This paper describes a comparison study on three different technologies (i.e., thermocouple, electrical resistivity probe and Time Domain Reflectometry (TDR)) that are commonly used for frost measurement. Specially, the paper developed an analyses procedure to estimate the freezing-thawing status based on the dielectric properties of freezing soil. Experiments were conducted where the data of temperature, electrical resistivity, and dielectric constant were simultaneously monitored during the freezing/thawing process. The comparison uncovered the advantages and limitations of these technologies for frost measurement. The experimental results indicated that TDR measured soil dielectric constant clearly indicates the different stages of the freezing/thawing process. Analyses method was developed to determine not only the onset of freezing or thawing, but also the extent of their development. This is a major advantage of TDR over other technologies.
In cold regions, freeze-thaw cycles induce ground settlement and cause the loss of load bearing capacity of subgrades. Soils can be very strong when they are frozen during the winter but become substantially weak in the spring when they are thawing [
A few technologies are available for frost measurement. All have certain advantages. However, their reliability and accuracy to measure freezing-thawing under field conditions are limited. The principles of common types of frost measurement devices are summarized in the following context.
Other technologies that have been employed for frost measurement include
Based on discussions with engineers in professional service, there are high expectations on further improving the existing freeze-thaw instrumentation. This motivates the authors to pursue this study. The goal is to review and compare the principles of common technologies for frost measurement.
TDR is a guide radar technology. It utilizes the propagation of electromagnetic wave to measure materials properties. The configuration of a typical TDR system as specified in ASTM D6780 [
TDR system schematic: (a) reflections in the TDR system; and (b) resulting TDR waveform.
Photo of the TDR system used in this study.
Information commonly obtained on material electrical properties include the apparent dielectric constant
The principle of TDR technology has been widely applied in different areas. Milestone for its applications in soils is set by the pioneering work of Topp et al. [
The travel velocity,
(a) Example of typical TDR signal; (b) influence of water content on TDR signals at similar dry densities.
Soils are generally multiphased systems consisting of water (both in free and constraint status), soil solids, and air. Water has a dielectric constant of around 81 at 20°C, which is much larger than that of soil solids (typically around 3 to 7) or air (around 1). The large contrast in the dielectric constant of water versus the other phases makes TDR signals very sensitive to the soil water content (Figure
Topp et al. [
Siddiqui and Drnevich [
When there is a phase change between water and ice, significant change in the dielectric properties of bulk soil specimen occurs. This is due to the fact that the dielectric constant of ice is approximately equal to that of solids, which is much smaller than the dielectric constant of free water. The effects of freezing/thawing on the soil dielectric constant are similar to those of drying/wetting. This makes it possible for TDR to measure the phase transition between soil water and ice.
TDR measures bulk electrical conductivity (
Dalton’s approach to obtain bulk electrical conductivity is based on analyzing the TDR signal attenuation and assumes the TDR signal decays exponentially as it travels along the measurement probe [
To compensate for the shortcomings of Dalton’s approach, Yanuka et al. [
Definitions of different voltage levels for a TDR waveform.
Although ( It could be difficult, if not impossible, to pick the characteristic voltages levels
Another approach to obtain bulk electrical conductivity is from the long-term response of a TDR system. This idea was initially explored as an effort to directly interpret the TDR waveforms from time domain signals [
Analysis using the transmission line theory indicated that the long-term responses of TDR system are equivalent to the analyses by a static circuit model [
The soundness of (
TDR measured electrical conductivity versus electrical conductivity meter measurement on bulk water.
The electrical resistivity,
This approach was used for calculating the bulk soil electrical resistivity in this paper.
An experimental program was conducted to compare the performance of frost measurement based on the temperature, electrical resistivity, and dielectric constant principles. An ASTM standard fine sand was used in the testing program. The soil specimens were first compacted into a compaction mold using standard procedures [
The temperature process were measured by a unique type of temperature sensor iButton@. The iButton@ integrates thermocouple with a processor and storage unit. It can be programmed to automatically sampling and storing the temperature data at preset time intervals. The data can then be retrieved by use of a reading unit (Figure
Photo of iButton and reader unit.
A metallic rod was installed in the center of the mold using a guide template. (Guide EM wave TDR requires at least two conductors as waveguide. The metallic rod and metallic mold act as one of the conductors of the waveguide, resp. EM wave propagate along the direction of the rod in the space between the metallic rod and the metallic mold [
Photo of specimens placed inside freezer
After the soil specimen was completely frozen under around
The dielectric constant, electrical resistivity, and temperature process in soil during the freezing/thawing process by analyzing experimental data. The experiments were repeated on a few specimens and consistent results were obtained. The results representative of experimental observations are shown in the following.
The use of temperature method for freezing-thawing measurement is based on the fact that the temperature of water remains at the freezing point during the crystallization process. Figure
(a) Monitored temperature evolutions during freezing process; (b) temperature during the thawing process (note: iButton 1: located around 1 inch from top surface; iButton 2: located around 1 inch from bottom of soil specimen).
The monitored temperature change during the thawing process resembles the inverse freezing process.
From the experimental observations, it can be seen that given accurately determined melting point, temperature method is able to tell when complete freezing or thawing occurs. It, however, does not tell the extent of freezing/thawing at a given time.
Advantages of temperature method include it is simple and requires inexpensive instrument.
As is known, salt in soil water can reduce its freezing point. This effect can be significant for cold regions where large amount of deicing salt are sprayed during the winter. From physics, the melting point of soil water is also affected by the external pressure. Thawing caused by traffic loads cannot be detected from soil temperature alone.
Figure
Monitored electrical resistivity and electrical conductivity: (a) freezing process; (b) thawing process.
For freezing process, the electrical resistivity continues to increase until reach a relatively stable value (which is indicative of soil being completely frozen). It, however, has no indication of the initialization of the soil water freezing process. On the other hand, during the thawing process, the electrical resistivity continues to decrease. There is no indication when the ice is completely thawed.
From the experimental data, it can be concluded that the electrical resistivity might not be a robust indicator for accurately determining the onset or completion of soil water freezing or thawing. This is because the electrical resistivity is not only affected by the freezing-thawing status, but also many other factors such as the soil structure, the hydraulic conductivity, and so forth.
Examples of TDR monitored signals during freezing are shown in Figure
Example TDR signals during the freezing process.
Figures
TDR monitored dielectric constant
As shown in these figures, different stages of freezing/thawing can be clearly identified from the trend of measured dielectric constant. These different freezing/thawing stages are noted in the figures.
From the definition, the degree of freezing, Si, at a certain point is defined as the percent of soil water that has turned into ice
The relationship between the gravimetric water content and the volumetric water content is
Due to the small magnitude of volume change, the density of soil solids during the freezing-thawing process can be assumed to be constant. Substituting (
By use of Siddiqui-Drnevich equation ([
Considering the fact that the dielectric constant of soils are temperature-dependent, the dielectric constants in (
Due to the range of temperature tested in this previous study, the relationship is applicable to soils in the temperature range of above freezing and under 40°C.
This method is extended to normalize the soil dielectric constant to 0°C. A convenient reference temperature is 0°C, that is, the freezing point of bulk water before ice starts to form. We first normalized the dielectric constant to 20°C. And then apply the TCF between 20°C and 0°C (0.97 and 1.10, resp., from (
With the dielectric constant of soils normalized to that at 0°C, (
Similarly the concept of degree of thawing,
With (
Degree of freezing/thawing from TDR measured dielectric constant.
A comparison study was conducted to evaluate three commonly used technologies for frost measurement. The principles of these technologies were first reviewed. Freezing-thawing experiments were conducted on soil specimens where the electrical resistivity, temperature, and dielectric constant data were simultaneously monitored. The comparison showed that methods based on temperature or electrical resistivity measurement cannot identify the extent of freezing/thawing in soils. They can at best serve as indicator of the complete frozen or completely thaw status. In the meanwhile, TDR technology was found to be able to accurately identify the various stages in the freeze/thaw process (such as the beginning and ending point of freeze/thaw process, the percent of soil water transition between liquid and solid status). A simple analyses procedure is developed, where the degree of freezing/thawing can be directly calculated from TDR measured dielectric constant. Fusion of different methods such as TDR and temperature or TDR and electrical resistivity also has potential to further improve the reliability in accurate freezing/thawing measurement.
The authors appreciate the support by staff of Cleveland Water Department (Alex Margevicius, Don Heuer, Teddy Tzeng, and Jonathan Brooks). The authors would also like to thank Roger Green of Ohio Department of Transportation for his comments on the practice issue of frost measurement. This work is partially supported by a REU grant from the National Science Foundation.