Studies of Apparent Seismic Wave Velocity

Apparent seismic wave velocities are studied by comparing the stress results obtained by a computer simulation with those obtained by a commonly used simplified engineering model. Two earth models with significantly different surface layers and two focal depths of energy release are used. The results from all four cases studied show that the apparent wave velocity at the free surface is determined by the properties of the material at depth where energy is released. A secondary, yet significant conclusion is the fact that the simplified plane wave propagation solution is a good predictor of the strains/stresses due to seismic waves, provided the appropriate apparent wave velocities are used

Improved Soil-Spring Method for Soil-Structure Interaction — Vertical Excitation

An improved Soil-Spring Method for vertical response analysis is proposed. The Soil-Spring Method belongs to the sub structuring methods of analyses for seismic soil-structure interaction. As originally developed the method has certain significant limitations. The proposed improvement is essentially iterative where, successively, layering, embedment, soil damping and frequency-dependent effects are introduced and adjusted until acceptable convergence is achieved. Additionally, input motion for embedded structures is specified using a simple procedure. The methodology is applied to the Lotung 1/4-scale containment model for three recorded earthquakes. The comparisons of the response results with the recorded data and with results obtained using state-of-the-art methods definitely establishes the improved Soil-Spring Method for seismic soil structure interaction as an analysis tool at least comparable to the more sophisticated methods

Infinitely many solutions for a Dirichlet boundary value problem depending on two parameters

In this paper, using Ricceri\u27s variational principle, we prove the existence of infinitely many weak solutions for a Dirichlet doubly eigenvalue boundary value problem

The Learning from the Large Scale Lotung Soil-Structure Interaction Experiments

Blind prediction analyses and subsequent correlation studies of a 1/4-scale reinforced concrete containment model constructed at Lotung, Taiwan subject to forced vibration tests and actual earthquakes are evaluated with the objective of validating soil-structure interaction (SSI) analysis methodologies commonly used in U.S. practice. The SSI methods used range from simple soil-spring representation to more complex finite-element methods and sub structuring techniques. Both forced vibration test (FVT) data and actual earthquake induced response data have been obtained for use in validating selected SSI analysis methodologies. Considering that for forced vibration tests only the stiffness and damping characteristics of the foundation are required (complexities of site response, wave scattering and stiffness degradation of soils are absent), the FVT evaluation shows that acceptable frequency predictions can be obtained by most of the methods; however, soil damping as obtained from geophysical methods does not seem to account for the total energy dissipation during SSI. A number of insights have been obtained with respect to the validity of SSI analysis methodologies for earthquake response. Among these are the following: vertical wave propagation assumption in performing SSI is adequate to describe the wave field; equivalent linear analysis of soil response for SSI analysis, such as performed by the SHAKE code, provides acceptable results; a significant but non-permanent degradation of soil modulus occurs during earthquakes; the development of soil stiffness degradation and damping curves as a function of strain, based on geophysical and laboratory tests, requires improvement to reduce variability and uncertainty; backfill stiffness plays an important role in determining impedance functions and possibly input motions; scattering of ground motion due to embedment is an important element in performing SSI analysis; more than the calculational techniques, the differences in response predictions are due to the modeling of the soil-structure system

Nontrivial solutions for nonlinear algebraic systems via a local minimum theorem for functionals

In this article, we use a critical point theorem (local minimum result) for differentiable functionals to prove the existence of at least one nontrivial solution for a nonlinear algebraic system with a parameter. Our goal is achieved by requiring an appropriate asymptotic behavior of the nonlinear term at zero. Some applications to discrete equations are also presented