INTRODUCTION
Raft is a foundation that is generally used to support a heavily loaded structure, as well as a structure founded on heterogeneous deposits. The analysis of raft foundation has undergone various developments and currently it is being analyzed with sophistication by incorporating the interaction between structure, raft and soil including time dependent nonlinear behavior. The oldest method is a rigid analysis, which is otherwise known as a conventional method. To properly evaluate the moments and forces in the foundation and superstructure, it is necessary to consider them as parts of a single compatible system. To overcome these difficulties, the sophisticated techniques, such as the Finite Element and Boundary Element technique are in current practice. Traditional methods of analyses have treated the raft as a loaded plate or a strip supported on a soil layer of linear elastic material. In the conventional method, contact pressure distribution is made static by assuming that the foundation element is a rigid plate on the Winkler medium, whereas in the soil line method, the relative flexibility of the foundation element was included. However, rigidity of the superstructure and continuity of soil mass are ignored in these methods. Vlasov and Leontiev proposed a twoparameter model in 1966 that accounts for the continuity of the soil medium and displacement.
Several continuum models have been developed assuming that soil is an isotropic, homogeneous and linearly elastic material. In the above mentioned methods, the focus was on the modelling of soil continuity and its influence on the contact pressure and moments. However, the relative stiffness of the foundation leads to a redistribution of the forces and moments on the superstructure.
Viladkar et al. (1991, 1992)
contributed immensely in understanding soilraftstructure interaction. Viladkar,
developed a coupled FE procedure with nonlinear idealization of soil using
a hyperbolic stressstrain relationship. Subsequently Godbole
et al. (1990) adopted the technique of a coupled finiteinfinite
element formulation for the general case of multistoreyed plane frames with
a combined soil foundation system. The nonlinear of soil mass relation was
included to study its effect on the redistribution of shear force and bending
moments in the structural members. Viladkar et al.
(1994) extended the coupled finite element for the interaction analysis
of the space frameraftsoil system considering soil nonlinearity. In this
nonlinear analysis, the stiffness of the structural slab was included as a part of superstructure. The proposed model
was studied by analysing the multistoreyed frame and it was concluded that
moment redistribution takes place in the interaction analysis. Noorzaei
et al. (1991, 1995a, b)
studied the effect of the flexibility of the foundation beam on the entire interaction
behavior of a plane frame, combined footing soil mass system. The coupled finiteinfinite
element formulation was adopted to physically represent the system and the nonlinearity
of the soil media was also included. The nonlinearity of the soil was included
by hyperbolic stressstrain model. They concluded that the differential settlements,
which influence the behavior of the structurefoundationsoil mass system, were
considerably reduced with an increase in the rigidity of the foundation.
As the stiffness of the foundation increases, it also absorbs more moments and there is consequently a significant reduction in the bending moments of the superstructure members.
Viladkar et al. (1993) developed a model to
include a timedependent behavior at constant loading. They concluded that redistribution
of shear forces, bending moment and torsional moments in the structure occur
due to differential settlements rather than the total settlements. They compared
the interacting results of the resulting structural behavior of with that when
interaction is neglected.
Noorzaei et al. (1995a) continued the work of
Viladkar as they analysed the interactions of space frameraftsoil system.Analysis
was carried out by modelling the superstructure as a Timoshenko beam element
and Mindlin plate bending element for structural slabs and the raft, respectively
with a hyperbolic model for the soil to account for the nonlinear behavior.
Noorzaei et al. (1995a) studied the soilstructure
interaction of a plane frame, combined footing soil system, taking into account
the elastoplastic behavior of the soil including strain hardening characteristics.
The elastoplastic behavior with and without strain hardening was examined in
their study. The axial forces and moments in the frame and the foundation varied
significantly between the methods analysed and are higher for the strain hardening
condition. In the next study, Noorzaei et al. (1995b)
discussed elastoplastic idealization of soil using six different yield criteria
in the soilstructure interaction analyses and also compared the results with
the results of nonlinear analyses. They reported that, in general, the transfer
of forces and moments takes place from exterior to interior columns when the
soil remains in an elastic state.
Rao (1995) compared the realistic halfspace continuum
approach and the planestrain approach and concluded that the realistic halfspace
continuum approach was superior to planestrain approach.
Daniel and Ilamparuthi (2001) compared the Winkler model
and elastic continuum model and reported higher settlement in the Winkler model
than in the elastic continuum model. They compared the bending moments in the
raft obtained by noninteractive analysis of elastic continuum with Wolfer method
and conventional rigid method bending moments. The moments obtained by the conventional
rigid method are always higher than the other two methods and the moments obtained
by the Wolfer method lie between those of the other two methods.
Dutt and Roy (2002) compared the various models available
in the literature and gave the strength and limitations of each model. They
have emphasis to physical modelling, since it appears that this modelling of
structure is straightforward.
Maharaj et al. (2004) developed a model by considering
the frame and raft as an elastic material and the soil as an elastoplastic material
by DruckerPrager yield criterion. They concluded that the flexibility of raft
increased the internal forces in the super structure. The flexible foundation
undergoes more differential settlement than the stiff foundation. By increasing
superstructure stiffness the differential settlement of foundation was reduced
to almost zero. By increasing foundation thickness the differential settlement
of foundation reduced to almost zero.
Conniff and Kionusis (2007) developed a model by replacing
the soil mass by threedegreeoffreedom elastoplastic medium. They concluded
that this model resulted in accurate settlements of the shallow foundations.
Manjeet (2006) developed a nonlinear behavoiur of
soil using the hyperbolic model. They concluded that nonlinearity of soil mass
plays an important role in the redistribution of forces in the superstructure.
Small (2001) proved that the use of simple spring models
for the soil behavior can lead to erroneous results. He compared the results
of simple finite layer techniques with threedimensional finite element techniques.
He showed that the type of structure and its stiffness have an effect on the
deformation of the foundation. He proved that the results of instrumented structure
have good agreement with the results of threedimensional finite element techniques.
In their subsequent papers, Daniel and Ilamparuthi (2004,
2005 and 2007) had studied the
effects of linear and nonlinear soil and reported higher settlement for nonlinear
soil than linear soil and more uniform contact pressure and a higher bending
moment for nonlinear soil than linear soil. The interactive analysis was carried
out by including the superstructure stiffness in the raftsoil. Moreover, they
reported the change in contact pressure and bending moments due to changes in
the stiffness of superstructure. In their next paper, the influence interaction
was carried out by changing the thickness of the raft and modulus of the soil
and they reported the changes in settlement, bending moment, contact pressure,
axial force and moments in the columns and beam moments.
The literature review presented above suggests that all the early investigators represented the column spacing of the frame as a constant and they have not increased or changed the frame column spacing and the effects of the frame column spacing has not been analysed. Thus, in the present study, the effect of frame column spacing on the interaction of a space frameraft and soil system is analysed.Further, parametric studies reported in the literature of soilraftstructure interaction are limited. Therefore, in the present study, the importance of the relative stiffness of raft, thickness of raft and modulus of soil is emphasised. The study reported in the literature on the nonlinear behavior of soils is also limited.
However, the soil behavior is nonlinear irrespective of sand and clay. As a result, in the present study, the effect of nonlinear behavior of soil is incorporated.For the nonlinear behavior of soil, the multi linear isotropic model (MISO) was adopted.
In the proposed study, different column spacings were carried out while including linear and nonlinear elastic behavior of the soil. The column spacings in the frames were 3, 4.5, 6 and 7.5 m. In the analysis, all three components, namely soil, raft and superstructure, are analyzed as a single compatible unit. The influence of column spacing on settlement, bending moment and contact pressure were studied. Thus, the initial tangent modulus of the stressstrain curve obtained from the laboratory triaxial test on sand was adopted as the Young’s modulus, Es.
A detailed parametric study was conducted by varying the relative stiffness
of the raft, Krs and soil modulus Es. The relative stiffness Krs is determined
based on the recommendation of Brown and Yu (1986),
which is as follows:
The influence of these two parameters on (the forces and moments in the superstructure and) the raft were studied. Further, analyses were carried out to examine the effect of non Linear (NL) soil behavior, since soil exhibits inelastic and nonlinear behavior from the beginning of loading.
Therefore, any model for the constitute soil behavior must account for this nonlinearity. Various models that account for a nonlinear response have been developed using the nonlinear elastic approach theory.Among one is theory of nonlinear elastic approach. This approach divides a nonlinear stress strain curve into number of linear parts. Such an approach has been adopted here in the multilinear isotropic (MISO) model. The details of MISO model adopted in this study are available in ANSYS^{10} elemental library.
PROBLEM DETAILS
The analysis was carried out on a space frame (3 bay x 5 bay)raftsoil system
with five stories. The quarter raft plans and column positions are shown in
Fig. 1ad. The column spacings are 3, 4.5,
6 and 7.5 m. It is assumed that the raft is placed directly on the sand medium.
In general, sand is treated as a non homogeneous material in which sand modulus
varies with depth. However, the trial analysis on the frameraftsoil system
including nonhomogeneity demonstrated that the settlement was greatly influenced
by nonhomogeneity, but there was only a marginal difference in the differential
settlement as well as member forces. Therefore, sand is assumed to have uniform
property with depth. The stiffness contribution of the wall and slab are not
included in the analysis.

Fig. 1: 
Plan of quarter rafts and position of columns; (a) 3 m, column
spacing, (b) 4.5 column spacing, (c) 6 m column spacing and (d) 7.5 column
spacing 
Table 1: 
Geometric and elastic properties of frame, raft and soil 


Fig. 2: 
Element discretization of frameraftsoil; (a) 3 m, column
spacing, (b) 4.5 column spacing, (c) 6 m column spacing and (d) 7.5 column
spacing 
The load on the slab, including selfweight and the weight of the wall, are considered and are applied as a uniformly distributed load on the beams. The geometric properties of frame and other properties adopted in the analysis are shown in Table 1.
FINITE ELEMENT MODEL
ANSYS finite element code is used. The finite element discretisation along
a vertical section of the space frame of 3 bay x 5 bay adopted in this study
is shown in Fig. 2ad.
A two noded beam element (BEAM 4) with six degrees of freedom per node is adopted for the beams and columns of the superstructure. The connections between them are treated as rigid. The soil medium below the raft has been modelled using eightnode brick element (SOLID 45), having three degrees of translation freedom in the respective coordinate directions at each node. The soil was idealized as an isotropic homogeneous, halfspace.For this analysis, the initial tangent modulus and Poisson's ratio (v_{s}) were the inputs. For the nonlinear analysis (NL), multilinear isotropic hardening (MISO) material was adopted, as stated in the earlier section.
To provide the required parameters as input for the MISO model, triaxial tests were conducted on Vellar river sand. The sand grain sizes used in the test varied between 1.15 and 3.85 mm with a uniformity coefficient of 2.94. The test was conducted at an average unit weight of 16.2 kN/m^{3} under two different confining pressures. The stressstrain relations (Fig. 3) were provided as input along with the respective initial tangent modulus values.Poisson’s ratio of the sand was generally between 0.20 and 0.40 and a value of 0.35 was therefore used in computations.
In order to fix the region of soil below the foundation, trial analyses were carried out and it was determined that the breadth and thickness of the soil medium was more than 2.5 times that of the least width of the foundations and that the variation in the settlement and contact pressures was marginal.
Therefore, the soil medium consideration in the quarter model extends 22.5 m in the x and y directions and 27 m in the z direction for the column spacing of 3 m, 33.75 m in the x and y directions and 40.5 m in the z direction for the column spacing of 4.5 m, 45 m in the x and y directions and 54 m in the z direction for the column spacing of 6 and 56.25 m in the x and y directions and 67.5 m in the z direction for the column spacing of 7.5 m as shown in the Fig. 2.
Vertical translation ceased at the bottom boundary, while lateral translation stopped at the vertical boundaries. The raft is modelled as a platebending element (Shell 93) with eight nodes having six degrees of freedom each. The moment is calculated in the raft per unit conta 174 length in the element coordinate system. The interface characteristics between the raft and soil were represented by the elements Targe I 70 and Conta 174.

Fig. 3: 
Stressstrain curve of sand 
The meshes in the soil medium were generated with fine meshes of size 0.5m
close to the raft and with coarser meshes of size 1.5m further away from the
raft. In the shell element of the raft, the meshes were generated with fine
meshes of size 0.5m. The Ansys package was validated for the settlement result
of Daniel and Illamparuthi (2007) as shown in the Fig.
19.
RESULTS AND DISCUSSION
The effects of various column spacings namely 3, 4.5, 6 and 7.5 m on their respective soil media, as shown in the Fig. 2 were analysed. The results of the effect of column spacing, effect of thickness of the raft, Krs, effect of young’s modulus of soil, Es and effect of nonlinearity of soil are presented below:
Settlement of raft: Figure 4 shows settlements along
sections B1B4 of rafts for the various column spacings namely 3, 4.5, 6 and
7.5 m, with Krs values of 0.0012, 0.0015, 0.0011 and 0.0016, respectively (Hereafter
these Krs values are collectively called lesser Krs values and/or 1 time Krs
values). The settlement was higher at the centre of the raft than the edge of
the raft, irrespective of column spacing.
Figure 5 shows settlements along the sections B1B4 of the
raft for 3, 4.5, 6 and 7.5 m column spacings with Krs values of 0.012, 0.015,
0.011 and 0.016, respectively. (Hereafter these Krs values are collectively
called higher Krs values and/or 10 times Krs values) Fig. 6
shows settlement variation for the various column spacings for the soil modulus
of 23 MPa and for lesser and higher Krs values.

Fig. 4: 
Settlement variation of along B1B4 of raft for various column
spacings (linear, lesser krs value) 

Fig. 5: 
Settlement variation of along B1B4 of raft for various column
spacings (linear, higher krs value) 

Fig. 6: 
Variation of settlement with column spacing (Es=23MPa, lessrr
and higher krs values) 
Figure 7 shows settlement variation for the various column
spacings, for the soil modulus of 23 MPa and 135 MPa and for lesser Krs value.
Figure 8 shows the settlements along sections B1B4 of raft
for the various column spacings of nonlinear soil. Figure 9
and 10 show settlement variation for the various column spacings
of linear and nonlinear soil both at the edge and the centre of the raft.
Bending moment in the raft: Bending moment variation due to different
column spacing was compared in Fig. 11 for the Es value of
23 MPa (the Krs values are shown in Fig. 11). The negative
and positive moments indicate hogging and sagging moments, respectively.

Fig. 7: 
Settlement variation with column spacing (Es = 23 MPa, Es
= 135 MPa and lesser krs value) 

Fig. 8: 
Settlement variation along B1B4 of raft for various column
spacings (nonlinear, lesser krs value) 
Figure
12 shows the moment variation for various column spacings for a soil modulus
of 23 MPa and for lesser and higher Krs values. Figure 13 shows the moment variation for various column
spacings for a soil modulus of 23 and 135 MPa and for lesser Krs values.
Figure 14 shows the moment variation for the various column spacings of linear and nonlinear soils and for a soil modulus of 23 MPa. Span moment and inner support moments of nonlinear soil showed a similar trend to that of linear soil.
Contact pressure below the raft: The contact pressure distribution along
B1B4 of the raft for various column spacings was shown in Fig.
15 for the soil modulus of 23 MPa and for lesser Krs values.

Fig. 9: 
Comparision of linear and nonlinear settlement for different
column spacings (edge settlement) 

Fig. 10: 
Comparision of linear and nonlinear settlement for different
column spacings (centre settlement) 
The contact pressure distribution along B1B4 of the raft for various column
spacings was shown in Fig. 16 for the soil modulus of 23
MPa and for higher Krs values. The contact pressure distribution along B1B4
of the raft for various column spacings is shown in Fig. 17
for the soil modulus of 135 MPa.
The contact pressure distribution for the nonlinear soil along B1B4 of the raft for various column spacings is shown in Fig. 18 for the soil modulus of 23 MPa and for lesser Krs values.
The effects of various column spacings namely 3, 4.5, 6 and 7.5 m on their
respective soil media, as shown in the Fig. 2 were analysed.

Fig. 11: 
Bending moment variation along B1B4 of raft for various column
spacing 

Fig. 12: 
Bending moment variation of with column spacing (Es=23 MPa,
lesser and higher krs values) 
The importance of effect of column spacing, effect of thickness of the raft,
Krs, effect of young’s modulus of soil, Es and effect of nonlinearity
of soil are discussed and presented below.
The effect of column spacing: Figure 4 shows settlements along sections B1B4 of rafts for the various column spacings with lesser Krs values. The settlement was highest for 7.5 m column spacing followed by that for the 6, 4.5 and 3 m column spacings.

Fig. 13: 
Bending moment variation with column spacing (Es = 23 MPa,
Es = 135 MPa and lesser krs values) 

Fig. 14: 
Comparision of linear and nonlinear bending moments for various
column spacing 
The settlement increased gradually as the column spacing increases from 3 to
7.5 m, as shown in Fig. 4. This was due to effect of column
spacing, the objective of the paper. Figure 5 shows settlements
along the sections B1B4 for the various column spacings with higher Krs values.
The raft with higher Krs values showed the similar trend of the rafts with lesser
Krs values.

Fig. 15: 
Contact pressure distribution along B1B4 of raft for various
columns spacings (linear, lesser krs value) 

Fig. 16: 
Contact pressure distribution along B1B4 of raft for various
column spacings (linear, higher krs values) 
However, the settlements were reduced considerably in the rafts with higher
Krs values. The settlement increased with increases in column spacing at both
the edge and centre of the raft, as shown in the Fig. 6. This
result gave the important implication that the settlement increased with increases
in column spacing of building frame. This was due to effect of column spacing,
the objective of the study.
The effect of raft thickness: In Fig. 6, at the edge
of rafts, rafts with higher Krs values had the same settlements as those of
lesser Krs values, irrespective of column spacing.

Fig. 17: 
Contact pressure distribution along B1B4 of raft for various
column spacings (linear, Es = 135 MPa, lesser krs values) 

Fig. 18: 
Contact pressure distribution along B1B4 of raft for various
column spacing (nonlinear, lesser krs values) 
In Fig. 6, rafts with higher Krs values resulted in less
settlement at the centre of the rafts than that of the rafts with lesser Krs
value, irrespective of column spacing and for soil modulus of 23 MPa.
The observations made in this study are similar to the analysis of
Viladkar et al. (1991), Maharaj et al.
(2004) and Daniel and Illamparuthi (2007). These
results gave the important implication that with higher raft thickness of foundation
resulted in lesser settlement. This was due to effect of raft thickness, Krs,
the objective of the study.

Fig. 19: 
Validation of ansys,settlement along b1b4 of raft (Column
spacing 6m, linear) 
The effect of young’s modulus of soil, Es: In Fig. 7, the 135 MPa soil modulus showed a similar trend to that of soil with a 23 MPa modulus. However, the 135 MPa modulus of soil resulted in less settlement at both the edge and centre of the raft than the soils with a soil modulus of 23 MPa. For the 135 MPa soil modulus, the settlement at the centre of the raft was marginally higher than the settlement at the edge of the raft, irrespective of column spacings and the difference in settlement between the 3 m column spacing and 7.5 m column spacing of the raft was also small. In addition, for 23 MPa soil modulus, the settlement at the centre of the raft was greater than the settlement at the edge of the raft, irrespective of column spacings and the difference in settlement between the 3 m column spacing and the 7.5 m column spacing of the raft was also high. These results gave the important implication that with higher young’s modulus of soil resulted in lesser settlement of the raft. This was due to effect of young’s modulus of soil, Es, the objective of the study.
The effect of nonlinearity of soil: In Fig. 9 and 10, the nonlinear soil showed a similar trend of the linear soil. The settlement in nonlinear soil also increased with column spacing. However, the settlement of nonlinear soil was higher than that of linear soil. The nonlinear soil showed higher settlement than linear soil as shown in the Fig. 9 and 10. These figures show substantial increases in the settlement of the raft, which is due to the nonlinear effects of soil.
The results gave the implication that the settlement of the nonlinear soil was higher than linear soil. This was due to the effect of nonlinearity of soil, the objective of the study.
Bending moment in the raft
The effect of column spacing: Bending moment variation due to different
column spacing was compared in Fig. 11. In general, the support
moment increased with the increases in column spacing. Moments below the column
locations were positive, except at the edge of the columns with 4.5 and 6 m
spacing. The bending moment variation in 3 and 7.5 m column spacing showed rigid
raft behavior, so that the moments, at both the support and the span were sagging.
The bending moment variation with 4.5 and 6 m column spacings showed flexible
raft behavior, so that support moments were sagging and span moments are hogging.
The moment below the edge of the column of 7.5 m column spacing was the highest
of all column spacings and it was 4.5 times higher than that of 3 m column spacing.
The moment variation in 3 m column spacing was much less than 4.5, 6 and 7.5 m column spacings and it showed very little variation between column locations and spans. The span moments were hogging for 4.5 and 6 m column spacing. Both the support moments and span moments were sagging in the 3 and 7.5 m column spacing. The support moment of 4.5, 6 and 7.5 m column spacing increased by 1.5, 2.75 and 5.12 times that of the 3 m column spacing support moment, respectively.
Figure 12 shows the moment variation for various column spacings. For the soil modulus of 23 MPa, the span moment and edge support moment of 4.5 and 6 m column spacings were hogging, whereas for 3 and 7.5 m column spacings, the span moment and edge support moment were sagging. However, all the inner support moments were sagging, irrespective of column spacing.
Inner support moments for higher Krs values were higher than those of lesser Krs values for 6 and 7.5 m column spacing, whereas, for 3 and 4.5 m column spacing, inner support moments were almost the same. The bending moment variation in 3 and 7.5 m column spacing showed rigid raft behavior. The bending moment variation with 4.5 and 6 m column spacings showed flexible raft behavior. This was due to the effect of column spacing, the objective of the study.
The effect of raft thickness: Span moments and edge support moments for higher Krs values were higher than those of lesser Krs values, irrespective of column spacing. So, the moment increased with increase in raft thickness. This was due to the effect of raft thickness, the objective of the study.
The effect of young’s modulus of soil: Figure 13 shows the moment variation for various column spacings. Bending moment variation with a soil modulus of 135 MPa showed the same trend as that of 23 MPa soil, but 135 MPa soil has a lower moment than 23 MPa soil. This was due to the effect of young’s modulus of soil, the objective of the study.
The effect of nonlinearity of soil: Figure 14 shows the moment variation for the various column spacings of linear and nonlinear soils. For nonlinear soil, the edge support moment of 4.5 m column spacing was hogging, whereas for 3, 6 and 7.5 m column spacing, the edge support moments were sagging. This was due to the effect of nonlinearity of soil, the objective of the study.
Contact pressure below the raft
The effect of column spacing: The contact pressure distribution along
B1B4 of the raft for various column spacings was shown in Fig.
15. At the centre part of the raft, the contact pressure for 6 and 7.5 m
column spacing was slightly higher than that of the 3 and 4.5 m column spacings.
The contact pressure distribution along B1B4 of the raft for various column
spacings is shown in Fig. 17 for the soil modulus of 135
MPa. At the centre part of the raft, the contact pressure for 6 m column spacing
was slightly higher than that of the 3 and 4.5 m column spacings. However, the
contact pressure for the 7.5 m column spacing lied between that of the 6 m column
spacing and 4.5 m column spacing. There is only a marginal variation in the
contact pressure below the raft due to the effect of column spacing, the objective
of the study.
The effect of raft thickness: The contact pressure distribution along B1B4 of the raft for various column spacings was shown in Fig. 16 for the soil modulus of 23 MPa and for higher Krs values.Contact pressure variation of higher Krs values showed the same trend as the lesser Krs values. There was no influence on the contact pressure due to the effect of raft thickness, the objective of the study.
The effect of young’s modulus of soil: In addition, for a soil modulus of 135 MPa, the contact pressures at the column supports was higher than the soil modulus of 23 MPa. This was due to the effect of young’s modulus of soil, the objective of the study.
The effect of nonlinearity of soil: The contact pressure distribution
for the nonlinear soil along B1B4 of the raft for various column spacings
is shown in Fig. 18 for the soil modulus of 23 MPa and for
lesser Krs values; at the column points, the contact pressure was the same for
all column spacings. However, at the end span of the 6 and 7.5 m column spacings,
the contact pressure was less than that of 3 and 4.5 m column spacings. This
was due to effect of nonlinearity of soil, the objective of the study.
CONCLUSIONS
Based on the analysis of the effect of column spacing on the behavior of a five storey, three bays by fivebays space frameraftsoil systems, the following important conclusions were drawn:
• 
The column spacing has a major effect on settlement. The settlement
increased considerably with the increases in column spacing. However, they
were influenced by the relative stiffness of raft Krs and the soil modulus
Es. Between the two parameters, Krs and Es, Es has a major influence on
both the edge and centre settlements, indicating the significance of the
soil modulus in determining raft performance 
• 
Between the linear and nonlinear analysis, settlement was
greater in the nonlinear analysis and the settlements were higher for higher
column spacings 
• 
The
rafts with 4.5 and 6 m column spacings were flexible; thus the moments
are in both the hogging and sagging regions. The rafts with 3 and 7.5
m column spacing were rigid rafts, so the moment is only in the sagging
region 
• 
The inner support moments increased as the column spacing
increases. The span and edge support moments varied between the sagging
and hogging moments and they were influenced by the two parameters: Krs
and Es. The Krs and Es, irrespective of linear and nonlinear analysis,
influenced the raft bending moment equally 
• 
In linear analysis, moments in the end span increased with
as the Es value increased, while Krs altered the moments below the interior
as well as the span moment in the interior panels of the raft. The reverse
was true for the nonlinear soil conditions 
• 
The column spacing has a marginal effect on the contact pressure,
but the two soil parameters, Krs and Es, influence the contact pressure.
The modulus of soil has a greater influence on the contact pressure. At
support points, the contact pressures were higher for a higher soil modulus 
Variation in contact pressure was significant between the linear and nonlinear soil conditions. Contact pressure distribution was more uniform in the nonlinear case and its magnitude was less than that of linear soil, particularly in the end panels of the raft.
NOTATIONS
B: 
Width of the raft 
E_{b}: 
Elastic modulus of beam 
E_{r}: 
Young’s modulus of raft 
Es: 
Elastic modulus of soil 
I_{b}: 
Moment of inertia of beam 
If: 
Influence Factor 
Ir: 
Moment of Inertia of raft 
Ksb: 
Relative stiffness between soil and building 
Krs: 
Relative stiffness between raft and soil 
L: 
Length of raft 
X: 
Distance along X axis 
1: 
Span of the beam 
P: 
Contact pressures from analysis 
q: 
Contact pressure, Total load/Area of the raft 
m: 
Number of storeys 
V_{s}: 
Poisson’s ratio of soil 
w: 
Settlement of the raft 