Study of nonlinear dynamic soil response to harmonic excitation using semi-analytical and numerical methods

Abstract

The strive for cleaner energy sources is one of the most demanding problems the world faces today. The role of offshore wind in the energy transition is becoming increasingly relevant. One of the areas where the industry expects to reduce conservatism and uncertainty in design is the interaction of the foundations of offshore wind turbines with the surrounding soil. Currently, it is known that the dynamic behavior and natural frequencies of the offshore wind turbines in design and in actual measurements do not match. This is mainly the result of inaccuracy and lack of understanding of the soil behavior and the interaction with the foundation piles. Therefore, this study is aimed at developing analytical and numerical methods to describe the nonlinear dynamic soil response as excited by a harmonic excitation representing a Dynamic Cone Pressure Meter. Measuring the dynamic soil properties more accurately and using them in design will reduce the uncertainties and conservatism in the design of foundation piles.

This study is divided in two main parts. In the first part a soil column is modeled. The numerical and semi-analytical methods to describe the one-dimensional linear and nonlinear dynamic soil response to a prescribed displacement are developed. The linear solution is obtained first since it is easier to get and interpret. It is also used to study the extent to which the nonlinearity influences the soil behavior. In the nonlinear analysis strain-dependent shear modulus and damping ratio are used. These are essential input parameters for conducting a ground response analysis. In this study, the curves constructed using the hyperbolic soil model are used for the expressions of strain-dependent shear modulus and damping.

In the second part of the study, the cavity expansion problem is modeled to simulate a Dynamic Cone Pressure Meter (DCPM) that will be used for in-situ investigation of dynamic soil properties. The response of the soil to a prescribed displacement/ stress at the cavity is found using the numerical method and the HBM. Using the HBM different assumed solutions are implemented to study the influence of the higher harmonics. The HBM is assessed for both a finite and an infinite medium, meaning when standing waves and propagating waves are formed respectively.

Overall, the HBM was found to have a comparable level of accuracy with the numerical method in modelling the nonlinear response of the soil column and the cavity problem. The difference results due to the limited number of harmonics used in the HBM and also due to the tolerances of the MALAB solvers used such as bvp5c and ode45. Both methods show that the nonlinearity affects the response considerably. As the nonlinearity increases, the amplitude and the phase shift of the response change. While it may be hard to interpret the results judging from the numerical solution only, they become much easier to understand by comparing them with the harmonic balance method. Moreover, while it takes hours to obtain the numerical solutions for different forcing frequencies, the frequency response function is obtained in a couple of minutes through the harmonic balance method. This shows that the harmonic balance method is a computationally efficient and powerful tool. Overall this study is an important step of the project that aims to develop a prototype of a DCPM for in-situ soil investigations. The DCPM will pave the way for the reduction of uncertainty in the soil-structure interaction models and help the offshore wind industry to increase cost efficiency while harvesting energy from a sustainable natural resource.