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Bearing Capacity of Strip Footing on Sand Layer Underlain by
Rockbase of Different Topography
هقدم هن
م. أيون حودى هطز
هاجستيز هيكانيكا التزبة وهندسة األساسات
eng_ayman_matar@yahoo.com
قسن العلىم الهندسية والفنىن التطبيقية
سخانيىن –كلية العلىم والتكنىلىجيا
م. هنذر أحود قاسن
هاجستيز هيكانيكا التزبة وهندسة األساسات
Monzerq1@hotmail.com
قسن العلىم الهندسية والفنىن التطبيقية
خانيىنس -كلية العلىم والتكنىلىجيا
هقدم الى
الوـؤتـوـز العلـوـى األول
دور الكليات والجاهعات فى تنوية الوجتوع
23/10/2013
2
Abstract
The current paper studies the bearing capacity of strip footings
resting a sand layer under by a rock stratum. The rock topography is
considered to be the junction between a horizontal surface and an inclined
surface coinciding under the footing.
A numerical parametric study is performed examine the relation
between the different geometric and stiffness parameters and the bearing
capacity of the footing. Sand layer stiffness is represented by its ratio to the
underlying rock stiffness (Er) and its angle of shear resistance (). Sand
layer topology is defined by its thickness (D), relative distance of rock crest
to the center of footing (X) and the slope of the underlying rock layer ().
Results obtained in this paper confirmed the sensitivity of the bearing
capacity to all the topology mentioned earlier. It also should that for weak
rocks-cement sand with (Er) larger than 40% show negligible effect of the
bearing capacity ratio.
Key words: bearing capacity, layered soils, numerical analysis.
3
الممخص
لحالى بدراسة األساسات الشريطية المرتكزة عمى طبقة سطحية من الرمل والتى يختص البحث ا
، تتغير طبوغرافيا الطبقة الصخرية من السطح األفقى الى السطح ترتكز بدورىا عمى قاعدة صخرية
وقد تم التركيز عمى ىذا الموضوع نظرا لعدم توافر ما يكفى من األبحاث فى ىذا المائل تحت القاعدة.
. المجال
، حيث قسمت المتغيرات تم دراسة المتغيرات المؤثرة فى ىذه المشكمة بطريقة التحميل العددى
األول يتمثل فى خصائص التربة والثانى يمثل األبعاد اليندسية لمقاعدة والتربة المؤثرة الى قسمين
لرمل والقاعدة أسفميا. درست خصائص التربة من خالل معامل المرونة الممثل بالصالبة النسبية بين ا
(. األبعاد اليندسية لمقاعدة والتربة )وزاوية االحتكاك لمتربة (Erالصخرية والتى يرمز لو بالرمز )
(، مكان األساس Dأسفميا قدمت بالمتغيرات الثالثة, سمك الطبقة الرممية والذى يرمز لو بالرمز )
(.بالزاوية ) (، ميل الطبقة الصخرية والذى يرمز لوXوالذى يرمز لو بالرمز )
أكدت النتائج بشكل عام أن مقاومة االرتكاز لألساسات الشريطية تتأثر بشكل واضح بالعوامل
المذكورة أعاله طالما كان سمك طبقة الرمل صغيرا بالمقارنة بعرض األساس، وكذلك يقل التأثر بيذه
العوامل كمما زادت الصالبة النسبية بين طبقة الرمل و الصخر.
قدرة تحمل التربة، التتابع الطبقى، التحميل العددى. :االفتتاحيةالكممات
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Introduction
The ultimate bearing capacity of shallow foundation is one of the major
geotechnical engineering problems, that highly governed by the nonhomogenity
of the bearing strata. The nonhomogenity may resulted from many
configurations; one of them is the stratified composition of the soil deposit.
Two-layer system was, and still, the field of numerous researches such as
Button (1953), Siva Reedy and Sirnivasan (1967), James et al (1969), Abdrabbo
and Mahmoud (1989) and Keny and Andrawes (1995). The relative rigidity
between the two layers was the most important factor, or almost the unique
factor, around which the previous studies were focusing such as Techeng
(1957), Brown and Meyerhof (1969), Meyerhof (1974), Meyerhof and Hanna
(1978), Hanna and Meyerhof (1980), Michalowski and Lei shi (1995), Merifield
(1999), Yin, Wang and Selvadurai (2001), Zhu, Lee and Jiang (2001) and Brad
Carter (2005).
The survey of the available literature indicated that there is a shortage and
information lag about the case of two-layer system composed of soil layer
overlying a rock base. A limited number of researches were concerning with the
case of a horizontal surface of the rock base such as Mandel and Salencon
(1969) and Cerato and Lutenegger (2006). Different topographies for the
surface of the rock base were not the subjects of the recently available
researches. The current paper is focusing on the effect of the rock surface
topography on the bearing capacity of shallow rigid strip footings. An inclined
5
rock surface was the considered, in which the surface was horizontal and at a
given crest, the surface was suddenly inclined to angle () with the horizontal.
Numerical parametric study was performed by using the finite element program
“PLAXIS”, (version 8.2).
The soil layer was considered as sand of variable unit weight () and
corresponding angle of internal friction (). The variation of sand properties
enabled the consideration of different values of the compression modulus (E).
The compression modulus of sand was normalized by the compression modulus
of rock via the ratio (Er), named Relative Rigidity of sand/rock system. The
variation of (Er) indicated the effect of sand properties on the bearing capacity
of strip footings. The geometry of the system was presented by the depth of
sand layer (D), the location of the footing center relative to the crest point (X),
the inclination angle of rock surface (), and the relative rigidity (Er). The
dimensions (D) and (X) were normalized by the footing width (B), as ratios
(D/B) and (X/B), respectively. Wide ranges for the abovementioned factors
were considered to investigate their effects on the bearing capacity of the strip
footings.
The analysis of the obtained results indicated that the bearing capacity
value was very sensitive to the system geometry in which the rock surface
topography was considered the most important factor. The effect of relative
6
rigidity of the soil/rock system on the bearing capacity of strip footing is
relatively obvious.
System Definition
The study aims to evaluate the bearing capacity of a shallow strip footing,
subjected to vertical concentric load and resting on nonhomogeneous soil strata.
The strata are composed of a top sand layer followed by a layer of rock of
infinite depth. The top surface of rock is suddenly changed from a horizontal
plane to inclined plane at a specified crest, as shown in figure. The horizontal
part of the rock surface is at a depth (D) below the foundation level. At the
crest, the rock surface is inclined with an angle () to the horizontal. The
location of the strip footing was related to the crest of the rock surface. A
distance (X) was used to define the location of the footing center right or left to
the crest according to the sign convention shown in Figure 1.
Figure 1 System Definition
Parametric Study
In the performed parametric study, the soil properties and the geometry of
the system are presented by different variables as follows:
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Soil Properties
The soil properties are presented via the relative rigidity (Er) that relate
the modulus of elasticity of soil (E1) to the modulus of elasticity of rock (E2),
as; ModulusRockE
ModulusSoilEEr
2
1 .
The soil modulus is chosen according to the considered unit weight () and the
corresponding angle of internal friction (). Consequently, the value of (E1) and
interns the value of (Er) were changed according to the value of () and (),
presented the range of variation of the relative rigidity (Er) and the
corresponding variation of the angle of internal friction () and variation of unit
weight ().
Table 1Considered Range of Soil Properties, E2 = 250 Mpa, as a constant
Relative Rigidity,
2
1
E
EEr
5% 10% 15% 40%
Angle of internal fiction, () 30o 32
o 35
o 40
o
Unit weight, (), (kN/m3) 17 18 19 20
Problem Geometry
The geometry of the system is presented through different variables such as;
Soil depth to footing width ratio, (D/B). The values of (D/B) are selected
to be 0.25, 0.5, 1.0 and 2.0.
Footing location to footing width ratio, (X/B). The analysis is considered
at (X/B) equal -4.0, -2.0, -1.0, -0.5, 0.0, +0.5, +1.0, +2.0 and +4.0.
8
Rock surface inclination angle, (). The values of () are varied from
zero to 60o with an interval of 15
o.
It is worth to mention that the presented ranges of geometry are considered for
each case of soil properties presented in Table 1.
Results and Discussions
For each case of loading, the ultimate bearing capacity was recorded and
normalized by the ultimate bearing capacity of a reference case. The reference
case was the case of strip footing under concentric vertical load resting at the
free surface of a homogeneous sand deposit. The normalization was presented
by the Bearing Capacity Ratio (BCR) which is:
CasereferencetheofCapacityBearingUltimate
CaseanyofCapacityBearingUltimateBCR
The effects of soil properties and geometry on values of BCR are
investigated and the subsequent sections present the effect of each parameter.
Effect of Soil Thickness
As presented and obvious through Figure 2 to Figure 6, the bearing capacity
ratio (BCR) is generally decreased with the increase of the soil thickness ratio
(D/B). This trend is existing regardingless to the soil rigidity (Er) or the other
system geometry factors ( and X/B). These results confirmed that the effect of
the rock base on the bearing capacity of the strip footing was vanished
once 00.1/ BD .
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a
= 0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
D/B
BCR
Er = 5%
Er = 10%
Er = 15%
Er = 40%
Figure 2 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with ()
b
= 15o
X/B = 0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
D/B
BCR
Er = 5%
Er = 10%
Er = 15%
Er = 40%
Figure 3 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er), with
()
c
= 30o
X/B = 0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
D/B
BCR
Er = 5%
Er = 10%
Er = 15%
Er = 40%
Figure 4 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er), with
()
d
= 45o
X/B = 0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
D/B
BCR
Er = 5%
Er = 10%
Er = 15%
Er = 40%
Figure 5 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er), with
()
e
= 60o
X/B = 0.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
D/B
BCR
Er = 5%
Er = 10%
Er = 15%
Er = 40%
Figure 6 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er), with
()
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Effect of Footing Location
According to the sign convention of the footing location coordinate (X), the
footing at negative coordinates was completely above the horizontal surface of
the rock base whereas, at positive coordinate it was completely above the
inclined surface of the rock base.
As a general observation, through Figure 7 to Figure 10, by moving the
footing far from the origin in negative direction of (X) the BCR is increased and
vice verse, the BCR is decreased by moving the footing in positive direction.
The effect of rock surface slope is decreased by moving either positively
or negatively along the (x) axis. In positive direction, the effect of rock surface
is vanished and the BCR decreased to 1.00, i.e. the bearing capacity is similar to
that of homogeneous bed of sand. On the other hand, in negative direction, the
bearing capacity increased to reach the value of a sand layer resting on a
horizontal bed of rock (=0).
Accordingly the effect of soil depth ratio (D/B) is controlling the BCR as
long as the footing was moving along the negative direction of (x) axis. The
comparison between the Figure 7 to Figure 10, can confirmed, as mentioned
before, that the sensitivity of the BCR to the variation of (X/B) is decreased
with the increase the relative rigidity (Er). Finally, as obvious in the figures,
satisfying two conditions, or even only one of them, is enough to vanish the
effect of the footing location ratio (X/B). One of these conditions is the
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increasing of the soil depth to be 00.1/ BD , whereas the other one is the
increasing of the soil rigidity to be %40rE .
a
= 15o
Er = 5 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
D/B=0.25
D/B=0.50
D/B=1.00
D/B=2.00
Figure 7 Effect of (X/B) on the Bearing Capacity
Ratio (BCR) at different values of (D/B), with
(Er=5%)
b
= 15o
Er = 10 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
D/B=0.25
D/B=0.50
D/B=1.00
D/B=2.00
Figure 8 Effect of (X/B) on the Bearing Capacity
Ratio (BCR) at different values of (D/B), with
(Er=10%)
c
= 15o
Er = 15 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
D/B=0.25
D/B=0.50
D/B=1.00
D/B=2.00
Figure 9 Effect of (X/B) on the Bearing Capacity
Ratio (BCR) at different values of (D/B), with
(Er=15%)
d
= 15o
Er = 40 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
D/B=0.25
D/B=0.50
D/B=1.00
D/B=2.00
Figure 10 Effect of (X/B) on the Bearing Capacity
Ratio (BCR) at different values of (D/B), with
(Er=40%)
Effect of Inclination angle of Rock Surface ()
In order to investigate the effect of the sudden change of rock surface into
different inclination angles, the relationships between (BCR) and footing
location ratio (X/B) were drawn for a range of () from = 0 to = 60o. These
relationships are shown in Figure 11 to Figure 14, at given values of (D/B),
chosen as 0.25, with different values of (Er).
12
As shown in Figure 11 to Figure 14, the general trend of the obtained
relationships is, as long as the footing is moving from the far location in
negative direction towards the crest or the point of change, the (BCR) was
gradually decreased, to be 1.00 at the far location in positive direction. This
behavior was discussed in the last section, so that it was not the objective of
Figure 11 to Figure 14.
The objective of Figure 11 to Figure 14 was presenting how the rate of
the decrement in (BCR) was highly affected by the inclination angle (). It is
obvious that the rate of reduction is increased with the increase of the angle ().
The largest effect is obtained once the center line of the footing is passing the
crest, i.e. at the location ratio (X/B = 0). It is worth to mention here, that all the
sensitivity of the (BCR) to the inclination angle (), as one of the system
geometry factors, is decreased to be vanished at the rigid soil of Er=40%.
a D/B = 0.25
Er = 5 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
Figure 11 Effect of footing location ratio (X/B) on
the (BCR) at different values of (), with (Er=5%)
b D/B = 0.25
Er = 10 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
Figure 12 Effect of footing location ratio (X/B) on
the (BCR) at different values of (), with (Er=10%)
13
c D/B = 0.25
Er = 15 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
Figure 13 Effect of footing location ratio (X/B) on
the (BCR) at different values of (), with
(Er=15%)
d D/B = 0.25
Er = 40 %
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-4 -3 -2 -1 0 1 2 3 4
X/B
BCR
Figure 14 Effect of footing location ratio (X/B) on
the (BCR) at different values of (), with
(Er=40%)
Effect of Relative Rigidity, (Er)
In order to investigate the effect of relative rigidity (Er), the relationships
between (BCR) and footing depth ratio (D/B) were drawn for a range of (Er)
from Er = Rigid Base, 1%, 5%, as shown in Table 2. These relationships, as
shown in Figure 15 to Figure 17, were drawn at given values of (), chosen as
(=0.0), with different values of surcharge ratio (Rq).
Besides the numerical range of (Er), Mandel and Salencon‟s (1969)
theory added to the figures as the theoretical solutions.
As shown in Figure 15 to Figure 17, the bearing capacity ratio (BCR) was
generally decreased with the increase of the soil thickness ratio (D/B). Besides
this general remark, the (BCR) was founded to be sensitive to the relative
rigidity (Er), as shown in the collected Figure 15 to Figure 17, the (BCR) is
generally increased with the increase of relative rigidity (Er).
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The objective of Figure 15 to Figure 17 is comparing the numerical
solutions and the theoretical solutions. The theoretical result is similar to the
result from numerical solution when the relative rigidity is equal rigid base.
It is obvious that the (BCR) in the theoretical solutions depend on the
higher relative rigidity, (Er=Rigid Base). But the (BCR) in the numerical
solutions depend on the relative rigidity where the (BCR) increased with the
increase the relative rigidity.
Table 2 Considered Range of Relative Rigidity
Relative Rigidity,
2
1
E
EEr
(Rigid
Base)
1% 5%
E2, (MPa) 1250 250
E1 = 12500 KPa, as a constant.
a
Rq=0.00B
=0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
D/B
BCR
Mandel &
Salencon (1969)Rigid Base
Er=1%
Er=5%
Figure 15 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er),with
(Rq=0.00B)
15
b
Rq=0.50B
=0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
D/B
BCR
Mandel &
Salencon (1969)Rigid Base
Er=1%
Er=5%
Figure 16 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er),with
(Rq=0.50B)
c
Rq=1.00B
=0.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
D/B
BCR
Mandel &
Salencon (1969)Rigid Base
Er=1%
Er=5%
Figure 17 Effect of (D/B) on the Bearing Capacity
Ratio (BCR) at different values of (Er),with
(Rq=1.00B)
Conclusions
The study aims to focus on the bearing capacity of a shallow strip footing,
subjected to vertical concentric load and resting on nonhomogeneous soil strata.
The strata were composed of a top sand layer followed by a rock bed of infinite
extent. The upper surface of rock was considered have a suddenly change from
a horizontal plane to inclined plane at a specified crest.
The ultimate bearing capacity was estimated to explain how it may affect
by different factors such as the relative rigidity of soil (Er), the system such as
depth (D), location of footing (X), inclination angle ().
A parametric study was carried out using a finite element method via the
well established program PLAXIS, which is intended for the analysis of
deformation and stability in geotechnical engineering projects. The parametric
study revealed the following conclusions:
16
The bearing capacity ratio (BCR) of single strip footing was generally
decreased with the increase of the soil thickness ratio (D/B).
The effect of the rock base on the bearing capacity of the strip footing was
vanished once 00.1/ BD .
If the strip footing is constructed far from the origin in negative direction of
(X) the BCR was increased and vice versa, the BCR was decreased by
moving the footing in positive direction.
Increasing the soil depth ratio 00.1/ BD and/or increasing the soil rigidity
%40rE were enough to vanish the effect of footing location ratio (X/B)
on the value (BCR).
BCR generally was decreased with the increase of the inclination angle of
rock surface () for the soil having the same value of relative rigidity (Er)
and the same location of footing (X).
The effect of the inclination angle of rock surface () is affected by moving
the footing either positively or negatively along the (x) axis. In positive
direction, the effect of the inclination angle of rock surface () is vanished
and the BCR decreased to 1.00, i.e. the bearing capacity is similar to that of
homogeneous bed of sand. On the other hand, in negative direction, the
bearing capacity increased to reach the value of a sand layer resting on a
horizontal bed of rock (=0).
17
The largest affect of the inclination angle of rock surface () is obtained
once the center line of the strip footing is passing the crest, i.e. at the location
ratio (X/B=0.0).
Increasing the soil rigidity %40rE were enough to vanish the effect of
inclination angle of rock surface ().
The (BCR) in the theoretical solutions, (Mandel and Salencon‟s (1969)),
depend on the higher relative rigidity, (Er=Rigid Base). But the (BCR) in the
numerical solutions depend on the relative rigidity where the (BCR)
increased with the increase the relative rigidity.
The results from the numerical solutions approved an agreement with the
results from the theoretical solutions such as Mandel and Salencon‟s (1969)
at (Er=Rigid Base).
18
References
[1] Button, S. J. (1953). “The Bearing Capacity of Footings on Two-Layer Cohesive
Subsoil”, Proceedings, 7th
International Conference on Soil Mechanics and
Foundation Engineering, Zurich, vol1, pp. 332-335.
[2] Reddy, A.S. and Srinivasan, R.J., (1967). “Bearing Capacity of Footings on Layered
Clays”, Journal of the Soil Mechanics and Foundations Division, ASCE, 93, SM2, pp.
83-99.
[3] James, C.H.C., Krizek, R.J., and Baker, W.H., (1969). “Bearing Capacity of Purely
Cohesive Soils with a nonhomogeneous Strength Distribution”, Highway Research
Record, No. 282, pp. 48-56.
[4] Abdrabbo, F. M., and Mahmoud, M. A. (1989). “Bearing Capacity of Shallow
Footing on Sand bed intervened by a Clay Layer”, Al-Azhar engineering first
conference.
[5] Kenny, M. J., and Andrawes, K. Z., (1995).” Technical note, „The Bearing Capacity
of Footings on Sand Layer overlying Soft Clay”, Geotechnique 47, No. 2, 339-345.
[6] Tcheng, Y., (1957). “Shallow Foundations on a Stratified Soil”, Proc. 4th ICSMFE,
London, Vol. 1, pp. 449-452.
[7] Brown, J.D., and Meyerhof, G.G., (1969). “An Experimental Study of the Ultimate
Bearing Capacity of Layered Clay Foundations”, Seventh International Conference on
Soil Mechanics and Foundation Engineering, 2: 45-51.
[8] Meyerhof, G.G., (1974). “Ultimate Bearing Capacity of Footing on Sand Layer
Overlying Clay”, Canadian Geotchnical Journal, Vol. 11, pp. 223-229.
[9] Meyerhof, G. G, and Hanna, A. M. (1978). “Ultimate bearing capacity of foundations
on layered soils under inclined load”, Canadian Geotechnical Journal, 15, pp. 565-
572.
19
[10] Hanna, A. M., and Meyerhof, G. G. (1980). “Design Charts for Ultimate
Bearing Capacity of Foundations on Sand overlying Soft Clay”. Canadian
Geotechnical Journal, 17: 300–303.
[11] Michalowski, R. L., and Shi, L. (1995). “Bearing Capacity of Footings over
Two-Layer Foundation Soils”, J. of Geotech. Engineering. ASCE, 121(5), 421–428.
[12] Merifield, R. S., Sloan, S. W. & Yu, H. S. (1999). “Rigorous Plasticity
Solutions for the Bearing cCapacity of Two-Layered Clays”, Geotechnique 49, No. 4,
471-490.
[13] Jian-Hua Yin, Yu-Jie Wang, and A. P. S. Selvadurai. (2001). “Influence of
nonassociativity on the bearing capacity of a strip footing”, Journal of Geotechnical
and Geoenvironmental Engineering, Vol. 127, No. 11, pp. 985-989.
[14] Zhu, D.Y., Lee, C.F. & Jiang, H.D., (2001). “A numerical Study of the
Bearing Capacity Factor N”, Canadian Geotchnical Journal, Vol. 38, pp.1090–1096.
[15] Brad Carter, (2005). “Bearing Capacity of a Strip Footing on a Layered Soil”
Senior Report, CE 5943, University of New Brunswick.
[16] Mandel, J., and Salencon, J., (1969). “Force portante d‟un sol sur une assise
rigide”, In Proc., VII Int. Conf. Soil Mechanics Foundation Engineering., Mexico
City, 2, pp. 157.
[17] Cerato, A. B. and Lutenegger, A. J. (2006). “Technical Note, Bearing
Capacity of Square and Circular Footings on a Finite Layer of Granular Soil
Underlain By A Rigid Base”, Journal of Geotechnical and Geoenvironmental
Engineering, Vol. 132, No. 11, ASCE, pp. 1496-1501.
20
List of Symbols
B Width of footing
BCR Bearing capacity ratio
D Depth of sand layer
E1 Young‟s modulus of elasticity of soil
E2 Young‟s modulus of elasticity of rock
Er Relative rigidity
X Location of footing
Rock inclination angle
Angle of internal friction of soil
Unit weight of soil
LIST OF FIGURES
Figure 1 System Definition ........................................................................................................ 6
Figure 2 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with
() .......................................................................................................................................... 9
Figure 3 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with
() ....................................................................................................................................... 9
Figure 4 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with
() ....................................................................................................................................... 9
Figure 5 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with
() ....................................................................................................................................... 9
Figure 6 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with
() ....................................................................................................................................... 9
Figure 7 Effect of (X/B) on the Bearing Capacity Ratio (BCR) at different values of (D/B),
with (Er=5%) ............................................................................................................................ 11
21
Figure 8 Effect of (X/B) on the Bearing Capacity Ratio (BCR) at different values of (D/B),
with (Er=10%) .......................................................................................................................... 11
Figure 9 Effect of (X/B) on the Bearing Capacity Ratio (BCR) at different values of (D/B),
with (Er=15%) .......................................................................................................................... 11
Figure 10 Effect of (X/B) on the Bearing Capacity Ratio (BCR) at different values of (D/B),
with (Er=40%) .......................................................................................................................... 11
Figure 11 Effect of footing location ratio (X/B) on the (BCR) at different values of (), with
(Er=5%) .................................................................................................................................... 12
Figure 12 Effect of footing location ratio (X/B) on the (BCR) at different values of (), with
(Er=10%) .................................................................................................................................. 12
Figure 13 Effect of footing location ratio (X/B) on the (BCR) at different values of (), with
(Er=15%) .................................................................................................................................. 13
Figure 14 Effect of footing location ratio (X/B) on the (BCR) at different values of (), with
(Er=40%) .................................................................................................................................. 13
Figure 15 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of
(Er),with (Rq=0.00B) ............................................................................................................. 14
Figure 16 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of
(Er),with (Rq=0.50B) .............................................................................................................. 15
Figure 17 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of
(Er),with (Rq=1.00B) .............................................................................................................. 15
LIST OF TABLES
Table 1Considered Range of Soil Properties, E2 = 250 Mpa, as a constant .............................. 7
Table 2 Considered Range of Relative Rigidity ...................................................................... 14
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