Reliability-Based Design of Suction Anchor Foundation for Floating ...

Reliability-Based Design of Suction Anchor Foundation for Floating Platforms Farrokh Nadima, Yunsup Shina, Zhongqiang Liua, Youhu Zhanga, Martine H. de Vriesb, Hilde Engelsenc a

Norwegian Geotechnical Institute, Oslo, Norway b Statoil, Forus, Norway c Aker Solutions, Fornebu, Norway

Abstract: Suction anchors are becoming the preferred foundation solution for mooring different types of floating structures used in the offshore petroleum industry. The design rules that define the required holding capacity of the suction anchor, and the (partial) safety factor(s) are specified in the relevant codes and guidelines and/or by the operator. However, in most design situations, it is not clear what reliability level the code/operator requirements imply in terms of the expected annual failure probability of the foundation. This paper presents a reliability-based design approach for suction anchors, where the design objective is to ensure that the annual probability of failure is less than a target value. Example calculations are presented for a suction anchor that is to be used as part of the foundation system for a semisubmersible at a clay site on the Norwegian Continental Shelf.

Introduction Since the early 1980s, suction caissons have been widely used as foundations and anchors for bottom-fixed and floating offshore structures. They are installed by self-weight and underpressure (suction) applied inside the caisson. It is estimated that, by the end of 2010, more than 1000 permanent offshore structures were installed using the suction anchor technology. Almost all of these structures are used in the oil and gas industry. There is, however, increased interest in the suction caisson technology in the offshore wind energy industry. It is expected that suction caissons will be used frequently as the foundation of both bottom-fixed and floating offshore wind turbines in the near future. The focus of this paper is on reliability-based geotechnical design of suction anchors that are used for mooring of floating structures (Figure 1). The geotechnical design aims at selecting the anchor dimensions (diameter, penetration depth and location of padeye) that provide adequate holding capacity to resist the chain tension that acts on the suction anchor in various design conditions. The tensile loads are transferred through a mooring line and chain to the padeye on the anchor. The padeye location is optimised such that the anchor provides maximum resistance under the design load conditions. The design rules that define the required holding capacity of the suction anchor, and the corresponding (partial) safety factor(s) are specified in the relevant codes and guidelines – e.g. ISO 19901-7 International Standard [9], DNV Recommended Practice E303 [7] and API-RP-2SK [4]. The platform operator may also define the required safety factors for different loading situation based on combination of requirements from different codes and standards.

Figure 1: Typical suction anchors used as foundation of a floating offshore platform (courtesy: NGI).

Throughout the paper, example calculations are presented for a suction anchor that is to be used as part of the foundation system for a semi-submersible at a clay site on the Norwegian Continental Shelf.

Calculation of Holding Capacity of a Suction Anchor 2.1 Required Inputs and Assumptions The anchor geometry (diameter, penetration depth and padeye location), soil properties and load characteristics are key input parameters to the suction anchor holding capacity calculations. Assessment of the soil properties at a clay site involves evaluation of the undrained shear strength profile, shear strength anisotropy, time dependent set-up effect (i.e. changes in anchorsoil interface roughness with time after installation) and effect of cyclic loading. Regarding the loads, it is necessary to know the design peak load and time history of the load in the mooring line during the design storm event. The latter is required for the evaluation of the effects of cyclic loading on soil properties, in particular the cyclic shear strength of the soil. There are also a number of other aspects that require assessment, which are described below. Tension crack: Depending on the location of the padeye, the anchor can rotate and translate in the horizontal direction when it is subjected to a combined horizontal and vertical load. The rotation can be positive or negative, implying that the top of the anchor displaces in the load direction or in the opposite direction to the load. A tension crack may develop behind the anchor if the top of the anchor rotates in the direction of the load. The development of the tension crack can significantly reduce the holding capacity. In practice, the padeye is often placed deep down (2/3 of total penetration or deeper) so that the anchor will rotate in the opposite direction to the load (counter-clockwise direction in Figure 2), ensuring no tension crack development. However, sometimes an existing anchor is reused, and could be exposed to load conditions that are different from those it was originally designed for. In this situation, the possibility of tension crack must be evaluated and, in case the development of a tension crack is possible, it should be taken into account in holding capacity analysis.

Tilt and mis-orientation: After installation the anchors may experience tilt and mis-orientation. The anchor design tolerances (±5° as per practice) with respect to tilt and mis-orientation should be considered. For re-evaluation of an existing anchor, the actual measured tilt and mis-orientation should be used in the calculations. Standards and code regulations: There are different design requirements in the different codes and standards used for suction anchor design. For example, the ISO 19901-7 International Standard [9] specifies an overall lumped safety factor for resisting the mooring line tension (Table B.2 of Annex B of [9]), whereas the DNV Recommended Practice E303 [7] specifies partial safety factors (load factor and material factor) for suction anchor design. The partial safety factors specified in [7] depend on the consequence class.

2.1 Holding Capacity of a Suction Anchor in Clay 2.1.1

Basic mechanical model

The analysis of the holding capacity of a suction anchor involves two steps. Step 1 calculates the chain tension reduction from the mudline to the padeye, as well as the chain angle, under the design load. Step 2 verifies that the capacity of the anchor under the padeye load satisfies the code- or operator-specified requirement. An iterative process is required between Steps 1 and 2 to find the ultimate mudline tension load that the anchor can withstand. Figure 2 presents a schematic sketch of the process.

Figure 2: Loads acting on the chain at seabed and on padeye.

Step 1. Chain analysis Results from a floating system motion analysis will give the mooring line tension load and line uplift angle at the dip-down point, which is the point of the mooring line intersecting the seabed. When the load is transferred through the soil from the dip-down point to the padeye and the line drags through the soil, the line tension is reduced and the line angle is changed due to the combined effect of soil friction and normal stress acting along the embedded chain line. The design load at the pad-eye is found through solving a sequence of limit equilibrium equations along the chain, which is discretized into finite length chain elements. In this study, the chain configuration under the applied loads was analysed using the procedure described by Mortensen [13]. Step 2. Anchor holding capacity analysis The anchor holding capacity for inclined loading can be either calculated by simplified limit equilibrium methods or by finite element analysis. In practice, simplified 2D finite element programs, for example SPCalc [16], are often applied due to simplicity and efficiency. In such

2D analyses, the 3D effects are considered by side shear factors that are calibrated from full 3D finite element analyses. Andersen et al. [2] and Jostad and Andersen [10] present calibration of the side shear factors and comparisons with 3D finite element analyses. The benefit of using a finite element model for such analyses is clear, since this allows evaluation of the failure mode automatically. In the current study, the soil-structure side shear factor was taken as 0.73 and the soil-soil side shear factor was taken as 0.7 based on the recommendations of Jostad and Andersen [10]. 2.1.2

Effects of cyclic loading on holding capacity

The cyclic shear strength of the clay is defined as the sum of the average and the cyclic shear stresses that causes failure after a specified number of load cycles. The cyclic shear strength is a function of the combination of average and cyclic shear stress levels and the number of load cycles. The cyclic strength of soil under undrained conditions is evaluated by the so-called strain accumulation procedure for a design load history using contour diagrams from high quality cyclic laboratory tests on undisturbed samples. More details on the cyclic accumulation procedure and determination of the cyclic shear strength is found in Andersen et al. [3]. For suction anchors, experience suggests that the cyclic shear strength of the soil may be greater than the reference static shear strength because of the effect of rapid rate of loading on soil strength. The enhanced strength due to shearing the soil at higher rate outweighs the strength degradation due to repeated loading. In the current study, the reference static shear strength was used for the anchor holding capacity analyses and the effects of cyclic loading were neglected.

Statistical Modelling of Loads Acting on the Anchor 3.1 Maximum Tensile Load in Mooring Lines at Various Return Periods The mooring system which has been studied, consists of wire and chain. The system has been designed in compliance with ISO 19901-7 [9]. The analyses were based on the frequency-domain model in the software package MIMOSA [12], which has been correlated and calibrated against model test results. The analyses were carried out for 24 headings (15 degrees steps). In order to provide a probability density function for the line tension at mudline, the maximum tension was calculated by short term response analysis and environmental loads with 1-year, 10-year, 100-year and 10000-year return periods. The characteristic n-year responses were estimated by extracting the 90%-percentile of the line tension. The maximum line tension at the seabed is taken as the maximum from all directions analysed. This is a simplified and conservative method to obtain probability density function for line tension. Calculation of line tension for arbitrary metocean conditions requires substantial number of analysis, which has not been part of the scope for the study performed.

3.2 Statistical Model for Annual Maximum Tensile Load in Mooring Lines The Type I extreme-value distribution, known also as Gumbel distribution, is a common probability distribution function used for statistical description of the largest annual storm-induced loads on offshore foundations. The calculated characteristic n-year maximum tension loads in the mooring line for the example case study are plotted on Gumbel distribution paper in Figure 3. The Gumbel distribution parameters (mean and standard deviation) can be obtained from any pair of return periods. The results of the reliability analyses, which are presented later, showed

that the load value at design point corresponds to a return period between 100 and 10000 years. Therefore, the distribution function parameters for the annual maximum tension in the mooring line were fitted to the load data for 100-year and 10000-year return periods.

Figure 3: Maximum annual mooring line loads plotted on Gumbel distribution paper.

Reliability Analysis for a Suction Anchor in Clay 4.1 Suction Anchor Geometry The cylindrical suction anchor in the example calculations has an outside diameter of 4.9 m and length of 10.5 m. The padeye is located 3.4 m above the anchor tip.

4.2 Statistical Description of Soil Properties At the study site, the soil conditions are characterized by an upper layer of very soft clay overlaying harder, overconsolidated clay layers. The key soil parameter for calculation of holding capacity of a suction anchor in clay is the undrained shear strength. The undrained shear strengths in the three soil units shown in Figure 4 were estimated by statistical analyses of the soil data, combined with well-documented correlations and experience. The procedures used for estimating the mean and standard deviation for independent and dependent soil variables were based on the recommendations in DNV-RP-C207 [6]. The parameters were assumed to either vary linearly with depth within each soil unit or be constant within the unit. The spatial variation of soil properties in the vertical direction was assessed using the procedure outlines by Nie et al. [14] and its effect on the standard deviation of the spatiallyaveraged undrained shear strength was accounted for in the calculations. Other sources of uncertainty, such as measurement error and limited soil data/samples, should ideally be addressed in evaluating the statistics of soil properties. However, not enough data were available to do this. Effects of spatial variability of soil properties in the horizontal direction were not taken into account. However, the effect of spatial averaging of soil properties in the horizontal direction on the calculated reliability of holding capacity of an anchor embedded in a layered soil, at a relatively shallow depth, is not expected to be significant. The blue line on the right-hand plot on Figure 4 shows the expected reference undrained shear strength for a normally consolidated clay at the site.

kPa Undrained shear strength, suuC , kPa 0

10 10

20 20

30 30

40 40

50 50

60 60

70 70

0 Mean (Calculated from from CPT) Mean ± 1*SD ((Calculated ((Calculated from from CPT)) CPT)) ' ssu = 0.23*p 0.23*p0 ' u

1

2 2

3 3 C C

Depth below seafloor, m

4 4

CAUC / CAUE DSS

5

6

7

8

9

10 10 C

11 11

12

Figure 4: Mean and mean ± 1 standard deviation of cone resistance and undrained shear strength suC.

The cone tip resistance, qc, and undrained shear strength, su were investigated because su is the key parameter for anchor holding capacity calculation and su can be derived from qc. The method developed by Lacasse et al. [11] to process statistically the cone resistance qc from the CPTU data was used. Figure 4 illustrates the mean ± one standard deviation of the cone resistance qc and undrained shear strength in triaxial compression type of loading suC. A lognormal distribution of qc and su is suggested as a reasonable assumption for the probability density function of the cone penetration resistance and undrained shear strength. The lognormal distribution also ensures that the qc/su-value parameters would not become negative in the probabilistic analyses of anchor capacity. The undrained shear strength of clay is highly anisotropic. The su-profile in Figure 4 is for undrained shear strength in triaxial compression type of loading. Based on the high quality laboratory tests from undisturbed soil sample from the study site, the following mean values of anisotropy ratios were respectively used for direct simple shear and triaxial extension modes of loading: suDSS/suC = 0.9, and suE/suC = 0.7. A coefficient of variation of 10% was used for anisotropy ratios as suggested by Andersen et al. [2].

4.3 Reliability Analysis of Holding Capacity Using SORM The first-order reliability method (FORM), as formulated by Hasofer and Lind [8], is the most common calculation method in structural reliability analysis today. Breitung [5] extended FORM and provided the theoretical basis for the second-order reliability method (SORM). The SORM approximation in the commercial software package STRUREL [15] was used in the analyses presented in this paper.

Both FORM and SORM require the definition of a limit state function g(X) such that g(X) ≥ 0 means satisfactory performance and g(X) < 0 means failure. X is a vector of basic random variables. The following limit state function was used in the calculation of the annual probability of anchor failure. 𝑔𝑔 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 ∗ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ∗ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 – 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 ∗ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠_𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

(1)

where 'capacity' is the reference static holding capacity of anchor, 'errmodel' is the modelling uncertainty parameter in holding capacity calculations, 'cyclic' is the ratio of cyclic capacity to reference static capacity, 'storm_load' is the annual maximum storm-induced load in mooring line at seabed, and 'errload' is the random variable describing the uncertainty in load calculation model. As mentioned earlier, the cyclic loading effects were neglected in the example calculation presented in this paper, i.e. the parameter 'cyclic' in Equation 1 was set equal to 1.0. In the reliability calculations, a response surface approach was used to functional relationship between the holding capacity and the undrained shear strength profile. Based on the physics of the case study problem, the uncertainty in the undrained shear strength profile and the uncertainty in the shear strength anisotropy are the main contributors to the uncertainty in the estimated holding capacity. The holding capacity of the anchor was calculated for combinations of three shear strength profiles, corresponding to µ, µ – σ, and µ – 2σ (µ = mean, σ = standard deviation, see Table 1, and three anisotropy factors corresponding to µ, µ – σ, and µ – 2σ. This required nine (3 × 3) deterministic calculations of holding capacity for the anchor. The reason for choosing these combinations was to get an accurate description of the limit state function at the design point (most likely combination of random variables at failure) in SORM analyses. The interpolation functions listed on Figure 5 were used to define the functional dependence of “capacity” on undrained shear strength and anisotropy factor. The dimensionless parameter ‘r’ on Figure 5 represents the change in the capacity in terms of number of standard deviations from the mean value of undrained shear strength, and the parameter dimensionless “s” does the same for the shear strength anisotropy factor. To utilize the response surface method for description of the anchor holding capacity, the performance function shown in (1) for SORM calculations was rewritten as: 9

𝑔𝑔 = 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 ∗ 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ∗ �� ℎ𝑖𝑖 ∙ 𝑥𝑥𝑖𝑖 � – 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 ∗ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠_𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑖𝑖=1

(2)

where hi are the interpolation functions listed in Figure 5 and xi are the holding capacities at nodes 1 through 9, which are listed in Table 1. The response surface approximation for anchor capacity makes it numerically efficient to use Monte Carlo simulation to estimate the failure probability. The combination of FORM/SORM approximation and response surface method, however, has several advantages over standard Monte Carlo simulation for achieving the objectives of this study. First, the sensitivity factors and coordinates of the design point are outputs of the FORM/SORM analyses. The design point coordinates can be used to calibrate the partial safety factors for deterministic design. Second,

for the FORM/SORM approach, it is sufficient that the response surface accurately approximates the variation of anchor capacity in the vicinity of the design point. The MCS would require an accurate description of the anchor capacity for all combinations of random variables, and hence a more complicated and computationally-intensive response surface. h1 = 0.25⋅r⋅ (1+r)⋅s⋅(1+s) h2 = 0.25⋅(1+r)⋅(2+r)⋅s⋅(1+s) h3 = 0.25⋅(1+r)⋅(2+r)⋅(1+s)⋅(2+s) h4 = 0.25⋅r⋅(1+r)⋅(1+s)⋅(2+s) h5 = – 0.5⋅(2r + r2) ⋅s⋅(1+s) h6 = – 0.5⋅(1 + r)⋅(2+r)⋅(2s + s2) h7 = – 0.5⋅(2r + r2)⋅(1+s)⋅(2+s) h8 = – 0.5⋅r⋅(1+r)⋅(2s + s2) h9 = (2r + r2) ⋅(2s+s2)

Figure 5. Design of response surface calculations with two random variables in normalized coordinate system. Table 1

Holding capacity calculations for response surface modelling of the example suction anchor. Values listed are the static holding capacities in kN with reference to mooring line load at mudline (Fig. 2).

Undrained shear strength profile Anisotropy ratios µ (suDSS /suC = 0.9,

Mean (µ)1

(µ - σ)1

(µ - 2σ)1

11300

9400

7450

10350

8600

6850

9375

7800

6200

suE/suC = 0.7)

µ - σ (suDSS /suC = 0.8, µ - 2σ (suDSS /suC = 0.7,

suE/suC = 0.62) suE/suC = 0.54)

1) See section 4.1 and Figure 4.

Results for Example Suction Anchor With reference to the limit state function in Equation 2, Table 2 lists the distribution functions of the basic random variables that were used in the reliability analyses. Table 2

Mean value, standard deviation and distribution functions of the basic random variables.

Variable errmodel

Distribution function Normal

Mean 1.0

Standard deviation 0.025

suC

Lognormal

See Figure 4

See Figure 4

suDSS/suC (1)

Beta (0.65 → 1.0)

0.9

0.1

errload

Normal

1.0

0.10

950 kN 980 kN storm_load Gumbel E C (1) su /su is assumed to be perfectly correlated with suDSS/suC

With the parameters listed in Tables 1 and 2, the annual failure probability of the anchor was calculated to be Pf,annual = 4.4⋅10-5 (βannual = 3.92). Figure 6 shows the contribution of the different basic random variables to the total uncertainty in foundation performance. Since the load

modelling contribution to the uncertainty is significant, a refinement of the load modelling is considered an area for further improvements for these analyses.

Figure 6. Relative contribution of uncertainty in basic random variables to uncertainty in performance of example anchor.

Figure 7 shows how the annual reliability index changes when the load on the anchor or the holding capacity of the anchor is scaled with respect to the Base Case.

Figure 7. Variation of the annual reliability index for the example anchor when the mooring line load is scaled up or down with respect to the Base Case (Note: β = 3.72 ⇒ Pf = 10-4).

Concluding Remarks This paper presented an approach for doing reliability-based design of suction anchors for mooring of floating structures. The analysis results can also be used to calibrate the partial safety factors in a deterministic design that would ensure that the annual probability of suction anchor failure is less than a target value. A typical design criterion for holding capacity of a suction anchor has the following format: 𝑅𝑅𝐶𝐶 (3) ≥ 𝑇𝑇𝐶𝐶−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∙ 𝛾𝛾𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 + 𝑇𝑇𝐶𝐶−𝑑𝑑𝑑𝑑𝑑𝑑 ∙ 𝛾𝛾𝑑𝑑𝑑𝑑𝑑𝑑 𝛾𝛾𝑚𝑚 where RC is the characteristic anchor resistance, γm is the resistance factor, TC-mean is the characteristic mean line tension, TC-dyn is the characteristic dynamic line tension, and γmean and γdyn are partial load factors. The values on the right-hand side of the design criterion above are specified by the codes (e.g. DNV-RP-E303). Once the design point holding capacity (including the effects of cyclic loading) for a given target annual failure probability is obtained, one could assess the corresponding characteristic capacity RC, and evaluate the minimum resistance factor γm required for achieving the target reliability level from inequality (3).

Acknowledgement This work described in this paper has been supported by Statoil. Their support and permission to publish the paper is gratefully acknowledged by the authors.

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