Comparative Analysis of the Use of the Pore Pressure and Humidity When Assessing the Influence of Soils in Transport Construction
Perm national research Polytechnic University, Russia
Submission: November 20, 2018; Published: December 13, 2018
*Corresponding Author:Kochetkov AV, Perm national research Polytechnic University, Russia.
How to cite this article:Kochetkov A. Comparative Analysis of the Use of the Pore Pressure and Humidity When Assessing the Influence of Soils in
Transport Construction. Civil Eng Res J. 2018; 7(1): 555704. DOI: 10.19080/CERJ.2018.07.555704
Now there is a question of reasonable applicability of indicators of pore pressure and humidity at an assessment of influence of indicators of soil in various environments and conditions of transport construction. Such an analysis can be carried out within the framework of the molecular kinetic theory of gases taking into account the photon interaction.
The real gas is not described by the clayperon-Mendeleev equation for ideal gases. Therefore, due to the needs of practice, many attempts have been made to create an equation of the state of real gases.
The most well-known equations for real gases are given in Table 1.
Some equations are a refinement of the equation of van der Waals (Dieterici and Berta), and equation Beattie-Bridgeman and Redlich-Kwong are empirical, without physical justification. In this case, Redlich writes in his article that the equation does not have a theoretical justification, but is, in fact, a successful
empirical modification of the previously known equations . A large number of equations due to the fact that no equation describes the behavior of real gases under all possible conditions (temperatures and pressures). Each equation has areas in which it best describes the state of the gas. But in other conditions, the same equation has large deviations from the experimental data. In practice, only the van der Waals equation is used in the form of direct calculations due to its simplicity. For other equations, either charts or tables of calculated values are typically used.
The meaning of the van der Waals equation is not only that it is the simplest, but it also has a clear and simple physical meaning. “Despite the fact that the equation of van der Waals equation is an approximate, it is sufficiently well suited to the properties of real substances, so basic provisions of the theory of van der Waals forces remain in force to the present time, exposed to the modern theories that only certain clarifications and additions” [2, p. 59]. “It was indicated that the modern theory of the equation of state of real gases is based on the fundamental provisions of the theory of van der Waals and develop these provisions further, and, having powerful mathematical apparatus of statistical mechanics, it gets the ability to produce all calculations are approximate, but quite accurate” [2, p. 60].
The citation clearly indicates that statistical mechanics is used for accurate calculations based on physical models.
The fact is that thermodynamics is a phenomenological science. It is possible to obtain experimental data on the state of gases at different thermodynamic parameters and to approximate the most suitable thermodynamic equation even without having any idea of the internal mechanisms of the processes occurring in the gases. This is exactly what the authors of the gas laws did: Lavoisier, Boyle, MARRIOTT, etc.
But if you try to delve into the essence of the processes occurring in gases, then a mathematical apparatus is inevitably necessary, taking into account the interaction of the molecules and atoms that make up the gases. This is the apparatus of statistical physics. But, to statistical physics problems of their own. “The exact theoretical calculation of the statistical sum of
gases or liquids with arbitrary Hamiltonian (2.6) is a problem
that lies far beyond the capabilities of modern statistical physics”
. Although,” it is possible to make a number of reasonable and
sufficiently good approximations that allow us to estimate the
statistical sum (2.1) and the configuration integral (2.8) for real
gases consisting of valence saturated molecules “ . The task
is still far from over. A reasonable choice of initial parameters
plays an important role in the difficulties faced by researchers
of real gases. We will carry out a methodical analysis of the
initial parameters used in the theory of gases. Currently, the
following thermodynamic parameters are used in the scientific
and educational literature: P (pressure), V (volume) and T
(temperature). If the temperature and volume are not in doubt,
the pressure, as a thermodynamic parameter, raises certain
questions. Consider the compressibility factor (a measure of
pressure of gases). It is believed that “the most convenient
measure of nonideality is the compressibility factor Z = pVm
/ RT, since for an ideal gas Z = l under any conditions” . For
example, it is proposed: “the thermal equation of state of a real
gas can be represented in the form pv = zRT,
where z is the compressibility factor, which is a complex
function of temperature and density (or pressure)” .
But as a parameter for determining the thermodynamic
state of the gas system, compressibility is not very suitable,
because firstly, it has a complex dependence on pressure and
temperature. Any explanation of why and what determines the
compressibility of gases is determined by the adopted model of
the structure of gases. The form of the compressibility function
for all real gases is given in  (Figure 1), and “for generality,
the reduced pressure π=p/PK and the reduced temperature
τ=T/TC are used as parameters here, where PK and TK are the
parameters of the substance at the critical point. Since for an
ideal gas at any parameters z=1, this graph clearly represents
the difference between the specific volume (density) of the real
and ideal gases at the same parameters” Figure 2.
Secondly, the compressibility of gases cannot be directly
measured during the working cycle of a thermodynamic
system, but only during specially conducted experiments.
Third, the compressibility of gases, in fact, is not a single curve,
but a family of curves, at different temperatures and the same
pressure, or at the same temperature, but different pressures,
the compressibility of the gas is different. In practical work,
the compressibility of gases is not measured, but calculated
according to the appropriate calculation formulas, according to
officially recognized methods. Therefore, the compressibility of
gases may well characterize the nonideality of gases but cannot
be accepted as an initial parameter in the theory of real gases.
Let’s see what else can serve as a replacement for the pressure
as the initial parameter. For this it is necessary to pay attention
to the parameters that are used in the statistical theory of gases.
The literature analysis shows that all statistical models of real
gases are constructed using such parameter as concentration.
Concentration is the number of atoms (molecules) per unit
This is not surprising, since it is the concentration that
determines the average distances between the gas molecules,
and hence the potential long-range forces of the molecules.
For example, according to the theory of van der Waals or any
other. Then, after establishing the laws of behavior of the
statistical system depending on the concentration, go to the
usual thermodynamic characteristics: P, V, Etc. The application
of pressure as a thermodynamic parameter is perfectly justified
in the theory of ideal gases, in which atoms interact only at
absolutely elastic collisions during chaotic thermal motion.
According to the theory of ideal gases, the relationship between
pressure and gas density is very simple :
P = NkT ……………… (1)
here P-pressure, MPa; N-concentration (1/m3); T –
At a constant temperature, the dependence between
concentration and pressure is linear:
P = const*N …………….. (2)
The concentration of N is equal to the number of molecules
per unit volume. Concentration is related to density by a simple
ρ = N*m …………………. (3)
where ρ is the density, N is the concentration, m is the mass
of the molecule.
In other words, in the theory of ideal gases, the gas pressure
is linearly proportional to the gas density. For real gases this is
never the case. The theory of real gases takes into account the
forces of interaction of a potential nature. “Real gases differ from
their model - ideal gases - in that their molecules are finite in
size and between them the forces of attraction (at considerable
distances between molecules) and repulsion (when molecules
approach each other)” . This leads to the fact that the density
of real gases will be nonlinear, and a simple replacement of the
concentration of the pressure in the volume, as is quietly done in
the theory of ideal gases cannot do.
Tradition of determining the parameters of gas pressure
is since when in science was not known that gases consist of
atoms [5, p. 36-65], and therefore, scientists could not operate
with concepts of the concentration of atoms in gases. We do not
consider it advisable to continue this vicious practice. Moreover,
as mentioned above in the theory of real gases directly refers to
the value of concentration, but in the final equations go to the
pressure, “the old-fashioned way.”
For Figure 3 graphs of helium density change depending on
pressure are given. The fat line is a theoretical line based on the
ideal gas model .
From Figure 3 it is clearly seen that for the graph of the
function for helium, not only does not coincide with the
theoretical, but the dependence of the density on the pressure is
not linear. We chose helium, not only because the characteristics
of this gas are well studied, but primarily because helium is the
most chemically inert gas. Due to its inertness, it is not located
to form compounds in molecules and other aggregations. That
is, in its chemical properties, it is closest to the ideal gas. We
chose helium, not only because the characteristics of this gas
are well studied, but primarily because helium is the most
chemically inert gas. Due to its inertness, it is not located to
form compounds in molecules and other aggregations. That is,
in its chemical properties, it is closest to the ideal gas. When
discussing compressibility as an initial parameter, we said
that the main disadvantage of compressibility as a parameter
is not direct measurements, but calculated values. Unlike
compressibility, the density of gases can be measured directly,
both in stationary gases (in tanks) and in pipelines. There are
several types of density meters for both liquids and gases.
Although densitometers are more expensive than manometers, but the gain in practical applications can be tangible.
Thus, based on modern theories of real gases, it seems more
logical to determine the properties of gases, depending not on
pressure, but on density.
1. First, because all models of statistical physics are
based on the concept of concentration, not on the concept of
2. Secondly, because it is the density that is closest to
the concept of concentration. And easily translated into one
3. Third, even if any characteristic of the gas (heat capacity,
thermal conductivity, etc.) linearly depends on the density, in
accordance with the models of the statistical theory of gases,
the translation of the values of these properties depending
on the pressure will make an additional nonlinearity,
depending on the density of the pressure. Especially if the
dependence of the function is nonlinear
As an example, consider the graphs of the dynamic viscosity
of helium. For Figure 4 graphs of helium heat capacity versus
pressure in the temperature range from 100K to 1000K are
presented. For comparison, graphs of dynamic viscosity versus
gas density are presented  (Figure 5).
The difference in the representations of the same gas
property depending on different parameters is clearly seen
from the graphs. The first thing we can say is that schedules
of dependence of dynamic viscosity to the density look easier
than the dependence of dynamic viscosity on the pressure is
because of the nonlinearity of the dependence of concentration
on pressure. In particular, viscosity graphs from pressure change
their direction of change. And at low temperatures so quickly
that the lines even intersect. Moreover, if at low temperatures
(lower lines in Figure 3), under high pressure upwards, at moderate temperatures, horizontal, and at high temperatures
(top line) a bit, about 2% down.
The graphs also depend on the density - all the lines are
almost parallel throughout. And they do not change their
behavior at all. But the fact that the graphs depending on the
density (concentration) look easier is not the most important
thing. The main thing is the epistemological value of such a
transition to another parameter .
1. Another proof of the influence of thermal photons
on the behavior of gases under different conditions is the
experimental data on the compressibility of gases under
2. Modern theories of real gases are unable to explain
the behavior of the compressibility function. Nothing to do
with the change in the density, and especially at different
temperatures. Because according to modern theories
repulsion of molecules should be observed only when
molecules are smaller than the size of molecules. And the
compressibility of gases should not depend on temperature
3. The hypothesis of a significant influence of thermal
photons on the mechanical properties of gases can explain
the behavior of the compressibility factor of gases.
4. With an increase in the density of the gas, the
compressibility factor increases because, together with
an increase in the density of gases, the number of photons
having a mechanical effect on the gas molecules also
5. As the temperature increases, the energy of thermal
photons increases, so does the compressibility factor
(resistance of the gas to compression). Because more
energetic photons have a stronger mechanical effect
(stronger push) on the gas molecules. That is why the
compressibility factor increases in the temperature range
from 10 to 150 K.
6. At temperatures of more than 150 K, the number of
thermal photons that have a mechanical effect on the gas
molecules decreases, since the radiation of the gas outside
increases. Increasing the number of photons leaving the
volume of gas.
7. Reducing the number of photons in the gas volume
reduces the internal pressure of the gas and, accordingly, the
compressibility factor decreases.
8. The moisture index (corresponding to the concentration
or density) used in the measurement of soil properties
more accurately and reliably (has a large proportion of the
explained dispersion) shows a more significant change in its
properties in comparison with the pore pressure.
9. Accordingly, there is no reason to move to foreign
standards based on pressure indicators in soils and other
environments of transport construction.