Ekofisk oil storage tank (Clausen et al., 1975)

Up to now, only regular harmonic loads have been investigated. One of the most famous field tests dealing with liquefaction is the Ekofisk test firstly reported by Clausen et al.

(1975). The Ekofisk gravity base foundation located in the North Sea is often used for validation and benchmark purposes because it was one of the first offshore foundations with which accumulation of excess pore pressure and deformation was investigated and studied. The foundation was installed in 1973 and has a diameter of 93 m and is 90 m tall.

The cylindrical structure has a permanent vertical force from a dead weight of 1900 MN and an area of 7400 m² with a load eccentricity of 36 m (Eide et al., 1981). This results to roughly 280 kPa bedding stress. The water depth is 70 m. Skirts against erosion and piping were attached but will not be modelled.

Soil data and loading conditions

The soil is layered with a 16 m sand layer and a 2 m thin clay layer with low plasticity.

Below the clay layer there is fine sand present again. For the design, a 26 m thick very dense sand layer with subsequent stiff clay is assumed (Eide et al., 1981). The relative density is 100% (Lee and Focht Jr., 1975). The angle of internal friction is reported to be 42.5^◦ with an assumed dilatancy angle of zero (Bjerrum, 1973). The permeability is assumed to be 1×10⁻⁵m/s with an oedometric stiffness of 48 MPa. Cyclic triaxial tests in the form of CSR−N_liq are reported by Lee and Focht Jr. (1975) for a relative density of 100%. A value ofα= 0.7 was chosen for the Seed and Booker (1976) equation. The design storm load consists of several load parcels with different load magnitudes (Table 6.1) (Lee and Focht Jr., 1975). The 100-year storm has a wave height of 23.8 m. The transition from hydrodynamic (wave height) to lateral load can be found in Taiebat (1999) (Rahman et al., 1977).

Literature review

Several back-calculations have already been done. Measurement results have been pre-sented by Clausen et al. (1975) and Bjerrum (1973). The first explicit back-calculation was done by Rahman et al. (1977).

Rahman et al. (1977) considered stress redistribution with an explicit approach. They used the vertical stress for normalisation of the excess pore pressure for R_u. The soil response was based on DSS test results with pre-shearing. Hence, the soil resistance can be assumed to be slightly increased due to pre-shearing. Rahman et al. (1977) calculated with an axisymmetric model and with D_r of 77% and 85%. They defined the CSR as τ /σ^′_v and used an equivalent design storm according to Seed and Rahman (1978).

Verruijt and Song (1991) calculated in a plane strain manner with D_r = 100%. They used u_max for the definition of the normalized excess pore pressure R_u.

Taiebat (1999) compared different modelling techniques with different normalisations and calculates larger R_u values over time compared to Rahman et al. (1977). A slightly different approach was published by Taiebat and Carter (2000).

When comparing these different approaches, Rahman et al. (1977) reports a normalized excess pore pressure at the off-edge of 32% and at the centre of 16%. Verruijt and Song

6.2 Back-calculation with results from field and 1g medium-scale tests

Table 6.1: 15-bin design storm with lateral load F (Taiebat and Carter, 2000).

Bin Cycles N Period T Wave height F

[1] [1] [s] [m] [kN]

1 236 5 0.5 3724

2 235 7.2 2 11134

3 243 10 6 99273

4 235 11.5 10 232832

5 141 12.5 14 384201

6 61 13.2 18 537584

7 16 13.4 22 678262

8 3 13.5 25 777527

9 16 13.4 22 678262

10 61 13.2 18 537584

11 141 12.5 14 384201

12 235 11.5 10 232832

13 243 10 6 99273

14 235 7.2 2 11134

15 236 5 0.5 3724

(1991) calculated off-edge 15 kPa and at the centre 26.5 kPa. Not all authors present the normalized excess pore pressure as well the excess pore pressure value, which makes comparison more difficult. The different results can mainly be explained by different soil data, modelling techniques and other definitions of normalized excess pore pressure.

However, the measurement system was not working during the storm in 1973 and, hence, only theoretical back-calculations can be compared.

Finite element model

An ABAQUS model with a Mohr-Coulomb failure criterion was used for the soil. The rigid gravity base foundation was modelled with a linear-elastic material law. The finite element model is a 3D model with C3D8 elements. The clay is modelled with similar cyclic soil properties but lower permeability. The dimensions of the model are chosen in order to minimize boundary effects. Drainage for the flow net calculation was allowed at the top and at side-edges of the model. No contact interface was used.

Back-calculation of Ekofisk tank

The Ekofisk tank back-calculation can be considered the most important back-calculation as it deals with sand layers. However, the contour approach cannot be used as the corresponding contour plots are not present. There are different ways to back-calculate this field test. Two different modelling ways were used in order to back-calculate the Ekofisk tank. Additionally to the reference procedure with a single dissipation calculation, the excess pore pressure was dissipated sequentially for each different storm bin. The stresses however, which are used to calculated the CSR, are assumed to be constant throughout the calculation. A sequential analysis considering stress redistributions can

be incorporated, but it comes with larger computational times. Hence, the stresses were estimated based on one calculation and the dissipation was done sequentially.

The design storm consists of different bins with same wave height. According to the presented EPPE method, the calculation is first done for undrained modelling conditions and then dissipation to account for partially drained conditions is considered. The single dissipation model uses a flow net calculation for the maximum storm load and the standard dissipation approach for the analytical superposition. The CSR values for each storm bin were estimated based on a single monotonic calculation, from which the respective shear stress amplitudes were derived. In case of the sequential dissipation analysis, the same CSR values for each integration point and storm parcel were used, but the excess pore pressure was calculated for each parcel separately and then dissipated. The resulting dissipated excess pore pressure field was used in order to derive a new equivalent number of cycles on which the number of cycles of the next storm parcel was added. This N_eq was used to calculate the subsequent excess pore pressure field.

Figure 6.14: Comparison of simplified and sequential EPPE calculation with data according to Rahman et al. (1977) and Taiebat (1999) for the location at the edge of the gravity base foundation in form of normalized excess pore pressure ratio.

Figure 6.14 shows the results at the edge of the structure for the EPPE equation approach with a single dissipation and a sequential dissipation with the results according to Rahman et al. (1977) in dashed-black and Taiebat (1999) with a solid black line. The maximum excess pore pressure of 40 kPa is reached after 3 hours in all cases. The first load parcels only generate a small amount of excess pore pressure. The solid blue line shows the upper excess pore pressure which is subsequently reduced due to dissipation (dashed blue line). The real result may be in between. The simplified calculation with only one single dissipation run (reference procedure) shows a slightly larger peak value but a faster decline in excess pore pressure after the peak value is reached. The results according to Rahman

6.2 Back-calculation with results from field and 1g medium-scale tests

et al. (1977) were transferred to the normalisation with the octahedral stress. Figure 6.15 shows the excess pore pressure without normalisation similar to Figure 6.14. The solid line in Figure 6.14 represents the excess pore pressure prior to and the dashed line after dissipation took place.

Figure 6.15: Comparison of simplified and sequential EPPE calculation for the location at the edge of the gravity base foundation in form of excess pore pressure.

The back-calculation shows a good agreement with data published by Rahman et al.

(1977). It is by far not a complete validation but it shows the effect of excess pore pressure accumulation as well as that the effect can be well estimated with the presented EPPE approach.