# Degradation of the Pile Load-Bearing Behaviour under Cyclic Axial Loading

Led by: | Prof. Dr.-Ing. Martin Achmus |

Team: | Dipl.-Ing. Dominik Schäfer, Dr.-Ing. Khalid Abdel-Rahman |

Year: | 2017 |

Funding: | BMWi |

Duration: | 02/2013 – 07/2017 |

Is Finished: | yes |

### Beschreibung:

The research project is integrated as sub-project 3.11 and the associated model tests as sub-project 4.7 in the collaborative project "Service life - research on the WTG support structures in the* alpha ventus* offshore test field – GIGAWIND *life*".

Foundation piles of resolved support structures for offshore wind turbines (OWT) are often subject to highly cyclic tensile and compressive loads due to wind and wave loads. It is known from a few test loads and modelling tests that cyclically axially loaded piles can exhibit a significant reduction in load-bearing capacity compared to their static load-bearing capacity. The main reasons for this are considered to be the compaction of the sands close to the pile casing as a result of the cyclic shear loads and thus the reduction of the radial stress as well as the reduction of the frictional contact from the ultimate shear strength to the residual shear strength.

Various authors have developed interaction diagrams from the few available tests. However, different soil parameters or pile geometries and stiffness cannot be taken into account with such diagrams. A generally valid calculation approach for this problem is currently not available.

A two-dimensional axially symmetrical model with four-node axially symmetrical elements (CAX4), which is calculated in the finite element programme ABAQUS (Abaqus 2012), is used to determine the degradation of the pile load-bearing capacity as a result of all the influencing variables mentioned above. In the first calculation step, the initial stress state of the soil is determined and then the corresponding soil elements are replaced by the pile with its own weight and the required contact conditions.

The characteristic static pile load-bearing capacity R_{k} is now determined for varying soil parameters and pile geometries and stiffnesses by loading the pile in tension until failure. This allows different mean X_{mitt} and cyclic load levels X_{zyk} to be defined and the pile to be loaded cyclically.

In the initial loading cycle, the shear strains occurring here for each element γ_{i} are calculated from the main strain components ε_{1}, ε_{2}, und ε_{3} according to equation (1) and their extremes γ_{max,i} und γ_{min,i} are used to calculate the shear strain amplitude γ_{xy,i} according to equation (2) (Fig. 3).

γ_{i} = (2/3⋅((ε_{1}-ε_{2})^{2}+(ε_{2}-ε3)^{2}+(ε_{1}-ε_{3})^{2})^{1/2} (1)

γ_{xy,i }= (γ_{max,i} - γ_{min,i})/2_{ } (2)

Silver & Seeds (1971) investigated the normal volume expansion as a result of cyclic shear loading in a large number of displacement-controlled single shear tests on sand, varying the storage density, superimposed load and shear strain over the number of cycles (Fig. 4).

Analytically, the observed cyclic contractance can be described as follows:

ε_{c} = (10^{1,71-2,82⋅ID+0,94⋅ID2} ⋅10^{1,23⋅logyxy})⋅(0,3+0,7⋅logN) (3)

The normal volume strain calculated from this is applied to the soil elements before the start of the next load cycle, which leads to a reduction in the radial stresses on the pile shell and consequently to a degradation of the pile bearing capacity. Due to the almost elastic behaviour of soil materials at very small strains, cyclic contractance is only applied to the soil elements when the limit shear strain γlim = 5-10-5 for sands according to Vucetić (1994) is exceeded.

The number of cycles N achieved until the pile breaks can be plotted in interaction diagrams (Fig. 2) for different pile geometries and soil properties. Piles that endure cycle numbers N > 1·10^{10} are assessed as cyclically stable and their accumulated pile heave is analysed.