Moment of tests conducted on clay soils.

 

Moment
carrying capacity of pad foundations

 

H.T.V.Fonseka

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University
of Moratuwa,Katubedda, Moratuwa Sri Lanka.      
[email protected]       

Dr.L.I.N. De Silva

University of Moratuwa , Katubedda, Moratuwa, Sri
Lanka.

 

Abstract:

 

 

 

 

Keywords:  Bearing capacity; laterite soil; finite
element analysis; Numerical modelling    

 

1.   
Introduction

Isolated pad footings are getting more
popular due to construction of steel fabricated structures. And also due to
construction of wind turbines and other towers also causes for the popularity
of pad footings. Most important factor to be considered in designing a pad
footing is bearing capacity. (Taiebat &
Carter, 2000). Bearing pressure of pad
foundations depends by the moment that induced on that foundation also. This
structures need to withstand for many lateral loads, such as wind loads. so
these structures need to  be designed to
carry moments.

Moment carrying capacity of pad footings
is also a important factor when consider the stability of  structures. Structures are designed by
assuming previous results of tests conducted on clay soils. But it is not
perfectly match with the Sri Lankan context. Sri Lanka has residual soils
(laterite soils) in many places. So the moment carrying capacity of pad
footings rests on laterite soils is a needing factor for economical designs. Otherwise
designers will underestimate the moment carrying capacity of pad foundations.
It will lead to a uneconomical design. (Patnaik, Nikraz, & Young, 2000)

The moment carrying capacity can be
increased by increasing the dimensions of footing. But it is not economical to
change the dimensions of footings always. (Patnaik, Nikraz,
& Young, 2000).
The moment carrying capacity of pad footings can be increased by changing the
depth of the foundation rests. But there is no proper investigation done to
check the moment carrying capacity of footings with the embedded depth.

 

2.     
Back ground

Moment carrying capacity can be
estimated by considering the bearing capacity of soil when there is a
eccentricity load acting on the foundation. There are many equations to
estimate the bearing capacity of the soil. Tazaghi(1943) have derived a equation
to estimate the bearing capacity. But it does not cover about the moments so
many other equations have been derived to overcome problems with this Tazaghi
equation.  

Vesic (1973), Meyerhof (1951),
Hansen(1961) are some equations that have been derived to calculate moment
carrying capacity of foundations. In every above equation the moment carrying
capacity of foundations are estimated by define effective width (B’) and
effective length (L’) according to the moment induced. From that effective
dimensions the moment capacity will be estimated.

In Tarzaghi equation of estimating
bearing capacity it is not considered that bearing capacity change with the
depth of the embedded depth of the foundations. But Vesic, Meyerhof , and
Hansen have considered the depth factor when estimating the moment carrying
capacity. Those shows that when embedded depth increases the bearing capacity
will also increase.       

2.1 Failure equations

Tazaghi bearing capacity equations have
not consider about moments and embedded depth when deriving the equation. So
that equation cannot be used to find the moment carrying capacity of footings.

Bearing capacity of a foundation resting
on cohesive soil subjected to a vertical loading can be estimated using
Meyerhof bearing capacity equation. (Equation 1)

 

-(1)

qu is ultimate bearing capacity on foundation.

c is cohesive shear strength of soil

q is vertical loading acting on the foundation.

B width of the foundation 

Nc ,Nq ,N? are bearing capacity
factors.

sc ,sq ,s? are factors which
consider about the shape of the foundation.

dc ,dq ,d?  are depth factors which consider aabout the
embedded depth of the foundation.

 

Bearing capacity of foundations resting
on cohesive soils subjected to vertical loading can be estimate using Vesic and
Hansen’s equations. These equations have been modified to estimate the bearing
pressure when there is inclination of load, ground, and base.

qu is ultimate bearing capacity on foundation.

c is cohesive shear strength of soil

q is vertical loading acting on the foundation.

B width of the foundation 

Nc ,Nq ,N? are bearing capacity
factors.

sc ,sq ,s? are factors which
consider about the shape of the foundation.

dc ,dq ,d?  are depth factors which consider about the
embedded depth of the foundation.

ic ,iq ,i? are load inclination
factors

gc ,gq ,g? are ground inclination
factors.

bc ,bq ,b? are base inclination
factors.

 

2.2  
Finite element Modelling

Finite
element modelling is a method of analysing stress and forces of different
structures. This modelling is used for the numerical analysis of pad footings.
Finite element modelling can be done in 2D or in 3D plane. 2D analysis is easy
to analysis and runs faster than 3D modelling. But 3D modelling will gives us
most accurate answer. For the finite element analysis there are many softwares
have been developed. But Plaxis can be used for simple geometry problems, since
it is more user friendly. Abaqus, Flac 3D, GTS-Nx Midas are also kind of
softwares used to model finite element modelling. These software can be used if
the problem is more complex. Such as when need to consider stability of piles
and walls. It is better to use more complex software.

In
the analysis it is assumed that foundation rests on a homogeneous laterite
soil. Model analysis it will take much time if the modelis complex. Time can be
redused  by making more simple the model.
Since the foundation is Square foundation it can be assumed symmetric on both
two axis. So the modelling can be done for the quarter of the foundation. From
this assumption the analysis time can be reduced. This analysis it is assumed
moment will apply on a one plane only. (Keyghobadi, Ardakani, Deshghani, &
Dezfooli, 2014)   

It is
assumed that the foundation is made of concrete. And concrete  properties have been included to the model
analysis. Since this rest on laterite soil it is assumed that foundation is
rigid foundation.  Previously found
experimental soil parameters are also included for the analysis.

Analysis
is done mainly for two conditions.

1.     
For
the experimental model conditions.

2.     
For
the real type foundation.

First
Experimental all 3 conditions will be analyse using this method. Then a real
foundation dimensions will be given and analyse it also.

When
analysis is done by giving a pure moment it cannot be identify the failure
point. Because when the moment increase the displacement also increase. So the
failure point cannot be clearly identify. For that foundation can be subjected
to a horizontal force other than moment. So the with the increase of moment we
could recognize the failure point with the help of horizontal load.
Displacement vs horizontal load curve will shows a maximum peak value. On that
point displacement can be taken as the failure displacement. Corresponding
moment will be the max moment. (Taiebat &
Carter, 2000)  Figure 1 shows vertical and horizontal forces
variation with the increase of vertical load.

Figure 1: horizontal and vertical responses with
deflection (Taiebat & Carter, 2000)

Finite
element  Analysis need to be done by
defining a mesh. The accuracy and the analysis running speed depends on the
mesh size we defined. Figure 2 show a mesh which was done to investigate
bearing capacity of square foundations by using plaxis 3D software.

Figure 2 : results of square foundation bearing
capacity analysis. (Keyghobadi, Ardakani, Deshghani, & Dezfooli,
2014)

2.3  
Experimental Tests

Experimental
tests will give more accurate and reliable answers with comparing to
theoretical and numerical analysis. Because those analysis were done by
assuming some assumptions. Experimental analysis are done without any analysis.
So the experiments need to be more accurate. Other results are compared with
the experimental results.

First
it is need to do some tests, to find soil parameters. Laterite soil parameters
find by doing some different tests. Tri axial test, sieve analysis ,proctor
compaction tests are some test that need to do. From that we need find soil
classification, soil shear parameters, maximum dry density, Modules of
elasticity, and Poisson’s ratios etc. the rest and expected results are shown
table1. 

 

 

Table 1:Soil test and
expected results

Test name

Soil parameters

Parameter

Notation

 

Triaxial test

Modules of Easticty

E

 

 

Poissions ratio

?

 

 

 

 Friction angle
 

Ø

 

Cohesion
 

C

Sieve
analysis

Classification
 

Proctor
compaction test

Optimum moisture content
 

?

 

Maximum
dry density

?
 
 

 

Foundation
size, embedded depth, and soil parameters will affect the moment carrying
capacity of pad footings. Even the size affect the moment carrying capacity it
is proposed to have only 300×300 size foundation. The model foundation is
expected to made of steel plate and connect a steel rod which will act as a
column. So  the loading can be given
through it.  Moment carrying capacity is
determine of the laterite soil. So it is not needed to change the soil type.

 

 Test is proposed to change the embedded depth
of the foundation and determine the moment capacity. It is proposed to test
moment capacity at 300mm,600mm and 750mm depths.it is proposed to conduct the
test on a Perspex box. The bearing capacity can affect 2X width of the
foundation area. So the minimum size of the Perspex box will be 1500mmX1500mm
box. Soil is proposed  to compact 75mm
thick layer by layer with coloured soil. So the failure pattern can be observed
after failure. Digging will done along the centre line. Compaction is proposed
to have more than 90% compaction.

 

The
loading will be done laterally with help of steel rod. It is proposed to have a
pully and loading system externally. Figure 3 shows how the loading (moment) will
apply to the foundation.

 

Figure 3: Loading system (Patnaik, Nikraz, & Young, 2000)

   

2.3 Data analysis

Data obtained by experimental, numerical
and theoretical results are need to be compared and analyse. Results can be analyse
by graphical or tabular methods.

This analysis will lead us to build
relationship between theoretical and Numerical with the experimental results. This
will helps us to compare all test.

From these analysis it will helps to
predict actual moment carrying capacity of real type foundations. And also this
will helps to find the reliability of each equation for the laterite soils.         

3. Conclusion

Experimental values will gives us more
accurate and real answers compared to theoretical and numerical analysis, so
from that results, numerical and theoretical results need to be adjust and
represent for laterite soils. This will helps to analyse real size foundations
in more accurate way.

Finding moment carrying capacity of pad
foundations leads for economical designs in Sri Lankan construction industry.

Acknowledgements

The authors who have done experiments
and numerical analysis. Presented the results more reliable way. And special
thanks goes to Dr.L.I.N. De Silva who is my research supervisor, for advising
and guiding me to do a good research.

 

References

 

Keyghobadi, M. H., Ardakani, A. R., Deshghani, M.,
& Dezfooli, M. G. (2014). 3d Numerical Analysis of bearing Capacity of
square foundations on geogrid reinforced soil . International Journal of
scentific research in knowlage, 416-424.
Patnaik,
A. K., Nikraz, H., & Young, S. M. (2000). Momentcarrying capaciy of
shallow isolated footings resting on sandy soils. Australian Geomechanics,
47-52.
Taiebat,
H. A., & Carter, J. P. (2000). Numerical studies of the bearing capacity
of shallow foundations on cohesive soil subjected to combined loading. Geotechnique,
409-418.