Parameters used in this paper for analysis are

Electrical resistance, voltage and temperature .Electrical Resistance is the

measure of how much a flow of current is opposed in the circuit. Voltage

between two point is a measure of work done per unit charge against a static

electric field to move a charge from one point to other . Temperature for soil is

measured using thermistor in field.

Various study have been conducted in pavement

engineering field to better understand the effect of frost in pavement design. To understand the

environmental factors effect on the pavement surface Seasonal monitoring

program (SMP) was introduced in 1992. SMP used various LTPP location sites for

its study of frost which included around 64 sections all around . As part of

this program freeze state is to be monitored

in the base , sub base and

subgrade of the pavement in US and Canada. This program uses electrical

resistivity and temperature sensor

technique. 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 diameter

hole. The probe consist of 36 wired metal electrodes spaced at 51 mm apart.

Measurement of voltage and current is done in field, while resistance is

calculated by dividing voltage by current. Resistivity is

calculated by dividing the voltage drop between two inner electrode by the

current passing through outer two electrode and which is then multiplied by geometric

factor. Soil temperature data are collected in field using 18 thermistors which

at 18 depths. In field thermistors are installed in a 0.25 m dia. hole. For SMP

study temperature data were used along with ER data to determine the Frost

penetration. All of these ER data are

interpreted by using the interactive program called Frost.

Electrical

resistivity technique is one of the many techniques to calculate frost depth in

pavement. It is based on the fact that electrical resistivity of soil increases

drastically when soil freezes. The method involves calculating electrical

resistivity and resistance using metal electrodes in field.

THEORETICAL

CONSIDERATION FOR ER DATA

Distilled water has relatively very high

volumetric resistivity, upto several hundred megaohms. But the water containing

even the small amount of impurities like in the soil, resistivity decreases to upto 20,000 ohms as there will be some particles to

conduct charge. The groundwater if frozen will have an abrupt rise in the electrical resistivity due to the

restriction offered to the charge carrier which is greater than

100,000 ohms. So we know that electrical resistance of soil increases if the

liquid is in frozen state as a result we can determine the condition of

subsurface water state.

Another

widely used method to predict the frost

penetration depth is by using the temperature profile of soil as function of

depth where freezing condition is assumed to exist at temperature below 00C.

Frost prediction using temperature usually

measures the depth accurately. But it is

not advisable at all condition. The freeze point of a soil changes if there is

presence of any mineral, salt, chemicals and other substance. During such

condition it is advisable to use other parameters too, to accurately predict

the frost depth in pavement. Due to this reason use of both ER data and temperature is advisable as one

type complements and increase the accuracy level of the other. Also before use

of resistivity parameters two things needs to be properly analyzed.

1) Minimum amount of moisture content in the soil

in order to make the resistance data meaningful.

2) Minimum amount of surface area required to ensure a reliable

reading.

EXISTING MODELS

Existing model for frost depth can be

classified into empirical, mechanistic

and mechanistic empirical models. These models are developed using an input

data to develop a function for output. Some might require input like heat capacity of soil, water whereas

other require only moisture content in the soil.

SHAW model is one very good approach to estimate the freeze

depth especially in the upper region of the soil. The model was initially

developed by Flerchinger and Saxton (1988 and 1989). This model accounts for

various complicated factors like melting, accumulation of snow,

Freezing/thawing of soil and other factors. The model is based on finite

differential approach of water and heat transfer in soil profile. The

relationship in SHAW model uses the parameters like latent heat of

fusion, latent heat of vaporization, specific heat capacity, volumetric ice

content.

Variation of air temperature represented as air

freezing index is another parameter that effect the frost depth. The first

known theoretical formula to calculate frost depth is Stefan equation. Stefan

equation takes freezing index, thermal conductivity, volumetric latent heat of

fusion into consideration for frost depth calculation. The equation is

represented as