these shape factors the shortest sides should be assumed as width.

5.1.2. DEPTH FACTORS

For foundations below surface level the sliding/failure surfaces will become longer, as shown in

Figure 5.2. The longer the sliding zone, the higher the force required for failure, and so the higher the

ultimate bearing capacity.

Figure 5.2: Influence of depth on sliding surfaces

qult

B

h

D


26

To account for the influence of the depth on the ultimate bearing capacity, a depth factor is added to

equation 5-2, as is shown in the equation 5-6.

Eq. 5-6

The depth factors proposed by Brinch Hansen (1970) are given by:

(

) Eq. 5-7

( ) (

) Eq. 5-8

Eq. 5-9

5.2 MEYERHOF (1951)

The ultimate bearing capacity theory by Terzaghi (1943) is adopted by Meyerhof (1951) in order to

create an equation describing the ultimate bearing capacity of an infinite long strip at a certain

foundation depth, D, in a purely cohesive material:

Eq. 5-10

The value of the coefficient is depending on the shape of the plastic zones which are according to

this theory given by the shapes shown in Figure 5.3.

Figure 5.3: Plastic zones in a deep foundation of purely cohesive material (Meyerhof, 1951)

For a perfectly smooth shaft ( ) the shape of the plastic zones results in a value of given by

whereas for a perfectly rough shaft ( ) the shape of the plastic zones results

in a value of given by .


27

5.3 CUTTING FORCE DURING PLOUGHING

To use the ultimate bearing capacity theory for predicting the cutting forces during ploughing, the strip

used in the bearing capacity theory can be rotated to vertical to represent the frontal area of the plough.

By rotating the strip the surcharge pressure can be replaced by the horizontal soil pressure, which

influence is assumed to be zero. In addition, the weight of the soil will act perpendicular to the sliding

surfaces, making its influence negligible.

The frontal area of the plough will not be represented by an infinite long strip but by a long and

narrow rectangle. The upper side of the plough is connected to the plough frame above the soil and so

no “end effect” is expected on this side of the rectangle whereas at the bottom side one “end effect” is

expected. The shape factor of equation 5-3 is accounting for two “end effects” and is rewritten to

equation 5-11 in order to account for only one “end effect”.

Eq. 5-11

The influence by the foundation is also rotated to vertical. As the plough is completely enclosed by

clay during the ploughing process, the upper limit, , of the depth factor should be used in the

equation to calculate the ultimate pressure in front of the plough.

( )⁄

[ (

)] Eq. 5-12

Taking both effects into account, the ultimate bearing capacity pressure that is generated in front of the

plough can be calculated by:

Eq. 5-13

The ultimate bearing pressure that can be generated in front of the plough can also be calculated using

the ultimate bearing capacity theory as proposed by Meyerhof (1951). As the strip in this theory is

rotated to vertical the influence by the weight of the soil is zero. The ultimate bearing pressure that can

be generated in front of the plough is given by:

Eq. 5-14

Wherein is given by 8.85.

Using one of both ultimate bearing capacity models, the cutting force in front of the plough can be

calculated by:

Eq. 5-15


28

5.4 APPLICABILITY OF THE MODEL

Foundations are not supposed to move whereas the narrow shaped ploughs are designed to move. This

means that the velocity effects are neglected in the ultimate bearing capacity theory. As the strength of

clay is known to increase with increasing deformation rates, the forces calculated by the ultimate

bearing capacity theory are the minimum expected cutting forces during ploughing.

The ultimate bearing capacity pressure that can be generated in front of the narrow shaped plough is

based on the simplification of the plough to a very narrow rectangle with a flat tip. The plough has

however a more streamlined tip that will probably reduce the required pulling force. The influence of

the tip shapes is not accounted for in the ultimate bearing capacity model, probably resulting in

conservative predictions for the cutting forces.

The narrow shaped plough is pushing the top of the cut soil upwards instead of sidewards, since this

requires a lower force. This effect is not accounted for in the ultimate bearing capacity model which

probably results in conservative predictions for the cutting forces.

With the discussed influences borne in mind it can be concluded the cutting force of the narrow

shaped ploughs is probably smaller than the values as calculated with the ultimate bearing capacity

theory.


29

6. SOIL FAILURE FOR NARROW TILLAGE TOOLS

Several models are developed in the agricultural industry to predict the horizontal force (draught) and

performance of narrow tillage tools (tines). These models are probably also applicable for predicting

draught forces on narrow shaped ploughs since the shape of a these ploughs can be simplified to that

of a narrow tine with an additional side surface.

The models reviewed and discussed in this chapter are the models of Hettiaratchi & Reece (1967),

Godwin & Spoor (1977), McKyes & Ali (1977) and Grisso et al. (1980). These models are based on

single failure of the soil as there is only accounted for the creating the rupture surfaces, and not for the

effects by the movement of the cut soil. The commonly used symbols and definitions used in these

models are summarised in Table 6-1.

Table 6-1: The common used symbols and definitions in the narrow tillage tool models

Symbol Definition Unit

Width of the tool m

Cohesion Pa

Soil-metal adhesion Pa

Depth of the tool m

Horizontal or draft force N

Vertical of lift force N

Dimensionless earth pressure coefficients -

Total force on the tool N

Surcharge pressure Pa

Rupture distance from tool to crescent m

Blade angle from horizontal °

Rupture angle from direction of travel °

Internal angle of friction °

External angle of friction °

Unit weight of the soil N/m3

6.1 HETTIARATCHI & REECE (1967)

Hettiaratchi & Reece analysed three dimensional soil failure and proposed it is composed of two

different regimes; the upper regime (assuming forward failure) and the lower regime (assuming

sidewards failure). The forward failure regime refers to failure ahead of the tool (see Figure 6.1) and

can only occur above a certain “critical depth” whereas the sidewards failure regime refers to the

movement of the soil to the sides of the tool (see Figure 6.2) which can only occur below this “critical

depth”. The “critical depth” is defined as the depth at which the wedge in front of the tool becomes

fully formed.


30

Figure 6.1: Forward failure (Hettiaratchi & Reece, 1967)

Figure 6.2: Sidewards failure (Hettiaratchi & Reece,

1967)

The total required draught force due to three dimensional failure is composed of the summation of the

forward failure force ( ), the sidewards failure force ( ) and the adhesion force up the cutting

interface.

6.1.1. FORWARD FAILURE REGIME

It may be assumed that the vertical failure regime in front of the loaded interface extends over the full

width and depth of the interface. The force on the interface can than directly be obtained from the

additive equation for plane failure in front of a wide cutting blade:

Eq. 6-1

The values for the N-factors in this equation can be found in the graphs published by Hettiaratchi et al.

(1966) or Hettiaratchi & Reece (1974). It should be noted that in addition to the four components of

there is also an adhesive force acting along the blade, given by; ( ( )⁄ ).

6.1.2. SIDEWARDS FAILURE REGIME

Total force due to the sideways failure exists out of a cohesive component and a gravitational

component. The total force due to the sideways failure can be expressed in terms of the effective

wedge dimensions as:

(

)

Eq. 6-2

In which is the effective width of the tine and is the effective depth of the tine, which are both

dependent on the depth of the tine in relation to the “critical depth”.

The critical aspect ratio is different for the situations and , in which is

representing a critical value related to the “critical depth” and given by ( ). For the

situation in which the value of is given by:


31

( )

Eq. 6-3

For the situation in which the value of is given by:

( )

Eq. 6-4

Wherein is given by:

(

)

Eq. 6-5

The values for the effective width ( ) and the effective depth ( ) are depending on the depth of the

tool in relation to the “critical depth” via the relations given in Table 6-2.

Table 6-2: Table for calculating the effective width and depth

Depth of tool Effective width (w) Effective depth (d1)

( )

The values for and are different for a perfectly smooth and a perfectly rough interface. For a

perfectly smooth interface ( ) the values for and can be calculated according to equation

6-6 and 6-7.

( ) Eq. 6-6

Eq. 6-7

In which is the angle of internal friction [°] and the angle given by ( ⁄ )

For a perfectly rough interface ( ) the values for and can be calculated according to

equation 6-8 and 6-9.

Eq. 6-8

[ ( ) ] Eq. 6-9

6.1.3. THE INFLUENCE OF THE INCLINED SURFACES

Failure patterns caused by inclined interfaces are more complicated in the case of three dimensional

soil failure. Using a semi-empirical relationship, this problem can however be simplified. The main

difficulty in this case, is in assessing the influence of the blade angle on the sidewards failure regime.


32

There are no difficulties with regard to the forward failure regime since the N factors in the equation

6-1 do already account for the change in failure geometries due to variations in blade angle. To

account for the inclined surfaces in the sidewards failure regime equation 6-2 is multiplied by an

inclination factor ( ). The expression for this inclination factor ( ) is given by:

( )

Eq. 6-10

6.1.4. THE TOTAL FORCE ON THE BLADE OR TINE

The total force on the tine due to the three-dimensional failure is the vector sum of , and the

adhesion force up to the cutting interface. The draught (horizontal) and lift (vertical) forces can be

obtained from the following set of equations:

Eq. 6-11

[ (

)

] Eq. 6-12

( ) Eq. 6-13

( ) Eq. 6-14

6.2 GODWIN & SPOOR (1977)

Godwin & Spoor proposed two basic mechanisms of soil failure in the cutting process. The upper part

of the cutting process assumes a crescent failure mechanism whereas in the lower region of the cutting

process a lateral failure mechanism is assumed (See Figure 6.3). In the crescent failure zone it is

assumed soil is moved forwards and upwards with a distinct shear plane being developed from the tine

base at a critical depth up to the surface. In the lateral failure zone it is assumed there is no vertical

movement of the soil, so that the soil has to be moved both in the direction of travel as well as

sidewards. The transition from the crescent failure mechanism to the lateral failure mechanism occurs

at the “critical depth”.

Figure 6.3: Conceptual mechanism of soil failure (Godwin & Spoor, 1977)


33

For tines with aspect ratios ( ) larger than unity, the complete soil is failing in crescent failure

whereas for tines with small aspect ratios (< 0.1) the soil is almost completely failing in lateral failure.

6.2.1. CRESCENT FAILURE

A passive failure mechanism is assumed to occur in the crescent failure area. The crescent is divided

in three sections, one linear section in front of the blade and two curved sections of constant radius on

either side of the linear section. (See Figure 6.4)

Figure 6.4: Crescent failure geometry (Godwin & Spoor, 1977)

The passive force by the linear section immediately ahead of the blade or tine can be determined using

equation 6-1. To account for the influence of the complex radial sections, an approximation method is

used in combination with the existing two-dimensional theory.

The maximum angle between the direction of travel and the curved section of the crescent is given by:

(

) Eq. 6-15

In which is the rupture distance ration and given by:

Eq. 6-16

This rupture distance ratio is dependent on the blade angle and can be found in graphs published by

Godwin & Spoor (1977).

The passive force necessary to cause shear failure of the volumetric element contained by sector

as shown in Figure 6.5 is given by:

( )

Eq. 6-17


34

Figure 6.5: 3D view crescent failure (Godwin & Spoor)

Figure 6.6: Side view crescent failure (Godwin & Spoor)

The total passive force on one curved section can be calculated by integration equation 6-17 between

the limits and . The horizontal and vertical force components can then be calculated by:

[

] [ ( (

))]

( ) [ ( ) ]

Eq. 6-18

[

] [ [

]

]

( ) [ ( ) ] Eq. 6-19

6.2.2. LATERAL FAILURE

Below the critical depth the soil is assumed to fail in a two-dimensional (horizontal) plane, regardless

of the blade angle. This failure mechanism is similar to the failure mechanism of a deep narrow

footing that is vertically orientated.

The resultant stress on the blade for a deep narrow footing is according to Meyerhof given by:

Eq. 6-20

In which is the magnitude of the geostatic stress given by:

Eq. 6-21

In which is the in-situ ratio between the horizontal and vertical stress of the soil at rest given by:

Eq. 6-22

The total horizontal force ( ) on the blade or tine by the lateral failure mechanism is given by the

integration of equation 6-20 between the limits of the total working depth ( ) and the critical depth

( ), which results in:

( )

( ) Eq. 6-23


35

The values for and

can be obtained from equations 6-24 and 6-25, Figure 6.7, and the theory

obtained by Meyerhof (1951).

[

( )

( ( [ ] ))

] Eq. 6-24

( )

( [ ] )

Eq. 6-25

Figure 6.7: Dimensionless N factors for lateral failure (Godwin & Spoor, 1977)

For the situation in which , the N factors by Meyerhof (1951) should be used.

6.2.3. THE TOTAL FORCE ON THE BLADE OR TINE

The total load is given by the vector sum of the force components obtained from the crescent failure

mechanism and the lateral failure mechanism. The total horizontal and vertical forces on the blade

(tool) are given by:

Eq. 6-26

Eq. 6-27

As in all soil mechanics problems the magnitude of the passive force is determined by the lowest force

for which soil failure can occur. Since the critical depth is the only variable in this equation, the value

of the critical depth for which the total force is at a minimum should be determined.


36

6.3 MCKYES & ALI (1977)

The soil failure model for narrow blades as proposed by McKyes and Ali is shown in Figure 6.8. In

this model straight lines are assumed to form the failure boundary surface, instead of a failure

boundary surface that is made by log spiral curves, as in the model of Godwin & Spoor. The straight

lines of the model are assumed to make an angle with the horizontal. This results in the draught

force being a function of the angle in combination with some other soil properties.

Figure 6.8: Proposed soil failure (McKyes & Ali, 1977)

The value for the angle can be determined using the principle that the soil will fail on the path of the

least resistance.

6.3.1. CRESCENT FAILURE

The crescent is divided in three sections, as shown in Figure 6.9. The centre section immediately

ahead of the blade is flanked by two side sections having straight sliding boundary surfaces.

Figure 6.9: Forces on the soil segments (McKyes & Ali, 1977)


37

The passive force necessary to cause failure of the centre part of the crescent is given by:

(

[ ( )]

)

( ) ( ) ( )

Eq. 6-28

The passive force necessary to cause failure of the volumetric element contained by the sector ,

as shown in Figure 6.9, is given by:

(

[ ( )]

)

( ) ( ) ( )

Eq. 6-29

Wherein is the rupture distance given by:

( ) Eq. 6-30

The maximum angle between the direction of travel and the curved section of the crescent is given by:

(

) Eq. 6-31

The total passive force by one side crescents can be calculated integrating equation 6-29 between the

limits and .

The total horizontal force components can be calculated by:

(

[

]

[ ( )] [

]

[

]) (

( ) ( ))

Eq. 6-32

This expression can be rewritten to the equation to calculate the total passive force on a wide blade:

Eq. 6-33

With the following relations for the associated horizontally orientated N-factors:

[

]

( ) ( )

Eq. 6-34

[ ( )] [

]

( ) ( )

Eq. 6-35


38

[

]

( ) ( )

Eq. 6-36

In these equations the value for is determined such that the value for of the total horizontal forces is

at a minimum.

6.4 GRISSO ET AL. (1980) AND PERUMPRAL ET AL. (1983)

The model of Grisso et al. (1980) and Perumpral et al. (1983) is quite similar to the model developed

by McKyes & Ali. The only difference with this model is that the influence of the side wedges is

replaced by forces acting on the centre. Like in the model of McKyes & Ali the centre wedge is

assumed to have a rupture plane making an angle with the horizontal. Using equilibrium conditions

on the centre wedge, the forces can be written in the Hettiaratchi & Reece earthmoving equation for

wide blades, with exception of the surcharge pressure component :

Eq. 6-37

With the following relations for the N-factors:

[

( ) ( )

( )] Eq. 6-38

[

]

( )

Eq. 6-39

( ) ( )

( )

Eq. 6-40

In which is the height of the soil in front of the tool at failure, , the average depth of the centroid of

the failure wedge, and the area on the side of the failure wedge. These last two can be determined

by:

( ) Eq. 6-41

And

(

) [(

) ] Eq. 6-42

As in all models, failure will occur when the resistance of the soil wedge is at a minimum (

).


39

The total draught (horizontal) and lift (vertical) forces can be calculated by:

( ) Eq. 6-43

( ) Eq. 6-44

6.5 ADVANTAGES AND DISADVANTAGES OF THE NARROW TINE MODELS

Hettiaratchi & Reece (1967) can be used without prior knowledge of the rupture distance. It can be

used for blade angles between 20° < < 160°, and calculation of the required draught and lift forces is

very straight forward. The model is known to overestimate the required forces for vertical blades,

whereas for inclined blades the model is known to underestimate these forces.

Godwin & Spoor (1977) requires prior knowledge of the rupture distance or a model predicting

rupture distance ratios. The graph for predicting the rupture distance ratio as given in Godwin & Spoor

(1977) is usable for blade angles up to 90 degrees. For larger angles up to 160 degrees, the graph as

proposed by Hettiaratchi & Reece (1966) can be to predict the rupture distance ratio.

McKyes & Ali (1977) require prior knowledge of the rupture distance ratio as the model dictates a

certain failure shape based on a combination of blade geometry and soil properties. The draught force

is a function of the angle which can be defined using the principle the total force function is

minimised with respect to this angle. The paper by McKyes & Ali (1977) describes a one wedge

model as well as a two wedge model. For comparison with the other narrow tine theories only the one

wedge model is reviewed. In general, the values predicted by the two wedge model are a bit lower

than the values predicted by the one wedge model. The model can predict the required draught force

for blade angles up to 90° but is unable to predict the associated lift force.

The model of Grisso et al (1980) and Perumpral et al. (1983) can be used for blade angles up to 90

degrees. The resulting equation for the passive earth force as proposed in this theory is a function of

the angle . This angle can be defined using the principle the total passive earth force is minimised

with respect to this angle.

The narrow tine models do not account for the influence of the ploughing velocity on the required

draught forces. In addition, the models do not account for the friction or adhesion along the sides of

the tine, which means the models are only predicting the force required to cut the soil in front of the

tool.


40

7. SUBSEA PLOUGH MODELS

Submarine ploughs have already been used for many years and several models have been created to

predict the towing forces of these narrow shapes ploughs in various soil conditions. In this chapter

several submarine plough models are discussed together with their advantages and disadvantages.

7.1 REECE AND GRINSTED (1986)

Reece & Grinsted (1986) have developed an empirical model for predicting required towing forces on

subsea ploughs. A distinction is made between sand and clay soils.

Coulomb already discovered in 1770 that there were two fundamental types of soil strength; frictional

and cohesive, associated with two different kinds of soil; sand and clay. For soil excavation mechanics

of dry soils, the following simple and empirical relations between force and plough-soil parameters are

determined.

The relation for sand cutting with a straight blade:

( ) Eq. 7-1

Cutting force [N]

Dimensionless coefficient [-]

Unit weight [N/m3]

Ploughing depth [m]

Ploughing width [m]

Internal friction angle [°]

The relation for clay cutting with a straight blade:

Eq. 7-2

Dimensionless coefficient [-]

Cohesion – Undrained shear strength [Pa]

These relations do only account for pushing up the soil wedge in front of the blade, as shown by the

area abc in Figure 7.1. The wedge in front of the cutting blade is pushed upwards between soil-soil

surface a-c and soil-metal surface b-c. Both equations 7-1 and 7-2 do account for soil-soil failure over

surface a-c. On the surface b-c, the sliding is resisted in sand by soil to metal friction described by

( ) whereas in clay it is resisted by a soil tangential adhesion. (It should be noticed that Figure 7.1

does not give the correct kinematic representation of the soil cutting process, as the previously layers

of cut soil should lie parallel to the soil-soil failure surface a-c)


41

Figure 7.1: Soil cutting by straight blades (Reece & Grinsted, 1986)

An additional complication is that the wedging action occurs under a pile of previously cut soil. With

a surcharge pressure the influence of these piles of previously cut soil can be taken into account. In the

general case where soil is unsaturated it can have both cohesion and friction. Considering these

complications Reece & Grinsted (1986) have come up with a general relationship as given in equation

7-3, and originating from the plane failure in front of a wide cutting blade (equation 7-1).

Eq. 7-3

Dimensionless coefficient for unit weight [-]

Dimensionless coefficient for adhesion-cohesion ratio [-]

Dimensionless coefficient for surcharge [-]

Surcharge [Pa]

7.1.1. CUTTING SATURATED CLAY

The submarine clays faced in offshore areas are normally completely saturated. Once saturated clay is

loaded rapidly, the load will be carried by the pore water, with the result that the strength of the clay is

independent of the load. During the earthmoving operation of ploughing the loading rates are such that

the strength of the clay is independent of the load and the clay can be considered frictionless.

The relationship for cutting saturated clay with a narrow blade, like a submarine plough, is given by:

Eq. 7-4

In which is a dimensionless coefficient depending on the machine geometry, and the ratio between

adhesion and cohesion of clay. This relationship is very useful since it shows the relation between

cutting depth and cutting force.

The given equation for cutting in saturated clay is independent of velocity, although Reece and

Grinsted admit a higher velocity will lead to somewhat higher pulling force. For the normal ploughing

velocities, the influence of velocity differences are expected to be small, and therefore the required

pulling force is assumed to be more or less constant.


42

7.1.2. ADVANTAGES AND DISADVANTAGES OF REECE & GRINSTED (1986)

Advantages: Disadvantages:

Coefficients are used to describe the

influence of the plough geometry and can

therefore be based on practical experiences

during operations.

Separate models for ploughing in sand and

clay.

Relationships are independent of velocity.

The only included soil parameters are

cohesion and the angle of internal friction.

Influence of adhesion-cohesion and

geometry is included in one factor, whereby

separate influences are difficult to identify.

7.2 INTERNAL MODEL

The internal model is developed by the manufacturer of the Sea Stallion 4 plough and based on Reece

& Grinsted, 1986. The model subdivides the required pulling force into two parts; a weight dependent

part and a soil cutting part, that is related to the ploughing velocity and ploughing depth. In coherence

with Reece and Grinsted (1986) the internal model provides separate equations for ploughing in sand

and clay soils.

Pulling force during ploughing in sand

( ) Eq. 7-5

Pulling force in sand [N]

Coefficient for the skids on sand [-]

Weight of the submerged plough [kg]

A coefficient for ploughing in sand [-]

A coefficient for ploughing in sand [-]

Ploughing velocity [m/s]

Depth exponent = 2.5 – 3.0 [-]

Pulling force during ploughing in clay

( ) Eq. 7-6

Pulling force in clay [N]

Coefficient for the skids on clay [-]

A coefficient for ploughing in clay [-]

A coefficient for ploughing in clay [-]


43

Depth exponent = 1.5 – 2.0 [-]

Coefficients depend on the plough type, its specific interaction with soil and

characteristics of the soil. When sufficient data is gathered for a specific plough geometry in various

soil conditions and with various ploughing velocities coefficients can be estimated using a curve

fitting method.

7.2.1. ADVANTAGES AND DISADVANTAGES OF THE INTERNAL MODEL

Since this model is based on the theory of Reece and Grinsted it has many advantages and

disadvantages in common.

Advantages: Disadvantages:

Simple relations.

Coefficients are used to describe the

influence of the plough geometry in

different soils, which can be based on

practical experiences during operations.

Relationships that are velocity dependent.

Separate models for ploughing in sand and

clay.

Highly empirical.

Untransparent, all parameters are caught

in one coefficient, whereby individual

influences of geometries and soil

parameters are difficult to identify.

Coefficients dependent on soil type,

which requires different coefficients for

all different soil types.


44

7.3 ADDITIONAL ADHESION

Extra friction terms can be added to the ultimate bearing capacity theory in order to develop a

complete force prediction model for the Sea Stallion 4 plough. Separate models are developed to

calculate the extra friction or adhesion along the skids, heel and share in sand and clay soil conditions.

7.3.1. ADDITIONAL FRICTION IN SAND

The friction on the skids can be calculated by:

( ) Eq. 7-7

The additional force on the skids in sand [N]

Angle of external friction [°]

Vertical load [N]

The friction on the share depends on the load perpendicular to the share, which in turn is depending on

the average soil stress and the side area of the share. The friction along the share can be calculated by:

( ) ( )

( )

Eq. 7-8

The additional force on the share in sand [N]

Side area of the share [m2]

Submerged soil density [kg/m3]

7.3.2. ADDITIONAL ADHESION IN CLAY

Adhesion will appear along the share, skids and heel during ploughing in clay soil conditions due to

adhesion between the steel-clay surfaces. The adhesion generated by the skids, share and heel can be

calculated by:

Eq. 7-9

Eq. 7-10

Eq. 7-11

The additional force on the skids, share and heel in clay [N]

Adhesion [Pa]

Area of the skids, share and heel [m2]


45

8. TIP SHAPE INFLUENCE

The models discussed in chapter 6 are made for flat frontal shapes. Zelenin (1950) and Sharifat (1999)

showed that the shape of the tip has a significant influence on the required cutting energy and thus the

required draught force. The tip shape of the cutting interface probably influences the flow pattern of

the soil and has therefore an influence on the required draught force.

Depending on the tip shape and soil properties a sharp tip shape will slide through the soil like a knife

whereby adhesion along the sliding plane mainly describes the soil-tool interaction, whereas for other

more blunt tip shapes a compacted soil wedge will form in front of the tool making the soil-soil

interaction over the sliding planes the main factor describing the soil-tool interaction. Intuitively, one

would expect that the tendency of a soil to slide along the cutting interface itself increases with an

increasing sharpness of this cutting interface. Zelenin (1950) claims that a compacted soil wedge

appears in front of a profile once the angle of the face exceeds 50°, as is shown in Figure 8.1.

Figure 8.1: The formation of compacted cores in front of various cutting interfaces (Zelenin, 1950)

Sharifat (1999) performed some experiments in order to compare the soil movement and required

cutting energy of four cutting interfaces. The experiments were performed for two different moisture

contents at relatively high cutting velocities (10-25 km/hr). The four different cutting interfaces used

in his experiments are shown in Figure 8.2.

Figure 8.2: The four different cutting interfaces used in the experiments a): 45° Triangular (T4), b): Elliptical (T3), c):

Flat (T2) and d) 90° Triangular (T1) (Sharifat, 1999)


46

The results from the experiments performed by Sharifat (1999) are shown in Figure 8.3 and Figure

8.4.

Figure 8.3: The used energy by the four different tools at a soil moisture content of 11.2%, a Cone index of 300 kPa

and speeds of 10, 15, 20 and 25 km/hr (Sharifat, 1999)

Figure 8.4: The used energy by the four different tools at a soil moisture content of 15.1%, a Cone index of 300 kPa

and speeds of 10, 15, 20 and 25 km/hr (Sharifat, 1999)

From these figures it can be concluded that the influence of the tip shape on the required cutting

energy and thus cutting force is quite significant, at least for the reviewed soil conditions and moisture

contents.

There are no relationships found in literature describing the influence of tip shapes in a quantified

manner. This makes it useful to investigate the influence of different tip shapes during the experiments

to be performed.


47

9. STRAIN-RATE DEPENDENT BEHAVIOUR OF CLAY

The strength of a cohesive soil during cutting is depending on the strain rate of the cutting process.

9.1 STRAIN-RATE DURING PLOUGHING (1)

The strain can comprises both the rate at which a material is expanding or shrinking and the rate at

which it is being deformed by progressive shearing whereby its volume is not changing. As during

ploughing the failure mechanism shown in Figure 9.1 is expected to occur, the strain rate during

ploughing is related to progressive shearing over the assumed shear planes.

Figure 9.1: The shear planes during failure

In the failure mechanism of Figure 9.1 the clay can be divided in two separate layers which are

subjected to parallel shear over their shear plane. The state of the clay at a certain time (t) can be

described by the location X(y,t) of each of the layers, whereby the location of the inner layer of the

shear plane is given by X(y,t) and the location of the outer layer of the shear plane is given by

X(y+d,t), whereby d is representing the thickness between the different layers (the shear plane). The

strain between the layers is given by the ratio between the relative displacement of the nearby layers:

X(y+d,t) – X(y,d), divided by the distance between these layers, d, whereby this distance is

approaching zero.

The strain over the different layers is thus given by:

( )

( ) ( )

( ) Eq. 9-1

And the strain rate is given by the derivative of the strain:

( ) (

) ( ) (

) ( )

( ) Eq. 9-2

Whereby

( ) is representing the velocity difference over the shear plane.


48

9.2 INFLUENCE OF THE VELOCITY ON THE UNDRAINED SHEAR STRENGTH

Various researchers have tried to make models to describe the strain rate dependent behaviour of clay.

Most of these models are rather similar and relate the undrained shear strength at a certain strain rate

to the undrained shear strength at a reference strain rate , using an exponential or logarithmic

function. For the failure mechanisms expected during ploughing in clay soils the strain rate is equal to

the velocity difference over the shear planes. Since the velocity difference over the shear planes is

directly related to the forward velocity of the plough, the strain rates as used in the equations found in

literature can be replaced by the ploughing velocities.

In general the increase in the undrained shear strength by increasing ploughing velocities is large

compared to the increase of the inertial force by this same velocity increase. The strain-rate

dependency relations are only valid above a certain velocity, which is in the order of 0.5-1 mm/s. The

exponential model proposed by various researchers is given by:

[

]

Eq. 9-3

According to Wismer & Luth (1972) with values ranging from 0.091 to 0.109. This exponential

model is quite similar to the logarithmic model that is proposed by other researchers, and which is

given by:

( [

]) Eq. 9-4

According to Dayal & Allen (1975) with values ranging from 0.03 to 0.25. As the velocities come

close to zero, the exponential model will result in values for close to zero whereas the logarithmic

model will result in negative values for . The logarithmic model is thus giving incorrect values for

low velocities.

In order to exclude the incorrect behaviour at low velocities from the exponential and logarithmic

strain rate dependency models, Miedema (1992) derived a more correct model. This model is based on

the exponential and logarithmic relations but allows for a yield stress (adhesion and/or cohesion) for a

material at rest. The model developed by Miedema (1992) is given by:

(

[

]) Eq. 9-5


49

10. THE BASE PLOUGH PULLING FORCE MODEL

As the discussed narrow tine models are very complex, and the subsea plough models highly

empirical, the ultimate bearing capacity theory with additional adhesion over the sides and heel of the

plough is chosen as base of the plough pulling force model.

The influences of ploughing angle, tip shape and ploughing depth is accounted for in separate

functions or factors, whereas the influence by the adhesion area is directly incorporated in the

adhesive force component of the base plough pulling force model.

The Nc coefficient is determined for the flat frontal tip shape, whereas the influence by other tip

shapes is related to the Nc coefficient for the flat frontal tip shape, via a tip shape relation or tip shape

factors.

The horizontal ploughing force is according to the base plough pulling model given by:

( ) ( ) ( ( ) ) Eq. 10-1

Horizontal ploughing force [N]

Ploughing angle [°]

Adhesion factor [-]

( ) Ploughing angle influence [-]

( ) Ploughing depth influence [-]

Tip shape influence [-]

Ploughing width [m]

Ploughing depth [m]

Dimensionless coefficient for cohesion [-]

( ) Undrained shear strength at ploughing velocity [Pa]

Adhesion area [m2]

The vertical ploughing force is according to the base plough pulling model given by:

( )

( ) Eq. 10-2

Vertical ploughing force [N]

Clay has a strain rate dependent behaviour whereby its shear strength is increasing with increasing

strain rates. The strain rate is given by the velocity difference over the parallel shear planes which in


50

turn are related to the ploughing velocity. The undrained shear strength of the clay at a certain strain

rate (ploughing velocity) can be related to the undrained shear strength at a reference strain rate

(reference velocity) via the following relation:

( ) (

)

Eq. 10-3

Undrained shear strength at reference velocity [Pa]

Reference velocity [m/s]

Ploughing velocity [m/s]

Velocity influence exponent [-]

Figure 10.1: Parameters used in the base prediction model

PART III: THE PRELIMINARY EXPERIMENTS

51



52

11. THE PRELIMINARY EXPERIMENTAL SETUP

This chapter describes the experimental setup designed and constructed to identify the failure/cutting

processes and deformation profiles that occur during ploughing in clay.

The preliminary experiments are in first instance set up to familiarise with the preparation processes,

the clay, and the force magnitudes that occur during ploughing in clay. Since the experiments are only

for orientating purpose they were as simple as possible. In order to keep the experimental setup

simple, it was only designed and constructed to pull object positioned parallel to the soil surface

through clay. The tip shapes of the profiles analysed in the preliminary experiments range from very

basic blunt tip shapes to more advanced and streamlined tip shapes.

In the preliminary experiments the following is examined:

The usability of the force prediction model as described in chapter 10.

The repeatability of the experiments.

The influence of different clays.

The profiles being reviewed in the different experiments are selected such that the following shape

influences can be examined as much as possible separately:

Size of the profiles.

Length of the profiles.

Tip shape of the profiles.

11.1 DESIGN OF THE PRELIMINARY EXPERIMENTAL SETUP

The experimental setup is designed such that standard blocks of clay with dimensions of

0.15x0.16x0.22 m can be used. The undrained shear strength of these clay blocks is measured and in

between 30-40 kPa. A jack is chosen to generate the required forces for pulling the different profiles

through the clay.

The pulling force is measured by load cells on both sides of the profile, whereas the position of the

profile in the clay is measured by a cable actuated position sensor. The position measurements are

moreover used to calculate the velocity during the experiments.

The experimental setup constrains the clay block over the sides in order to make deformations of the

clay block as a whole impossible. This is done to reflect the natural situation, in which the clay is also

unable to de deform in lateral direction, as much as possible.

A sketch of the experimental setup is shown in Figure 11.1.


53

Figure 11.1: Sketch of the preliminary experimental setup

The deformation profile of the clay during the experiments is recorded with cameras. To visualise

these deformations a painted square grid is applied to the surface of the clay. After the profile is pulled

through the clay, the clay block is split in two parts over the length of the trench, whereafter each of

these parts is scanned with a laser in order to make a deformation profile over the depth of the trench.

11.2 DIFFERENT PROFILES ANALYSED DURING THE EXPERIMENTS

The profiles selected to be pulled through the clay are small enough to minimise the effect of the sides

of the box on the pulling force. The profiles are additionally selected such that the following geometric

influences could be examined as much as possible separately:

Length of the profiles

Size of the profiles

Tip shape of the profiles

The profiles analysed in the preliminary experiments are shown in Figure 11.2 whereas the reasons to

select these profiles are described in Table 11-1.


54

Figure 11.2: Profile shapes analysed in the preliminary experiments

Table 11-1: Profiles used in the preliminary experiments

Profile Experiments Reason to select the profile

Cylinder ø12 2 Investigate the repeatability of the experiments

Cylinder ø12 1 Executed in clay from a clay extraction site in Deest to review

the usability of this clay for the main experiments

Square 10x10 1 Compare to the other square profiles to identify a possible size

relation

Square 12x12 1 Compare to the cylinder to identify a possible shape factor

Square 12x12 1 Performed with a joint in the middle of the clay box to identify

the possible influence by this joint

Square 14x14 1 Compare to the other square profiles to identify a possible size

relation

Square 10x10

- Rotated over 45° 1

Compare this profile to the square 14x14 to identify a possible

shape factor for the streamlined tip shape.

Rectangle 12x24 2

Compare to the other rectangular shapes to identify a possible

relation for adhesion of the different plough lengths, and to

investigate the repeatability of the experiments

Rectangle 12x24 –

sharp tip of 90° 1

Compare to the rectangle 12x24 to identify a possible

influence of the sharp tip

Rectangle 12x36 1 Compare to the other rectangular shapes to identify a possible

relation for adhesion of the different plough lengths

Rectangle 12x36 –

sharp tip of 90° 1



Rectangle 12x36 –

sharp tip of 45° 1



Rectangle 5x50 1 Compare to the other rectangular shapes to identify a possible

relation for adhesion of the different plough lengths.

12 12 12

12

24

12

36

5

50

14

1410

10

12

24

12

36

14 12

36


55

11.3 PREPARATIONS FOR THE PRELIMINARY EXPERIMENTS

Before the experiments could be started a lot of preparations had to be executed. First, the clay blocks

needed to be constrained into a steel box, in order to make deformations of the clay in the directions

perpendicular to the surface impossible. To constrain the clay into the steel box, a frame was

constructed in which two block of clay were laid on a table, onto which the steel box was positioned

and pushed into the blocks. The joint between the blocks was positioned in the starting zone of the

experiments, where the cutting processes is expected to be in development so that the influence by the

joint is limited. Pictures showing the procedure wherein the steel box is pushed into the clay are given

in Figure 11.3 and Figure 11.4.

Figure 11.3: The setup to push the box into the clay

Figure 11.4: The box pushed halfway into the clay blocks

After the clay is pushed into the steel box an opening is made through the clay to position the

experimental profile. (See Figure 11.5 and Figure 11.6)

Figure 11.5: Pushing the profile through the clay

Figure 11.6: Clay after the starting hole is made


56

A square grid is provided to the clay using a steel grid that is placed on the surface of the clay and

being sprayed with orange paint. (See Figure 11.7 and Figure 11.8)

Figure 11.7: Preparations for marking

Figure 11.8: Clay box after marking

When the clay is marked with the grid it is positioned into the experimental setup. The steel box was

completely restrained in the setup using beams that were clamped to the box by clamps. This is done

to prevent the clay from deforming in transverse direction.

11.4 EXPERIMENTAL PROCEDURE

At the start of each experiment all sensors are checked. When all sensors worked correctly, the

cameras were switched on and the experiment was started. The rotary arm is connected to the jack,

and by rotating the arm, the jack is pulling the profile upwards. The profile was pulled upwards

through the clay to around 3-4 cm below the top of the block in order to gain results that are not

influenced by the boundaries of the box. Figure 11.9 and Figure 11.10 show the experimental setup

together with the equipment necessary for measuring the forces and displacements during the

experiment.

Figure 11.9: The complete experimental setup

Figure 11.10: The clay box into the experimental setup


57

11.5 AFTER THE EXPERIMENTS

When the experiment was finished the testing profile was removed from the clay with minimum

disturbances to the clay. A cutting wire was used to split the remaining block in two, after which the

steel box was removed from the setup and split in two parts, unscrewing the bolts on the top and

bottom of the box. Each of these parts was placed on a table and scanned with a laser in order to

identify the shape of the trenched surface. A profile could be created once the angle of the laser was

known in combination with a reference length and height of the beam positioned along the clay. The

table equipped with laser and reference beam is shown in Figure 11.11 and Figure 11.12.

Figure 11.11: Setup to measure the trenched surface

Figure 11.12: The height profile of the trenched surface

After the profile of the trenched surface was measured, the undrained shear strength of the clay blocks

was measured using a field vane (see Figure 11.13). The undrained shear strengths and residual

strengths are measured at three spots on the surface of each part of the clay blocks, as is shown in

Figure 11.14.

Figure 11.13: The field vane

Figure 11.14: The measuring locations


58

11.6 TEST REPORT

The test report contains all data measured during the experiments along with the most important

particulars on the clay before the experiments and any notable events during execution of the

experiments. The undrained shear strengths of the clay block are measured and reported together with

the locations of these measurements. Lastly, the report contains four graphs presenting the processed

data of the load cells and the position sensor.

Figure 11.15: Lay-out of the test report

General remarks:

During all experiments the velocities were fluctuating through rotating of the arm of the jack by hand.

The average velocities of all the experiments are close to each other and in between 2 and 3 mm/s.

Experiments 1 to 12 were executed in a timespan of three weeks from each other, whereas the

experiments 13, 14 and 15 were executed two month after the first experiments. In this time span the

clay blocks had dried a little bit resulting in an increased strength of the clay.

General information about the experiment

Particulars noted before and during

execution of the experiment

Calculated velocities

Measured loads from which the average

load is calculated

Measured loads after the experiment

(profile is not moving anymore but

still being pulled against clay)

Measured undrained shear strengths

Small fluctuations due to noise on the

position measurements


59

12. THE RESULTS OF THE PRELIMINARY EXPERIMENTS

In this chapter the average measured forces during the preliminary experiments are presented, and

influences of length, size and tip shape are analysed. An overview of the variables and influences

analysed with the results of the preliminary experiments is given in Figure 12.1.

Figure 12.1: Overview of the variables and influences analysed with the results of the preliminary experiments

The force development during each of the experiment is analysed in order to come up with an average

value of the required pulling force. An overview of the average measured pulling forces is given in

Appendix B, whereas the complete test reports of the experiments are given in Appendix C.

12.1 THE BASE PREDICTION MODEL

The plough pulling force model of chapter 10 can be rewritten to a model for the preliminary

experiments, given by:

Eq. 12-1

Total pulling force [N]

Adhesion factor [-]

Ploughing width [m]

Ploughing depth [m]

Adhesion length (including tip length) [m]

Dimensionless coefficient for cohesion [-]

Undrained shear strength [Pa]

Preliminary experiments

Clay usabilityGeometrical influences

Properties experimental setup

RepeatabilityJoint between

blocksProfile length Profile width Tip shape Pottery clay

Clay from a clay extraction site

Cutting component Adhesion component


60

12.2 REPEATBILITY OF THE EXPERIMENTS

In order to make the results of the different experiments comparable to each other the experiments

should be repeatable. The repeatability of the experiments is checked by performing one of the

experiments twice. The measurements of these experiments are showing the same results, as is shown

in Graph 12.1, from which it can be concluded that the experiments do have a good repeatability.

Graph 12.1: Repeatability (su = +/- 33 kPa, vavg = +/- 2.5 mm/s)

12.3 LENGTH INFLUENCE

In order to find the values for the adhesion factor and the Nc coefficient of the profile with a flat

frontal shape, a flat profile with a width of 12 mm was tested with three different lengths: 12, 24 and

36 mm. The measured pulling forces in these experiments are shown together with the predicted

forces in Graph 12.2.

Graph 12.2: Length influence (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/- 2.5 mm/s)

As only the length is increasing between the different profiles of Graph 12.2, the adhesion factor can

be determined. This adhesion factor can in turn be used in equation 12-1 to determine the Nc

coefficient for a flat frontal tip shape.

0

100

200

300

400

500

600

ø12 [1] ø12 [2]

Forc

e [N

]

Repeatability

Measured pulling force

0

100

200

300

400

500

600

700

800

■12x12 [1] ⌷12x24 [2] ⌷12x36

Forc

e [N

]

Length influence

Adhesion component

Cutting component



61

Using the measured forces and geometries of the profiles ⌷12x36 and ■12x12 in equation 12-1 results

in:

As the cutting force component is equal for both profiles the above equations can be subtracted from

each other in order to define the value of the adhesion factor:

As the adhesion factor is defined to be 0.34, the Nc coefficient for a flat frontal tip can be calculated,

using equation 12-1 and the geometry and measured force of the square profile ■12x12:

12.4 SIZE INFLUENCE

During the preliminary experiments the square profile was tested with three different dimensions: 10,

12 and 14 mm. As suggested by the force prediction model the trend between these different sizes is

expected to be linear.

Graph 12.3: Size influence (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/- 2.5 mm/s)

0

100

200

300

400

500

600

700

800

■10x10 ■12x12 [1] ■14x14

Forc

e [N

]

Size influence

Adhesion component

Cutting component



62

As shown in Graph 12.3 the line of the measured forces is not linear. As the number of executed

experiments is limited it is difficult to state whether the trend line should be linear or not. The profile

with dimensions of 12 mm had a rougher surface than the profiles with dimensions of 10 and 14 mm,

which probably had an influence on the required pulling force. Additionally the supressing trend-line

of the measured forces can also originate from an increasing with-over-depth ratio of the larger

squared profiles. As a result of this increasing width-over-depth ratio there is more discharge of soil to

the surface, possibly supressing the increase rate of the required pulling force.

12.5 TIP SHAPE INFLUENCE

During the preliminary experiments different tip shapes are tested in order to identify possible

advantages of certain tip shapes. The tip shapes that are compared to each other in the different

experiments are; a flat tip, a cylindrical tip, a sharp edged tip with a frontal angle of 90°, and a sharp

edged tip with a frontal angle of 45°. In Graph 12.4 the cylindrical and flat tip shape both with a

frontal width of 12 mm are compared to each other. The square profile has some more adhesion along

its sides compared to the cylindrical profile, which represents therefore a part of the difference

between the measured forces of both profiles.

Graph 12.4: Tip influence, cylinder compared to blunt (su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/ 2.5 mm/s)

The Nc coefficient for the circular frontal tip shapes can be calculated using equation 12-1 and the

geometry and measured force of the circular profile ø12.

As the Nc coefficient for the circular tip shape is 8.2, this tip shape requires an 18% lower cutting force

compared to the flat tip shape.

0

100

200

300

400

500

600

700

800

ø12 [2] ■12x12 [1]

Forc

e [N

]

Tip shape influence [1]

Adhesion component

Cutting component



63

The profile ⌷12x36 with flat frontal tip shape is modified to a profile with a sharp tip of 90° and a

profile with a sharp tip of 45°. The measured forces for the profile 12x36 with different tip shapes are

plotted in Graph 12.5.

Graph 12.5: Tip influence, 90° and 45° sharp edged tip compared to blunt

(su = +/- 33 kPa, Nc = 10, αa = 0.34, vavg = +/- 2.5 mm/s)

As can be seen from Graph 12.4 the measured force of the 90° sharp edged tip is only a bit smaller

than the measured force of the profile with a flat frontal tip. This means that the cutting forces of both

tip shapes are equal to each other and the 90° sharp edged tip thus also has an Nc coefficient of 10. The

influence of the 90° tip shape is probably limited due to the shape of the failure zones. As shown in

Figure 5.1 a wedge of soil is formed in the active Rankine zone in front of the flat frontal tip shape,

which will move along with the profile. In clay soils this soil wedge has a sharp frontal angle of 90°,

which is equal to the 90° tip shape, making the influence of this shape limited.

As can be seen from Graph 12.5 the measured force of the 45° sharp edged tip shape is significantly

lower than the measured forces of the blunt and 90° sharp edged tip shapes. The Nc coefficient for the

sharp edged 90° tip can be calculated using equation 12-1 and the geometry and measured force of the

sharp edged profile 12x36 <=45°:

As the Nc coefficient for the 45° sharp edged tip shape is 8.2, this tip shape requires an 18% lower

cutting force compared to the flat tip shape.

The values of the Nc coefficients as calculated in this section are based on a width-over-depth ratio of

1:6. For other width-over-depth ratios the Nc coefficients are probably different, but it is

acknowledged that the tip shape has an influence on the required cutting force. The Nc coefficients for

0

100

200

300

400

500

600

700

800

⌷12x36 12x36 <=90° 12x36 <=45°

Forc

e [N

]

Tip shape influence [2]

Adhesion component

Cutting component



64

the width-over-depth ratio of 1:6, as determined with the results of the preliminary experiments, are

collected in Table 12-1.

Table 12-1: The Nc coefficients for various tip shapes (w/d ratio of 1:6)

Tip shape Nc coefficient

Flat tip 10

90° sharp edged tip 10

45° sharp edged tip 8.2

Circular tip 8.2

The deformation profiles at the surface of the clay differed significantly from each other for the

different tip shapes (see Figure 12.2 to Figure 12.5). During the experiments with flat/blunt tip shapes

the top layer of clay was pushed over the length of the flat tip, whereas the 45° sharp edged tip was

nicely sliding through the soil. The 90° sharp edged tips were also sliding through the soil, but less

effectively than the 45° tip shape, and with more disturbances to the soil alongside the sliding/cutting

plane and with more discharge to the surface of the soil. The deformation profile of the circular tip

was close to that of the 90° sharp edged tip although there was less accumulation of clay alongside the

sliding/cutting plane of the profile.

Figure 12.2: Deformation profile flat frontal shape

Figure 12.3: Deformation profile circular frontal shape

Figure 12.4: Deformation profile sharp frontal shape

Figure 12.5: Deformation profile frontal edge of 45°


65

For a width-over-depth ratio of 1:6, the thickness of the top layer of clay that moved over the length of

the flat frontal profile was quite significant compared to the total depth. For smaller width over depth

ratios, the relative thickness of the upper layer of clay that will be pushed over the flat frontal surface

of the profile is decreasing, minimizing its influence and therefore probably resulting in an increase in

the total relative force.

12.6 INFLUENCE OF THE JOINTS BETWEEN THE BLOCKS

In the preliminary experiments the influence of the joints between the clay blocks is analysed, by

executing three experiments with joints at different locations in the box. In the first of these

experiments the profile ⌷12x24 was tested with a joint between the blocks in the start-up zone of the

experiment whereas in the second experiment the profile ⌷12x24 was tested with a joint somewhat

passed the middle of the box. The average measured forces of these experiments did not differ from

each other. In the third experiment, the profile ■12x12 was tested with a joint exactly halfway the box.

The measured signals from all three experiments are shown in Graph 12.6 together with the locations

of the joints. The graph is not showing a significant drop or increase in the measured forces around the

location of the joints. There is some scatter in the measured signals, but this scatter is present over the

full length of the experiment. It can thus be concluded that the position of the joint does not have an

influence on the required pulling force.

Graph 12.6: Graph showing the influence of the joints between the clay blocks

12.7 EXPERIMENT WITH A BLOCK OF NATURAL CLAY

During the preliminary experiments, one experiment was performed with natural clay originating from

a clay extraction site in Deest (The Netherlands). In comparison to the experiments performed with the

standard blocks of clay, the measured force was increasing over the full length of the experiment,

whereas for the experiments performed with the standard clay blocks the measured forces were more

or less constant over the full length of the experiments. In addition, the natural clay appeared to be

500

550

600

650

700

750

800

850

0:00:00 0:00:22 0:00:45 0:01:07

Forc

e [N

]

Time [hr:min:s]

Influence of the joints between the blocks

⌷12x24 [1] - su=32kPa

⌷12x24 [2] - su=32kPa

■12x12 [2] - su=45kPa


66

inhomogeneous. At some locations the clay had an undrained shear strength of 44 kPa whereas on

other locations this strength was 64 kPa, which is a difference of +/- 45%. From both findings it can be

concluded that the natural clay is inappropriate for being used in the main experiments.


67

13. VALIDATION OF THE BASE PREDICTION MODEL

The forces predicted by the base force prediction model of equation 12-1 are compared to the forces

measured during the experiments, in Graph 13.1. In this graph the predicted forces are subdivided in a

cutting force component and an adhesive force component. The complete overview of the predicted

forces together with the measured forces is given in Appendix B.

Graph 13.1: Overview measured and predicted forces (su = +/- 33 kPa, αa = 0.34, vavg = +/- 2.5 mm/s)

As shown in Graph 13.1 the predicted forces are on average equal to the measured forces. For some

profiles the predicted forces are somewhat higher than the measured forces whereas for other profiles

this is the other way around. On average the absolute difference between the measured and predicted

forces is 6%. The largest difference between the measured and predicted forces is 30% and occurs for

the profile ⌷5x50.

To gain a better insight in the differences between the measured and predicted forces, and therefore

the applicability of equation 12-1, the measured and predicted forces of all the preliminary

experiments are plotted against each other in Graph 13.2.

Graph 13.2: Relation between measured and predicted forces (su = +/- 33 kPa, αa = 0.34, vavg = +/- 2.5 mm/s)

0

100

200

300

400

500

600

700

800

900

Forc

e [N

]

Experimental profile

General overview

Adhesion component

Cutting component

Measured force

0

200

400

600

800

1000

0 200 400 600 800 1000

Mea

sure

d f

orc

e [N

]

Predicted force [N]


68

From this graph it can be conclude that the base prediction model is a reasonable model to estimate the

required pulling forces for very short profiles moving parallel to the surface.


69

14. CONCLUSIONS OF THE ORIANTATING EXPERIMENTS

Using the Nc coefficients and adhesion factors as determined with the results of the preliminary

experiments, the average absolute difference between the measured and predicted forces is 6%. The

maximum difference between the measured and predicted values is 30% and occurs for the profile

⌷5x50. As the differences between the measured and predicted forces are relatively small for most of

the experiments, the ultimate bearing capacity theory in combination with additional adhesion over the

sides of the profiles is a reasonable model for predicting the required pulling forces.

It is difficult to state firm conclusions from the results of the preliminary experiments, since only 15

experiments were performed. However, some interesting relations and trends could be identified:

Properties of the experimental setup:

o The joint between the clay blocks had no influence on the required pulling force.

Geometrical influences:

o Analysing the results of the experiments, the adhesion factor of the used clay is

determined on 0.34.

o The increase in the required pulling force is decreasing with increasing dimensions of the

square shaped profiles. The exact reason for this decrease cannot be given but probably it

is originating from an increasing width-over-depth ratio in which a relatively larger layer

of soil is being discharged to the surface.

o The value of the Nc coefficient is depending on the tip shape of the profile and the width-

over-depth ratio of the ploughing process. The Nc coefficients for various tip shapes, and

a width-over-depth ratio of 1:6, are given in the table below.

Table 14-1: The Nc coefficients for various tip shapes (w/d ratio of 1:6)

Tip shape Nc coefficient

Flat tip 10

90° sharp edged tip 10

45° sharp edged tip 8.2

Circular tip 8.2

From this table it can be concluded that the required cutting force for a circular and a 45°

sharp edged tip shape is reduced by 18% compared to the required cutting force of a flat

frontal tip shape.

Clay usability:

o The used clay blocks had an consistent undrained shear strength and are considered

suitable for the main experiments.

o The natural clay originating from the extraction site in Deest (The Netherlands) is not

appropriate for being used in the main experiments, as the clay it is too inhomogeneous

to make the results of the experiments comparable.


70

71

BIBLIOGRAPHY

Allan, P. (1998) Selecting Appropriate Cable Burial Depths, A methodology in selecting appropriate

cable burial depths. IBC Conference on Submarine Communications. The future of network

infrastructure, Cannes, November 1998.

Aubeny C.P. & Shi H. (2007) Effect of rate-dependent soil strength on cylinders penetrating into soft

clay. IEEE journal of oceanic engineering, Vol. 32, No. 1, Page 49-56.

Barnes, G. (2010) Soil Mechanics, Principles and practice. Palgrave Macmillan.

Brinch Hansen J. (1961) A general formula for bearing capacity, The Danish geotechnical institute,

Bulletin No 11, Page 37-46.

Beindorff, R. (2011). New ways to calculate forces and velocities on a submarine narrow trench

lough, in sandy soil. Thesis report Delft University of Technology.

Dayal, U. & Allen, J.H. (1975) The Effect of Penetration Rate on the Strength of Remolded Clay and

Sand Samples, Canadian Geotechnical Journal 12, Page 336-348.

Gilbert Gedeon, P.E. (1992) Bearing Capacity of Soils. U.S. Army Corps of Engineers, Engineer

manual No. 1110-1905.

Godwin, R.J. & Spoor, G. (1977) Soil failure with narrow tines. J. agric. Engng Res., Page 213-228.

Grisso R.D. & Perumpral J.V. (1985) Review of models for predicting performance of narrow tillage

tools. TRANSACTIONS of the ASAE, Vol. 28, Page 1062-1067

Hettiaratchi, D.R.P. & Reece A.R. (1966) The calculation of passive pressure in two-dimensional soil

failure. J. agric. Engng Res. 11, Page 89-107.

Hettiaratchi, D.R.P. & Reece, A.R. (1967) Symmetrical three-dimensional soil failure. Journal of

Terramechanics, Vol 4, No. 3, Page 45-67.

Hettiaratchi, D.R.P. & Reece A.R. (1974) The calculation of passive soil resistance. Géotechnique 24,

No. 3, Page 289-310.

Kroes, G. (2010) Subsea cable installation, a technical guide. Magazine for The offshore wind

industry No 04.

72

Kulhawy, F. & Mayne, P. (1990) Manual on estimating soil properties for foundation design.

Research project by the geotechnical engineering group of the Cornell university.

McKyes, E. & Ali, O.S. (1977) The cutting of soil by narrow blades. Journal of Terramechanics, Vol.

14, No. 3, Page 43-58.

McKyes, E. (1985) Soil cutting and tillage. Elsevier Science Publisher B.V.

Meyerhof G.G. (1951) The ultimate bearing capacity of foundations, Géotechnique Vol 2, Issue 4.

Miedema, S.A. (1992) New Developments of Cutting Theories with respect to Dredging, the Cutting of

Clay. Proc. WODCON XIII, Bombay India 1992.

Miedema S.A. (2012) Dredging processes, The cutting of sand, clay & rock, Soil mechanics. Lecture

notes Delft University of Technology.

Mole, P., Featherstone, J., & Winter, S. (1997) Cable protection - Solutions through new installation

and burial approaches. Cable & Wireless Marine.

Nobel A. (2013) On the excavation process of a moving vertical jet in cohesive soil. Doctoral thesis

Delft University of Technology.

Perumpral J.V., Grisso R.D. & Desai C.S. (1983) A soil-toll model based on limit equilibrium

analysis. Transactions of the ASAE 26(4), Page 991-995.

Reece, A.R. & Grinsted, T.W. (1986) Soil mechanics of submarine ploughs. OTC 5341.

Sharifat K. (1999) Soil translocation with tillage tools. Phd report at the Department of Agricultural

and Bioresource Engineering at the University of Saskatchewan.

Terzaghi, K. (1943) Theoretical Soil Mechanics. John Wiley and Sons, New York (1943)

Tomlinson (1970) The adhesion of piles driven in stiff clay. CIRIA Research report No. 26.

Verruijt, A. (2007) Soil Mechanics. VSSD.

Wismer R.D. & Luth H.J. (1972) Rate effects in soil cutting. Journal of Terramechanics, Vol 8, No. 3,

Page 11-21.

Zelenin, A. N. (1950) Basic physics of the theory of soil cutting. Moscow, Russia: Kolos

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