This work is licensed under a Creative Commons Attribution 4.0 International License

Parametric Numerical Study on the Impact of Intenal

Friction Angle and Pile Diameter on Soil Deformation in

Nasiriyah

Raghad Adel Fahad

Civil Engineering, University of Thi-Qar, Nasiriyah, Iraq

*Corresponding author E-mail: [email protected]

DOI:10.52113/3/eng/mjet/2025-13-02-/45-57

Abstract

Clarifying the behavior of the soil near the bored pile foundation tips through estimating the boundary of the influence

has a great benefit theoretically and practically in the accurate design of pile foundations. This research presents an

advanced geotechnical analysis of the piles in Nasiriyah soil applied to the foundation of the Al-Iskan Interchange project.

The study employed finite element analysis, utilizing the Plaxis3d Foundation software to systematically investigate the

impact of variations in internal friction angles and pile diameters on soil deformations. Through a parametric study, the

research sheds light on the intricate relationship between these key parameters and the behavior of the soil. The findings

reveal compelling insights: deformations exhibit a discernible pattern in response to internal friction angle and pile diameter

alterations. Specifically, deformations demonstrate a diminishing trend with an increasing internal friction angle, while a

contrasting escalation is observed with larger pile diameters. This nuanced understanding highlights the importance of

selecting the depth to which the pile is driven. The depth refers to the soil with optimal values for internal friction angles

and pile diameters in engineering projects, with direct implications for enhancing stability and minimizing deformation.

Keywords: Geotechnical Analysis, Finite Element Analysis, Plaxis3dFoundation Software, Internal Friction Angle, Pile Diameter.

1. Introduction

Foundations are the essential and vital elements that constitute the base or support of a particular structure [1]. Foundations

are used to bear and distribute loads evenly, aiding in the stability and balance of the system or structure [2]. They are

considered fundamental to maintaining the continuity and organization of various systems, whether they are engineering,

social, or even mental [3]. They form the bedrock, both literally and metaphorically, upon which the edifice of any

construction rests. In this intricate case between the terrestrial and the man-made, understanding the principles and

significance of foundations becomes paramount [4]. Within the scope of our advanced study on the impact of foundations

on the Al-Hawraa Project, it becomes evident that piles play a crucial role in this context [5]. These engineering elements

are key components responsible for transferring and directing the loads generated by the bridge towards the underlying

soil. Our analysis specifically addresses the role of piles in this context, highlighting their significant effect on vertical and

horizontal deformations in the surrounding soil [6] [7]. Through our prominent study, we observe how piles interact with

variations in the internal friction angle and pile diameter. It becomes apparent that the technology of load redirection and

distribution employed by piles significantly contributes to reducing pressure on the soil, thereby improving the stability of

the building [8] [9]. In this context, piles are not only a means of load transfer but also a primary tool for enhancing the

stability of the surrounding soil [10] [11]. In recent years, the Finite Element Analysis (FEA) was an analytical engineering

method used to study complex structural interactions and estimate stresses and deformations in intricate structures. FEA

divides the structure into smaller units called elements, where the behavior of each element is analyzed individually, and

the results are then combined to form a comprehensive representation of the entire structure. Plaxis3dFoundation is a finite

element software specifically crafted for geotechnical engineering analysis [12]. It provides sophisticated capabilities for

modeling intricate soil-structure interaction challenges, encompassing scenarios like pile rafts and footings. Additionally,

Muthanna Journal of Engineering and Technology, Vol. (13), Issue (2), (Year) 2025

Muthanna Journal of Engineering and Technology

Website: https://muthjet.mu.edu.iq/

Submitted 8 March 2025, Accepted 10 May 2025, Published online 16 May 2025

Muthanna Journal of Engineering and Technology

Plaxis3dFoundation offers specialized geotechnical functionalities, including the modeling of soil behavior, consideration

of pile-soil-raft interaction, and the simulation of foundation load responses [13]. This study addresses a problem in soil-

structure interaction, focusing specifically on the Al-Hawraa Project. The challenge revolves around understanding the

impact of variations in internal friction angle and pile diameter on deformations and stresses in the surrounding soil.

Lina Xu (el.) [14] conducted a study on the impact of increasing the diameter of the foundation at a specific depth. The

study revealed that soil areas were less affected by external loads distributed over the region, especially in areas where an

increase in the

foundation diameter occurred. The study showed that increasing the foundation diameter at a specific depth contributes to

reducing the effect of distributed external loads on the surrounding areas. This work bears some resemblance to the study

conducted in this paper, where the impact of diameter and internal friction angle is investigated. The study explores how

these factors influence the depths and areas of soil that are affected and distorted due to external loads.

Milad and Vahid [15] conducted a comprehensive study on the influence of soil parameters, including excavation depth,

soil column weight, and pile diameter. Through meticulous investigation and finite element analysis using the Plaxis2d

software, the results revealed that both excavation depth and soil unit weight exhibit varying degrees of effectiveness

compared to other parameters. Notably, pile diameter emerged as a critical factor, showcasing that alterations in its

dimensions lead to significant changes in the areas of soil affected by external loads.

The aim of this study is to illustrate how foundation design can be enhanced to ensure the stability of the Al-Hawraa Project

amidst these variations. The impact of piles will be analyzed using finite element analysis techniques, with a focus on

improving the understanding of soil-structure interactions. The purpose of this study can be summarized in the following

points:1. Examine the impact of variations in the internal friction angle on deformations in the soil surrounding the Al-

Hawraa Project 2. Analyze how pile diameter influences the stresses resulting from applied loads. 3. Investigate the

interaction of piles with the surrounding soil and estimate its effects on the overall stability of the structure. 4. Improve the

understanding of fundamental interactions between piles and soil to enhance foundation design. 5. Provide practical

recommendations for enhancing the stability of the Al-Hawraa Project based on the results obtained from the analysis.

2. The Study Area

This study focuses on the soil in Nasiriya applied to Al-Iskan Interchange Project, the southern region of Iraq (Figure 1).

Nestled within the historical landscape of Mesopotamia, Nasiriyah holds a significant position both geographically and

culturally. Nasiriyah is situated by providing coordinates. The Tigris River flows nearby, influencing the city's landscape

and contributing to its historical importance. The city's topography is characterized by describing any notable geographical

features [14]. The study relied on the analysis of data obtained from Al-Iskan Interchange Project, as illustrated in Figure

2. The figure depicts the approved project location, which served as the primary source of information for this research.

Fig. 1: Geographical Documentation of Nasiriyah

City's Location on the Map of Iraq.

Fig. 2: Geographic Analysis of Al-Iskan

Interchange Project

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3. Developing the Theoretical Framework

In this context, the theoretical framework explores the relationship between changing the internal friction angle of the

soil and the development of vertical and horizontal deformations in the soil in the presence of foundations with piles, along

with the impact of altering the pile diameter on these deformations. Assumptions about the deformation shape around the

end of a pile in sandy soil are based on engineering models and mechanical failure analysis. These

models rely on various hypotheses and equations to estimate soil behaviour under different loads. Some of the

assumptions and models that can be used include:

3.1. Terzaghi Model:

This engineering model was developed by Terzaghi for evaluating the failure of the soil and for studying its behaviour

in terms of loading. Terzaghi’s Theory is based on the ideas of stress distribution in the layers of the soil under loading. In

the Theory, it is argued that in soil failure, the stress derived from the load exceeds the stiffener strength of the soil. This

failure can be prophesized through evaluating stresses and pressures in the soil layers taking into consideration information

about the type of soil and loads likely to be applied to the soil layers. The Terzaghi Model employs specific failure criteria

in order to plot results for soil failure such as the Mohr-Coulomb failure criterion [15]. With reference to this criterion, the

shear strength of the soil is measured with respect to the consolidated stresses. Other theories might have different failure

criteria or assumptions on the manner the soil fails [3]. For Terzaghi, deformations around the pile end are cone shaped

[16], which drives into the soil from the pile as depicted in figure 3b.

3.2. Eslami and Fellenius Model

The Eslami & Fellenius Model is a model that is used in the area of soil engineering to determine and forecast failure of

soils. This model uses simple mechanics of principles and stress-strain theory to analyze response of soil under loading as

well as failure mode of soil. The originality of this model resides in the fact that it does not only assess structural loads but

also calculated stresses and strains, thus estimating that a particular type of failure, vertical collapse, lateral slide or surface

bend will occur in a specific soil. Other theories may give a general idea of the mode of failure of a soil without necessitating

the expected failure modes. Eslami and Fellenius offered some recommendations in regard to the deformation shape which

is present in the soil around the pile end as suggested in [5] and[17] and[18] present an oval deformation shape as depicted

in Fig. 3(a).

3.3. Janbu's Model

Janbu’s Theory is a geotechnical theory defined for the assessment of the stability and mechanical response of soil under

loading conditions. This model was originally established by the Norwegian engineer Rolf Johan Janbu while he was

working on the researches of geotechnical stability ad soil mechanics. Using Janbu’s Theory, it is assumed that the soil

mass acts like a continuous medium that can be modeled mechanically in the simplest form. It includes triangles for the

soil by certain assumptions that were made (Figure 3c ) [18].

3.4. Vesic's Model

Vesic’s model is a geological model applied to determine the state and stress/deformation properties of the soil mass

under load. It seeks to analyze the behavior of the soil and how it will deform depending on the loads to be imposed on it.

Vesic’s model has been derived with elastic and static principles with similar response of the soil to that of an elastic

engineering material. This Theory employs mathematics, in particular differential equations to define deformations and

stress in the soil under applied loads. Vesic shows that in response to loads, the deformation of the soil can be modeled by

a cavity beneath the end of the pile as presented in fig 3d [19].

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Fig. 3: Suggested soil deformation profile around the end of the pile a) Eslami & Fellenius model b)

Terzaghi model c) Janbu's Model d) Vesic’s Model

These moodles rely on assumptions, laboratory experiments, and field observations to apply them to soil behaviour.

Typically, the deformation length is assumed to be greater at the upper end of the pile than at its lower end. This is attributed

to the presence of frictional resistance force in addition to the end-bearing resistance. Consequently, this combination

results in a larger deformation in the upper region of the pile's end. Advanced computer analysis and mathematical models

are preferred for more accurate deformation estimations.

4. Methodology

This engineering study employs four distinct friction angles to analyze and comprehend their influence on the soil.

Simultaneously, four varying diameters of piles are utilized to estimate and analyze the resulting deformations in the soil.

Subsequently, the data is analysed using PlaxisFoundation3d V20, the finite element analysis software. The Mohr-Coulomb

(MC) constitutive model has been chosen to characterize the soil's behaviour. The Modified (MC) model is a commonly

used linear elastic model, offering a direct and clear approach to simulating soil behaviour. Another useful approximation

for soil behaviour is a perfectly plastic model, particularly effective as an initial estimation. In a Plaxis3d program,

conducting a mesh convergence study is essential for selecting the appropriate mesh size. The available built-in mesh

options include Very Coarse, Coarse, Medium, Fine, and Very Fine, with each mesh consisting of elements. To assess the

impact of mesh type on boundary condition bearing capacity values in stress concentration regions, the effect of each mesh

type was investigated independently.

Three layers represent the site's soil profile, and the pile was tested at a depth of 25 meters. Table 1 provides a detailed

presentation of each soil layer's geotechnical characteristics. A 1.5-meter-diameter bored pile that was 18 meters embedded

below the earth surface was used in this investigation. Table 2 provides specifics on the pile's composition and mechanical

characteristics.

Table 1: The parameters of the soil profile.

Depth (m)

0-4

4-8

8-11

11-13

13-50

Soil description

stiff clay

Sand

stiff clay

Medium stiff clay

Very stiff clay

Modulus of elasticity, Es (kN/m2)

55000

67200

65000

30000

100000

Poisson's ratio, ν

0.3

0.25

0.3

Cohesion, c (kN/m2)

Un drain shear strength (kN/m2)

110

130

200

Dry unit weight, γd (kN/m3)

18.5

Total unit weight, γt (kN/m3)

19.8

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Table 2: Details of the concrete pile.

Identification

Value

Material model

Linear elastic

Modulus of elasticity, Ep (kN/m2)

25×106

Poisson's ratio

0.15

Type of material

Non-porous-concrete

Material density (kN/m3)

Various potential applications can be harnessed through the use of Plaxis3d software for calculating the ultimate bearing

capacity of different soils and analyzing their impact on soil layers. In this study, soil bearing capacity was calculated using

numerical analysis. The study revealed that Very Fine and Fine meshes provided more accurate results and were closer to

the actual field values. Therefore, the choice of mesh size should balance accuracy and computational efficiency based on

the specific needs of the analysis and available resources. This results in generating a numerical model (Figure 4) at node

number 10935, centred within dimensions of 20×20 meters. The outcome of this analysis provides a refined and lucid

representation of the impact and deformations. Two key components that make for proficient soil analysis are internal

friction angle and diameter. Figure 5 illustrates the flow of scientific work in this study, clearly depicting the overall

structure and key steps of the research process.

Fig. 4: The Soil General Mesh Model

In this study, the range of angle of soil friction consisting of four values (32, 38, 42, 50) are considered to observe

deformations occurring during angle variations. The depths of these deformations, resulting from numerical analysis, are

then determined and correlated with other findings in the study.

Similarly, the study adopts variations in the diameters of the foundation piles (0.3, 0.35, 0.4, 0.45) m and subjects them

to numerical analysis processes. Subsequently, the changes in the soil layers beneath the pile are monitored. This includes

observing alterations in the depths of vertical deformations and horizontal distortions on both sides of the foundation pile.

10935

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Fig. 5: Numerical Design Overview.

5. Results and Discussion

It is crucial to highlight the extent to which soil-bearing capacity is affected by applied loads and how this impacts soil

behaviour, including the degree of deformation resulting from the stresses induced by these loads. The numerical analysis

results demonstrated the soil-bearing capacity using the finite element method. The study revealed that Very Fine and Fine

meshes provided more accurate results and were closer to the actual field values. However, it's noted that analyzing these

finer meshes requires more time due to increased computational complexity (Table 3). Therefore, the choice of mesh size

should balance accuracy and computational efficiency based on the specific needs of the analysis and available resources.

The results indicated that the bearing capacity obtained from the numerical analysis closely matched the actual field values,

as shown in Table 1. This outcome encouraged the utilization of the software's capabilities to analyze the impact of loads

on soil layers and determine the depths affected.

Table 3: Comparison of results for various mesh size values.

Size of mesh

The actual Bearing

Capacity (ton)

The Bearing Capacity

resulting from numerical

analysis (ton)

Total number of nodes

Analysis time

(minutes)

Very coarse

450

437

2920

Coarse

450

440

9464

Medium

450

447

12051

Fine

450

449

16988

30-45

Very fine

450

26880

30-45

5.1. Effect of ɸ on the influence zone

The angle of internal friction (ɸ ) refers to the angle between two surfaces inside the material, where the force parallel

to these two surfaces is equivalent to the applied vertical force. When dealing with the sand soil, understanding the (ɸ ) is

important to determine its behaviour during loading. This parameter is used in the design of engineering foundations such

as piles, as well as in understanding ground movement and geotechnical design [21].

Table 4 presents the result of four piles in soil, where the soil represents loose, medium, dense, and very dense cases,

according to the selected angle of internal friction. It displays the numerical results obtained by finite element solution.

The first column denotes the proposed soil type, and the second column specifies the friction angle at which it is chosen.

Meanwhile, the third and fourth columns depict the depths of vertical deformations, and the fifth and sixth columns detail

the outcomes of horizontal deformations in the soil resulting from applied loads. The numerical results confirmed that

altering the friction angle significantly affects the depth of both vertical and horizontal deformations in the soil, as indicated

in columns three and four. In the case of loose soil with a friction angle of 38o, the results showed vertical deformation

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depths at the upper and lower ends of the pile to be 7.9 and 2.0 m, respectively. Similarly, the results of columns five and

six reveal horizontal deformations in the soil, 3.0 m in both directions. While the soil behaviour is evident in case four

(Very Dense) with a friction angle of 50o, soils with this angle value may be like sand and gravel, where the value of the

friction angle exceeds 45о with increasing gradation and cohesion of the material and the quality of the grains. Also,

crushed stone, which gives a California bearing capacity of 100%, is considered a material with high density and excellent

cohesion, and its internal friction angle may reach 50о, as illustrated in Table 4. The results showed vertical deformation

depths at the upper and lower ends of the pile to be 4.3 and 2.0 m, respectively. Then, the results of columns five and six

reveal horizontal deformations in the soil, 2 m in both directions.

Furthermore, the depths of vertical and horizontal deformations in the soil, influenced by external loads, are affected and

must be considered. The first case, shown in Table 4, with a 38o angle, has the greatest vertical and horizontal influence

depth compared to the other cases. Meanwhile, the results indicate that the depths of deformations in the fourth case with

a 50o angle exhibit less vertical and horizontal deformation.

Table 4: Vertical and horizontal boundary of deformation for soil with different ɸ

Soil Type

Φ (degree)

Vertical Deformation

Horizontal Deformation

Upper Limit (m)

Lower Limit (m)

Right Limit (m)

Left Limit (m)

Loose

32o

7.9

2.0

3.0

Medium

38o

7.8

1.95

3.2

Dense

42o

6.1

1.6

2.5

Very Dense

50o

4.3

1.3

2.0

Figure 6 (a) observes a reduction in vertical strain with increasing internal friction angle, which can be attributed to

enhanced soil particle interlocking and shear resistance. Higher internal friction angles promote stronger particle

interactions, thereby limiting the ability of soil to undergo significant vertical compression or settlement. These findings

have implications for soil engineering practices, emphasizing the importance of considering internal friction angle in design

and analysis to predict soil behaviour and deformation more accurately.

Based on the available information, we can examine the equation. The relationship between vertical deformations (upper

and lower limits) in soil and the internal friction angle (Figure 6a) can be expressed mathematically using the following

equations:

U= 0.1516 tan (Φ) (1)

L= 0.04 tan (Φ) (2)

Where:

U: upper limits, L: lower limits, Φ: friction angle

Figure 6b illustrates the relationship between the friction angle (Φ ) and horizontal deformations on both sides of a

foundation. The findings suggest that the changes in deformations are minor or barely noticeable, leading to the proposal

of an equation to understand this relationship better. The results revealed an equation that relates the friction angle (Φ ) to

the horizontal deformations of the soil:

Y = 0.0628 tan (Φ) (3)

where:

y= right and left limits, ɸ: friction angle

This equation provides insights into how changes in the friction angle impact horizontal deformations.

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Fig. 6: Failure envelope plot with friction angle. a: upper and lower limits V friction angle

b: right and left V friction angle

At the same time, the deformations of soil were accurately described by presenting a shown in Figure 7 (a, b, c, d)

generated from the numerical analysis. Regarding Figure 7a, the deformation states are explained comprehensively and

precisely. The vertical deformation depth at the upper and lower ends of the pile is evident, in addition to horizontal

deformations in both directions.

Significant deformations in both vertical and horizontal directions are evident at the ends of the foundation pile. The

analysis emphasizes the areas of soil affected by the applied loads, as depicted in Figure 7a. In the figure, red lines indicate

the impact on the soil near the end of the foundation pile due to the applied loads. These lines progress from the closest to

the farthest away from the pile, demonstrating changes in the depth and extent of deformations in the soil. The progression

of lines can be described as follows:

1. The line closest to the pile tip represents the most heavily impacted zone by the applied loads, resulting in deep

vertical and horizontal deformations within the soil.

2. The subsequent line represents a slightly less affected area than the first line, showing a reduction in the depth of

vertical and horizontal deformations.

3. Further away from the pile, the gradient of lines towards the last line shows a gradual decrease in the impact on

the soil. Each line represents an area of decreasing influence on the soil's deformation.

4. The last line, farthest from the end of the pile, represents the least affected area of the soil, with a significant

reduction in the extent of vertical and horizontal deformations caused by the applied loads.

This analysis provides valuable insights into how the applied loads affect the soil at different distances from the pile

foundation, highlighting variations in deformation depths and impacts across the soil profile.

In Figure 7b, a similar mechanism is observed in depicting the area subjected to stress due to applied loads, employing

a comparable approach. The line closest to the pile tip represents the region most susceptible to stresses compared to the

farthest and last line, which signifies the least impacted area. This interpretation follows a consistent pattern where the line

nearest to the pile tip denotes the most stress-affected zone, gradually diminishing as it moves towards the line farthest

from the pile's end. The decreasing order of impact is evident, with the final line indicating the least affected area.

Afterwards, we move to the final Figure 7d, illustrating how deformations have decreased and contracted compared to

Figure 7a, with an increase in the internal friction angle of the soil. This alteration resulted in reduced vertical deformations

compared to the previous cases, while it is observed that the vertical deformation remains unaffected by this change. The

diminishing values of the internal friction angle correlate with decreased depths of vertical deformations, showcasing a

discernible impact on the overall deformation behaviour.

With this explanation, one can understand how the depth of deformations in the soil gradually decreases with increasing

distance from the end of the foundation pile, with the greatest impact in the nearest zone and decreasing gradually in the

farther regions. Consequently, the relationship between the internal friction angle and the depth of the influence zone of

soil is demonstrated. The consequences analysis emphasized that with an increase in the internal friction angle of the soil,

the soil becomes less affected to the applied loads. Consequently, the depth of soil deformation decreases (Figure 7).

Muthanna Journal of Engineering & Technology

Fig. 7: Depth of soil deformation for a: loose, b: medium, c: dense, and d: very dense

5.2. Pile diameter effect

The impact of the pile diameter on the soil depends on many factors. One of these factors is the distribution of pressure,

where an increase in the footing diameter reduces pressure on the soil, thus affecting its ability to bear loads. The footing

diameter can also influence the stability of the foundation, contributing to increased stability in the soil. In some cases, an

increased footing diameter may lead to a greater transfer of pressure to the lateral walls of the soil, affecting the geologic

structure of the soil in the surrounding area.

At the same time, this part discussed researching the influence of various diameters of piles on the deformation leading

to the soil. The values of vertical and horizontal deformations in the picked points in the soil are shown in table 5 for

different diameter (0.3, 0.35, 0.4, 0.45 m) of a single pile as per numerical analysis. Another important study was performed

by researcher Surendra Patel et al. [22] where the effects of internal friction angle of soil and pile length-to-diameter ratio

on the soil bearing capacity were investigated. The results showed an increase in the value of the internal friction angle of

the soil increases the modulus of elasticity and, hence, the load-bearing capacity of the soil, thus decreasing both the vertical

and horizontal movements of the soil. However, the study of the load-displacement behaviour of piles revealed that an

increase in the length-diameter ratio is favourable to the load-carrying capacity of the soil and, consequently, the depth of

the observed deformation. These conclusions show that the internal friction angle and the geometry of piles are decisive in

improving the stability and deformability of the soil under loads.

Table 5 has five columns, which are explained as follows: the first column shows the recommended diameters for this

work and is the basis for the investigations done for this study. The third and fourth columns display the degree of vertical

displacement in the soil, and the fourth and fifth columns represent the degree of lateral movement in the soil. As presented

in Table 5, there is a significant difference when using a diameter of 0.3m, with the vertical deformation above the pile

reaching 6.25m and that below the pile reaching 1.55m. The results of deformations at a diameter of 0.35 m were slightly

different from the previous findings. Table 5 illustrates that the depths of deformations above and below the pile were 6.35

and 1.56 m, respectively. This indicates an increase in the depth of vertical deformation in the soil, which is in line with

the increase in diameter.

Similarly, for both diameters (0.4, 0.45) m, the numerical analysis results yielded depths of vertical deformations above

and below the pile. For a diameter of 0.4 m, the values were (6.45, 1.6) m, and for a diameter of 0.45 m, the values were

(6.55, 1.6) m. This indicates an increase in the depth of vertical deformation in the soil, corresponding to the increase in

the diameter of the pile. In the same manner, Table 5 illustrates the numerical analysis results for vertical deformations on

both sides of the pile, corresponding to columns four and five. Presented scientifically and precisely, these values reveal

the vertical deformation depths for the specified conditions. The results of the last two columns indicate that horizontal

deformations did not show a significant impact. For instance, with a diameter of 0.3 m, the value of horizontal deformation

was 2.5 m on both the left and right sides of the pile.

Similarly, both diameters, 0.35 m and 0.4 m, yielded identical results. Finally, for a diameter of 0.45 m, the horizontal

deformation value was 2.6 m, showing a slight difference from the previous results that is considered negligible. In the

case of horizontal deformations, the deformations occurring on both sides of the pile were symmetrical in all scenarios

with different diameters. They remained consistent and unaffected by the variation in the diameter. Finally, the last two

columns in Table 5 explain the complete vertical range and horizontal range of the impact boundaries.

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Table 5: Presents numerical results for deformation depths using varying diameters

Diameter of pile

(m)

Vertical Deformation

Horizontal Deformation

Effective

length in

vertical

direction

(m)

Effective

length in

horizontal

direction

(m)

Upper Limit (m)

Lower Limit (m)

Right Limit (m)

Left Limit (m)

0.30

6.25

1.55

2.5

7.8

0.35

6.35

1.56

2.5

7.91

0.40

6.45

1.6

2.5

8.05

0.45

6.55

1.65

2.6

8.2

5.2

Figure 8 illustrates and demonstrates the relationship between the diameter of the column and the depth of deformations

affecting the soil in both vertical and horizontal directions. Figure 8a shows the vertical deformations above and below the

column, where the study results indicate an increase in soil deformation with an increase in column diameter. Consequently,

it is possible to infer an equation representing the increase in deformations with increasing diameter, with a constant value

for the equation. The equation is as follows:

U= 16.739 D (4)

L= 4.1626 D (5)

Where:

U: upper limits, L: lower limits, D: diameter of pile

Previous researchers have conducted numerous studies to define the zone of soil affected by applied loads, highlighting

the significance of this topic. Due to the significance of load-bearing capacity in soil, extensive scientific effort has been

dedicated to estimating the degree and the size of the influenced area. Meyerhof (1956) [23] proposed a hypothesis about

the relationship between the effective depth of soil supported by a pile and the pile diameter, with clear reluctance to add.

Depending on the type of soil, the area of the effective depth in which piles can be fully utilized is likely to be limited to

(1-2) times the diameter of the pile where the soil is sandy; but maybe (3-5) times the diameter of the pile for clayey sub-

surface materials. This relationship confirms that the pile diameter is equally essential for assessing the degree of soil

deformation and ranking the depth of influence in cohesive and granular soils. Paul and Simons, in their work presented in

2005, put forward a hypothesis on clay soils asserting that distances influenced by loads exhibit greater extent than granular

soils. That is why they noted that the affected depth could increase up to (3-4) times the pile diameter due to the softer and

more compressible nature of clay soils. This increased depth is due to the relatively low bearing capacity of clay soils as

they resist the applied loads, leading to a wider influence zone of the pile. On the other hand, Bowles (1996) [24] proposed

that the depth of soil affected by loads for soils with high bearing capacity generally extends to about 1.5 to 3 times the

foundation width. This range reflects the depth of significant stress distribution, especially in strong, load-bearing soils.

Figure 8b illustrates the relationship between the diameter (D) and horizontal deformations on both sides of a foundation.

The findings suggest that the changes in deformations are minor or barely noticeable, leading to the derivation of an

equation to better understand this relationship. The results revealed an equation that relates the diameter (D) to the

horizontal deformations of the soil:

y = 6.251 D (6)

where:

y= right and left limits, D= diameter of pile

This revised statement provides a clearer and more scientific explanation of the relationship depicted in the figures,

highlighting the findings of the study regarding soil deformations concerning column diameter variations.

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Fig. 8: Failure envelope plot with diameter. a: Upper and lower limits V diameter b: right and left limits V diameter

Figures 9 (a, b, c, d) illustrate the vertical and horizontal deformations of the soil resulting from numerical analysis.

These figures provide a clear depiction of the deformation depths, showcasing the outcomes of the numerical analysis in a

scientific, precise, and effective manner. Figure 9a illustrates the vertical and horizontal deformations in the soil influenced

by external loads, as previously explained. The red lines indicate the gradients of the areas affected by stresses. Figures 9b,

9c, and 9d depict the gradient of soil area influence based on changes in diameter. Through the analysis of the generated

figures, it is evident that with an increase in pile diameter, the impact on the soil intensifies, consequently leading to an

increase in the vertical depth of surrounding deformation. On the other hand, it is observed that the horizontal deformation

on either side of the foundation remains unaffected by this change. This description is provided in a scientific, accurate,

and effective manner. Clearly and precisely, Figure 9 demonstrates that vertical deformations increase with the diameter

while horizontal deformations remain largely unaffected.

Fig. 9: Depth of soil deformation for piles with different diameters a: D= 0.3, b: D= 0.35, c: D= 0.4, and d: D=0.4.

Based on the comprehensive scientific findings presented, we can determine the nature and extent of influence exerted

by both the friction angle and pile diameter on soil behaviour, particularly in shaping and determining the depths of

deformations. Increasing the friction angle (φ) has a mitigating effect on soil deformations, reducing their magnitude.

Conversely, enlarging the pile diameter augments the depth of deformations observed within the soil subjected to external

loads. These observations prompt inquiries into the specific types of influence exerted by these factors, their impacts on

soil morphology, and the feasibility of deriving mathematical equations to describe these relationships. Additionally, it

raises the question of whether it's possible to identify and integrate various influencing factors—such as length, diameter,

and soil properties, into a unified model or equation.

Muthanna Journal of Engineering & Technology

6. Conclusions

In this study, both the diameter and the angle of internal friction were changed to study the changes that occur in soil

deformations due to induced stresses. Modern modelling techniques (Plaxis3d) were used, and the results were presented

in a detailed and comprehensive manner. The results of this study were as follows:

The friction angle (ɸ) represents soil characteristics that influence its ability to resist deformations caused by external loads.

Installing the piles in soil with a high friction angle enhances the foundation stability and reduces deformations. Higher ɸ

values improve the soil's capacity to withstand pressures without significant distortions.

The diameter of the pile directly affects the depth of deformations in the surrounding soil.

Increasing the pile diameter expands the area affected by deformations, thereby increasing the depth of deformations due

to external pressures.

This conclusion emphasizes the importance of studying influencing factors on soil behaviour and the intricate interactions

between them. It highlights the need for ongoing research and development in geotechnical engineering to enhance

understanding and improve soil-related engineering practices.

Muthanna Journal of Engineering & Technology

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