*3.3.1 Coulomb friction "Bilinear" model*

Present industry procedure is to evaluate the soil resistance with a Coulomb friction model, as shown in **Figure 12**, which expresses the lateral resistance as the product of the effective submerged pipeline vertical force (submerged pipe weight minus hydrodynamic lift force) and a soil friction coefficient that depends solely on soil type. Recommended values of the Coulomb friction coefficient, *μ*, lie in the range 0.2–0.8, while the displacement to mobilise this resistance is typically 0.1 pipe diameters [20, 23, 24, 29].

#### *3.3.2 Tri-linear pipe-seabed interaction model*

The experiment results show that the pipe-soil lateral motion is far more complicated than simple coulomb friction. An improved model is essential in order to mimic *Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays DOI: http://dx.doi.org/10.5772/intechopen.85549*

**Figure 12.** *Coulomb friction model analysis.*

• A single friction factor "Coulomb friction model" approach, where the lateral soil resistance is related to the submerged weight of the pipeline and the soil type. This approach is fairly simplified, as it does not pertain to pipe embedment;

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

• A two-component model, where the lateral soil resistance consists of a sliding resistance component and a lateral passive pressure component [20, 23, 27];

• A plasticity model approach: Zhang et al. initially developed the plasticity model for calcareous sand and clays [28]. However, the clay's model is established on the behaviour of shallow flat footings in which a large lateral

Therefore, the Coulomb friction approach and the two-component soil resistance

models for the assessment of SCR global response are presented in this chapter.

Present industry procedure is to evaluate the soil resistance with a Coulomb friction model, as shown in **Figure 12**, which expresses the lateral resistance as the product of the effective submerged pipeline vertical force (submerged pipe weight minus hydrodynamic lift force) and a soil friction coefficient that depends solely on soil type. Recommended values of the Coulomb friction coefficient, *μ*, lie in the range 0.2–0.8, while the displacement to mobilise this resistance is typically 0.1 pipe

The experiment results show that the pipe-soil lateral motion is far more complicated than simple coulomb friction. An improved model is essential in order to mimic

and

**Figure 11.**

*Depiction of typical* V*-*z *behavior [7].*

movement does not occur.

*3.3.1 Coulomb friction "Bilinear" model*

*3.3.2 Tri-linear pipe-seabed interaction model*

diameters [20, 23, 24, 29].

**56**

the effects of soil strength and the load history of the catenary pipeline as well as the associated pipe embedment on the lateral seabed soil resistance. The improved empirical model utilises two components to predict the seabed resistance to lateral pipeline movements, resulting in the improved so-called "two-component model."

The two-component model uses an empirical formula to assess the soil resistance to lateral pipeline motions. The first component depends on the vertical pipe weight (pipe weight minus hydrodynamic lift force) and imitates the sliding resistance of the pipeline along the soil surface, while the second component depends on the pipe penetration and soil strength.

Generally, the two-component models are based on empirically fitting laboratory test data. A summary of some of the proposed formulas is given in **Table 1**. The peak lateral soil resistance is a key parameter for the on-bottom pipeline movement. Several reported methods [20, 23, 27, 30] have been published for the assessment of the lateral soil resistance. These determined resistances were then compared with the results of the available pipe model tests.

**Figure 13** shows the lateral load response from step 0 to 3, characterised as follows [31]:


#### **3.4 SCR/seabed axial interaction**

The axial soil resistance for SCR movement is typically modelled using the Coulomb friction model, which is adopted to evaluate the axial resistance of a partially embedded riser pipe, and is expressed as [25, 32]:

$$F\_x = \mu\_A \mathcal{W}\_s \tag{6}$$

where *F*<sup>x</sup> is the axial soil resistance and *μ<sup>A</sup>* is the coefficient of axial coil friction. The typical values for axial friction have been reported to vary between 0.2 and 0.5 for clay soil [33].


sophistication and accuracy. **Table 2** have been addressed for appropriate modelling of the physical SCR-seabed interaction process and graded with a three levels ranging from *α* which represents state-of-the-art practice, *β* a compromise method and *γ* a conservative method. General and brief discussion on the components

*Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays*

*SCR-seabed interaction models*: The majority of experimental studies carried out in recent years have presented the non-linear behaviour of SCR-seabed interaction and trenching effects in the TDZ. An SCR in the TDZ was recently identified as a fatigue hotspot that substantially increased fatigue damage under the SCR-seabed interaction phenomenon. Better understanding of the significance of SCR-seabed interaction behaviour and soil properties improves the fatigue life prediction in the TDZ. Most of the existing riser models unrealistically simplified SCR-seabed interaction behaviour by assuming a rigid or linearly elastic seabed. Trench formation and trench deepening have also significant influence on SCR-seabed response.

*Pipe-seabed interaction models*: Experimental model tests and analytical models of vertically loaded horizontal pipes in clay sediment provided valuable information for better awareness of SCR-seabed interaction in the TDZ. These experimental and analytical data produce the general load/deflection curve for pipe-seabed interaction and necessary information for validation of *V*-*z* model and determination of

*Cyclic loading*: SCR-seabed interaction processes should cover vertical and lateral responses to cyclic loading. Movement and oscillation of the SCR in the TDZ will cause trenching and dynamic embedment of the SCR into the seabed. Seabed stiffness degradation due to cyclic oscillations has a significant influence on the behaviour of an SCR in the TDZ, and especially on the SCR's strength and fatigue performance. After the seabed soil approaches the maximum strength throughout the applied cyclic loading, the seabed soil tends to lose strength and stiffness with the increase in plastic embedment during cyclic oscillations. The seabed soil stiffness degradation mechanism comprises stiffness reduction presented in uplift, suction, and separation as well as the re-penetration process. The degradation of soil stiffness with cyclic loading is best captured by the non-linear seabed model. *Wave loading*: The use of regular wave theories does not adequately represent wave loading on SCRs. However, when used, the level of sophistication in random wave loading is highly variable. For example, the length of simulation used to estimate response levels differs widely. Most studies use simplifying assumptions due to the extensive computational time needed to perform random time domain

*Analysis (coupled vs. uncoupled)*: SCRs have a relative effect on the motions of a floating unit, which in turn affects the SCR fatigue life. In a coupled analysis, the floating unit and SCR are modelled together including their mass, stiffness and damping. Coupled analysis is computationally demanding, especially for robust finite element mesh size. In uncoupled analysis, platform wave frequency is computed in separate models by different programs. Once the floating unit motions are obtained, either from coupled or uncoupled analysis, they are imported as input into the riser analysis software for the uncoupled riser analysis. In uncoupled analysis, the riser is considered to have no effect on the platform at its top. These effects

The literature review introduced in this chapter reveals that the SCR motion at the TDP is predominantly lateral, vertical and cyclic in nature. SCRs are the subject

are usually negligible, and an uncoupled analysis is adequate.

presented in **Table 2** are as follows:

*DOI: http://dx.doi.org/10.5772/intechopen.85549*

geotechnical parameters used in the model.

simulation properly.

**5. Further research**

**59**

#### **Table 1.**

*Lateral resistance models of partially embedded pipelines in soft clay.*

**Figure 13.** *Schematic of the tri-linear soil resistance model.*

#### **4. Summary of SCR-seabed interaction models technique**

A number of scientific papers have been published on the study of soil-riser interaction. **Table 2** details the considerable diversity in the level of sophistication used in the analysis of SCR-seabed interaction response in a representative set of studies published in the last 25 years, with five areas previously highlighted as commonly conservative and broken into components of increasing degree of

#### *Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays DOI: http://dx.doi.org/10.5772/intechopen.85549*

sophistication and accuracy. **Table 2** have been addressed for appropriate modelling of the physical SCR-seabed interaction process and graded with a three levels ranging from *α* which represents state-of-the-art practice, *β* a compromise method and *γ* a conservative method. General and brief discussion on the components presented in **Table 2** are as follows:

*SCR-seabed interaction models*: The majority of experimental studies carried out in recent years have presented the non-linear behaviour of SCR-seabed interaction and trenching effects in the TDZ. An SCR in the TDZ was recently identified as a fatigue hotspot that substantially increased fatigue damage under the SCR-seabed interaction phenomenon. Better understanding of the significance of SCR-seabed interaction behaviour and soil properties improves the fatigue life prediction in the TDZ. Most of the existing riser models unrealistically simplified SCR-seabed interaction behaviour by assuming a rigid or linearly elastic seabed. Trench formation and trench deepening have also significant influence on SCR-seabed response.

*Pipe-seabed interaction models*: Experimental model tests and analytical models of vertically loaded horizontal pipes in clay sediment provided valuable information for better awareness of SCR-seabed interaction in the TDZ. These experimental and analytical data produce the general load/deflection curve for pipe-seabed interaction and necessary information for validation of *V*-*z* model and determination of geotechnical parameters used in the model.

*Cyclic loading*: SCR-seabed interaction processes should cover vertical and lateral responses to cyclic loading. Movement and oscillation of the SCR in the TDZ will cause trenching and dynamic embedment of the SCR into the seabed. Seabed stiffness degradation due to cyclic oscillations has a significant influence on the behaviour of an SCR in the TDZ, and especially on the SCR's strength and fatigue performance. After the seabed soil approaches the maximum strength throughout the applied cyclic loading, the seabed soil tends to lose strength and stiffness with the increase in plastic embedment during cyclic oscillations. The seabed soil stiffness degradation mechanism comprises stiffness reduction presented in uplift, suction, and separation as well as the re-penetration process. The degradation of soil stiffness with cyclic loading is best captured by the non-linear seabed model.

*Wave loading*: The use of regular wave theories does not adequately represent wave loading on SCRs. However, when used, the level of sophistication in random wave loading is highly variable. For example, the length of simulation used to estimate response levels differs widely. Most studies use simplifying assumptions due to the extensive computational time needed to perform random time domain simulation properly.

*Analysis (coupled vs. uncoupled)*: SCRs have a relative effect on the motions of a floating unit, which in turn affects the SCR fatigue life. In a coupled analysis, the floating unit and SCR are modelled together including their mass, stiffness and damping. Coupled analysis is computationally demanding, especially for robust finite element mesh size. In uncoupled analysis, platform wave frequency is computed in separate models by different programs. Once the floating unit motions are obtained, either from coupled or uncoupled analysis, they are imported as input into the riser analysis software for the uncoupled riser analysis. In uncoupled analysis, the riser is considered to have no effect on the platform at its top. These effects are usually negligible, and an uncoupled analysis is adequate.

#### **5. Further research**

The literature review introduced in this chapter reveals that the SCR motion at the TDP is predominantly lateral, vertical and cyclic in nature. SCRs are the subject

**4. Summary of SCR-seabed interaction models technique**

**Author Lateral soil resistance formulas Comments**

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

Monotonic *μ* ¼ 0*:*2 *β* ¼ 39*:*3

Penetration � 2 *β* ¼ 31*:*4

Penetration � 2.5 *β* ¼ 15*:*7

Clays (Su < 70 kPa)

Soft clays (0.15 < Su < 8 kPa)

energy

*μ* ¼ 0*:*2

*μ* ¼ 0*:*2

Cyclic (oscillations below the monotonic breakout load [<static failure])

Cyclic (large displacement oscillations)

*FR* calculated considering accumulated

*β* = empirical soil passive resistance

*Su* = undrained shear strength of the

*γD* � ��0*:*<sup>392</sup> *<sup>z</sup> D* � �<sup>1</sup>*:*<sup>31</sup>

*<sup>D</sup>* = normalised initial pipe penetration

*DSu* normalised vertical load due to

2 *su γ*0*D*

h i � �

dim*ensionless* ¼ *μv* þ

dim*ensionless* <sup>¼</sup> *Fy SuD zinit*

the effective pipe weight

*<sup>v</sup>* <sup>¼</sup> <sup>1</sup> � <sup>0</sup>*:*65 1 � exp � <sup>1</sup>

*Lateral resistance models of partially embedded pipelines in soft clay.*

*Fy* ¼ *μ W*<sup>0</sup> ð Þþ � *FL FR μ* ¼ 0*:*2

3 ffiffiffiffiffiffiffi *Su γ*0 *D* <sup>r</sup> *zinit D*

*A* = 0.5 � embedded area

*Fy* ¼ *μ W*<sup>0</sup> ð Þþ � *FL βSuA=D Fy* = lateral soil resistance *μ* = sliding resistance coefficient *W*<sup>0</sup> = submerged pipe weight FL = hydrodynamic lift

coefficient

*Fy* ¼ *FC* þ *FR Fy* ¼ *μ W*<sup>0</sup> ð Þþ � *FL FR FR* <sup>¼</sup> <sup>4</sup>*:*13*DSu Su*

� �

*Fy* � �

*<sup>v</sup>* <sup>¼</sup> *<sup>V</sup>*

*<sup>f</sup>*ð Þ*<sup>y</sup> res*

*Schematic of the tri-linear soil resistance model.*

clay

Wagner et al. [23]

Brennodden et al. [20]

Verley and Lund [27]

Bruton et al. [30] *Fy*

**Table 1.**

**Figure 13.**

**58**

A number of scientific papers have been published on the study of soil-riser interaction. **Table 2** details the considerable diversity in the level of sophistication used in the analysis of SCR-seabed interaction response in a representative set of studies published in the last 25 years, with five areas previously highlighted as commonly conservative and broken into components of increasing degree of


**Author**

 **Year** **Model**

**61**

**Analytical models**

**Model**

**Analytical models**

**tests**

**tests**

**γ**

**Rigid**

**Linear**

**Non-linear**

**Trenching**

**Rigid**

**Linear**

**Non-linear**

**Trenching**

**Vertical Lateral Regular Irregular Uncoupled**

**seabed**

**seabed**

**seabed**

**effects**

**seabed**

√

Akpan et al. [48] 2007

Karunakaran

2005

√

> et al. [9]

Bridge et al. [17] 2004

Giertsen et al.

2004

√

 √

 √

 √

√√

√

√

√

√√

√

 √

*Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays*

 √

 √

 √

[49]

Bridge et al. [3]

Langner [50]

Bridge and

2002

√

> Willis [51]

Thethi and

2001

√

> Moros [10]

Willis and West

2001

√

[52]

Pesce et al. [53] Verley and Lund

1995

[27]

Hale et al. [54]

Dunlap et al.

1990

[15]

Brennodden

1989

> et al. [20]

Morris et al. [22] 1988

Wagner et al.

1987

[23]

**Table 2.** *Level of complexity*

 *used in SCR-seabed*

 *interaction*

 *technique.*

 1992

 1998

√

√

√ √

√

√

√

 √

√

 √

 √

 √

 √

 √

 2003

√

 2003

√

**seabed**

**seabed**

**effects**

 **β**

 **α**

 **α**

 **γ**

 **β**

 **α**

 **α**

**ααβ**

 **α**

 **β**

 **α**

 **Coupled**

√

√

√

 √

*DOI: http://dx.doi.org/10.5772/intechopen.85549*

**SCR-seabed interaction models**

**Pipe-seabed interaction models**

**Cyclic loading**

 **Wave**

**Analysis**

**loading**

#### *Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

#### *Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays DOI: http://dx.doi.org/10.5772/intechopen.85549*


**Table 2.** *Level of complexity used in SCR-seabed interaction*

 *technique.*

**Author**

**60**

 **Year** **Model**

**Analytical models**

**Model**

**Analytical models**

**tests**

**tests**

**γ**

**Rigid**

**Linear**

**Non-linear**

**Trenching**

**Rigid**

**Linear**

**Non-linear**

**Trenching**

**Vertical Lateral Regular Irregular Uncoupled**

**seabed**

**seabed**

**seabed**

**effects**

√

√

 √ √

**seabed**

Sharma and

2011

> Aubeny [34]

Cao [35] Cardoso and

2010

Silveira [36] Hodder et al.

2010

[37]

Jin et al. [38] Kimiaei et al.

2010

√

[39]

Nakhaee [40,

2008 and

2010

41]

Aubeny et al.

2006 and

2009

[18, 42] Randolph and

2009

> Quiggin [19]

Oliphant et al.

2009

√ √ √

[43]

Bruton et al.

2006 and

2008

[6, 30] Clukey et al.

2008

[44]

Palmer [11] Sen [45, 46] Xia et al. [47]

 2008

 2008

 2008

√

√

√

 2010

2010

√

√ √ √

√

√

√

√

√

√

√

√√ √

√

√

 √

 √ √

√

√

 √

 √

√

 √

√√

√√

 √

 √ √

 √

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

 √

 √

 √

**seabed**

**seabed**

√

 √

**effects**

 **β**

 **α**

 **α**

 **γ**

 **β**

 **α**

 **α**

**ααβ**

 **α**

 **β**

 **α**

 **Coupled**

**SCR-seabed interaction models**

**Pipe-seabed interaction models**

**Cyclic loading**

 **Wave**

**Analysis**

**loading**

of much ongoing research, particularly with respect to fatigue and interaction with the seabed at the TDP. The current SCR's analysis is performed using simplified pipe-seabed interaction models and disregards the SCR's embedment into the seabed as well as soil suction effects in the TDZ; this will affect the predicted SCR response. Previous experiments showed that the soil suction effect can increase the bending stress of SCRs in the TDZ. The predominant offshore soil condition in a deepwater environment is soft clay soil with small undrained shear strength. Field observations have introduced that the trench is a common feature due to the SCR pipe penetration into the seabed. However, there are few published literatures that investigate the trenching effects of the riser pipe in the TDZ on the SCR's dynamic structural behaviour and fatigue performance.

with the research literature. In this chapter, the main objective was to explore the various modelling approaches used in recent studies towards better clarification of

The seabed response due to riser loading and the trench formation phenomenon are of great significance for safe and economic riser design. Current studies of SCR technology focused on better understanding of the TDZ and its interaction with the seabed soil. The soil-riser interaction involves a number of complexities, including non-linear soil behaviour, trench width and depth variability and softening of the seabed soil under cyclic loading. The seabed-riser interaction modelling allows the effect of physical phenomena, such as lateral resistance, soil suction forces and vertical seabed stiffness on the SCR performance to be identified and investigated. Non-linear seabed-riser model interaction will determine the influence of the seabed response model on SCR fatigue. A small change in seabed stiffness can result in a small change in bending stress, but this causes a significant change in fatigue life. Therefore, the need for seabed-riser interaction modelling to be as realistic as possible is evident. A comprehensive review of the recent studies on the SCR-

After reviewing the different parts of literature relevant to this study, some of the required knowledge to be used in the current and future research is acquired and some other existing gaps in the field are identified. This chapter has presented a review of the state-of-the-art SCRs with seabed interaction and analysis techniques. It has also discussed the existing theories for modelling SCR-seabed interaction with detailed explanation of currently used methods for evaluating the SCR structural performance in the TDZ. The research gap addressed in this chapter is under the

the response behaviour of pipe-soil interaction under cyclic motions.

*Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays*

*DOI: http://dx.doi.org/10.5772/intechopen.85549*

seabed interaction was introduced.

**Author details**

Hany Elosta

**63**

investigation and ongoing research by the author.

Subsea SURF Lead, TechnipFMC, Lysaker, Norway

provided the original work is properly cited.

\*Address all correspondence to: hanyelosta@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Seabed stiffness degradation due to cyclic motion is an important parameter in order to estimate the SCR fatigue in the TDZ. This aspect is not well investigated, and the seabed is traditionally not properly modelled in the current SCR fatigue analysis. Existing literature has introduced that fatigue damage is highly sensitive to the soil model utilised in the fatigue estimation calculation. The seabed non-linear model, to simulate the SCR-seabed interaction, has been shown to be more sophisticated compared to those SCR-seabed interactions with linear soil springs.

It can be concluded from the summary of models presented in the existing literature survey that:


The aforementioned research gap points are subjected to ongoing research and investigations and being tackled by the authors.
