In this study, the author has studied the following soil parameters and their relationship at various temperatures. The study is performed on locally available soil and the soil gradation curve after sieve analysis suggests that the soil is well-graded sand. The Cu and Cc of the soil found is 8.33 and 1.09 respectively. The gradation curve for the soil is shown in figure 3.1.
After performing the experimental studies on frozen soil, the following relationship between parameters of frozen and unfrozen soil at varying temperatures are found.
Weight Function
The weight of frozen soil can be found if, the weight of the same soil at room temperature, its water content and the temperature at which weight is to be determined is known. By entering the data obtained in the laboratory, Eureqa software gives the following relationships (Fig. 3.2) The weight function would be:
W’= f(W,w, T) ……..(7)
where w is the water content of soil at room temperature.
W is the weight of soil at room temperature
T is the temperature of frozen soil.
The relationship found is:
W’ = W+ 0.992w - 0.000208 W(-T) ……..(7A)
This relationship has a maximum error of 0.18.
Void Ratio
The void ratio of soil will change with temperature as the volume of water gets increased when it changes from liquid state to iced state. Thereby increasing the volume of voids while the volume of soil solids remains the same. Therefore, the void ratio will increase which is confirmed practically too. By entering data obtained in the laboratory, the following relationship is obtained by the eureqa Software (Fig. 3.3).
e’=f(e, T) ……..(8)
e’= e + 0.00503(-T) ……..(8A)
Where T is in Degree Celsius.
The graph between percentage change in void ratio vs temperature suggests that at higher water content the change in void ratio is more and a steep curve is obtained as compared to lower water content as shown in figure 3.4. This is because more water will convert into ice and the volume of voids will increase sharply in case of higher water content.
Bulk Density of Soil
The weight of soil solids remains constant but the weight of water changes with the change of temperature thereby changing the bulk density of soil. Therefore, a relationship may exist between the bulk density at room temperature to the bulk density at frozen temperature.
After entering the data obtained in laboratory, the following relationship is obtained by eureqa software(Fig. 3.5)
The function is
γt'=f(γt,w,T) ……..(9)
γt' = γt - 0.0019(-T)γt2 ……..(9A)
As the graph in Fig. 4.13 suggests that the change in bulk density will be steeper when working with higher water content. Also, the rate of change in bulk density with temperature decreases as the temperature is decreasing. This is because the density of ice is smaller than that of water.
Degree Of Freezing
Analogous to the degree of saturation (S), the degree of freezing (F) would tell the degree up to which the soil is frozen. For example, the soil is fully saturated i.e., all the pores are filled with water. At -2 degrees Celsius, a fraction of water will get crystallized but at -20 degrees Celsius, all the water will get frozen. Therefore, the degree of freezing will give an idea about the degree up to which the water in pores of soil is frozen. The data obtained from the laboratory leads to the following result in eureqa software (Fig. 3.7)
S= (w* Gs)/e ……..(10)
The relationship is given by,
F= f(w,e’,T) ……..(11)
F= (2.77 w/e’) - 0.0387(T) ……..(11A)
where F is the degree of freezing computed as,
F= VI/Vv ……..(11B)
Porosity
The porosity of soil is a function of temperature. When the temperature becomes negative, the water present in the pores converts into ice which expands in volume. The increased volume of ice at first tries to occupy all the void space. Once occupied, on further increase in water content, more water turns into ice which expands more than the void space. This thereby increases the volume of voids. When the volume of voids increases, the porosity will also increase. By entering data obtained from the laboratory in the Eureqa software, the following relationship is obtained (Fig. 3.8). The function of porosity with temperature can be given by;
n’= f(n,w,T) ……..(12)
(n') = 0.3376 + 0.0003*T + 0.74*n2 - 0.00069*w*cos(234*n3) ……..(12A)
Where,
n’= Porosity of frozen soil
T= Temperature in degree Celsius
n= Porosity at room temperature
The above function has a maximum error of 0.021.
In figure 3.9, a graph between the percentage of change in porosity vs temperature is plotted. The trend of the curve suggests that at more water content, the change is more visible marked with a steep slope. This is because more water will convert into ice and the volume of voids will increase sharply in case of higher water content.
After performing the soil parameters analysis on eureqa software above, the author comes across various results as follows:
a) W’ = W+ 0.992w - 0.000208 W(-T)
Using this formula, one can obtain the water content of frozen soil if the weight of frozen soil, the weight of soil at room temperature, and the temperature of frozen soil are known. This formula thereby helps in calculating the water content of the soil sample theoretically.
b) e’= e + 0.00503(-T)
Using this formula, one can obtain the void ratio of frozen soil if the void ratio of the same soil sample at room temperature and the temperature of frozen soil is also known.
c) γt' = γt - 0.0019(-T)γt2
Using this formula, one can calculate the bulk density of frozen soil sample, if the bulk density of same soil sample under room temperature is known along with the temperature at which frozen bulk density is required.
d) F= (2.77 w/e’) - 0.0387(T)
Using this formula, one can calculate the degree of freezing which will indicate the amount of freezing that occurred in the frozen sample. This term is analogous to the degree of saturation in normal room temperature soil which tells the amount of saturation of soil sample.
e) (n') = 0.3376 + 0.0003*T + 0.74*n2 - 0.00069*w*cos(234*n3)
Using this formula, one can obtain the porosity of frozen soil if the porosity of same soil sample at room temperature is known and the temperature of frozen soil is also known.
Where,
W’= Weight of Frozen soil.
W = Weight of soil at room temperature.
T = Temperature at which soil is being investigated.
W = Water content of the soil.
γt’ = Bulk unit weight of frozen soil.
γ t = Bulk unit weight of soil at room temperature.
F = Degree of freezing.
n = Porosity of soil at room temperature.
n’ = Porosity of frozen soil.