Download Thermal signatures of land mines buried in mineral and organic soils

Infrared Physics & Technology 43 (2002) 303–309
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Thermal signatures of land mines buried in mineral
and organic soils––modelling and experiments
K. Lamorski a, P. Prez gowski b, W. Swiderski c,*, D. Szabra c,
R.T. Walczak a, B. Usowicz a
a
Institute of Agrophysics, Polish Academy of Sciences, Doswiadczalna 4, 20-290 Lublin 27, Poland
b
PIRS, Pregowski InfraRed Services, Zachodzacego, Slonca 36, 01-495 Warsaw, Poland
c
Military Institute of Armament Technology, Prymasa Wyszynskiego 7, 05-220 Zielonka, Poland
Abstract
A model of thermal phenomenon in soil developed to determine its thermal signatures in case of buried land mines in
presented in the paper. Thermal signature values of a mine buried in two types of soil having different properties were
compared using mathematical–statistical modelling. Results generated by modelling have been verified by laboratory
experiment. 2002 Published by Elsevier Science B.V.
Keywords: Thermal signature; Buried land mines; Modelling
1. Introduction
The problem of the mines existing in the soil is
an important problem in the world. Experts estimated that nowadays there exist about 120 millions of buried mines left in more than 60 countries
around the world. There is a serious threat for
civilian populations. Because of little efficiency of
traditional methods on detection of buried mines
in recent years many worldwide institutions have
started the work to improve mine disposal effectiveness. Also in Poland the work has been carried
out how to use infrared radiation for mine detection. Our obtained results were presented on many
*
Corresponding author. Tel.: +48-22-6833403; fax: +48-227819935.
E-mail addresses: [email protected] (P. Pregowski),
[email protected] (W. Swiderski), [email protected].
lublin.pl (R.T. Walczak).
special conferences [1–3]. The basis for the thermovision methods of mine detection is a temperature signature of the mine on the soil surface.
Thermal signatures of mines buried in the soil
originate from different heat transport parameters
of the soil medium and the mine. Efficiency of this
methods is strongly connected with external condition and state and structure of the soil. In our
existing works [4,5] as and in many other author’s
works [6,7] was assumed that soil in which a mine
is buried was homogeneous. In natural conditions
most often the top layer of soil is organic and
bottom layer is mineral. This problem is much
more complicated and is considered in this paper.
2. Modelling
The main issue in the thermodetection of mines
buried in the soil is to determine proper conditions
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K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
for making measurements. Heat flow in the soil
material is determined mainly by soil material
properties and boundary conditions on the ground
surface. As we have no influence on the natural
meteorological conditions, which determines heat
flux on the ground surface, we have to do our best
to ensure optimal conditions for thermovision
measurements. This includes choosing proper
times and camera adjustments for making measurements. Good understanding of energy transport phenomena in the soil medium is crucial in
this task.
In our paper we present a physical model which
describes heat transfer in the soil medium. This
model is used for analysing heat transfer and
mine signatures creation in layered soil medium,
under natural conditions. Heat capacity and heat
conductivity of mine may in general differ from
surrounding soil heat transport properties. That
makes it possible to detect mines by measuring soil
surface temperature which is not homogeneous
due to mine inclusion in soil medium.
Heat flux qT in a soil medium may be described
by the Fourier’s law (1) where k (W/m K) is thermal conductivity and rT (K/m) is a spatial gradient of temperature T.
qT ¼ krT
ð1Þ
If there are no sources thermal in soil medium
we can describe the energy conservation law in the
form of continuity equation (2).
Cv
oT
¼ rqT
ot
ð2Þ
Finally heat transport in the soil may be described in general by the following equation, which
is a consequence of the energy conservation law
and Fourier’s law.
Cv
oT
¼ rðkrT Þ
ot
ð3Þ
This parabolic partial differential equation describes heat transport in isotropic, non-homogeneous medium. Volumetric heat capacity Cv (J/
m3 K) and heat conductivity k depend in general
on spatial position.
It is a well known fact [8,9] that the heat
capacity of soil Cv and soil heat conductivity k
depends on temperature and soil moisture. Due to
that fact we have to take into account soil moisture content changes in our model. As it is described by Darcy’s law, water flow in porous
materials takes place due to gradient of soil water
potential. This is described by equation (4) where
the soil water potential is a sum of two components. Pressure head h (m) which is associated with
interactions between soil particles and water, is a
function of soil moisture content. The second part
of soil water potential is gravity head which is a
consequence of gravity forces affecting soil water.
Gravity head is simply a distance from somewhere
defined reference level. In (4) qw (kg/m2 s) is a
water flux, ql (kg/m3 ) is a water density and K (m/
s) is a soil water conductivity.
qw ¼ ql Krðh þ zÞ
ð4Þ
The soil water conservation law we can write in
the form of following equation,
o ð ql h Þ
¼ rqw
ot
ð5Þ
where h is a volumetric soil water content (m3 /m3 ).
Darcy equation combined with a conservation
law, gives Richard’s equation which describes soil
water transport phenomena in the soil medium.
Cw
oh
¼ rð Krðh þ zÞÞ
ot
ð6Þ
In this equation we have taken into account
functional dependence between pressure head and
soil moisture content h ¼ hðhÞ. Differential soil
water capacity Cw (m1 ) which appears in this
formulation of Richard’s equation is described by
the following formula:
Cw oh
oh
ð7Þ
Eqs. (6) and (3) describe heat and water transport phenomena in any geometry despite of coordinate system.
If we assume that soil transport parameters may
only depends on vertical coordinate, and if we assume that other mines are far enough (Fig. 1), then
we can describe our problem of heat and moisture
transport in axial coordinates. Eqs. (6) and (3) take
the following form in axial coordinates, when we
K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
305
The net radiation at the soil surface Rn (W/m2 )
is an energy flux exchanged at the soil surface due
to radiation phenomena. Water flux of the water
evaporating from the soil surface E (kg/s m2 ) generates energy flux due to latent heat of vaporisation L (J/kg). Sensible heat flux HS (W/m2 ) is
exchanged between soil surface and atmosphere
due to air convection. The soil surface is cooled or
heated due to differences in air temperature and
soil surface temperature. G is a net heat flux at the
soil surface (W/m2 ), which is taken as a Neumann’s type boundary condition for the heat
transport equation. The net radiation at the soil
surface Rn is described by:
Rn ¼ ð1 alÞIG þ R1 Sem
ð11Þ
where al is albedo of soil surface, IG is a global
incoming radiation (W/m2 ), R1 is long-wave radiation of atmosphere (W/m2 ) and Sem is energy flux
radiated from the soil surface due to its temperature. The long-wave radiation of atmosphere is
calculated from the following formula [10]:
4
Fig. 1. The geometry of considered space in the model.
discard dependence on angle u in axial coordinate
system, which is the result of the assumed spatial
homogeneity of soil profile:
oT 1 o
oT
o
oT
¼
rk
k
Cv
þ
ð8Þ
ot
r or
or
oz
oz
oh 1 o
oh
o
oh
¼
rK
K
Cw
þ
þ1
ð9Þ
ot r or
or
oz
oz
We have a system of two non-linear time dependent partial differential equations of parabolic
type in two dimensions. We have to determine
boundary conditions, initial conditions and functional dependence of transport parameters to solve
them.
On the bottom of calculation area and on the
sides there are no-flow Neumann boundary conditions. Heat flux through soil surface may be
calculated from the energy balance equation.
Rn þ HS þ LE þ G ¼ 0
ð10Þ
1:2
R1 ¼ rðTa þ 273:16Þ ½0:605 þ 0:048ð1370Ha Þ ð12Þ
where Ta is temperature of air (C) and Ha is absolute air humidity (kg/m3 ). Sem , is calculated as
follows:
Sem ¼ erðTs þ 273:16Þ4
ð13Þ
where e is a soil surface emissivity, r is the StefanBoltzmann constant (W/m2 K4 ), TS is temperature
of the soil surface (C). Evaporation rate and a
sensible heat flux are described by the Penman
type equations [10].
The Mualem and Van Genuchten model (14) of
soil water retention curve is used to describe the
dependence between soil moisture and pressure
head. This model does not describe hysteretic behavior of soil moisture–pressure head dependence,
which is common in real soils, but it is simple in
adaptation in practical calculations. Soil water
residual capacity hR (m3 /m3 ) is the amount of
water which is bounded on the soil particles even
in a dry state. The other parameters of that model
are: hS (m3 /m3 ) is a volumetric saturated soil water
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K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
content, a and n are parameters without clear
physical meaning.
11=n
1
h ¼ hR þ ðhS hR Þ
ð14Þ
n
1 þ ðahÞ
Differential soil water capacity described by the
Eq. (7) when using soil water curve formula (14)
takes the form:
n
Cw ¼
n ð12n=nÞ
ð1 nÞðahÞ ðhS hR Þð1 þ ðahÞ Þ
h
ð15Þ
Soil water conductivity may be expressed as
follows [4] in Eq. (16) when using the Mualem–
Van Genuchten model for water retention.
n
o2
nþ1
n ð1n=nÞ
1 ðahÞ ½1 þ ðahÞ KðhÞ ¼ KS
ð16Þ
ðn1=2nÞ
½1 þ ðahÞn Soil heat capacity and soil heat conductivity
may be calculated using a statistical model described elsewhere [2].
3. Measurements
In order to test the model introduced above at
different but controlled in laboratory conditions
the laboratory set-up was built (Fig. 2). Temperature profiles in soil consisted of top organic and
bottom mineral layers were registered in the middle of experiment. There are two basic categories of
soil material existing frequently in nature. Organic
Fig. 2. Testing set-up.
Table 1
Components of soils
Organic matter
Quartz
Other minerals
Zagrody (m3 /m3 )
Kuwasy (m3 /m3 )
0.028
0.815
0.156
0.767
0.12
0.221
layer is determined buy the soil obtained from
localities of Kuwasy and mineral from localities of
Zagrody. These compositions of the soils are introduced in Table 1. All investigations were carried
out using the AGEMA SW TE and LW thermal
cameras and set of instruments for measuring:
temperature on buried mine, temperature on profile of the soil, temperature on surface of the soil,
moisture of the soil, irradiance of the surface and
state of external conditions. The measurement field
takes the central part of the set-up and the wooden
specially isolated container with dimension 900 750 300 mm. The temperature sensor and plastic mine (radius 320 mm and height 85 mm)
were placed inside the soil filled container in precisely determined spots. The mine was placed in
the middle of the measurement field. Inside edge
installed lamps determined dimensions of the container.
4. Results
In Figs. 3–6 there are presented values of thermal parameters of mineral (Zagrody) and organic
(Kuwasy) soils. These soils were used in computer
simulation as well as in laboratory experiment.
Values of the soil heat capacity and thermal conductivity were calculated using the model described earlier. These thermal parameters of soils
are very different. This is caused by the different
content of water and of organic material. Thermal
conductivity of organic material, which is a basic
component of organic soil is much lower than of
quartz. This fact decides on values of thermal parameters of soils.
In Fig. 7 is shown a comparison of change of
temperatures in soil profile obtained from computer simulation and results obtained in laboratory experiment. These results were obtained for a
soil profile where the top layer of organic soil was
K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
Fig. 3. Conductivity of sample mineral soil. r is bulk density
(mg/m3 ).
Fig. 4. Heat capacity of sample mineral soil.
Fig. 5. Conductivity of sample organic soil.
Fig. 6. Heat capacity of sample organic soil.
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K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
Fig. 9. Results of laboratory experiment.
Fig. 7. Comparison of change of temperatures in soil profile by
simulation and experiment.
3 cm and under it was immediately buried a mine
placed in the middle of the soil containers. The
centre soil was warmed by lamps about 60 minutes
with power 500 W/m2 , water content w:c: ¼ 0:3.
At the start external temperature was 20 C and
then we cooled freely by 60 min at speed wind of
0.05 m/s.
In Fig. 8 is shown an example of simulation of
dynamics heat propagation for a laboratory system as in Fig. 2 and assumptions as above: Patterns of temperature in half vertical section of the
Fig. 8. Computer simulation results.
soil from the centrally placed mine for conditions
as above.
In Fig. 9 are shown examples of thermograms
obtained in the middle of research of plastic mines
in the laboratory set-up of Fig. 2. Thermograms
from cameras LW present typical effect of thermal
inertia in generating signatures of plastic mines.
They introduce heating and cooling phase of mines
for conditions as above.
5. Conclusions
• Developed model made possible analysis of flow
of energy in a soil–mine system and simulation
of thermal signatures dependences on properties of soil and mine.
• The laboratory experiment confirmed correctness of the accepted assumptions for the developed physical–mathematical model of heat and
water flow in the soil.
• Prediction of thermal signature of buried mines
in mineral soil with the top layer of on organic
type is much more complicated than for sandy
soil.
• We confirmed the large influence of the soil superficial layer on thermal signatures creation of
buried mines.
• Different external conditions and thermal features of the very dry and very wet soil or density
K. Lamorski et al. / Infrared Physics & Technology 43 (2002) 303–309
differences of soils show that detection of the
same mine could be possible provided that quite
different criteria were used.
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