ENVIRONMENTAL GEOMECHANICS CE-641 Lecture No. 18 Prof. D N Singh - - PowerPoint PPT Presentation
ENVIRONMENTAL GEOMECHANICS CE-641 Lecture No. 18 Prof. D N Singh Department of Civil Engineering 23.10.2018 Lecture No. 18 Lecture Name: Geomaterial Characterization
CE-641 Lecture No. 18
Department of Civil Engineering
23.10.2018 Lecture No. 18 Lecture Name: Geomaterial Characterization
IMPORTANCE (in REAL LIFE SITUATIONS)
HIGH LEVEL RADIOACTIVE WASTE DISPOSAL HIGH VOLTAGE UNDERGROUND POWER CABLES ROADS, PIPELINES, STRUCTURES IN COLD REGIONS AGRI- & AQUA-CULTURE FIELDS/ SOLAR PONDS GROUND IMPROVEMENT TECHNIQUES (SOIL HEATING & FREEZING) ENERGY CONSERVATION SCHEMES TRANSMISSION OF HOT FLUIDS (CHEMICALS/GAS) HEAT LOSS FROM THE BASEMENTS OF BUILDINGS
THERMAL PROPERTIES
THERMAL RESISTIVITY (inverse is Conductivity, k) RT (inverse is Conductivity, k) THERMAL DIFFUSIVITY () SPECIFIC HEAT (Cp) Cp=(RT..)-1 is the density of the media K CAN BE CORRELATED TO HYDRAULIC CONDUCTIVITY
Factors Influencing Thermal properties of Geomaterials
Type of Soil Moisture Content Distribution and Size of the Grains Density of the Soil Temperature and Pressure Presence of Contaminants Method of Measurements
Cp, RT, and can be used for geomaterial characterization
The Transient Method
Grounded junction Insulated T-type Thermocouple Stainless steel tube of dia 1.2mm Thermocouple leads
6mm dia copper tube Power supply leads Thermocouple leads (T-type) Nichrome wire Thermocouple 95 mm
T-type thermocouple Thermal probe
Thermal probes and thermocouples
Temperature indicator
0000
Set Off on
Switch
300 600 900 1200 1500
big
S
000.0 000.0 000.0
Constant Power Supply Unit
A.C. Power Supply
Field Thermal Probe
000.0
Timer
Temperatures Fine tuning
Coarse tuning
small
Current
Laboratory thermal probe
THERMODET DDTHERM (software)
Field thermal probe
Various Devices used for Thermal Property Determination
1
2 2
r r r t
Transient Method Governing Equation for Line Heat Source in an Infinite Medium Initial and boundary conditions: = 0 , for t = 0, r =
r
Solution of the Differential Equation:
1 n n n
n.n! u 1 γ lnu k π 4 Q ) θ θ (
2
is the Euler’s constant and is equal to 0.5772.
r
1 2 1 2
t t ln k π 4 Q ) θ θ (
1 T
4π Q s. R
For r0 and t, the higher order terms of u can be neglected
5 10 15 20 25 30 35 40 20 40 60 80 100
(b)
t (min)
0.1 1 10 100 20 40 60 80 100
(a) s
(
0C)
70 mm Thermocouple leads Power leads 25 mm thick Perspex disk 20 mm thick Styrofoam Thermal probe Top cap Bottom cap Thermocouple Rubber washer Compacted soil 140 mm Cap of the probe Rubber washer 220 mm long SS tube 25 mm thick Styrofoam 5 mm thick Perspex disk
Details of the thermal property detector (THERMODET)
10 20 30 40 50 60 70 80 90 100 20 30 40 50 60 70 (b)
(
0C)
t (min)
1 10 100 20 30 40 50 60 70
(a)
Variation of temperature with time for THERMODET
50 2
t T D
where is the thermal diffusivity D is the diameter of the soil sample T is the time factor corresponding to 50% change in temperature t50 is the time corresponding to 50% change in temperature
120 100 80 60 40 20 0.01 0.1 1
H=2D H= T
(%)
Percentage change in temperature versus time factor curves
Variation of thermal resistivity with dry-density
200 400 600 800 1000 1200 (c) (b) (a)
WC SS BC WS
250 300 350 400
d (g/cm
3) SG1 SG2 SG3
RT (
0C-cm/W) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 600 800 1000 1200 1400
FA-1 FA-2 FA-3 BFS SF 10 20 30 40 100 200 300 400 500 600
1.3 1.6
d (g/cm
3)Soil WS SS BC WC FA-3
RT(
0C-cm/W)
w (%)
Variation of thermal resistivity with moisture content
Variation of thermal diffusivity with dry-density
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 15 20 25 30 35 40 (x10
2/s)
d (g/cm
3)
FA-1 FA-2
FA-3
BFS SF
10 20 30 40 20 25 30 35 40 45 50 55 60 65 70
} 1.3
d=1.6 g/cm
3
Soil WS SS BC WC FA-3
(x10
2/s)
w (%) Variation of thermal diffusivity with moisture content
Variation of specific heat with dry-density
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.5 1.0 1.5 2.0 2.5 3.0
Cp(J/
0C.g)
FA-1 FA-2 FA-3 BFS SF
d (g/cc)
5 10 15 20 25 30 35 40 0.5 1.0 1.5 2.0 2.5 3.0
WS SS BC WC FA-3
Cp (J/
0C.g)
w (%)
Variation of specific heat with moisture content
Generalized Relationships
Generalized thermal resistivity relationships, termed as DDTHERM, have been proposed by Singh and Devid (2000). Dry (single-phase) soils 1/RT = [a.10(0.6243 d - 3)] Moist (single-phase) soils Clays and silts 1/RT = [b.10(0.6243 d - 3)] 1/RT = [1.07log(w)+c].[10.(0.6243 d-3)] where RT is the soil thermal resistivity (C.cm/W), w is the moisture content (%) and d is the dry-density of the soil (g/cm3). a, b and c depend on the % fraction of the soil and its moisture content and determining these parameters is a big challenge
Fraction a Clay 0.219 Silt Silty sand 0.385 Fine sand 0.340 Coarse sand 0.480 Gravel 0.21
W (%) Fraction b 4>w2 Clay 0.243 Silt 0.254 5w>4 Clay 0.276 Silt 0.302
Fraction c w (%) Clay
>5 Silt
Silty sand 0.12 1 Fine sand 0.70 Coarse sand 0.73 Gravel 0.8
For clay and silt phase: Weight = (phase %), when 5 w(%) 2. Weight = Minimum of the (Absolute c value or phase %), when w (%) >5 Silty-sand, fine-sand coarse-sand and gravel: Weight = (phase %c of the phase)+ phase %, when w (%)>1 Weight = a of the phase, when w (%)<1 (dry soils)
It is quite difficult to state the quantitative value of resistivity
fact that the type of the soil is not clearly defined in most of the practical situations. For instance, the word clay can cover a wide variety of soils.
Effect of the type of soil
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 200 400 600 800 1000 1200 1400
Black Cotton Soil Silty Sand Fine Sand Coarse Sand Fly Ash
Thermal Resistivity (deg C-cm/watt) Dry density (g/cc)
Heat conduction through soil is largely electrolytic, the quantity of water present plays an important role. The amount of water present is dependent on a number of factors viz. weather, time of the year, nature of the sub-soil and the depth of permanent water table. Dry soils depict low conductivity. It is mainly due to the presence of air, a poor conductor (4000°C-cm/watt), separates the solid grains (4°C-cm/watt) of the soil. If the moisture content (Resistivity of water 165°C-cm/watt) of the soil increases, then conductivity also increases. Saturated soil has high conductivity as compared to the water. The moisture content, from where rate of decrease of resistivity is less, is known as critical moisture content for the soil.
Effect of moisture content
5 10 15 20 25 30 35 200 400 600 800 1000 1200 1400
Dry density 1.0g/cc 1.1g/cc 1.2g/cc 1.3g/cc 1.4g/cc Thermal Resistivity (deg C-cm/watt) Moisture Content ( % )
Determination of Thermal Properties in a Geotechnical Centrifuge
Though, several analytical and numerical models are available to model heat migration in geomaterials they lack simulation of the prototype conditions in terms of in-situ stresses. To overcome this, field tests, which are relatively costly, time consuming and difficult to perform, are found to be of immense help. Under these circumstances, a geotechnical centrifuge should be used for studying heat migration in geomaterials.
Summary of scaling factors
PARAMETER SCALING FACTOR Length 1/N Void ratio 1 Acceleration N Force 1/N2 Stress 1 Strain 1 Velocity N Mass 1/N3 Mass density 1
Time (diffusion)
1/N2 Hydraulic Conductivity N Thermal conductivity
?
Thermall diffusivity
?
Specific heat
?
Heat flux ?
Data logger Batteries Axis of rotation Rheostat Micro switch Switch-on Switch-off Test setup Thermocouple leads Power supply leads Geomaterial
Centrifuge Setup
Thermal properties at Different Centrifugation Efforts
1 10 100 10 100 1000 10000
SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB
RT (
0C-cm/W)
1 10 100 10
10
10
10
10
SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB
(m
2/s)
50 100 150 200 1 2 3 4 5 SS-D1 SS-D2 SS-D3 SS-D4 SS-SUB
Cp (J/g-
0C)
N
Krishnaiah, S. and Singh, D. N., “A Methodology to Determine Soil Moisture Movement Due to Thermal Gradients”, Experimental Thermal and Fluid Science, 27, 2003, 715-721. Krishnaiah, S. and Singh, D. N., "Centrifuge modelling of heat migration in soils," International Journal of Physical Modeling in Geotechnics.4(3), (2004), 39-47
Some results
5 10 15 20 25 20 30 40 50 60 70 80
125 100 50 N=1
5 10 15 20 25 r(cm) 0.3 1.5 2.0 3.0 4.0 5 10 15 20 25
(
0C)
t (min)
5 10 15 20 25 1 2 3 4 5 20 30 40 50 60 70
(
0C)
r (cm)
t (min) 5 10 15 20 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
r z
10 20 30 40
(%)
r (m)
35 days 25 days 15 days t=10 days
N 50 100 125
Time modeling
20 40 60 80 100
r=2.0 m r=1.5 m
R
2=0.9762
N 50 100 125 Best-fit for all data
(%)
t (days)
0.9801 50 100 150 200 250 20 40 60 80 100 0.9625 50 100 150 200 250
SS-D2 SS-D1
0.9856
Modeling of models
Descritization
θ (°C) Results
Mathematical Modelling (Using ANSYS 6.0)
Perspex mold Thermocouple (TC) Thermal probe Soil sample r
Test setup
5 10 15 20 25 30 20 30 40 50 60 70 80
2 3
(
0C)
4
r=1.5 cm
ANSYS 6.0 Experimental
t (min)
Validation of ANSYS results with experimental results
(C) Finite Element Model Centrifuge test x rp (cm) tp (min) rm (cm) tm (min) 32.05 75 12905 1.5 10 1.83 28.84 100 15485 2.0 10 1.88 26.80 150 17105 3.0 10 1.90
Scale factor for time
N log t t log x
10 m p 10
x m p