 Open Access
 Total Downloads : 250
 Authors : Prof. Binaya Kumar Panigrahi, Er. Tophan Tripathy, Er. Biranchi Narayan Panda
 Paper ID : IJERTV4IS110355
 Volume & Issue : Volume 04, Issue 11 (November 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS110355
 Published (First Online): 19112015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
An Inquest into the Bearing Capacity Problems of Surface Footing on Uniform Sand
Prof. Binaya Kumar Panigrahi Prof. & Head,
Civil Engineering Department, GIET, Baniatangi, Bbsr751013,India
Er. Tophan Tripathy
Asst. Prof,
Civil Engineering Department, GIET, Baniatangi, Bbsr751013,India
Er. Biranchi Narayan Panda Assistant Engineer,
Govt. of Odisha
Abstract Status of soilstructure interaction today has a grey area which is yet to be understood well. Bearing capacity of soil with reference to a particular type, size and depth of footing is dependent upon not only on the shear characteristics of soil but also on the footing, in so far as its surface or smoothness is concerned. In order to get a better understanding about the aforesaid matter, a model study (of footing) has been taken up with different sized and typed(concrete and steel) footings of varying roughness/smoothness in a soil medium which is sand. It has been established that the bearing capacity factor Ny is not a function of angle of internal friction only, surface roughness of the footing has also a considerable effect on the value of Ny . The surface roughness of the footing increases the bearing capacity factor Ny considerably in case of dense sand .
Keywords Bearing capacity,Surface roughness

INTRODUCTION
Bearing capacity (ultimate) of a footing is defined as the minimum intensity of pressure at which a footing shall fail either in shear or due to excessive settlement. Besides field loading tests the analytical methods for calculating soil bearing capacity may be summed up as theory of plasticity, classical earth pressure theory, theory of elasticity and methods relying on laboratory experimental results. Some of the early researchers who worked on this problem are W,J.M..Rankine (1985), H.E.Pauker (1989),Bell(1915),
L.Prandtl (1920), K.Terzaghi (1943), W.S.Houlsby (1956) etc. Out of these Russian military engineer cornel Pauker and Rankine postulated their theories of bearing capacity of cohesion less soil based on earth pressure theories. Prandtl's bearing capacity equation based on plastic equilibrium theories was applicable to cohesive or C SOIL. With Terzaghi and Taylor's correction the modified Prandtl's formula could he used for non cohesive soil ( c=0).
Terzaghi's analysis for ultimate bearing capacity of a footing was based on partly theory and partly experimental. It was an improvement on the Prandtl's theory of plastic equilibrium.
During derivation of the equation of bearing of a strip footing, Terzaghi assumed the footing to be rough and also the two slanting lines of the elastic triangular wedge just below the footing make an angle of with the horizontal. However
later model tests conducted by De Beer and Vesic (l958) showed that the Terzaghi's assumed rupture surface for bearing capacity failure is correct but the two slanting sides of the elastic prism make an angle of 45Â°+/2 with the horizontal instead of () with the horizontal. Based on this mechanism of failure the ultimate bearing capacity of a strip footing may be written as
Qc =Qc+Qq+Qy .(1)
Where Qc, Qq and Qy, are bearing capacity due to cohesion, surcharge and unit weight of the soil respectively. In deriving this theory Terzaghi assumed that the failure surface does not extend above the base of the footing i.e. the shear resistance aboNe the base of the footing is neglected. To obviate this lapse of the assumption surface footings have been chosen for analysis. With this strategy Qq=0. Also by choosing sand as the load bearing medium Qc= 0, so
Q u= Qy (2)
In addition to the above 3 types of uniform sand (4,75 mm to 2mm, 2 mm to 425Âµ and < 475Âµ) were chosen as the load bearing medium. The purpose of taking uniform sand was to keep , more or less constant through out the testing.
After Terzaghi's simplified pioneering work many researchers (Mayerhoff,1951,1963;Lundgren and Mortensen,1953;Balla,1962;) gave their solutions which showed that the hearing capacity factors Nc, Nq do not change in a remarkable manner, on the other hand the value of `Ny' for any particular value of change in a wide manner which may be due to the assumption of a wedge shape soil zone located directly below the footing. However this investigation veers around Terzaghi's mode of analysis.
Thus equation of bearing capacity of a surface footing on sand according to Terzaghi i.e. equation (2) can be written as
Qu= 0.5Y B Ny (3)

EXPERIMENTAL SET UP
The test was carried out in a masonry tank having an internal dimension of 60cm*60cm*30 cm. A mild steel loading frame was used, to the center of which a hollow vertical shaft (guide pipe) has been welded. The solid iron rod,
which carries the loading platform at its top passed through the hollow cylindrical metal shaft. The bottom of the iron rod was threaded so that either the smooth steel footing or small metal plate in case of rough concrete footing is used, this plate rests over the concrete block used as footing. There is a horizontal bolt connected to the hollow vertical shaft to clamp and unclamp the iron rod carrying the loading platform. To accommodate higher intensity of loading a wooden platform has been attached to the steel loading platform by nut and bolt arrangement. Two dial gauges with magnetic base are used for measuring the settlement of footings. The dial gauges used have a least count of 0.001 cm and 5 cm range. The dial gauges were mounted on two opposite sides of the wooden platform to measure the settlement of the footing. Steel (smooth base) and concrete (rough base) footings of circular (5.08 cm and 6.35 cm and square (5.08 cm* 5.08 cm and
6.35 cm * 6.35 cm) shape are used.
Three types of dry uniform sand (4.75 mm to 2mm, 2 mm to 425Âµ and < 475Âµ) representing coarse, medium and fine sand were used as the load bearing medium. The properties of sands were given in Table1.
TABLE I. PROPERTIES OF SANDS
Sl.N
o
Particle Size
Specifi c Gravity
Relativ e Density (ID) in
%
Placem ent Density (Kg/m3
)
Uniformi ty coefficie nt (CU )
Coeffic ient of Curvat ure ( CC
)
1
4.75mm to 2mm(Coars e Sand)
2.605
69.76
1541
–
–
2
2mm to 425Âµ
(Medium Sand)
2.616
63.67
1542
1.33
0.947
3
Finer than 425Âµ (fine Sand
2.718
62.80
1519
1.75
1.329
The loading frame was put across the masonry tank so that the axial loading shaft occupies the central position. After the loading platform was loaded to desired degree, the rod carrying the platform was unclamped and the settlement was observed for a period of 24 hours before applying the next load increment .This procedure was repeated till failure of footing took place. The experimental set up was shown in figure 1. The value of bearing capacity factor 'Ny' was calculated from the experimental ultimate bearing capacity value for both smooth and rough footings.
Figure 1: Experimental set up

TEST RESULTS
TABLE II. COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 5.08CM X5.08CM)
in Degree
Smooth Footing
Rough Footing
Difference
% Increase
40
72.18
168.47
96.29
133.40
42
118.72
365.105
246.385
207.53
44
195.44
562.06
366.62
187.58
Bearing capacity factor 'Ny'
FIGURE 2: COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 5.08CM X5.08CM )
600
500
400
300
200
100
0
Smooth
Rough
40 42 44
Angle of Internal Friction''
in Degree
Smooth Footing
Rough Footing
Difference
% Increase
40
78.48
182.46
103.98
132.49
42
134.8
372.76
237.96
176.53
44
199.28
577.39
378.11
189.73
TABLE III. COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 6.35CM X6.35CM )
Bearing capacity factor 'Ny'
FIGURE 3: COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 6.35CM X6.35CM )
700
600
500
400
300
200
100
0
Smooth
Footing Rough Footing
40 42 44
Angle of Internal Friction''
TABLE IV. COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 5.08CM )
FIGURE 5: COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 6.35CM )
500
400
300
200
100
Smoot
h Footing
Angle of Internal Friction''
44
42
40
0
Bearing capacity factor 'Ny'
in Degree
Smooth Footing
Rough Footing
Difference
% Increase
40
58.835
152.92
94.08
159.90
42
108.76
293.62
184.86
169.97
44
146.90
441.99
295.09
200.87
TABLE VI. COMPARISON OF BEARING CAPACITY FACTOR NY FOR SMOOTH CIRCULAR FOOTINGS(CASSIDY VS. EXPERIMENTAL)
Experimental Values
in Degree According to Cassidy
5.08cm 6.35cm
40 50.46 58.83 58.31
Bearing capacity factor 'Ny'
FIGURE 4: COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 5.08CM )
500
400
300
200
100
Smooth
Footing
Rough Footing
Angle of Internal Friction''
44
42
40
0
TABLE V. COMPARISON OF NY VALUES FOR SMOOTH AND ROUGH FOOTING( 6.35CM )
42 96.316 108.76 109.07
44 142.172 146.9 158.40
Bearing capacity factor 'Ny'
FIGURE 6 : COMPARISON OF BEARING CAPACITY FACTOR NY FOR SMOOTH CIRCULAR FOOTINGS(CASSIDY VS. EXPERIMENTAL)
180
160
140
120
100
80
60
40
20
0
Cassidy
5.08cm
6.35cm
40 42 44
Angle of Internal Friction''
in Degree
Smooth Footing
Rough Footing
Difference
% Increase
40
58.31
141.41
83.1
142.51
42
109.07
289.02
179.95
164.98
44
158.4
460.89
302.49
190.96
TABLE VII. COMPARISON OF BEARING CAPACITY FACTOR NY FOR ROUGH CIRCULAR FOOTINGS(CASSIDY VS. EXPERIMENTAL)
in Degree
According to Cassidy
Experimental Values
5.08cm
6.35cm
40
129.4
152.92
141.41
42
279.64
293.62
289.02
44
429.88
441.99
460.89
Bearing capacity factor 'Ny'
FIGURE 7 : COMPARISON OF BEARING CAPACITY FACTOR NY FOR ROUGH CIRCULAR FOOTINGS(CASSIDY VS. EXPERIMENTAL)
500
400
300
200
100
Cassidy
5.08cm
6.35cm
40
42
44
Angle of Internal Friction''
0

CONSLUSION
Graphs of bearing capacity factors versus angle of internal friction were drawn for all the above cases. The comparison between smooth and rough footings were shown in figure 2 to 5.From figure 2 to 5, the bearing capacity factor `Ny' of square footings was approximately 2.3 times than that of smooth one in fine sand and 2.8 times in case of medium and coarse sand. The same trend also holds well in case of circular footings. In case of rough footings, with increase in angle of internal friction the value of bearing capacity factor NY increases at a faster rate as compared to smooth footings.

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