th 50 igc 17 – 19 december 2015, pune, maharashtra, indiaigs/ldh/files/igc 2015 pune/theme 3...

50th

IGC

50th

INDIAN GEOTECHNICAL CONFERENCE

17th

– 19th

DECEMBER 2015, Pune, Maharashtra, India

Venue: College of Engineering (Estd. 1854), Pune, India

1Dr. Sunil S. Pusadkar, Associate Professor, Department of Civil Engineering, Govt. College of Engineering, Amravati, India,

e-mail: [email protected] 2Piyush V. Kolhe, PG Scholar, Department of Civil Engineering, Govt. College of Engineering, Amravati, India,

e-mail: [email protected]

INTERFERENCE OF TWO CLOSELY SPACED CIRCULAR FOOTINGS

SUBJECTED TO ECCENTRIC LOADS

Dr. Sunil S. Pusadkar1, Piyush V. Kolhe

2

ABSTRACT

The footings in the field generally interfere with each other to some extent and are rarely isolated

due to heavy loads and unavailability of good construction sites. However, the footings may be subjected

to eccentric load due to vertical and horizontal loads transmitted through the superstructure or inclined

columns or wind load. The tilt of a footing is directly proportional to the moment acting on it and load

may be replaced by eccentric or eccentric-inclined load.

Kumar and Ghosh (2007) determined the ultimate bearing capacity (UBC) of two interfering strip

footings using two failure mechanisms. Kumar and Bhoi (2009) determined the UBC of two interfering

strip footings and found that interference effect becomes even more substantial with an increase in the

relative density of sand. Lee et al. (2009) studied the effects of multiple footings on sand and found that

load response and UBC at S/B = 3.0 are similar to isolated footing. Kouzer and Kumar (2010)

investigated the UBC of a new strip footing placed on a cohesionless soil medium and found that

efficiency factor for bearing capacity (ξγ) generally reaches a maximum at S/B = 0. Srinivasan and Ghosh

(2011) studied the effect of interference between two nearby surface circular footings and found that the

bearing capacity and settlement of interfering circular footing decreases with increase in spacing between

the footings and efficiency factors are found to be the maximum at S/B = 0.5. Nainegali et al. (2013)

studied the interaction of two closely spaced rigid strip footings resting on homogeneous soil bed

subjected to inclined loading using ABAQUS and found that the settlement of interfering footings in the

range of working load decreases with increase in the clear spacing between the footings. Krabbenhoft and

Damkilde (2014) determined the bearing capacity of a strip foundation subjected to an inclined, eccentric

load using FEM on cohesionless soil with varying surcharges and friction angles to study the effect of

positive and negative load inclination.

The present study brings the interference of two closely spaced rigid circular footings on

homogeneous soil bed subjected to eccentric loads. The ultimate bearing capacity and settlement of two

closely spaced footings were studied by Finite element software PLAXIS 2D. The foundation soil was

modeled as elasto-plastic material obeying the Mohr-Coulomb failure criterion. The whole soil domain

was considered to take into account both symmetric and asymmetric case. The soil domain was

discretized with15-noded plane strain triangular elements. The load eccentricity (e) and clear spacing (S)

between the adjacent footings was varied. The eccentricity of load varied from 0.1B to 0.25B along the

width for both sides and the spacing between the footings was varied from 0.5B – 3.0B. The analysis was

carried out for different combination of load eccentricity of the footings such as inward – inward, outward

– outward and inward – outward.

Dr. Sunil S. Pusadkar, Piyush V. Kolhe

The ultimate bearing capacity and the settlement of adjacent footings were found to be decrease

with increase in load eccentricity for different combination of loads. The effect of interference of adjacent

footings was not found to be significant when spacing between the footings is greater than 2.5B. The

variation of efficiency factor was found to be decrease with increase in spacing between the footings. The

ultimate bearing capacity was found to be more in case of inward – inward eccentric load case than other

two as shown in Figure 1. This may be due to development of the strong stress confinement zoned below

the adjacent footings. It also shows that the settlement reduces with eccentric load which may be due to

contribution of footing rotation and sliding during the failure.

Figure 1: Variation of UBC and Settlement with Different Spacing between the Interacting Footings

Keywords: Interference, Circular Footings, PLAXIS 2D, FEM, Eccentric Load

References: 1. Kumar J. and Ghosh P. (2007), “Ultimate Bearing Capacity of Two Interfering Rough Strip Footings”, Int.

Journal of Geomechanics, Volume 07, ASCE, pp. 53-62.

2. Kumar J. and Bhoi M. K. (2009), “Interference of two closely spaced strip footings on sand using model tests”,

J. Geotechnical and Geo-environmental Engineering, Volume 135, Issue 4, pp. 595-604.

3. Lee J., Eun J. and Salgado R. (2009), “Strain Influence Diagrams for Settlement Estimation of Both Isolated

and Multiple Footings in Sand”, J. Geotechnical and Geo-environmental Engineering, Volume134, pp. 417-

427.

4. Kouzer K. and Kumar J. (2010), “Ultimate Bearing Capacity of a Footing Considering the Interference of an

Existing Footing on Sand”, J. of Geotech and Geology Engineering, Volume 28, pp. 457-470.

5. Srinivasan V. and Ghosh P. (2011), “Interaction problem of circular footings on homogeneous soil deposit”,

Proceedings of Indian Geotechnical Conference, Kochi, pp. 823-826.

6. Nainegali L., Basudhar P.K. and Ghosh P. (2013), “Interference of Two Asymmetric Closely Spaced Strip

Footings Resting on Non-homogeneous and Linearly Elastic Soil Bed”, Int. Journal of Geomechanics, Volume

13, ASCE, pp. 840-851.

7. Nainegali L., Basudhar P.K. and Ghosh P. (2013), “Interaction of Nearby Strip Footings under Inclined

Loading”, Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering,

Paris, pp. 58-66.

8. Krabbenhoft S. and Damkilde L. (2014), “Bearing capacity of strip footings in cohesionless soil subject to

eccentric and inclined loads”, Int. Journal of Geomechanics, Volume 14, ASCE, pp. 1-18.

50th

IGC

50th


17th

– 19th



INTERFERENCE OF TWO CLOSELY SPACED CIRCULAR FOOTINGS

SUBJECTED TO ECCENTRIC LOADS

Dr. S. S. Pusadkar, Associate Professor, Dept. of Civil Engineering, GCOE, Amravati, [email protected]

Piyush V. Kolhe, PG Scholar, Department of Civil Engineering, GCOE, Amravati, [email protected]

ABSTRACT: The foundations in the field generally interfere with each. This work presents the study of behaviour

of closely spaced footings subjected to eccentric loads using PLAXIS 2D. The load eccentricity (e) and clear

spacing (S) between the adjacent footings was varied. It was observed that the UBC and settlement of interacting

footings decreases as load eccentricity and spacing between the footings increases. The results show that an

efficiency factors with respect to bearing capacity and settlement (ξγ) and (ζδ) decreases with increase in spacing

between the footings. The efficiency factors found to be below one for eccentricity of 0.15B and more. The

interference effect was not found to be significant for spacing greater than 2.5B.

INTRODUCTION

The foundations are placed close to each other due

to heavy loads and unavailability of good

construction sites. In this case, respective stress

isobars overlapped leading to the interference

phenomenon. It was observed that the interacting

footings behave differently than the isolated

footing and the interference of failure zones alters

the bearing capacity and load-settlement behaviour

of footings from the isolated footing condition.

However, in case of retaining walls, abutments,

columns, stanchions, portal framed buildings,

waterfront structures, industrial machines, oil/gas

platform in offshore area, the foundations may be

subjected to moments and shears in addition to

vertical loads and the bearing capacity and

settlement behaviour found to be different than the

vertical loads.

The researchers studied the interference

effect under vertical load using numerical as well

as experimental approach. However, the limited

study was observed on interference of footings

under eccentric load.

Kumar and Ghosh (2007), Kumar and Bhoi

(2009), Lee et al. (2009), Kouzerand Kumar

(2010), Srinivasan and Ghosh (2011) studied the

interference effect under vertical load and used

numerical methods such as method of stress

characteristics, upper or lower bound methods,

finite difference and finite element methods or

conduct laboratory model experimental tests to

study the behaviour of interacting footings.

Nainegali et al. (2013) studied the effect of

interference of footings subjected to inclined load.

Krabbenhoft and Damkilde (2014) studied the

analysis of isolated footing subjected to eccentric-

inclined load. The researchers observed that the

ultimate bearing capacity of each individual

footing was increased relative to that of an isolated

footing and also observed that UBC and settlement

of interacting footings increases as spacing

between the footings decreases under vertical load

and also interference effect was not found to be

significant after spacing greater than three times

the width of footings.

However, limited study was observed on

interference of footings subjected to eccentric

loading owing to vertical and horizontal loads

transmitted through the superstructure or inclined

columns or wind load. Therefore, the present work

was focus on study of the interference effect of two

closely spaced circular footings subjected to

eccentric loads. The various parameters considered

for the analysis were load eccentricity varied from

(0B – 0.25B) and spacing between the footings

varied from (0.5B – 3.0B). The results were plotted


in the form of efficiency factors to study the

of load eccentricity (e) and spacing between the

interacting footings (S).

PROBLEM DEFINITION

The two interacting circular footings subjected to

eccentric load (Inward – Inward) is shown in Fig.

1. The footings were separated by a distance of (S)

and of equal width (B).The analysis wa

out for three eccentric load cases i.e.

Inward [I-I], Outward – Outward [O-O]

Outward [I-O]) depending upon the position

eccentric load. The soil was assumed as

homogeneous for depth 10B followed by hard

stratum. The properties for soil bed and footing are

shown in Table 1 and Table 2.

Fig. 1: Two adjacent circular footings subjected to

inward – inward eccentric load

Table 1: Material properties of footings

Parameters Description

Material type Elasto

Normal stiffness (EA, kN/m) 5x10

Flexural rigidity (EI, kNm2/m) 8500

Equivalent thickness (d, m) 0.1428

Table 2: Material properties of soil bed

Parameters Description

Soil Sand

Material model Mohr- Coulomb

Type of material behavior Drained

γunsat, (kN/m3) 17

γsat, (kN/m3) 20

ficiency factors to study the effect

of load eccentricity (e) and spacing between the

footings subjected to

Inward) is shown in Fig.

eparated by a distance of (S)

and of equal width (B).The analysis was carried

(Inward –

O], Inward –

position of

sumed as

followed by hard

The properties for soil bed and footing are

Two adjacent circular footings subjected to

Description

Elasto-plastic

5x106

8500

0.1428

Description

Sand

Coulomb

Drained

17

20

E’, (kN/m2)

Cohesion (cref , kN/m2)

Friction angle (Φ)

Poisson’s ratio (υ)

ANALYSIS The analysis was carried out using

software, PLAXIS 2D. The finite element mesh

was generated with 15-noded plane strain

triangular elements. The footings were placed on

the surface of soil and have perfect contact with the

soil. The whole failure domain was considered in

the present analysis to take care of both

symmetrical and asymmetrical problems. In the

present analysis, the soil model of 20 B x 10 B was

used and width of footing (B) was taken as 1m.

The analysis was carried out for footings subjected

to eccentric load using three cases

combinations of eccentricity of left footing (L

and right footing (Re), spacing of footing

in Table 3.

Table 3: Different cases for interacting f

Case Condition Le

(m)

A

I - I 0,

0.10,

0.15,

0.20,

0.25

B O - O

C I - O

The analysis of two adjacent

footings resting on homogeneous soil bed

subjected to eccentric load was stud

PLAXIS 2D. Fig. 2 shows the footings with soil

modelled in PLAXIS 2D and corresponding output

of the analysis. The two adjacent footings were

placed at spacing of S and 15

plane strain elements were used to discretize the

soil domain and suitable boundary

assigned at the far end boundaries of the domain.

The mesh was made finer along the footings to

take care of stress concentration. The footings were

loaded eccentrically with varying (e)

0.25 m for different spacing between the fo

varying from 0.5B – 3.0B.

25000

0.1

34

0.3

analysis was carried out using finite element

software, PLAXIS 2D. The finite element mesh

noded plane strain

triangular elements. The footings were placed on

the surface of soil and have perfect contact with the

soil. The whole failure domain was considered in

t analysis to take care of both

symmetrical and asymmetrical problems. In the

present analysis, the soil model of 20 B x 10 B was

used and width of footing (B) was taken as 1m.

The analysis was carried out for footings subjected

ee cases for various

combinations of eccentricity of left footing (Le )

, spacing of footing as shown

interacting footings

Re

(m)

Spacing

(m)

0.10,

0.15,

0.20,

0,

0.10,

0.15,

0.20,

0.25

0.5,

1.0,

1.5,

2.0,

2.5,

3.0

The analysis of two adjacent circular

resting on homogeneous soil bed

subjected to eccentric load was studied using

shows the footings with soil

in PLAXIS 2D and corresponding output

of the analysis. The two adjacent footings were

placed at spacing of S and 15-noded triangular

plane strain elements were used to discretize the

soil domain and suitable boundary conditions was

assigned at the far end boundaries of the domain.

The mesh was made finer along the footings to

The footings were

eccentrically with varying (e) from 0 m –

0.25 m for different spacing between the footings

50th

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50th


17th

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Fig. 2 (a) shows the deformed mesh pattern

after the failure occurs. Fig. 2 (b) and (c) illustrate

the output of analysis in the formed of load

displacement curve and total displacement

contours.

(a)

(b)

(c)

Fig. 2: Two adjoining footings subjected to vertical

eccentric load

RESULTS AND DISCUSSION

The analysis was carried out in PLAXIS 2D using

soil model and soil properties as discussed above

for two adjacent circular footings subjected to

eccentric load with different spacing between the

footings.

The ultimate bearing capacity (UBC) qu and

settlement at failure were obtained from load

displacement curve and the results were plotted

between ultimate bearing capacity (qu) and spacing

between interacting footings (S) for all cases. It

was found that UBC and settlement decreases as

the spacing between the footings increases. Fig. 3

shows the ultimate bearing capacity and settlement

of footings with increase in spacing between the

footings for Case A with eccentricity of left footing

(Le = 0.10B) and eccentricity of right footing (Re)

varied from (0B – 0.25B) and found similar trend

for all the cases.

Fig. 3: UBC and settlement for Case A (Le =

0.10B)

(a)

(b)


Fig. 4 and Fig. 5 shows the UBC

settlement of interacting footings for Case B and

Case C with Le= 0.10B respectively. Similarly the

results were obtained for all different eccentricity

and spacing.

(a)

(b)

Fig. 4: UBC and settlement for Case B (Le =

0.10B)

Fig. 4 and Fig. 5 shows the UBC and

settlement of interacting footings for Case B and

. Similarly the

results were obtained for all different eccentricity

UBC and settlement for Case B (Le =

Fig. 5: UBC and settlement for Case C (Le =

0.10B)

After obtaining the UBC and settlement for

different eccentricities, position of eccentric load

and different spacing, the bearing capacity

efficiency factor (ξγ ) and settlement efficiency

factor (ξδ) for each case were determined.

bearing capacity efficiency factor

expressed as ratio of bearing capacity of isolated

footing in presence of other footing to the bearing

capacity of isolated footing subjected to central

vertical load. The settlement efficiency factor

(ξδ) can be defined as the ratio of s

isolated footing in presence of other footing to the

settlement of isolated footing subjected to central

vertical load.

It was observed that the efficiency factors

(ξγ) and (ξδ) were decrease monolithically with

increase in spacing between the footings and

eccentricity for particular load condition.

shows the efficiency factors for Case A. The

efficiency factors are observed to decrease with

increase in spacing of footing and eccentricity of

load. It was also observed that ultimate bearing

capacity and settlement of footings subjected to

both central vertical loads is more than that when

subjected to both eccentric loads. The reduction in

settlement with eccentric load may be due to

contribution of footing rotation and sliding during

the failure.

(a)

UBC and settlement for Case C (Le =

obtaining the UBC and settlement for

different eccentricities, position of eccentric load

and different spacing, the bearing capacity

and settlement efficiency

each case were determined. The

factor (ξγ ) can be

earing capacity of isolated

footing in presence of other footing to the bearing

subjected to central

The settlement efficiency factor

the ratio of settlement of

isolated footing in presence of other footing to the

settlement of isolated footing subjected to central

t was observed that the efficiency factors

were decrease monolithically with

increase in spacing between the footings and

eccentricity for particular load condition. Fig. 6

e efficiency factors for Case A. The

efficiency factors are observed to decrease with

footing and eccentricity of

It was also observed that ultimate bearing

capacity and settlement of footings subjected to

both central vertical loads is more than that when

subjected to both eccentric loads. The reduction in

load may be due to

contribution of footing rotation and sliding during

(b)

50th

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17th

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(i) (ξγ) and (ζδ) for Case A (Le = 0B)

(ii) (ξγ) and (ζδ) for Case A (Le = 0.10B)

(iii) (ξγ) and (ζδ) for Case A (Le = 0.15B)

(iv) (ξγ) and (ζδ) for Case A (Le = 0.20B)

(v) (ξγ) and (ζδ) for Case A (Le = 0.25B)

Fig. 6: ξγ andζδ for footings subjected to inward –

inward vertical eccentric load (Case A)

Fig. 7 and Fig. 8 show the efficiency factors

for bearing capacity (ξγ) and settlement (ζδ) for

Case B and Case C. From these results, the effect

of interference of adjacent footings subjected to

eccentric load was not found to be significant when

spacing between the footings is greater than 2.5B

and the efficiency factors were found to be more in

case of inward – inward eccentricity than outward

– outward and inward – outward case as the strong

confining zone formed below the adjoining

footings. The efficiency factors found to below one

for eccentricity of 0.15B and more. The adjacent

footings will try to act as isolated footing for

spacing greater than 3.0B.

(i) (ξγ) and (ζδ) for Case B (Le = 0B)

(ii) (ξγ) and (ζδ) for Case B (Le = 0.10B)


(iii) (ξγ) and (ζδ) for Case B (Le = 0.15B)

(iv) (ξγ) and (ζδ) for Case B (Le = 0.20B)

(v) (ξγ) and (ζδ) for Case B (Le = 0.25B)

Fig. 7: ξγ and ζδ for footings subjected to inward –

inward vertical eccentric load (Case B)

(i) (ξγ) and (ζδ) for Case C (Le = 0B)

(ii) (ξγ) and (ζδ) for Case C (Le = 0.10B)

(iii) (ξγ) and (ζδ) for Case C (Le = 0.15B)

(iv) (ξγ) and (ζδ) for Case C (Le = 0.20B)

(v) (ξγ) and (ζδ) for Case C (Le = 0.25B)

Fig. 8: ξγ and ζδ for footings subjected to inward –

inward vertical eccentric load (Case C)

Fig. 9 shows the comparison of UBC and

total settlement of adjacent circular footings for all

three cases with Re and Le = 0.15B indicating the

increase in ultimate bearing capacity with decrease

50th

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– 19th



in spacing and decrease in settlement with increase

of spacing.

(a)

(b)

Fig. 9: Comparison of UBC and total deformation

for Case (A, B & C) for Le and Re = 0.15B

CONCLUSIONS The UBC and settlement of adjoining footings

decreases as the spacing and eccentricity of load

increases. The efficiency factors found to be below

one for eccentricity of 0.15B and more for different

combination of loads. The interference effect was

not found to be significant for spacing greater than

2.5 times the width of footings. The rotational or

tilting failure may lead to reduction in total

deformation. The interacting footings will behave

like isolated footing for spacing greater than 3

times the width of footings. The effect of eccentric

load position shows that when load position is

inward-inward eccentric, the ultimate bearing

capacity was found to be maximum while for

outward-outward position of loads it was

minimum. The similar results were also observed

for settlement of footing.

REFERENCES

1. Kumar J. and Ghosh P. (2007), “Ultimate

Bearing Capacity of Two Interfering Rough

Strip Footings”, Int. Journal of Geomechanics,

Volume 07, ASCE, pp. 53-62.

2. Kumar J. and Bhoi M. K. (2009), “Interference

of two closely spaced strip footings on sand

using model tests”, J. Geotechnical and Geo-

environmental Engineering, Volume 135, Issue

4, pp. 595-604.

3. Lee J., Eun J. and Salgado R. (2009), “Strain

Influence Diagrams for Settlement Estimation

of Both Isolated and Multiple Footings in

Sand”, J. Geotechnical and Geo-environmental

Engineering, Volume134, pp. 417-427.

4. Kouzer K. and Kumar J. (2010), “Ultimate

Bearing Capacity of a Footing Considering the

Interference of an Existing Footing on Sand”,

J. of Geotech and Geology Engineering,

Volume 28, pp. 457-470.

5. Srinivasan V. and Ghosh P.(2011), “Interaction

problem of circular footings on homogeneous

soil deposit”, Proceedings of Indian

Geotechnical Conference, Kochi, pp. 823-826.

6. Nainegali L., Basudhar P.K. and Ghosh P.

(2013), “Interference of Two Asymmetric

Closely Spaced Strip Footings Resting on

Nonhomogeneous and Linearly Elastic Soil

Bed”, Int. Journal of Geomechanics, Volume

13, ASCE, pp. 840-851.


7. Nainegali L., Basudhar P.K. and Ghosh P.

(2013), “Interaction of Nearby Strip Footings

under Inclined Loading”, Proceedings of the

18th International Conference on Soil

Mechanics and Geotechnical Engineering,

Paris, pp. 58-66.

8. Krabbenhoft S. and Damkilde L. (2014),

“Bearing capacity of strip footings in

cohesionless soil subject to eccentric and

inclined loads”, Int. Journal of Geomechanics,

Volume 14, ASCE, pp. 1-18.

th 50 igc 17 – 19 december 2015, pune, maharashtra, indiaigs/ldh/files/igc 2015 pune/theme 3...

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