Effect of pile geometry

Figure 7.51 shows exemplarily the influence of different pile geometries. The lateral load is kept constant similar to the reference model (F_min = 0 MN and F_max = 13.6 MN).

This means that the load level is not equal for all investigated cases. The value ζb is

7.6 Parameter study on monopile foundation

0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00

Figure 7.50: Final excess pore pressure ratio field R_u for anisotropic soil permeability with smallerkf value in vertical direction.

Figure 7.51: Overview of post-cyclic capacity for different diameters and pile lengths for N = 30 cycles and the reference soil with reference load condition.

depicted in Figure 7.51. The load level decreases for a larger pile diameter and a larger embedded length. Regarding the post-cyclic capacity, the cyclic degradation decreases with increasing diameter and pile length. The degradation is directly correlated to the spatial distribution of the CSR field which correlates to the monotonic bearing capacity and the applied maximum global lateral load (cf. Figure 7.16). For the given load there is a degradation of capacity in the worst case of 50%.

The largest post-cyclic capacity is estimated for the smallest load level. Figure 7.52 shows a comparison between different pile lengths for a diameter of D = 8 m regarding the excess pore pressure ratio. Hence, two effects influence the structural response. The first is the bearing behaviour of pile and the second is the load level. The area of liquefaction decreases for increasing embedded length and so does the spatial distribution. For an increasing embedded length, there is less influence at the pile toe and generally in the lower part of the pile. It can clearly be seen, that for larger dimensions less damage is present within the soil for the post-cyclic response.

Figure 7.53 shows related CSR fields for a diameter of 8 m and different embedded lengths.

The degradation decreases for an increasing pile length. Also the load bearing behaviour by means of the spatial distribution is changed. Similar to the excess pore pressure ratio,

0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00

0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00

0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75 0.83 0.92 1.00

(a) (b) (c)

Figure 7.52: Excess pore pressure ratio fieldR_ufor an embedded length of L = 25 m (a), L = 30 m (b) and L = 35 m (c) for a pile diameter of D = 8 m.

there is less damage in the lower part of the pile for increasing pile length. The location of the largest CSR values moves upwards. The area in which the laterally loaded pile activates its bedding can clearly be seen.

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.20 0.23 0.26 0.29 0.32 0.35

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.20 0.23 0.26 0.29 0.32 0.35

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.20 0.23 0.26 0.29 0.32 0.35

(a) (b) (c)

Figure 7.53: CSR field for an embedded length of L = 25 m (a), L = 30 m (b) and L = 35 m (c) for a pile diameter of D = 8 m.

8 Conclusion and outlook

8.1 Discussion of the results

The proof against cyclic loading is an essential part within the design. This work con-tributes to the current research on cyclically loaded offshore foundations with the aim of estimating the cyclic degradation of soil-structure interaction under excess pore pres-sure build-up considering partially drained conditions for sandy soils. Regardless of the applied load type, whether using an irregular storm loading or a simplified equivalent number of cycles, the cyclic effect on the structure must be taken into account according to the standards. However, the standards do not specify a uniform procedure. Only the DNV-RP-C212 specifies an explicit procedure with high-quality cyclic laboratory re-sults. Currently, there is no consistent concept for verification against excess pore pressure accumulation as well as cyclic accumulation of deformation, which is reflected in the men-tioned inconsistent procedures within the framework of practical projects. The research presented is particularly concerned with a simple, explicit estimation procedure that can be easily evaluated by engineering judgment.

Cyclic soil response

The general soil behaviour under cyclic loading is presented with load- and displacement-controlled cyclic direct simple shear tests. Even though cyclic soil behaviour is investi-gated for many years, such a detailed investigation of one sandy material for all different boundary conditions, as given in this thesis, is only present for a few sands which are often used in scientific investigations. With the results of the cyclic laboratory tests, one semi-empirical equation for excess pore pressure estimation is calibrated and additionally contour plots are derived. From the different investigated mathematical frameworks for the derivation of contour plots, one approach could be assessed as advantageous. With this equation, the excess pore pressure accumulation for different mean stresses is derived in order to be used in the numerical explicit framework. Different mathematical frame-works are investigated and one equation is assessed as especially applicable due to its easy use and high controllability.

Besides the contour plots for excess pore pressure, also shear strain contour plots are derived. Since cyclic data is present for different relative densities, a scaling approach is investigated as well. Different relative densities and vertical stresses are examined and the results are compared with a scaling approach for a fast estimation of contour plots.

Scaling of existing contour plots can be very helpful if not enough tests for one particular soil are present. The results of the scaling investigations are compared with a large amount of literature data and a good agreement is found.

The performance of cyclic triaxial tests is very time consuming, but in order to show the influence for one specific soil, several symmetric two-way and one-way cyclic loading tests are carried out. The induced damage from cyclic compression triaxial tests under isotropic dissipation is significantly less compared to the cyclic direct simple shear (DSS) tests.

Regarding cyclic tests, DSS tests are faster to perform even though triaxial tests will give higher quality results, but also a smaller (non-conservative) degradation. Nevertheless, the cyclic direct simple shear tests showed a large deviation under the same boundary conditions. This could possibly have been prevented by using dry pluviation instead of dry tamping for all tests and also including a pre-shear phase. This is however not done in order to not influence the results in any way, but to have a cyclic database without preconditioning. The consideration of pre-shearing can enhance the cyclic resistance.

Also influences between different soil preparation procedures should not be neglected. A pluviated soil sample will fail after a smaller number of cycles than a tamped one.

The external global load is mainly load-controlled but due to stress redistributions or other model assumption displacement-controlled element boundary conditions can arise. This is important because there is a large deviation between both responses when comparing the trend of excess pore pressure over the number of cycles. When analysing the soil response of an implicit model, mainly load-controlled conditions occur. Since cyclic results are present, a transfer from load- to displacement-controlled conditions is performed, but the accuracy is improvable.

Calibration of implicit model

The SANISAND model is able to realistically reproduce many different geotechnical sce-narios under cyclic and monotonic loading. With faster computers and better algorithms, the use of more sophisticated models will become more popular. Implicit computation with an appropriate soil model can improve the understanding of soil-structure interaction under complex loading conditions such as cyclic loading. However, the calibration is not trivial, and not all soil properties can be calibrated in one calibration set. Regarding the reference soil, the model is first calibrated with the standard critical state parameters and then an objective function is used in conjunction with a genetic optimization algorithm.

This algorithm can also be used in case a newer version is available. When calibrated, the SANISAND model can reproduce a wide range of stresses and void ratios as well as cyclic and monotonic loading. However when comparing the number of cycles to liquefaction for different element tests, the SANISAND tends to underestimate the number of cycles to liquefaction and the calculated results should therefore be treated with caution.

EPPE approach

This thesis highlights how excess pore pressure accumulates under different conditions and how this can be approximated with a simple numerical framework. The main objective of this work is to develop a methodology as simple and transparent as possible for predicting the bearing behaviour of a cyclically loaded foundation based on cyclic element tests, to validate it with experiments, and to make it easier for engineers to implement the procedure. A generic methodology for the estimation of excess pore pressure accumulation around cyclically loaded foundation is developed. There are some model assumptions in

8.1 Discussion of the results

order to keep the approach comprehensible. The influences of these simplifications on the bearing capacity have been discussed and all assumptions in the reference procedure can be justified. The concept can also be used without a degradation of the stiffness and with a simplified excess pore pressure estimation, for instance according to Seed et al.

(1975b). There is a larger bearing capacity, if an interpolation between cyclic direct simple shear (DSS) and cyclic triaxial test results is done. This is expected since cyclic triaxial compression results will yield smaller cyclic accumulations. The use of cyclic DSS results is recommended since they can be performed much easier and will result in conservative bearing capacity estimations. Although the use of contour plots is favourable, the author stresses that the use of a semi-empirical equation approach is reasonable for instance when only a limited number of tests are available. A small deviation within the regression analysis of the contour curve has no significant influence on the final load-bearing capacity. The influence of a simplified contour input, using only contour plots for LTR = 0, is also not very pronounced.

The main part of this thesis and the related calculations are based on a constant equivalent number of load cycles, although this is not feasible for a practical application. Therefore, for practical applications, a detailed procedure for the consideration of a design storm is presented in Appendix B. Furthermore, multistep DSS tests are used to investigate the accuracy of the accumulation procedure.

Currently, an extensive validation is not fully possible. The existing model tests on monopiles have some drawbacks, and the field tests like the Ekofisk tank are not well documented so they can only be partially verified. This is mainly because the sensors did not measure during the storm. However, in this thesis a first comprehensive comparison of tests and predictions has been shown. For advancements in the sophisticated explicit and implicit models, high-resolution, well-documented model tests are needed.

Investigation with EPPE approach

The method comes along with some model assumptions. All of these have systematically been addressed and showed that especially the ones which come with high computational effort can be simplified. The reference procedure presented seems to be very reasonable.

Different load types lead to different capacity degradations from which the symmetric one-way loading shows the largest degradation based on the assumption for the input contour plot. The procedure does also work with a simplified regression analysis of load-controlled cyclic laboratory tests or with the derived strain-based contour plot based on displacement-controlled test results. It is not clear if load- or displacement-controlled cyclic tests shall be performed. However, if the latter are used, it leads, in this case, to a slightly larger capacity.

The dissipation approach to consider partially drained conditions can be used in differ-ent ways. From the differdiffer-ent dissipation approaches, the standard approach gives the most reasonable results compared to simplified or sequential calculations. The standard dissipation does not accurately describe the dissipation behaviour of a soil, but is a conser-vative approach compared to the complex dissipation approach. An iterative calculation, in which the stresses are used after a degradation in order to calculate the CSR field

again, seems not to be necessary, because the results of the first run are accurate enough related to the additional computation effort. The volumetric strain can be estimated and the order of magnitude seems reasonable. The incorporation in the framework can easily be done, if needed. Small layers (general soil stratigraphy) with a very low permeability can influence the excess pore pressure distribution. This leads to the fact that the soil-structure response for other sites can be different and, therefore, a numerical estimation is essential.

All performed analyses show that the post-cyclic capacity is reasonably estimated with the reference EPPE method. The use of the more complex dissipation method will lead to larger capacities – especially for an increasing number of cycles. The effect of both methods is amplified with a sequential analysis, although a mandatory analysis in such a way does not seem to be necessary. A simplified analysis by using a 1D finite differences model will lead to slightly larger capacities but neglects spatial influences. There is no need to use the equivalent number of cycles for the input of the dissipation model.

The stress - strain response already takes the complete soil response into account. This includes also the reduction of stiffness. To directly consider the stress - strain response, a simplified hardening model is added to the Mohr-Coulomb model. Herein, an idealised stress - strain for all integration points or an integration-point specific curve is introduced.

The exact stress-strain curve is based on the excess pore pressure generation and dissi-pation. A more simplified way of considering a degraded soil response is to consider a reduced stiffness modulus. The concept is also developed and presented in this work. Due to this effect, a softer soil-structure interaction occurs.

With a sensitivity study the general response of the soil structure interaction is investi-gated. The system response to a varied diameter is obvious. Furthermore, there is a very clear decrease of the capacity for a decreased permeability. The influence of the number of cycles is not pronounced, because of the relatively high permeability and due to the superposition approach. Overall, the method entails a high level of usability.

Application of implicit model

The calibrated SANISAND constitutive model is used to investigate the monopile response from an implicit perspective. Since the model does approximate the stress-strain relations more accurately, the constitutive model is also used in conjunction with the explicit EPPE approach. The monotonic load-displacement curve is stiffer compared to the one of the Mohr-Coulomb model. When using a more sophisticated constitutive model within the EPPE approach, a different excess pore pressure field R_u arises. In this case, the derived damage is less compared to the reference EPPE procedure.

The cyclic back-calculation of the initial reference system is not possible with the available version of the SANISAND model since the model overestimates the cyclic damage and shows some convergence problems. A calculation is possible with a smaller load. This generally agrees with the statements from the literature. The excess pore pressure ratio calculated explicitly is less compared to the implicitly calculated R_u field. However, this is to be expected because of the overestimation of induced damage by the sophisticated soil model. When performing an implicit calculation, the resulting excess pore pressure

8.2 Recommendations for estimation of excess pore pressure in