6.2 Back-calculation with results from field and 1g medium-scale tests
6.2.4 Conclusion
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.
7 Application of estimation methods on monopile foundations
The developed excess pore pressure estimation concept has been presented in Chapter 6.
The general soil response was evaluated for a reference soil from high-quality laboratory results (Chapter 5). Regression analyses have been performed on the results of the cyclic element tests and furthermore contour plots were derived.
In the following, different variations are applied to the developed reference estimation procedure and the influence on the overall bearing behaviour of different modifications to the design process will be shown. A reference monopile will be used with a diameter of D = 9 m and an embedded length of L = 27 m with a load eccentricity of e = 40 m.
The wall thickness is assumed to be constant with t = 100 mm. An equivalent num-ber of cycles was set to Neq = 30 for all calculations. The sand has a permeability of kf = 3.7×10−4m/s for a relative density of Dr = 0.85. The storm period is assumed to be T = 10 s. The ultimate monotonic bearing capacity was derived from monotonic p-y springs with the approach according to Thieken (2015) (Fult = 68 MN from Figure 7.1).
The ULS load is assumed to be in the range of 30% of the bearing load. For the cyclic part, the ULS load (or the maximum load from the design storm) is usually applied only a few times. In order to have a larger number of equivalent cycles and to be able to show its influence, the cyclic load was chosen to be roughly 20% of the bearing load with 30 cycles. This is by no means an estimation of structural loads, but more a derivation of a reasonable load level to investigate the structural response and influencing parameters.
For comparison, the load at a deformation criterion of 0.1D is 37.4 MN. The monotonic load-displacement curve from the numerical calculation is also depicted in Figure 7.1 and leads to a similar bearing capacity for the 0.1D criterion (Figure 7.1). The mono-pile is investigated under a symmetric one-way load with a maximum load of 13.6 MN (Fmin = 0 MN, Fmax = 13.6 MN) (i.e. the corresponding maximum moment with respect to soil surface oscillates between Mmin = 0 MNm and Mmax = 544 MNm). Hence, the cyclic values are ζc = 0 and ζb = 0.20 (orζb = 0.367, depending on the used criterion for the definition of ultimate bearing capacity).
7.1 Numerical model for the reference system
The described analysis was carried out in the finite element program ABAQUS. The three-dimensional numerical model of a monopile consists of approximately 30,000 C3D8(P) elements. Based on the symmetry only one half is modelled to reduce the computational
(a) (b)
Figure 7.1: Load-displacement curve (a) and moment-rotation curve (b) for the reference mo-nopile from analytical calculation with results from finite element model.
effort (Figure 7.2). In the preliminary analyses the mesh resolution and the model di-mension have been optimized to reach an appropriate balance of computational effort and sufficiently accurate results. The evaluation was done with MATLAB (MathWorks, 2021).
Figure 7.2: Numerical model of the reference system in the finite element software ABAQUS.
The final model has a width of 12-times the diameter and a depth of 1.5-times the pile length. The model is fixed in all degrees of freedom at the bottom, in normal direction at the periphery and in y-direction at the symmetry plane. The monopile is modelled with a linear-elastic behaviour with a Young’s modulusE = 2.1×108kN/m2, a Poisson’s ratio ν = 0.27 and a buoyant steel unit weight γsteel′ = 68 kN/m3. The load is applied on a reference point which is connected to the monopile with a coupling constraint.
The soil parameters are shown in Table 7.1. The initial horizontal earth pressure at rest
7.1 Numerical model for the reference system
was calculated according to k0 = 1−sin(φ′) (Jaky, 1944) and the angle of dilatancy with ψ = φ′ −30 (non-associated flow rule). Regarding the plasticity of the soil, an elasto-plastic material law with Mohr-Coulomb failure criterion and stress-dependent stiffness was used. The linear-elastic, ideal-plastic model with stress dependent stiffness modulus considers all main key mechanism of the soil response. A more sophisticated model with hardening will yield more accurate results, but the increased calibration process is not necessary for the excess pore pressure estimation method. Also the differentiation between the initial stiffness and the un- and reloading stiffness may increase accuracy, but will not lead to substantially different results. The main objective is to estimate the stresses within the soil elements which are then transferred to stress ratios (CSR, MSR, LTR) in order to derive the cyclic response. Especially, in case of this simplified procedure, the Mohr-Coulomb material law is sufficiently accurate and does only need a small number of (five) input parameters, which all have clear physical meanings. Nevertheless, this constitutive model could be interchanged if needed (see Section 7.5). The stress dependent stiffness modulus, i.e. the oedometric stiffness, is considered with the following equation:
Es =κ p′ref σoct′ p′ref
!m
(7.1) Herein, p′ref is the atmospheric reference stress (100 kPa), σoct′ is the current octahedral effective stress in the considered soil element and κ and λ are soil dependent stiffness parameters.
Table 7.1:Soil properties for numerical calculation.
κ λ ν φ′ c δ kf ψ γ′
[1] [1] [1] [◦] [kPa] [◦] [m/s] [◦] [kN/m3] 670 0.5 0.25 38 0.1 2/3φ′ 3.7×10−4 8 11
For the contact modelling the elasto-plastic master-slave concept between the monopile and the adjusted soil was used in a way that a connection between the soil and the structure is present as well as their relative displacement is possible. The maximum coefficient of friction in the sand-steel interface is set to δ= 2/3φ′ and linearly mobilized within an elastic slip value of duel = 1 mm. The calculation is executed in several steps.
First, the initial conditions are set, in which the horizontal stress is calculated with the relation of Jaky (1944). Subsequently, the monopile and the contact are activated with a wished-in-place method. Afterwards, the mean lateral and the related moment and eventually the maximum lateral load are applied. For the consolidation analysis, the ABAQUS model is extended in order to enable a coupled pore fluid and stress analysis. For the hydraulic consolidation analysis the drained model was converted into a simple linear-elastic coupled model by changing the element type to C3D8P. The boundary conditions were adapted for the additional degree of freedom. The weight of the pore fluid is set to γwater = 10 kN/m3. The bulk modulus of the pore fluid Kw in the coupled analysis was set to 2.092×106kPa for T = 10◦C.