# Parameters increases drastically when soil freezes. The method

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.

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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

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