*5.1. Updating Structural Dynamics Uncertainty*

In this subsection, we present the updated structural reliability based on an updated structural dynamics uncertainty. First, we present a sensitivity study on updating soil stiffness, followed by a case study based on in situ soil stiffness calibration [33].

#### 5.1.1. Soil Stiffness Sensitivity

The effect of updating thesoil stiffness mean value, *μks*, for joint 13CU is presented in Figure 5 and in Table 4. It is assumed that new information from a digital twin is obtained; in this particular case, the mean value of uncertainty related to structural dynamics, *μXd* , is updated. The results are derived by using the limit state Equation (1) with the standardbased variables provided in Table 2 and updated values for *μXd* .

As seen in Figure 5, the soil stiffness has a significant impact on the fatigue lifetime. Updating the soil stiffness by a factor of 0.5 (resulting in reducing the mudline pile stiffness by half) results in a reduction in lifetime by a factor of 0.3. In contrast, increasing the soil stiffness by a factor of 2.0 results in a lifetime increase by more than fourfold (>100 years). The effect of updating soil stiffness on joint 40BU is negligible, as indicated in Figure 6.

Note that in Figures 5 and 6 (and the other figures describing structural reliability as a function of time), the reliability generally decreases with time, albeit non-monotonically in some cases. For example, consider the green curve in Figure 5, where a local increase in reliability around year 20 is observed. This is due to a limited number of Monte Carlo simulations, but we note that this limitation does not qualitatively affect the conclusions drawn from the analyses.


**Table 4.** Fatigue lifetime derived for different distributions of *Xd*.

**Figure 5.** Impact of updating soil stiffness on structural reliability-joint 13CU.

**Figure 6.** Impact of updating soil stiffness on structural reliability-joint 40BU.

5.1.2. Reliability Update-Soil Stiffness

Based on the results presented in [33], we assume the soil stiffness distribution function after the update can be approximated by a normal distribution with mean value of 4.7 and CoV = 0.12, i.e., *ks* ∼ N 4.7,(4.7 × 0.12)<sup>2</sup> . The soil stiffness uncertainty is propagated through the numerical model, and the uncertainty on stress ranges was estimated according to the method presented in Section 3.3. It was assumed, for illustrative purposes, that the soil stiffness is the only uncertain parameter affecting the *Xd* uncertainty, i.e., *α* = *ks*. The *Xd* uncertainty is quantified and its updated value was applied together with the nominal uncertainty values for the remaining stochastic variables in (1). The updated *Xd* distribution (mean value and CoV) as a result of the soil updating is presented in Table 5.

The soil stiffness update results in a reduction in the mean value of *Xd* for all joints except three joints in the splash zone (joints 40CL, 40BL and 40CU). The CoV of *Xd* is reduced for all joints because the CoV of *Xd* is reduced from the initial value of 0.10 for all joints. The structural reliability after the soil update is presented in Figure 7 alongside the lifetime compared to the nominal model presented in Table 5. After the soil update, we can observe an increase in fatigue life in four joints close to the mudline (13CU and 13BU) and in the lowest X-joint (25BL and 25BU). Compared to the nominal model, we can conclude that for both critical joints (40BU and 13CU), the fatigue lifetime is increased after the update. Note that the fatigue lifetime in joint 40BL is reduced despite a reduced CoV. That is due to the fact that for this joint, two opposite effects of the soil update are merged; namely, the positive effect of the reduced CoV (0.006 vs. 0.10) and the negative effect of the increased mean value (1.07 vs. 1.00).

The general conclusion holds that if both the mean value and CoV are reduced, then the fatigue lifetime is increased, while if both of the values are increased, then the opposite result holds. If either mean or CoV is reduced while the other is increased, the fatigue lifetime can either increase or decrease depending on the extent of the increase/decrease in mean value and CoV.

**Table 5.** Effect of updating soil stiffness on fatigue lifetime.


**Figure 7.** Structural reliability after the soil stiffness update. (*ks* update based on the study in [33]).
