Moment

carrying capacity of pad foundations

H.T.V.Fonseka

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.