a developed fem-bem practical technique to consider …

A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO

CONSIDER SSI IN THE LATERAL ANALYSIS FOR

MULTISTORY BUILDINGS

By

Abdelrahman Mohamed Ibrahiem Ali Elmeliegy

A Thesis Submitted to the

Faculty of Engineering at Cairo University

In Partial Fulfillment of the Requirements for the Degree of

Master of Science

In

Structural Engineering

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

2017




By





Master of Science

In


Under the Supervision of


GIZA, EGYPT

2017

Prof. Dr. Youssef F. Rashed

Professor of Structural Analysis and Mechanics

Structural analysis and mechanics Deptartment

Faculty of Engineering

Cairo University




By





Master of Science

In


Approved by the

Examining Committee

Prof. Dr. Youssef Fawzy Rashed, Thesis Advisor

(Professor at Faculty of Engineering; CairoUniversity)

____________________________

Prof. Dr. Sameh S. Fahmy Mehanny, Internal Examiner

(Professor at Faculty of Engineering; CairoUniversity)

____________________________

Prof. Dr. Ibrahiem Mahfouz, External Examiner

(Professor at Faculty of Engineering; Benha University)

____________________________


GIZA, EGYPT

2017

iv

DEDICATION

To whom I would never be without their guidance and support

To my mother, father, brother and sisters A.M.Elmeliegy

Feb.2017

v

ACKNOWLEDGEMENT

First of all due thanks go to God the most merciful and most graceful. Who

without his guidance and inspiration nothing could have been accomplished.

I also wish to express my deep indebtedness to Prof. Dr. Youssef Fawzy

Rashed, Professor of Structural Analysis and Mechanics, Structural Engineering

Department, Faculty of Engineering, Cairo University, for his generous guidance and

encouraging, sincere help, consistent support by all means and asking, valuable

suggestions, and precise advice through all stages of this research work, I express my true

thanks and gratitude for opening my mind to the true values of sincere and creativity. I

have learned many lessons in working under his guidance and leadership that I will

remember for an extremely long time.

My thanks also go to my colleagues, especially Dr.Taha Abou Elnaga, Eng.

Ahmed Fady, Eng. Anas Abu Rawash and all friends who supported me all the way to

achieve this work.

A.M.Elmeliegy….February,2017

vi

Engineer: Abdelrahman Mohamed Ibrahiem Ali Elmeliegy

Date of Birth: 27/05/1991

Nationality: Egyptian

E-mail: [email protected]

Phone:0127 321 5801

Address: 27 Yasser Elgeheny - Omrania - Giza - Egypt

Registration Date: 1/10/2013

Awarding date: 2017

Degree: Master of Science

Department: Structural Engineering

Supervisor:

Prof. Dr. Youssef Fawzy Rashed

Examiners:

Prof. Dr. Youssef Fawzy Rashed

Prof. Dr. Sameh S. Fahmy Mehanni, (Internal Examiner)

Prof. Dr. Ibrahiem Mahfouz, (External Examiner)

Title of Thesis:

A DEVELOPED FEM-BEM PRACTICAL TECHNIQUE TO CONSIDER SSI IN

THE LATERAL ANALYSIS FOR MULTISTORY BUILDINGS

Keywords:

BEM; Soil-structure interaction; static condensation; foundation-soil flexibility; static

soil-structure interaction.

Summary:

In this thesis, a new practical technique for the analysis of buildings including soil-

structure interaction is suggested. The new analysis is based on sub-structuring approach

where the system is partitioned into two main parts which are the superstructure part and

the raft-soil part. A static condensation technique is implemented at the column-raft

interface. A developed algorithm representing the column-raft interface is implemented

to ensure compatibility and equilibrium at that interface. Current practical analysis of SSI

is implementing the static condensation at the raft-soil interface which is time consuming

and tediously job. The new analysis has shown less time and effort in the modeling and

analyses. This technique of analysis is presented here only for linear analysis. However,

this technique can be extended to include nonlinear analysis such as no tension SSI, soil

nonlinearity SSI.

vii

Table of Contents Table of Contents .......................................................................................... vii

Chapter 1 Introduction and Background ......................................................... 1

1.1 General ...................................................................................................................... 1

1.2 Sources of Soil structure interaction ......................................................................... 1

1.2.1 Kinematic interaction: .................................................................................................... 2

1.2.2 Inertial interaction: ......................................................................................................... 2

1.3 Methods of soil structure interaction modeling ........................................................ 3

1.3.1 The direct approach [15-16] ........................................................................................... 3

1.3.2 The Substructure approach [17] ..................................................................................... 5

1.4 Methods of soil representation: ................................................................................. 7

1.4.1 The Winkler model ......................................................................................................... 7

1.4.2 The multi-Parametric model [19-20] .............................................................................. 7

1.4.3 The elastic half space model ........................................................................................... 8

1.5 Available solutions in practice .................................................................................. 8

1.5.1 The uncoupled manually iterative method ..................................................................... 9

1.5.2 The conventional method in practice............................................................................ 11

1.6 Thesis objectives ..................................................................................................... 12

1.7 Thesis outline .......................................................................................................... 14

1.8 Conclusions ............................................................................................................. 14

Chapter 2 Used Numerical Methods And Softwares.................................... 15

2.1 Introduction ............................................................................................................. 15

2.2 The finite element method (FEM) [31] ................................................................... 15

2.2.1 Advantage of the FEM: ................................................................................................ 15

2.2.2 Disadvantage of the FEM: ............................................................................................ 15

2.3 The ETABS software [33] ...................................................................................... 16

2.3.1 ETABS modeling and simulation capabilities .............................................................. 16

2.3.2 ETABS analysis capabilities ........................................................................................ 16

2.3.3 Used ETABS files ........................................................................................................ 17

2.4 Used structural objects and terminology in ETABS building model ..................... 19

2.4.1 Joint objects: ................................................................................................................. 19

2.4.2 Support object:.............................................................................................................. 19

2.4.3 Line objects: ................................................................................................................. 19

viii

2.4.4 Area / shell objects: ...................................................................................................... 19

2.4.5 Meshes / divisions: ....................................................................................................... 19

2.4.6 Body Constraint: ........................................................................................................... 20

2.4.7 Diaphragm constraint: .................................................................................................. 20

2.5 The boundary element method (BEM) [36]............................................................ 20

2.6 Raft terminology used in BEM/PLPAK ................................................................. 21

2.6.1 Raft foundation: ............................................................................................................ 21

2.6.2 Boundary elements: ...................................................................................................... 21

2.6.3 Nodes: ........................................................................................................................... 21

2.6.4 Extreme points: ............................................................................................................. 21

2.6.5 Colum load modeling: .................................................................................................. 21

2.6.6 Wall load modeling in PLPAK: ................................................................................... 22

2.7 Soil terminology used in BEM/PLPAK .......................................................................... 23

2.7.1 Subgrade reaction (K): ................................................................................................. 23

2.7.2 Elastic modulus (E): ..................................................................................................... 23

2.7.3 Poison’s ratio (v): ......................................................................................................... 23

2.7.4 Soil layers: .................................................................................................................... 23

2.7.5 Soil cells/divisions: ....................................................................................................... 23

2.8 The PLPAK software package [40] ................................................................................. 25

2.8.1The PlGen: .................................................................................................................... 27

2.8.2 PLView: ........................................................................................................................ 27

2.8.3 PL.exe: .......................................................................................................................... 27

2.8.4 PLPost: ......................................................................................................................... 27

2.8.5 PLCoreman: .................................................................................................................. 28

2.8.6 Used PLPAK files ........................................................................................................ 28

2.9 Soil modeling in PLPAK: ....................................................................................... 31

2.9.1 Winkler model: ............................................................................................................. 31

............................................................................................................................................... 32

2.9.2 EHS modeling: ............................................................................................................. 33

2.6 Conclusions ............................................................................................................. 34

Chapter 3 The Proposed New Technique ..................................................... 35

3.1 Introduction ............................................................................................................. 35

3.2 The developed translator ......................................................................................... 35

3.2.1 Translator.exe ............................................................................................................... 35

ix

3.3 Rotational stiffness implementation in SSIPAK/PLPAK ....................................... 38

3.4 Illustrative Example ................................................................................................ 39

1- Structural drawings ........................................................................................................ 39

2- ETABS 3D Model ......................................................................................................... 39

3- Data base file ................................................................................................................. 42

3.5 Methodology and automation ................................................................................. 44

3.6 The graphical user interface SSIPAK ..................................................................... 48

3.7 Conclusions ............................................................................................................. 49

Chapter 4 Numerical examples ..................................................................... 50

4.1 Introduction ............................................................................................................. 50

4.2 Example set 1 .......................................................................................................... 50

4.3 Example set 2 .......................................................................................................... 71

4.4 Example set 3 .......................................................................................................... 92

Bare frame results: ........................................................................................................ 93

Shear wall results .......................................................................................................... 96

4.5 Example set 4 .......................................................................................................... 99

Chapter 5 Summary, Conclusions and Recommendations for Future Work

..................................................................................................................... 102

4.1 Summary ............................................................................................................... 102

5.2 Conclusions ........................................................................................................... 102

5.3 Recommendations for future work ....................................................................... 103

ARABIC SUMMARY .................................................................................... 2

x

LIST OF TABLES

Table 4.1The fundamental periodic time in seconds for example 1 – with rotational

stiffness ............................................................................................................................. 70

Table 4.2 The fundamental periodic time in seconds for example 1 – without rotational

stiffness ............................................................................................................................. 70


stiffness. ............................................................................................................................ 91


stiffness. ............................................................................................................................ 91

Table 4.5 Section properties for example set 3 [8]. .......................................................... 92

Table 4.6 The soil properties according to work done by [8]. .......................................... 92

Table 4.7 Time period for different modes of shape – 4 floors. ....................................... 95

Table 4.8 Time period for different modes of shape - 16 floors. ...................................... 95

Table 4.9 Time period for different modes of shape - 4 floors. ........................................ 98

Table 4.10 Time period for different modes of shape - 16 floors. .................................... 98

Table 4.11 Section properties according to work done by [12]. ....................................... 99

Table 4.12 The soil properties according to work done by [12]. ...................................... 99

Table 4.13 The fundamental time period for 6-floors multi-story framed building. ...... 100

Table 4.14 The fundamental period for 12-floors multi-story framed building. ............ 101

xi

LIST OF FIGURES Figure 1.1(a) The effect of soil flexibility on the lateral deformation. (b) The effect of

neglecting soil flexibility. ---------------------------------------------------------------------------- 3 Figure 1.2The direct approach of soil-structure interaction.. ----------------------------------- 4 Figure 1.3 The substructure method of soil-structure interaction.. ---------------------------- 6 Figure 1.4 Soil representation using Winkler springs.. ------------------------------------------ 7

Figure 1.5 The Uncoupled iterative technique used in design firms. ------------------------ 10 Figure 1.6 The conventional method used in practicaldesign firms (a),(b).. --------------- 11 Figure 1.7 The proposed new method of static condensation.. ------------------------------- 13 Figure 2.1 The structure of the ETABS .e2k file. ---------------------------------------------- 17 Figure 2.2 The structure of point coordinates .txt ETABS file. ------------------------------ 18

Figure 2.3 The structure of static load cases .txt file. ------------------------------------------ 18

Figure 2.4 The structure Support Restraint .txt file. ------------------------------------------- 18

Figure 2.5 the structure of Support Reactions.txt file. ----------------------------------------- 18 Figure 2.6 The structure of Point Spring Force.txt file ---------------------------------------- 19

Figure 2.7 Soil and boundary elements discretization for a typical raft on Winkler

foundation. ------------------------------------------------------------------------------------------- 22

Figure 2.8 Soil and boundary elements discretization for a typical raft on EHS. --------- 24 Figure 2.9Flow chart show the PLPAK components ------------------------------------------ 26 Figure 2.10 The structure of the model.txt file. ------------------------------------------------ 28

Figure 2.11 The structure of the material .txt file. --------------------------------------------- 29 Figure 2.12 The structure of the slab .txt file. -------------------------------------------------- 29

Figure 2.13 The structre of the soil support .txt file. ------------------------------------------- 29 Figure 2.14 The structure of the .aip file. ------------------------------------------------------- 30 Figure 2.15 The structure of the .ipu file. ------------------------------------------------------- 30

Figure 2.16 The structure of the .run file. ------------------------------------------------------- 30

Figure 2.17 The Winkler cell discretization in the PLView. --------------------------------- 32 Figure 2.18 Practical raft on Winkler modeled using PLGen -------------------------------- 32 Figure 2.19EHSPAk add-on start menu --------------------------------------------------------- 33

Figure 3.1 he structure of . c file. ----------------------------------------------------------------- 36

Figure 3.2 The structure of the .k file. ----------------------------------------------------------- 36 Figure 3.3 The structure of the LC.txt file. ------------------------------------------------------ 36 Figure 3.4 The structure of the column load.txt file. ------------------------------------------ 37 Figure 3.5 The structure of the $Runstiff$ file. ------------------------------------------------ 37 Figure 3.6 The input and output files used by translator. ------------------------------------- 38

Figure 3.7 The rotational stiffness implementation procedure. ------------------------------ 39 Figure 3.8 The structural drawings using AutoCAD.------------------------------------------ 40 Figure 3.9 The ETABS 3D model. --------------------------------------------------------------- 41

Figure 3.10 a & b The steps to export the database file containing the required text files.

--------------------------------------------------------------------------------------------------------- 42 Figure 3.11 The database file containing the required text files. ---------------------------- 43 Figure 3.12 The raft model in PLGEN. ---------------------------------------------------------- 44

Figure 3.13 The raft model in PLVIEW. -------------------------------------------------------- 44 Figure 3.14 Flow chart shows the proposed technique. --------------------------------------- 47

xii

Figure 3.15 The graphical user interface (SSIPAK). ------------------------------------------ 48 Figure 4.1. Exapmle 1 plan ------------------------------------------------------------------------ 51 Figure 4.2 ETABS 3D modeling of example 1 super structure. ----------------------------- 52 Figure 4.3 PLPAK 2D modeling of example 1 raft foundation. ----------------------------- 52

Figure 4.4 SAP2000 3D modeling of example 1- Direct method. --------------------------- 53 Figure 4.5 SAP2000 3D modeling of example 1- Direct method. --------------------------- 53 Figure 4.6 Lateral Deflection in X-direction for example 1- E=2000 t/m2 (with rotational

stiffness). --------------------------------------------------------------------------------------------- 54 Figure 4.7 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=2000 t/m2

(with rotational stiffness). ------------------------------------------------------------------------- 54 Figure 4.8 Drift SSI/NSSI ratio in X-direction for example 1 E=2000 t/m2 (with

rotational stiffness). --------------------------------------------------------------------------------- 55

Figure 4.9 Inter story drift in X-direction for example 1- E=2000 t/m2 (with rotational

stiffness). --------------------------------------------------------------------------------------------- 55 Figure 4.10 Lateral Deflection in X-direction for example 1 E=2000 t/m2 (without

rotational stiffness). --------------------------------------------------------------------------------- 56 Figure 4.11 Lateral Deflection SSI/NSSI in X-direction for example 1 E=2000 t/m2

(without rotational stiffness).---------------------------------------------------------------------- 56 Figure 4.12 Inter story drift in X-direction for example 1 E=2000 t/m2 (without rotational

stiffness). --------------------------------------------------------------------------------------------- 57

Figure 4.13 Drift SSI/NSSI ratio in X-direction for example 1- E=2000 t/m2 (without


Figure 4.14 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000

t/m2 (with rotational stiffness). ------------------------------------------------------------------- 58 Figure 4.15 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (with



stiffness). --------------------------------------------------------------------------------------------- 59 Figure 4.17 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (with

rotational stiffness). --------------------------------------------------------------------------------- 59 Figure 4.18 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (without

rotational stiffness). --------------------------------------------------------------------------------- 60 Figure 4.19 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000

t/m2 (without rotational stiffness). --------------------------------------------------------------- 60 Figure 4.20 Inter story drift in X-direction for example 1- E=5000 t/m2 (without

rotational stiffness). --------------------------------------------------------------------------------- 61 Figure 4.21 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (without


Figure 4.22 Lateral Deflection in X-direction for example 1- E=10000 t/m2 (without



t/m2 (without rotational stiffness). --------------------------------------------------------------- 62 Figure 4.24 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without


xiii


stiffness). --------------------------------------------------------------------------------------------- 63 Figure 4.26 Lateral Deflection in X-direction for example 1- E=10000 t/m2(without



t/m2 (without rotational stiffness). --------------------------------------------------------------- 64 Figure 4.28 Inter story drift in X-direction for example 1- E=10000 t/m2 (without


rotational stiffness). --------------------------------------------------------------------------------- 65 Figure 4.30 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (with



t/m2 (with rotational stiffness). ------------------------------------------------------------------- 66 Figure 4.32 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (with

rotational stiffness). --------------------------------------------------------------------------------- 67 Figure 4.33 Inter story drift in X-direction for example 1- E=20000 t/m2 (with rotational

stiffness). --------------------------------------------------------------------------------------------- 67 Figure 4.34 Lateral Deflection in X-direction for example 1- E=20000 t/m2 (without



t/m2 (without rotational stiffness). --------------------------------------------------------------- 68


rotational stiffness). --------------------------------------------------------------------------------- 69 Figure 4.37 Inter story drift in X-direction for example 1- E=20000 t/m2 (without


Figure 4.38 Exapmle 2 plan. ---------------------------------------------------------------------- 72 Figure 4.39 ETABS 3D modeling of example 2 super structure. ---------------------------- 73 Figure 4.40 PLPAK 2D modeling of example 2 raft foundation. ---------------------------- 73

Figure 4.41 SAP2000 2D view. ------------------------------------------------------------------- 74 Figure 4.42 SAP2000 3D modeling of example 2- Direct method. ------------------------- 74

Figure 4.43 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (with



t/m2 (with rotational stiffness). ------------------------------------------------------------------- 75 Figure 4.45 Inter story drift in X-direction for example 2- E=2000 t/m2 (with rotational


rotational stiffness). --------------------------------------------------------------------------------- 76 Figure 4.47 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (without


t/m2 (without rotational stiffness). --------------------------------------------------------------- 77

xiv

Figure 4.49 Inter story drift in X-direction for example 2- E=2000 t/m2 (without




t/m2 (with rotational stiffness). ------------------------------------------------------------------- 79 Figure 4.52 Lateral Deflection in X-direction for example 2- E=5000 t/m2 (with

rotational stiffness). --------------------------------------------------------------------------------- 79 Figure 4.53 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (with

rotational stiffness). --------------------------------------------------------------------------------- 80 Figure 4.54 Inter story drift in X-direction for example 2- E=5000 t/m2 (with rotational

stiffness). --------------------------------------------------------------------------------------------- 80



t/m2 (without rotational stiffness) . -------------------------------------------------------------- 81 Figure 4.57 Inter story drift in X-direction for example 2- E=5000 t/m2 (without



Figure 4.59 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (with



t/m2 (with rotational stiffness). ------------------------------------------------------------------- 83 Figure 4.61 Drift SSI/NSSI ratio in X-direction for example 2- E=10000 t/m2 (with



stiffness). --------------------------------------------------------------------------------------------- 84 Figure 4.63 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (without


t/m2 (without rotational stiffness) . -------------------------------------------------------------- 85 Figure 4.65 Inter story drift in X-direction for example 2- E=10000 t/m2 (without


rotational stiffness). --------------------------------------------------------------------------------- 86 Figure 4.67 Lateral Deflection in X-direction for example 2- E=20000 t/m2 (with



t/m2 (with rotational stiffness). ------------------------------------------------------------------- 87




xv






rotational stiffness). --------------------------------------------------------------------------------- 90 Figure 4.75 The structural layout and dimensions [8]. ---------------------------------------- 92

Figure 4.76 The time period for mode 1- 4 floors. --------------------------------------------- 93 Figure 4.77 The time period for mode 3 - 4 floors. -------------------------------------------- 93 Figure 4.78 The time period for mode 4 - 4 floors. -------------------------------------------- 93

Figure 4.79 The time period for mode 1- 16 floors. ------------------------------------------- 94 Figure 4.80 The time period for mode 3 - 16 floors.------------------------------------------- 94 Figure 4.81 The time period for mode 4 - 16 floors.------------------------------------------- 94

Figure 4.82 The time period for mode 1 - 4 floors. -------------------------------------------- 96 Figure 4.83 The time period for mode 3 - 4 floors. -------------------------------------------- 96

Figure 4.84 The time period for mode 4 - 4 floors. -------------------------------------------- 96 Figure 4.85 The time period for mode 1 - 16 floors.------------------------------------------- 97 Figure 4.86 The time period for mode 3 - 16 floors.------------------------------------------- 97

Figure 4.87 The time period for mode 4 - 16 floors.------------------------------------------- 97 Figure 4.88 The structural layout and dimensions according to work done by [12]. ----- 99

Figure 4.89 The fundamental time period for 6-floors mutli-story framed building. --- 100 Figure 4.90 The fundamental period for 12-floors multi-story framed building. --------- 101

1

Chapter 1 Introduction and Background

1.1 General

According to many reports [1], construction industry has witnessed a very rapid growth

particularly in multi-story buildings because of tendency to urbanization and industrial

development.

Considering multi-story building from 3 to 20 stories with raft foundations , it is common

– in structural engineering – mainly in the analysis of building at design firms not taking

into account the flexibility of the sub structure (foundations and underneath soil) in the

analysis of the superstructure. They often carry out design as two parts independently.

Generally, buildings are assumed to be fixed or hinged at the ground level. As a

consequence, the evaluated responses due to different types of load cases especially the

lateral loads (earthquakes and wind loads) do not truly present the accurate behavior of

the structure. Raft and soil stiffness will add more flexibility to the structure; so that the

overall stiffness will be decreased and a more realistic and economic designs could be

achieved. On the other hand, the lateral deflection and the inter-story drift will increase

with increasing the soil flexibility. Although this is more conservative for the structures,

the safety of the structure due to lateral deflection should be re-evaluated so, it is

important to consider soil-structure interaction in the analysis.

1.2 Sources of Soil structure interaction

In the structural analysis, the assumption of fixed base for the building especially for the

building on soft or medium soil is not realistic [2-14]. Usually designers are assuming

fixed or hinged base for the sake of simplicity. This assumption may be accepted if the

structure will be constructed on rock layer or if the relative stiffness of the substructure

(soil-foundation system) compared to the superstructure is high.

In the most occasions, existence of soil induces two separate effects on the structure, first,

the amplitude and the direction of the free ground motion from the bed rock will be

adjusted ( amplified or degraded) at the level of structure’s base [3]. Second, hence the

underneath soil is flexible, the forces acting on the masses of the structures will enforce

the supporting systems (raft foundation..etc.) and the underneath soil to deform. These

two phenomena are referred to as kinematic interaction and inertial interaction,

respectively. In fact, kinematic interaction is the inability of the foundation to match the

soil deformations due to the free field ground motion. On the other hand, the inertial

interaction can change the structure periodic time (T) hence the structure response to the

seismic loading. These two effects are discussed in more detail in the following sections.

2

1.2.1 Kinematic interaction:

Kinematic interaction is the inability of rigid foundation to match the movement of soil

under ground motion. Due to the effect of existence of soil mass, the ground motion

amplitude and frequency will change at each point depending on soil and ground motion

characteristics. Also, the ground motion decreases with the increasing of depth.

Moreover, due to the existence of raft foundation which is much more stiffn relative to

soil stiffness, the ground motion waves may suffer from scattering at foundations corners

and deviation so, the base of super structure will be exposed to different ground motion

than the free field motion. So, there is need to use some transformation to transform the

free field motion into foundation input motion using some mathematical transformation

techniques. Yet, the kinematic interaction plays an important role in case of loose soil

with high level of ground water table and in soft soils. In this thesis, only the inertial

interaction will be considered.

1.2.2 Inertial interaction:

In the second type of interaction, the existence of flexible material under the foundation

of the super structure is denoted as inertial interaction. Inertial forces which are induced

by foundation motion during the lateral loading can cause the underneath soil to deform

figure 1.1 (a). Hence more flexibility will be added to the super structure. That means the

dynamic characteristics of the structure such as fundamental periodic time and structure

responses such as lateral deflection, base shear and inter-story drifts will differ from those

of the fixed/hinged base structure figure 1.1 (b). So, base shear, story shear, lateral

deflection and inter-story drift should be re-computed.

The soil-structure interaction effect can be evaluated and assessed by comparing the same

structure responses subjected to lateral loading with and without soil underneath the

foundation systems. This is usually causing increasing in natural periodic time due to

flexibility of existing soil added to the system.

In most cases, inertial interaction has beneficial effect on the structure as base shear and

story shear will decrease with gaining more ductility in the structure which allow for

more energy dissipation. However, in some rare cases, it has detrimental effects on the

structure especially for low rise buildings [5]. Gazetas & Mylonakis, [2-4] demonstrated

the possible severities of neglecting soil structure interaction for a certain soil and seismic

characteristics. They demonstrated that the increase in the natural periodic time may

cause an increase in the seismic demand of the structure.

3

(a)

1.3 Methods of soil structure interaction modeling Basically there are two approaches for the soil structure interaction analysis.

1.3.1 The direct approach [15-16]

In this approach, the structure, foundation system, and the underneath soil are modeled

together as a unit. The entire system is solved in a single step as shown in figure 1.2. In

this method, soil is modeled as a finite solid element with the corresponding elastic

modulus (E) and Poisson’s ratio (v), also it can be modeled using boundary element

method taking the advantages of no meshing in the domain and less computational time

[16]. The boundary conditions are implemented so that the soil continua almost represent

the soil block under the structure. The structure is modeled using the beam elements for

the beams and columns whereas the slabs; raft and shear walls are modeled using shell

elements. The advantage of that method is that it can be used for complex geometries and

different material properties. Also it can be used for the nonlinear interaction analysis

[15].

Figure 1.1(a) The effect of soil flexibility on the lateral deformation. (b)

The effect of neglecting soil flexibility.

4

However, the preparation of data and modeling complexity makes it difficult to be

implemented in the field of engineering practice besides, if the size of the structure is big

which is the case for practical buildings, the user cannot use this method efficiently.

Another disadvantage of this method is the modeling of an infinite media as a finite one

with artificial boundary conditions. This can cause energy trapping within the model and

cause error in the computation process. So, there are some techniques that have been

developed to solve this problem such as using non-reflecting boundaries [15] to absorb

energy or using dampers [15] to prevent energy from reflecting back into the model.

Since most of the ground motions are usually recorded on the ground surface without

considering the existence of the structure, therefore, in constructing a finite element

modeling to model soil-structure interaction, all ground motions must be refined to obtain

the bedrock motion before using those as the input motions for such modeling approach.

So it is very complex to obtain the bedrock ground motion especially in case of complex

soil profiles.

Figure 1.2The direct approach of soil-structure interaction.

5

In this thesis, the direct method is used as verification for the proposed technique with

only static lateral loads to overcome the problem of preventing energy. This method can

be used as verification for small problems only, practical examples cannot be solved as it

requires large computers which are not available.

1.3.2 The Substructure approach [17] In the substructure approach the soil-structure interaction problem is divided into two

independently substructures as shown in figure 1.3. The substructure number one is the

structure itself including the raft foundation. The substructure number two is the soil half

space. The coupling process between the substructure no.1 and the substructure no.2 is

undertaken with various algorithms [17] which basically ensures the equilibrium and

compatibility at the interface between the soil and the structure.

In this approach, it is assumed that no separation and slippage occur at the interface

between the structure and the soil subdomain. In static interaction analysis, the entire

structure is initially considered rested on an initial value of linear springs.

After the analysis is done, the reaction forces are equilibrated at the interface and are

hence subjected with the same values and in opposite direction on the soil subdomain as

external forces. Then, the analysis of soil subdomain under the predefined loads is carried

out. The response of the soil subdomain in terms of deformation can be computed. Using

iterative technique with an acceptable tolerance, the compatibility and equilibrium can be

achieved [17].

In case of the static soil-structure interaction analysis, only the inertial interaction is

regarded in the analysis where kinematic interaction has no effect. As demonstrated

previously, the main advantage of the substructure method of soil-structure interaction is

its flexibility which makes it efficient. Also, nonlinear soil-structure interaction analysis

can be done in an appropriate way [17] .

6

Figure 1.3 The substructure method of soil-structure interaction.

The substructure no.1

The substructure no.2

7

1.4 Methods of soil representation:

There are different methods to represent and model the soil. From these methods we can

mention the Winkler method, two parameter method and elastic half space method [15].

1.4.1 The Winkler model

The Winkler Model [18] is the most used model for soil-structure interaction analysis by

structural engineers. This is due to its simplicity. It is considered as the oldest method to

model the underneath soil. This model depends on representing the soil as finite number

of springs on a rigid base as shown in figure (1.4).

In this model, no coupling between springs which means deformation will be

immediately under each spring individually where the deflection at the other point is

zero. The springs have only the vertical degree of freedom.

The stiffness of uncoupled springs can be evaluated using different methods, all of these

methods are based on the linear relationship between force (Ri) and deflection (δi)at a

certain point as shown in equation (1).

Ki= Ri / δi. (1)

Although the Winkler model is one of the simplest ways of soil modeling, it is also the

least accurate. The primary deficiency of the model is that there is no unique value of K

for a certain type of soil. This means that the subgrade reaction is not considered as a

property among the different soil properties.

1.4.2 The multi-Parameter model [19-20]

The multi-parameter models have been developed to refine the Winkler soil

representations. In these models two or more independent constants with elastic behavior

are predefined. These constants are used to consider the shear deformation of the soil,

hence Winkler springs will be coupled. Most of these models use elastic beam, elastic

membrane or springs as an elastic interaction element which can transfer the load in the

transversal direction. Examples of these models are illustrated in the work of Filonenko-

Figure 1.4 Soil representation using Winkler springs.

8

Borodich [21-22] who used deformed pre-tensioned membrane as an interaction element

between Winkler springs, Pasternak [23] who used a shear layer to couple the spring

elements, Loof and kerr [24] who used a shear layer with springs to couple the springs

elements, Haber- Shaim who used a plate as an interaction element, Hetenyi [25] who

used a plate-spring system for coupling between springs and Rhines [26] who used a

system of springs-plate-shear layer to couple springs. These models have also the

deficiency of that they are not considered a property among the different soil properties.

1.4.3 The elastic half space model

Continuum is defined in continuum mechanics by a continuously distributed mass

through the space. The simplest elastic continuum is described with linear elastic

isotropic behavior given by Hook’s law.

Without failure criteria the elastic medium has infinite tension and compression capacity,

which is not real for soil. Several constitutive relations exist, with different failure criteria

in tension and compression. Several analytical solutions due to different loading cases

have been developed for the elastic half space.

Boussinesq [20] and Mindlin [27] considered the soil as an elastic, homogenous,

isotropic, , and infinite half space. Steinbrenner [28] considered the presence of a rigid

layer under the considered surface soil finite layer. For all previous models, normal

stresses in horizontal direction and shear stresses are neglected as well as the horizontal

displacements at top and bottom of the medium.

Due to these assumptions, these methods are not suitable to study stresses inside the

medium. Several numerical methods can be used to analyze the elastic semi-finite

continuum such as finite element method and boundary element method.

1.5 Available solutions in practice

In practice, the most common method is the Winkler spring model despite of its several

shortcomings previously presented.

The ACI committee [29] suggested using elastic half space technique with Boussinesq

theory instead of Winkler model for accurate modeling. Unlike the Winkler and the two-

parameter models, the elastic half space method uses data obtained from geotechnical

investigations such as elastic modulus E and Poison’s ratio v. Nowadays, the uncoupled

iterative method [30] is used widely in many design companies and they make use of

EHS to represent the soil medium. However, it takes a long time and huge effort through

structural and geotechnical analyses to still obtain an approximate solution [30].

9

1.5.1 The uncoupled manually iterative method

In this section the uncoupled iterative method is discussed. In this method the

substructure approach is used. In other words the structure including the raft foundation

and soil is modeled separately where the soil is modeled as a continuum elastic half

space. The sub-structuring is done at the soil-raft interface. The method is based on

manual iterative procedure which is done at the soil-raft interface to ensure that

compatibility and equilibrium have been achieved. At each stage of the iterative process,

the results of one analysis form the boundary conditions for the subsequent analysis using

the vertical equilibrium as shown in figure 1.5. This method is used by some consultant

and design firms [30]. However, this method of coupling requires much time and efforts

to be done properly. This is because the static condensation which is done at the soil-raft

interface

results in many degrees of freedoms unlike the case of doing condensation at the raft-

columns interface. Another method of sub-structuring to overcome these shortcomings is

the core of this thesis and presented in details in chapter 3.

The steps of this method are demonstrated in cycles as follow:

a. The first iteration (n)

1- The soil flexibility matrix [F] is computed from EHS program such as

Pdisp [42].

2- The vertical structural loads {Q} are applied directly to the ground

surface, and the vertical surface displacements {ws }1 are obtained as

follow {ws}1 = [ F ] x {Q}. Such displacements are computed using a

software package called the VDisp – a software package for elastic half

space problems.

3- The raft is founded on bed of springs of vertical nodal stiffness as follow

{Ks}1 = {Q/(ws)1}. However, most of design companies use a preliminary

suggested formulate to get the subgrade reaction which can be evaluated

as 100-120 of soil bearing capacity in t/m/m2.

4- The entire structural loading {L} - including any imposed moments – is

applied to the raft on springs, and the vertical spring forces {P}1 are

obtained by conventional methods of structural analysis. Initial values of

vertical raft displacement {wk }1 are also computed to be compared to the

corresponding ground displacement profile.

10

The second iteration (n+1)

5- The vertical spring forces {P}1 are applied directly to the ground surface,

and the vertical surface displacements {ws}2are obtained as follow {ws}2 =

[ F ] x {P}1. .

6- The raft is founded on bed of springs of vertical nodal stiffness as follow

{Ks}2 = {P/(ws)2}.

7- The entire structural loading {L} is applied to the raft on springs, and the

vertical spring forces {P}2 are obtained as before. Values of vertical raft

displacement {wk}2 are also computed to be compared to the

corresponding ground displacement profile.

The iterative process is continued until satisfactory convergence is

achieved.

Figure1.5The Uncoupled iterative technique used in design firms.

11

1.5.2 The conventional method in practice

Although the previous method in section 1.5.1 is used by some design firms, the most of

design firms uses the method presented in the current section. In this method, the

superstructure is modeled on fixed/hinged base and analysis is carried out based on this

assumption.

The reactions from the superstructure are reversed into the foundation system and then

the analysis is done

(a) [12] (b) [12]

as shown in figure 1.6 (a). So, the interaction between the underneath soil and the

foundation is taken but the effect of the foundation-soil flexibility on the superstructure is

omitted. Moreover, the common method to represent the soil is Winkler uncoupled

springs, which means that there is no realistic representation of soil and hence less

accurate results than modeling soil as elastic half space.

Figure 1.6 The conventional method used in practicaldesign firms (a),(b).

12

In some rare cases, the entire structure is modeled including the raft foundation [12]. The

soil is modeled as Winkler uncoupled springs as shown in figure 1.6 (b).

1.6 Thesis objectives

The main objective of this work is to develop a practical tool to consider soil-structure

interaction in the analysis of building rested on raft foundation which can be used by

design engineers in design firms easily and efficiently. The new idea is based on the

availability of the ETABS program [32] which is widely used in design firms for the

analysis and design of building as presented in chapter 2 in section 2.3. Also, there is a

program called PLPAK [40] see chapter 2 section 2.5 through which soil can be modeled

as elastic half space. The soil-structure interaction procedure is carried out using an

iterative technique. Unlike the uncoupled iterative technique presented in section 1.5.1,

this technique is based on a static condensation at the raft - columns interface as shown in

figure 1.7. This will produce much less degrees of freedom and hence much less effort

and computation time. The new practical technique is aimed to be automated, also a

graphical user interface for the work is going to be developed to ease the use for

engineers in the practice.

The thesis objectives can be summarized as below.

To develop a new algorithm to couple the structure with the soil in the analysis

of multi-story buildings rested on raft foundations to consider the effect of static

soil-structure interaction.

To implement this tool to couple the well-known commercial finite element

program named ETABS which is used for the analysis of buildings with a

boundary element based program named PLPAK which is used for the analysis

of slabs and foundation on elastic half space.

To develop graphical user interface for the code to be efficiently used used in

practice.

13

Figure 1.7 The proposed new method of static condensation.

14

1.7 Thesis outline

A very short overview for each chapter in this thesis is presented as follows.

Chapter 1: introduces briefly the problem, presents the background of the problem and

previous work done in that area.

Chapter 2: introduces the finite element method and its disadvantages, the ETABS

software and its main components. The boundary elements method’s advantages and

disadvantages are also listed. PLPAK components and its adds-on are presented.

Chapter 3: the proposed technique is presented with detailed explanation and flow

chart showing how to automate and use this technique in practice. Also the developed

GUI main buttons are demonstrated in details.

Chapter 4: numerical examples and results are presented. A comparison and

verification to internationally published papers are shown. Framed and shear wall

structures are used in this chapter. Lateral deflection, lateral deflection ratio SSI/NSSI,

Drift, Drift Ratio SSI/NSSI are used for the comparisons.

Chapter 5: summary, conclusion and recommendation for future work are presented.

1.8 Conclusions

In this chapter, an overview for the thesis was discussed followed by an introduction

about the soil structure interaction sources, methods of soil structure interaction, models

used to represent the soil and available solutions in practice. The advantages and

disadvantages for such a method were reviewed. Finally, the objectives of this thesis

were stated.

In the next chapter, the boundary element method is reviewed. Soil modeling in BEM and

PLPAK is also reviewed. Finally The PLPAK software package is presented with its

available methods to model soil.

15

Chapter 2 Used Numerical Methods And Softwares

2.1 Introduction

In this chapter a brief review about finite element method FEM is presented. The ETABS

program as a software applying the FEM is also reviewed with its main components and

capabilities. The ETABS files with different extensions are presented in details. The

boundary element method is also reviewed. The PLPAK program – A BEM Based

program as an application for the direct BEM for Reissner’s plate is also presented. Soil

modeling methods in PLPAK is reviewed as well.

2.2 The finite element method (FEM) [31]

The finite element method is a numerical method for solving linear partial differential

equations. According to the FEM [31], the entire domain of the considered problem is

discretized into smaller subdomains which only are connected at their corner nodes. The

unknowns of the problem are the deflections and rotations in the directions of prescribed

degrees of freedom. The values of these unknowns are obtained from the solution of

equilibrium and compatibility equations assembled from all elements. Due to the wide

usage of the FEM, there are many established commercial programs that are based on the

method such as ETABS [32], SAP2000 [33], ANSYS [34] etc.

2.2.1 Advantage of the FEM:

The advantages of the FEM can be summarized into,

a) ability to model different geometries and nonlinear materials

b) obtained system matrices are positive definite, banded, and sparse

c) Widely tested approach

d) Commercial availability

e) Flexibility

2.2.2 Disadvantage of the FEM:

The disadvantages of the FEM can be summarized into,

a) The FEM requires the use of powerful computers of considerable speed and

storage capacity.

b) It is difficult to ascertain the accuracy of numerical results when large structural

systems are analyzed.

c) The method is poorly adapted to a solution of the so-called singular problems

(e.g., plates and shells with cracks, corner points, discontinuity internal actions,

etc.), and of problems with unbounded domains.

d) The method presents many difficulties associated with problems of C1 continuity

and nonconforming elements in plate (and shell) bending analysis.

16

e) Large effort and time consuming in discretization of the domain and no flexibility

in modification

2.3 The ETABS software [33]

The ETABS stands for Extended (Three-Dimensional) Analysis of Building Software. It

is one of the most well-known and commercially available analysis software which is

used widely in the structural analysis of buildings. ETABS software is developed using

the finite element method as a numerical modeling technique in the analysis of structures.

Unlike SAP2000, ETABS has more advanced computation algorithms which are

implemented to analyze any complex high rise structure in lesser time and memory. Also

ETABS has more user friendly input options to generate the complex high rise structure's

model. The model can include different or integrated structural systems with the ability to

solve complex problems easily [35].

In addition to that, ETAB software has design features according to many codes of

design with unique calculation notes that is widely used by design firms.

2.3.1 ETABS modeling and simulation capabilities

ETAB software has a friendly graphical user interface GUI. Modeling capabilities that

can be done using ETABS GUI are summarized below.

a) Different types of structural elements such as frame and shell elements.

b) Different types of support restraints simulation including roller, hinged and fixed

supports.

c) Different types of nonlinear support element such as gap element.

d) Different types of constraints including body, plate, weld, diaphragm constraints.

e) Different types of load cases and conditions including gravity loads and lateral

loads.

2.3.2 ETABS analysis capabilities

ETAB software solver can do the following analyses.

a) Static and dynamic analyses.

b) Linear and nonlinear analyses.

c) Seismic and pushover analyses.

d) Construction staged analysis.

e) Geometric nonlinearity analysis.

17

2.3.3 Used ETABS files In this section, important input and output files that are used in this thesis are presented in

details.

2.3.3.1 ETABS model file (.e2k)

This file contains all ETABS model data including name of the model, saving date,

coordinate system, point coordinates, point assignments, line assignments, load cases..etc.

this file can be exported directly from the ETABS GUI and re-imported again. The

structure of the .e2K file is shown in figure 2.1.

Figure 2.1 The structure of the ETABS .e2k file.

18

2.3.3.2 ETABS data base file (.txt)

This data base file contains model data as well as the analysis data in separate text

formatting files. This file can be exported directly from the ETABS model after

analysis is done. Only in this thesis, five files are used in the proposed technique.

These files structures are shown in figures 2.2 – 2.6.

1- Point Coordinates .txt file:

This file contains the points labels and X,Y, and Z coordinates as shown in figure

2.2.

2- The Static Load Cases.txt file:

This file contains the different load cases that were entered by user and the self-

weight multiplier for each case as shown in figure 2.3.

3- The Supports (Restraints).txt file:

This file contains the support labels and restrained directions as shown in figure

2.4.

4- The Supports Reactions.txt file:

This file contains the support labels, load case and the corresponding reactions in

each direction as shown in figure 2.5.

Figure 2.2 The structure of point coordinates .txt ETABS file.

Figure 2.3 The structure of static load cases .txt file.

Figure 2.4 The structure Support Restraint .txt file.

Figure 2.5 the structure of Support Reactions.txt file.

19

5- The Point Spring Forces.txt file:

This file contains the spring labels, load cases and the spring forces in each

direction as shown in figure 2.6.

2.4 Used structural objects and terminology in ETABS building model

In this section, different objects and terminologies used in ETABS building model are

reviewed. These can be divided to the following:

2.4.2 Joint objects:

Joints are automatically generated at the corners and ends of all other types of other

objects mentioned below.

2.4.2 Support object:

Used to model and represent supporting conditions. It includes roller, hinge, fixation and

Winkler supports. It can be modified to restraint degree of freedom in customized

directions.

2.4.3 Line objects:

There are four types of line objects used in modeling.

1- Frame element: used to model beams, frames, trusses and bracing systems.

2- Cable element: used to model cables.

3- Tendon element: used to model pre-stressing tendons in pre-stressed concrete.

2.4.4 Area / shell objects:

Used to model slabs, walls and other two dimensional elements. This includes thin and

thick shells.

2.4.5 Meshes / divisions:

Each area object is divided into a number of relatively small subareas. The dimensions of

these subareas depend on the problem type and dimensionality and the degree of

accuracy pursued.

Figure 2.6 The structure of Point Spring Force.txt file

20

2.4.6 Body Constraint:

A body constraint causes all of its constrained joints to move together as a three-

dimensional rigid body. By default, all degrees of freedom at each connected joint

participate. However, you can select a subset of the degrees of freedom to be constrained.

This Constraint can be used to:

1- Model rigid connections, such as where several beams and/or columns frame

together.

2- Connect together different parts of the structural model that were defined using

separate meshes.

3- Connect Frame elements that are acting as eccentric stiffeners to Shell elements.

2.4.7 Diaphragm constraint:

A diaphragm Constraint causes all of its constrained joints to move together as a planar

diaphragm that is rigid against membrane deformation. Effectively, all constrained joints

are connected to each other by links that are rigid in the plane, but do not affect out-of-

plane (plate) deformation.

This constraint can be used to model concrete floors in building structures, which

typically have very high in-plane stiffness especially in lateral analysis.

2.5 The boundary element method (BEM) [36]

The boundary element method is a numerical method for solving linear partial differential

equations which have been formulated as boundary integral equations. It can be applied

in many disciplines in engineering and science including solid mechanics, fluid

mechanics, acoustics, electromagnetism, fracture mechanics, and plasticity.

In contrast with other energy methods like finite element method, the boundary element

method discretization is only on the problem boundaries. The direct and indirect

boundary element methods are the two branches of the BEM. The direct BEM formulates

the problem in terms of variables that have definite physical meanings, such as

displacements of the boundary nodes of the plate. In contrast, the indirect BEM uses

variables whose physical meanings cannot always be clearly specified.

The advantages of the boundary element method are reducing problem dimensionality,

requiring low memory, it focuses on the body boundary, good for incompressible

materials, easy to define and vary boundary elements, accurate and good for stress

concentrations.

In practicality, there are already several programs which are developed using boundary

element method and adopted for the solution of many engineering problems [37-40].

21

2.6 Raft terminology used in BEM/PLPAK

In this section, important terminologies used in modeling of raft foundation in

BEM/PLPAK are presented. Consider figures 2.7 and 2.8.

2.6.1 Raft foundation:

In the PLPAK, raft foundation is modeled using flat Reisinner’s plate theory [36] (flat

shear deformable plate) with 3 DOF; two rotational D.O.Fs about X and Y axes and the

third D.O.F is a translation in Z axis as shown in figure 2.7 and 2.8.

2.6.2 Boundary elements:

Consider an arbitrary raft with the plan shown in figure 2.7. In the boundary element

method, the problem is discretized only on the boundaries. In the PLPAK, boundaries can

be discretized into customized numbers upon user preferences and problem conditions.

The solution in terms of displacement and tractions is carried out only on the boundary

elements then using other numerical techniques, the internal displacements and tractions

can be calculated.

2.6.3 Nodes:

These nodes are the nodes which define the type of the boundary element whether it is

constant, linear or quadratic boundary element. See figure 2.7.

2.6.4 Extreme points:

These are the points which separate a boundary element from another one. See figure 2.7.

2.6.5 Colum load modeling:

In the proposed technique, there are two methods of modeling columns load. These two

methods are column load modeling without rotational stiffness and column load

modeling with rotational stiffness.

2.6.5.1 Column load modeling without rotational stiffness:

In this case, each column load is located using the coordinates of each corner of the load

area. The loaded area is the interface between raft and column cross section. This area is

considered a square with length of (L) where L is the minimum dimension of the column

cross section. There are three types of loads that can be represented at each loaded area:

1- Force in direction of axis Z distributed on that area. This force represents the

action of the column in the direction of Z-axis.

2- Moment about X-axis.

3- Moment about Y-axis.

22

2.6.5.2 Column load modeling with rotational stiffness:

In this case, each column loaded area is divided into 9 equal squared areas. Each square

has a dimension of L/3. The only load is acting on each subarea is the force in Z-axis.

The resultant forces/moments for the total 9 subareas definitely equal the applied force,

moment about X-axis and moment about Y-axis.

2.6.6 Wall load modeling in PLPAK:

In this section, wall load modeling in PLPAK is presented. There are two methods of

modeling wall load in PLPAK similar to that of column load modeling. The difference is

that wall load is not considered as an assembled load at the interface between the wall

and raft. In this thesis, the wall load is considered as a number of neighboring column

loads. The number of column loads depends on the number of divisions/meshes that wall

is divided in the ETABS model. Each column load can be represented as in section

(2.6.5.1) and (2.6.5.2) depending on the type of analysis wanted to be carried out.

Figure 2.7 Soil and boundary elements discretization for a typical raft on Winkler foundation.

23

2.7 Soil terminology used in BEM/PLPAK In this section, the important terminologies and objects used in modeling of soil in the

PLPAK is presented.

2.7.1 Subgrade reaction (K):

It is an approximate value representing the stiffness of the soil. This value does not

depend on geotechnical investigation so, it is not unique for a certain soil. The subgrade

reaction is based on approximate relationships.

2.7.2 Elastic modulus (E): It is a unique property for a certain soil type. This property is retrieved from the

geotechnical investigation and does not depend on approximate relationships.

2.7.3 Poison’s ratio (v):

It is the ratio between the transverse strain to the longitudinal strain. In soil modeling

within the PLPAK, soil poison’s ratio must be entered only if soil is going to be modeled

using elastic half space.

2.7.4 Soil layers:

As will be mentioned later in section 2.9.2, soil can be modeled as elastic continuum half

space coupled with stiffness method. This continua can be modeled as several layers as

shown in figure. For each layer, it is required to enter the total depth, Poison’s ration and

the Young’s modulus of that layer. Then each layer’s stiffness are computed and

assembled at the interface between soil and raft. The only degree of freedom that is

considered in the layering is the vertical one.

2.7.5 Soil cells/divisions:

There are two methods for modeling foundation-soil system in BEM/PLPAK. The first

method is to model the soil as Winkler. The second method is to model the soil as elastic

half space.

24

In the following subsection, the direct boundary integral equation for shear deformable

plate rested on Winkler/elastic half space is reviewed. The applications of these integral

equations in the PLPAK software are presented.

Figure 2.8 Soil and boundary elements discretization for a typical raft on EHS.

25

2.8 The PLPAK software package [40]

The PLPAK software [40] is a developed research program which is developed by a

research group named CUFE-BE at faculty of engineering Cairo university. PLPAK uses

the direct boundary element method as a numerical method to solve linear partial

differential equation which governs the shear deformable plate bending problems named

Reissner’s plate [36]. It can solve slabs and foundations on elastic foundation such as

Winkler and E.H.S. The program has a unique graphical user interface (GUI) for

structural 2-D modeling analysis of building slabs and foundations. The program consists

mainly of five integrated parts:

1- Model Generator executive file (PLGen).

2- Visualization and simulation executive file (PLView).

3- The command line solver. (Pl.exe).

4- Post-processing and results executive file (PLPost).

5- The core manager executive file (PLCoreMan).

And there are other adds-on packages for the PLPAK such as (PLDesign, EHSPAK,

PTPAK, and LTPAK). The four parts are integrated together to solve and visualize the

results as in the following flow chart shown in figure 2.9.

26

Figure 2.9Flow chart show the PLPAK components

27

The main purposes of each part are listed below:

2.8.1The PlGen:

The main object of this part is to generate the input files. The input files

Includes material properties, columns locations, column loads, load cases, patch loads,

wall support, wall support assembly , wall load assembly, soil support ( EHS-Winkler),

slabs thickness, slabs geometry, boundary discretization, boundary condition, soil support

discretization, opening and beams data.

2.8.2 PLView:

The main purpose of the PLView is to simulate and visualize the boundary element

models generated later using the PLGen module or from user text input. It can be used to

show and hide the boundary elements, boundary element numbering, extreme nodes,

node numbering, points, points numbering, elements directions, loads, supports,

boundary conditions, internal points, additional internal points. Also, the entire model can

be viewed in tables. Each table can be edited easily. Also, a check button is available to

check if the model is geometrically and algorithmically valid or not.

2.8.3 PL.exe:

Simply, it is the executable file containing the solver. The required input files for Pl.exe

are the files containing the entire data of the boundary element model ( .in) file, The

mode of run and the destination of the model on the hard disk (.run) and other input files

such $run$, Lic, $Plcontl$. The output file , definitely are the solution of the problems in

terms of displacement (.u) files and traction (.t) files at the boundary elements. There are

other files accompanied by the output files like (.out), ( .stt) , (.log), (.bs), (.ber), (.ipu),

(ips) text files.

2.8.4 PLPost:

The PLPost is a post-processing tool of the PLPAK. It takes the output files obtained

from PL.exe and present the results in many ways as follows: 1- Demonstrates result at

certain point. 2- Demonstrates result along a certain strip. 3- Demonstrates result over

certain area as contour map. 4- Demonstrates soil reactions or soil contact pressure. 5-

Demonstrates results in a tabulated form. Also, in the PLPost any required load

combination could be performed.

This part is responsible for presenting the results of the boundary element model. This

part shares the same graphical interface with the PLView, because it represents the results

over the graphical representation of the boundary element model.

28

2.8.5 PLCoreman:

The PLCoreMan is the head of the PLPAK program. It is the manager of all files and the

caller of the executable files and other subroutines, through which, you may run the other

PLPAK components. It reads the input data files then calls the command-line solver

PL.exe which - as mentioned above - solves the problem and generates output files.

PLCoreMan also connect all parts of the PLPAK package. Also, through PLCoreMan,

modes of run and solution can be changed if needed.

2.8.6 Used PLPAK files

In this section, important input and output files that are used in this thesis are presented in

details.

2.8.6.1 PLGEN text format files

In this section, the PLGEN text format files are described in details. These are 14 files

named as follows.

1- model.txt :

This file contains the name of the other 13 files to be read later as shown in figure

2.10.

Figure 2.10 The structure of the

model.txt file.

29

2- Material .txt:

In this thesis, material name and its properties is defined as shown in figure 2.11.

3- Slab.txt :

This file contains raft data as shown in figure 2.12.

4- Soil support .txt :

This file contains the soil support data as shown in figure 2.13.


material .txt file.

Figure 2.12 The structure of the slab .txt file.

Figure 2.13 The structre of the soil support

.txt file.

30

The column load.txt and Lc.txt structure are presented later in chapter 3. The

other files contain zero as they will not be used.

2.8.6.2 Other files

1- .aip file :

This file contains the number of additional internal points needed to carry out post

processing. Also contains the coordinates of each internal point as shown in figure

2.14.

2- .ipu file :

This file contains the post processing results at the internal points. The results are

presented in terms of Uz , Rx and Ry as shown in figure 2.15.

3- .run file :

This file contains the path of the input and output files generated by PL.exe as

shown in figure 2.16

Figure 2.14 The structure of the .aip file.

Figure 2.15 The structure of the .ipu file.


.run file.

31

2.9 Soil modeling in PLPAK:

In PLPAK, soil can be represented as Winkler continous springs or as elastic half space.

The later is based on Mindlin [20], Boussinesq [27], and Steinbrenner [28] equation are

coupled with boundary element method to represent the soil as an elastic continuum

stiffness cells [30] as reviewed in section 2.3.2.

2.9.1 Winkler model:

In BEM, soil is modeled as a continuous Winkler spring cells with vertical DOF only

[41] as shown in figure 2.7. In the Winkler model, soil cells are considered uncoupled.

Each soil cell deflection is function only of the applied load. There is no contribution of

the other Winkler patches in the behavior of a certain patch.

Soil underneath a raft is modeled as Winkler springs in PLPAK by directly drawing soil

patches underneath the corresponding raft domain only. Hence, stiffness of soil and its

divisions in two directions are defined. These procedures are shown in Figures 2.17 and

2.18.

32

Figure 2.17 The Winkler cell discretization in the PLView.

Figure 2.18 Practical raft on Winkler modeled using PLGen

33

2.9.2 EHS modeling:

In BEM, soil can be represented as an elastic continuum half space using many methods

[30]. In the PLPAK, the BEM coupled with the stiffness matrix approach are

implemented in order to model soil as a continuous coupled media. In this method of

modeling, soil is only modeled at the interface between raft and soil as a continuous

coupled soil cells or patches. Each single patch has stiffness in direction of the Z-axis

only. This interface is considered as a condensation of the entire stiffness of the soil

continuum at the top layer of the soil.

Soil underneath a raft is modeled as elastic half space in PLPAK by directly drawing four

side polygon containing raft domain, define stiffness of soil and divide it to specified

number in two directions. Soil underneath raft is modeled by defining stiffness of soil in

PLPAK by –ve value then the EHSPAK package is triggered to define the soil profile as

shown in Figure 2.7. This package can export stiffness matrix of soil hence the rest of

solution procedures are carried out to get results in the PLPost.

Figure 2.19EHSPAk add-on start menu

34

2.6 Conclusions In this chapter, an overview about the finite element method is presented. The ETABS

program is presented with its main components and some modeling terminologies. Also,

the boundary element method and its two branches were reviewed.. The PLPAK software

package and its main components were presented with its available methods to model soil

with modeling terminology about SSI modeling.

In the next chapter, the proposed technique is presented. Each file structure is also

illustrated.

35

Chapter 3 The Proposed New Technique

3.1 Introduction

In the previous chapter, the finite element method and its applications were discussed.

The ETABS software and its components were illustrated. Also, BEM was reviewed. The

PLPAK software and its main components were presented. Modeling of Soil as Winkler

uncoupled springs and as EHS was also discussed. In this chapter, the proposed technique

of including the SSI in the lateral analysis of buildings is discussed. The developed

Translator.exe is illustrated in detail followed by an illustrative example. The entire

methodology of the work is illustrated in details with flow chart presentation. The

developed graphical user interface is presented as a method to automate the proposed

analysis technique.

3.2 The developed translator

In this section, the developed translator is illustrated in detail. The methodology of the

translation is discussed. The proposed technique to implement translation stiffness is

illustrated. Also, the proposed technique to implement the rotational stiffness in the

analysis is illustrated. The input and output files are presented in detail.

3.2.1 Translator.exe

The main object of this executable file is to translate the required data from the

superstructure model in ETABS to be modeled in the PLPAK software. The translation

procedure is carried out after the analysis of the superstructure in ETABS is done. The

user has to export five files which will be used by translator to generate the PLPAK raft-

soil model. The input and output files the that translator uses are presented in details in

the below subsections.

3.2.1.1 Input files

In this section, the translator input files are presented.

1- IterID.txt file:

This file contains the number of iterations that has been done. In the beginning, no

iteration is done, so the value written in the file is zero. This file will be used in

later section if it is required to carry out more than one iteration.

2- ETABS database file:

These five files are presented in section 2.3.3.2 in details.

36

3- MDim.txt file:

This file contains the minimum dimension of the columns in the structural plan.

This will be used later to define and locate the loaded area of each column/wall in

PLGEN model.

3.2.1.2 Output files

1- Load case name .aip files :

These files are generated for each load case exported from ETABS model. The

structure of this file is presented previously in section 2.3.3.2

2- Load Case name .c files:

These files are generated for each load case exported from ETABS model. Each

file contains the support reactions of a certain load case. The structure of this file

is shown in figure 3.1.

3- Load Case name .k files:

These files are generated for each load case exported from ETABS model. Each

file contains the support label and Winkler spring stiffness value. This file is used

as a data updater for the ETABS model data. The structure of this file is shown in

figure 3.2.

4- LC.txt file :

This file is written in PLPAK format. This file contains the number of the load

cases translated from ETABS and the name of each load case. The structure of

this file is shown in figure 3.3.

Figure 3.1 he structure of . c file.

Figure 3.2 The structure of the .k file.


LC.txt file.

37

5- Column Load .txt file:

This is written in PLPAK format. This file contains the number of column load

and the column load values for each load case. The number of column loads can

be the same number of the supports; this is the case of column load modeling

without rotational stiffness or can be the number of supports multiplied by 9; in

this case, the rotational stiffness is implemented. The structure of this file is

shown in figure 3.4.

6- $Runstiff$ file:

This file is generated from translator. This file contains the path of the .c file, .k

file and .ipu file mentioned previously in section 2.8.6.2. The structure of this file

is shown in figure 3.5.

Figure 3.4 The structure of the column load.txt file.

Case load 1

Case load n

Figure 3.5 The structure of the $Runstiff$ file.

38

The input and output files that are used by the translator can be illustrated in a flow chart

diagram as shown in figure 3.6.

3.3 Rotational stiffness implementation in SSIPAK/PLPAK

In this section the assumption and the procedure to implement the rotational stiffness in

the proposed analysis is illustrated. Consider a part of a raft surrounding a column as

shown in figure 3.7. In order to consider the rotational stiffness of the raft-soil system in

the analysis of buildings with SSI, a relatively small segment of the raft is considered.

This segment is assumed to have linear behavior. This means that it tends to rotate as a

rigid body. This assumption is acceptable as long as the dimensions of this segment does

not exceed the column dimensions. Knowing the deflection of two points on the line and

assuming the rotational angle is very small so that Ø = sin Ø = tan Ø. The rotation about

Y-axis can be estimated as Ryy = (Uz9 –Uz5) /L where the rotation about X-axis can be

estimated as Rxx=(Uz7 –Uz3) /L.

Figure 3.6 The input and output files used by translator.

39

3.4 Illustrative Example

In this section, an illustrative example is presented with detailed steps. This is to show the

process to translate the data of the super-structure ETABS model and construct the raft-

soil PLGEN model in PLPAK.

1- Structural drawings: In most cases, the designers have the structural drawings in

cad formatting. It is the key to begin the modeling on ETABS as shown in figure

3.8.

2- ETABS 3D Model: Designers always use the structural drawings to construct the

ETABS 3d modeling as shown in figure 3.9. ETABS model have to be modeled

in a correct way. All load cases should be included. For the first iteration, the end

conditions for each column will be fixed or hinged.

Figure 3.7 The rotational stiffness implementation procedure.

40

Figure 3.8 The structural drawings using AutoCAD.

41

Figure 3.9 The ETABS 3D model.

42

3- Data base file: in this step, the user have to open the data base of the ETABS and

begin to select some important files which will be used later as shown in figure

3.10 (a & b).

Figure 3.10 a & b The steps to export the database file containing the required text files.

43

It should be noted that different load cases can be selected. Also, user has to export the

following files. The structure of these file was presented in section 2.3.3.2. These files are

a- Point coordinates

b- Static load cases figure

c- Support (Restraints) Assignments figure

d- Support reactions figure

The database file which will be exported from ETABS is shown in figure 3.11.

4- Run translator.exe:

In this step, translator .exe is executed. The input and output files that required for

the translation process is presented previously in section 3.2.1.

5- PLPAK model:

In this step, PLGEN model is generated. The generated files from translator are

then imported in text formatting. The model is shown in figure 3.12-3.13.

Figure 3.11 The database file containing the required text files.

44

Figure 3.12 The raft model in PLGEN.

Figure 3.13 The raft model in PLVIEW.

45

3.5 Methodology and automation

In this section, a flow that chart describes the entire process of including soil-structure

interaction in the analysis of building is presented as shown in figure 3.14. A detailed

description of thte function of each part is presented. The proposed new technique can be

summarized in the following steps. These steps can generally be divided into 4 main

groups of steps.

a- The preparation of the models

This includes the preparation of the ETABS and PLPAK model.

1- Prepare the structural drawing as discussed in section 3.4-1.

2- Import the structural drawing to ETABS and create ETABS model as discussed in

section 3.4-2.

3- Run analysis for the ETABS model and check results.

4- Export the required files listed below:

i. Model.e2k.

ii. Point coordinates .txt.

iii. Support (Restraint).txt.

iv. Static load cases.txt.

v. Support reactions.txt.

vi. Point spring reactions.txt.

5- Save the ETABS files in one folder.

6- Create the raft model on PLGEN. This model includes only the raft, soil data. No

loads are included in this step.

7- Export the PLGEN into text formatting and generate the 14 files described in

section 2.8.6.

8- Save the PLGEN model and the text formatting files in one folder.

b- Analysis

1- The analysis starts with executing the translator.exe file.

2- First, the IterID.txt is read. If zero, the support reactions file will be read

besides the other files. If not, it means the first iteration is done. So, the

translator will read the point spring force.txt besides the other files.

3- The user will be asked about the minimum dimension of the column. It is

required to distribute the load on an adequate area. Also to define the small

segment which is important for the rotational stiffness’s calculation.

4- The translator.exe will translate the ETABS and generate two file in PLPAK

text formatting.

5- Also, load case name . k , load case name . c , load case name. aip and

$RunStiff$ files are generated.

46

c- Post processing

1- Modify the run mode of PL.exe from 1 to 2 in the load case name. run file.

This file is located at each load case folder.

2- Copy the load case .aip file and paste it in its corresponding load case file.

3- Run again from the PLCorman the PL.exe.

4- Load case name.ipu file is generated for each load case.

5- Execute the spring stiffness calculator.exe

6- The load case name.k for each load case is generated.

d- Edit the model.e2k

1- Run the edit etabs .e2k.exe.

2- The new model.e2k file is generated.

3- Import the new model.e2k file and check the new model.

47

Fig

ure

3.1

4 F

low

ch

art

sh

ow

s th

e p

rop

ose

d t

ech

niq

ue.

48

3.6 The graphical user interface SSIPAK

In this section, a graphical user interface for the work done in this thesis is presented. The

aim of the GUI SSIPAK is to automate the previous processes described in section 3.5 to

be easy for practical use. The GUI SSIPAK consists of 12 main buttons and controls as

shown is figure 3.15. A detailed explanation for each control is presented as below.

1- Control 1 : a browse button to define the path of the ETABS model and the

exported files from ETABS.

2- Control 2 : a browse button to define the path of the PLPAK/PLGEN model and

the PLPAK text format files.

3- Control 3 : the minimum column dimension has to be entered by theuser in this

box.

4- Control 4 : execute the translator.

5- Control 5 : copy and replace the old LC.txt and Column load.txt.

6- Control 6 : open new window of the PLGEN.

Figure 3.15 The graphical user interface (SSIPAK).

1

2

3

4

5

6

7

8

9

10

11

0

12

0

49

7- Control 7 : copy the .aip files into corresponding load case folder and modify the

run mode from 1 to 2.

8- Control 8 : a drop down menu to select which load case for which spring stiffness

is to be calculated.

9- Control 9 : run the spring stiffness calculator

10- Control 10 : shows the new values of Kz ,Krx and Kry in tabulated format.

11- Control 11 : execute the edit etabs .e2k file.

12- Control 12 : open new window of ETABS.

3.7 Conclusions

In this chapter, the translator .exe is presented. The input and output files required for the

translator are described in detail. An illustrative example that shows the detailed steps to

translate the required model data from ETABS model to PLPAK model is presented. The

rotational stiffness implementation technique to include the rotational stiffness in the soil-

structure interaction is also illustrated. The methodology used to include soil-structure

interaction in the analysis of buildings is illustrated with flow chart. Finally, a graphical

user interface to automate the entire process is developed to facilitate the use of this

technique.

50

Chapter 4 Numerical examples

4.1 Introduction In the previous chapter, the proposed technique to account for the soil structure

interaction in the analysis of multi-story building resting on raft foundation was

discussed. In this chapter, several Numerical example sets are tested and results are

compared to numerical methods and previously published results to verify the proposed

technique. In addition, results are also compared to those obtained from the finite element

method.

4.2 Example set 1

It is as 10 Story framed building with symmetric plan subjected to static lateral force.

In this example, a typical framed building with symmetric plan and elevation as shown in

figure 4.1 consists of 10 stories, 5 meter for the first story and 3m for the 9 remaining

stories remaining. This structure is subjected to static lateral loading. A 0.5 t/m static

lateral distributed load is applied in the positive direction of X- axis. All columns of the

building are 0.4 x 0.7 m except the corner columns that are 0.5 x 0.5 m. Also, all slabs are

0.18 m with beams 0.3 x 0.7 m as shown in figure 4.1. The raft foundation thickness is

1.2 m. Analyses were carried out using substructure approach where the super structure is

modeled using ETABS - the well-known finite element commercial program – figure 4.2.

The raft foundation and the underneath soil are modeled using PLPAK – a developed

package for solving shear deformable plates on Winkler and elastic half space based on

boundary element method and stiffness method figure 4.3. Lateral deflection, lateral

deflection ratios (SSI/NSSI), Drift and drift ratios (NSSI/SSI) are obtained. The results

are compared to the same structure modeled using the direct method. SAP2000 – finite

element well known commercial program is used figure 4.4– where the soil is modeled

as isotropic, elastic material using solid element with 8 nodes in each corner, at each

corner 3 translation degree of freedom. Different types of soil (E=2000, 5000, 10000 and

20000 t/m2) with ν = 0.4, 0.4, 0.25 and 0.25 respectively are used. Also two types of

equivalent Winkler method are used in the comparison. The subgrade reactions

corresponding to a certain value of E are obtained using Boit and Vesic equation shown

below.

51

Figure 4.1. Exapmle 1 plan

52

Figure 4.3 PLPAK 2D modeling of example 1 raft foundation.

Figure 4.2 ETABS 3D modeling of example 1 super structure.

53

Figure 4.4 SAP2000 3D modeling of example 1- Direct method.


54

Example 1 Results:

For E=2000 t/m2

(With rotational stiffness)

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3 3.5

Sto

ry H

eig

ht

(m)

Lateral Deflection Ratio SSI/NSSI

CONTINUM MODEL

FIXED BASE

Proposed technique

Winkler according to Boit equation

Winkler according to Vesic equation

Figure 4.6 Lateral Deflection in X-direction for example 1- E=2000 t/m2 (with rotational stiffness).

Figure 4.7 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=2000 t/m2 (with

rotational stiffness).

0

5

10

15

20

25

30

35

0 0.05 0.1 0.15

Sto

ry H

eig

ht

(m)

Lateral Deflection

Lateral Deflection (m)

CONTINUM MODEL

FIXED BASE

Proposed technique



55

0

5

10

15

20

25

30

35

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique



0

5

10

15

20

25

30

35

0 0.001 0.002 0.003 0.004 0.005 0.006

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUUM MODEL

Fixed Base

Proposed technique



Figure 4.9 Inter story drift in X-direction for example 1- E=2000 t/m2 (with rotational stiffness).

Figure 4.8 Drift SSI/NSSI ratio in X-direction for example 1 E=2000 t/m2 (with rotational

stiffness).

56

- For E=2000 t/m2

(without rotational stiffness):

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5

Sto

ry H

eig

ht

(m)


Lateral deflection ratio

CONTINUM MODELHINGED BASEProposed technique without rotational stiffnessWinkler according to Boit equationWinkler according to Vesic equation

0

5

10

15

20

25

30

35

0 0.05 0.1 0.15 0.2

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

HINGED BASE

Proposed technique without rotational stiffness



Figure 4.10 Lateral Deflection in X-direction for example 1 E=2000 t/m2 (without rotational

stiffness).

Figure 4.11 Lateral Deflection SSI/NSSI in X-direction for example 1 E=2000 t/m2 (without


57

Figure 4.12 Inter story drift in X-direction for example 1 E=2000 t/m2 (without rotational stiffness).

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Sto

ry H

eig

ht

(m)

Interstory drift

INTER STORY DRIFT

Continuum ModelHinged baseProposed technique without rotational stiffnessWinkler according to Boit equationWinkler according to Vesic equation

0

5

10

15

20

25

30

35

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODEL

HINGED BASE




Figure 4.13 Drift SSI/NSSI ratio in X-direction for example 1- E=2000 t/m2 (without rotational

stiffness).

58

- For E=5000 t/m2

(with rotational stiffness):

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Sto

ry H

eig

ht

(m)

Lateral Deflection


CONTINUM MODELFIXED BASEProposed TechniqueWinkler according to Boit equationWinkler according to Vesic equation

0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)


Lateral Deflection ratio SSI/NSSI

CONTINUM MODEL

FIXED BASE

Proposed Technique






59

0

5

10

15

20

25

30

35

0 0.001 0.002 0.003 0.004 0.005

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODELFIXED BASEProposed TechniqueWinkler according to Boit equationWinkler according to Vesic equation

0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODELFIXED BASE

Proposed Technique



Figure 4.17 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (with rotational stiffness).


60

- For E=5000 t/m2


0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

HINGED BASE

Proposed Technique without rotational stiffness



0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

HINGED BASE




Figure 4.18 Lateral Deflection in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

Figure 4.19 Lateral Deflection Ratio SSI/NSSI in X-direction for example 1- E=5000 t/m2 (without


61

Figure 4.20 Inter story drift in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

HINGED BASE




0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODEL

HINGED BASE




Figure 4.21 Drift SSI/NSSI ratio in X-direction for example 1- E=5000 t/m2 (without rotational stiffness).

62

- For E=10000 t/m2


0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

FIXED BASE

Proposed Technique



0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

FIXED BASE

Proposed technique





Figure 4.22 Lateral Deflection in X-direction for example 1- E=10000 t/m2 (without rotational

stiffness).

63

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Fixed BASE

proposed technique


Winkler according Vesic equation

0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique





stiffness).

64

- For E=10000 t/m2


0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1 0.12

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

HINGED BASE




0

5

10

15

20

25

30

35

0 0.5 1 1.5

Sto

ry H

eig

ht

(m)


CONTINUM MODEL

HINGED BASE


Winkler according Boit equation


Figure 4.26 Lateral Deflection in X-direction for example 1- E=10000 t/m2(without rotational stiffness).



65

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008 0.01 0.012

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Hinged base




0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00 2.50

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio


Figure 4.28 Inter story drift in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

Figure 4.29 Drift SSI/NSSI ratio in X-direction for example 1- E=10000 t/m2 (without rotational stiffness).

66

- For E=20000 t/m2


0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06

Sto

ry H

eig

ht

(m)

Lateral Deflection


CONTINUM MODEL

FIXED BASE

Proposed technique



0

5

10

15

20

25

30

35

0 0.5 1 1.5

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

FIXED BASE

Proposed technique






67

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

Continuum Model

Fixed base

Proposed technique



0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODELFIXED BASEProposed techniqueWinkler according to Boit equationWinkler according to Vesic equation


Figure 4.32 Drift SSI/NSSI ratio in X-direction for example 1- E=20000 t/m2 (with rotational stiffness).

68

- For E=20000 t/m2


0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1

Sto

ry H

eig

ht

(m)




0

5

10

15

20

25

30

35

0.95 1 1.05 1.1 1.15

Sto

ry H

eig

ht

(m)



CONTINUM MODEL

FIXED BASE





stiffness).



69

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008 0.01 0.012

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

Continuum Model

Hinged base




0

5

10

15

20

25

30

35

0.00 0.50 1.00 1.50 2.00

Sto

ry H

eig

ht

(m)

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE




Figure 4.37 Inter story drift in X-direction for example 1- E=20000 t/m2 (without rotational

stiffness).


stiffness).

70

Table 4.1The fundamental periodic time in seconds for example 1 – with rotational stiffness

Continuum Model Proposed

technique

Boit Vesic

NSSI 1.8776 1.8776 1.8776 1.8776

E=2000 2.54 2.22 2.74 3.25

Ratio 1.35 1.18 1.46 1.73

E=5000 2.141 2.06 2.13 2.27

Ratio 1.14 1.10 1.13 1.21

E=10000 2.04 1.96 2.13 2.27

Ratio 1.09 1.04 1.13 1.21

E=20000 1.98 1.94 2.05 2.09

Ratio 1.05 1.03 1.09 1.11

Table 4.2 The fundamental periodic time in seconds for example 1 – without rotational stiffness

Continuum Model Proposed technique Boit Vesic

NSSI 2.643 2.643 2.643 2.643

E=2000 3.05 2.94 3.29 3.71

Ratio 1.15 1.11 1.24 1.40

E=5000 2.836 2.8 2.82 2.92

Ratio 1.07 1.06 1.07 1.10

E=10000 2.77 2.74 2.82 2.92

Ratio 1.05 1.04 1.07 1.10

E=20000 2.71 2.69 2.67 2.8

Ratio 1.03 1.02 1.01 1.06

71

4.3 Example set 2

It is a 10 Story shear wall framed building subjected to static lateral force. In this

example, a typical shear wall framed building shown in figure 4.38 consists of 10 stories,

5 meter for the first story and 3m for the 9 story remaining. This structure is subjected to

static lateral loading. A 0.5 t/m static lateral distributed load is applied in the positive

direction of X- axis. All columns of the building are 0.4 x 0.7 m except the corner

columns are 0.5 x 0.5 m. Also, all slabs are 0.18 m with beams 0.3 x 0.7 m as shown in

figure 4.38. The raft foundation thickness is 1.2 m. Analyses were carried out using

substructure approach where the super structure is modeled using ETABS - the well-

known finite element commercial program – figure 4.39. The raft foundation and the

underneath soil are modeled using PLPAK – a developed package for solving shear

deformable plates on Winkler and elastic half space based on boundary element method

and stiffness method figure 4.40. Lateral deflection, lateral deflection ratios (SSI/NSSI),

Drift and drift ratios (NSSI/SSI) are obtained. The results are compared against the same

structure modeled using direct method. SAP2000 – finite element well known

commercial program is used figure 4.41 – where the soil is modeled as isotropic, elastic

material using solid element with 8 nodes in each corner, at each node 3 translation

degree of freedoms. Different types of soil ( E=2000,5000,10000 and 20000 t/m2) with ν

= 0.4,0.4,0.25 and 0.25 respectively are used. Also two types of equivalent Winkler

method are used in the comparison. The subgrade reactions corresponding to a certain

value of E are obtained using Boit and Vesic equation previously mentioned.

72

Figure 4.38 Exapmle 2 plan.

73

Figure 4.39 ETABS 3D modeling of example 2 super structure.

Figure 4.40 PLPAK 2D modeling of example 2 raft foundation.

74

Figure 4.41 SAP2000 2D view.


75

Example 2 Results:

For E=2000 t/m2

(with rotational stiffness)

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06

Sto

ry H

eig

ht

m


lateral Deflection m

CONTINUM MODEL

FIXED BASE

Proposed technique



Figure 4.43 Lateral Deflection in X-direction for example 2- E=2000 t/m2 (with rotational

stiffness).

0

5

10

15

20

25

30

35

0 1 2 3 4

Sto

ry H

eig

ht

m



CONTINUM MODEL

FIXED BASE

Proposed technique





76

0

5

10

15

20

25

30

35

0 0.001 0.002 0.003

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Fixed Base

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 1 2 3 4

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique



Figure 4.46 Drift SSI/NSSI ratio in X-direction for example 2- E=2000 t/m2 (with


77

- For E=2000 t/m2

(without rotational stiffness)

0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Sto

ry H

eig

ht

m



CONTINUM MODEL

FIXED BASE

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 1 2 3 4 5

Sto

ry H

eig

ht

m



CONTINUM MODELHINGED BASEProposed techniqueWinkler according to Boit equationWinkler according to Vesic equation



78

0

5

10

15

20

25

30

35

0 0.001 0.002 0.003 0.004 0.005 0.006

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Hinged Base

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 2 4 6 8 10

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

HINGED BASE

Proposed technique





79

- For E=5000 t/m2

(Rotations are fixed)

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04

Sto

ry H

eig

ht

(m)

Drift

lateral Deflection (m)

CONTINUM MODEL

FIXED BASE

Proposed technique





0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5

Sto

ry H

eig

ht

m


Lateral defelction ratio

CONTINUM MODEL

FIXED BASE

Proposed technique




80

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002

Sto

ry H

eig

ht

m

Drift

INTER STORY DRIFT

CONTINUM MODEL

FIXED BASE

Proposed technique



Figure 4.53 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2 (with rotational

stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique




81

- For E=5000 t/m2


0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Sto

ry H

eig

ht

m



CONTINUM MODEL

HINGED BASE

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5

Sto

ry H

eig

ht

m

Laterl Deflection Ratio SSI/NSSI


CONTINUM MODEL

HINGED BASE

Proposed technique




rotational stiffness) .

82

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

HINGED BASE

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 1 2 3 4

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

HINGED BASE

Proposed technique



Figure 4.58 Drift SSI/NSSI ratio in X-direction for example 2- E=5000 t/m2

(without rotational stiffness).

83

- For E=10000 t/m2

(Rotations are fixed)

0

5

10

15

20

25

30

35

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Sto

ry H

eig

ht

m



CONTINUM MODEL

FIXED BASE

Proposed technique



Figure 4.59 Lateral Deflection in X-direction for example 2- E=10000 t/m2 (with rotational

stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m



CONTINUM MODELFIXED BASEProposed techniqueWinkler according to Boit equationWinkler according to Vesic equation



84

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Fixed Base

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique

Winkler aacording to Boit equation



stiffness).

85

- For E=10000 t/m2



stiffness).

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05

Sto

ry H

eig

ht

m



CONTINUM MODEL

HINGED BASE

Proposed technique



0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m



CONTINUM MODELHINGED BASEProposed techniqueWinkler according to Boit equationWinkler according to Vesic equation


rotational stiffness) .

86

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

Continum Model

Hinged Base

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

HINGED BASE

Proposed technique


Winkler accoding to Vesic equation


stiffness).

87

- For E=20000 t/m2

(with rotational stiffness)

0

5

10

15

20

25

30

35

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Sto

ry H

eig

ht

m



CONTINUM MODEL

FIXED BASE

Proposed technique





0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m



CONTINUM MODEL

FIXED BASE

Proposed technique




88

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Fixed base

Proposed technique




89

- For E=20000 t/m2

(Rotations are free)

0

5

10

15

20

25

30

35

0 0.01 0.02 0.03 0.04 0.05

Sto

ry H

eig

ht

m


lateral Deflection (m)

CONTINUM MODEL

HINGED BASE

Proposed technique




stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

(m)


Lateral deflectionj ratio

CONTINUM MODEL

FIXED BASE

Proposed technique




stiffness).

90

0

5

10

15

20

25

30

35

0 0.0005 0.001 0.0015 0.002 0.0025

Sto

ry H

eig

ht

(m)

Drift

INTER STORY DRIFT

CONTINUM MODEL

Fixed base

Proposed technique




stiffness).


stiffness).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2

Sto

ry H

eig

ht

m

Drift Ratio

Drift Ratio

CONTINUM MODEL

FIXED BASE

Proposed technique



91

Table 4.3 The fundamental periodic time in seconds for example 2 – with rotational stiffness.

Continuum Proposed

technique

Boit Vesic

Fixed Base 1.13 1.13 1.13 1.13

E=2000 1.94 1.71 1.46 1.48

Ratio 1.72 1.51 1.29 1.31

E=5000 1.66 1.41 1.42 1.51

Ratio 1.47 1.25 1.26 1.34

E=10000 1.43 1.33 1.38 1.41

Ratio 1.27 1.18 1.22 1.25

E=20000 1.34 1.31 1.33 1.36

Ratio 1.19 1.16 1.18 1.20

Table 4.4 The fundamental periodic time in seconds for example 2 – without rotational stiffness.

Continuum Proposed

technique Boit Vesic

Hinged Base 1.14 1.14 1.14 1.14

E=2000 1.99 1.72 1.718 1.8

Ratio 1.75 1.51 1.51 1.58

E=5000 1.6 1.47 1.718 1.76

Ratio 1.40 1.29 1.51 1.54

E=10000 1.47 1.38 1.53 1.68

Ratio 1.29 1.21 1.34 1.47

E=20000 1.37 1.33 1.42 1.489

Ratio 1.20 1.17 1.25 1.31

92

4.4 Example set 3

This example set consists of 4 examples; two of these examples are bare framed multi-

story building with 4 and 16 stories while the other two examples are framed-shear wall

multi-story building with 4 and 16 stories. The results in terms of time period (T) per

seconds are compared and verified with respect to the work done by B.R. Jayalekshmi

and H.K.Chinmayi [8]. The structural layout and dimensions are taken as shown in figure

4.75. The section properties and soil properties are considered due to the shown values in

table 4.5 and 4.6 respectively.

Figure 4.75 The structural layout and dimensions [8].

Table 4.5 Section properties for example set 3 [8].

Soil Type Description Poission's ratio

Young's

modulus E

(kn/m2)

Sb Rock 0.3 8.40E+06

Sc Dense soil 0.3 1.91E+06

Sd Stiff soil 0.35 4.46E+05

Se Soft soil 0.4 1.03E+05

No. of

stories Column Dimensions(m)

Shear wall

thickness (m)

Upto3 stories Above 3 stories

4 0.32x0.32 0.32x0.32 0.15

16 0.6x0.6 0.5x0.5 0.25

Table 4.6 The soil properties according to work done by [8].

93

Bare frame results:

0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type

Fundamental Period - Mode 1 - 4 Floors

continuum model [8]Proposed technique

Figure 4.76 The time period for mode 1- 4 floors.

0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type

T - Mode 3 - 4 Floors

Continuum model [8]

Proposed technique

Figure 4.77 The time period for mode 3 - 4 floors.

0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type

T - Mode 4- 4 Floors

Continuum model [8]

Proposed technique


94

Figure 4.79 The time period for mode 1- 16 floors.

00.5

11.5

22.5

33.5

4

Tim

e P

erio

d (

sec)

Soil type


Continuum model [8]

Proposed technique

0

0.5

1

1.5

2

2.5

3

Tim

e P

erio

d (

sec)

Soil type


Continuum model [8]

Proposed technique


0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type


Continuum model [8]

Proposed technique


95

Table 4.7 Time period for different modes of shape – 4 floors.

Continuum model [8] Proposed technique Ratio

Mode 1 Mode 3 Mode 4 Mode 1 Mode 3 Mode 4

Fixed 0.85 0.71 0.26 0.857 0.72 0.26 1.01

sb 1 0.75 0.29 0.86 0.72 0.26 0.86

sc 1 0.75 0.29 0.868 0.72 0.26 0.87

sd 1 0.75 0.29 0.872 0.72 0.26 0.87

se 1.01 0.76 0.29 0.88 0.72 0.263 0.87

Table 4.8 Time period for different modes of shape - 16 floors.

Continuum model [8] Proposed technique Ratio


Fixed 3 2.28 0.89 2.97 2.42 0.94 0.99

sb 3.51 2.5 1.01 3.02 2.42 0.95 0.86

sc 3.52 2.5 1.01 3.17 2.42 0.95 0.90

sd 3.55 2.5 1.02 3.24 2.42 0.95 0.91

se 3.66 2.51 1.02 3.33 2.42 0.95 0.91

96

Shear wall results:


0

0.2

0.4

0.6

0.8

1

1.2T

ime

Per

iod

(se

c)

Soil type


Continuum model [8]

Proposed technique

0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type

T- Mode 3 - 4 Floors

Continuum model [8]

Proposed technique


0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type

T - Mode 4- 4 Floors

Continuum model [8]

Proposed technique


97


0

0.5

1

1.5

2

2.5

Tim

e P

erio

d (

sec)

Soil type


Continuum model[8]

Proposed technique

0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type


Continuum model [8]

Proposed technique


0

0.2

0.4

0.6

0.8

1

1.2

Tim

e P

erio

d (

sec)

Soil type


Continuum model [8]

Proposed technique


98


Mode Continuum [8] Proposed technique Ratio


Fixed 0.18 0.159 0.055 0.165 0.16 0.06 0.917

Sb 0.19 0.158 0.045 0.199 0.17 0.06 1.04

Sc 0.22 0.158 0.045 0.25 0.17 0.06 1.13

Sd 0.29 0.158 0.046 0.31 0.17 0.08 1.06

Se 0.41 0.158 0.046 0.44 0.19 0.15 1.07


Mode Continuum [8] Proposed technique Ratio


Fixed 1.28 0.5 0.27 1.279 0.48 0.264 1.00

Sb 1.34 0.52 0.28 1.47 0.48 0.28 1.10

Sc 1.46 0.52 0.3 1.61 0.48 0.28 1.10

Sd 1.76 0.53 0.33 1.93 0.48 0.3 1.10

Se 2.25 0.54 0.35 2.28 0.48 0.327 1.01

99

4.5 Example set 4

This example consists of 2 examples; one of these examples is bare framed multi-story

building with 6 stories while the other example is framed multi-story building with 12

stories. The results in terms of time period (T) per seconds are compared and verified

with respect to the work done by [12]. The structural layout and dimensions are taken as

shown in figure 4.88. The soil properties are considered due to the shown values in table.

Table 4.11 Section properties according to work done by [12].

Model Beam Size

(cm)

Slab thickness

(cm)

Column

(cm)

Raft thickness (cm)

6-Story 25x60 15 60x60 60

12-Story 25x60 15 80x80 100

Table 4.12 The soil properties according to work done by [12].

Soil

condition

Poisson's

ratio

Modulus of

elasticity E

(t/m2)

Kx

(t/m2/m)

Kyb

(t/m2/m)

Kz

(t/m2/m)

Stiff soil 0.33 24480 1127.21 1127.21 1417.29

Medium

soil

0.33 12240 563.6 563.6 708.64

Soft soil 0.33 6120 281.8 281.8 354.32

Figure 4.88 The structural layout and dimensions according to work done by [12].

100

6-floors multi-story framed building results:

Table 4.13 The fundamental time period for 6-floors multi-story framed building.

Time (sec) Raft on

Winkler [12] Proposed technique Ratio

Fixed 0.98 0.98 1.00

Stiff Soil 1.07 1.00 0.93

Medium Soil 1.12 1.04 0.93

Soft Soil 1.21 1.09 0.90

0.00

0.50

1.00

1.50

Fixed Stiff Soil Medium Soil Soft Soil

Tim

e P

eri

od

T (

sec)

End Condition

Time period (sec) - 6 Stories

Raft on Winkler [12]

Proposed technique

Figure 4.89 The fundamental time period for 6-floors mutli-story framed building.

101

12-floors multi-story building results:

Table 4.14 The fundamental period for 12-floors multi-story framed building.

Time (sec)

Raft on

Winkler

[12]

Proposed

technique Ratio

Fixed 1.92 1.87 0.97

Stiff Soil 2.15 1.98 0.92

Medium Soil 2.32 2.08 0.90

Soft Soil 2.60 2.24 0.86

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Fixed Stiff Soil Medium Soil Soft Soil

Tim

e P

eri

od

T (

sec)

End Condition

Time period (sec) - 12 Stories

Raft on Winkler [12]

Proposed technique

Figure 4.90 The fundamental period for 12-floors multi-story framed building.

102

Chapter 5 Summary, Conclusions and Recommendations for

Future Work

4.1 Summary

This thesis presents a new method to consider soil-structure interaction in the analysis of

the multi-story buildings. This is done by coupling the 3D modelling tool of ETABS and

the EHS in PLPAK to consider SSI in the lateral analysis of multi-storey buildings. This

coupling technique is considered as a modified sub-structuring technique. This coupling

technique has advantages over the current technique in practice. These advantages are

mainly the static condensation is carried out at the columns-raft interface not at the raft-

soil interface, this can produce much less degrees of freedom for which the static

condensation is carried out compared to the number of degrees of freedom that can be

produced from the case of applying contestation at raft-soil interface. Also, the number

of iterations required to achieve a certain convergence in the proposed technique is one or

two iterations compared to non-convergence iterations in case of using the available

technique in practice. A practical graphical user interface is developed to ease the use of

this technique in practice by engineers.

5.2 Conclusions

- New practical technique based on FEM-BEM is introduced to consider SSI in

the lateral analysis for multistory building rested on raft foundation.

- This technique has shown a good agreement with FEM continuum models

with different types of structures and with two internationally published

papers.

- The fundamental periods of buildings (T) increases with increasing

substructure flexibility.

- The Lateral Deflection and Inter story drift are increasing with increases

substructure flexibility.

- The effect of soil is increasing with height increase.

- Vertical stiffness of soil-raft system is the predominate factor.

- Rotational stiffness of soil-raft system has small participation in the structure

response due to lateral loads (10-15 %).

- Rotational stiffness participation is increasing with the decrease of E of soil.

- Rotational stiffness has more influence in case of framed structure than

structures with shear walls.

- For shear wall structure, translation stiffness in X-Y direction has more

influence than rotational stiffness.

- Finally, it can be concluded that although conventional design procedure

omitting SSI is conservative it is required to ensure the structural safety due

to lateral deflection.

103

5.3 Recommendations for future work

The future work can be considered in the following directions:

1) No tension SSI.

2) Structures Pounding including SSI.

3) Soil-Pile-Raft-Structure interaction.

4) Nonlinear SSI (Iterative – Elastoplastic – Actual Curve).

5) Nonlinear/Pushover analysis including SSI.

6) Progressive collapse including SSI.

104

REFERENCES

[1] Informs web site, http://www.construction-ic.com/

[2] George Gazetas, Grorge Mylonakis; Seismic soil-structure interaction: new

evidence and emerging issues- Soil Dynamics III, ASCE, Special Geotechnical

Publication, 1998, Vol. 2.

[3] George mylonakis and George Gazetas; seismic soil-structure interaction:

beneficial or detrimental?, Journal of Earthquake Engineering- Journal of

Earthquake Engineering 4(3):277-301 · July 2000 with 269 Reads. DOI:

10.1080/13632460009350372.

[4] George Gazetas, Grorge Mylonakis, Soil-Structure Interaction Effects on Elastic

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[5] Bhattacharya, K., Dutta, S. C., and Dasgupta, S., (2004), “Effect of Soil

Flexibility on Dynamic Behaviour of Building Frames on Raft Foundation”,

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Build., 22: 1075–1082. doi:10.1002/tal.753

[7] B. R. Jayalekshmi and H. K. Chinmayi, “Effect of Soil Flexibility on Seismic

Force Evaluation of RC Framed Buildings with Shear Wall: A Comparative Study

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[8] Mengke Li, Xiao Lu, Xinzheng Lu; Influence of soil-structure interaction on

seismic collapse resistance of super-tall buildings-2014.

[9] Halkude S.A, Kalyanshetti M.G., Bareklikar S.M; Seismic Response of R.C.

Frames with Raft Footing Considering Soil Structure Interaction-2014.

[10] B. R. Jayalekshmi and H. K. Chinmayi, “Effect of Soil Flexibility on Seismic

Force Evaluation of RC Framed Buildings with Shear Wall: A Comparative Study

of IS 1893 and EUROCODE8,” Journal of Structures, vol. 2014, Article ID

493745, 15 pages, 2014. doi:10.1155/2014/493745

[11] Abdel Raheem, S.E., Ahmed, M.M. & Alazrak, T.M.A. Int J Adv Struct Eng

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[12] Hemet S. Chore, P.A.Dode; Soil Structure Interaction of Tall Buildings-2015

[13] VivekGarg and M.S.Hora, (2012) “A review Interaction Behavior of Structure-

Foundation-Soil System”. International Journal of Engineering Research and

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december 2012, pp.639-644

[14] Siddhath G. Shah, Solanki C.H., Desai J.A; Soil structure interaction analysis

methods-State of art- Review-2011.

[15] M.N. Viladkar, Karisiddappa, P. Bhargava, P.N. Godbole; Static soil-structure

interaction response of hyperbolic cooling towers to symmetrical wind loads-

2005.

[16] Jahromi HZ, Izzuddin BA, Zdravkovic L, 2009, A domain decomposition

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foundations.Engineering analysis with boundary elements.2005; 29:859-877. [41] http://www.oasys-software.com/products/engineering/pdisp.html

https://www.csiamerica.com/products/etabs

https://www.csiamerica.com/products/sap2000

http://www.ansys.com/products/Structures

http://www.comp-engineering.com/products/ETABS/etabs.html

https://www.integratedsoft.com/

http://www.beasy.com/

http://www.gpbest.com/

http://www.be4e.com/

http://www.oasys-software.com/products/engineering/pdisp.html

ARABIC SUMMARY

2

محتىي انزســبنت

نخشبت انشأ خز ف الاعخببس انخأثش انخببدل ب االخشاح ؽشمت عهت نلأحخبل انشسبنت يػع

أباة ببب كب ه : خست، حذخ انشسبنت عه دبل جببتنهبب انعشػت لأ

انببة الأول : مقذمــت ، اسببة جد زا انخأثش، ؽشق حثم يمذيت ع انخأثش انخببدل ب انخشبت انشأ خؼ زا انببة

ش انخببدل ب انخشبت انشأ كزنك انطشق انخخهفت نخثم انخشبت.انخأث

انطزق انعذدت وانبزامج انمستخذمتانببة انثبو : انذذدت اسخخذايبث عة انذذدة انذذدتبطشمت انعبطش يمذيت ثى حعشفعشع زا انببة

بشبيج ال PLPAK. كب ا حطشق ان حمذى بشبيج ال كم ؽشمت عه دذة يضاث

ETABS كم يب انخعشف بكبث.

انجذذة انمقتزحت انطزقتانببة انثبنث : ظس نخهك انخطاث.انخػخ ب انمخشدت يعمذو زا انفظم طفب خطة بخطة نهطشمت

أمثهت عذدت: انزابعانببة .مذو زا انببة عذة يسبئم يخؼت يمبست عبيت ب انطشمت انمخشدت انطشق الاخش

انببة انخبمس: انخلاصت والاستىتبجبث واقتزاحبث نهعمم انمستقبه إن سشد نبعغ الإلخشادبث نمبؽ انبذث انسخمبهتهخض زا انببة يب حى اجبص ف انبذث ببلاػبفت

1

عبذانشد محمد ابشاى عه انهج مهىذس:

27/05/1991 تبرخ انملاد:

يظش انجىست:

1/10/2013تبرخ انتسجم:

2017 تبرخ انمىح:

انذست الاشبئتانقسم:

سخش انعهويبج انذرجــــت:

انمشـــــــــزف:

أ.د. ىسف فىس راشذ

انممتحىىن:

أ.د. ىسف فىس راشذ

أ.د. سبمح سمز فهم مهى )ممتحه داخه(

أ.د. ابزاهم محفىظ )ممتحه خبرج(

عىىان انزسبنت:

انمىشأ -ف الاعتببر تأثز انتزبت طزقت عمهت مبتكزة رابطت به طزقت انعىبصز انحذودت وانمحذودة نلاخذ

.انمتببدل عه انمىشئبث انمعزضت لاحمبل جبوبت

كهمبث دانت:

–انهبشت( -اؼغبؽت )انخشبت -انخكثف الاسخبحك -أنخأثش انخببدل ب انخشبت انشأ -ؽشمت انعبطش انذذدت

انخأثش الاسخبحك انخببدل ب انخشبت انشأ

:انزسبنتمهخص

ف زا انبذث حى الخشاح ؽشمت عهت جذذة كفء لاخز انخأثش انخببدل ب انخشت انشئبث انعشػت لادبل جببت.

فب خى حمسى انسأنت ان جضئ( انخ Sub structuringحعخذ ز انطشمت ف الاسبط عه ؽشمت انخمسى )

شأ )غش شبيم انهبشت( انجضء الاخش جضء خبص ببنخشبت ببلاػبفت ان انهبشت. يفظه؛ جضء خبص ببنجضء انعه نه

( عه انسخ انبس ب انهبشت الاعذة. كب ا حى Static condensation حى اسخخذاو ؽشمت انخكثف الاسخبحك )

حضا انخافك الاصاد عذ رنك انسخ.بشيجت ز انطشمت عذ انسخ انبس ب انهبشت الاعذة نهخأكذ ي حذمك الا

دبنب خى اسخخذاو ؽشمت يشبب ي انخكثف الاسخبحك نك عذ انسخ انبس ب انهبشت انخشبت بذس سخهك جذا

لخب يمبست ببنطشمت انمخشدت.

اسخخذايب ف انخذهم انلاخط لادمب ف زا انبذث حى اسخخذاو ز انطشمت ف انخذهم انخط فمؾ يع رنك ك

بسنت بطشمت يببششة.

طزقت عمهت مبتكزة رابطت به طزقت انعىبصز انحذودت وانمحذودة نلاخذ ف

ل عه انمىشئبث انمعزضت لاحمبل جبوبت انمىشأ انمتببد-تببر تأثز انتزبتالاع

إعـذاد

عبذانزحمه محمد ابزاهم عه انمهجمهىذس /

جبيعت انمبشة - سسـبنت يمذيت إن كهت انذسـت

كجضء ي يخطهببث انذظـل عه دسجت

سخش انعهويبج

ف

الإشبئتانذست

عخذ ي نجت انخذ:

انشئس()انششف أ.د. ــىسف فىسي راشــذ

جبيعت انمبشة( - كهت انذست - الإشبئتسخبر لسى انذست أ)

ــــــــــــــــــــــــــــــــــــــــــــــــــــــــ

)انخذ انذاخه( سبمح سمز فهم مهىأ.د.

جبيعت انمبشة( - كهت انذست -شبئت لسى انذست الإسخبر أ)


خذ خبسج(ان) بزاهم محفىظإأ.د.

جبيعت بب( - كهت انذست - الإشبئتسخبر لسى انذست أ)


القاهــرة جامعــة - الهندســة كليــة

مصـرالعربيــة جمهوريـة - الجيـزة 2017


ل عه انمىشئبث انمعزضت لاحمبل جبوبت انمىشأ انمتببد-تببر تأثز انتزبتالاع

إعـذاد

عبذانزحمه محمد ابزاهم عه انمهجمهىذس /

جبيعت انمبشة -سسـبنت يمذيت إن كهت انذسـت


يبجسخش انعهو

ف


حذج إشـشاف

ذأ.د. ــىسف فىسي راشــ

حذهم يكبكب الاشبءاثأسخبر

جبيعت انمبشة - كهت انذست

القاهــرة جامعــة - الهندســة كليــة مصـرالعربيــة جمهوريـة - الجيـزة

2017


ل عه انمىشئبث انمعزضت لاحمبل جبوبتدانمىشأ انمتبب-تأثز انتزبتالاعتببر

إعـذاد

عبذانزحمه محمد ابزاهم عه انمهجيذط /

انمبشةجبيعت -سسـبنت يمذيت إن كهت انذسـت


سخش انعهويبج

ف


القاهــرة جامعــة - الهندســة كليــة

مصـرالعربيــة جمهوريـة - الجيـزة

2017

a developed fem-bem practical technique to consider …

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