# Capacity of Suction Anchor

**DOI:**https://doi.org/10.1007/978-981-10-6963-5_204-1

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## Definition

The suction anchors are usually cylindrical units with large diameter (*D* of 3–8 m), open at the bottom and closed at the top, and generally with an aspect ratio (length to diameter, *L*/*D*) of two to six. The anchoring line is connected to the padeye attached to the side of the caisson at a depth down the mudline. The capacity of suction anchor is therefore the ability to resist the permanent and environmental loading from the anchor line during the operational conditions.

## Failure Mechanism

The capacity of suction anchor is highly dependence of soil plasticity flow around the foundation. Many influential factors, especially for the complicated boundary conditions, such as anchor geometry, type of mooring system (loading direction and magnitude), installation performance, soil conditions, time after installation, durations of applied sustained loading, cycles of loading, etc., should be explicitly accounted for to investigate the failure mechanism.

In the following subsections, the typical failure mechanisms under uniaxial (including mainly vertical and horizontal) and inclined loading are discussed.

### Under Vertical Uplift Loading

#### Reverse End Bearing Failure

Reverse end bearing failure can be relied upon for a suction anchor if the top cap is sealed and the soil response is undrained, typically when the anchor is subjected to short-term (transient) loading. Passive suction is generated in the anchor, so that the soil plug is pulled out together with the caisson. The failure mode at the bottom during uplift was similar to that during compression and was referred to as “a reverse end bearing mechanism.”

#### Sliding Failure

When suction anchor is subjected to a sustained (drained) loading or the anchor lid is vented, reverse end bearing cannot be generated, and the failure occurs along the internal and external skirt.

#### Tensile Failure

When partially drained condition prevails, such as when the suction anchor is pulled out at intermediate rates, passive suction may be generated partially, so that the caisson and the internal soil plug tends to detach from the soil below the caisson.

### Under Optimal Horizontal Loading

The suction anchors under pure horizontal loading is rarely found offshore, while drag angle at the padeye is typically at a small angle of 10°–20° in the catenary mooring system. Meanwhile, the padeye position is often optimized in design, allowing the anchor to slide horizontally with minimal rotation.

### Under Inclined Loading

The failure mechanism under inclined loading depends on the position of the centerline intercept for the applied load (varying with padeye position and loading angle), the length of the suction anchor, and the soil properties (Supachawarote 2006). The impact of tensile crack on the failure mechanism is examined by Fu et al. (2020).

The maximum holding capacity is obtained if the chain is attached at a depth where the anchor moves largely in horizontal translation with minimal rotation. This is called the “optimal padeye depth.”

When the centerline intercept is located above the optimal padeye position, the anchor rotates forward, and combinations of wedge flow around and full circular rotational failure were observed. For the short anchor, the wedge and rotational flow mechanisms were observed, without the flow around region. For the longer anchor, the flow around region increasingly dominates.

While when the centerline intercept is located below the optimal padeye position, a backward rotation was observed, and the rotational flow failure extends to the mudline. And with the centerline loading point moves deeper, the full circular rotational failure eventually moves below the soil surface, which is evident for anchor with increasing length. For long anchor, the circular rotational flow failure is only observed below the tip of the anchors; and only combination of the wedge and flow around mechanisms was observed within the anchor length.

## Design Method of Evaluating Capacity

The load capacity of a suction caisson anchor, assuming a sealed cap, is derived from bearing resistance between the soil and the projected area of the caisson (on a vertical plane for horizontal resistance and the cross-sectional area for reverse end bearing), aided by frictional resistance along the outside of the caisson shaft. Reverse end bearing relies on passive suctions developed within the soil plug, and so consideration needs to be given to the time over which these can be sustained.

### Vertical Uplift Capacity

#### Equation

- (a)
For undrained conditions, with a nondimensional diameter

*T*_{k}(=*c*_{v}/*vD*, where*c*_{v}is the consolidation coefficient,*v*is the loading velocity,*D*is the diameter of the anchor) recommended to be less than 0.002 (Deng and Carter 2000), the passive suction is thought to be sustained during loading

- (b)
For drained condition, (

*T*_{k}> 0.6), the passive suction is not generated during loading

- (c)
For partially drained condition (0.002 <

*T*_{k}< 0.6), passive suction is partially generated

_{se}and A

_{si}are the external and internal shaft surface area, A

_{e}is the external cross-sectional area, α

_{e}and α

_{i}are the coefficient of external and internal shaft friction, N

_{c}is the reverse end bearing factor,

*s*

_{u}is the undrained shear strength at tip level, \( {\overline{s}}_{u(t)} \)is the average undrained shear strength over penetrated depth at time t after installation,

*W*′

_{plug}is the effective weight of the soil plug, and

*W*′ is the submerged caisson weight.

#### Evaluation of Parameters α and N_{c}

The soil shear strength around the anchor is thought to be remold due to disturbance during skirt penetration during self-weight penetration. And this strength recovers later with time following installation, due to a combination of thixotropy and consolidation (Andersen et al. 2005), which however remains below the intact undrained shear strength. This process is referred as “setup” and has been expressed conveniently with αs_{u}, with α < 1. A base value of α of 0.65 was proposed for suction caisson design (Anderson and Jostad 2004), subjected to their specific soil properties. The shaft friction depends on the anchor surface roughness, soil type, and over-consolidation ratio. And Chen et al. (2009) suggests method of installation (referring jacking or suction installation) leads to negligible difference in α based on the centrifuge and LDFE numerical studies. And their results also suggest α of 15–20% lower than those recommended by the American Petroleum Institute (API) for driven piles in normally consolidated clays. It should also be noted that lower values of friction coefficient for internal shaft friction compared with external friction were reported in the model tests conducted on double-walled caisson (Jeanjean 2006).

The reverse end bearing *N*_{c} is a function of soil property and the aspect ratio (*L*/*D*) of the anchor. For an anchor with *L*/*D* of 2 in the over-consolidated kaolin clay, Fuglsang and Steensen-Bach (1991) reported the centrifuge and laboratory tests, suggesting the reverse bearing capacity factors varying between 6.5 and 8.5. This is lower than the theoretical lower bound results of 9.2 for the caisson with *L*/*D* of 2 (Martin 2001). Other centrifuge tests for the anchor with the same aspect ratio (Clukey and Morrison 1993) suggested that reverse end bearing is around 11. This high magnitude of *N*_{c} may be related to the vane shear strength adopted for the interpretation, which leads to an overestimation of 25% (Watson et al. 2000). Considering the loading mode (monotonic transient loading, cyclic loading, and long-term sustained loading), the reverse end bearing falls in a wider range of 9.1–14.6 (Randolph and House 2001). And a conservative *N*_{c} value of 9 is suggested to be taken, due to the strain-softening nature of the response as the caisson is extracted. A bearing capacity factor of *N*_{c} = 9 irrespective of the aspect ratio for suction anchor is also suggested by El-Gharbawy and Olson based on the results of the laboratory tests in kaolin clay. And by contrast, an *N*_{c} value of 12 is found to be mobilized at large displacements (Jeanjean 2006), although values of around 9 were mobilized at the displacement where peak external shaft friction was achieved. Hence it is rational to take *N*_{c} as of 9 is appropriate.

### Optimal Horizontal Capacity

#### Equation

*D*

_{e}is the external diameter of the caisson,

*N*

_{p}is the lateral bearing capacity factor, and \( {\overline{s}}_u \)is the average undrained shear strength over penetrated depth.

#### Evaluation of Parameters N_{p}

In Eq. 8, *Z* stands for the normalized depth (*z/D*) at which the soil failure mechanism transits from the wedge failure to the localized flow around failure for a fully rough soil-pile interface in idealized weightless soil. The value of *Z* is related to the normalized strength homogeneity parameter *λ. N*_{pd} stands for the limiting bearing capacity factor mobilized in a localized flow-around mechanism, expressed as a function of the interface roughness factor *α* (0 ≤ *α* ≤ 1), according to the plasticity solution.

### Inclined Load Capacity

In the presence of both vertical and horizontal loading, a reduction occurs in the pure vertical and horizontal capacities, as the caisson is simultaneously displaced vertically and laterally (or rotated). Clukey et al. (2003) suggested for the loading angles applied by the catenary mooring line system, which are generally less than 20° from the horizontal, the caisson capacity is dominated by the horizontal capacity, and the capacity may be estimated by the capacity under pure translation divided by the cosine of the loading angle at the padeye. Conversely for high loading angles from the horizontal applied by taut and semi-taut mooring systems (generally in excess of 30°), the caisson capacity is essentially governed by the vertical capacity of the caisson and maybe approximately taken as the vertical capacity divided by the sine of the loading angle.

*L*/

*D*), location, and direction of the applied load. The shape of the failure envelopes for suction anchor may be modelled by an elliptical relationship

*H*

_{ult}and

*V*

_{ult}are the uniaxial horizontal and vertical capacities, respectively, and the exponents

*a*and

*b*vary with caisson aspect ratio

*L*/

*D*according to Supachawarote (2006).

*L*from the optimal centerline location and reduces sharply beyond this range.

### Consideration in Design

#### The Effect of Crack on the Suction Anchor Capacity

The inclined load capacity of a suction anchor will also depend on whether a crack develops along the trailing edge of the caisson. A crack is normally formed for suction anchors with a long aspect ratio in over-consolidated soils. The finite element results (Fu et al. 2020) show a reduction of up to 50% for any loading angle (the reduction is mainly found at the optimal padeye depth and maintained for loading angles of up to about 45° for *L*/*D* = 1.5, 2, and 3 in homogeneous soil).

### Considering Site Conditions

Some changes in site conditions should be explicitly accounted for in the design of geotechnical capacity of suction anchor. The soil scour around a suction foundation is an important scenario in design, where the soil migration around foundation might occur under the wave and current loading. The volume of soil mobilized by foundation is therefore changed, resulting in a significant decrease in capacity. In some cases, the shallow gas accumulation inside a suction foundation also should be given attention (Gylland and de Vries 2008). Additionally, the trenching is another issue and most likely to occur particularly when using semi-taut to taut mooring configurations with caisson employed in the soft deposits. Considerable motion of ground chain could lead to the remolded softening and erosion of soil particles, forming a curved trench in the vicinity of foundation. O’Neill et al. (2018) presented a method to interpret and estimate the primary mechanism of trenching development.

### Considering Cyclic Loading Effect

Offshore foundations are often cyclically loaded in both calm sea condition and extreme events (i.e., storm or hurricane event). For suction anchor, the cyclic wind, wave, current, and structural loadings are transferred to the foundation by mooring lines. It gives rise to pore pressure accumulation for soil around foundation, which is one of the principle concerns in design of foundation’s capacity. Regarding clay, the strain softening may occur as the pore pressure accumulates, and both soil stiffness and strength can significantly reduce. Regarding sands, the earlier densification may occur during cyclic loading, then pore pressure starts accumulating, and finally a state of liquefaction may be present with the effective stress of soil almost being zero. Therefore, the continual buildup of excess pore pressure in soil under cyclic loading potentially results in a significant decrease in capacity of foundation.

Based on laboratory cyclic triaxial (TA) and direct simple shear (DSS) tests, Andersen (2015) presented a method to assess the accumulation of pore pressure, which is dependence of cyclic shear ratio τ_{cy}/σ′_{vc}. τ_{cy} is the cyclic shear stress (kPa), and σ′_{vc} is the vertical consolidation pressure (kPa). The corresponding cyclic shear strength τ_{cy,f} at failure was indicated using a strain contour diagram, with the equivalent number of cycles to failure captured at the permanent cyclic shear strain of 15%. Besides, many soil models based on the critical soil mechanics theory were numerically developed in the last three decades, to describe and interpret the cyclic behavior of soil. However, no constitutive model has been developed to date, enabling to represent all the key characteristics of cyclic soil response, as many factors may influence the cyclic performance of soil, i.e., cyclic stress level, loading frequency, over-consolidation ratio, static pre-shearing, etc. In practice, the alternative option available for engineers is choosing a soil material factor (ISO 2016) or considering the uncertainty by a partial factor of capacity (ISO 2016), when the cyclic loading effect is necessary to be considered.

### Considering Reconsolidation Effect

For suction anchor, an allowable duration is often found after its installation, e.g., 3 to 6 months. This gives an opportunity for consolidation under self-weight prior to commencing operations. During consolidation, the excess pore pressures generated by the self-weight preloading dissipate reducing the void ratio of soil and enhancing the soil strength, hence increasing the foundation capacity. It is notable that the dissipation of pore pressure also occurs during the cyclic loading condition, as the pore pressures in fact generated during a cyclic duration and will dissipate in the subsequent cycles. The appropriate consideration of reconsolidation in service design is necessary to develop a reliable and economical method.

From some centrifuge model tests (Bienen et al. 2010; Fu et al. 2015), the significant increase in bearing capacity of a preloaded foundation in clay was found, for instance, a gain in bearing capacity of 30% after 10% of consolidation and a doubling after 80% of consolidation under a vertical preload of 50% of the ultimate vertical load.

## Notation

*a* Parameter depending on *L*/*D*

*A*_{e} External cross-sectional area

*A*_{se} External shaft surface area

*A*_{si} Internal shaft surface area

*b* Parameter depending on *L*/*D*

*c*_{v} Consolidation coefficient

*D* Diameter of suction anchor

*D*_{e} External diameter of suction anchor

*H*_{max} Optimal horizontal capacity

*H*_{ult} Uniaxial horizontal capacity

*L* Length of suction anchor

*N*_{c} Reverse end bearing factor

*N*_{p} Lateral bearing capacity factor

*s*_{u} Undrained shear strength at tip level

\( {\overline{s}}_u \) Average undrained shear strength over penetrated depth

\( {\overline{s}}_{u(t)} \) Average undrained shear strength over penetrated depth at time t after installation

*T*_{k} Nondimensional diameter

*W′* Submerged weight of suction anchor

*W′*_{plug} Submerged weight of soil plug

*v* Loading velocity

*V*_{ult} Vertical pullout capacity

*z*_{cl} Centerline loading depth

α Coefficient of shaft friction

α Parameter depending on *L*/*D*

α_{e} Coefficient of external shaft friction

α_{i} Coefficient of internal shaft friction

β Parameter depending on *L*/*D*

τ_{cy} Cyclic shear stress

τ_{cy,f} Cyclic shear stress at failure

σ′_{vc} Vertical consolidation pressure

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