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GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE
Prof. J. N. Mandal
Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Module - 3LECTURE- 14
Geosynthetic properties and test methods
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
RECAP of previous lecture….. Permittivity or cross plane permeability Constant Head permeability test Falling head permittivity test
Transmissivity or in - plane permeability Full length in-plane flow Radial in-plane flow
Endurance properties Abrasion test or Abrasion resistance Ultraviolet (sunlight) degradation Gradient ratio (clogging) test Hydraulic conductivity ratio (HCR) (clogging) test
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Geosynthetic clay liners (GCLs) properties and test methods
Geosynthetic clay liners consists of bentonite clay or other verylow permeability material which is sandwiched betweengeotextiles and/or geomembrane. These are used as hydraulicbarriers.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Bentonite properties
Property Value
Water content 7.082 %
Liquid limit 407.53 %
Plastic limit 37.21 %
Plasticity index 388.73%
Various properties of sodium bentonite
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Developed GCLs in dry condition
Geosynthetic clay liners (GCLs)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Mass per unit area of Geosynthetic clay liners (ASTM D5993)
Test sample of size 100 mm 100 mm
Weighting machine with an accuracy of 0.01g
Samples are oven dried at 110C for 24 hours Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Initial moisture content of the clay component of GCLs (wclay)can be estimated as follows:
%100xm
mA
M
wclay
GCLi
clay
Mi = initial mass of GCLs specimen, and
A = area of the specimen
mGCL = dry mass per unit area of the GCLs, and
mclay = mass per unit area of dry clay component (g/m2),
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Tensile strength of GCLs
Wide-width tensile strength of GCL-A and GCL-B isdetermined according to ASTM D4595 standard
Strain rate = 10 mm/ min
GCLs test specimen in UTM Machine
Width = 200 mm
Gauge length = 100 mm
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Tensile strength vs. elongation curve for GCL-A and GCL-B
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Free swelling test (ASTM D 5890)
Free swelling of Sodium Bentonite clay
The graduated cylinder is filled with 100 ml de-ionized water.
2 gm sample of dried and finely ground bentonite clay isdispersed into the cylinder in 0.1g increments.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
A gap of minimum 10 minutes between two successiveadditions is maintained to allow for full hydration andsettlement of the clay at the bottom of the cylinder.
Measure the volume of settled clay occupied bycylinder after 24 hours.
The standard certified minimum swelling index value is24 ml/ 2gm (ASTM D5890).
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fluid loss (ASTM D5891) Fluid Loss is a measure of bentonite slurry’s ability to form alow permeability filter cake.
The test is performed in a 3-inch diameter cylinder of 2.5inches in height. A porous stone is placed at the base of thecylinder with a thin filter paper placed over it and together theyrepresent the porous formation.
A predetermined ratio of bentonite and water is mixed in amixer to form solid slurry. 6 % of the slurry is poured into thecylinder. The cylinder is then pressurized to 100 psi. As waterdrains from the bottom of the cylinder, a filter cake forms onthe filter paper retarding the flow of filtrate.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Filtrate is allowed to flow for the first 7.5 minutes of the test. Then flow is collected for the next 30 minutes.
The volume collected or total fluid loss in 30 minutes is measured and reported in milliliters (ml).
A lower amount of filtrate collected indicates the bentonite is more effective at sealing and therefore less permeable. The reported value must be more than 18 mm as per the ASTM D5891.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Moisture Absorption
Water content versus time for GCL-Aplaced in contact with sand at variouswater contents (After Daniel et al.1993)
Soil with only 2% watercontent can result 50%hydration of GCLs afterone month
The time of hydration isvery rapid.
Sodium bentonite, present in GCLs, can absorb water fromthe adjacent soil.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Water content versus time for GCL-B placed in contact with sand at various water contents (After Daniel et
al.1993)Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Hydraulic conductivity of GCLs [IS 2720 (17)]
It is the ability of a GCL to allow the passage of liquidthrough it. The lesser is the hydraulic conductivity, better isthe performance of GCLs in field.
Since GCLs contain mostly bentonite clay, its hydraulicconductivity is calculated by falling head permeability test.The tests are conducted according to IS 2720 (17).
To achieve the field condition, GCLs are covered withsand having a permeability value considerably greater thanGCL so that it does not affect the permeability of GCL.
It is observed that head loss is almost constant after 20days. Therefore, the hydraulic conductivity is calculated after20 days.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Rigid wall permeameter setup
Permeability of GCLs is decreased with the increase inbentonite quantity.
The needle punching of GCLs didn’t affect its permeabilitytoo much. The small holes created by needle punching areself healed due to the bentonite swelling.
Permeameter test setup for hydraulic conductivity test
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Variation of hydraulic conductivity with respect to bentonite quantity
Hydraulic conductivity of GCL-A and GCL-B is less than110-11 m/s when the bentonite quantity is greater than 5.5kg/m2. Generally the hydraulic conductivity of Compacted ClayLiners is in the range of 10-9 m/s.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Hydraulic conductivity of the GCLs with different amountof bentonite
Bentonite mass per unit area
(kg/m2)
Hydraulic conductivity For
GCL-A (m/s)
Hydraulic conductivity For
GCL-B (m/s)3.5 4.510-8 6.710-9
4.5 7.110-10 3.110-10
5.0 2.610-10 7.410-11
5.5 5.510-11 4.210-11
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
c
c
ttHi
33.96.0
6.05i
A.t
tH.kqc
ccCCL
sec/m1033.911
6.06.05)101(q 388
CCL
sec/m102511006.0
006.05)103(q 3810GCL
37.21033.9
1025qq
8
8
CCL
GCL
Example: H = height of canal or reservoir = 5 m, tc =thickness of CCL = 600 mm, tg = thickness of GCL = 6 mm,kc = 1 x 10-8 m/sec, kGCL = 3 x 10-10 m/sec
For geosynthetic clay liner, tg = 6 mm, kGCL = 3 × 10-10 m/s
The flow through GCL is 3 times higher than CCL
For compacted clay liner,Solution:
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
X-ray diffraction test
X-ray diffraction (XRD) is a versatile, non-destructivetechnique that reveals detailed information about thechemical composition and crystallographic structure ofbentonite.
XRD test was performed in Metallurgical Department of IITBombay. This test is performed to know the completemineralogical structure of sodium bentonite. This test isbased on Bragg's Law.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Bragg’s law:2 d. sin = n Where,d = lattice inter-planar spacing of the crystal, = X-ray incidence angle (Bragg angle), = wave length of the characteristic x-ray, andn = order of diffractionBy varying the angle ‘’, the Bragg's Law conditions aresatisfied for different d-spacing in polycrystalline materials.
Plotting the angular positions and intensities of theresultant diffracted peaks of radiation produces a patternwhich is characteristic of the sample. The XRD testmachine available in IIT Bombay is shown in Fig 2.61.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.61 X-ray Diffraction Test facility available in IIT Bombay
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
0
5
10
15
20
0 50 100 150Position (2 Theta)
Spac
ing
(Å)
The various observations from the test are shown in Fig 2.62.
(A)Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.62. Various results of X-ray diffraction test
0204060
80100120
0 50 100 150
Position (2 Theta)
Rel
ativ
e in
tens
ity (%
)
(B)
0
100
200
300
400
500
0 50 100 150
Position (2 Theta)
Heig
ht (c
ts)
(C)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The complete description of Na-Bentonite is determined byusing JCPDS (Joint Committee on Powder DiffractionStandards) software.Form the Fig 2.62(B), for 100% relative intensity the value of2 Theta (2) is determined which is 31.2. Corresponding tothis 2 Theta value, the spacing is found to be 2.376 A0 fromFig 2.62 (A).Now the analysis is done in JCPDS in a spacing range of2.375 A0 (Lower limit) to 2.377 A0 (Upper limit). The mainmineral component of bentonite is found to bemontmorillonite (69.89%).
The chemicals present in this bentonite are shown in Table2.12.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Minerals Value (%)
SiO2 69.89
Al2O3 14.66
MgO 4.02
Na2O 2.64
CaO 2.05
Table 2.12 Chemicals present in sodium bentonite
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Shear Strength of GCLs
Bentonite has very low shear strength after hydration. So theunreinforced GCLs show very low shear strength. For highershear-strength applications, reinforced GCLs are required inwhich the carrier geotextiles are connected by needle punchedfibers that transmit the shear stress across the bentonite layers.
For the stability analysis, the internal shear strength and interfaceshear strength is evaluated through direct shear box tests. Theinternal shear strength represents the shear strength betweengeotextile and bentonite layer while the external shear strengthrepresents the shear strength between the GCL and adjacentmaterial (sand and geosynthetics). All the tests were carried out indirect shear box of cross section area 60 mm × 60 mm.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Internal shear strength of GCLsInternal shear strength of the GCLs is determined with directshear box test. All the tests are carried out according to theIS 13326 (part1), 1992 (reaffirmed in 2002). The strain rate inall the cases was 1.0 mm/min. Normal stresses rang was 50-150 kPa.
The tests were performed in two different states: drycondition and hydrated condition (free swell).
An acrylic block is used to hold the GCLs at proper position.For avoiding the movement of GCL during the testing, GCL isglued to acrylic block using adhesive.
Fig 2.63 shows the various GCL samples attached withacrylic block to be used in shear box.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.63 GCLs samples attached with acrylic blockProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay
0
20
40
60
80
100
120
0 2 4 6 8 10
Horizontal dispalcement (mm)
Shea
r stre
ss (k
Pa)
50 kPa100 kPa150kPa
The various results for both dry and wet conditions forGCL-A and GCL-B are shown in Fig 2.64 to Fig 2.68.
Fig 2.64 Shear stress versus horizontal displacement for GCL-A (dry)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
0
10
20
30
40
50
60
0 2 4 6 8 10
Horizontal dispalcement (mm)
Shea
r stre
ss (k
N/m
2 )
50 kPa100 kPa150kPa
Fig 2.65 Shear stress versus horizontal displacement for GCL-A (wet)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
0
20
40
60
80
100
120
140
0 2 4 6 8 10
Horizontal dispalcement (mm)
Shea
r stre
ss (k
Pa)
50 kPa100 kPa150kPa
0
10
20
30
40
50
60
70
0 2 4 6 8 10
Horizontal dispalcement (mm)Sh
ear s
tress
(kPa
)
50 kPa100 kPa150kPa
Fig 2.66 Shear stress versushorizontal displacement forGCL-B (dry)
Fig 2.67 Shear stress versushorizontal displacement forGCL-B (wet)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The peak failure envelop for all these cases are shown in Fig 2.68
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140 160
Horizontal dispalcement (mm)
Shea
r stre
ss(k
Pa)
GCL-A (dry)GCL-A (wet)GCL-B (dry)GCL-B (wet)
Fig 2.68 Peak failure envelop for both GCL-A and GCL–Bunder dry and wet conditions
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Sample
condition
Adhesion
(kPa)
Friction angle
,(degree)
Horizontal peak
displacement
(mm)
R2
Dry 13.8 32.77 1.8-2.4 0.9948
Wet 9.81 15.01 2.1-3.3 0.9967
Sample
condition
Adhesion
(kPa)
Friction angle
,(degree)
Horizontal peak
displacement
(mm)
R2
Dry 15.88 35.407 3.3-3.6 0.9989
Wet 14.87 18.53 2.4-3.0 0.9952
The detailed results of the direct shear box tests aretabulated here in Table 2.13 and Table 2.14.
Table 2.13 GCL-A results
Table 2.14 GCL-B results
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Summery of the GCL-A and GCL-B properties: The various physical, mechanical and hydraulic properties of GCL-A and GCL-B are tabulated in Table 2.15.
(Note:
Ca = adhesion between the bentonite and geotextile ofGCLs, and
= interface friction angle between the bentonite andgeotextile of GCLs)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Table Properties of GCL-A and GCL-BProperty GCL-A GCL-B
Bentonite Granular Na-bentonite Granular Na-bentonite
Bentonite quantity 5.5 kg/m2 5.5 kg/m2
Upper carrier geotextile Needle punched
Non-woven Geotextile
Needle punched
Non-woven Geotextile
Lower carrier geotextile Needle punched
Non-woven Geotextile
Needle punched
Non-woven Geotextile
Mass per unit area of geotextile 248 g/m2 206 g/m2
Mass per unit area of GCL 5.62 kg/m2 5.58 kg/m2
Thickness 10.6 mm 7.2 mm
Moisture content 12.2% 11.66%
Tensile strength 16.56 kN/m 20.01 kN/m
Elongation at peak load 143.8% 100%
Hydraulic conductivity 5.510-11 m/s 4.210-11 m/s
Shear strength (dry) ca = 13.8 kPa, = 32.77 ca = 15.88 kPa, = 35.40
Shear strength (wet) ca = 9.81 kPa, = 15.01 ca = 14.87 kPa, = 18.53Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
GCLs as composite linersThe waste generates leachate that flows gravitationallydownward into the groundwater. Therefore, it is needed toprovide a suitable barrier layer or system.
GCLs can be used to reduce the leakage rate. The basicconcept and placement of GCLs are illustrated in Fig. 2.29.
CCLs onlyProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay
CCLs with geomembrane
Fig.2.29 Concept and placement of GCLs
GCLs with geomembrane
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
In case of GCLs, the liquid can not be penetrated into theclay liner because of the transmissivity of geotextile. Theliquid can flow along the plane of the geotextile. Giroudand Bonaparte (1989) developed the equation as follows:
g c l wk ( h t )q
ln ( 2 t / b )
Where,q = flow rate (m3/sec),Kgcl = Permeability of GCLs (m/sec),hw = total head loss (mm),t = thickness of GCLs (mm),andb = width of slit in geomembrane (mm).
In case of GCLs with geomembrane, for rectangular slit ingeomembrane with slit length greater enough than width,
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
In case of GCLs with geomembrane, for circular hole ingeomembrane,
Where,
d = hole diametre (mm)
gcl wk (h t)dq
(1 0.5d / t)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
gcl wk (h t)q
ln(2t / b)
Example 2.1.
Kgcl = 6x10-11m/s, hw = 350 mm, b = 1.5 mm, and t = 5mm
q = π x 6x10-11 x (0.350 + 0.005) / ln (2 x 0.010 / 0.0015)
= 6.69 x 10-11 / 1.897
= 3.52 x 10-11 m3/sec
Solution:
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Example 2.2.It is the same problem as in example 1 with diameter (d) = 1.5 mm. Calculate the discharge.
gcl wk (h t )dq
(1 0.5d / t )
Solution:For circular hole in Geomembrane,
1111
10x0118.0
005.00015.0x5.01
0015.0x)005.0350.0(x10x6xq
q = 0.0118 x 10-11 m3/secProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Tensile Strength of Nano MaterialA Nanotalc is added to the polypropylene to increase thetensile strength of the polypropylene. The polypropylenesample collected from product application and researchcentre of Reliance Industries, Chembur, Mumbai as shown inthe Fig 2.70
Fig 2.70 Polypropylene grains obtained in raw form (Source:PARC, RIL. INDIA)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The sample was prepared using the procedure as perASTM D 638.
The mixing is done by heating the polypropylene to itsmelting point. It causes breaking of bonds between its platestructures which exist in its natural form. Once the meltingis complete, the Nanotalc forms cross linkages within thesample enhancing the strength of the sample.
A suitable amount of the sample was placed in the oven forovernight heating at a temperature of 105 degreecentigrade. The polypropylene was then moulded as perASTM type V sample for tensile strength testing using aMicro-Compounder as shown in the Fig 2.71.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.71 DSM Twing screw Micro-Compounder, 5cc (Source:Central facility, Department of metallurgy and Material sciences)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The Micro-Compounder was run at 150 RPM for thepreparation of neat polypropylene sample at a temperatureof 230 degree centigrade.
In the injection mould the cylinder temperature was kept at240 degree centigrade while the mould temperature waskept at 50 degree centigrade.
The samples were allowed in injection moulding unit formoulding and cooling for approximately 2 minutes.
Fig 2.72 shows the Injection mould for preparation of ASTMType V sample.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.72 Injection mould for preparation of ASTM Type V sample (Source: Central facility, department of metallurgy and
material science, IITB Bombay)Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.73 Dimension of a Type V sample (Source: ASTM D638-03)
Dimension of the sample is shown in Fig 2.73 andTable 2.16.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Dimensions Length (mm) Tolerance (mm)
W: width of the narrow
section
3.18 ± 0.5
L: length of the narrow
section
9.53 ± 0.5
WO: width overall 9.53 + 3.18
LO: length overall 63.5 no max
G: gage length 7.62 ± 0.25
D: distance between grips 25.4 ± 5.0
R: radius of fillet 12.7 ± 1.0
T: thickness of sample 3.2 ± 0.2
Table 2.16 Dimension of ASTM sample Type V (Source: ASTM D638-03)
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The prepared sample is shown in Fig 2.74.
Fig 2.74 Prepared samples marked for testing tensile strength
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
The ultimate tensile strength machine is shown in Fig 2.75.Failure of the sample along the gage length is shown inFig 2.76.
Fig 2.75 Tensile testing machine Fig 2.76 Failure of the sample along the gage length
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Fig 2.77 Stress-strain curve of the sample
The stress strain curve is shown in Fig 2.77.
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Sample
No.
Tensile
Modulus
(GPa)
Ultimate
Strength
(MPa)
Ultimate
Strain
(mm/mm)
Tensile
Strength
(MPa)
1 1.1008 38.73 5.796 34.22
2 0.9713 40.36 6.468 40.31
3 0.9402 37.60 5.633 38.01
4 1.0434 35.39 4.888 34.99
5 1.0434 38.33 5.654 37.88
The addition of Nanotalc causes improvement of the tensilestrength up to 3.6% approximately. The mechanicalproperties of the tested samples are shown in Table 2.17.
Table 2.17 Mechanical properties of tested samples
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Junction strength of geocellThe junction strength of geocell is shown in Fig.2.78
Fig.2.78 Junction strength testProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Ultimate versus allowable geosynthetics properties
The laboratory test values can not be used directly indesign. It is preferable to use suitable modified values for insitu condition.
Most cases, performance tests are not possible andfeasible. So, the reduction factors should be considered forsite specific design(Koerner,2005)
JCTJNTBDCDIDCR
ultallow RFRFRFRFRFRF
TT
Strength related problems:
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Where,
Tult = ultimate tensile strength (ASTM D 4595),
Tallow = Long term tensile strength of geotextile (kN/m),
RFCR = Reduction factor for creep,
RFID = Reduction factor for installation damage,
RFCD = Reduction factor for chemical degradation,
RFBD = Reduction factor for biological degradation,
RFJNT = Reduction factor for joint (seams andconnections),
RFJCT = Reduction factor for junction
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Application areas Strength related problems
•Unpaved roads•Retaining walls•Embankments•Bearing capacity•Slope stabilization•Rail roads•Pavement overlays•Pave roads•Roadways•Foundations•Concrete overlays•Bridge piles for fill placement•Flow related problems
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
allow ultSBC Cr IN CC BC
1ψ = ψRF RF RF RF RF
Ψult = Ultimate permittivity
Ψallow = Allowable permittivity
RFSCB = Reduction factor for soil clogging and blinding,
RFCR = Reduction factor for creep of voids,
RFIN = Reduction factor for intrusion into voids,
RFCC = Reduction factor for chemical clogging, and
RFBC = Reduction factor for biological clogging.
Flow related problems:
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Application areas for flow related problems
•Retaining wall filters
•Erosion control filters
•Landfill filters
•Under drain filters
•Gravity and pressure drainage
•Embankment protection, coastal, lakes, rivers andstreams
•Ditch armoring
•Filter below fabric form
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
•Beneath gabions
•High embankments
•Silt fences and screens
•Culvert outlets
•Vertical drains
•Trench drains
•Base course drains
•Toe drains in dams
•Pipe wrapping
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
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Any question?
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay
Prof. J. N. Mandal
Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]
Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay