optimizing conventional design methods for …...within the raft foundation within the raft...

* * * * Corresponding author, Tel: +234Corresponding author, Tel: +234Corresponding author, Tel: +234Corresponding author, Tel: +234-803-380

OPTIMIZING CONVENTIONAL DESIGN METHODS FOR REINFORCED OPTIMIZING CONVENTIONAL DESIGN METHODS FOR REINFORCED OPTIMIZING CONVENTIONAL DESIGN METHODS FOR REINFORCED OPTIMIZING CONVENTIONAL DESIGN METHODS FOR REINFORCED

CONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONS

1,2 1,2 1,2 1,2 DEPARTMENT OF CIVIL

EEEE----mail addresses: mail addresses: mail addresses: mail addresses:

ABSTRACTABSTRACTABSTRACTABSTRACT

Without a proper design and construction of foundations, problems such as cracking, settlement of buildings may Without a proper design and construction of foundations, problems such as cracking, settlement of buildings may Without a proper design and construction of foundations, problems such as cracking, settlement of buildings may Without a proper design and construction of foundations, problems such as cracking, settlement of buildings may

occur and even to the extent that a whole building may collapse within its design life. Therefore, a proper and occur and even to the extent that a whole building may collapse within its design life. Therefore, a proper and occur and even to the extent that a whole building may collapse within its design life. Therefore, a proper and occur and even to the extent that a whole building may collapse within its design life. Therefore, a proper and

adequate foundation system is readequate foundation system is readequate foundation system is readequate foundation system is required to maintain the safety of a building. quired to maintain the safety of a building. quired to maintain the safety of a building. quired to maintain the safety of a building.

requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations.

supplement the supplement the supplement the supplement the conventional conventional conventional conventional theoretical designtheoretical designtheoretical designtheoretical design

which is designed according to the current European code. Rwhich is designed according to the current European code. Rwhich is designed according to the current European code. Rwhich is designed according to the current European code. R

within the raft foundation within the raft foundation within the raft foundation within the raft foundation based onbased onbased onbased on the the the the

This is followed by This is followed by This is followed by This is followed by the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area

of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained.

concrete cross section area of raft slab foundations should be used as compression reinforcement in order to concrete cross section area of raft slab foundations should be used as compression reinforcement in order to concrete cross section area of raft slab foundations should be used as compression reinforcement in order to concrete cross section area of raft slab foundations should be used as compression reinforcement in order to

prevent differential settlements. The required nominal area of compression reinforcement is 0.9% of the cross prevent differential settlements. The required nominal area of compression reinforcement is 0.9% of the cross prevent differential settlements. The required nominal area of compression reinforcement is 0.9% of the cross prevent differential settlements. The required nominal area of compression reinforcement is 0.9% of the cross

section area of the concrete ssection area of the concrete ssection area of the concrete ssection area of the concrete section.ection.ection.ection.

KeywordsKeywordsKeywordsKeywords: compression reinforcement, raft foundations, finite element, optimization, flexure.

1. INTRODUCTION1. INTRODUCTION1. INTRODUCTION1. INTRODUCTION

Reinforced concrete rafts are designed to transmit the

loads of the building in order to distribute them over

the whole area under the raft and thereby

load per unit area on the ground [1]. Distributing the

loads this way causes little, if any

settlement [1]. But more precise methods, such

finite element computations, should be used in the

design of raft foundations where ground

interaction has a dominant effect [2]. Subgrade

reaction models are often not appropriate [2]. T

design of a raft foundation is prone to significant

uncertainties. The effect of the spatial variation of soil

properties which induces foundation stresses and/or

displacements that cannot be predicted when

assuming soil homogeneity [3], the variation of elastic

modulus of soil, presence of rock media

uncertainties may give rise to differential settlement

within the raft foundation and subsequently its

structural failure.

380-2973


CONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONSCONCRETE RAFT FOUNDATIONS

G. A. MahmudG. A. MahmudG. A. MahmudG. A. Mahmud1111,*,*,*,* and O. S. Abejideand O. S. Abejideand O. S. Abejideand O. S. Abejide2222

IVIL ENGINEERING, AHMADU BELLO UNIVERSITY, ZARIA,

mail addresses: mail addresses: mail addresses: mail addresses: 1111 [email protected], 2222 [email protected]



quired to maintain the safety of a building. quired to maintain the safety of a building. quired to maintain the safety of a building. quired to maintain the safety of a building. This presentation is the modeling of the This presentation is the modeling of the This presentation is the modeling of the This presentation is the modeling of the

requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations. requirements of compression reinforcements in raft foundations. The model helpThe model helpThe model helpThe model helpssss to to to to confirm confirm confirm confirm

theoretical designtheoretical designtheoretical designtheoretical design. For val. For val. For val. For validation, a reinforced concrete idation, a reinforced concrete idation, a reinforced concrete idation, a reinforced concrete

which is designed according to the current European code. Rwhich is designed according to the current European code. Rwhich is designed according to the current European code. Rwhich is designed according to the current European code. Results indicate that there is differential settlement esults indicate that there is differential settlement esults indicate that there is differential settlement esults indicate that there is differential settlement

the the the the settlementsettlementsettlementsettlement and and and and stressstressstressstress patterns obtained from patterns obtained from patterns obtained from patterns obtained from a coded a coded a coded a coded

the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area

of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained. of the raft slab until uniform settlement is obtained. The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage



: compression reinforcement, raft foundations, finite element, optimization, flexure.

designed to transmit the

distribute them over

and thereby reduce the

load per unit area on the ground [1]. Distributing the

if any, appreciable

ore precise methods, such as

finite element computations, should be used in the

design of raft foundations where ground-structure

interaction has a dominant effect [2]. Subgrade

reaction models are often not appropriate [2]. The

design of a raft foundation is prone to significant

the spatial variation of soil

properties which induces foundation stresses and/or

displacements that cannot be predicted when

, the variation of elastic

modulus of soil, presence of rock media and design

differential settlement

the raft foundation and subsequently its

Reinforced concrete is a complicated material to be

modeled within finite element packages

material model in the finite element model should

inevitably be capable of representing both the elastic

and plastic behaviour of concrete in compression and

tension [4]. If the finite element method is to be a

useful tool in the design of reinforced concrete flat

plate structures, accurate modeling is a pre

[5]. Accurate modeling involves understanding the

important relationships between the physical world

and the analytical simulation

accurately modeling boundary conditions should

never be underestimated or neglected in the analysis

of any structure, particularly reinforced concrete flat

plates [5]. ABAQUS is a powerful and comprehensive

tool which provides the user with a

environment, extensive library of material models

comprehensive meshing environment

contact modeling capabilities

include linear, nonlinear and

capabilities, high performance computing, b

Nigerian Journal of Technology (NIJOTECH)

Vol. 33 No. 4, October

Copyright© Faculty of Engineering,

University of Nigeria, Nsukka, ISSN: 1115

www.nijotech.comhttp://dx.doi.org/10.4314/njt.v33i4.


NIGERIA.

[email protected]



This presentation is the modeling of the This presentation is the modeling of the This presentation is the modeling of the This presentation is the modeling of the

confirm confirm confirm confirm a valuable a valuable a valuable a valuable provision to provision to provision to provision to

idation, a reinforced concrete idation, a reinforced concrete idation, a reinforced concrete idation, a reinforced concrete raft foundation iraft foundation iraft foundation iraft foundation is modeled s modeled s modeled s modeled

esults indicate that there is differential settlement esults indicate that there is differential settlement esults indicate that there is differential settlement esults indicate that there is differential settlement

a coded a coded a coded a coded finite element model. finite element model. finite element model. finite element model.

the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area the addition of compression reinforcement from 0.1% to 0.9% based on the cross sectional area

The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage The results obtained suggest that a suitable percentage of the of the of the of the



: compression reinforcement, raft foundations, finite element, optimization, flexure.

Reinforced concrete is a complicated material to be

modeled within finite element packages[4]. A proper

inite element model should

inevitably be capable of representing both the elastic

and plastic behaviour of concrete in compression and

If the finite element method is to be a

useful tool in the design of reinforced concrete flat

es, accurate modeling is a pre-requisite

Accurate modeling involves understanding the

important relationships between the physical world

and the analytical simulation. The importance of

accurately modeling boundary conditions should

mated or neglected in the analysis

of any structure, particularly reinforced concrete flat

ABAQUS is a powerful and comprehensive

tool which provides the user with a powerful modeling

extensive library of material models,

nsive meshing environment, comprehensive

contact modeling capabilities, advanced analysis which

include linear, nonlinear and robust multiphysics

, high performance computing, best-in-class

Nigerian Journal of Technology (NIJOTECH)

4, October 2014, pp. 490 – 496

Copyright© Faculty of Engineering,

University of Nigeria, Nsukka, ISSN: 1115-8443

www.nijotech.com http://dx.doi.org/10.4314/njt.v33i4.9

OOOOPTIMIZIPTIMIZIPTIMIZIPTIMIZING NG NG NG CCCCONVENTIONAL ONVENTIONAL ONVENTIONAL ONVENTIONAL DDDDESIGN ESIGN ESIGN ESIGN MMMMETHODS FETHODS FETHODS FETHODS F

Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology,

visualization capabilities, and analysis using

specialized techniques.

This work presents the FEA modeling of the

requirements of compression reinforcements in raft

foundations using ABAQUS. The model help

confirm and provide a valuable supplement to the

theoretical design. For validation, a reinfo

concrete raft foundation is modeled

conventionally designed according to Eurocode [6]

provisions. The results indicate that there is

differential settlement within the raft foundation

based on the settlement and stress patterns obtained

from the finite element model (FEM). This is followed

by the addition of compression reinforcement from

0.1% to 0.9% based on the cross sectional area of the

raft slab until uniform settlement is obtained.

2. 2. 2. 2. DESIGN OFDESIGN OFDESIGN OFDESIGN OF SIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONS

A reinforced concrete raft foundation is conventionally

designed according to Eurocode [6]. The raft consists

of eight column loads with four corner and four

Figure 1: Reinforcement detailing of the designed raft foundation

Figure 2: Raft foundation and soil layer configuration adopted

0.50

75H06-200T

75H12-200B

4.00

ETHODS FETHODS FETHODS FETHODS FOR OR OR OR RRRREINFORCED EINFORCED EINFORCED EINFORCED CCCCONCRETE ONCRETE ONCRETE ONCRETE RRRRAFT AFT AFT AFT FFFFOUNDATIONSOUNDATIONSOUNDATIONSOUNDATIONS,,,, G. A. MahmudG. A. MahmudG. A. MahmudG. A. Mahmud

Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology, Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014

, and analysis using

This work presents the FEA modeling of the

requirements of compression reinforcements in raft

. The model helps to

provide a valuable supplement to the

. For validation, a reinforced

s modeled which is

conventionally designed according to Eurocode [6]

The results indicate that there is

differential settlement within the raft foundation

patterns obtained

. This is followed

the addition of compression reinforcement from

0.1% to 0.9% based on the cross sectional area of the

raft slab until uniform settlement is obtained.

SIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONSSIMPLE RAFT FOUNDATIONS

raft foundation is conventionally

The raft consists

of eight column loads with four corner and four

internal loads of an office building. All the corner

columns carry a load of 458.33KN each and internal

columns carry 666.66KN each. Each column has an

area of 0.5m by 0.5m. The assumed bearing capacity of

the soil is 100KN/m2 and is assumed to be distributed

linearly. Soil density is assumed to be firm with two or

more types of soil forming the sub

foundation is calculated as 75m

5m by 15m is chosen for the foundation. The number

and area of reinforcements are derived using the most

critical values of the shear forces and bending

moments.

Compression reinforcement is then added to the

design at various percentages ranging from 0.1% to

0.9% of the cross sectional area of the raft slab.

3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS

The size and dimension of the soil layer and raft

foundation model adopted for

analysis can be seen in the diagram shown in Figure 2.

BOTTOM PLAN


Figure 2: Raft foundation and soil layer configuration adopted for the finite element analysis.

15.00

4.00 4.00

17H08-300T

17H20-300B

G. A. MahmudG. A. MahmudG. A. MahmudG. A. Mahmud & O. S. Abejide& O. S. Abejide& O. S. Abejide& O. S. Abejide

Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014 491

internal loads of an office building. All the corner

columns carry a load of 458.33KN each and internal

carry 666.66KN each. Each column has an

area of 0.5m by 0.5m. The assumed bearing capacity of

and is assumed to be distributed

linearly. Soil density is assumed to be firm with two or

more types of soil forming the sub-soil. The area of the

foundation is calculated as 75m2 and a dimension of

5m by 15m is chosen for the foundation. The number

and area of reinforcements are derived using the most

critical values of the shear forces and bending

Compression reinforcement is then added to the

design at various percentages ranging from 0.1% to

0.9% of the cross sectional area of the raft slab.

3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS3. FINITE ELEMENT ANALYSIS

The size and dimension of the soil layer and raft

foundation model adopted for the finite element

analysis can be seen in the diagram shown in Figure 2.


for the finite element analysis.

5.00

0.60



The 3D deformable solid parts involved in the analysis

consist of the soil layer, concrete slab and steel

reinforcements. The dimensions of the steel

reinforcements used are obtained from the foundati

design as seen in Figure 1 while the dimension of the

soil layer and the slab can be seen in Figure 2. Figures

3 to 9 show the stepwise modeling of the foundation

raft and components in ABAQUS.

Figure 3: Soil layer part in ABAQUS

Figure 4: Concrete slab part in ABAQUS

Figure 5: Tensile reinforcement running along the length

Figure 6: Tensile reinforcement running along the width



3D deformable solid parts involved in the analysis

consist of the soil layer, concrete slab and steel

reinforcements. The dimensions of the steel

reinforcements used are obtained from the foundation

design as seen in Figure 1 while the dimension of the

soil layer and the slab can be seen in Figure 2. Figures

3 to 9 show the stepwise modeling of the foundation

Figure 3: Soil layer part in ABAQUS

Concrete slab part in ABAQUS

Figure 5: Tensile reinforcement running along the

Figure 6: Tensile reinforcement running along the

Elastic soil, concrete and steel are used to define the

properties of the parts in the model. Soil, concrete and

steel sections are then created using these properties

and the sections assigned to the individual parts

accordingly. An elastic material is us

an isotropic hardening rule.

one to model the stiffness effects of a distributed

support without actually modeling the details of the

support [7, 8].

Figure 7: Interaction between concrete slab and elastic soil surface

The soil material is assumed to have a density of

1900kg/m3and is assigned a Poisson’s ratio of 0.3.

Foundation stiffness per area of 100×10

applied to the top surface of the soil layer.

compressive strength of 45MPa is assigned to

concrete part. A plastic strain of 0.0035 and a density

of 2400kg/m3 are also assumed for the concrete. The

Young’s modulus and Poisson’s ratio are taken to be

36GPa and 0.2 respectively. An elastic, perfectly plastic

material is used for the reinforci

reinforcing bars are 3D solid elements embedded in

the concrete. They exhibit an elastic

and transfer of loads to the concrete through the

reinforcements is achieved by introducing tension

stiffening to the concrete model. The

element option is used to model the interaction/bond

between the concrete and reinforcing bars. The

reinforcing bars are the embedded elements while the

concrete slab is the host element. A solid homogeneous

steel section is assigned to the reinf

isotropic hardening. The steel is assigned a tensile

strength and strain of 500MPa and 0.003 respectively.

The density of steel is taken as 7850kg/m

modulus and Poisson’s ratio of 200GPa and 0.3 are

assigned to the reinforcemen

Linear hexahedral elements of type C3D8R

in ABAQUS are used in defining the mesh for the entire

assembly. This fine mesh will help in improving the

accuracy of the results obtained after the analysis.



Elastic soil, concrete and steel are used to define the

properties of the parts in the model. Soil, concrete and

steel sections are then created using these properties

and the sections assigned to the individual parts

accordingly. An elastic material is used for the soil with

an isotropic hardening rule. Elastic foundations allow

to model the stiffness effects of a distributed

support without actually modeling the details of the

Figure 7: Interaction between concrete slab and

oil surface

The soil material is assumed to have a density of

and is assigned a Poisson’s ratio of 0.3.

Foundation stiffness per area of 100×103 N/m2 is

applied to the top surface of the soil layer. A

compressive strength of 45MPa is assigned to the

concrete part. A plastic strain of 0.0035 and a density

are also assumed for the concrete. The

Young’s modulus and Poisson’s ratio are taken to be

36GPa and 0.2 respectively. An elastic, perfectly plastic

material is used for the reinforcing bars. The

reinforcing bars are 3D solid elements embedded in

the concrete. They exhibit an elastic-plastic behavior

and transfer of loads to the concrete through the

reinforcements is achieved by introducing tension

stiffening to the concrete model. The embedded

element option is used to model the interaction/bond

between the concrete and reinforcing bars. The

reinforcing bars are the embedded elements while the

concrete slab is the host element. A solid homogeneous

steel section is assigned to the reinforcing bars with

isotropic hardening. The steel is assigned a tensile

strength and strain of 500MPa and 0.003 respectively.

The density of steel is taken as 7850kg/m3. A Young’s

modulus and Poisson’s ratio of 200GPa and 0.3 are

assigned to the reinforcements respectively.

Linear hexahedral elements of type C3D8R prescribed

in ABAQUS are used in defining the mesh for the entire

assembly. This fine mesh will help in improving the

accuracy of the results obtained after the analysis.



Figure 8: Discretization of structure into elements and nodes.

Concentrated loads and boundary conditions are

applied to the assembly on the surfaces of the parts.

The loads are applied on the surface of the nodes of the

concrete slab. Four edge loads and four internal loads

are applied with magnitudes of 458.33×10

666.66×103N respectively. The loads are applied along

the y-axis and are given a negative value for downward

action. An encastre boundary condition (U1 = U2 = U3

= UR1 = UR2 = UR3 = 0) is applied to the sides and

bottom of the soil block which restricted

moving or rotating in all directions. The top surface of

the soil layer is not restricted and is allowed to deform

in all directions. The edges of the slab are assigned a

boundary condition in the form of YASYMM (U1 = U3

= UR2 = 0) which only allows movement along the y

axis and rotation along both x-axis and z

of this is to allow the raft foundation to deform in the

direction of the loads.

Figure 9: Applied loads and boundary conditions

There are two steps involved in this analysis; the initial

and the created “slab load step”. Interactions are

created in the initial step while loads and boundary

conditions are created and applied in the slab load

step. The slab load step has a maximum number

increments. The initial increment size is 1, the

minimum 1E-005 and the maximum 1.

A set of field output and history output requests are

created in the slab load step. A full analysis job is

created, submitted and run with results obtained. The

analysis is repeated for models with additional amount

of compression reinforcement; the additional amount

ranging from 0.1% to 0.9% of the cross sectional area

of the raft slab.



of structure into elements and

Concentrated loads and boundary conditions are

applied to the assembly on the surfaces of the parts.

The loads are applied on the surface of the nodes of the

concrete slab. Four edge loads and four internal loads

pplied with magnitudes of 458.33×103N and

N respectively. The loads are applied along

axis and are given a negative value for downward

An encastre boundary condition (U1 = U2 = U3

= UR1 = UR2 = UR3 = 0) is applied to the sides and

ottom of the soil block which restricted it from

moving or rotating in all directions. The top surface of

the soil layer is not restricted and is allowed to deform

in all directions. The edges of the slab are assigned a

SYMM (U1 = U3

= UR2 = 0) which only allows movement along the y-

axis and z-axis. The aim

of this is to allow the raft foundation to deform in the

Figure 9: Applied loads and boundary conditions

are two steps involved in this analysis; the initial

”. Interactions are

created in the initial step while loads and boundary

conditions are created and applied in the slab load

step. The slab load step has a maximum number of 100

increments. The initial increment size is 1, the

005 and the maximum 1.

A set of field output and history output requests are

created in the slab load step. A full analysis job is

created, submitted and run with results obtained. The

lysis is repeated for models with additional amount

; the additional amount

ranging from 0.1% to 0.9% of the cross sectional area

4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION

The finite element analysis carried out for a normall

designed draft foundation model according to the

provisions of the code yielded results indicating that

the tensile reinforcement provided is insufficient to

provide adequate resistance against deformation and

differential settlement. The addition of compression

reinforcement increases the resistance until uniform

settlement is obtained at a value 0.9% of the concrete

cross section area of the raft slab.

4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation

The Von Mises stress pattern obtained after the

analysis for the raft foundation models can be seen in

the deformed diagram of the models shown in Figures

10 to 17. The Von Mises stress refers to the theory

called Maxwell-Huber-Hencky

ductile failure [7]. The analysis shows that there are no

Von Mises stresses within all the raft foundation

models. The contour blue indicates zero Von Mises

stresses and hence, it is an indication that the

foundation is stable after the deformation caused by

the applied loads.

Figure 10: No additional compression

Figure 11: 0.1% additional compression reinforcement



4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION4. RESULTS AND DISCUSSION

The finite element analysis carried out for a normally

draft foundation model according to the

provisions of the code yielded results indicating that

the tensile reinforcement provided is insufficient to

provide adequate resistance against deformation and

differential settlement. The addition of compression

einforcement increases the resistance until uniform

settlement is obtained at a value 0.9% of the concrete

cross section area of the raft slab.

4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation4.1 Stress patterns in the raft foundation

The Von Mises stress pattern obtained after the

t foundation models can be seen in

the deformed diagram of the models shown in Figures

10 to 17. The Von Mises stress refers to the theory

Hencky-Von Mises criterion for

ductile failure [7]. The analysis shows that there are no

es stresses within all the raft foundation

models. The contour blue indicates zero Von Mises

stresses and hence, it is an indication that the

foundation is stable after the deformation caused by

Figure 10: No additional compression reinforcement













additional compression reinforcement



4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation

The immediate settlement of the raft foundation

models takes place in the direction in which the load is

applied. The spatial displacement of the models can be

seen in Figures 18 to 25. It can also be seen that the

maximum immediate settlement in the normally

designed raft foundation model according to the

provisions of the design code [6]

where the loads are applied while the minimum

immediate settlement occurred at the center where

there is an upward heave. The result indicates that

there is differential settlement in the raft foundation

after the deformation. After the application of

compression reinforcement, a uniform settlement is

obtained at 0.9% as shown in Figure 25.

Figure 18: No additional compression reinforcement





4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation4.2 Settlement of the raft foundation

The immediate settlement of the raft foundation

the direction in which the load is

applied. The spatial displacement of the models can be

seen in Figures 18 to 25. It can also be seen that the

maximum immediate settlement in the normally

designed raft foundation model according to the

design code [6] occurred at the points

where the loads are applied while the minimum

immediate settlement occurred at the center where

there is an upward heave. The result indicates that

there is differential settlement in the raft foundation

formation. After the application of

compression reinforcement, a uniform settlement is

obtained at 0.9% as shown in Figure 25.

No additional compression reinforcement









0.1% additional compression reinforcement

additional compression reinforcement




Figure 24: 0.8% additional compression


5. CONCLUSION5. CONCLUSION5. CONCLUSION5. CONCLUSION

On the basis of the study carried out, the following

conclusions may be drawn:

I. The variation of the amount of reinforcement in

compression and tension in a raft foundation

plays a significant role and affects the moments

and deformations of the foundation.

II. Compression reinforcement is effective in

providing resistance against differential

settlement in a reinforced concrete raft

foundation.

III. Settlement estimates of a foundat

guess of the footing deformation after a load has

been applied as proved from the nodal

representations of elements in the finite element

analysis display.






On the basis of the study carried out, the following

The variation of the amount of reinforcement in

compression and tension in a raft foundation

plays a significant role and affects the moments

and deformations of the foundation.

Compression reinforcement is effective in

providing resistance against differential

settlement in a reinforced concrete raft

ettlement estimates of a foundation is the best

guess of the footing deformation after a load has

as proved from the nodal

representations of elements in the finite element

OOOOPTIMIZIPTIMIZIPTIMIZIPTIMIZING NG NG NG CCCCONVENTIONAL ONVENTIONAL ONVENTIONAL ONVENTIONAL DDDDESIGN ESIGN ESIGN ESIGN MMMMETHODS FETHODS FETHODS FETHODS FOR OR OR OR RRRREINFORCED EINFORCED EINFORCED EINFORCED CCCCONCRETE ONCRETE ONCRETE ONCRETE RRRRAFT AFT AFT AFT FFFFOUNDATIONSOUNDATIONSOUNDATIONSOUNDATIONS,,,, G. A. MahmudG. A. MahmudG. A. MahmudG. A. Mahmud & O. S. Abejide& O. S. Abejide& O. S. Abejide& O. S. Abejide

Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology, Nigerian Journal of Technology, Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014Vol. 33, No. 4, October 2014 496

IV. The overall settlement of the raft foundation was

reduced by about 80% due to the increase in the

stiffness of the foundation, indicating that

settlements can be reduced by up to 80% when it

occurs.

V. The finite element analysis is a very precise

method for the design and analysis of raft

foundations.

It is therefore suggested that a suitable percentage of

the concrete cross section area of raft slab foundations

should be used as compression reinforcement in order

to increase the foundation stiffness and prevent

differential settlements. The amount of compression

reinforcement is derived from the more precise

method of finite element analysis by comparing results

from the conventional design method in terms of the

code’s provisions for differential settlement within the

raft foundations. This amount is obtained as 0.9% of

the concrete cross section for the current design code

[6] and may be generally applied for the design of

reinforced concrete raft foundations.

6. REFERENCES6. REFERENCES6. REFERENCES6. REFERENCES

[1] Stephen Emmitt and Christopher Gorse A.Barry’s Introduction to Construction of Buildings, 2ndEdition, John Wiley and Sons. pp .61 – 64, 2010.

[2] Eurocode 7: EN 1997-1Geotechnical Design - Part 1: General Rules. European Standard, CEN, Brussels,

2004.

[3] Niandou, Halidou/Breysse, Denys“Reliability Analysis

of a Piled Raft Accounting for Soil Horizontal

Variability”,Computers and Geotechnics, 34 (2). pp

71-80,2006.

[4] SinaeiHamid, Mahdi Shariati, Amir HoseinAbna,

Mohammed Aghael and Ali Shariati, “Evaluation of

Reinforced Concrete Beam BehaviorUsing Finite

Element Analysis by ABAQUS”,Academic Journal, Scientific Research and Essays Vol. 7(21), pp. 2002-

2009, 7 June, 2012

[5] Deaton James B.“A Finite Element Approach to

Reinforced Concrete Slab Design”,School of Civil and Environmental Engineering Thesis, Georgia

Institute of Technology, Virginia, pp. 11-25,2005.

[6] Eurocode 2: EN 1992-1-1Design of Concrete Structures - Part 1-1: General Rules and Rules for Buildings, CEN, Brussels,2008.

[7] Hand F. R., Pecknold D. A. and Schnobrich W. C.“A

Layered Finite Element Nonlinear Analysis of

Reinforced Concrete Plates and Shells”Civil Engineering Studies, SRS No. 389, University of

Illinois, Urbana, Illinois, 1972.

[8] SimuliaDassaultSystemes“ABAQUS Unified

FEA3DSDassaultSystemes”,http://www.3ds.com/.

Last accessed 4/10/2012.

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