model is used because no excess pore pressure based on the SANISAND model will be used. The dissipation step within the EPPE procedure is still performed unchanged. The objective of this comparison is to see how the distribution of excess pore pressure ratio field changes due to a more sophisticated soil model. This is of interest because it takes more time to calibrate such a sophisticated model, but it may not be necessary since the key mechanisms for generating and dissipating excess pore pressure are already sufficiently included in the reference EPPE approach.
Figure 7.35 shows the octahedral stress at global mean load (a) and equivalent shear stress at maximum global load (b) for reference conditions and the SANISAND model.
The stresses increase over depth and larger stresses concentrate in the upper half of the passive side. From these values, the CSR and MSR can be derived, which are used for the derivation of excess pore pressures from cyclic laboratory tests. Figure 7.36 shows the resulting CSR field. In comparison to the EPPE approach (Figure 7.3 (d)), there is a similar spatial extension in passive pile direction and also a similar distribution around the toe of the pile. In both cases very low CSR values are derived around the point of rotation.
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
Figure 7.36:CSR field for reference conditions and the SANISAND model.
In a subsequent step, these CSR and MSR fields were used to derive the excess pore pres-sure ratio for N = 1. The excess pore prespres-sure ratioRu field is depicted in Figure 7.37 (a) with the corresponding excess pore pressure ∆u in Figure 7.37 (b). The induced damage is more severe in terms of its spatial distribution compared to the one derived with the reference EPPE approach (Figure 7.5 (a)) with a large damaged area at the toe of the pile and on the passive side. The presented field is used to derive integration point specific decay curves and perform a superposition. The final post-dissipatedRu field is depicted in Figure 7.37 (c) (with the corresponding ∆u in Figure 7.37 (d)). The spatial distribution is similar, but there are still more areas in the lower pile region and inside the pile which are degraded. The resulting damage is more pile-near.
The induced damage is, in this case, smaller with a very similar final spatial distribution compared to the case based on the Mohr-Coloumb model.
Results of implicit cyclic loading calculation
Since the SANISAND model is able to capture cyclic loading, the system response is analysed under repeated loading and the results are compared to the explicit approach with the cyclically calibrated input parameters. The low number of cycles of N = 20
7.5 Application of SANISAND model
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 1.00
0.00 19.47 38.94 58.42 77.89 97.36 116.83 136.30 155.78 175.25 194.72 214.19 233.66
(a) (b)
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 9.30 18.60 27.90 37.20 46.50 55.80 65.10 74.40 83.71 93.01 102.31 111.61
(c) (d)
Figure 7.37: Excess pore pressure ratio fieldRu(a) and excess pore pressure field ∆uafter N = 1 (b) and excess pore pressure ratio field Ru (c) and excess pore pressure field ∆u after dissipation (d) by using monotonic SANISAND model in EPPE approach.
reduces the accumulation of large numerical errors. The maximum load of the symmetric two-way loading was reduced to 4 MN with a load eccentricity of e = 40 m, because the SANISAND model overestimates the induced damage within the soil. The reason that the more sophisticated model does not adequately estimate the induced cyclic damage is that the current version of the model does not describe the dilatant and contractant soil response accurate enough (cf. Appendix Figure A.15). For a comparison with the EPPE approach with a Mohr-Coulomb constitutive model, Figure 7.39 shows the load-displacement curve at mudline. The finite element model was not hydraulic-mechanically coupled. The resulting structure response is stiffer and results for a larger displacement could not be derived due to numerical issues.
0.00 0.02 0.03 0.05 0.07 0.08 0.10 0.12 0.13 0.15 0.17 0.18 0.20
0.00 0.47 0.94 1.41 1.88 2.35 2.82 3.29 3.76 4.23 4.70 5.17 5.64
(a) (b)
Figure 7.38: Excess pore pressure ratio field Ru for EPPE approach with a global maximum load of 4 MN (a) and excess pore pressure ratio ∆u (b).
Figure 7.39: Comparison of monotonic response by using SANISAND model for the reference monopile with already presented EPPE results.
Figure 7.38 (a) shows the EPPE procedure applied to the same boundary conditions (reduced load) for a better comparability. Due to the decreased global load there is obviously less damage induced. No element is fully liquefied. The excess pore pressure ∆u is depicted in Figure 7.38 (b). The excess pore pressure is quite small, because although there are larger octahedral stresses, only approximately 10% of these are calculated to be excess pore pressure.
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)
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
(c) (d)
Figure 7.40: Excess pore pressure ratioRu field for symmetric one-way loading (a, c) and sym-metric two-way loading (b, d) and for a permeability of 3.7×10−4m/s (a, b) and 1×10−6m/s (c, d).
7.5 Application of SANISAND model
Figure 7.40 (a) shows the implicitly calculated excess pore pressure normalized to the same octahedral stress (at global mean load) as used in the EPPE approach. The excess pore pressure was read at the last peak of the global harmonic load. The load period was set to 10 s. The damage is mainly induced in the upper part of the pile. There are no additional areas of partial liquefaction around the pile toe or within the pile.
Damage is induced in a same area compared to the explicitly calculated case. The excess pore pressure ratio Ru is however significantly larger. This was expected because the SANISAND model overestimated the number of cycles to liquefaction when calibrated.
Moreover, liquefaction in this context must be taken with caution, because herein the stresses change over the course of the calculation and do furthermore redistribute. A criterion which bases on the initial octahedral stress is, hence, not a sound criterion for liquefaction.
At this point, the influence of different initial void ratios could be investigated. However, a detailed analysis of an implicit calculation of the reference structure is not in the focus of this thesis. Nevertheless, the influence between symmetric one-way loading as well as symmetric two-way loading is shown in Figure 7.40. The excess pore pressure decreases with increasing distance to the foundation and shows a maximum value right below the surface. Figure 7.40 (c) shows results for a decreased permeability. If the excess pore pressure cannot dissipate, large values accumulate over time and induce larger damage on the loaded pile side. One difference to the EPPE procedure can be seen for a two-way load. Figure 7.40 (c) and (d) show a symmetric two-way loading with the same global load amplitude as used for Figure 7.40 (a). In case of symmetric two-way loading, damage accumulates on both piles sides, whereas in EPPE only one quarter of a cycle is calculated and hence only one side of the pile experiences degradation. However, this effect does not influence the pile capacity, because the same direction is used for both calculation steps.
Figure 7.40 shows that also for two-way loading, a decreased permeability leads to larger induced damages.
Figure 7.41: Excess pore pressure ratio ∆u build-up for point 8 m/0 m/-8 m for symmetric one-way loading.
For an implicit calculation, also the accumulation effect can be plotted for the integration
points. Exemplarily, the excess pore pressure ∆u over the number of cycles is plotted in Figure 7.41 for one integration point. There is no significant accumulation effect, because of the large permeability. This agrees well with the final excess pore pressure field depicted in Figure 7.40 (a).
(a) (b)
Figure 7.42: Equivalent shear stressσeq′ (a) and equivalent shear strainγeq (b) over the number of cycles with applied regression for 8 m/0 m/-8 m.
Instead of investigating the soil-structure interaction in greater detail, the results of the finite element model will be used to investigate qualitatively some of the open questions.
In order to investigate the different soil element response by means of load-controlled and displacement-controlled boundary conditions, the stress and strain conditions will be evaluated around the monopile. Herein, displacement-controlled conditions can only occur due to stress-redistributions. For this analysis, the equivalent shear stress as well as the equivalent shear strain are plotted over the number of cycles. If load-controlled conditions are present, the equivalent shear stress σ′eq (amplitude and mean value) will be constant over the course of the calculation; the same applies to the equivalent shear strain γeq,cyc (Figure 7.42 (a)). Therefore, the peak values for both indicators for each integration point are evaluated over the 20 cycles, which is the assumed number of cycles for which no significant numerical error may accumulate for this implicit model.
The inclination of the regression line is used as an indicator for the load type (Figure 7.42), which allows three categories to be differentiated. The stress can be constant and the shear strain can change (or vice versa) or there can be elements for which both values change significantly over the calculation. Figure 7.43 shows a comparison of the regression inclination. The blue points have a larger inclination in stress than in strain. This means that either the strain is almost constant and the stress changes or the strain is not constant, but the change in stress is larger compared to the change in strain. Thereby, Figure 7.43 (a) and (b) show results for symmetric one-way loading while symmetric two-way loading is depicted in (c) and (d). The permeability is 3.7×10−4m/s in (a) and (c) and 1 ×10−6m/s in (b) and (d). Either way for all cases, over the course of the calculation no pattern for displacement-controlled conditions can be seen. Some areas
7.5 Application of SANISAND model
(a) (b)
(c) (d)
Figure 7.43: Differentiation between load- and displacement-controlled (blue) test conditions around a monopile foundation for symmetric one-way loading (a, b) and symmetric two-way loading (c, d) and for a permeability of 3.7×10−4m/s (a, c) and 1× 10−6m/s (b, d).
arise in case of a smaller permeability in the upper pile region due to a larger excess pore pressure accumulation (Figure 7.43 (c,d)). While this very simplified analysis is not a sufficient criterion, it does suggest that cyclic load-controlled tests are representative for the element conditions. Further investigations are necessary to make a well-founded statement in this regard.
Besides the analysis of the load type, it is also possible to investigate how the cyclic loading characteristics change over the course of the calculation. Therefore, the CSR is calculated by using the octahedral stress prior to each individual cycle and the half of the span of the equivalent shear stress in order to calculate the cyclic shear stress amplitude (Figure 7.44).
A changed CSR value is derived for each new cycle. The results for point 8 m/0 m/-8 m are depicted in Figure 7.45 (a) with a comparison of the CSR which is calculated with the EPPE approach (with SANISAND as a constitutive model for a global load of 4 MN). The
(a) (b)
Figure 7.44: Equivalent shear stressσeq′ (a) and octahedral stressσ′oct (b) over number of cycles for point 8 m/0 m/-8 m.
same is subsequently done with the derivation of MSR. Figure 7.45 (b) shows the results for one integration point. The LTR is roughly at 20 and does not change significantly, which means that due to stress redistributions the load type within one soil element is not changed. The CSR for the explicit case is larger compared to the one from the implicit calculation. This can be seen as more conservative. In case of the MSR, the explicit calculation assumes a smaller value, but does not influence the soil response in a way the CSR does. The estimation of MSR in terms of the more influencing parameter CSR in the EPPE procedure is conservative and can, hence, be seen as reasonable.
(a) (b)
Figure 7.45: CSR (a) and MSR (b) from implicit calculation with comparison of explicit EPPE approach for point 8 m/0 m/-8 m based on an evaluation of a monotonic calculation with the SANISAND model.
7.5 Application of SANISAND model
Interim summary
An implicit calculation with the reference monopile model was performed and the results for the integration points were analysed in terms of different aspects. The constitutive model was also used in conjunction with the explicit EPPE approach. Some conclusions can be drawn based on the simplified analysis with a homogenous soil layer and the SANISAND model:
• The cyclic back-calculation of the initial reference system is not possible with the available version of the model. The SANISAND model overestimates the cyclic damage and shows some convergence problems. A calculation was possible with a smaller load.
• 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 Ru arises. In this case, the derived damage is less compared to the reference EPPE procedure. If a calculation with a newer SANISAND version is done, there may be a better agreement of induced damage. The results look very promising.
• The excess pore pressure ratio calculated explicitly is less compared to the implicitly calculatedRu field. However, this was to be expected because of the overestimation of the induced damage by the sophisticated soil model.
• When performing an implicit calculation, the resulting excess pore pressure field is, compared to the EPPE approach, more close to the pile and there are less individual areas in which liquefaction occurs, but there is a much more pronounced area on the passive side.
• For a different permeability and a different global load type, there are the expected changes in excess pore pressure build-up.
• The presence of load- or displacement-controlled conditions was investigated and it was shown that the model assumption of this thesis, namely load-controlled tests, is applicable. Even though displacement-controlled tests need to be used or a com-bination of both, the capacity would only be slightly larger, as presented in the last section.
• The derived CSR and MSR values do change over the course of the calculation, but the derived values for the very same boundary conditions calculated with the EPPE approach yield conservative CSR values. This means that the procedure can be applied in its current form. A more detailed analysis with a SANISAND-MS model is necessary in future .