Geomechanics of Soft Ground Improvement by Perforated
Piles: Review and Case Study
SUDIP BASACK, GAUTAM DAS, SK ASIF IQBAL, JYOTIRMOY DEB
Elitte College of Engineering, Affiliation: MAKA University of Technology,
Kolkata 700113, INDIA
Abstract: - Civil Infrastructure built on soft and compressible soil is likely to collapse due to undrained shear failure
or unacceptable settlement of supporting foundations. Incorporation of adequate ground improvement technique with
the aim of upgrading the strength and stiffness of the weak soil is essential in such cases. Amongst various established
methods adopted worldwide for improving soft ground, using perforated piles is a relatively emerging technique. Such
piles not only transmit the structural load into the subsoil beneath in a manner similar to the conventional piles, but
also assist in radial consolidation of soft soil due to perforated side walls. This paper presents a brief overview on the
investigations carried out on this new technique. Also, a typical case study has been presented. As observed, the axial
pile capacity progressively increased while settlement reduction took place, with accelerated radial consolidation.
Key-Words: - Axial capacity, Ground settlement, Radial consolidation, Skin friction, Soft ground, Stress concentration ratio
Received: April 15, 2021. Revised: November 20, 2021. Accepted: December 22, 2021. Published: January 10, 2022.
1
Introduction
Many parts of the world including alluvial plains and
coastal regions consists of soft compressible soils
with average shear strength seldom exceeding
20-30 kPa. Infrastructures build on such soft ground
are likely to fail unless the foundation soil is
significantly improved. In particular, foundations on
soft clay deposits can cause excessive settlement
initiating undrained failure of infrastructure if proper
ground improvement is not carried out [1], [2].
Reducing long-term settlement of infrastructure
and providing cost-effective foundations with
sufficient load-bearing capacities are national
priorities for infrastructure development in most
countries. Much modern infrastructure is constructed
over poor quality ground and is subject to greater
static and dynamic loading than previously
experienced. Appropriate ground improvement
techniques can be adopted to prevent unacceptable
excessive and differential settlement and increase the
bearing capacity of the foundations at much lower
cost. Over several decades, different ground
improvement techniques have been developed, which
include stone columns, preloading with prefabricated
vertical drains, piling, geogrids and chemical
stabilization [3], [4], [5].
Among various methods of soft soil
improvement, installation of prefabricated vertical
drains (PVDs) or stone columns (SCs) with
preloading is one of the well-established and
effective techniques practiced worldwide [6]. The
method involves acceleration in the soft soil
consolidation by shortening of the drainage path via
radial consolidation. Piles without reinforcement,
known as concrete injected columns [7], and
installation of strong piles are other methods of soft
soil improvement [8]. In case of vertical drains with
preloading, the consolidation takes place for several
years, if not vacuum assisted which is costly, and
simultaneously PVDs do not possess additional stiffness
to withstand the majority of imposed loading from
superstructure [9]. In case of SCs, the time of
consolidation is much reduced due to higher hydraulic
conductivity of stone aggregates, and simultaneously the
column-soil relative stiffness provides additional bearing
capacity to the reinforced soft clay [10]. Through the pile
foundation, the structural load is transmitted to the stiffer
soil layers underlying the soft soil deposits. In absence of
any radial consolidation, the soft soil is not improved [11].
In case of chemical stabilization, the admixtures undergo
chemical reaction with the soft clay particles and thus the
strength and stiffness of soil is improved [5], [12].
The relative merits and demerits of different
methods are summarized in Table 1.
The piles transmit the structural load to the deeper
soil stratum. Basically, the load transmission takes place
by means of frictional resistance between the pile surface
and soil. Such piles are termed as ‘frictional pile’ or
‘floating pile’. In the cases where the bases of the piles are
embedded into stiffer soil layer or rock, significant base
resistance is offered to the pile compared to the friction.
Such piles are termed as ‘end bearing pile’. This is
illustrated in Fig.1 below.
Fig 1. Load transfer mechanism of pile
Soft
clay
Stiff soil or rock
clay
Q Q
Ground surface
Floating pile
End bearing pile
Pile
type
Stress
condition
Floating
pile >>
End
bearing
pile
<<
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Table 1. Comparison of various ground improvement
techniques
Technique
Advantage
PVD with
preloading
Accelerated radial
consolidation;
convenient and
cost effective;
suitable for deep
soft clay deposit.
Sand drains
Faster radial
consolidation than
PVD; suitable for
deep soft clay
deposit; moderate
relative stiffness.
Stone
columns
Faster radial
consolidation than
sand drains; high
relative stiffness.
Piles
Significantly high
load bearing
capacity; very
high relative
stiffness; suitable
for deep soft clay
deposit.
Chemical
stabilization
Effective rise in
strength,
durability and
workability of
soil; Convenient
It is expected that the pile foundation can also
assist in radial consolidation in case the side wall is
permeable. Such pile may be termed as perforated
piles. Limited research carried out on perforated piles
indicate that they are expected to assist in accelerated
soft soil consolidation as well as carry the foundation
load as conventional piles. This paper presents a brief
overview on the existing knowledge on the behavior
of perforated pile and a typical case study to illustrate
its load transfer and soft ground improvement
characteristics.
It is observed that conventional piles, having
possessed significant relative pile-soil stiffness,
transmit the imposed load to the subsoil beneath
through skin friction and end bearing, but they do not
assist in soft soil improvement by consolidation. The
PVDs and stone columns, although assist in
consolidation, have limited relative stiffness, hence
not effective in load-transfer mechanism. Perforated
piles serve both the purpose. Although past
contributions investigated the consolidation
characteristics of perforated piles, studies conducted
on capacity and settlement analysis of perforated
piles are rather limited. The current paper aims to
carry out a preliminary study to bridge up the
knowledge gap.
Available information on perforated pile
performance is quite limited. The primary aim of this
paper is to carry out a literature review and to provide
preliminary analytical formulations pertaining to
load bearing capacity, consolidation characteristics and
settlement analysis of soft ground improvement by
perforated piles.
2
Literature Review
The perforated piles, unlike conventional piles, assist in
radial consolidation, apart from transmitting the
superstructure loads to the subsoil below. The concept of
perforated piles was initially proposed by Mei et al. [13]
and later, its radial consolidation and load transfer
characteristics were studied through theoretical and
laboratory studies by various researchers [14], [15], [16].
Ni et al. [14] carried out laboratory model tests on
concrete permeable piles with drainage hole on its
circumference. A series of uniaxial and flexure tests were
conducted with permeable concrete pile and the results
were compared with equivalent conventional piles. The
crack pattern, deflection profile and the induced strains
were investigated. As observed, although the permeable
piles assist in accelerated radial consolidation, the axial
compressive strength of such piles have been decreased to
some extent because of reduced cross sectional area due
to the drainage holes. The flexural strength, on the other
hand, was found to increase due to redistribution of the
bending stresses.
Ni et al. [15] conducted a numerical study based on
3-dimensional finite and infinite element approaches. The
soil displacement and excess pore water pressure
dissipation were studied through consolidation analysis of
perforated driven piles. The numerical results were
compared with existing analytical solutions and available
field data. It was observed that an optimum radial
consolidation was achieved for the drainage area below
50% of the overall circumferential area of the piles.
Ni et al. [16] performed laboratory investigations on
the radial consolidation by perforated driven piles in soft
clay. The perforated piles were found to be effectively
dissipate the excess pore water pressure. When such piles
are used in groups, the consolidation characteristics were
found to improve further. Based on the test results, zone
of influence of the permeable piles were proposed.
Wang et al. [17] developed a semi-analytical
consolidation solution of perforated pile using mixed
boundary condition. Instead of providing drainage hole,
PVDs were installed in the pile circumference. It was
observed that increase the number of PVD strips would
provide a better consolidation performance, instead of
increase in its width.
Chen et al. [18] provided analytical solution to
characterize the pile-soil interface boundary for
consolidation analysis driven permeable pipe pile in soft
clay. Also, a set of laboratory model tests were performed
with permeable pipe pile, single and group, embedded in
remoulded saturated soft clay bed prepared in a
rectangular confining chamber. The excess pore water
pressure was measured by a series of piezometers installed
in the soil bed. It was observed that the optimum
improvement was achieved at the centre of pile group; the
influence zone was found as function of depth.
The consolidation characteristics of perforated driven
piles in soft saturated clay is illustrated in Fig.2.
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3
Geomechanical Characteristics of
Perforated Pile
The load transfer mechanism of perforated pile is
similar to that of a conventional driven pile in soft
clay. The consolidation characteristics, on the other
hand, is like a vertical drain. Due to pile-soil relative
stiffness, arching does take place on ground surface
around the pile in case of embankment loading, the
mechanism being similar to a typical stone column.
These aspects have been described herein.
3.1 Load Transfer: Ultimate Axial Capacity
The ultimate axial capacity of a typical pile in clay is
obtained by the following correlation [8]:
(1)
where, Qu is the ultimate axial capacity, Qs is the
shaft capacity, Qb is the base restraint and Wp is the
self-weight of pile, which are given respectively by:
󰇛󰇜

(2)

󰇛
󰇜 (3)

(4)
where, Do and Di are the outer and inner diameter
of the pile, α is the adhesion factor, χ is the
perforation density defined as the ratio of the total
areas of the drainage holes to the circumference,

is the undrained cohesion of soil at depth z below
ground surface, Nc is the Terzagi’s bearing capacity
factor, is the vertical stress imparted on the pile
base, and is the unit weight of pile.
The undrained failure of foundation is important
in case of soft saturated clay. Although drainage of
excess pore water pressure from soil occurs via the
pile perforations, the undrained pile capacity has
been derived by Equations (3) and (4). The drained
capacity of piles is usually taken for over-
consolidated clay on long-term basis [19].
The undrained cohesion is one the most
significant soil strength parameter of soft clay which
is required to evaluate the undrained pile capacity. In
most cases, the undrained soil strength has been
idealized to increase linearly with depth [20].
Simultaneously, the undrained cohesion also
increases with time due to consolidation [21]. Hence,
the undrained cohesion (
) in the above Equations
has been expressed as a function of both z and t.
The correlation for the non-dimensional
perforation density χ is given by:

󰇡

󰇢
 (5)
where, nh is the total number of holes in the pile
circumference, Dh is the diameter of an individual
hole.
Various correlations are available for the adhesion
factor α. After the American Petroleum Institute [22],
(a) (b)
Fig 2. (a) Typical perforated pile, and (b) load-transfer and
consolidation mechanisms.
the following correlation holds good:

 

  (6)
󰇛
 󰇜
 
The above correlation has later been modified as
follows [23]:
󰆒


󰆒

󰆒


󰆒

(7)
where,
󰆒 is the effective overburden pressure at the
interface at a depth of z.
3.2 Soil Arching
The arching effect is evident in case of embankment
loading. Due to significant pile-soil relative stiffness, the
soil arches over the pile, initiating a parabolic vertical
stress distribution on the ground surface. This
phenomenon is termed as the soil arching [24].
It is well established that the soil strength progressively
increases with the consolidation. Therefore, the arching is
essentially time dependent. The vertical stress on the
ground surface is given as [21]:
󰇛󰇜󰇟󰇛
󰇜󰇠󰇛
󰇜 (8)
where, q(r) is the vertical stress on the ground surface
at a radial distance of r from the pile surface, Fs is a stress
function which depends upon the pile-soil stress
concentration ratio ns and N is a geometrical parameter,
given as,
(9)
The stress concentration ratio is given by:
󰇛
󰇜 (10)
where, re is the radius of influence and wp is the vertical
wsur
Embankment
(unit weight =
γe)
Perforated pile
Inner core
Ground
surface
Soft
clay
he
󰇛󰇜󰇛 󰇜󰇛󰇜
󰇛󰇜
Parabolic
Do = 2ro
L
r
z
󰇛󰇜
󰇛󰇜
󰆒󰇛󰇜
0 < t < t’
r
z
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stress on pile. Since the soft clay undrained gradually
increases with time as the consolidation progresses,
the parameter ns also increase with time, till a steady
state value is attained.
In case of PVDs, the value of ns is unity, while for
SCs, its value varies between 2 to 5 [25]. In case of
pile, however, the value of ns is expected to be more
than that for SCs due to significantly higher pile-soil
relative stiffness, although no definite information is
available on this aspect. In addition, unlike PVDs and
SCs, the pile-soil interface is subjected to shear stress
initiating a differential settlement between the soil
and the pile, which is likely to alter the load transfer
mechanism in a different way [26].
3.3 Soft Clay Consolidation
Due to perforations, the piles also act as vertical
drains to assist radial consolidation. Due to larger
diameter and higher hydraulic conductivity, the rate
of consolidation in case of these perforated piles is
expected to be much greater than PVDs and SCs.
The flow of pore water during the consolidation is
predominantly radial (horizontal towards the pile),
although there shall also be a minor vertical
component as well. Neglecting this vertical
component, the differential equation for radial
consolidation is given by [27]:
󰇛
󰇜 (11)
where,


, 
, urt is the excess
pore water pressure at the coordinate (r, t) in the
space-time frame and cvr is the coefficient of radial
consolidation, given by:

(12)
where, kh is the horizontal permeability of soft
clay, mv is its volumetric compressibility and is
the unit weight of water.
Due to excess pore water pressure dissipation, the
soft soil will strengthen and stiffen significantly,
resulting in enhanced ultimate pile capacity at the end
of consolidation. The concept of installation of
perforated piles involves partial replacement of weak
soil with the piles which act as in-situ reinforcement
to the soft cohesive soil. Ground improvement by
perforated piles are adopted to support embankments,
bridge abutments, tanks as well as large industrial,
commercial and marine structures [28].
4 Case Study
In this section, the field performance of a prototype
perforated pile supporting a typical rectangular
embankment has been studied. The post-
consolidation pile capacity due to enhanced soil
strength, settlement reduction and radial
consolidation characteristics have been analyzed
through simplified formulations. In absence of
appropriate theoretical model, these parameters were
evaluated using existing results valid for stone
columns. Although they might not be specifically
applicable in case of perforated piles, those results
were used as a preliminary study. However, a more
accurate analysis demands rigorous theoretical modelling.
The practical application of perforated pile at the site
has been illustrated by a hypothetical case study, where a
semi-infinite soft clay deposit has been improved by a
concrete perforated pile and the preloading is imparted
by an embankment, as shown in Fig.3, [29], [30]. The
analysis and the performance of the perforated piles in
terms of soft ground improvement has been studied, as
described herein.
Fig 3. A typical case study
4.1 Ultimate Axial Capacity of Pile
The ultimate axial pile capacity has been evaluated using
Equations (1-4) above. The values of α have been
computed using Equations (6-7) above. Choosing bulk
unit weight of soft clay as 18 kN/m3, the depth-wise
variation of α has been shown in Fig.4.
Fig.4. Depth-wise variation of adhesion factor
Considering Nc = 9.0 [8] and γp = 25 kN/m3, the pre-
consolidation values of ultimate axial capacity of the pile
is evaluated, as given in Table 2.
bf (=2m)
he
be
2H
1V
=10 kPa
cu
z
Di
Do
1m
1 kPa/m
L
N.B.:
Es /cu =100
[8], [29], [30]
Embankment dimensions
Top width
(bf)
Height
(he)
Base
width (be)
2 m
6 m
26 m
7 m
30 m
8 m
34 m
N.B.:(1) Embankment side slope =
2H:1V; (2) Pile dimensions: L = 20 m,
Do = 1 m, Di = 0.2 m, perforation
density = 30%.
Embankment
Ground
surface
Perforated
concrete
pile
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Basack et al. [31] carried out parametric studies to
provide design curves for radial consolidation and
resulting improvement of bearing capacity for stone
column reinforced soft clay. The soft ground
improvement was quantified by a non-dimensional
improvement factor β defined as the ratio of post-
consolidation to pre-consolidation undrained
cohesion of soft clay.
For different embankment heights, the value of N
has been estimated from the following correlation:

(13)
The average vertical stress on the ground surface
is given as,
 (14)
where, is the bulk unit weight of the
embankment material.
The stress concentration ratio has been estimated
from the following correlation:
(15)
where, and are the Young’s modulus of the
pile and the soil respectively.
A set of design curves portraying the variation of
β with 
for different values of N and ns is
available [31]. Assuming =20 kN/m3 and
Ep=30 GPa, different values of β have been
extrapolated for different embankment heights. The
post-consolidation ultimate axial pile capacity has
been estimated from the following correlations:
(16)

󰇛
󰇜 (17)
(18)
where,
,
and
are the post-consolidation
values of shaft capacity, base restraint and net
ultimate capacity of the pile, respectively.
For different values of embankment heights, the
imposed vertical stress on the ground surface is likely
to vary. Accordingly, the post-consolidation pile
capacities shall also alter. Using the above
correlations, the different values of post
consolidations have been calculated [32]. This is
depicted by a bar chart shown in Fig.5.
4.2 Settlement Analysis
Apart from the requirement of adequate factor for
pile design, the settlement under imposed load must
not exceed the acceptable limits. Hence, the
settlement analysis has also be included in the present
case study. The method of computation is described
below.
Assuming the volumetric compressibility of the
clay as mv = 3 x 10-6 m2/N, the settlement of the clay
layer at a degree of consolidation of U = 90% without
the pile has been computed from the following
correlation [31]:


(19)
Table 2. Pre-consolidation ultimate axial pile capacity
Capacity
Method
Shaft
capacity,
Qs (kN)
Base
capacity,
Qb (kN)
Self
weight,
W (kN)
Net
capacity,
Qu (kN)
API [23]
730
475
377
828
API [22]
835
475
377
930
Fig 5. Post-consolidation axial pile capacities
where,  is the change in the effective overburden
pressure at the centre of the clay element.
To compute the settlement of ground surface with pile,
the methodology proposed by Basack et al. [31] has been
followed, where a settlement factor ξ was introduced,
which was defined as the ratio of average ground
settlements with and without reinforcement at 90%
consolidation. The variation of ξ with N for different
values of ns were proposed by a set of curves. The average
ground settlement with piles has been computed using
these curves by extrapolation. The values of ground
settlements are shown in Fig.6.
As observed, the average ground settlement increases
with the ascending embankment height following a fairly
linear pattern. Due to the presence of the pile, the average
ground settlement has been significantly reduced
compared to those obtained without the pile. For the
embankment heights of 6 m, 7 m and 8 m, the values of
settlement factor ξ has been estimated as 0.165, 0.175 and
0.189 respectively. Accordingly, the percentage of
settlement reduction compared to unreinforced soft
ground has been calculated [󰇛󰇜]. This
implied that the values of relevant settlement reduction
have been 83.5%, 82.5% and 81.1%, respectively.
Fig 6. Variation of ground settlement with embankment height
Case-A Case-B Case-C
Case
A
B
C
he
6 m
7 m
8 m
β
1.1
1.25
1.5
API [23]
API [23]
API [22] API [22]
he (m)
Parameter
6
7
8
ξ
0.169
0.175
0.189
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4.3 Consolidation Characteristics
To study the consolidation characteristics,
appropriate theoretical analysis and experimentations
(laboratory or field) are necessary. In absence of such
data, an approximate analysis has been carried out in
the present case study. The existing consolidation test
data with the perforated single pile from the
laboratory model tests by Chen et al. [18] has been
utilized herein. To obtain the consolidation time
results, the appropriate laboratory data has been
multiplied by a non-dimensional conversion factor ς
given by:


󰇡
󰇢 (20)
where, the suffixes f and l refer to the values of the
relevant parameters corresponding to field and
laboratory, respectively.
Considering the horizontal permeability of the
soft clay in the field as 1 x 10-9 m/s, the value of ς has
been evaluated as 208.33. Using the laboratory test
results [18], the time pattern of variation of the degree
of consolidation is plotted, as depicted in Fig.7. The
details of analysis have been available elsewhere
[32].
Fig 7. Variation of degree of consolidation with time
The field data has been estimated based on
extrapolating the laboratory test results using Eq. (20)
above. It has been observed that the improvement
factor β has been 1.1, 1.25 and 1.5 in the cases of
embankment heights of 6m, 7m and 8m, respectively
(see Fig.5). Thus, due to increased soil strength
initiated by radial consolidation, the ultimate pile
capacity has been increased by 10%, 25% and 50%,
respectively. Moreover, the perforated piles have
been quite effective as a vertical drain, assisting the
radial consolidation, as observed in Fig.7. The field
consolidation using extrapolated laboratory test data
progressed faster compared to the laboratory results.
Level of accuracy of such observation requires a
more rigorous analytical or numerical modelling.
5 Critical Analysis and Research
Directives
Soft ground improvement using perforated piles is a
relatively new but quite effective technique.
However, due to limited study, theoretical and
experimental knowledge available is rather limited.
This necessitates the importance of conducting a thorough
and detailed study including theoretical analysis
(analytical and numerical), laboratory model tests
incorporating the critical parameters and instrumented
field trials. In parallel, the cost effectiveness of the new
technique should as well be analyzed to critically
understand the benefits achieved over the other
established soft ground improvement techniques. This
should be followed by developing design
recommendations associated with appropriate charts and
curves to assist the practicing engineers.
Accordingly, the research directions should follow the
path satisfying each of the above steps sequentially. The
proposed flow-chart of execution of the research is
presented in Fig. 8 below.
No Yes
Fig 8. Research directives: proposed flow-chart
6 Conclusions
Perforated piles used for soft ground improvement is
relatively new but promising technique. This paper
presents a brief overview the existing studies carried out
on this emerging study area. The literature review
indicates that the numerical, analytical and laboratory
investigations carried out has been rather limited, thus the
field is in infantry stage.
The study reveals that the perforated piles not only
transmit the structural loads quite effectively to the subsoil
beneath through shaft friction and end bearing, but they
are also quite effective in reducing the settlement and
accelerating radial consolidation. Simplified correlations
have been proposed to estimate ultimate capacity of these
perforated piles.
Start
Analytical and
numerical modelling
Small-scale
laboratory model tests
Full-scale
instrumented field trial
Validation: comparison of laboratory and field
data with analytical and numerical results
Satisfactory
Validation?
Analyze cost-effectiveness
Develop design
recommendations
Stop
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A typical case study on the effectiveness of
perforated piles embedded in soft clay deposit under
embankment loading has been carried out. While the
pile capacity has been found to increase by 10-50%
due to consolidation, significant settlement reduction
of 81.3-83.5% was observed. The consolidation
characteristics were also studied by reasonable
extrapolation of the available laboratory test data,
which indicated acceleration.
It is proposed that extensive theoretical and
experimental investigations should be conducted
together with cost effectiveness, followed
subsequently by appropriate design
recommendations for practicing field engineers.
7 Acknowledgements
The authors thankfully acknowledge the
infrastructural supports received from Pinnacle
Educational Trust, Kolkata, India, during execution
of the study. The work is carried out at Elitte College
of Engineering, Kolkata, India.
Notations:
bf =
Top width of embankment
be =
Bottom width of embankment
𝑐𝑢
𝑧𝑡 =
Undrained cohesion of soil at point (z, t)
𝑐𝑢
𝐿𝑡 =
Undrained cohesion of soil at point (L, t)
cvr =
Co-efficient of radial consolidation
𝑐𝑣𝑟
𝑓 =
Co-efficient of radial Consolidation in field
𝑐𝑣𝑟
𝑓 =
Co-efficient of radial consolidation in laboratory
Do =
Outer diameter of pile
Di =
Inner diameter of pile
Dh =
Diameter of an individual hole
Ep =
Young’s modulus of pile
Es =
Young’s modulus of soil
Fs =
Stress function
He\ =
Height of embankment
Hs =
Height of soil layer
kh =
Horizontal permeability of soft clay
L =
Length of pile
mv =
Volumetric compressibility
ns =
Stress concentration ratio
nh =
Total number of holes in the pile circumference
Nc =
Bearing capacity factor
Q =
Load carrying capacity of pile
Qb, Qs, Qu =
Base restraint; shaft friction, axial capacity of pile
𝑄𝑏
𝑓,𝑄𝑠
𝑓,𝑄𝑢
𝑓=
Post-consolidation base restraint, shaft friction
and net axial capacity of pile
𝑄𝑏
𝑓 =
Post-consolidation net ultimate base restraint
𝑄𝑢
𝑓 =
Post-consolidation net ultimate capacity of pile
r =
Radial distance
rp =
Radius of pile
re =
Radius of influence
U =
Rate of consolidation
urt =
excess port water pressure at point (r, t)
w(r) =
Vertical stress on ground surface
wp =
Vertical stress on pile
wav =
Average vertical stress on ground surface
wsur =
Surcharge load
wp =
Self-weight of pile
z =
Depth
α =
Adhesion factor
β =
Non-dimensional improvement factor
γe =
Unit weight of embankment
γp =
Unit weight of pile
γs =
Unit weight of soil
σv =
End bearing capacity
σz' =
Effective overburden pressure
τv =
Skin friction
ς =
Non dimensional conversion factor
χ =
Perforation density
χf =
Perforation density in field
χl =
Perforation density in laboratory
∆p =
Change in overburden pressure
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Conflict of Interest Statement
The authors declare that there is no conflict of interest
in this paper.
Authors’ Contributions
Sudip Basack is responsible for overall supervision
and execution; Goutam Das conducted drafting and
revision; Sk Asif Iqbal and Jyotirmoy Deb carried out
literature survey, writing and revisions.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.4
Sudip Basack, Gautam Das,
SK Asif Iqbal, Jyotirmoy Deb
E-ISSN: 2224-3429
28
Volume 17, 2022
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
Infrastructural supports received from Pinnacle
Educational Trust.