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Behavior of Geosynthetic Reinforced Soil
Under Isolated Foundations
سلوك التربة المقواة بالمواد الجيوصناعية تحت القواعد المنفصله
By
Haytham Emad Herzallah
Supervised by
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Civil Engineering
August/2018
Dr. Mamoun Alqedra Dr. Mohammed Arafa
زةــغب ةــالميــــــة اإلســـــــــامعـالج
البحث العلمي والدراسات العليا عمادة
الهندسةة ليــــــك
في الهندسة المدنية ماجستير
الهندسة االنشائية
The Islamic University of Gaza
Deanship of Research and Graduate Studies
Faculty of Engineering
Master of Civil Engineering
Structural Engineering
i
إقــــــــــــــرار
أنا الموقع أدناه مقدم الرسالة التي تحمل العنوان:
Behavior of Geosynthetic Reinforced Soil Under
Isolated Foundations
سلوك التربة المقواة بالمواد الجيوصناعية تحت القواعد المنفصله
الخاص، باستثناء ما تمت اإلشارة إليه حيثما ورد، وأن هذه الرسالة ككل أو أي أقر بأن ما اشتملت عليه هذه الرسالة إنما هو نتاج جهدي
لنيل درجة أو لقب علمي أو بحثي لدى أي مؤسسة تعليمية أو بحثية أخرى. االخرين جزء منها لم يقدم من قبل
Declaration
I understand the nature of plagiarism, and I am aware of the University’s policy on this.
The work provided in this thesis, unless otherwise referenced, is the researcher's own work, and
has not been submitted by others elsewhere for any other degree or qualification.
:Student's name هيثم عماد حرزهللا اسم الطالب:
:Signature التوقيع:
5/9/2018 التاريخ:Date:
ii
Abstract
Reinforced soil material is combining earth and reinforcement material. The reinforced soil is
obtained by placing extensible or inextensible materials such as metallic strips or polymeric
reinforcement within the soil to obtain the desired properties, strengthening of soil geosynthetic
fiber reinforced is one of the most used strengthening techniques recently. It offers an attractive
solution to enhance shear and tensile capacities of soil.
Behavior in shear and tensile of reinforced soil externally strengthened with geosynthetic fiber is
highly affected by the way in which these composites are bonded to the soil.
The main objective of this research is to study the strengthening of reinforced soil with
geosynthetic fiber using non‐linear finite element models. The research made use of the
commercial finite element modeling software (ANSYS18) to prepare the finite element models
and to study the influence of the important parameters on the overall response of strengthened soil,
in order to achieve the optimum utilization of such strengthening technique, in terms of load
bearing capacity and possible stress values.
Modeling of concrete foundation, soil and reinforcement material using ANSYS18 finite element
program which deals with many problems and comparing the obtained results with analytical
solution. These parameters study are effect of depth of geosynthetic layer, effective of geosynthetic
layer width under foundation, effect of using two geosynthetic fiber layers with different depth,
Effect of geosynthetic in different soil types and effect of different geosynthetic types in one type
of soil. The analysis of results proved that the general behavior of the FE models shows a good
agreement with corresponding closed form investigations results, and that ANSYS18 is capable of
producing results in good agreement with closed form equations.
The parametric study has proved that the optimal depth that could use the fiber is between the
range 0.25 to 0.45 meter under the foundation, increasing the number of fibers layers increases the
stiffness of the soil, and improve shear capacity, and decreases settlement.
Further, each reinforced material has different effect on stress values depending on the properties
of reinforced material will be used, which gives the designer various option to be used.
Moreover, using many layers of reinforced material will not have that much effect on the stresses
in soil.
iii
Abstract In Arabic
او وضعها طريق خلط المادة الداعمة بالتربه عنإما التربة مع هايتم دمج صناعية او طبيعية للتربة هي عبارة عن مواد المقويةالمواد
. بشكل طبقات بين طبقات التربة اسفل او بجاور العناصر االنشائية
فايبر. بوليميرك و على سبيل المثال شبكات الحديدالصناعية او الطبيعية للتربة كمقوياتتوجد العديد من المواد التي تستخدم
و األقل تكلفة عملية اإلنشاء والتشيدرق سهولة في طا ويعتبر من اكثر اليعتبر من اكثر التقنيات استخدام المقويةالتربة باستخدام المواد تقوية
بين العديد من طرق تحسين خواص التربة.
ستخدم لزيادة مقاومة قوة الشد والقطع التي تتعرض لها التربة تحت العناصر النشائية كالقواعد ت هي مادة تصنع من البوليمرات جيوتيكستايل
.والمرافق العسكريةحتى في الطرق والسيما الطرق السريعة أو المعرضة ألحمال عالية كالمطارات او والحوائط االستنادية
هو نمذجة التربة المقوية باستخدام احد برامج النمذجة باسلوب طرق العناصر المحدده النتاج نموذج يحاكي من هذا البحث الهدف الرئيسي
تصور للسلوك المتوقع للتربة والحلول الممكن التي تتعرض لها التربة لتقدم للمصمم أثيراتوالت الواقع الخاص بالتربة وإظهار نتائج للقوى
اتخاذها.
مقاومة التربة لقوى الشد والضغط وتوزيع جميع الضغوط في التربة بشكل زيادةبت أن استخدام جيوتيكستايل سيساعد على سيتهذا البحث
منتظم مما يقلل من اخطار انهيار التربة ويقلل من تكاليف تحسين التربة في المشاريع االنشائية.
ح وطرق اسهل في تقييم وفق معطيات اوضالعمل لنمذجة انواع اخرى من المواد الداعمه و قدرةباالضافة ان هذا البحث يعطي الباحثين ال
.واالوفر من حيث القيمة واالقل استهالكا للوقت والتصميم
iv
Acknowledgment
I would like to thank Allah that give the power and patient to achieve this thesis. I also would like
to thank my thesis advisor Dr. Mamoun Alqedraand and Dr. Mohammed Arafa, in Department of
Civil Engineering, Islamic University of Gaza. The door to Dr. Mamoun Alqedraand and Dr.
Mohammed Arafa office was always open whenever I ran into a trouble spot or had a question
about my research or writing. they consistently allowed this paper to be my own work but steered
me in the right the direction whenever he thought I needed it.
I would also like to thank the expert Mohammed Dader who were involved in the ANSYS18
validation for this research project. Without his passionate participation and input, the validation
could not have been successfully conducted.
Haytham Emad Herzallah
Gaza ‐ 2018
v
Dedication
I must express my very profound gratitude to my parents and to my beloved parents (Emad
Herzallah & Sahar Ammar), brothers (Yasser & Ahmad), and sister (Tala) for providing me with
unfailing support and continuous encouragement throughout my years of study and through the
process of researching and writing this thesis. This accomplishment would not have been possible
without them.
I also extend my heartiest gratitude to my wife (Fedaa Al-Sousy), for here constant support to
provide the needed work environment to achieve this work.
Thank you.
vi
Table of Contents
Declaration ....................................................................................................................................... i
Abstract ........................................................................................................................................... ii
Abstract In Arabic .......................................................................................................................... iii
Acknowledgment ........................................................................................................................... iv
Dedication ....................................................................................................................................... v
Table of Contents ........................................................................................................................... vi
List of Figur ................................................................................................................................... ix
List of Tables ................................................................................................................................. xi
List of Equations ........................................................................................................................... xii
Chapter 1 Introduction .................................................................................................................... 2
1.1 Background ........................................................................................................................... 2
1.2 Problem Statement ................................................................................................................ 4
1.3 Aim and Objectives ............................................................................................................... 4
1.4 Methodology ......................................................................................................................... 5
1.5 Theses layout. ........................................................................................................................ 6
Chapter 2: literature Review ........................................................................................................... 8
2.1 Introduction: .......................................................................................................................... 8
2.2 The Soil Reinforcement Concept .......................................................................................... 9
2.3 Types of Soil Reinforcement............................................................................................... 11
2.3.1 Natural fibers .................................................................................................................... 11
2.3.2 Manufactured (man-made) fibers ..................................................................................... 13
2.4 Behavior of Reinforced Soil ................................................................................................ 17
2.4.1 Principle ........................................................................................................................ 17
2.4.2 Factors Affecting the Behavior of Reinforced Soil: ..................................................... 19
2.4.3 Influence of Fill Material:............................................................................................. 19
2.4.4 Influence of Reinforcement Characteristics: ................................................................ 19
2.4.5 Interaction Between Soil and Geosynthetic .................................................................. 21
2.4.6 Measurement of Soil-Reinforcement Interaction: ........................................................ 22
2.5 Laboratory Testing. ............................................................................................................. 28
2.6 Effect on Peak Strength ....................................................................................................... 29
2.7 Concluding Remarks ........................................................................................................... 31
vii
Chapter 3 Modeling of Foundations and Soil using Finite Element Method ............................... 33
3.1 Introduction ......................................................................................................................... 33
3.2 Steps and Procedure of finite Element Method ................................................................... 33
3.2.1 Step 1 Discretize and Select the Element Types .......................................................... 33
3.2.2 Step 2 Select a Displacement Function ........................................................................ 34
3.2.3 Step 3 Define the Strain/Displacement and Stress/Strain Relationships ...................... 34
3.2.4 Step 4 Derive the Element Stiffness Matrix and Equations ......................................... 34
3.2.5 Step 5 Assemble the Element Equations to Obtain the Global .................................... 35
3.2.6 Step 6 Solve for the Unknown Degrees of Freedom (or Generalized Displacements) 35
3.2.7 Step 7 Solve for the Element Strains and Stresses ....................................................... 36
3.2.8 Step 8 Interpret the Results ........................................................................................... 36
3.3 Finite Element Modeling of Reinforced Soil .......................................................................... 36
3.3.1 Modeling of Foundations.............................................................................................. 36
3.3.2 Modeling of soil............................................................................................................ 37
3.3.3 Soil Foundation Interaction .......................................................................................... 38
3.3.4 Material Modeling ........................................................................................................ 39
3.3.5 Material Modeling of Foundation and soil ................................................................... 39
3.3.6 Material Modeling of Contact Element (surface to surface) ........................................ 41
3.3.7 Surface-to-Surface Contact Elements ........................................................................... 42
Chapter 4 Modeling of Reinforced Soil and Foundations using ANSYS .................................... 44
4.1 Introduction ......................................................................................................................... 44
4.2 Modeling of Reinforced Soil ............................................................................................... 44
4.2.1 Modeling of Geosynthetic ............................................................................................ 44
4.2.2 Modeling of soil............................................................................................................ 46
4.2.3 Modeling of Reinforced Concrete ................................................................................ 48
4.2.4 Modeling of Foundation-Soil Contact & Geosynthetic-Soil Contact .......................... 48
4.3 Soil and Geosynthetic Meshing Generation ........................................................................ 50
4.3.1 Soil Meshing: ................................................................................................................ 51
4.3.2 Geosynthetic Meshing: ................................................................................................. 51
4.3.3 Soil Mass Boundaries ................................................................................................... 51
4.4 Application of Loading ....................................................................................................... 52
4.5 Model Validation................................................................................................................ 53
viii
4.5.1 Ansys Stress Soil Computation .................................................................................... 53
4.5.2 Closed Form Solution Based on Theory of Elasticity .................................................. 54
4.5.3 Comparison of FEM ANSYS Modeling and Analytical Results ................................. 55
4.5.4 laboratory Testing Validation ....................................................................................... 58
4.5.3 Comparison of FEM ANSYS Modeling and Laboratory Results ................................ 60
4.6 Parametric Study ................................................................................................................. 61
Chapter 5 Analysis Results of Reinforcement Soil Using ANSYS .............................................. 63
5.1 Introduction ......................................................................................................................... 63
5.2 Effect of Depth of geosynthetic .......................................................................................... 63
5.3 Effect of Using Second Geosynthetic Layer With Different Depths .................................. 66
5.4 Effect of Geosynthetic in Different Soil Types ................................................................... 69
5.5 Effect of Using Different Geosynthetic Types in One Type of Soil ................................... 72
5.6 Effect of Geosynthetic Layer Width in Distribution of Stress in The Soil ......................... 74
Chapter 6 Conclusion and Recommendation. ............................................................................... 79
6.1 Conclusion ........................................................................................................................... 79
6.2 In Particle Life ..................................................................................................................... 79
6.3 Recommendation for Future Studies ................................................................................... 80
References ..................................................................................................................................... 81
ix
List of Figur
Figure 2. 1 Typical Examples of Soil Reinforcement Application ............................................... 10
Figure 2. 2 Specimen deformation pattern for (left) unreinforced clay soil specimens and (right)
clay soil reinforced with 0.25% PP of 19 mm ............................................................................. 14
Figure 2. 3 Geosynthetic Material ................................................................................................ 16
Figure 2. 4 Effect of reinforcement on a soil element ................................................................. 18
Figure 2. 5 Long Term Behavior of Polymer Reinforcement . ..................................................... 20
Figure 2. 6 Common Type of Soil Reinforcement . ..................................................................... 22
Figure 2. 7 Failure Mechanisms in a Reinforced Soil Retaining Wall . ....................................... 24
Figure 2. 8 Direct Shear and Pull-out Test Results Collected ..................................................... 25
Figure 2. 9 Friction Angle Dependence on Stress Level. ............................................................. 26
Figure 2. 10 Histogram of Direct Shear and Pull-out Test Results . ............................................ 27
Figure 2. 11 Stress-strain relation for non-woven reinforced soil ................................................ 29
Figure 2. 12 Stress-strain relation for woven reinforced soil........................................................ 30
Figure 3. 1 8-node Geometry SOLID65 ....................................................................................... 37
Figure 3. 2 Foundation soil and element discretization (Quarter model) ..................................... 38
Figure 3. 3 Interface Surface between foundation and soil .......................................................... 38
Figure 3. 4 Material Modeling of soil ........................................................................................... 40
Figure 3. 5 linear Drucker-Prager ................................................................................................. 41
Figure 4. 1 Shell281 ...................................................................................................................... 45
Figure 4. 2 Fiber Modeling ........................................................................................................... 46
Figure 4. 3 Modeling of the soil.................................................................................................... 47
Figure 4. 4 Modeling of the foundation ....................................................................................... 48
Figure 4. 5 Soil Foundation Contract Surface Stress .................................................................... 49
Figure 4. 6 Soil Meshing ............................................................................................................... 51
x
Figure 4. 7 Soil Mass Boundaries ................................................................................................. 52
Figure 4. 8 Application of Loading............................................................................................... 53
Figure 4. 9 Soil Stress Value After ANYSY Solution .................................................................. 53
Figure 4. 10 Determination of stress below the corner of a flexible rectangular loaded area ...... 54
Figure 4. 11 Stress of Soil Under Corner of Foundation .............................................................. 57
Figure 4. 12 Stress of Soil Under Corner of Foundation .............................................................. 57
Figure 4. 13 Schematic Diagram of the Test Set-Up .................................................................... 58
Figure 4. 14 Description of the Model .......................................................................................... 59
Figure 4. 15 Settlement Values to Evaluate ANSYS18 Model .................................................... 60
Figure 5. 1 Depth of Geosynthetic Layer dimensions are in CM ................................................. 63
Figure 5. 2 Stress in soil with Different Depth of Geosynthetic Layer ........................................ 64
Figure 5. 3 Depth of the two geosynthetic layers under foundation dimensions are in CM ........ 66
Figure 5. 4 Stress in soil with Different Depth of second Geosynthetic Layer ............................ 67
Figure 5. 5 Soil Types All Dimensions in CM ............................................................................. 69
Figure 5. 6 Effect of Geosynthetic in Different Soil Types .......................................................... 71
Figure 5. 7 Different Geosynthetic Types in One Type of Soil All Dimensions in CM .............. 72
Figure 5. 8 Effect of Geosynthetic materials in loose Sand .......................................................... 73
Figure 5. 9 Stress Distribution for 4.5 m Width Geosynthetic Layer ........................................... 74
Figure 5. 10 Geosynthetic Layer Width All Dimension in CM .................................................... 75
Figure 5. 11 Width of 0.4q Stress Under Foundation in Deferent Depth ..................................... 76
xi
List of Tables
Table 2. 1 Effect of reinforcement on unconfined compressive strength test .............................. 30
Table 4. 1 geosynthetic Material Properties ................................................................................. 44
Table 4. 2 Sand Properties ............................................................................................................ 46
Table 4. 3 Concrete Material Properties ....................................................................................... 48
Table 4. 4 Stress Values to Evaluate ANSYS18 Model ............................................................... 55
Table 4. 5 Properties of Geosynthetics ......................................................................................... 59
Table 4. 6 Description of the Model ............................................................................................. 59
Table 4. 7 Settlement Values to Evaluate ANSYS18 Model........................................................ 60
Table 5. 1 Stress in soil with Different Depth of Geosynthetic Layer .......................................... 64
Table 5. 2 percentage of decreasing in stress ................................................................................ 65
Table 5. 3 Stress in soil with Different Depth of second Geosynthetic Layer .............................. 67
Table 5. 4 Soil Types Properties (Donald et al., 2001) ................................................................ 70
Table 5. 5 Effect of Geosynthetic in Different Soil Types ........................................................... 70
Table 5. 6 Different Geosynthetic Types Prosperities .................................................................. 72
Table 5. 7 Effect of Geosynthetic materials in loose Sand ........................................................... 73
Table 5. 8 Stress in Soil with Different Width of Geosynthetic Layer ......................................... 75
Table 5. 9 Width of 0.4q Stress Under Foundation in Deferent Depth ........................................ 76
xii
List of Equations
Equation 1 cohesion value c ......................................................................................................... 41
Equation 2 Boussinesq’s equation ................................................................................................ 54
1
Chapter 1 Introduction
2
Chapter 1 Introduction
1.1 Background
Soil reinforced material is a material formed by combining soil and reinforcement material. It can
be obtained by using extensible or inextensible materials in soil layers or mixed with soil particles
to get the needed properties and improving in soil mechanism as example of this reinforced
material polymeric reinforcement or metallic strips. This reinforced material improves tension
resistance by soil mass in a way that soil alone could not do it. Due to internal friction between
soil particles and reinforced material the tensile resistance is obtained, because the stresses that are
created within the mass are transferred from soil to the reinforcement strips by friction.
Reinforcement of soil is practiced improving the mechanical properties of the soil being reinforced
by the inclusion of structural elements. The reinforcement improves the earth by increasing the
bearing capacity of the soil. It also reduces the liquefaction behavior of the soil. Reinforced earth
is not complex to achieve. The components of reinforced earth are soil, skin and reinforcing
material. The reinforcing material may include steel, concrete, glass, planks etc. Reinforced earth
has so many applications in construction work. Some of the applications include its use in
stabilization of soil, construction of retaining walls, bridge abutments for highways, industrial and
mining structures. In most of the current civil engineering applications, the reinforcement
generally consists of geosynthetic sheets or strips of galvanized steel, arranged horizontally or in
the directions in which the soil is subject to the undesirable tensile strains. Compared to the
geosynthetic sheets, metal strips are assumed to be relatively inextensible at the stress levels
experienced in civil engineering applications (Okechukwu, Okeke, Akaolisa, Jack, & Akinola,
2016).
In the early days, the metal strips were used as reinforcement, the concept of improving the strength
of a soil mass by adding reinforcements within it. The soil should preferably be cohesion less,
characterized by high frictional properties, in order to prevent the slip between the soil and the
reinforcement. The surface texture of the reinforcement should also be as rough as possible for
similar reasons. An internally stabilized system such as reinforced earth involves reinforcements
installed within and extending beyond the potential failure mass. The reinforcement comprises of
reinforcing elements which is in the form of strips set at certain intervals disposed in horizontal
layers. On the facing of the structure, a certain type of boundary or skin is required to retain the
earth particles that are not in contact with reinforced strips. A reinforced soil mass is somewhat
analogous to reinforced concrete in that the mechanical properties of the mass are improved by
3
reinforcement placed parallel to the principal strain direction to compensate for soil's lack of tensile
resistance (Nand. 2005).
As a result of combining reinforced fibers and the soil improving in tensile properties of the soil
is obtained. The concept of combining two materials quite familiar and could be seen in many real
cases as concrete combined with steel bars. It combines the high compressive strength of concrete
with tensile strength of steel, but relatively low tensile strength of concrete. As well, soils which
have similar condition , soil tensile strength could be improved when it combined with reinforced
material will also be strengthened by the add materials. By using this kind of strength
improvement is obtained by surface interaction between the soil and the reinforcement through
friction and adhesion. The reinforced soil is obtained by placing extensible or inextensible
materials such as geosynthetic or discrete fibers within the soil to obtain the needed properties
(Nand. 2005).
Soil reinforcement through metallic strips, grids or meshes and polymeric strips sheets is now a
well-developed and widely accepted technique of earth improvement.
Typical early uses of reinforced soil by using branches of tress include use of branches of tree etc.
to support tracks over boggy areas and to build huts. Also, it can be found in the nest of bird’s hat
use mud and clay incorporating with leaves and small tree sticks to give the nest the need strength
to hold the eggs and chick of the bird. This example is familiar sights that give an indicate of
reinforced soil that we learn from environment. In addition, the ancient civilization used this
concept in building magnificent structural using reinforced soil concepts like Babylonian temples
and Great Wall of China. Moreover, in 19th century tree branches were used as reinforced material
in retaining walls back fills that was used to reduce soil pressure on the retaining walls and reduce
the thickness of the walls to give the most economical structural. Some researchers believe that
the first usage of Textile as reinforced material was in road construction in South Carolina in the
beginning of 1930s. but, the also indicates that the first use of woven synthetic fabrics for erosion
control was made in 1958 by Barrett (Nand. 2005).
The technique of soil reinforcement is versatility, easy of construction and cost effectiveness on
the construction phase. This technique is especially used cities and urban locations where building
and lands are close to each other and the need of improve the soil with easier, most economical
ways and keep all around structural safe is required.
4
In the last 30 years the usage of reinforced soil has become wide spread in the field of geotechnical
engineer due to many reasons such as most economical and easy construction compared to those
of conventional methods. Reinforcement of soil is practiced improving the mechanical properties
of the soil being reinforced by the inclusion of structural element such as cells, grids, lime/cement
mixed soil, granular piles, synthetic sheet, metallic bars or strips, etc (Okechukwu et al., 2016).
1.2 Problem Statement
In Gaza Strip many areas suffer from weak and not suitable soil to build the structural on it, which
lead to do several procedures to improve soil mechanism and properties.
One of the solution to improve the soil properties using reinforced material within the soil.
Studying soil reinforcement under foundations requires several complicated models, to understand
the behavior of such a soil-structural interaction problem.
With the availability of several comprehensive finite element’s packages, it would be possible to
study the behavior reinforced soil for foundations and retaining structure using finite element
model. By using a developed validated computer model, the study of all significant parameters
influencing such soil-structure interaction would be much effective. Further, optimist type, layout
and dimensions of the soil reinforcement could be achieved.
1.3 Aim and Objectives
The aim of this study is to develop a finite element computer model to simulate the behavior of
geosynthetic soil reinforcement for foundations.
The developed computer model would enable more understanding of soil structural interaction of
reinforced material and soil, furthermore, the validated computer model will be utilized to study
the significant of the parameters influencing soil reinforcement.
to achieve the aim of the current study the following will be carried out: -
1. Study the behavior of various types of soil reinforcement for isolated foundation.
2. Sing ANSYS18 as the suitable finite element computer software to form modeling.
3. Estimate a finite elements model to simulate the soil and the reinforcing layers.
4. Validation and verification of the developed computer model using mathematical equation
for estimating stress in soil.
5. Carry out a parameter study using the developed model.
5
1.4 Methodology
The following methodology was followed in this research to achieve the research objectives:
a. Review of available literature related to the research subject: A review for available
literature for the finite element modeling and analytical works related to strengthening of
soil was conducted.
b. Development of the Finite Element models using ANSYS: Non‐linear three-dimensional
finite element models were developed to simulate the behavior of soil, foundation and
geosynthetic, using the commercial finite element modeling software (ANSYS). As
following
1. Modeling of properties of concrete for the foundation.
2. Modeling of properties of soil.
3. Modeling of properties of geosynthetic.
4. Defining interface between foundation and soil, soil and geosynthetic.
5. Preparing the model geometry and selection of element types based on the real
materials properties and the element types available in ANSYS.
6. Determination of boundary conditions that were used in the model.
7. Fixing of analysis assumptions (where needed).
8. Carrying out the nonlinear analysis.
9. Getting the analysis results.
c. Models Verification: Finite element models were calibrated with mathematical equation
results available in the chapter 3 based on the following criteria
1. Stress distribution and stress curves.
2. Stress values and measures.
3. Effective depth of stress under foundation.
d. Performing a Parametric Study: After verification of Finite Element models, a
parametric study was performed using ANSYS to evaluate the effect of the following
parameters on the behavior of reinforced soil:
1. Depth of the geosynthetic layer under foundation.
6
2. Depth of the two geosynthetic layers under foundation
3. Effect of geosynthetic in different soil types
4. Effect of different geosynthetic types in one type of soil.
5. Effect of geosynthetic layer width in distribution of stress in the soil.
1.5 Theses layout.
This thesis consists of six chapters: Chapter 1: Introduction, Chapter 2: Literature Review, Chapter
3: Finite Element Modeling of Reinforced Soil, Chapter 4: M Modeling of Reinforced Soil and
Foundations using ANSYS, Chapter 5: Analysis Results of Reinforcement Soil Using ANSYS,
and Chapter 6: Conclusions and Recommendations
7
Chapter 2: literature Review
8
Chapter 2: literature Review
2.1 Introduction:
Plant roots consider as a natural means of combination between randomly fiber in the soils. Plants
roots improve soil strength and stability of soil especially in high natural slobs. thus, the concept
of reinforced soil is recognized 5000 years ago.
Many examples of reinforced soil are discovered in the ancient civilization such as Great Wall of
China (branches of trees were used to improve tensile strength of soil), ziggurats of Babylon
illustrate that woven mats were used to improve tensile strength of soil, etc. In modern history soil
stability is one of main goals lead to use fibers in soil , this concept was developed by Vidal
(Kaniraj & Gayathri, 2003).
Improving of soil shear resistance using fibers was the main conclusion by Vidal which was the
first step in understanding the benefit of incorporating fibers randomly with soil mass under
structural. then, efforts for using fiber materials, as result of past and natural experience, Vidal
discovery was emerged in 1966, since that year about 4500 structures in 45 countries have been
built using principle of soil reinforced material (Abtahi, Okhovat, & Hejazi, 2009).
The first product of reinforced material is polyester filaments before modern reinforced material
such as geosynthetic entered to the geotechnical engineering market under the traditional brand of
‘‘Texsol’’. This product was used in retaining walls and for high level lands and slope protections.
However, discrete fibers that distribute is soil mass randomly, known as short fiber soil
composites, have obvious attraction between 1980 and 2000 in many geotechnical engineering
applications, not only in scientific research environment, but also implement in real field. Since
the late 1980s Synthetic staple fibers have been used in soil, most initial studies recommended to
use polymeric fibers in construction to provide the needed improvement in soil. In conclusion, the
principle of reinforcing soil with natural fibers were created in ancient times. This lead that
synthetic fiber and short natural soil composites had recently attracted attention in geotechnical
engineering for the second time. Therefore, they are still a relatively new technique in geotechnical
projects (Abtahi et al., 2009).
During the last ten years there has been a considerable increase in the use of reinforced soil
structures as a solution for civil engineering problems. Traditional solutions have lost ground, or
have been improved, to match the engineering requirement with the cost and time saving that were
provided by the solution of using reinforced soil. Research associated with this area has also
9
flourished over the last decade, because of the increase in demand for such structures.
Nevertheless, research has not been able to keep pace with the advance of construction techniques
and challenges in design. As a result, designs of reinforced soil structures, in most cases, have been
based on conservative assumptions or on the observations of the performance of real structures as
guidelines for design procedures. This way of solving problems (know how, not knowing why),
although practical, is not the most economical and, besides, is contradictory to the scientific
approach (knowing how because one knows why). Tests with small apparatus were also performed
to investigate the influence of factors like scale on test results. The main concern of the present
work was to show the programming behavior the influence of the presence of inclusions such as
geosynthetics on the behavior of the reinforced soil matrix (Milligan, 1987).
Some conclusions reached may be applied on a wider basis. The analytical part that follows in
chapter 4 will be compared with computer results on ANSYS model used for this research,
followed by the model results, discussions and conclusions.
The work ends with a presentation of the main conclusions and suggestions for future work. The
present work provides some answers of the soil behavior after adding reinforced material.
2.2 The Soil Reinforcement Concept
To reinforce a soil by means of an inclusion consists of placing the inclusion in regions of the soil
matrix where its presence will cause a favorable redistribution of stresses and strains. The inclusion
causes an increase in strength of the composite material and a decrease in its compressibility.
Higher loads can be applied to the reinforced soil structure than in the case for an unreinforced
one. In figure 2.1 some typical examples of reinforced soil structures are presented, with the
mechanisms provided by the reinforcement to improve the performance of the structure (Milligan,
1987).
Other forms of soil reinforcement or improvement are available such as soil nailing, deep
compaction, pile driving, etc. However, the study of these techniques does not fall within the scope
of the present work.
Because soils have very little tensile resistance, the use of reinforcement in regions of tensile
strains is highly attractive. Not only the region where the reinforcement is placed is important, but
also the orientation of the reinforcing element.
10
Placing the reinforcement in regions of tensile strains and, in particular, on orientations coinciding
with the direction of principal tensile strains, will cause the reinforcement to inhibit the
development of tensile stresses in that region of the soil and also increase the shearing
characteristics of the region of the soil and also increase the shearing characteristics of the material
(McGown, 1984).
The orientation of the tensile principal strain will be dependent on geometry, construction
technique and type of load imposed on the structure. In the case of gravitational load in retaining
walls or embankments, the direction of minor principal strains (tensile) coincides approximately
with the horizontal (Milligan, 1987).
In a reinforced unpaved road, the presence of the reinforcement, as a frictional layer between fill
and foundation, restrains the lateral movement of the fill material as the foundation is deformed,
Figure 2. 1 Typical Examples of Soil Reinforcement Application
11
with the additional settlement reducing effect caused by the vertical component of the load in the
reinforcement (see Figure 2.1).
In effect, soil reinforcement is not a new technique at all. In ancient times man used to reinforce
structures by means of reed matting, and the Ziggurat of Agar Quf, in Mesopotamia (1400 BC), is
a major example of this. The technique was revived by Henri Vidal in the 60s on a commercial
basis, using metal strips as reinforcing material. The strong and fast advance of the plastic industry
over the last two decades has put forward this material as a major competitor to steel.
Fears related to corrosion of steel reinforcement have also added to the increasing attention
directed to plastic reinforcement.
2.3 Types of Soil Reinforcement
The main definition of fiber-reinforced soil can be illustrated as a soil mass that contains
distributed, discrete elements, i.e. fibers, that provide an obvious improvement in the mechanical
properties and behavior of the soil composite. Fiber reinforced soil behaves as a composite material
in which fibers of relatively high tensile strength are embedded in a matrix of soil. Shear stresses
in the soil mobilize tensile resistance in the fibers, which in turn imparts greater strength to the
soil. (Hejazi, Sheikhzadeh, Abtahi, & Zadhoush, 2012)
Now there are two main items for using fibers in the soil discrete and sheet fibers. each type can
be obtained from different materials natural or manufactured fiber in this section each type will be
described.
2.3.1 Natural fibers
At the present time, using of reinforced material is widely distributed around the word. as a result
of a greater awareness to environment, filling up landfills, uncontrol consuming of plant resources,
pollution of planet and that non-renewable resources will not last forever. So, there is a need to
more environmentally friendly materials.
As indicated in the introduction of this chapter natural fibers is known from long time ago some
researches indicate that it was known from 5000 years ago. in addition many developing countries
due to of the rareness of cement and earth blocks they start to use natural fibers because of their
availability and low cost.
12
Some natural fibers and their features in soil projects are briefly described:
1. Coconut (coir) fiber
The matured coconut fruit is covered with fibrous material, this cover can be used as discrete fibers
which is normally 50–350 mm long and consist mainly of lignin, tannin, cellulose, pectin and other
water-soluble substances. However, due to its high lignin content, decomposing of this natural
material takes place much more slowly than any other natural fibers. So, this type of fiber considers
long life lasting, with approximate service life of 4–10 years. The water absorption of that is about
130–180% and diameter is about 0.1–0.6 mm.
Coconut retains much of its tensile strength when wet. It has low cohesion, but the elongation is
much higher.
The putrefaction of coconut fibers depends on the medium of embedment, the climatic conditions
and is found to hold 80% of its tensile strength after 6 months of embedment in clay. coconut fibers
geo-textiles are presently available with wide ranges of properties which can be economically
utilized for temporary reinforcement purposes. (Hejazi et al., 2012)
2. Sisal
Sisal is one of discrete fibers that is classified as lingo-cellulosed fiber in which its normally used
as a gypsum plaster reinforcement in gypsum sheets or border in building industry with 60–70%
of water absorption and diameter about 0.06– 0.4 mm.
This type of fibers could be extract from leaves of the plants, which consider very small vary in
size, between 6–10 cm in width and 50–250 cm in length.
One of the most obvious advantages that Sisal fibers reduce the dry density of the soil. In addition,
the more length and soil content with sisal fibers the drier density of the soil reduces.
Moreover, when he length of fibers is more than 20 mm the shear stress is increased non-linearly,
also the shear stress of soil will decrease consequently when length of Sisal is increased. The
percentage of fiber content also improves the shear strength. But beyond 0.75% fiber content, the
shear stress reduces with increase in fiber content. (Hejazi et al., 2012)
13
3. Palm fibers
Filament textures of palm discrete fibers in date has a very special properties such as low costs,
plenitude in the region, durability, lightweight, tension capacity and relative strength against
deterioration.
Palm fibers extracted from decomposed palm trees are found to be having low tensile strength,
modulus of elasticity and very high-water absorption and brittle.
Jamellodin et al. (2010) conclude that improves could be achieved by using palm fibers in the
failure deviator stress and shear strength parameters of the soft reinforced soil. It is observed that
the fibers act to interlock particles and group of particles in a unitary coherent matrix thus the
strength properties of the soil can be increased. (Hejazi et al., 2012)
4. Flax
Flax is considered as the oldest textile fiber was known to humens. It has been used to produce of
linen cloth since ancient times. Flax is a slender, blue flowered plant grown for its fibers and seeds
in many parts of the world. It also improved the ductility of the soil–cement composite with the
addition of flax fibers. An enamel paint coating was applied to the fiber surface to increase its
interfacial bond strength with the soil. Fiber length of 85 mm along with fiber content levels of
0.6% was recommended by the authors. (Cheah & Morgan, 2009)
2.3.2 Manufactured (man-made) fibers
1. Polypropylene (PP) fibers
Currently, PP fibers is used to reduce the shrinkage properties, resist chemical and biological
degradation and enhance soil strength. PP Fibers can be found in two shapes sheets and discrete
In addition, Puppala and Musenda (2000) conclude that PP fiber reinforcement decreased both
volumetric shrinkage strains, improved the unconfined compressive strength of the soil and swell
pressures of the expansive clays (Puppala & Musenda, 2000).
As a result of experiments on field test in which a sandy soil was stabilized with PP fibers, Santoni
and Webster (2001) indicated that using of PP fibers technique showed great potential for military
airfield and road applications, moreover a 203-mm thick sand fiber layer was sufficient to support
substantial amounts of military truck traffic. also indicated using of emulsion binder helps in fixing
surface binder and provide prevention of fiber pullout under traffic. The effects of PP fiber
14
inclusions on the soil behavior could be visually observed during the triaxial testing and/or UCS
testing shown in figure 2.2. (Santoni & Webster, 2001).
2. Polyethylene (PE) fibers
polyethylene (PE) can be found as strips or
sheets. The advantages of using polyethylene
fibers with soil mass has been also investigated
to a limited extent.
Teishev, Incardona, Migliaresi, & Marom
indecated that fracture energy of soil mass is
increased due to the small friction of high
density polyethylene fibers (Teishev,
Incardona, Migliaresi, & Marom, 1993).
High Density Polyethylene fibers as indicated previously increases fracture energy of soil. In last
decade, Geofibers were most used which is made from polyethylene fibers, the general physical
and mechanical properties are 1–2 in. long discrete PP and/or PE fibrillated or tape strands, are
blended or mixed with clay or sand soils. This lead to improve stress–strain response due to tension
developing in soil. Although, improvements in fatigue behavior were not noted. Kim et al. used
Polyethylene fibers of waste fishing net mixed with light weight soil which is derived from
dredging process. waste fishing net increases the compressive strength of soil of 0.25% in optimum
case as concluded by Teishev, Incardona, Migliaresi. (Teishev et al., 1993)
One of the main reason to use polyethylene fibers is an environmental purposes of landfill the
waste PE-based materials in geotechnical engineering.
3. Glass fibers
Consoli et al (1998). conclude that peck strength of silty sand could be improved by mixing glass
fibers with soil, and he also tested and exanimated the change in mechanical behavior of reinforced
cemented soil mixed with glass fibers, Polypropylene fibers and Polyethylene fibers (Consoli,
Prietto, & Ulbrich, 1998).
The conclusion of his investigation showed that polypropylene fibers improved the brittle behavior
of cemented soils, however it showed slight decreeing in deviatoric stresses at failure. On the other
Figure 2. 2 Specimen deformation pattern for (left)
unreinforced clay soil specimens and (right) clay soil
reinforced with 0.25% PP of 19 mm: (Santoni & Webster,
2001)
15
hand, glass fiber and polyethylene fiber decreased the brittle behavior of cemented soils and
slightly increased deviatoric stresses at failure.
Maher and Ho (1994) investigate the behavior of glass fibers and Polypropylene fibers composites
and indicate that the increase in the ultimate compressive strength was more obvious in the glass
fiber-reinforced material (Maher & Ho, 1994).
Conversely, polypropylene fibers overcome glass fiber. In addition Maher and Ho concluded that
the using of 1% to 4% of fiber glass within cemented sand lead to increase ultimate compressive
strength 1.5 times compared to non-fiber-reinforced cemented sand (Hejazi et al., 2012).
At this time, fiberglass strings could be used to improve the properties less cohesion soils types.
The effective usage amount of glass fiber weight is approximately between 0.10% and 0.20% of
the weight of the soil mass mixture. Laboratory tests and experimental studies have illustrated that
soil mixed with glass fibers increase soil cohesion of soil between 100 and 300 KN/m2. It is worth
to mention that fiber glass reinforced material is an effective promoting seed adhesion and root
penetration (Hejazi et al., 2012).
4. Nylon fiber
Kumar and Tabor (2003) investigated the nylon discrete fiber strength within silty clay with
different percentage of mixing and degree of compaction. The conclusion of this investigation that
the peak and residual strength of the samples for a compaction percentage around 93% is much
higher in comparison to samples compacted at the higher densities (Kumar & Tabor, 2003).
Gosavi et al. (2004) concluded that CPR value of soil improved by approximate 50% compared to
unreinforced soil when soil is mixed by nylon fibers and jute fibers, while improved percentage of
CPR using coconut fiber may reach 96% (Gosavi & Patil, 2004).
The maximum used quantities of fiber mixed within the soil found to be 0.75% of the soil mass
and any addition quantities more than 0.75% will not lead to any obvious and significant
improvement in CBR value. As well, in addition in construction field showed that lacerate carpet
waste fibers up to 70 mm long could be mixed into soil with classic equipment. The usage of low
cost fibers from carpet waste could result a big range of usage in reinforced soil and more cost-
effective construction.(Hejazi et al., 2012)
16
5. Steel fibers
Steel strips or sheets reinforcements used in concrete structures rehabilitation or enhancement can
be also used in reinforced soil–cement composites. steel fibers can enhance the soil strength;
however, this development in soil strength is not as much as soil improvement when using other
types of reinforced martial mentioned previously. Ghazavi and Roustaie (2010) concluded that
using polypropylene fibe in cold climates, where soil is affected by freeze–thaw cycles is preferred
than using steel fibers, due to the small unit weight of polypropylene fibers possess smaller unit
weight compared with steel fibers. In other words, the former fibers decrease the sample volume
increase more than steel fibers (Ghazavi & Roustaie, 2010).
6. Geosynthetic Fibers
Geosynthetics are cancellous sheets reinforced material which is also known as construction
fabrics, road rugs, filter fabrics, synthetic fabrics or simply fabrics. This reinforced material is
made of synthetic materials that is produced from bonding fibers such as nylon, polypropylene,
polyvinyl chloride, polyester, glass, and different mixtures of these materials. As a synthetic
construction material, geosynthetics are used for a variety of purposes such as separators,
reinforcement, filtration and drainage, and erosion control. Some types of geosynthetics are made
of materials such as netting and mulch matting. Mulch mattings are jute or other wood fibers that
have been formed into sheets and are more stable than normal mulch. Netting is typically made
from plastic, jute, cotton, or paper, or cotton and can be used to hold the mulching and matting to
the ground. Netting can also be used alone to stabilize soils while the plants are growing; however,
it does not retain moisture or temperature well. Mulch binders (either asphalt or synthetic) are
sometimes used instead of netting to hold loose mulches together. Geosynthetics can aid in plant
growth by holding seeds, fertilizers, and topsoil in place. Fabrics come in a wide variety to match
the specific needs of the site and are relatively inexpensive for certain applications. (Wade, Pai,
Eisenberg, & Colford Jr, 2003)
geosynthetic reinforced soil is usually
manufactured from longitudinal and transverse,
the transverse members work in parallel of the
free edge or face structure and behave as support
or anchors, the shape of geosynthetic material is
shown in the figure 2.3. to get the most efficiency results to retain transverse members in position.
Figure 2. 3 Geosynthetic Material
17
Witch is working as anchors or support that need to be stiff relative to their length. The longitudinal
members may be flexible having a high modulus of elasticity not susceptible to creep. The pitch
of the longitudinal members, pL is determined by their load-carrying capacity and the stiffness of
the transverse element. The pitch of the transverse elements, pT depends upon the internal stability
of the structure under consideration. A surplus of longitudinal and transverse elements is of no
consequence provided the soil or fill can interlock with the grid. Mono and Bi Oriented grid are
shown in Figure 2.3. (Okechukwu et al., 2016)
2.4 Behavior of Reinforced Soil
2.4.1 Principle
An internally stabilized system such as reinforced soil involves reinforcements installed within
and extending beyond the potential failure mass. Reinforced earth is a material formed by
combining soil and reinforcement. The reinforcement comprises of reinforcing elements which is
in the form of strips set at certain intervals disposed in horizontal layers.
On the facing of the structure, a certain type of boundary or skin is required to retain the earth
particles that are not in contact with reinforced strips. A reinforced soil mass is somewhat
analogous to reinforced concrete in that the mechanical properties of the mass are improved by
reinforcement placed parallel to the principal strain direction to compensate for soil's lack of tensile
resistance.
Combining reinforced fibers and the soil improve tensile properties of the soil. This concept is
quite familiar and where used in many different cases and condition and could be seen in many
real cases such as concrete combined with steel bars. It combines the high compressive strength of
concrete with tensile strength of steel, but relatively low tensile strength of concrete. As well, soils
which have similar situation, soil tensile strength will be improved when it combined with
reinforced material. By using this kind of strength improvement is obtained by surface interaction
between the soil and the reinforcement through friction and adhesion. The reinforced soil is
obtained by placing extensible or inextensible materials such as geosynthetic or discrete fibers
within the soil to obtain the needed properties (Okechukwu et al., 2016).
Soil known to have high compressive strength and low tensile strength. One of the main objectives
of mixing or using reinforced material is to increase the tensile resistance of the soil. Without using
reinforced material soil may fail under shear or by excess of the settlement. compressive strain and
lateral tensile strain are generated from axial load that is applied to reinforced soil, as illustrated
18
by model in Figure 2.4. when reinforced material has axial tensile stiffness greater than that of the
soil, that lead to lateral movements of the soil which is occurred if soil can move relative to the
reinforcement (Nand. 2005).
Movement or displacement of the soil particles, relative to the reinforcement, will create shear
stresses at the soil/ reinforcement interface, these shear stresses are redistributed back into the soil
in the form of internal confining stress.
As conclusion the strain in unreinforced soil is more than the strain within the reinforced soil mass
for the same amount of stresses, this is indicated in figure 2.4 where δhr < δh. and δvr < δv,
provided the surface of the reinforcement is sufficiently rough to prevent the relatively movement
and the axial tensile stiffness of reinforcement is more than that of soil. reinforcement (Nand..
2005).
Figure 2. 4 Effect of reinforcement on a soil element (Nand. 2005)
19
2.4.2 Factors Affecting the Behavior of Reinforced Soil:
For the good performance of a reinforced soil structure three factors are of utmost importance:
a. Nature and mechanical characteristics of the soil;
b. Nature and mechanical characteristics of the reinforcement;
c. Interaction between soil and reinforcement and how this affects the response of each
material.
In fact, the factors above are linked together and the discrimination of a component due to each
one exclusively is not easy. Nevertheless, some individual characteristics can be distinguished as
follows. (Milligan, 1987).
2.4.3 Influence of Fill Material:
Granular material has been the standard requirement for fill material In reinforced soil structures.
This requirement comes from the obvious fact that highly frictional materials will develop a higher
bond with reinforcement than poor materials. Recommendations on percentage of fines in the fill
material can be found in Schlosser and Elias (1978) and Brown & Rochester (1979). (Palmeira,
2009)
Aggressive fill material should be avoided. Other researchers used silty clayey sand as a fill
material for a reinforced wall and concluded that, despite construction difficulties and pore
pressure development, cost savings could be achieved in comparison with the utilization of
granular material imported over substantial distances. (Palmeira, 2009)
Palmeira (2009) have found high friction coefficients between phosphonyls and geosynthetic.
(Palmeira, 2009)
He also reported fill material savings in a reinforced access road on soft ground where poor quality
fill material was used. Recent research work using pulverized fuel ash and chalk as fill materials
have been carried out at Strathclyde University and at the Transport and Road Research
Laboratory, respectively. (Palmeira, 2009)
2.4.4 Influence of Reinforcement Characteristics:
In the last decade the most common types of reinforcements are made of steel or plastic. Related
to steel reinforcement, the main concern is corrosion.
20
This is not only a function of steel properties but also of environmental characteristics. The usual,
but not economical solution, is to increase the thickness of the reinforcement, as a safety measure
against corrosion.
Galvanizing, plastic coating or the utilization of stainless steel or aluminum strips can also be
employed, but also with increasing cost of the structure.
Plastic reinforcement is of a more complex nature, where time and temperature dependency may
play an important role in its behavior. The continuous industrial development has provided a large
variety of high tensile strength and stiff reinforcement materials. (Palmeira, 2009)
The remaining uncertainties regarding plastic reinforcement are its durability and long-term
behavior (creep). Durability will depend on the reinforcement material and environmental
characteristics. Some data on degradation resistance of some synthetic fibers are presented in gold.
(McGown, 1984).
Figure 2. 5 Long Term Behavior of Polymer Reinforcement (McGown,1984).
21
Creep behavior depends on type of reinforcement, stress level and temperature. Studies by
McGown et al (1984) have shown that since the factors affecting the time dependent behavior of
a reinforcement are identified and quantified, safe designs incorporating creep allowances can be
achieved. Figure 2.5 presents the results of creep studies performed by McGown et al (1984) for a
polymer reinforcement.
Figure 2.5a permits the identification of a tendency to failure caused by creep. Figure 2.5b allows
for the determination of the load in the reinforcement as a function of the strain and elapsed time.
Results of this kind should be provided as a rule and not an exception in manufacturers. (McGown,
1984)
Direct shear tests on reinforced sand in a medium size shear box, with the reinforcement inclined
to the shear plane, have shown that reinforcement longitudinal stiffness is an important parameter,
although bending stiffness seems to show negligible effect on test results. Palmeira reached the
same conclusions regarding longitudinal stiffness using numerical analysis to model pull-out tests.
(Palmeira, 2009)
Form of reinforcement is very important since it influences markedly the failure mechanism
developed and the degree of bond between soil and reinforcement. This and other reinforcement
characteristics strongly related to bond are discussed next. (Palmeira, 2009)
2.4.5 Interaction Between Soil and Geosynthetic
Bond between soil and reinforcement is of major importance to reinforced soil structures design.
It depends on soil type, reinforcement type and how they interact with each other. The degree of
interaction between soil and reinforcement as well as the failure mechanism developed is a
function of the reinforcement form. In figure 2.6 some typical reinforcements are shown with the
main mechanisms involved between them and the surrounding soil. (McGown, 1984)
22
Geosynthetics and plain metal strips generate bond with soil by a frictional mechanism. In grids,
depending on the geometry, the bearing mechanism may prevail due to the interaction between
grid bearing members and surrounding soil (figure 2.5). using photo elasticity, has clarified and
identified different mechanisms of interaction between soil and reinforcement. Of great
importance is then the identification of the right mechanism and the choice of a convenient and
accurate way of measuring the magnitude of bond
stresses between soil and reinforcement. The measurement of soil reinforcement interaction is
discussed in the following sections.
2.4.6 Measurement of Soil-Reinforcement Interaction:
Accurate testing conditions must be chosen to measure bond stresses between soil and
reinforcement. Although some studies tests can be found in the literature, testing procedures under
plane strain conditions are preferred because this is the most common case in real reinforced soil
structures. some of the testing procedures that have been used to study soil-reinforcement
interaction are presented. The most common testing methods are direct shear and pullout tests.
Boundary conditions may change from study to study using these tests. Nevertheless, boundaries
seem to vary more among pull-out tests than direct shear and they also appear to influence pull-
out test results more than direct shear tests.
Despite some differences in equipment or boundary conditions, as follows:
Figure 2. 6 Common Type of Soil Reinforcement (McGown,1984).
23
a. The most effective way of placing the reinforcement is in the regions of tensile strains, in
particular, coinciding with the direction of minor principal (tensile) strain. In regions of
compressive strains, the reinforcement may not affect or may decrease the strength of the
reinforced soil;
b. Reinforcement longitudinal stiffness is a very important variable for the response of
reinforced soil samples. The composite material can present a brittle or ductile behavior,
depending on the stiffness of the inclusion. The behavior of the reinforcement as a stiff or
extensible material may also be conditioned by the stress level;
c. Reinforcement bending stiffness is not of major importance in the behavior of reinforced
sand samples undergoing direct shear; sing triaxial.
d. The form and degree of roughness of the reinforcement is of utmost importance for the
load transfer between soil and reinforcement and for the overall strength of reinforced
samples. Dyer (1985) has emphasized the fact that the main mechanism of interaction
between a grid reinforcement and the surrounding soil is due to bearing.
In figure 2.7 possible internal failure mechanisms in a retaining wall structure are presented as an
example. If failure along surface 1-2 occurs, the mechanism involved in region A is of sliding of
soil on the plane of reinforcement. If failure along surface 3-4 prevails, soil and reinforcement, as
a composite material, is sheared. In the case of failure along the length 5-6, because of insufficient
anchorage, sliding of the reinforcement inside the soil matrix takes place. (Dyer & Daul, 1985)
24
Based on this example, the choice of direct shear tests and pull-out tests to represent each specific
situation seems sensible. A good guess for the orientation of a planar failure surface in figure 2.7,
based on earth pressure theories would result in a angle of (π/4 + ɸ/2) with the horizontal measured
from the bottom corner of the wall, ~ being the soil friction angle. For most granular backfills, this
expression would lead to orientations between 60° and 70° for the failure plane.
As a result, values between 20° to 30° are obtained for the angle formed by the normal to the
failure plane and the reinforcement direction (ɸ in figure 2.7) at the intersection between failure
plane and reinforcement plane (region B in figure 2.7). In fact, in direct shear tests with the
reinforcement inclined to the shear plane, values of ɸ = 30° have been found to be the most efficient
orientation for the reinforcement (Juran, Ider, & Farrag, 1990) which is also the direction where
coincidence between reinforcement orientation and direction of minor principal strain occurs in a
direct shear box when testing dense sand.
In the case of direct sliding of soil on reinforcement, Sarsby & Marshal (1983) have shown that a
polymer grid reinforcement (Netlon SR2) can develop an interface friction angle equal to the soil
friction angle. Jewell et al (1984) proposed an equation to obtain a friction coefficient between soil
and reinforcement in direct sliding as a function of the soil strength parameters, reinforcement
form and geometry. (Juran et al., 1990)
Figure 2. 7 Failure Mechanisms in a Reinforced Soil Retaining Wall (McGown,1984).
25
For potential failure surface intersecting the reinforcement layer, Jewell (1980) has demonstrated
that a limit equilibrium analysis may be successfully used to obtain reinforcement forces in a direct
shear box. The freedom of choice of boundary conditions for pull-out tests seems to be either an
advantage or a limitation of the test. (McGown, 1984)
An advantage in the sense that simple boundary conditions can be chosen to eliminate some
obstacles to the interpretation of results and a limitation because, if some precautions are not taken,
the result of the test may be affected by the boundaries.
Angles of friction between soil and reinforcement obtained in pull-out tests greater than the friction
angle of the soil alone have been reported. This has been attributed to boundary conditions or soil
dilatancy. The usual criterion to check the reliability of a test result is that the interface angle of
friction between soil and a plain sheet of reinforcement cannot be greater than the angle of friction
for the soil alone. A collection of data on direct shear and pull-out test results is presented in figures
2.8 a and b. (McGown, 1984)
Most of the data in figure 2.8a was originally collected by Richards & Scott (1985) with some
additions made. Reinforcements presenting bearing-like mechanisms were avoided in order to
Figure 2. 8 Direct Shear and Pull-out Test Results Collected (McGown,1984)
26
have a common basis for comparison. Reinforcement types are various geosynthetics and plain
metal sheets (Richards & Scott, 1985).
Independently from boundaries and test arrangements, two marked patterns of results arise in
figure 2.8a:
1. Most of the interface friction angle values (δ) are smaller than the soil friction angle (ɸ).
Values of δ greater than ɸ may be expected to be due to boundary or scale problems or to
inaccurate measurement of the soil friction angle. Also, most of the values of interface
friction angles for geosynthetics are within the limits 0.75 ɸ < δ < ɸ;
2. Plain metal reinforcement, besides showing a larger scattering of results, presents smaller
values of interface friction angle (0.3 ɸ < δ <0.7 ɸ). sands is shown. In this figure the
difference between maximum friction angle is plotted against mean stress level for several
sands at some relative density index (ID) values. This shows the dependency of the friction
angle on stress level. Some soil friction angles have been also obtained from test conditions
different from plane strain, which is usually the case in pull-out tests. Figure 2.9 shows that
the friction angle obtained for a sand is dependent on whether a plane strain or an
axisymmetric condition is imposed to the sample. In real reinforced soil walls the vertical
stress near the wall can be greater than the stress due to the weight of the soil alone.
McGrown (1984) have reported pressures at the base of reinforced earth wall models, near
the corner of the wall, up to 2.5 times greater than the pressure due to the weight of
soil.(McGown, 1984)
Figure 2. 9 Friction Angle Dependence on Stress Level (McGown,1984).
27
3. Scale: may impose additional difficulties in interpreting results. The influence of factors
such as the relation between soil particle size and container volume, side friction and low
stress levels must be quantified and considered. the influence of scale on the magnitude of
results was obtained from models. (McGown, 1984)
4. Mechanism of Interaction: bearing-like mechanisms presented by ribbed strips or grids are
usually quantified in terms of bond strength using the same approach as for flat
reinforcements. This may lead to "friction angles" between soil and reinforcement greater
than the soil friction angle. However, this seems not to be the appropriate way of
approaching grid or ribbed strip behavior. A grid buried in soil should be seen as a
succession of anchor members providing bearing resistance and interfering with each other.
It is fundamental, for this sort of reinforcement, that the bearing mechanism is understood
to be accurately quantified. Three dimensional effects involved in the case of pull-out tests
of strips should also be pointed out. Of course, the simple comparison between a test result
and the soil friction angle is not a guarantee of accuracy for the result or reliability in the
test procedure. Nevertheless, it provides an upper limit for judgement of values obtained
from tests. Figure 2.10 shows the histogram plot for test results presented in figures 2.9 a
and b. figure 2.10 a emphasizes the higher adherence between soil and geosynthetics
compared with plain steel reinforcement. figure 2.9 b. (Juran et al., 1990)
is not as accurate as figure 2.10a, in the sense that there are fewer pullout test results published in
the literature than direct shear test results. Nonetheless, the same trend is observed in the case of
pull-out tests.
Figure 2. 10 Histogram of Direct Shear and Pull-out Test Results (McGown,1984).
28
A larger spreading of results is a measure of the effect of different boundary conditions but, for
geosynthetics, the mean value of δ / ɸ from pull-out tests compares very well with the value
obtained from direct shear tests. Pull-out tests are extremely useful interference between bearing
members of a grid reinforcement. Boundary conditions can be chosen that make the interpretation
of the test results easier than in direct shear tests with the reinforcement inclined to the central
plane. Although some pioneer methods of predicting pull-out resistance are available (Juran et al.,
1990).
2.5 Laboratory Testing.
Various studies have been conducted in the laboratory using unconfined compression tests, triaxial
compression tests and direct shear tests and it has been found that the reinforcement of soil by
discrete fibers causes an increase in the strength of soil and reduction in the post peak loss of
strength.
Ramaswamy and Aziz (1989) conducted unconfined compression tests on compacted soil samples
of diameter of 100 mm and 200 mm length. All the samples were compacted at OMC of 25% and
two layered reinforcement was used in testing, the tests revealed that UCS of soil was increased
due to incorporation of jute geotextiles (Rahmanian, Suraya, Shazed, Zahari, & Zainudin, 2014).
Ghavami et al. (1999) used natural fibers (coconut fibre and sisal) for reinforcing the soil and
found that the natural fibers enhanced the ductility and the strength of soil (Ghavami, Toledo Filho,
& Barbosa, 1999).
Akbulut et al. (2007) found that the increase in scrap tire rubber content resulted in an increasing
UCS value and after it reached an optimum amount there was a reduction in strength of reinforced
soil. This optimum amount and length of reinforcement were found to be 2% and 10 mm
respectively (Akbulut, Arasan, & Kalkan, 2007).
Hu et al. (2009) conducted tests on GRS samples reinforced with nonwoven geotextiles and
concluded that the UCS of reinforced soil increased with decrease in reinforcement spacing and
increase in relative density of soil. Due to reinforcement, composite soil exhibits a flexible and
ductile failure (Hu, Song, & Zhao, 2009).
Amin chegenizadeh and Hamid Nikraz (2012) conducted a series of UCS tests and concluded that
fiber content, type of fiber and length of fiber have significant effect on the performance of
reinforced soil. Fiber content and length of fiber cause an increase in the strength of soil by a
29
considerable amount. Plastic fiber is more effective than natural fiber (Chegenizadeh & Nikraz,
2012).
2.6 Effect on Peak Strength
In case of two layer woven and non- woven geotextile, the failure planes were bserved above the
top of geotextile. Some typical graphs are shown in figure 2.11 and figure 2.12 for non-woven and
woven geotextiles respectively. The observation made in laboratory test is presented in tabular
form in table 2.1 (Chegenizadeh & Nikraz, 2012)
Peak strength of and percentage axial strain have been increased to a considerable amount with the
inclusion of woven reinforcement compared to non-woven reinforcement. More the number of
layers of woven geotextile, more the strength of soil. The stress–strain behavior of reinforced soil
is consistent with several past studies (Haeri, Noorzad, & Oskoorouchi, 2000).
Effect of number of layers on peak strength is very predominant in case of woven geotextiles as
compared to non-woven geotextiles as shown in figure 8. Soil reinforced with woven geotextiles
exhibits more ductile and flexible failure as compared to non-woven geotextiles.(Chegenizadeh &
Nikraz, 2012)
Figure 2. 11 Stress-strain relation for non-woven reinforced soil (Chegenizadeh &
Nikraz, 2012)
30
Table 2. 1 Effect of reinforcement on unconfined compressive strength test (Chegenizadeh & Nikraz, 2012)
Figure 2. 12 Stress-strain relation for woven reinforced soil (Chegenizadeh & Nikraz, 2012)
31
Woven type geotextiles are more effective compared to non-woven geotextiles to improve the peak
shear strength of soil. With increase in number of layers, unconfined compressive strength
increases for woven geotextiles. Nonwoven geotextiles causes some increase in the unconfined
compressive strength, but effect of the number of layers is negligible as compared to woven
geotextiles. Soil reinforced with woven geotextiles exhibits more ductility and flexible behavior
as compared to non-woven geotextiles (Chegenizadeh & Nikraz, 2012).
2.7 Concluding Remarks
In conclusion as shown in this chapter the soil reinforced material can be divided into two main
types natural type and manmade type.
Each type has a unique property that has different influence on the soil and could be used in various
condition. The reinforced material could be used as discrete or sheets and strips.
Most previous researches and studies discussed the mechanical properties and material behavior
of soil reinforced material. Each type was tested and examine in the lab to determine how it will
affect and improve the soil and what advantages this material will add to the soil.
Moreover, some researchers obtained equations and factor explained mathematically the behavior
of soil after adding reinforced material.
Most researchers recommended to obtain a computerized model that could give a visible result
and simulate the behavior of the reinforced soil to give all designer and engineers a clue about the
behavior of soil.
In the following chapters of this thesis a finite element model of reinforced soil will be conducted
to study the behavior under different loading and layout conditions.
32
Chapter 3 Modeling of
Foundations and Soil using
Finite Element Method
33
Chapter 3 Modeling of Foundations and Soil using Finite Element Method
3.1 Introduction
This section presents the general steps included in any finite element method formulation and
solution to an engineering problem. Typically, for the structural stress- analysis problem, the
engineer seeks to determine displacements and stresses throughout the structure, which is
in equilibrium and is subjected to applied loads. For many structures, it is difficult to determine
the distribution of deformation and stress using conventional methods, and thus the finite element
method is necessarily used.
There are two general direct approaches traditionally associated with the finite element method as
applied to structural mechanics problems. One approach, called the force, or flexibility, method,
uses internal forces as the unknowns of the problem. To obtain the governing equations, first the
equilibrium equations are used. Then necessary additional equations are found by introducing
compatibility equations. The result is a set of algebraic equations for determining the redundant
or unknown forces.
The second approach, called the displacement, or stiffness, method, assumes the displacements of
the nodes as the unknowns of the problem. For instance, compatibility conditions requiring that
elements connected at a common node, along a common edge, or on a common surface before
loading remain connected at that node, edge, or surface after deformation takes place are initially
satisfied. Then the governing equations are expressed in terms of nodal displacements using the
equations of equilibrium and an applicable law relating forces to displacements.
3.2 Steps and Procedure of finite Element Method
3.2.1 Step 1 Discretize and Select the Element Types
Step 1 is to divide the body of the structural into finite element equivalent system. These divided
elements is associated nodes with a choose of the most preferred and appropriate element type so
it could model the behavior of the material as mush close to actual physical behavior. their
variation in size, type and total number of elements to be used for the material body primarily
matters of engineering judgment. The element must be small to give most accurate result and large
enough to reduce the calculation efforts. Small elements (and possibly higher order elements) are
generally desirable where the results are changing rapidly, such as where changes in geometry
occur; large elements can be used where results are relatively constant. The discretized body or
34
mesh is often created with mesh-generation programs or preprocessor programs available to the
user (Chandrupatla, Belegundu, Ramesh, & Ray, 2002).
3.2.2 Step 2 Select a Displacement Function
In step 2 choosing displacement function within each element. Defining function within the
element by using element nodal values. Linear, quadratic, and cubic polynomials are frequently
used functions because they are simple to work with in finite element formulation. However,
trigonometric series can also be used.
For two-dimensional element, function of displacement using coordinates in plane pf xy plane, xz
plan or yz plan. This function can be expressed in terms of the nodal unknowns (in the two-
dimensional problem, in terms of an x and a y component). The same general displacement
function can be used repeatedly for each element. Hence the finite element method is one in which
a continuous quantity, such as the displacement throughout the body, is approximated by a discrete
model composed of a set of piecewise-continuous functions defined within each finite domain or
finite element (Chandrupatla et al., 2002).
3.2.3 Step 3 Define the Strain/Displacement and Stress/Strain Relationships
Strain/displacement and stress/strain relationships are necessary for deriving the equations for
each finite element. In the case of one-dimensional deformation, say, in the x direction, the strain
is related to displacement u by
𝜀𝑥 =𝑑𝑢
𝑑𝑥
for small strains. In addition, the stresses must be related to the strains through the stress/strain
law—generally called the constitutive law. The ability to define the material behavior accurately
is most important in obtaining acceptable results. The simplest of stress/strain laws, Hooke’s law,
which is often used in stress analysis, is
given by 𝜎𝑥 = 𝐸𝜀𝑥
where 𝜎𝑥= stress in the x direction and E= modulus of elasticity.(Bathe, 2006)
3.2.4 Step 4 Derive the Element Stiffness Matrix and Equations
Initially, the development of element stiffness matrices and element equations was based on the
concept of stiffness influence coefficients, which presupposes a background in structural
35
analysis. There are other alternative methods which do not require this special background, namely
direct equilibrium method, work or energy methods, and methods of weighted residuals.
In Direct Equilibrium Method, the stiffness matrix and element equations relating nodal forces to
nodal displacements are obtained using force equilibrium conditions for a basic element, along
with force/deformation relationships.(Dhatt, LefranÃ, & Touzot, 2012)
In Work or Energy Methods, the stiffness matrix and equations for two- and three- dimensional
elements, it is much easier to apply a work or energy method. The principle of virtual work (using
virtual displacements), the principle of minimum potential energy, and Castigliano’s theorem are
methods frequently used for derivation of element equations.
3.2.5 Step 5 Assemble the Element Equations to Obtain the Global
Assembling.nodal.equilibrium.equation.of.this.individual.element.into.the.global.nodal.equilibriu
m...equations....There.are.another...direct...method...of.superposition.(called...the...direct...stiffne
ss...method),.whose...basis...is...nodal...force.equilibrium,.can.be.used.to.obtain.the.global.equati
ons.for.the.whole.structure..Implicit.in.the.direct.stiffness.method.is.the.concept.of.continuity,.or.
compatibility,.which.requires.that the
structure.remain.together.and.that.no.tears.occur.anywhere.within.the.structure. (Bathe, 2006)
3.2.6 Step 6 Solve for the Unknown Degrees of Freedom (or Generalized Displacements)
Equation below, modified to account for the boundary conditions, is a set of simultaneous
algebraic equations that can be written in expanded matrix form as
{
𝐹1
𝐹2
⋮𝐹𝑛
} = [
𝐾11
𝐾21
⋮𝐾𝑛1
𝐾12
𝐾22
⋮𝐾𝑛2
⋯⋯⋮
⋯
𝐾1𝑛
𝐾2𝑛
⋮𝐾𝑛𝑛
]
where now n is the structure total number of unknown nodal degrees of freedom. These equations
can be solved for the ds by using an elimination method (such as Gauss’s method) or an iterative
method (such as the Gauss–Seidel method). The ds are called the primary unknowns, because they
are the first quantities determined using the stiffness (or displacement) finite element method
(Chandrupatla et al., 2002).
36
3.2.7 Step 7 Solve for the Element Strains and Stresses
For the structural stress-analysis problem, important secondary quantities of strain and stress (or
moment and shear force) can be obtained because they can be directly expressed in terms of the
displacements determined by solving the element equations in global direction.(Dhatt et al., 2012)
3.2.8 Step 8 Interpret the Results
The final goal is to interpret and analyze the results for use in the design/analysis process.
Determination of locations in the structure where large deformations and large stresses occurs
generally important in making design/analysis decisions. Postprocessor computer programs help
the user to interpret the results by displaying them in graphical form (Chandrupatla et al., 2002).
3.3 Finite Element Modeling of Reinforced Soil
Modeling of foundations is consisting of three basic material modeling. foundation, fiber
geosynthetic, and soil are the elements which should be modeled as the real elements.
To simulate the whole system this section will present the modeling criteria of each element in
finite element method.
3.3.1 Modeling of Foundations
For modeling of foundation consider as element SOLID65 8-node brick elements were used for
the 3-D modeling of solids. In concrete applications, the solid capability of the element may be
used to model the concrete. The solid is capable of cracking in tension and crushing in
compression. The element is defined by eight nodes having three degrees of freedom at each node:
translations in the nodal x, y, and z directions (Li & Zhang, 2009).
The concrete element is like the 8-node (3-D Structural Solid) element with the addition of special
cracking and crushing capabilities. The most important aspect of this element is the treatment of
nonlinear material properties as shown in Figure 3.1. The concrete is capable of cracking (in three
orthogonal directions), crushing, plastic deformation, and creep. The rebar is capable of tension
and compression, but not shear. They are also capable of plastic deformation and creep (Li &
Zhang, 2009).
37
3.3.2 Modeling of soil
The soil is considered as element SOLID5 and is treated as an isotropic, homogenous and elastic
half space medium. In this study depth of soil was assumed to be 15 m this depth were chosen
depending on that the effective of stress under foundation equal to 5*width of the foundation
(Donald et al., 2001).
For the nonlinear analysis, the initial tangent modulus (Es) and Poisson’s ratio (μs) are the inputs.
The soil medium below the foundation was modeled using the eight-node brick element having
three degrees of freedom of translation in the x, y and z directions at each node. To find the extent
of the soil region to be used in the study, many trial analyses are carried out. It is found that for
the width and the thickness of the soil medium more than 2.5 times the least width of the isolated
foundations shows a negligible influence on the settlement and the contact pressure as shown in
Figure 3.2. The vertical translation is arrested at the bottom boundary while the lateral translation
is arrested at the vertical boundary. (Li & Zhang, 2009)
Figure 3. 1 8-node Geometry SOLID65
38
3.3.3 Soil Foundation Interaction
In finite element analysis, soils and foundation are modeled as eight nodes hexahedron element.
Soil- foundation interaction is particular; because the two materials are very different from each
other and usually do not match deformation compatibility conditions on their contact surfaces.
Soil and foundation maybe relatively slip, which belongs to boundary condition nonlinear
problems. Thus, contact element should be taken into consideration. (Li & Zhang, 2009)
The elastic modulus of foundation is about 100 times of soils’ in most situation, so the soil-
foundation interaction is the rigid-to-flexible face-to-face contact problem. (Donald et al., 2001)
Figure 3. 2 Foundation soil and element discretization (Quarter model)
Figure 3. 3 Interface Surface between foundation and soil
Interface Surface
Load
39
The foundation rigid surface referred to the target surface, meanwhile the surface of the soils
deformable body is referred to the contact surface. Put the loads beyond foundation on the top of
foundation to simulate the load case at the normal operation. The diagrammatic sketch of
foundations model is showed in Figure 3.3.(Li & Zhang, 2009)
3.3.4 Material Modeling
The modeling of materials depends on the type of structural behavior of these materials. The
behavior of the material is either linear or nonlinear.
Nonlinear structural behavior arises from many causes, which can be grouped into these principal
categories:
• Changing status
• Geometric nonlinearities
• Material nonlinearities
Changing Status (Including Contact): Many common structural features exhibit nonlinear
behavior that is status-dependent. For example, a tension-only cable is either slack or taut; a roller
support is either in contact or not in contact. Status changes might be directly related to load (as in
the case of the cable), or they might be determined by some external cause. (ANSYS, 2011)
Situations in which contact occurs are common to many different nonlinear applications.
Contact forms a distinctive and important subset to the category of changing-status nonlinearities.
Geometric Nonlinearities: If a structure experiences large deformation, its changing geometric
configuration can cause the structure to respond nonlinearly. Geometric nonlinearity is
characterized by "large" displacements and/or rotations. (ANSYS, 2011)
Material Nonlinearities: Nonlinear stress-strain relationships are a common cause of nonlinear
structural behavior. Many factors can influence a material's stress-strain properties, including load
history (as in elastoplastic response), environmental conditions (such as temperature), and the
amount of time that a load is applied (as in creep response) (ANSYS, 2011)
3.3.5 Material Modeling of Foundation and soil
The concrete material model predicts the failure of brittle materials. Both cracking and crushing
failure modes are accounted for.
40
The criterion for failure of concrete due to a multiaxial stress state can be expressed in the form
(Fanning, 2001).
Material Modeling of soil (Drucker-Prager) The Drucker-Prager material model is used for
pressure-dependent inelastic behavior of materials such as soils, rock, concrete, and powder. The
Drucker-Prager plasticity model is different from typical metal plasticity models since it contains
a dependence on hydrostatic pressure. For metal plasticity (assuming Von Mises or similar yield
surface), only the deviatoric stress is assumed to cause
yielding.
yield surface in principal stress space, this results in a
cylinder whose axis is the hydrostatic pressure line,
indicating that yielding is independent of the hydrostatic
stress state. For the Mises yield surface, theoretically,
one could have infinite hydrostatic compression, and no
yielding would occur. (Drucker-Prager)
On the other hand, the Drucker-Prager plasticity
model has a term that is dependent on the hydrostatic pressure. For a linear yield surface (“linear”
referring to the linear shape when plotted in the plane of effective stress vs. hydrostatic pressure),
this means that if there is some hydrostatic tension, the yield strength would be smaller.
Conversely, as hydrostatic compression increases, so would the yield strength. When the yield
surface is plotted in principal stress space, it would look like a cone, as shown in the Figure on the
left.
The two main characteristics that result is that (a) the yield strength changes, depending on the
hydrostatic stress state and (b) some inelastic volumetric strain can occur, as defined by the flow
potential. Because of these points, the Drucker-Prager material model is used for geomechanics or
powder compaction or any other application where both hydrostatic dependence and inelastic
volume strain are important (Imaoka, 2008).
Figure 3. 4 Material Modeling of soil
41
Drucker-Prager Model: Besides reviewing the
yield surface in principal stress space, as shown
earlier, one can also look at the yield surface along
the plane defined by the effective stress and
hydrostatic pressure. The linear Drucker-Prager
yield surface would look as illustrated below.
The two main items that are required for the
linear Drucker-Prager case are the slope (“angle of internal friction”) and the value at which it
intersects the y-axis (i.e., the yield strength at zero hydrostatic pressure, related to the “cohesion
value”.
The cohesion value c is related to the yield strength 𝜎𝑦via the relationship
𝐶 = √3(3−sin 𝜃)
6 cos(𝜃)𝜎𝑦 Equation 1 cohesion value c
Note that the intersection occurs at 𝜎𝑦
√3 , so sometimes this is rewritten as (𝐶 =
√3(3−sin 𝜃)
6 cos(𝜃)𝜎𝑦)
The angle of internal friction θ describes the slope of the yield surface. One can imagine that if the
angle is zero, this would imply no dependence on hydrostatic pressure – effectively, this would
change the behavior to the Mises yield surface. There is a third parameter for the Drucker-Prager
material model – the dilatancy angle of that describes the flow potential. If f θ = θf the flow is
associative. If θf = 0 no inelastic volumetric strains will be produced (Imaoka, 2008).
3.3.6 Material Modeling of Contact Element (surface to surface)
Contact problems are highly nonlinear and require significant computer resources to solve. It is
important to understand the physics of the problem and take the time to set up your model to run
as efficiently as possible.
Contact problems present two significant difficulties. First, you generally do not know the regions
of contact until you've run the problem. Depending on the loads, material, boundary conditions,
and other factors, surfaces can come into and go out of contact with each other in a largely
unpredictable and abrupt manner. Second, most contact problems need to account for friction.
There are several friction laws and models to choose from, and all are nonlinear. Frictional
response can be chaotic, making solution convergence difficult. (ANSYS, 2018)
Figure 3. 5 linear Drucker-Prager (Imaoka, 2008))
42
If you do not need to account for friction in your model, and the interaction between the bodies is
always bonded, you may be able to use the internal multipoint constraint feature (available for
certain contact elements) to model various types of contact assemblies and surface-based
constraints. Another alternative is to use constraint equations or coupled degrees of freedom
instead of contact to model these situations. Constraint equations are only available for small strain
applications.
3.3.7 Surface-to-Surface Contact Elements
Finite element programs support both rigid-to-flexible and flexible-to-flexible surface- to-surface
contact elements. These contact elements use a “target surface” and a "contact surface" to form a
contact pair. To create a contact pair, assign the same real constant number to both the target and
contact elements (ANSYS, 2011).
These surface-to-surface elements are well-suited for applications such as interference fit assembly
contact or entry contact, forging, and deep-drawing problems. Using these elements for a rigid
target surface, you can model straight and curved surfaces in 2-D and 3-D, often using simple
geometric shapes such as circles, parabolas, spheres, cones, and cylinders. More complex rigid
forms or general deformable forms can be modeled using special preprocessing techniques.
(ANSYS, 2011)
Surface-to-surface contact elements are not well-suited for point-to-point, point-to- surface, edge-
to-surface, or 3-D line-to-line contact applications, such as pipe whip or snap-fit assemblies. You
should use the node-to-surface, node-to-node, or line-to-line elements in these cases. You also can
use surface-to-surface contact elements for most contact regions and use a few node-to-surface
contact elements near contact corners. (ANSYS, 2011)
The surface-to-surface contact elements only support general static and transient analyses,
buckling, harmonic, modal or spectrum analyses, or substructure analyses.
43
Chapter 4 Modeling of
Reinforced Soil and
Foundations using ANSYS
44
Chapter 4 Modeling of Reinforced Soil and Foundations using ANSYS
4.1 Introduction
This chapter aims at modeling soil and soil reinforcement using ANSYS finite element program
which deals with many problems. Modeling of foundations is discussed in this chapter as a 3D
element structure.
The benefit of using a 3D element structure is for getting better solutions than 2D elements. The
procedure for modeling is by defining the element materials for soil and concrete.
Choosing the most appropriate element type for soil and concrete which is done within chapter.
Then applying the contact element between surfaces, foundation-soil, fiber-soil.
4.2 Modeling of Reinforced Soil
This section shows the procedure of modeling all elements of soil, geosynthetic and foundation,
which consists of modeling of soil, foundation, geosynthetic, foundation soil contact, geosynthetic
soil contact, meshing of the model, constraints of the model, and applying load.
4.2.1 Modeling of Geosynthetic
The geosynthetic element in this current study is modeled by adding the geosynthetic properties
to ANSYS library as new material. table 4.1 shows properties of the geosynthetic were defined in
ANSYS library
Table 4. 1 geosynthetic Material Properties
Description Geosynthetic Types Properties Unit
Uniaxial Biaxial Non-Woven
Young’s Modulus 6.30 x 1014 3.6 x 1010 2.1 x 1010 Pa
Poisson’s Ratio 0.3 0.28 0.244 ------
Density 240 200 250 Kg/m3
Thickness 1 1 1.2 mm
Table 4.1 is showing data filled in ANSYS18 of geosynthetic element which is divided into smaller
elements to have the most appropriate simulation to reality 8-node material which used for the 3-
D modeling of solids. The element is defined by eight nodes having three degrees of freedom at
each node: translations in the nodal x, y, and z directions, as shown in Figure 4.2.(Michalowski,
2008)
45
Shell 281 suitable for analyzing thin to moderately-thick shell structures. The element has eight
nodes with six degrees of freedom at each node: translations in the x, y, and z axes, and rotations
about the x, y, and z-axes. (ANSYS, 2018)
Shell281 is well-suited for linear, large rotation, and/or large strain nonlinear applications. Change
in shell thickness is accounted for in nonlinear analyses. The element accounts for follower (load
stiffness) effects of distributed pressures. (ANSYS, 2018)
Shell281 may be used for layered applications for modeling composite shells or sandwich
construction. The accuracy in modeling composite shells is governed by the first-order shear-
deformation theory
The element formulation is based on logarithmic strain and true stress measures. The element
kinematics allow for finite membrane strains (stretching). However, the curvature changes within
a time increment are assumed to be small. (ANSYS, 2018)
Figure 4. 1 Shell281(ANSYS, 2018)
46
4.2.2 Modeling of soil
The soil element in the current study is modeled by adding the soil properties to ANSYS18 library
as Sand (Solid 5), table 4.2 shows properties of the soil were defined in ANSYS18 library.
(ANSYS, 2018)
Table 4. 2 Sand Properties (Donald et al., 2001)
Description Value Unit
Young’s Modulus 2.00 x 1010 Pa
Poisson’s Ratio 0.23 ------
Bulk Modulus 1.235 x 1010 Pa
Shear Modulus 8.1327 x 109 Pa
Friction Angle 17 Degree
Table 4.2 is showing data filled in ANSYS18 of Soil element which is divided into smaller
elements to have the most appropriate simulation to real soil.
Soil is 8-node material which used for the 3-D modeling of solids. The element is defined by eight
nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions,
as shown in Figure 4.3.
Figure 4. 2 Fiber Modeling
47
The material properties of soil should use the Drucker-Prager which is different from typical metal
plasticity models since it contains a dependence on hydrostatic pressure. For metal plasticity
(assuming Mises or similar yield surface), only the deviatoric stress is assumed to cause yielding
– when plot the yield surface in principal stress space, this results in a cylinder whose axis is the
hydrostatic pressure line, indicating that yielding is independent of the hydrostatic stress state. For
the Mises yield surface, theoretically, one could have infinite hydrostatic compression, and no
yielding would occur. (ANSYS, 2018)
Figure 4. 3 Modeling of the soil
Displacement on side areas in X,Y =0
Displacement on side areas
in X,Y, Z =0
48
4.2.3 Modeling of Reinforced Concrete
The reinforced concrete foundation in the current study are modeled using Concrete Element
(Solid 65) which is available in ANSYS18 library in solid elements as shown in Figure 4.4.
SOLID65 is an 8-node material which used for the 3-D
modeling of solids. The solid is capable of cracking in tension
and crushing in compression. The element is defined by eight
nodes having three degrees of freedom at each node:
translations in the nodal x, y, and z directions.
The concrete element is like the 8-node (3-D Structural Solid)
element with the addition of special cracking and crushing
capabilities. The most important aspect of this element is the
treatment of nonlinear material properties.
The concrete is capable of cracking (in three orthogonal
directions), crushing, plastic deformation, and creep.
The material properties are defined by two components modulus of elasticity E=3.00x1010 and as
shown in table 4.3. (ANSYS, 2018)
In addition, the dimension of the modeled isolated foundation will be 2x2x0.4 m.
Table 4. 3 Concrete Material Properties (Donald et al., 2001)
Description Value Unit
Density 2300 Kg/m3
Young’s Modulus 3.00 x 1010 Pa
Poisson’s Ratio 0.18 ------
Bulk Modulus 1.562 x 1010 Pa
Shear Modulus 1.271 x 109 Pa
4.2.4 Modeling of Foundation-Soil Contact & Geosynthetic-Soil Contact
A contact element was modeled in ANSYS18 according to a certain criterion. The contact surface
between foundation-soil and geosynthetic-soil allow the two surfaces to move along each other.
Figure 4. 4(Modeling of the foundation)
49
This movement generates stresses in contact area. Many variables control the movement between
the two surfaces, such as the friction coefficient of concrete and soil as shown in Figure 4.5.
Real friction used in this contact element by determining the amount of friction between the soil
and foundation.
in this model the stress is what need to be study and compare to the mathematical equations which
are used to calculate the stress to ensure that the model is working and gives values accurate and
precise to the mathematical equations which will be shown in this chapter.
Contact elements have two surfaces to make the contact between, the target surface which is soil
and the contact surface which is foundation and next evaluate it with geosynthetic.
Figure 4.5 shows soil contact stresses. The stresses in the top part of the soil under the foundation
have the highest values of the stresses and showing that stress is distributed under the foundation
as bulb shape that give a first indication showing real evaluation of stress under the foundation.
This means that the model simulates the real problem.
For geosynthetic the stress in the soil will drop around the geosynthetic and this shows that the
contact between the soil and geosynthetic is working correctly and have a obvious effect on the
soil and all results will be shown in chapter five.
Figure 4. 5 Soil Foundation Contract Surface Stress
50
The target surface and contact surface were modelled in ANSYS 18 using Targe 170 and Conta
173, respectively. Targe 170 is used to represent various 3-D target surfaces for the contact
elements. While, CONTA 173 is used to represent contact and sliding between 3-D target surfaces
and a deformable surface defined by this element
4.3 Soil and Geosynthetic Meshing Generation
High-quality FEA mesh generation is often a time intensive and costly process within the current
iterative parametric product design cycle.
This is especially true in the case of hexahedral meshes that are useful in simplifying and
improving the accuracy of finite element models.
There are two types of meshing volumes in ANSYS. Tetrahedral and hexahedral meshing type.
In this study hexahedral meshing type will be used which is consider more suitable than tetrahedral
type of meshing. In addition, the results of calculation by hexahedral meshing is more accurate
than result by tetrahedral meshing type.
51
4.3.1 Soil Meshing:
Before meshing soil, soil element has to be divided into 8 sub divided elements. The plane which
divides the whole element of the soil is the same horizontal plane of soil tip and the two planes
divide the soil in vertical plane is the foundation side planes as shown in Figure 4.6.
4.3.2 Geosynthetic Meshing:
Meshing of the fiber is made by sub boxes of the fiber element in order to distribute the load in
exact way as the real situation. Depth of the foundation divided in to three elements and area of
the fiber divided in to smaller areas which results on sub volumes.
4.3.3 Soil Mass Boundaries
ANSYS program is a finite element program which means that the element used in the developed
model must be defined in finite dimensions. Constraints must be defined as roller in the vertical
sides of the soil and let the soil move in vertical way. At the bottom of soil, constraints on X, Y, Z
Figure 4. 6 Soil Meshing
52
dimensions must be fixed not to let the soil move in vertical or horizontal direction as shown in
Figure 4.7.
The constraints for soil are made in two directions UX and UZ in order to make the soil move in
the UY direction.
4.4 Application of Loading
The application of load on the developed model is carried out using pressure rather than nodal
loads. Nodal loads excessive deformation in node of application, which lead to some errors and
model flounder so in this model pressure loads chosen application of the load to avoid excessive
deformation. Another reason for choosing pressure load is to simulate the real loads applied on
the foundation from columns and superstructure on the foundation as shown in Figure 4.8 and the
chosen value for the load is 0.5 MPa.
Figure 4. 7 Soil Mass Boundaries
Displacement on side areas in X,Y =0
Displacement on side areas
in X,Y, Z =0
53
4.5 Model Validation
4.5.1 Ansys Stress Soil Computation
To save time of analysis the developed
model, symmetry must be applied to the
model. Symmetry of the model facilitates
reading results of the model in simple way.
Figure 4.9 shows the symmetry of soil
which shows the stresses on soil after
analysis that can help in understanding the
behavior of soil in easy way.
Figure 4. 8 Application of Loading
Figure 4. 9 Soil Stress Value After ANYSY Solution
54
4.5.2 Closed Form Solution Based on Theory of Elasticity
In this section is proving that the
analysis gives values that is equal to
real calculation of the stress in the soil
using stress below a rectangular area.
The integration technique of
Boussinesq’s equation also allows the
vertical stress at any point A below the
corner of a flexible rectangular loaded
area to be evaluated. (Donald et al.,
2001)
The total stress increase caused by the
entire loaded area at point A may now be obtained by integrating the following equation
𝐼𝑐 = 𝐼𝑛𝑓𝑙𝑢𝑛𝑐𝑒 𝐹𝑎𝑐𝑡𝑜𝑟 =1
4𝜋(
2𝑚𝑛√𝑚2+𝑛2+1
𝑚2+ 𝑛2+ 𝑚2𝑛2+1 𝑥
𝑚2+ 𝑛2+2
𝑚2+ 𝑛2+1+ tan−1 2𝑚𝑛√𝑚2+ 𝑛2+1
𝑚2+ 𝑛2+1− 𝑚2𝑛2)
𝑤ℎ𝑒𝑟𝑒 𝑚 =𝐵
𝑍 , 𝑛 =
𝐿
𝑍
𝐴𝑣𝑎𝑟𝑎𝑔𝑒 𝑆𝑡𝑟𝑒𝑠𝑠 = ∆𝜎 = 𝑞𝑜𝐼𝑐 Equation 2 Boussinesq’s equation
By using the above equation and procedures stress can be evaluated under center and corner of
the studied foundation in different depth where foundation dimension is B= 2m and L= 2m.
Load will be applied is equal to 0.5 MPa same as the applied load in the ANSYS model.
Results will be compared to the result of ANSYS by calculating division in values as the following
table 4.4.
Figure 4. 10 Determination of stress below the corner of a flexible
rectangular loaded area (Donald, Hammes, Frami, & Krajcik, 2001)
55
4.5.3 Comparison of FEM ANSYS Modeling and Analytical Results
Table 4. 4 Stress Values to Evaluate ANSYS18 Model
Depth (m)
Foundation Corner Foundation Center
Stress (KN/m2)
ANSYS Stress (KN/m2)
Deviation Percentage
%
Stress (KN/m2)
ANSYS Stress Deviation
Percentage %
0 ------- 91.39 ------- ------- 365.56 -------
0.5 ------- 87.81 ------- ------- 351.25 -------
1 87.61 81.40 7.63 350.44 325.60 7.63
1.5 60.52 64.80 6.60 242.08 253.58 4.53
2 42.01 45.65 7.97 168.05 169.32 -0.75
2.5 30.12 32.40 7.04 120.47 125.14 3.73
3 22.37 24.60 9.08 89.47 95.65 6.46
3.5 17.15 17.35 1.16 68.59 75.66 9.34
4 13.51 13.25 1.96 54.04 57.24 5.59
4.5 10.89 10.12 7.62 43.57 45.20 3.62
5 8.95 8.51 5.19 35.81 38.35 6.63
5.5 7.48 7.64 2.10 29.92 31.42 4.78
6 6.34 6.10 3.90 25.35 27.54 7.95
6.5 5.44 5.21 4.34 21.74 22.87 4.93
7 4.71 4.82 2.25 18.85 20.32 7.25
7.5 4.12 3.98 3.57 16.49 17.63 6.48
8 3.64 3.54 2.70 14.54 15.26 4.71
8.5 3.23 3.33 3.01 12.92 13.33 3.08
9 2.89 2.74 5.40 11.55 11.74 1.57
9.5 2.60 2.68 3.09 10.39 10.61 2.06
10 2.35 2.52 6.82 9.39 9.90 5.12
10.5 2.13 2.24 4.76 8.53 8.72 2.16
Table 4.3 shows stress comparison between the values obtained from computer model and
analytical to evaluate that the model is working correctly and equal or near the real values of stress
under foundation, however the closed form equation cannot give a solution for stress in the first
56
meter due the equations range and derivative that may be near to zero or zero which result a
negative result that cannot be taken as a real result and this was shown Boussinesq’s equations.
On the other hand, FEM can give and obtain a value for any depth under foundation in the model
which should be near the value of the applied load especially in the contact surface area between
foundation and soil that must be near 500 kN/m2 but as shown in above table and below graphs
the maximum value of stress is equal 365.56 kN/m2 which is a result of many reasons as following
1. Soil properties and definition of the material in ANSYS showed that the load will be
disrupted due to the soil which has lose particles that consolidate with each other by
friction which cause stress to distribute immediately after the load is applied which will
never be equal to applied area load.
2. The meshing applied to the soil is considered a course to give accurate solution. Due
unavailability of computers and processors that could analysis and evaluate this type of
dense meshes, the results were accepted many trials that was obtained by researcher. And
this result was the best result of all obtained models.
3. The load applied on the soil is considered very large in order to make the result clear and
comparisons could be obtained and give more scene to the reader to understand the
behavior of the model.
For all above reasons the corresponding values obtained from the closed form solution deviation
and FEM the comparison showed that the deviation between the computer and calculated valves
is less than 8% which is acceptable, and the model could be taken for more models to obtain the
most and useful conditions to use the geosynthetic material in reinforced soil.
Results show small deviation between the mathematical equation and ANSYS result as shown in
table 4.4 and Figure 4.11 & Figure 4.12 the average division is equal to 4.81% although the used
mishes consider course, but the division consider small and can be built on in this research.
57
1.56.5
11.516.521.526.531.536.541.546.551.556.561.566.571.576.581.586.591.596.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Stre
ss (
KN
/m2
)
Depth (m)
Stress of Soil Under Corner of Foundation
Corner Stress (KN/m2) Corner ANSYS Stress (KN/m2)
Figure 4. 12 Stress of Soil Under Corner of Foundation
1.56.5
11.516.521.526.531.536.541.546.551.556.561.566.571.576.581.586.591.596.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Stre
ss (
KN
/m2
)
Depth (m)
Stress of Soil Under Corner of Foundation
Corner Stress (KN/m2) Corner ANSYS Stress (KN/m2)
Figure 4. 11 Stress of Soil Under Corner of Foundation
58
4.5.4 laboratory Testing Validation
The load tests were conducted in a combined test bed cum loading frame assembly. The sand beds
were prepared in a steel test tank with inside dimensions 900 x 900 x 600 mm. The model footing
used for the tests was square in shape; the footing was made of 25 mm thick rigid steel plate and
measured 150 x 150 mm. The base of the model footing was roughened by fixing a thin layer of
sand to it with epoxy glue. A hydraulic jack welded against a reaction frame was used to push the
footing slightly into the bed for proper contact between the soil and the footing. A schematic
diagram of the test set- up is shown in figure 4.13 (Latha & Somwanshi, 2009).
The sand used in this study was dry sand with coefficient of uniformity (Cu) 3.04, coefficient of
curvature (Cc) 1.13, effective particle size (D10) 0.27 mm and specific gravity 2.63. The
maximum and minimum dry unit weights of the sand were obtained as 16.7 kN/m3 and 13.4
kN/m3. According to the Unified Soil Classification System, the soil is classified as poorly graded
sand with letter symbol SP. The friction angle of the sand at 70% relative density (Dr), as
determined from standard triaxial compression tests on dry sand sample was 44o (Latha &
Somwanshi, 2009).
Figure 4. 13 Schematic Diagram of the Test Set-Up (Latha & Somwanshi, 2009)
59
Geosynthetics is used to reinforce sand bed in the model tests, Uniaxial geogrid (UG). The load-
elongation behavior of these geosynthetics was determined from standard multi-rib tension test
and is shown in table 4.5 presents the properties of geosynthetics (Latha & Somwanshi, 2009)
Table 4. 5 Properties of Geosynthetics (Latha & Somwanshi, 2009)
Description Value Unit
Young’s Modulus 4.34 x 1010 Pa
Poisson’s Ratio 0.3 -----
Density 0.380 g/m3
Thickness 1 mm
Description of laboratory model and ANSYS18 model for validation will be as shown in table 4.6
and figure 4.14
Table 4. 6 Description of the Model
Description Value Unit
Foundation Dimension (B) 150 x 150 mm
Layers Number (N) 4 No
u 100 Mm
h 100 mm
dr 400 mm
Geosynthetics Width (b) 890 mm
Figure 4. 14 Description of the Model (Latha & Somwanshi, 2009)
60
4.5.3 Comparison of FEM ANSYS Modeling and Laboratory Results
The results were obtained in table 4.7 and figure 4.15 by getting the percentage of settlement in
reference with the footing dimension where B = 150 mm and s = Settlement value.
Table 4. 7 Settlement Values to Evaluate ANSYS18 Model
Figure 4. 15 Settlement Values to Evaluate ANSYS18 Model
-14
-12
-10
-8
-6
-4
-2
0
0 50 100 150 200 250 300 350 400 450
s/B
(%
)
Load (kN/m2)
Setelment of Soil Under Corner of Foundation
Labatory s/B(%) ANSYS18 s/B(%)
Load
(kN/m2) Laboratory s/B (%)
ANSYS18 s/B
(%)
Deviation
Percentage
0 0 0.00 0
48 -0.3 -0.32 6.7
86 -1.1 -1.15 4.5
132 -2.2 -2.12 3.6
180 -3.4 -3.32 2.4
225 -4.8 -4.75 1.0
270 -6.1 -6.29 3.1
320 -7.8 -8.02 2.8
365 -9.4 -9.98 6.2
415 -11.5 -12.20 6.1
61
Table 4.7 shows settlement percentage comparison between the values obtained from computer
model and laboratory to evaluate that the model is working correctly and equal or near the real
values of stress under foundation.
The results showing small division between the two models with average 3.64 % which consider
very small and minor, however this deviation is occurred due to several reasons as following
1. Human error during applying lab test and inaccuracy in reading gages and numbers
2. The meshing applied to the soil is considered a course to give accurate solution. Due
unavailability of computers and processors that could analysis and evaluate this type of
dense meshes, the results were accepted many trials that was obtained by researcher. And
this result was the best result of all obtained models.
3. The load applied on the soil is considered very large in order to make the result clear and
comparisons could be obtained and give more scene to the reader to understand the
behavior of the model.
Results show small deviation between the laboratory tests results and ANSYS18 result as shown
in table 4.7 and Figure 4.15 although the used mishes consider course, but the division consider
small and can be built on in this research.
4.6 Parametric Study
After obtaining the model with result is acceptable which is one of the goals of this research. In
the coming chapter 5 many parametric will be conducted to evaluate the most optimized case for
using geosynthetic reinforcement in soil.
In addition, all developed models would give designers practical solutions for any special
structural. To reach this goal several parameters was studied as following.
1. Using one layer of geosynthetic in different depths.
2. Effect of using two layers in various depth.
3. Uniaxial geosynthetic material will be used in different types of soil.
4. Effect of different types of geosynthetic on the soil improving.
5. The optimum width of geosynthetic material under foundation.
All this parametric was studied through several models will be conducted to get the most optimize
model for using geosynthetic material under foundation.
62
Chapter 5 Analysis Results of
Reinforcement Soil Using
ANSYS
63
Chapter 5 Analysis Results of Reinforcement Soil Using ANSYS
5.1 Introduction
In this chapter several models will be generated to get the optimum and most adequate usage of
reinforcement elements in soil.
In addition, this analysis will give structural designer the clear hint and clue to use the geosynthetic
material in the best and most useful way to achieve the main goal of engineering the safest and
most economic structural and most effect way.
Following 5 different modeling cases for geosynthetic will be studied as following: -
1. Depth of the geosynthetic layer under foundation.
2. Depth of the second geosynthetic layers under foundation
3. Effect of geosynthetic in different soil types
4. Effect of different geosynthetic types in one type of soil.
5. Effect of geosynthetic layer width in distribution of stress in the soil.
After evaluation all the models a comparison will be conducted to determine the optimum case of
using geosynthetic material in the soil to improve the soil properties and behavior to the applied
load.
Before start modelling several points must be taken in consideration as following: -
1. The soil type will be used for all cases is loose sand except case three mentioned above
many types of soil will be evaluated and generated.
2. The geosynthetic will be used for all cases is uniaxial except case four mentioned above
different types and properties of geosynthetic will be used to evaluate the results.
3. The load will be applied for all cases is 0.5 MPa.
4. Foundation is isolated with diameter 2x2x0.4 m dimension.
Models was generated as will be shown in this chapter.
5.2 Effect of Depth of geosynthetic
Uniaxial geosynthetic layer will be used under foundation in different depth and model will be
conducted to evaluate the optimum depth the can be used to lay the geosynthetic layer under
foundation figure 5.1 shows how the geosynthetic will be used in different depth.
a ➔ is the depth of geosynthetic will be evaluated.
Figure 5. 1 Depth of Geosynthetic Layer dimensions are in CM
64
In this case different depths for geosynthetic will be conducted in models so each model will be
for a certain depth of geosynthetic (a = 0.2, 0.3, 0.45, 0.6, 0.75, 0.9, 1.2 and 1.5 m) and results of
these models is shown in table 5.1 and figure 5.2.
Table 5. 1 Stress in soil with Different Depth of Geosynthetic Layer
Depth
(m)
Stress (KN/m2)
Without
Geosynthe
tic
Depth a
= 0.3 m
Depth a
= 0.45 m
Depth a
= 0.50 m
Depth a
= 0.6 m
Depth a
= 0.75 m
Depth a
= 0.9 m
Depth a
= 1.2 m
Depth a
= 1.5 m
0 365.56 280.58 281.36 298.57 310.57 326.68 332.34 344.18 359.76
0.5 351.25 251.23 254.68 277.68 288.68 305.14 312.38 324.22 339.80
1 325.60 230.36 223.50 224.64 234.64 236.69 243.65 255.49 271.07
1.5 253.58 191.68 190.89 184.86 192.86 178.66 177.68 189.97 190.68
2 169.32 146.73 146.63 142.54 150.54 141.11 139.19 137.51 134.16
2.5 125.14 113.38 110.38 111.64 119.64 113.68 110.58 108.90 105.55
3 95.65 88.69 88.98 86.68 94.68 91.36 89.78 88.10 84.75
75.00
95.00
115.00
135.00
155.00
175.00
195.00
215.00
235.00
255.00
275.00
295.00
315.00
335.00
355.00
375.00
0 0.5 1 1.5 2 2.5 3
Str
ess
(K
N/m
2)
Depth (m)
Stress Under Center of Foundation Using Geosynthetic Layer with Different Depth
Stress Without Geotextile Geotextile Depth 0.5m (KN/m2) Geotextile Depth 0.3 m (KN/m2)
Geotextile Depth 0.45 m (KN/m2) Geotextile Depth 0.6 m (KN/m2) Geotextile Depth 0.75 m (KN/m2)
Geotextile Depth 0.9 m (KN/m2) Geotextile Depth 1.2 m (KN/m2) Geotextile Depth 1.5 m (KN/m2)
Figure 5. 2 Stress in soil with Different Depth of Geosynthetic Layer
65
Figure 5.2 shows the result of soil stress at different location of geosynthetic layer. Each location
was expressed by (a) model, the first model when a = 0.3 m shows that value of the stress decreases
from 356.56 kN/m2 to 280.58 kN/m2 immediately under the foundation with decrease of 84.98
KN/m2 this mean that 23% of the stress was taken by the reinforced material and the stress was
taken by the soil take was 77 % of the stress which gives clue that the soil improved and could
take more stress before failure.
For model with depth a = 0.45 m it shows that the stress goes down to reach 281.36 kN/m2 that is
very close to value of a = 0.3 m this indicate that the two cases have the same effectiveness on soil.
In addition, the more depth in soil shows the value of stresses is less than the first case with a=
0.3m but still the different between the two cases is very minor and consider equal in values,
however its shown that stress in soil between depths 0 m to 1.5 m is more efficient for a = 0.3 m
but stress between 2 m to 3 m depth a = 0.45 m is more efficient on soil behavior.
The result of model a = 0.5 m at depth 0 stress was 298.57 kN/m2 which decrease about 18% from
stress without adding geosynthetic that mean the more deep the geosynthetic from the foundation
the less effective gives comparing with a= 0.3 and a= 0.45 , but the stress in depths (1.5 m to 3 m)
the value of the stress drop less than what the first two model (a= 0.3 and a = 0.45 m) and this
indicate that the effect of the geosynthetic show more effectiveness in stress under the geosynthetic
layer more than above the geosynthetic layer.
For model a = 0.6m at depth equal to 0 the stress value is 310.57 kN/m2 which decrease about
15% from stress without adding geosynthetic, more over the value of stress in deep depths is higher
than the values of a= 0.3 and a =0.45 and a = 0.5 this illustrate that the effective of geosynthetic
constructed in shallow depth is more efficient in the stress of the soil.
At a = 0.75 and a= 0.9 the values of stress in soil between 0 m to 1 depth much higher comparing
to previous models. The stress drops 10% in average from stress without adding geosynthetic. In
this case the soil takes a lot of stresses before the geosynthetic start working and decrease the value
of the stress to the needed value before the soil collapse, on the other hand at depth between 1.5 to
3 m the stress drops 23 % in average but still under the foundation is very high and does not give
the designer the needed safe condition and soil behavior that helps to construct the needed
structural without any risks.
For a= 1.2 and a= 1.5 it obvious that the stress under foundation is very close to the values of stress
without adding geosynthetic. The real effective of geosynthetic start after 1.5 m depth which drop
about 10% in average which illustrate that efficiency of geosynthetic does not work as required
this lead that geosynthetic become useless and does not improve the soil behavior as required.
In this case the soil may collapse before geosynthetic starts working and be efficient.
Moreover, at depth more than 2 m under the foundation all studied models give stress values close
to each other and in some models, it is equal to the stress without using geosynthetic which indicate
that stress after 1 m depth from the geosynthetic has minor effect on soil.
As a result, it’s obvious that the less depth the geosynthetic is constructed the more effective it
become and more useful so model a = 0.3m and a = 0.45m is the best case that this study
recommended to be used.
Below table 5.2 gives the percentage of decreasing in stress for each model in comparison with
stress without geosynthetic and gives more indication how is affecting the behavior of the soil
65
Table 5. 2 percentage of decreasing in stress
Percentage of Stress Reduction =Strees at Depth a
Strees Without Geosynthetic 𝑥 100
Depth
(m)
Stress (KN/m2)
Without
Geosynthetic
Depth a
= 0.3 m
Percentage
of Stress
Reduction
Depth a
= 0.45
m
Percentage
of Stress
Reduction
Depth a =
0.50 m
Percentage
of Stress
Reduction
Depth a
= 0.6 m
Percentage
of Stress
Reduction
0 365.56 280.58 23% 281.36 23% 298.57 18% 310.57 15%
0.5 351.25 251.23 28% 254.68 27% 277.68 21% 288.68 18%
1 325.60 230.36 29% 223.5 31% 224.64 31% 234.64 28%
1.5 253.58 191.68 24% 190.89 25% 184.86 27% 192.86 24%
2 169.32 146.73 13% 146.63 13% 142.54 16% 150.54 11%
2.5 125.14 113.38 9% 110.38 12% 111.64 11% 119.64 4%
3 95.65 88.69 7% 88.98 7% 86.68 9% 94.68 1%
Depth
(m)
Stress (KN/m2)
Without
Geosynthetic
Depth a
= 0.75 m
Percentage
of Stress
Reduction
Depth a
= 0.9 m
Percentage
of Stress
Reduction
Depth a =
1.2 m
Percentage
of Stress
Reduction
Depth a
= 1.5 m
Percentage
of Stress
Reduction
0 365.56 326.68 11% 332.34 9% 344.18 6% 359.76 2%
0.5 351.25 305.14 13% 312.38 11% 324.22 8% 339.8 3%
1 325.60 236.69 27% 243.65 25% 255.49 22% 271.07 17%
1.5 253.58 178.66 30% 177.68 30% 189.97 25% 190.68 25%
2 169.32 141.11 17% 139.19 18% 137.51 19% 134.16 21%
2.5 125.14 113.68 9% 110.58 12% 108.9 13% 105.55 16%
3 95.65 91.36 4% 89.78 6% 88.1 8% 84.75 11%
66
5.3 Effect of Using Second Geosynthetic Layer With Different Depths
Two uniaxial geosynthetic layer will be used under foundation the first layer will be under constant
depth equal to 0.3 m under foundation and this depth was chosen as a result of first case that shows
at depth 0.3 m was the optimum and most effective model.
The second layer will be in different depth different depth and model will be conducted to evaluate
the most effective depth the can be used to put the second geosynthetic layer under foundation
figure 5.3 shows how the geosynthetic will be used in different depth.
(a) dimension is the depth of second layer of geosynthetic will be evaluated.
Figure 5. 3 Depth of the two geosynthetic layers under foundation dimensions are in CM
67
In this case different depths for second geosynthetic will be conducted, so each model will be for
a certain depth of geosynthetic b= (0.5, 0.6, 0.75, and 0.9 m) as shown in figure 5.3 results of
these models is shown in table 5.3 and figure 5.4.
Table 5. 3 Stress in soil with Different Depth of second Geosynthetic Layer
Depth (m)
Stress (KN/m2)
Stress Without
Geosynthetic
b= 0.5 m
Depth
b= 0.6 m
Depth
b= 0.75 m
Depth
b= 0.90 m
Depth
0 365.56 263.68 268.36 269.47 270.58
0.5 351.25 240.38 250.42 253.88 257.34
1 325.6 217.86 205.65 217.06 228.47
1.5 253.58 185.00 173.44 182.895 192.35
2 169.32 143.48 140.68 145.68 150.68
2.5 125.14 109.35 108.45 110.585 112.72
3 95.65 86.94 85.71 89.01 92.31
Figure 5. 4 Stress in soil with Different Depth of second Geosynthetic Layer
75
95
115
135
155
175
195
215
235
255
275
295
315
335
355
375
0 0.5 1 1.5 2 2.5 3
Stre
ss (
KN
/m2
)
Depth (m)
Stress Under Center of Foundation Withe Different Geotextile Depth
Stress Without Geotextile b= 0.5 m Depth b= 0.6 m Depth
b= 0.75 m Depth b= 0.90 m Depth
68
In this case the results of models are very close to each other as shown in figure 5.4 and table
5.3.
The results of model b = 0.5 shows that the stress under the foundation at depth 0 and 0.5m from
the bottom of the foundation is the smallest and gives the best results in comparison to other
models.
The stress decreased 28 % under foundation at depth equal to 0 for model b = 0.5 m comparing to
stress in soil without using geosynthetic and decreased 6% more than using one layer of
geosynthetic. that illustrate the using two layers of geosynthetic improve the behavior of the soil
but not that mush effectiveness comparing to using one layer at location 0.3 m under foundation.
however at depths more than 1 m stress values become close to each other in comparing with not
using geosynthetic.
In addition, in model b = 0.6 m the stress decreased 26.5 % under foundation at depth equal to 0
comparing to stress in soil without using geosynthetic, moreover decreased 4% more than using
one layer of geosynthetic at depth 0.3 m. that also prove the using of two layers of geosynthetic
improve the behavior of the soil but not that mush effectiveness. however at depths more than 1 m
stress values become close to each other in comparing with not using geosynthetic.
For models b = 0.75 and b= 0.9 m the stress decreased 26 % under foundation at depth equal to 0
comparing to stress in soil without using geosynthetic, moreover decreased 3.5% more than using
one layer of geosynthetic at location equal to 0.3 m form bottom of the foundation. that also prove
the using of two layers of geosynthetic improve the behavior of the soil but not that mush
effectiveness comparing to using one layer at depth 0.3 m. however at depths more than 1 m stress
values become close to each other in comparing with not using geosynthetic.
In conclusion model b = 0.5 is the most optimum model and the easier case to be constructed in
the site for two reasons
1. Will be less cost in the depth of excavation
2. Time of construction will be less comparing to other models
Moreover, at depth more than 2 m under the foundation all studied models illustrate that values of
stress are very close and, in some models,, it is equal to the stress without using geosynthetic and
that lead the stress after 1 m depth from the geosynthetic has minor effect in the stress of soil and
support the results obtain from Case 01 of this study.
69
5.4 Effect of Geosynthetic in Different Soil Types
Effect of geosynthetic in developing behavior and properties of soil. In this case four types of soil
will be obtained silty sand, loose sand, dense sand and clay the chosen of soil types were specified
in accordance to Gaza Strip soil classifications used and found in constructions site and lands.
As result of case 01 conclusion the most adequate and effective the depth of geosynthetic layer
will be constructed under foundation is 0.3 m depth as shown in figure 5.5.
Before starting modeling, soil properties must be determined, table 5.4 shows the soil properties
will be used in modeling.
Figure 5. 5 Soil Types All Dimensions in CM
70
Table 5. 4 Soil Types Properties (Donald et al., 2001)
Description Soil Types Properties
Unit Silty Sand Loose Sand Dense Sand Clay
Young’s
Modulus 7.00 x 109 2.00 x 1010 4.8 x 1010 5.00 x 109 Pa
Poisson’s Ratio 0.3 0.23 0.25 0.12 ------
Bulk Modulus 5.83 x 109 1.235 x 1010 3.2 x 1010 2.19 x 109 Pa
Shear Modulus 2.69 x 109 8.1327 x 109 1.92 x 1010 2.23 x 109 Pa
Friction Angle 12 17 22 9 Degree
After adding to ANSYS 18 all the needed properties of soil will be used in modeling and results
is obtained as shown in table 5.5 and figure 5.6.
Table 5. 5 Effect of Geosynthetic in Different Soil Types
Depth (m) Stress (KN/m2)
Loss Sand Dense Sand Silty Sand Clay
0 280.58 276.83 295.25 310.57
0.5 251.23 235.65 263.35 288.68
1 214.15 199.45 229.67 254.35
1.5 179.34 164.86 191.36 210.64
2 144.23 130.92 152.74 160.35
2.5 113.38 105.66 125.65 125.74
3 88.69 82.13 92.35 94.68
71
The results of modeling different soil types show the various values of stress depending on soil
properties. As known in civil engineering the dense sand is the preferred type to be used for
structural construction, so it will behave mush better than any other types in this research.
It is obvious that dense sand behaves better than other types of soils because of better mechanical
properties, however the loose and silty sand show stress values that consider mush better in
comparing with the clay
The clay after adding the reinforced material the value of the stress at 1 m depth is equal 254.35
KN/m2 which is very high in comparing to the mathematical results as shown in table 4.3 in
chapter four which is equal to 350 KN/m2.
Also, it must be taken in consideration that the clay proprieties have many variables that effect the
behavior of the clay. This variable need a new study to discuss this variable and it effect on the
clay behavior. But still the model shows that the clay behavior developed and achieve the goal of
this studied that the geosynthetic material improves the behavior of clay.
Moreover, the sand types that were studied give a clue the better the sand properties are used the
better behavior it will be obtained after adding geosynthetic material to soil which is shown in the
results as shown in figure 5.6.
75.00
95.00
115.00
135.00
155.00
175.00
195.00
215.00
235.00
255.00
275.00
295.00
315.00
335.00
355.00
375.00
0 0.5 1 1.5 2 2.5 3
Str
ess
(KN
/m2
)
Depth (m)
Stress Under Center of Foundation Withe Different Soil Types
Loss Sand Dense Sand Silty Sand Clay
Figure 5. 6 Effect of Geosynthetic in Different Soil Types
72
In this research one of the goals is to prove that the reinforced material will improve behavior of
soil and will give the designer bigger ranges is designing any structural easier.
5.5 Effect of Using Different Geosynthetic Types in One Type of Soil
In this case different types of geosynthetic material will be used to evaluate how each type will
develop in loose sand behavior
The model will be obtained as shown in figure 5.7 the geosynthetic layer will be c= 0.3 m depth
under foundation and soil will be loose sand.
Before starting modeling, geosynthetic properties must be determined table 5.4 chose the soil
properties will be used in modeling.
All geosynthetic properties were as specified in the data sheet obtained from manufactural data
sheets.
Table 5. 6 Different Geosynthetic Types Prosperities (Infante, Martinez, Arrua, & Eberhardt, 2016)
Description
Geosynthetic Types Properties Unit
Uniaxial Biaxial Non-
Woven
Young’s
Modulus 6.30 x 1014 3.6 x 1010 2.1 x 1010 Pa
Poisson’s Ratio 0.3 0.28 0.244 ------
Density 240 200 250 Kg/m3
Thickness 1 1 1.2 mm
Figure 5. 7 Different Geosynthetic Types in One Type of Soil All Dimensions in CM
73
In this case effect of different geosynthetic in developing behavior and properties of soil as shown
in table 5.7 and figure 5.8.
Table 5. 7 Effect of Geosynthetic materials in loose Sand
Depth (m)
Stress (KN/m2)
Stress Without
Geosynthetic Uniaxial Biaxial Non-Woven
0 365.56 280.58 314.25 351.96
0.5 351.25 251.23 273.84 303.96
1 325.60 230.36 253.40 278.74
1.5 253.58 191.68 212.76 236.17
2 169.32 146.73 162.87 167.76
2.5 125.14 113.38 119.05 125.00
3 95.65 88.69 92.24 95.93
The results of modeling different geosynthetic materials show the various values of stress
depending on the geosynthetic material will be used in the model.
First, it is obvious that Uniaxial geosynthetic has the higher effect on soil comparing to soil without
geosynthetic. At depth 1 m from the bottom of the foundation the value of stress is 230.36 kN/m2
and the stress under foundation at the same depth without geosynthetic 325.60 kN/m2 that lead
that Uniaxial geosynthetic drop the stress value 29 % that is fabulae improving.
Second, Biaxial geosynthetic has the less effect on soil comparing to Uniaxial geosynthetic. At
depth 1 m from the bottom of the foundation the value of stress is 253.40 kN/m2 and the stress
75.0095.00
115.00135.00155.00175.00195.00215.00235.00255.00275.00295.00315.00335.00355.00375.00
0 0.5 1 1.5 2 2.5 3
Str
ess
(KN
/m2
)
Depth (m)
Stress Under Center of Foundation Withe Different Geosynthetic
Types
Stress Without Geotextile Uniaxial Biaxial Non-Woven
Figure 5. 8 Effect of Geosynthetic materials in loose Sand
74
under foundation at the same depth without geosynthetic 325.60 kN/m2 that lead that Biaxial
geosynthetic drop the stress value 22 % that is consider a good improving.
Third, is obvious that Non-Woven geosynthetic has the less effect on soil comparing to Uniaxial
geosynthetic. At depth 1 m from the bottom of the foundation the value of stress is 278.74 kN/m2
and the stress under foundation at the same depth without geosynthetic 325.60 kN/m2 that lead
that Non-Woven geosynthetic drop the stress value 14 % that is consider a very low improving.
Moreover, at depth more than 2 m under the foundation all studied models that values of stress is
very close to each other and in some models, it is equal to the stress without using geosynthetic
and that lead the stress after 1 m depth from the geosynthetic has minor effect in the stress of soil.
As a result, the decrees in stress values in soil depends on the reinforced material properties and
how it will drop the stress in soil. In addition, this gives the designer the option to choose the
needed reinforced material to be used depending how much effect the designer need. And it must
take in consideration the more improvement needed the more it will cost.
5.6 Effect of Geosynthetic Layer Width in Distribution of Stress in The Soil
In this case effect of width of geosynthetic in distribution of soil. And several constants should be
taken in consideration first depth of geosynthetic is equal to 0.3 m under foundation because it was
the most effective model as a result from first case. Second soil type is loose sand. Third the stress
distribution will be studied is equal 0.4q as shown in figure 5.9. forth geosynthetic will be from
Uniaxial type.
In figure 5.10 shows how the models will be obtained for this case (d) dimension showing how
much the geosynthetic layer will exceed the foundation edge.
0.4q
Stress Width
Depth
Figure 5. 9 Stress Distribution for 4.5 m Width Geosynthetic Layer
75
In this case effect of different geosynthetic layer width is obtained and the effect in distribution of
0.4q stress table 5.8 is showing how the stress value will change.
Table 5. 8 Stress in Soil with Different Width of Geosynthetic Layer
Depth (m)
Stress (KN/m2)
Stress Without
Geosynthetic
d =0.25 d = 0.75 d= 1.25 d= 1.75 d = 2.0 m
0 365.56 283.83 280.58 280.30 280.02 280.02
0.5 351.25 254.64 251.23 250.95 250.67 250.67
1 325.60 232.91 230.36 230.08 229.80 229.80
1.5 253.58 194.04 191.68 191.40 191.12 191.12
2 169.32 150.18 146.73 146.45 146.17 146.17
2.5 125.14 116.63 113.38 113.10 112.82 112.82
3 95.65 91.94 88.69 88.41 88.13 88.13
As results shows that the result of stress is approximately equal in all models were obtained and
decrees the value of stresses with the same percentage.
Figure 5. 10 Geosynthetic Layer Width All Dimension in CM
76
Table 5. 9 Width of 0.4q Stress Under Foundation in Deferent Depth
Depth (m)
Stress Width (m)
Stress Without
Geosynthetic
d =0.25 d = 0.75 d = 1.25 d = 1.75 d = 2.0 m
0 8.95 8.27 7.65 5.5 5.3 5.3
0.5 8.85 7.57 6.95 4.97 4.77 4.77
1 9.35 8.27 7.49 5.81 5.61 5.61
1.5 9.65 8.97 8.27 6.45 6.25 6.25
2 9.895 9.215 8.525 6.545 6.345 6.345
2.5 10.02 9.34 8.56 7.03 6.83 6.83
3 10.12 9.44 8.74 7.35 7.15 7.15
Figure 5. 11 Width of 0.4q Stress Under Foundation in Deferent Depth
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25
Wid
th (
m)
Depth (m)
Width of 0.4q Stress Under Foundation in Deferent Depth Using One Layer with Different Width of Geotextile
Width of the Stress Without Geotextile(m) d =0.25
d = 0.75 d= 1.25
77
in table 5.9 and figure 5.11 it is showing how is different width of 0.4q stress. it’s clear that the
width has changed a lot after adding the geosynthetic material.
when d = 0.25 m it decreases the width about 12.5% in comparing with the width of not using
geosynthetic material at depth 0.5 m for the bottom of the foundation.
but when d= 0.75 and a= 1.25 the effect was more efficient it decreases the width of the stress
about 21.4% and 34.3% respectively which shows a better result than the first model.
However, for models d = 1.25, d= 1.75 and d=2 the values start to be close to each other its even
became equal for models d = 1.75 and d = 2. That gives a conclusion the effect of geosynthetic in
decreasing the width of stress must kept between d= 0.25 to d = 1.25 that gives the most effective
result.
78
Chapter 6 Conclusion and
Recommendation.
79
Chapter 6 Conclusion and Recommendation.
This research has achieved the goals were determined at the beginning of study. This research
shows that geosynthetic material is an efficient material to improve the soil behavior and gives any
designer many options for designing any structural with the most economic and easy construction
of the designed structural.
6.1 Conclusion
In summary the result can obtained from this study is the following
1. ANSYS simulation program can simulate the behavior of soil and reinforced material
as shown in chapter 4 of this study.
2. The most effective depth to construct the geosynthetic material is in range between 0.3
to 0.6-meter depth as shown in chapter 5.
3. Adding second layer of geosynthetic material will improve the soil properties and helps
the soil to take more stress.
4. Using geosynthetic model will give designers clues of the behavior of soil.
5. This model will save calculation time for designer to determine the best case and most
efficient usage of geosynthetic.
6. Any type of reinforced material could be added to the model to study the behavior of
the soil and reinforced material.
7. Reinforced material works with any type of soil but the effect on stress depending on
the properties of soil will be used which will help the designer to determine how much
improving is needed for the structural.
8. Each reinforced material has different effect on stress values depending on the
properties of reinforced material will be used, which gives the designer various option
to be used.
9. The distribution of stress can be controlled by using different width of reinforced
material but must take in consideration the it must be kept in the effective range between
0.25 m to 1.25 m from the edge of the foundation as shown in this research.
6.2 In Particle Life
1. This model can be used for any other types of foundation
2. This model used in this study can be used with other types of reinforced material (Steel
Sheets, natural fiber and discrete fiber etc.
80
3. This model can obtain the settlement may occur under the foundation and how the
reinforced material can resist this settlement.
6.3 Recommendation for Future Studies
1. For future studies this model could be the starting key for more cases such effect of
reinforcement material on different types of clay, using fibers or steel as reinforced
material.
2. A study could be obtained to study the coast and working management efficiency by
using geosynthetic material in soil
3. Study the effect of using discrete fiber for soil reinforcement using finite element
method model.
81
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