Nano-scale Geo-Mechanics- 12th Aug PPSU.pptx

NANO-GEO-MECHANICS:
CHALLENGES TO
CALCULATE FRICTION
FOR GEO-MATERIAL
Prof. Samirsinh P Parmar,(CL016)
Dr.Atindra D Shukla
International Conference on Academic &
Industrial Innovations
P P Savani University (PPSU), Surat, India
[August 12-13, 2023]

OUTLINE OF THE PRESENTATION
ICAIEE- 12T H AUGUST - 2023 2
• Introduction
• Review of literature
• Nano-geo-mechanics to study Nano scale geotechnical engineering
• Nano-mechanics as a tool to study macro-level material properties through continuumization
• Factors affecting nanoscale friction
• Methods to calculate nano scale friction
• Equations governing calculation of Nano friction between surfaces
• Equations governing Nano Surface coating frictional forces
• Coupled behavior of Nano-micro and Micro- Macro mechanism
• Challenges in calculation of Nano friction applicable to geomaterials. (i.e. geo-mechanics)
• Concluding remarks

KEYWORDS:
 Nano mechanics,
 Geo-materials,
 Nano scale friction,
 Governing equations,
 Macro-nano behavior of geomaterials.

INTRODUCTION
(After Lucas Frerot et al. 2023)
• Prediction of soil behavior is still
challenging task.
• The constitutive relationship derived
by mainly macro or micro-mechanics
• Parameters that affects the
constitutive relationship changes for
the particle size of macro level to
Nano level

INTRODUCTION
Nano-geo-mechanics is the emerging branch of engineering to analyse soil behaviour at Nano
level particle size (i.e. 10-9m), which signifies molecular or quantum molecular behaviour.
Nano-geo- mechanics is mostly dominated by forces exerted at atomic or molecular scale.
Cm- mm 10-6 10-9

AFM Images
Typical Atomic Force Microscope images of : (a) bentonite, (b) montmorillonite, (c)
kaolin, (d) halloysite, (e) silica, and (f) graphene oxide nanoparticles.
7

ROUGHNESS AT DIFFERENT SCALES
RPC-1 ,19PH16 NANO COAT INGS ON
GEOT EXT ILES
8
After - Tribology on the Small Scale: A Modern Textbook on Friction, Lubrication,
and Wear, Second Edition, C. Mathew Mate and Robert W. Carpick, Oxford University
Press, 2019.

RPC-1 ,19PH16 NANO COAT INGS ON
GEOT EXT ILES
10
Sr.
No.
Author Year Paper Journal/Conf.
1
Marzieh Kadivar, Kazen
Barkhordari, Mehdi Kadivar
2011 Nanotechnology in Geotechnical Engineering
Advanced Materials research ,
Switzerland.
2 Dr. Amit Srivastava 2011
Nanotechnology in Civil Engineering and
construction: A review on state of the art and
future prospects
Proceedings of Indian Geotechnical
Conference December 15-17, 2011,
Kochi (Paper No.R-024)
3
Zaid Hameed Majeed,
Mohd Raihan Taha
2013
A review of stabilization of soils by using nano
materials
Australian Jouranl of Basic and
applied Sciences, 7 (2)
4
Onuegbu O. Ugwu,
M.ASCE1 ; Julius B. Arop2
; Clifford U. Nwoji3 ; and
Nwolisa N. Osadebe4
2013
Nanotechnology as a Preventive Engineering
Solution to Highway Infrastructure Failures
e Journal of Construction
Engineering and Management, Vol.
139, No. 8, August 1, 2013.
5 Dr. S.G.Shah 2014
An overview of applications of
nanotechnology for geotechnical engineering;
( Nano geotechnical engineering)- A future
scope
Applied mech. Dept. SVNIT surat
6
Ali Akbar Firoozi, Mohd
Raihan Taha, Ali Asghar
Firoozi
2014 Nanotechnology in Civil Engineering EJGE, Vol.19 (2014), Bund. T
NANOTECHNOLOGY APPLICATIONS IN GEOTECHNICAL ENGINEERING

Sr.
No.
Author Year Paper Journal/Conf.
7 Yu Huang 2016
Experimental studies on Nanomaterials for
soil improvement: A review Environemental earth Science
8 Xianglei Zheng 2016
Applications of Nanotechnology in
Geotechnical Engineering
Ph.D. Theis, Arizona State
University
9
Navid Ghasabkolaei a
, Asskar Janalizadeh
Choobbasti a , Nader
Roshan a , Seiyed E.
Ghasemi b 2017
Geotechnical properties of the soils modified
with nanomaterials: A comprehensive review
Archives of Civil and
Mechanical Engineering 17
(2017) , pp 639-650.
10
Abhishek Arya1 ,
Ashwani Jain2 2017
A REVIEW OF GEOTECHNICAL
CHARACTERISTICS OF NANO ADDITIVES
TREATED SOILS
International Conf. on
Receent Development in
Engieering Science,
Humanities and Management
11 Mohd Raihan Taha 2018
Recent developments in Nanomaterials for
Geotechnical and Geoenvironmental
Engineering
MATEC Web of conferences
149
NANOTECHNOLOGY APPLICATIONS IN GEOTECHNICAL ENGINEERING

REVIEW OF LITERATURE
Sr. No. Researchers Concluding Remarks
1 Voyiadjis, 2003;
Srinivasan et. al.,
2005
The macro or micro scale behavior is ultimately the integral behavior of
nano-mechanical behavior of continuum
2 Cui et al. 1996;
Kaliakin et al. 2000;
Ling et al. 2002,
2003; Manzari 2004
Nano-mechanics offers a highly intricate understanding of material behavior,
thanks to its nano-level length scales and pico to femto seconds time
scales.
3 Anandarajah, 2004,
1994; Peters, 2004
Both continuum and discrete mechanics approaches excel in offering
macro-scale material behavior
4 Smith, 1998; Shroll
and Smith, 1999
Nano-mechanics is the preferred tool for analyzing intricate behaviors in
geo-materials, such as clay-fluid interaction.
Selected Researchers and their contribution in Nano-geo-mechanics

NANO SCALE FRICTIONAL FORCES
CONTRIBUTION BY DIFFERENT
FACTORS.
ETotal = ECoul + EVDW + E Bond Stretch + E Angle Bend + E Torsion ___________(1)
In the given equation, the terms ECoul and EVDW represent the non-bonded energy components known
as Coulombic energy and van der Waals energy, respectively.
The remaining three terms correspond to the explicit bonded energy components associated with bond
stretching, angle bending, and torsion dihedral.
Table-1 provides a summary of the significant characteristics of these energy components.

Sr.No. Forces Governing Equations Remark
1 Coulombic
In the given context, qi and qj denote the charge of the two
interacting atoms (ions), e represents the electron charge, and
εo refers to the permittivity (dielectric constant) of a vacuum.
The Coulombic energy relies on the classical depiction of charged
particle interactions and exhibits an inverse relationship with the
distances rij.
2 Van der Waals Lennard-Jones Potential Energy
Where, Do and Ro represent pragmatic parameters.
The second term corresponds to the van der Waals energy, which
represents the attractive molecular interactions.
3 Bond Stretch E Bond Stretch = k1(r − ro) 2
In this context, r denotes the separation distance between the
bonded atoms, ro is the equilibrium bond distance, and k1
represents an empirical force constant.
The bond stretch term can be expressed as a straightforward quadratic
(harmonic) equation.
4 Angle Bend E Angle Bend = k2 (θ−θo) 2
In this case, θ represents the measured bond angle for the
configuration, θo is the equilibrium bond angle, and k2 is the
angle bend force constant.
The angle bend energy equation for a bonded system is commonly
formulated using a harmonic potential.
5 Torsion ETorsion = k3 (1 + cos3ϕ)
Where, k3 is an experimental force constant and ϕ is the
dihedral angle.
The torsional dihedral interactions, represented by the dihedral angle ϕ,
are defined as the angle formed by the terminal bonds of a quartet of
sequentially bonded atoms when viewed along the axis of the
intermediate bond.
Notes Supplementary terms can be incorporated into the total potential energy expression of (1), including an out-of-plane stretch term,
particularly for systems with a planar equilibrium structure.
Table-1 Nano scale frictional forces contribution by different factors

1.3. NANO-MECHANICS AS A TOOL TO STUDY
MACRO-LEVEL MATERIAL PROPERTIES THROUGH
CONTINUUMIZATION
A bridge is required to connect Nano-mechanics and continuum mechanics,
offering detailed Nano-scale material behavior as well as macro-scale material
behavior at the continuum level.
This bridge allows the integration of Nano-mechanics with well-established
modern continuum mechanics, as illustrated in Table 2.
Essentially, Nano-mechanics will furnish the fundamental properties required by
continuum mechanics (e.g., continuum mechanics parameters shown in Table
2), while continuum mechanics will handle the micro and macro scale behavior
of geo-materials.

TABLE-2 EQUATIONS GOVERNING MICRO-
MECHANICAL BEHAVIOR OF PARTICLES
Sr.
No.
Micromechanical
Behaviour
Form of Governing Equations Notations References for contribution
1
Rotation of
Particles
Where, Ws′′,ξ,ᾱ, and ds′′ are the
plastic rotation tensor, constant,
back stress, and distortion,
respectively.
Dafalias (1998), Cosserat
(1909), Song and Voyiadjis
(1999 to 2005), Voyiadjis and
Kattan (1990, 1991)
2
Interaction of
Particles
Where, ῁ε vp ˙ἐvp v , and k are
the normalized strain rate, visco-
plastic volumetric strain rate and
a constant, correspondingly.
Di Prisco and Aifantis (1999),
Zbib (1994), Zbib and Aifantis
(1988), Voyiadjis and Song
(2005), Song and Voyiadjis
(2005a)
3
Damage of
particles
Where, λd, g and σ are the
damage strain, damage
multiplier, damage potential, and
stress, respectively.
Voyiadjis and Song (2005a)

4
Viscosity of pore
fluid
where, f, fs,po, ηvp,˙¯p, Bii, and
m1 are the dynamic yield surface,
static yield surface, mean principal
stress, viscosity, time rate of the
mean stress, the differentiation of
fwith stress, and a constant,
respectively,
Perzyna (1963, 1966, 1988),
Song and Voyiadjis (2005a),
Voyiadjis and Song (2005)
5
Flow
characteristics
of pore fluid
where, n, ρs, ρw aw, Kws, υs,
Pw and b are the porosity, mass
density of the soil, mass density of
the water, acceleration of water,
permeability tensor, solid velocity,
pore water pressure, and body
force vector.
Coupled theory of mixtures
Biot (1955, 1978), Prevost
(1980, 1982), Muraleetharan et
al. (1994), Schrefler et al.
(1990), Wei and Muraleetharan
(2002) Song and Voyiadjis
(1999 to 2005) Voyiadjis and
Song (2000 to 2005)
Sr.
No.
Micromechanical
Behaviour
Form of Governing Equations Notations References for contribution

TABLE- 3 DISTINGUISHED AVERAGING
METHODS
Sr.
No.
Method Equations Notation Remark Reference
1
RVE Where, A′ is the
property at upper scale,
V is the volume of RVE,
A is the property at
lower Scale.
Just like the homogenization
technique in continuum
mechanics, this method fully
encompasses the incorporation of
molecular interactions.
Belytschko and Xiao
(2003), Huang and
Jiang (2005)
Liu et al. (2005)
Belytschko (2005)
Song and Al-Ostaz
(2005)
2
Equivalent
beam or
truss
element
This represents the continuum
formulation of molecular
mechanics. The stiffness input
parameters, like Young's modulus,
were determined by comparing
the potential energy for stretching
to the corresponding strain
energy, as follows:
This method proves to be less
effective in simulating dynamic
processes, such as the interaction
between minerals and pore fluids.
Li and Chou (2003)
Odegard et al. (2001)
Ostoja-Starzewski,
(2002),Srinivasan et
al. (2005), Wang et al.
(2005)

NANO MECHANICS - CHARACTERISTICS
Nano mechanics offers the fundamental characteristics of discrete elements, whereas the
process of continuumization bridges the gap between discrete elements and continuum,
resulting in macro-level behaviour. (Cosserat brothers 1909; Anandarajah 2004; Tordesillas et
al. 2004; Peters, 2004).
The Nano-mechanics technique for soils presents unique challenges and must be
distinct from that used for other continuous materials. The following outlines the rational
procedure:
1) Use Nano-mechanics to study grain and grain-liquid interactions.
2) Determine the material properties of discrete particles and their surroundings.
3) Convert the discrete attributes to continuous properties using a continuumization
approach.

1.4. FACTORS AFFECTING NANOSCALE
FRICTION
i. Surface roughness: The roughness of the contacting surfaces can have a significant
effect on nano scale friction. Rough surfaces tend to have higher friction forces than
smoother surfaces.
ii. Adhesion: Adhesion between the contacting surfaces can affect the friction force at the
Nano scale. Strong adhesion between surfaces can increase the frictional force, while
weak adhesion can decrease it.
iii. Surface chemistry: The chemical properties of the surfaces in contact can influence
Nano scale friction. The presence of surface contaminants or changes in the surface
chemistry can affect the frictional force.
iv. Applied load: The magnitude of the applied load can influence Nano scale friction.
Higher loads can result in greater friction forces.
v. Sliding velocity: The velocity at which the surfaces slide past each other can affect
Nano scale friction. Generally, higher sliding velocities can result in higher friction
forces.

vi. Temperature: Temperature can have a significant effect on Nano scale friction.
Changes in temperature can cause changes in the chemical and physical
properties of the contacting surfaces, which can affect the frictional force.
vii. Lubrication: The presence or absence of a lubricant can also affect Nano scale
friction. Lubricants can reduce friction by reducing adhesion between surfaces and
providing a barrier between them.
 Understanding the factors that influence Nano scale friction is important for
developing effective strategies to control and reduce friction at the nanoscale.
 By manipulating these factors, it may be possible to design surfaces and materials
with reduced friction forces, which could have important applications in a wide range
of fields, including nanotechnology, biotechnology, and materials science.
1.4. FACTORS AFFECTING NANOSCALE
FRICTION

1.5. METHODS TO CALCULATE NANO SCALE
FRICTION
Calculating Nano scale friction between surface coatings can be challenging due to the complex
interplay of various factors involved.
Several approaches can be used to estimate Nano scale friction between surface coatings:
1. Atomic force microscopy (AFM),
provide information on:
1. the surface topography,
2. adhesion, and
3. frictional forces at the Nano scale.
This technique can be used to compare the frictional
forces of different surface coatings under different
conditions, such as varying applied loads, sliding
velocities, and temperatures.

1.5. METHODS TO CALCULATE NANO SCALE
FRICTION
Another approach is to use computer simulations, such as
2. Molecular dynamics (MD)
MD simulations can provide atomistic-level details of
the interaction between surfaces, which can be used to
estimate frictional forces.
The simulations provide an opportunity to explore the
impact of various factors on Nano scale friction, including
surface roughness, adhesion, and lubrication.

1.6. EQUATIONS GOVERNING NANO SURFACE
COATING FRICTIONAL FORCES
The frictional forces of Nano surface coatings are governed by equations
that rely on diverse factors, including :
• The type of coating,
• Surface roughness,
• Material properties, and
• Environmental conditions in which the coating is applied.

SOME GENERAL EQUATIONS THAT CAN BE
UTILIZED TO DESCRIBE THE FRICTIONAL
BEHAVIOR OF NANO SURFACE COATINGS:
1. Amontons' law: This law states that the frictional force between two surfaces is proportional to the
normal force pressing the surfaces together. Mathematically, it can be expressed as:
F_friction = μ*F_normal
Where, μ is the coefficient of friction.
Jianping G (2004), further classified the friction as Adhesion-controlled and Load-controlled friction.
2. Archard's equation: The Archard wear equation serves as a fundamental model for characterizing
sliding wear, founded on the principles of asperity contact theory. It is given by
V = kFN/(H*ρ)
Where, V is the wear volume, k is the wear coefficient, F is the applied load, N is the number of sliding
cycles, H is the hardness of the material, and ρ is its density.

SOME GENERAL EQUATIONS THAT CAN BE UTILIZED TO DESCRIBE THE
FRICTIONAL BEHAVIOR OF NANO SURFACE COATINGS
3. Coulomb's law of friction: The law stipulates that the frictional force between two surfaces is directly
proportional to the normal force and remains unaffected by the contact area between the surfaces.
Mathematically, it can be expressed as follows:
F_friction = μ*N,
Where, N is the normal force.
4. Johnson-Kendall-Roberts (JKR) model: This model is used to describe the contact mechanics of
elastic spheres in contact with a flat surface. It is given by
F_adhesion = (3/2)E(R_1*R_2)/(R_1+R_2)*δ^(3/2),
Where, F_adhesion is the adhesive force, E is the elastic modulus, R_1 and R_2 are the radii of the two
contact surfaces, and δ is the distance between them.
5. Derjaguin-Muller-Toporov (DMT) model: This model is similar to the JKR model but assumes that the
contact is dominated by van der Waals forces. It is given by
F_adhesion = πR^2W,
Where, R is the radius of the contact area and W is the surface energy

1.7. COUPLED BEHAVIOR OF NANO-
MICRO AND MICRO- MACRO
MECHANISM
Micromechanical behavior involves
 grain rotation,
 grain interactions like grain interlocking,
 pore fluid viscosity, and
 grain integrity.
(after - Voyiadjis and Song, 2003)
Fig-3 ASTM Soil classification according to grain size along with the forces affecting soil behavior.

2. CHALLENGES IN CALCULATION OF
NANO FRICTION APPLICABLE TO GEO-
MATERIALS.
Scale dependence:
Friction at the nanoscale is influenced by various factors such as surface roughness, interfacial
interactions, and atomic rearrangements.
These phenomena are strongly scale-dependent, and their effects become more pronounced as the
system size decreases.
Accounting for these scale-dependent effects is a challenge in accurately calculating nano friction in
geomaterials.

MATERIALS.
Multiscale modeling:
Geomaterials exhibit a hierarchical structure, spanning multiple length scales from nanometers
to meters.
To accurately capture the friction behavior, it is often necessary to employ multiscale modeling
approaches.
However, bridging the gap between different scales and integrating the information across the
scales poses a significant challenge.
Developing effective multiscale models that can capture the essential frictional behavior at the
nanoscale and upscale it to larger scales is an ongoing research area.

MATERIALS.
Surface characterization:
Accurate characterization of surface roughness and topography is crucial for understanding
and predicting Nano friction.
Geomaterials often exhibit complex and heterogeneous surface structures, making their
characterization challenging.
High-resolution techniques, such as atomic force microscopy (AFM) and scanning electron
microscopy (SEM), are commonly employed.
However, the process of extracting meaningful information from the obtained data and
integrating it into friction models is a challenging task that requires careful consideration.

MATERIALS.
Interfacial interactions:
Friction at the nanoscale is governed by interfacial interactions between atoms or molecules.
In the case of geomaterials, these interactions can be highly complex due to the presence of
various chemical and physical forces, such as van der Waals forces, adhesion, electrostatic
interactions, and surface hydration.
Capturing the full range of interfacial interactions and their impact on friction is a significant
challenge in the calculation of Nano friction in geomaterials.

MATERIALS.
Computational complexity:
The calculation of Nano friction involves atomistic simulations, such as molecular dynamics
(MD), which can be computationally intensive.
Geomaterials typically consist of a large number of atoms, and simulating their behavior over
relevant time and length scales requires significant computational resources.
Efficient algorithms and parallel computing techniques are necessary to overcome the
computational complexity associated with Nano friction calculations in geomaterials.

SIZE AND AMOUNT OF THE PARTICLES
THAT MAKES - SOIL

3. CONCLUSION:
Nano-geo-mechanics presents exciting opportunities for advancing our understanding of geotechnical
processes and improving the design and performance of geotechnical systems.
The scale dependence of friction in geomaterials has been highlighted as a crucial factor, with surface
roughness, interfacial interactions, and atomic rearrangements playing significant roles.
The characterization of complex and heterogeneous surface structures poses challenges in accurately
capturing the Nano-scale properties of geomaterials.
Multiscale modeling approaches have been acknowledged as a valuable means of bridging the gap
between various length scales and capturing crucial frictional behavior.

Nano mechanics,
Geo-materials,
Nano scale friction,
Governing equations,
Macro-nano behavior of geomaterials.
SUMMARY
Nano mechanics,
Geo-materials,
Nano scale friction, Nano- Geo
Governing equations,
Macro to nano behavior of geomaterials.

SELECTED REFERENCES
1) Anandarajah, A. (2004), “Sliding and Rolling Constitutive Theory for Granular Materials,” Journal of Engineering
Mechanics, Vol. 130, No. 6, June 1, pp. 665–680 DOI: 10.1061/(ASCE)0733-9399(2004)130:6(665)
2) Belytschko, T. (2005), “Computational Studies of Nanofracture,” McMat 2005 Conference, Baton Rouge, LA
(Plenary Lecture 1.P2)
3) Cui, L., Cheng, A. H-D., Kaliakin, V. N., Abousleiman, Y. and Roegiers, J.-C. (1996), “Finite Element Analysis of
Anisotropic Poroelasticity: A Generalized Mandel’s Problem and an Inclined Borehole Problem,” International
Journal for Numerical and Analytical Methods in Geomechanics, Vol. 20, pp. 381–401.
https://doi.org/10.1002/(SICI)1096-9853(199606)20:6<381::AID-NAG826>3.0.CO;2-Y
4) De Boer, R. (1996), “Highlights in the historical development of the porous media theory: Toward a consistent
macroscopic theory,” ASME, Applied Mechanics Reviews, Vol. 49, No. 4, pp. 201–262.
https://doi.org/10.1115/1.3101926
5) Desai, C.S., Basaran, C. and Zhang, W. (1997), “Numerical algorithms and mesh dependence in the disturbed
state concept,” International Journal for Numerical Methods in Engineering, Vol. 40, No. 16, 1997, pp. 3059–
3083. https://doi.org/10.1016/S0045-7825(97)00159-X
6) Desai, C.S. and Zhang, W. (1998), “Computational aspects of disturbed state constitutive models,” Computer
methods in applied mechanics and engineering, Vol. 151, No. 3–4, pp. 361–376. https://doi.org/10.1016/S0045-
7825(97)00159-X

SELECTED REFERENCES
7) Kaliakin, V.N., Dechasakulsom, M. and Leshchinsky, D. (2000), “Investigation of the Isochrone Concept for Predicting
Relaxation of Geogrids,” Geosynthetics International, Vol. 7, No. 2, pp. 79–99. https://doi.org/10.1680/gein.7.0167
8) Katti, D.R., Pradhan, S.M. and Katti, K.S. (2004), Modeling The Organic- Inorganic Interfacial Nanoasperities In A
Model Bio-Nanocomposite, Nacre, J. Reviews on Advanced Materials Science, n 6, 162–168.
9) Ling, H.I., Anandarajah, A., Manzari, M.T., Kaliakin, V.N. and Smyth, A. (2003), Constitutive Modeling of
Geomaterials, Inelastic behavior committee, engineering mechanics div. ASCE, CRC Press, p. 212. DOI:
10.1061/(ASCE)0733-9399(2004)130:6(621)
10) Lee and Finn (1967), “Drained Strength Characteristics of Sands,” Journal of Soil Mechanics and Foundations
Division, ASCE, Vol. 93, No. SM6, pp. 117–141. https://doi.org/10.1061/JSFEAQ.000104
11) Meng, W.J., and Voyiadjis, G.Z., “Structure and Mechanical Properties of Ceramic Nanocomposite Coatings,” Trends
in Nanoscale Mechanics Vol. 9: Analysis of Nanostructured Materials and Multi-Scale Modeling, Part I
Nanomechanics, Chap. 4, Edited by V.M. Harik and M.D. Salas (ICASE, NASA Langley Research Center), Kluwer
Academic Publishers, The Netherlands, 2003, pp. 89–120. DOI: 10.1007/978-94-017-0385-7_4
12) Manzari, M.T. (2004), “Application of micropolar plasticity to post failure analysis in geomechanics,” International
Journal of Numerical and Analytical Methods in Geomechanics, Vol. 28, Issue 10, pp. 1011–1032. DOI:
10.1002/nag.356

CITE THIS WORK AS
Parmar S.P. and Shukla A.D. (2023) Nano-Geo-Mechanics: Challenges to calculate
friction for Geomaterials, Int. Conf. on Academic & Industrial Innovations, P P
Savani University (PPSU), Surat, India. pp. 1-11.

OTHER PUBLICATIONS BY AUTHOR
Parth Patel, & Samirsinh P. Parmar. (2022). Experimental and Analytical Study on Uplift Capacity of
Square Horizontal Anchor in Cohesionless Soil. Journal of Advances in Geotechnical Engineering,
5(3), 1–14. https://doi.org/10.5281/zenodo.7298849
Samirsinh Parmar. (2022). The Experimental Failure behaviour of a Prestressed Concrete Electricity
Transmission Pole: A Case Study for Kannauj Soil, Uttar Pradesh, India. Journal of Engineering
Analysis and Design, 3(3), 1–13. https://doi.org/10.5281/zenodo.5837583
Akbar K.B & Samirsinh Parmar,(2021) " Experimental and analytic study of the uplift capacity of a
horizontal plate anchor embedded in geo-reinforced sand", Proceedings of First Indian Geotechnical
and Geoenvironmental Engineering Conference IGGEC-21, pp-1-16.
Samir Parmar, & R.M. Patel. (2021). Bearing Capacity of Isolated Square Skirted Foundation on
Cohesionless Soil: An Experimental and Analytical Study. Journal of Advances in Geotechnical
Engineering, 4(2), 1–11. https://doi.org/10.5281/zenodo.5229164
And many more…!

THANK YOU
Samirsinh P Parmar
Spp.cl@ddu.ac.in
samirddu@gmail.com
www.ddu.ac.in

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