Frequency analysis of time‐domain reflectometry (TDR) with application to dielectric spectroscopy of soil constituents

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 707-718 ◽  
Author(s):  
Richard Friel ◽  
Dani Or
Keyword(s):  
Dielectric Properties ◽  
Dielectric Permittivity ◽  
Frequency Domain ◽  
Time Domain ◽  
Dominant Role ◽  
Primary Objective ◽  
Time Domain Reflectometry ◽  
Complete Picture ◽  
Frequency Dependent ◽  
Additional Information

Standard analyses of time‐domain reflectometry (TDR) waveforms in environmental sciences use traveltime along waveguides and reflection amplitude to infer water content and bulk electrical conductivity, respectively. TDR waveforms contain additional information on the frequency‐dependent dielectric permittivity of media, which can be extracted through transformation of TDR waveforms into the frequency domain. The primary objective of this study was to provide a more complete picture of TDR responses in the frequency domain and to improve estimation of dielectric properties. The frequency content of TDR waveforms interacting with various constituents was measured and compared with predictions based on known dielectric properties and waveguide geometries. The study highlights the dominant role of the S11 scatter function, which describes how a TDR signal is modified by media properties and probe configuration. Scatter functions derived from transformed TDR waveforms into the frequency domain were used for estimation of frequency‐dependent dielectric properties of wet soils. The main results were (1) a more complete picture of TDR waveforms in the frequency domain; (2) estimation and use of scatter functions for TDR‐based dielectric permittivity estimation; and (3) highlights of potential usefulness and limitations of a commonly used TDR cable tester (Tektronix 1502B) and waveguide design for estimation of frequency‐dependent dielectric properties of porous media.

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

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