Parameters used in this paper for analysis areElectrical resistance, voltage and temperature .Electrical Resistance is themeasure of how much a flow of current is opposed in the circuit. Voltagebetween two point is a measure of work done per unit charge against a staticelectric field to move a charge from one point to other . Temperature for soil ismeasured using thermistor in field.
Various study have been conducted in pavementengineering field to better understand the effect of frost in pavement design. To understand theenvironmental factors effect on the pavement surface Seasonal monitoringprogram (SMP) was introduced in 1992. SMP used various LTPP location sites forits study of frost which included around 64 sections all around . As part ofthis program freeze state is to be monitored in the base , sub base andsubgrade of the pavement in US and Canada. This program uses electricalresistivity and temperature sensortechnique. Resistivity data include resistance, voltage, and resistivity. At the selected SMP sites collection of ER data are done every month, every other year using electrical resistivity probes.
The resistivity probe is permanently installed in the 0.25 m diameterhole. The probe consist of 36 wired metal electrodes spaced at 51 mm apart.Measurement of voltage and current is done in field, while resistance iscalculated by dividing voltage by current. Resistivity iscalculated by dividing the voltage drop between two inner electrode by thecurrent passing through outer two electrode and which is then multiplied by geometricfactor.
Soil temperature data are collected in field using 18 thermistors whichat 18 depths. In field thermistors are installed in a 0.25 m dia.
hole. For SMPstudy temperature data were used along with ER data to determine the Frostpenetration. All of these ER data areinterpreted by using the interactive program called Frost. Electricalresistivity technique is one of the many techniques to calculate frost depth inpavement. It is based on the fact that electrical resistivity of soil increasesdrastically when soil freezes. The method involves calculating electricalresistivity and resistance using metal electrodes in field. THEORETICALCONSIDERATION FOR ER DATADistilled water has relatively very highvolumetric resistivity, upto several hundred megaohms.
But the water containingeven the small amount of impurities like in the soil, resistivity decreases to upto 20,000 ohms as there will be some particles toconduct charge. The groundwater if frozen will have an abrupt rise in the electrical resistivity due to therestriction offered to the charge carrier which is greater than100,000 ohms. So we know that electrical resistance of soil increases if theliquid is in frozen state as a result we can determine the condition ofsubsurface water state.Anotherwidely used method to predict the frostpenetration depth is by using the temperature profile of soil as function ofdepth where freezing condition is assumed to exist at temperature below 00C.Frost prediction using temperature usuallymeasures the depth accurately. But it isnot advisable at all condition. The freeze point of a soil changes if there ispresence of any mineral, salt, chemicals and other substance.
During suchcondition it is advisable to use other parameters too, to accurately predictthe frost depth in pavement. Due to this reason use of both ER data and temperature is advisable as onetype complements and increase the accuracy level of the other. Also before useof resistivity parameters two things needs to be properly analyzed. 1) Minimum amount of moisture content in the soilin order to make the resistance data meaningful.
2) Minimum amount of surface area required to ensure a reliablereading. EXISTING MODELSExisting model for frost depth can beclassified into empirical, mechanisticand mechanistic empirical models. These models are developed using an inputdata to develop a function for output. Some might require input like heat capacity of soil, water whereasother require only moisture content in the soil.SHAW model is one very good approach to estimate the freezedepth especially in the upper region of the soil. The model was initiallydeveloped by Flerchinger and Saxton (1988 and 1989).
This model accounts forvarious complicated factors like melting, accumulation of snow,Freezing/thawing of soil and other factors. The model is based on finitedifferential approach of water and heat transfer in soil profile. Therelationship in SHAW model uses the parameters like latent heat offusion, latent heat of vaporization, specific heat capacity, volumetric icecontent. Variation of air temperature represented as airfreezing index is another parameter that effect the frost depth. The firstknown theoretical formula to calculate frost depth is Stefan equation. Stefanequation takes freezing index, thermal conductivity, volumetric latent heat offusion into consideration for frost depth calculation. The equation isrepresented as