NEHRP Clearinghouse
- Title
- Dispersion Relations of an Elastic Rod Embedded in an Elastic Soil.
- File
- PB81120404.pdf
- Author(s)
- Parnes, R.
- Source
- National Science Foundation, Washington, DC. Engineering and Applied Science., February 1980, 29 p.
- Identifying Number(s)
- 16
- Abstract
- Failure of buried pipes during earthquakes is believed to be due to resonant or near-resonant behavior under certain prescribed ground motion inputs. For any given wavelength, the resonant frequencies of the system are immediately known once the phase velocities of the system are established. These phase velocities are dependent on the wavelengths of waves propagating in the system and thus reveal the dispersive character of the system. The model considered is represented by an elastic rod of radius 'a' embedded in a linear elastic medium, and the interaction between the surrounding soil and pipe is assumed to occur through a shear mechanism acting at the interface. The problem is then to consider at what velocities a wave of wavelength lambda can propagate under steady state conditions. Results are presented in the form of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase velocities are established.
- Keywords
- Dispersion relations; Seismic waves; Subsurface structures; Earthquake engineering; Resonant frequency; Soil dynamics; Elastic shells; Pipelines; Earthquakes