**1. Introduction**

Catenary steel compliant risers (SCRs) have joined the riser family, building on the catenary equation that has assisted in creating bridges across the world. SCRs are commonly used with TLPs, FPSOs, semisubmersibles and spars, as well as fixed structures, compliant towers and gravity structures. SCRs have been accompanied by floating platforms since 1994 and were first used as export risers for Auger TLP in an 872 m water depth [1, 2]. Since then, SCRs have been employed with many applications. The number of SCRs is increasing quickly because of its simplicity, economic effectiveness, and well-known material properties. A free-hanging simple catenary riser is connected to a floating production vessel and the riser hangs at a prescribed top angle. The riser is free-hanging and gently curves down to the seabed at the touchdown point (TDP). At the TDP, the SCR pipe embeds itself in a trench and then evenly rises to the surface where it rests, and is effectively a static pipeline. SCRs may be described as consisting of three portions [3], as shown in **Figure 1**:


**Figure 1.** *General SCR arrangement.*

A complex interaction between the SCR and seabed is experienced when the SCR is subjected to oscillatory motions. For SCRs, the most critical fatigue hotspot occurs in the TDZ. The SCR-seabed interaction is an essential key factor that should be considered in strength and fatigue assessment. How to precisely model this interaction response is still an issue and has been a hot field for academic research. A number of researches have been focused on understanding the soil-riser interaction. Better predictions of the SCR's fatigue life require an accurate characterisation model of seabed stiffness as well as a realistic description of the load/deflection curve. Therefore, this chapter gives a state-of-the-art review of the recent research on soil-riser interaction models. Briefly, a series of previous work associated with seabed-riser interaction mechanism and simulation models, as well as load/ deflection models, will be described and discussed.

#### **2. SCR configuration design**

The catenary riser length is estimated using simple geometric considerations, as following [4]:

$$L = \left(\frac{D - (MBR)A}{\cos \theta}\right) + (\mathbf{0}.5\pi (MBR)A) \tag{1}$$

its configuration under a set of static forces. The catenary equation gives a good first approximation for this, but in their basic formulation it only involves loads due to riser weight and assumes a riser pipe of zero bending stiffness, as presented before. However, the SCR static analysis is a large deflection non-linear behaviour problem with the influences of bending and tensional stiffness included. Therefore, many approaches have been developed to handle this problem using a combination of catenary equations and numerical techniques through iterative analysis. A review of existing approaches can be found in [5]. **Figure 3** shows an example of static configuration of an SCR in a 910 m water depth with a hang-off angle of 20° and a 273 mm outer diameter connected to the floating platform (FP) in the zero mean offset position (i.e., the FP is in its initial position without drifting in any direction),

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

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**Figure 2.**

**Figure 3.**

**49**

*Static configuration of SCR model.*

*Schematic of SCR configuration and vessel offsets.*

which is calculated using OrcaFlex/finite element analysis (FEA) software.

where L is the total length of the riser, *D* is the water depth, A is a factor depending on severity of environment (1.0 for mild environments and 1.2 for severe environments), θ is the riser top angle to vertical, typically between 10 and 25 degrees depending on severity of environment and water depth, and MBR is minimum bend radius based on 80% material yield strength. An additional riser pipeline length of approximately 750 m should be included to allow for TDP movement between near and far offset conditions as shown in **Figure 2**.

The SCR's static configuration must be determined before carrying out the dynamic analysis. The initial stage of any analysis of an SCR is the computation of *Geotechnical Response Models for Steel Compliant Riser in Deepwater Clays DOI: http://dx.doi.org/10.5772/intechopen.85549*

**Figure 2.** *Schematic of SCR configuration and vessel offsets.*

A complex interaction between the SCR and seabed is experienced when the SCR is subjected to oscillatory motions. For SCRs, the most critical fatigue hotspot occurs in the TDZ. The SCR-seabed interaction is an essential key factor that should be considered in strength and fatigue assessment. How to precisely model this interaction response is still an issue and has been a hot field for academic research. A number of researches have been focused on understanding the soil-riser interaction. Better predictions of the SCR's fatigue life require an accurate characterisation model of seabed stiffness as well as a realistic description of the load/deflection curve. Therefore, this chapter gives a state-of-the-art review of the recent research on soil-riser interaction models. Briefly, a series of previous work associated with seabed-riser interaction mechanism and simulation models, as well as load/

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

The catenary riser length is estimated using simple geometric considerations, as

where L is the total length of the riser, *D* is the water depth, A is a factor depending on severity of environment (1.0 for mild environments and 1.2 for severe environments), θ is the riser top angle to vertical, typically between 10 and 25 degrees depending on severity of environment and water depth, and MBR is minimum bend radius based on 80% material yield strength. An additional riser pipeline length of approximately 750 m should be included to allow for TDP move-

The SCR's static configuration must be determined before carrying out the dynamic analysis. The initial stage of any analysis of an SCR is the computation of

þ ð Þ 0*:*5*π*ð Þ *MBR A* (1)

deflection models, will be described and discussed.

*<sup>L</sup>* <sup>¼</sup> *<sup>D</sup>* � ð Þ *MBR <sup>A</sup>* cos *θ* 

ment between near and far offset conditions as shown in **Figure 2**.

**2. SCR configuration design**

following [4]:

**48**

**Figure 1.**

*General SCR arrangement.*

its configuration under a set of static forces. The catenary equation gives a good first approximation for this, but in their basic formulation it only involves loads due to riser weight and assumes a riser pipe of zero bending stiffness, as presented before. However, the SCR static analysis is a large deflection non-linear behaviour problem with the influences of bending and tensional stiffness included. Therefore, many approaches have been developed to handle this problem using a combination of catenary equations and numerical techniques through iterative analysis. A review of existing approaches can be found in [5]. **Figure 3** shows an example of static configuration of an SCR in a 910 m water depth with a hang-off angle of 20° and a 273 mm outer diameter connected to the floating platform (FP) in the zero mean offset position (i.e., the FP is in its initial position without drifting in any direction), which is calculated using OrcaFlex/finite element analysis (FEA) software.

**Figure 3.** *Static configuration of SCR model.*

Generally, SCRs have a limited amount of additional pipeline length available to accommodate the FP motions. Alterations in the catenary suspended length are obtained by the riser either being picked up or laid down on the seabed. Limitations are approached when either the SCR tension at the FP becomes too great as the FP drifts away from the TDP (far load case, as shown before in **Figure 2**) or when the bending stresses near the seabed become too great as the FP drifts towards the touchdown point (near load case). SCRs are less appropriate for FPSO applications where vessel offsets are considerably higher. **Figure 4** shows the effect of the horizontal vessel offset on the horizontal projection of the TDP. While the top of the SCR has the highest tension and lowest bending moment, the TDP has the lowest tension and the highest bending moment. The maximum bending stress and effective tension along the SCRs' arc length and the horizontal projection of the TDP due to the vessel offsets are presented in **Figures 5** and **6**, respectively.

The vessel offset governs the maximum bending stress at the TDP and also the maximum tension at the riser's top end. In the left region of **Figure 6**, where the

vessel drifts towards the TDP (near load case), the bending stress at the TDP is increased rapidly within small change in the vessel offset. In the intermediate region, the bending stress and tension are slightly increased with the vessel offset. In the right region, where the vessel drifts away from the TDP (far load case), the bending stress slightly decreased, while the tension increased. Therefore, the conclusion from these results is that the vessel mean position should be offsetting the TDP with a roughly distance of 0.75–1.5 of the water depth. Furthermore, the catenary equation is a simple implementation tool to figure out the load distribution, geometric properties and static loads on an SCR. The specialist non-linear/FEA is implemented for the SCR design to tackle the complex nature of non-linear, large deflection behaviour of SCRs and to be post-processed quickly. The evaluation of the forces and behaviour of SCRs in the TDZ need more sophisticated methods.

*Alterations of maximum bending stress and effective tension with the horizontal projection of the TDP.*

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SCR pipe penetration is defined as the depth of penetration of the pipe invert (bottom of pipe), relative to the undisturbed seabed as shown in **Figure 7**. Pipe penetration affects the riser pipe-seabed contact area, which subsequently affects the axial and passive soil resistance against the riser. Consequently, the passive soil resistance influences the lateral breakout force. Heave of seabed soil during embedment increases the local penetration of the SCR pipe by raising the soil surface level against the shoulders of the pipe. The typical geometry of heave produced during vertical embedment of an SCR pipe is such that the nominal penetration is approximately 50%

The SCR-seabed interaction response characteristic is a highly non-linear phenomenon. It is important not to restrict the modelling of this interaction to a linear seabed model approximation and the riser analysis techniques must be improved by refining the riser-seabed interaction [7]. SCR-seabed interaction modelling should involve vertical and lateral soil responses to the cyclic loading oscillations of the SCR in the TDZ, which can cause trenching and dynamic embedment of the SCR into the

less than the local embedment relative to undisturbed seabed surface [6].

**3. Models for seabed response**

**Figure 6.**

**51**

**3.1 Problem description of an SCR pipe embedment**

**Figure 4.** *Effect of the vessel offsets on the horizontal projection of the TDP.*

**Figure 5.** *Alterations of maximum bending stress and maximum effective tension with the horizontal vessel offset.*

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

#### **Figure 6.**

Generally, SCRs have a limited amount of additional pipeline length available to accommodate the FP motions. Alterations in the catenary suspended length are obtained by the riser either being picked up or laid down on the seabed. Limitations are approached when either the SCR tension at the FP becomes too great as the FP drifts away from the TDP (far load case, as shown before in **Figure 2**) or when the bending stresses near the seabed become too great as the FP drifts towards the touchdown point (near load case). SCRs are less appropriate for FPSO applications where vessel offsets are considerably higher. **Figure 4** shows the effect of the horizontal vessel offset on the horizontal projection of the TDP. While the top of the SCR has the highest tension and lowest bending moment, the TDP has the lowest tension and the highest bending moment. The maximum bending stress and effective tension along the SCRs' arc length and the horizontal projection of the TDP due

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

The vessel offset governs the maximum bending stress at the TDP and also the maximum tension at the riser's top end. In the left region of **Figure 6**, where the

to the vessel offsets are presented in **Figures 5** and **6**, respectively.

*Effect of the vessel offsets on the horizontal projection of the TDP.*

*Alterations of maximum bending stress and maximum effective tension with the horizontal vessel offset.*

**Figure 4.**

**Figure 5.**

**50**

*Alterations of maximum bending stress and effective tension with the horizontal projection of the TDP.*

vessel drifts towards the TDP (near load case), the bending stress at the TDP is increased rapidly within small change in the vessel offset. In the intermediate region, the bending stress and tension are slightly increased with the vessel offset. In the right region, where the vessel drifts away from the TDP (far load case), the bending stress slightly decreased, while the tension increased. Therefore, the conclusion from these results is that the vessel mean position should be offsetting the TDP with a roughly distance of 0.75–1.5 of the water depth. Furthermore, the catenary equation is a simple implementation tool to figure out the load distribution, geometric properties and static loads on an SCR. The specialist non-linear/FEA is implemented for the SCR design to tackle the complex nature of non-linear, large deflection behaviour of SCRs and to be post-processed quickly. The evaluation of the forces and behaviour of SCRs in the TDZ need more sophisticated methods.

#### **3. Models for seabed response**

#### **3.1 Problem description of an SCR pipe embedment**

SCR pipe penetration is defined as the depth of penetration of the pipe invert (bottom of pipe), relative to the undisturbed seabed as shown in **Figure 7**. Pipe penetration affects the riser pipe-seabed contact area, which subsequently affects the axial and passive soil resistance against the riser. Consequently, the passive soil resistance influences the lateral breakout force. Heave of seabed soil during embedment increases the local penetration of the SCR pipe by raising the soil surface level against the shoulders of the pipe. The typical geometry of heave produced during vertical embedment of an SCR pipe is such that the nominal penetration is approximately 50% less than the local embedment relative to undisturbed seabed surface [6].

The SCR-seabed interaction response characteristic is a highly non-linear phenomenon. It is important not to restrict the modelling of this interaction to a linear seabed model approximation and the riser analysis techniques must be improved by refining the riser-seabed interaction [7]. SCR-seabed interaction modelling should involve vertical and lateral soil responses to the cyclic loading oscillations of the SCR in the TDZ, which can cause trenching and dynamic embedment of the SCR into the

An appropriate SCR-seabed interaction model must be used. The TDZ is one of

the key locations where the fatigue damage happens. The sophistication of the interaction model depends on the type of analysis and accuracy required. These interaction models vary from a simple rigid seabed with soil friction coefficients to more sophisticated ones, including vertical and lateral stiffness, friction and

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

A potential fatigue damage of the SCR in the TDZ is related to maximum bending stress in the SCR, which relies on the soil stiffness of the seabed and the motions of the SCR. For example, the SCR on a soft seabed will have reduced bending stresses when a load is applied, while the one on a rigid seabed will have more critical bending stresses. A rigid surface generally contributes a conservative result, since it is unyielding, while the non-linear soil model is a better approximation of a seabed. Extreme offsets of the floating production unit with soft seabed model may then give higher stresses than those calculated on rigid seabed stiffness, since the catenary pipeline must be broken out of the seabed soil and high suction forces must be overcome. **Figure 8** shows a schematic of an SCR close to the TDP with the forces acting on a rigid seabed. The shear force *F* in the near horizontal

suction.

then d<sup>3</sup>

**Figure 8.**

**53**

*3.2.1 Rigid and elastic seabed*

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

segment close to the TDP is given by:

*<sup>F</sup>* <sup>¼</sup> *dM*

force that is transmitted to the soil [2, 11] is given by:

*Configuration of SCR close to TDP with a rigid seabed.*

*dx* <sup>¼</sup> *<sup>d</sup>*

*dx EI <sup>d</sup>*<sup>2</sup>

*<sup>F</sup>* <sup>¼</sup> *EI <sup>w</sup> H*

to zero, and there is a concentrated reaction force. Since *<sup>k</sup>* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffi

*y dx*<sup>2</sup> " # !

The bending moment at the TDP diminishes from the catenary bending moment

*FTDP* <sup>¼</sup> *<sup>w</sup>* ffiffiffiffiffiffiffiffiffiffiffi

*y*/d*x*<sup>3</sup> = (*w*/*H*)ke�*kx* and the shear force close to the TDP is thus given by:

<sup>¼</sup> *EI <sup>d</sup>*<sup>3</sup>

*y dx*<sup>3</sup> !

� �*ke*�*kx* (3)

*EI=H* p (4)

(2)

*H=EI* p , the TDP shear

**Figure 7.** *Schematic illustration of the SCR-seabed interaction in the TDZ.*

seabed. A typical schematic illustration of the SCR-seabed interaction and trench formation in the TDZ are shown in **Figure 7**.

#### **3.2 SCR/seabed vertical interaction**

The application of SCR systems has increased with the progressive development of hydrocarbon production further offshore and into deeper waters. The SCR-soil interaction at touchdown with the seabed is a major key factor for SCRs. An SCR is subjected to oscillatory motions from the host vessel and wave action. Therefore, the SCR experiences a complex interaction between the riser and seabed in the touchdown area, and deep trenches thus cut into the seabed in the buried zone beyond the TDP [8–10].

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

An appropriate SCR-seabed interaction model must be used. The TDZ is one of the key locations where the fatigue damage happens. The sophistication of the interaction model depends on the type of analysis and accuracy required. These interaction models vary from a simple rigid seabed with soil friction coefficients to more sophisticated ones, including vertical and lateral stiffness, friction and suction.

### *3.2.1 Rigid and elastic seabed*

A potential fatigue damage of the SCR in the TDZ is related to maximum bending stress in the SCR, which relies on the soil stiffness of the seabed and the motions of the SCR. For example, the SCR on a soft seabed will have reduced bending stresses when a load is applied, while the one on a rigid seabed will have more critical bending stresses. A rigid surface generally contributes a conservative result, since it is unyielding, while the non-linear soil model is a better approximation of a seabed. Extreme offsets of the floating production unit with soft seabed model may then give higher stresses than those calculated on rigid seabed stiffness, since the catenary pipeline must be broken out of the seabed soil and high suction forces must be overcome. **Figure 8** shows a schematic of an SCR close to the TDP with the forces acting on a rigid seabed. The shear force *F* in the near horizontal segment close to the TDP is given by:

$$F = \frac{dM}{d\mathbf{x}} = \frac{d}{d\mathbf{x}} \left[ EI \left( \frac{d^2 y}{d\mathbf{x}^2} \right) \right] = EI \left( \frac{d^3 y}{d\mathbf{x}^3} \right) \tag{2}$$

then d<sup>3</sup> *y*/d*x*<sup>3</sup> = (*w*/*H*)ke�*kx* and the shear force close to the TDP is thus given by:

$$F = EI \frac{w}{H} \text{\(\frac{w}{H}\)} ke^{-kx} \tag{3}$$

The bending moment at the TDP diminishes from the catenary bending moment to zero, and there is a concentrated reaction force. Since *<sup>k</sup>* <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffi *H=EI* p , the TDP shear force that is transmitted to the soil [2, 11] is given by:

$$F\_{\rm TDP} = w \sqrt{\rm EI/H} \tag{4}$$

**Figure 8.** *Configuration of SCR close to TDP with a rigid seabed.*

seabed. A typical schematic illustration of the SCR-seabed interaction and trench

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

The application of SCR systems has increased with the progressive development of hydrocarbon production further offshore and into deeper waters. The SCR-soil interaction at touchdown with the seabed is a major key factor for SCRs. An SCR is subjected to oscillatory motions from the host vessel and wave action. Therefore, the SCR experiences a complex interaction between the riser and seabed in the touchdown area, and deep trenches thus cut into the seabed in the buried zone

formation in the TDZ are shown in **Figure 7**.

*Schematic illustration of the SCR-seabed interaction in the TDZ.*

**3.2 SCR/seabed vertical interaction**

beyond the TDP [8–10].

**Figure 7.**

**52**

where *F*TDP is the concentrated reaction at the TDP, assuming a rigid surface seabed, *F*<sup>f</sup> is the reaction to the pipe resting on the seabed, as shown in **Figure 8**.

For the elastic soil response, configuration of an SCR close to the TDP is shown in **Figure 9** by representing a seabed with a linear elastic model. The curvature in the surface zone (i.e., the pipeline is resting on the seabed) is zero. In the TDZ, the riser's pipe is resting on linear elastic foundations. The solution for a beam element resting on an elastic foundation can be found in [12, 13], who introduced solutions that can be implemented for SCR-seabed interaction.

#### *3.2.2 Non-linear load/deflection model*

The current practice for the FEA of SCR-seabed interaction response is to model this interaction as structural soil springs [10] by using the developed models for buried pipelines and strip foundation theory. The conventional modelling of riserseabed interaction use the non-linear elastic load/deflection curves, as described in [14]. Since the resistance force does not exceed the friction resistance limit (μV), the soil spring has a constant stiffness coefficient, *K*. The load/deflection model has zero resistance force at zero displacement, as the pipe displacement is increasing the resistance force also increases linearly until the peak seabed resistance is approached. When the seabed friction exceeds the limit friction force, the resistance force becomes constant with changing pipe displacement (large displacements occur without a further increase in the friction resistance force) and the spring stiffness becomes zero (i.e., slip occurs). The maximum seabed resistance load is given by the backbone curve [15], which corresponds to virgin penetration of the riser pipe into the seabed.

Linear soil stiffness can be used by FEA codes to model the non-linear riserseabed interaction curves. Linear soil stiffness is defined as the ultimate bearing load divided by the riser pipe displacement, as given below:

$$K = \frac{V}{\Delta} \tag{5}$$

stiffness is using a linear stiffness to represent the backbone curve in riser-seabed interaction analysis. It is assumed that the riser will penetrate into the seabed until the bearing load equals the submerged riser pipe weight; *w* = *V*<sup>u</sup> where *w* is the

The typical *V*-*z* curve patterns [17, 19], as shown in **Figure 11**, of pipe-soil interaction are produced by laboratory model experiments [15] of vertically loaded horizontal pipes in weak sediment. These curves can be divided into four different paths. The pipe-soil interaction process is described and the depiction of the development of the interaction curve is given in **Figure 11**, associated with the uplift/ re-penetration cycle. If the riser pipe continues to experience oscillatory loading movement, the *V*-*z* interaction curve will repeat the loop enclosed by path 1-2-3-1

One of the main issues encountered with the use of the SCR is the large lateral movements on the seabed due to the FP motions and marine environment. Thus, better understanding of the lateral soil resistance to SCR pipe movements must be considered for SCR design. Many researchers had focused on studying and investigating the pipe-seabed lateral interaction response [6, 20–24]. Three different approaches [25, 26] can be considered for determining the lateral soil resistance of

The non-linear soil model is recently developed and based on a hyperbolic secant stiffness formulation proposed by Bridge et al. [17], Aubeny et al. [18], and Randolph and Quiggin [19]. The non-linear seabed model is more sophisticated than the linear model, as it models the non-linear hysteretic behaviour of the seabed in the vertical direction, including modelling of suction effects when the SCR rises up sufficiently. The model uses data such as the pipe diameter, the seabed soil shear strength profile with depth and the soil density as its primary sources. Different functions are used for the initial penetration, for uplift and for re-penetration, whilst the function parameters are updated each time a penetration reversal occurs. This enables the model to capture the hysteretic behaviour of the seabed soil response and the increasing penetration of the pipe under cyclic loading in the

submerged riser pipe weight, and *V*<sup>u</sup> is the ultimate bearing load.

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*Static and secant stiffness for non-linear seabed* V*-*z *model.*

under the assumption of a non-degradation model.

**3.3 SCR/seabed lateral interaction**

partially embedded pipelines:

**55**

vertical plane.

**Figure 10.**

where *K* is the soil stiffness per unit length; *V* is the force per unit length; Δ is the riser pipe displacement. Different approaches are used to characterise the linear seabed stiffness, such as secant, tangent and Young's modulus stiffness, for more details see Barltrop et al. [16]. Herein, the secant stiffness type is considered because it is more stable than the tangent stiffness approach and is being used to model the load/deflection curve. The secant stiffness is the average stiffness between two points, typically the origin and the point in question, see **Figure 10**. Static seabed

**Figure 9.** *SCR's configuration close to TDZ with linear elastic seabed.*

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

**Figure 10.** *Static and secant stiffness for non-linear seabed* V*-*z *model.*

stiffness is using a linear stiffness to represent the backbone curve in riser-seabed interaction analysis. It is assumed that the riser will penetrate into the seabed until the bearing load equals the submerged riser pipe weight; *w* = *V*<sup>u</sup> where *w* is the submerged riser pipe weight, and *V*<sup>u</sup> is the ultimate bearing load.

The non-linear soil model is recently developed and based on a hyperbolic secant stiffness formulation proposed by Bridge et al. [17], Aubeny et al. [18], and Randolph and Quiggin [19]. The non-linear seabed model is more sophisticated than the linear model, as it models the non-linear hysteretic behaviour of the seabed in the vertical direction, including modelling of suction effects when the SCR rises up sufficiently. The model uses data such as the pipe diameter, the seabed soil shear strength profile with depth and the soil density as its primary sources. Different functions are used for the initial penetration, for uplift and for re-penetration, whilst the function parameters are updated each time a penetration reversal occurs. This enables the model to capture the hysteretic behaviour of the seabed soil response and the increasing penetration of the pipe under cyclic loading in the vertical plane.

The typical *V*-*z* curve patterns [17, 19], as shown in **Figure 11**, of pipe-soil interaction are produced by laboratory model experiments [15] of vertically loaded horizontal pipes in weak sediment. These curves can be divided into four different paths. The pipe-soil interaction process is described and the depiction of the development of the interaction curve is given in **Figure 11**, associated with the uplift/ re-penetration cycle. If the riser pipe continues to experience oscillatory loading movement, the *V*-*z* interaction curve will repeat the loop enclosed by path 1-2-3-1 under the assumption of a non-degradation model.

#### **3.3 SCR/seabed lateral interaction**

One of the main issues encountered with the use of the SCR is the large lateral movements on the seabed due to the FP motions and marine environment. Thus, better understanding of the lateral soil resistance to SCR pipe movements must be considered for SCR design. Many researchers had focused on studying and investigating the pipe-seabed lateral interaction response [6, 20–24]. Three different approaches [25, 26] can be considered for determining the lateral soil resistance of partially embedded pipelines:

where *F*TDP is the concentrated reaction at the TDP, assuming a rigid surface seabed, *F*<sup>f</sup> is the reaction to the pipe resting on the seabed, as shown in **Figure 8**. For the elastic soil response, configuration of an SCR close to the TDP is shown in **Figure 9** by representing a seabed with a linear elastic model. The curvature in the surface zone (i.e., the pipeline is resting on the seabed) is zero. In the TDZ, the riser's pipe is resting on linear elastic foundations. The solution for a beam element resting on an elastic foundation can be found in [12, 13], who introduced solutions

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

The current practice for the FEA of SCR-seabed interaction response is to model this interaction as structural soil springs [10] by using the developed models for buried pipelines and strip foundation theory. The conventional modelling of riserseabed interaction use the non-linear elastic load/deflection curves, as described in [14]. Since the resistance force does not exceed the friction resistance limit (μV), the soil spring has a constant stiffness coefficient, *K*. The load/deflection model has zero resistance force at zero displacement, as the pipe displacement is increasing the

resistance force also increases linearly until the peak seabed resistance is

load divided by the riser pipe displacement, as given below:

approached. When the seabed friction exceeds the limit friction force, the resistance force becomes constant with changing pipe displacement (large displacements occur without a further increase in the friction resistance force) and the spring stiffness becomes zero (i.e., slip occurs). The maximum seabed resistance load is given by the backbone curve [15], which corresponds to virgin penetration

Linear soil stiffness can be used by FEA codes to model the non-linear riserseabed interaction curves. Linear soil stiffness is defined as the ultimate bearing

*<sup>K</sup>* <sup>¼</sup> *<sup>V</sup>*

where *K* is the soil stiffness per unit length; *V* is the force per unit length; Δ is the riser pipe displacement. Different approaches are used to characterise the linear seabed stiffness, such as secant, tangent and Young's modulus stiffness, for more details see Barltrop et al. [16]. Herein, the secant stiffness type is considered because it is more stable than the tangent stiffness approach and is being used to model the load/deflection curve. The secant stiffness is the average stiffness between two points, typically the origin and the point in question, see **Figure 10**. Static seabed

<sup>Δ</sup> (5)

that can be implemented for SCR-seabed interaction.

*3.2.2 Non-linear load/deflection model*

of the riser pipe into the seabed.

**Figure 9.**

**54**

*SCR's configuration close to TDZ with linear elastic seabed.*

**Figure 11.**

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

• 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;

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

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

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

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

**Figure 13** shows the lateral load response from step 0 to 3, characterised as

(0–1) First load breakout, with elastic response characterised by the mobilisation displacement and a

(1–2) Suction release phase and elevation correction, depending on initial pipe embedment;

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

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

*Fx* ¼ *μAWs* (6)

penetration and soil strength.

*Coulomb friction model analysis.*

follows [31]:

**Figure 12.**

for clay soil [33].

**57**

the results of the available pipe model tests.

(2–3) Steady state of residual friction.

**3.4 SCR/seabed axial interaction**

peak that is dependent on the initial pipe embedment;

partially embedded riser pipe, and is expressed as [25, 32]:


Therefore, the Coulomb friction approach and the two-component soil resistance models for the assessment of SCR global response are presented in this chapter.
