MS7.5 - Dynamic Soil-Structure Interaction and Wave Propagation

Periodic wave propagation in a Euler-Bernoulli beam resting on a bilinear elastic foundation has been subject of recent analytical investigations. To realistically model embedding media with different reactions in compression and tensile conditions, different stiffnesses of the foundation for positive and negative values of the displacements have been considered. Several interesting behaviors have revealed by the analyses, such as veering-like phenomena with changes from single wave to multiple wave solution, and cusp points in the wave path. If interest is moved from macro- to micro- and nano-scale, materials and structures have been shown to display peculiar performances which are strongly related to their very small size. Indeed, the mechanical properties undergo a significant size effect, which in turn influences the static and dynamic behavior on the model. To account for the size effect in modelling the material behavior at the nanoscale, classical continuum elasticity, which is a scale free theory, cannot be resorted, so that nonlocal model have to be adopted. In this framework, a nonlocal model of Euler-Bernoulli beam resting on a bilinear elastic foundation is proposed, in order to possibly describe the behavior of carbon nanotubes embedded in elastic medium with different compression and tensile stiffnesses. The variational formulation is developed by resorting to a generic quadratic form of the elastic potential energy density. The ensuing equation of motion is governed by the sixth order spatial derivative, instead of the fourth order one obtained from the classical elasticity theory. The wave propagation is analytically investigated in order to describe the behavior of periodic waves with single and multi periodicity. The influence of scale length material parameters as well as foundation stiffnesses on the beam dynamical properties is discussed.

From the literature as well as from relevant standards, recommendations for the numerical modelling of soil-structure interaction problems involving seismic actions are well known, e.g. ASCE/SEI 4-16. For human-induced excitations very little specific guidance has been published in the past. However, while in the past FEM software for geotechnical engineering and FEM software for dynamic soil-structure problems were two sets with virtually no intersection, geotechnical FEM software now includes a dynamics feature, while general purpose software has been extended by means to model infinite half spaces. Hence, geotechnical engineering firms have powerful tools to extent their consulting business also into dynamics, and they certainly do. There are, however, many pitfalls when dealing with human-induced vibrations, which are beyond the requirements of seismic analyses. Using the generic example of a machine foundation on a homogeneous half space excited by harmonic loads with excitation frequency between 4 Hz and 64 Hz an extensive sensitivity study on mesh design, frequency domain vs. time domain analysis, time integration procedure and other numerical choices was conducted, which provided guidance on the impact of each of these choices on the vibration amplitude of the foundation as well as the free field. Furthermore, some focus is put on the limits set by the hardware availability in geotechnical consulting firms.

In the near future, geothermal energy is bound to play a critical role in the transition to sustainable energy sources. Micro-earthquakes may be induced by the underground operations performed at the geothermal power plants. In most cases, these vibrations are considered a general nuisance similar to the vibrations resulting from railway track operations. However, given the heightened public concern regarding induced seismicity, it is crucial to identify and analyze the effects of these micro-seismic events on the built environment. In this contribution, we present a numerical technique for the simulation of buildings subjected to geothermal induced seismicity. We apply a substructure method, where the soil is represented as a continuum using the integral transform method (ITM) and the building as a discrete structure using the finite element method (FEM). The soil is assumed to be horizontally layered and the coupled system linear. The structure model represents a low-rise residential building. The focus lies on the computation of the three-dimensional seismic free field displacements, which represents a preliminary step of the whole simulation workflow. The seismic excitation of soil-structure-interaction (SSI) systems is more baffling than the case of external loads applied to the structure: the dynamic response of the coupled system results from the transfer of vibrational energy from the seismic source to the foundation, after the wave propagates through the soil. Therefore, the form and the location of the load application can be open to more than one interpretation. It can be demonstrated that, for the semi-analytical elastodynamical solution, as in the ITM case, the seismic excitation can be converted to an equivalent load acting at the interaction nodes between soil and structure. To compute these equivalent loads, one has to compute the free field displacements at these interaction nodes. Here, we showcase the computation of the three-dimensional free field displacements caused by the induced far-field wave field. The latter is defined at a certain depth of the soil and can be arbitrarily distributed in space and time and is generated with a different technique, where the model encompasses the source and the far field.

Past earthquakes and contemporary research reveal that dynamic soil-structure interaction (SSI) could significantly alter the structural response of a building during an earthquake. These effects are functions of several parameters, including structural system, foundation type and geotechnical characteristics of the subsoil. Previous studies discovered that SSI effects are more prominent for structures supported by shallow foundations. However, increasing the foundation size for high-rise buildings tends to decrease the SSI effects in lateral deflections and foundation rocking. Further, the structural response of wall-frame structures differs from Moment-Resisting Frame (MRF) structural system. The present article extends earlier findings to investigate the influences of shallow foundation size on the seismic response of short and medium heights of reinforced concrete buildings resting on soft soil deposits. In addition, the inertial soil-structure interaction effects on MRF and wall-frame systems are studied and compared. A nonlinear Winkler foundation model (BNWF) is adopted to represent the soil domain. The model allows accounting for plastic deformation in the subsoil and considers the soil damping. The structural elements are modelled based on distributed plasticity mechanism to capture the inelastic response of the structures. A six-story and twelve-story building with various foundation sizes and different structural systems are numerically simulated in OpenSees software. The buildings are subjected to five moderate earthquake records for time history analysis in the time domain. The results are expressed in terms of period lengthening, lateral deflection, inter-story drift, and base shear forces. The results reveal a noticeable influence of foundation size on dynamic characteristics and seismic response of MRF structures. Increasing foundation length decreases the structures' lateral deflection and base shear forces. However, these effects are less observable for the short-height structure. On the other hand, the wall-frame system is relatively more influenced by SSI effects than the MRF system. The effects of period elongation and increasing base shear forces due to SSI are more noticeable for wall-frame systems, and these effects are maximum for stiffer structures. Similarly, the increase in maximum lateral displacement and storey drift is higher in wall-frame buildings compared to MRF structures, particularly in the lower stories of the building.