Structure-soil interaction for horizontally polarised shear waves

Abstract

When modelling a structure-soil system, interaction stresses at the interface of the structure and the surface of soil layer influence the dynamic behaviour of the system. These interaction stresses are not accounted for in many simplified models that evaluate the behaviour of the soil layer and the structure separately. Modelling a fully coupled system requires extensive computation that changes with every alteration to the model. Having a general framework of equations that can be easily adapted to each specific case can therefor be of great value.
In this thesis, we model the soil layer as a homogeneous, elastic continuum with two boundary conditions. One boundary condition is a kinematic excitation at the bottom of the soil layer, which is formulated in terms of a Fourier series with prescribed coefficients. The boundary condition at the top of the soil layer is a stress function, formulated as a Fourier series with unknown coefficients. The general solution of the equation of motion is then solved in terms of these known and unknown coefficients. The structure is modelled as an inextensible mass or as a mass-spring system, which is excited by an external force at the interface with the soil layer, formulated in the same Fourier terms and unknown coefficients as for the soil layer. The unknown coefficients are solved by means of an interface condition between the soil layer and the structure.
This computational method provides an equation of motion for the soil layer that depends on the applied structure model. When the structure model is altered, for example by a mass-spring system instead of a single mass, only the interface condition has to be reevaluated to find a solution for the equation of motion of the soil layer and the structure. This thesis shows that this computational model, where we write the specific solution to the equation of motion in terms of unknown Fourier series coefficients, does indeed work.
By analysing the stress distribution at the interface between the soil layer and the structure for different frequencies, results show that the stress is resonant at the natural frequencies of the system. The stress distribution is nearly uniform for most frequencies, but the stresses increase at the sides of the interface at the natural frequencies. It can also be shown that the interaction stresses increase with the frequency.
When analysing various transfer functions, the influence of the stress interaction between the soil layer and the structure is most visible. Computing a fully coupled system shows that the natural frequencies of the system are affected by the structure on the top of the soil layer. First, the natural frequencies are partially shifted to lower frequencies. Secondly, not all natural frequencies lead to infinite resonance: the transfer functions show an alternating pattern of finite and infinite responses to the excitation at the natural frequencies.
The transfer functions of added mass-spring systems, for example, used to model multi story buildings, also shows the influence of the interaction stress compared to the isolated model of the structure. The coupled system shows again that the natural frequencies are partially shifted and not all natural frequencies lead to infinite resonance.
It can be concluded that the interaction stress in a fully coupled system has a significant impact on the system and should be taken into account when modelling a structure-soil system. The tested computational method is good way to do so.