Objectives: To study the phenomenon of loss of contact of rectangular plates resting over cohesive soils. Study the effect of various L/B ratios on Critical Relative Rigidity (CRR), the effect of eccentricity of loading on CRR and effect of poisons ratio on CRR over the phenomenon of loss of contact. Methodology: Analysis is carried out for a Rectangular Footing resting on cohesive soils subjected to an eccentric concentrated load, with eccentricity in the middle one-third of its shorter and longer span dimension with varying poisons ratio from 0.1 to 0.5 with an interval of 0.05 and the loss of contact of footing with the underlying soil phenomena is analyzed using the ANSYS 12.0 and the CRR values are obtained for different L/B ratios up to two distribution The term Relative Rigidity (RR) which takes into account the properties of soil and footing is considered for the analysis. It considers the parameters like dimensions of footing, thickness and the young’s modulus of the footing and the modulus of subgrade reaction of the soil. The Critical Relative Rigidity (CRR) is the value of RR where the soil experiences loss of contact with the overlying footing and the Critical Relative Rigidity (CRR) values are obtained for various L/B ratios up to the two-way distribution. Findings: With the increase in the eccentricity of concentrated load the CRR value decreased and with the increase of L/B ratio the CRR value increased and for an increase in poisons ratio for all L/B ratios and eccentricities CRR value decreased. Applications: Useful in the design of footings in different soil bed conditions by altering the dimensions and making the design economical.

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 1, January 2017, pp. 488–497, Article ID: IJCIET_08_01_056
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
STUDY ON LOSS OF CONTACT OF
RECTANGULAR PLATES RESTING ON
COHESIVE SOIL
Sai Sowmith N
PG Student, Civil Engineering Department,
K L University, Vaddeswaram, A. P, India
Ch.Hanumantharao
Professor, Civil Engineering Department,
K L University, Vaddeswaram, A. P, India
ABSTRACT
Objectives: To study the phenomenon of loss of contact of rectangular plates resting over
cohesive soils. Study the effect of various L/B ratios on Critical Relative Rigidity (CRR), the
effect of eccentricity of loading on CRR and effect of poisons ratio on CRR over the
phenomenon of loss of contact. Methodology: Analysis is carried out for a Rectangular
Footing resting on cohesive soils subjected to an eccentric concentrated load, with
eccentricity in the middle one-third of its shorter and longer span dimension with varying
poisons ratio from 0.1 to 0.5 with an interval of 0.05 and the loss of contact of footing with
the underlying soil phenomena is analyzed using the ANSYS 12.0 and the CRR values are
obtained for different L/B ratios up to two distribution The term Relative Rigidity (RR) which
takes into account the properties of soil and footing is considered for the analysis. It
considers the parameters like dimensions of footing, thickness and the young’s modulus of
the footing and the modulus of subgrade reaction of the soil. The Critical Relative Rigidity
(CRR) is the value of RR where the soil experiences loss of contact with the overlying footing
and the Critical Relative Rigidity (CRR) values are obtained for various L/B ratios up to the
two-way distribution. Findings: With the increase in the eccentricity of concentrated load
the CRR value decreased and with the increase of L/B ratio the CRR value increased and for
an increase in poisons ratio for all L/B ratios and eccentricities CRR value decreased.
Applications: Useful in the design of footings in different soil bed conditions by altering the
dimensions and making the design economical.
Key words: Critical Relative Rigidity, Relative Rigidity, Rectangular Footing, soil structure
interaction, loss of contact.
Cite this Article: Sai Sowmith N and Ch.Hanumantharao, Study On Loss of Contact of
Rectangular Plates Resting on Cohesive Soil. International Journal of Civil Engineering and
Technology, 8(1), 2017, pp. 488–497.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1

2. Study On Loss of Contact of Rectangular Plates Resting on Cohesive Soil
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1. INTRODUCTION
The response of soil under loading plays a vital role in developing the accurate design of footings.
Plates over the elastic foundation of various soils play a principal role in the contemporary design
engineering, as the behavior of soil under different loading is very complicated, the footings are in
general designed assuming that it has full contact with soil which does not happen in practical. So
less light is thrown to study the behavior of soil and phenomenon of loss of contact. If the footing
resting on a soil has rigidity less than that of the soil then footing resting on the soil experiences loss
of contact. The factor of safety for design can also be decreased by taking in account the above study
and the concept of soil structure interaction.
The successful applications of the principles of structural engineering arc intricately linked to
dying ability of die engineer to model the structure and its support conditions in order to perform an
accurate analysis and a subsequently "correct" design. Arriving at a realistic model is complicated
in foundation analysis by the extreme difficulty of modeling the soil structure interaction1.
The
circular and rectangular plates on Winkler’s foundation he has considered an elastic circular thin
plate on a tensionless foundation. The analysis has done on the effect of the lift-off on the response
of circular plate for different loads2-3
.
2. METHODOLOGY
To incorporate both the footing and soil properties directly the following equation is adopted4
Where
RR Relative Rigidity
Ks Modulus of the subgrade reaction
L footing length
E modulus of elasticity of footing
B footing length in shorter direction
2.1 FINITE-ELEMENT MODELING AND ANALYSIS
Analysis is carried out using finite element method (FEM) modeling5-8
in ANSYS 12.0 for
rectangular plates of different L/B Ratios varying from 1.2 to 2 considering the two-way distribution
for different poison ratios of cohesive soils ranging from 0.1 to 0.5 with an interval of 0.05 and by
selecting the suitable element shell 63 for the analysis of the footings resting on cohesive soils with
different modulus of subgrade reaction subjected to the eccentric concentrated load in both
longitudinal and transverse direction up to the middle one-third, the thickness of Footing is taken to
be 300mm and edge length of mesh for the plate is considered to be 100 mm as there is no further
change in the deflection if the mesh length is reduced less than 100 mm and an assumed
concentrated load of 500KN considering the eccentricities is imposed on the plate in vertical (Y)
direction as shown in Figure 1., analysis is carried out and the displacement in y-direction is obtained
and the iterations are carried out with different RR values to obtain the CRR values.

3. Sai Sowmith N and Ch.Hanumantharao
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Figure 1 Modeled Rectangular Plate Using Ansys
3. RESULTS AND DISCUSSION
By varying the different parameters like L/B ratio from 1.2 to 2.0 considering the two-way
distribution, eccentricity in the longitudinal, transverse directions up to middle one-third, poisons
ratio varying from 0.1 to 0.5 with interval 0.05 the CRR values are obtained and the following graphs
are plotted. The deflection of the plate after analysis is as shown in Figure 2.
Figure 2 Vertical Displacement of Plate

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3.1. CRR vs. e/B ratio in transverse direction
From Figure 3. it is observed that as the eccentricity of concentrated load increases, the CRR Value
decreased, and the percentage decrease of the CRR values for L/B ratio varying from 1.2 to 2.0
considering two-way distributions the percentage of the CRR reduction from eccentricity 0 to 0.1334
as shown in Table 1.
Table 1. Percentage Reduction in CRR for increasing eccentricity
L/B 1.2 1.4 1.6 1.8 2.0
e/B 79.5% 82.18% 83.87% 84.66% 83.653%
Figure 3 CRR vs. e/B ratio for a particular L/B Ratio in transverse direction
This is because as the L/B Ratio is kept constant the footing Rigidity is also constant. If the
eccentricity increases there is every chance of loss of contact so as to bring the plate in contact with
the soil, Soil rigidity should be reduced hence the CRR is reduced.
3.2. CRR vs. e/L ratio in longitudinal direction
From Figure 4. it is observed that as the eccentricity of concentrated load increases, the CRR Value
decreased, and the percentage decrease of the CRR values for L/B ratio varying from 1.2 to 2.0
considering two-way distributions the percentage of the CRR reduction from eccentricity 0 to 0.1334
as shown in Table 2.
Table 2. Percentage Reduction in CRR for increasing eccentricity
L/B 1.2 1.4 1.6 1.8 2.0
e/B 80.09% 79.51% 78.13% 79.33% 79.16%

5. Sai Sowmith N and Ch.Hanumantharao
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Figure 4. CRR vs. e/L ratio for a particular L/B Ratio in longitudinal direction
This is because as the L/B Ratio is kept constant the footing Rigidity is also constant. If the
eccentricity increases there is every chance of loss of contact so as to bring the plate in contact with
the soil, Soil rigidity should be reduced hence the CRR reduced.
3.3. CRR vs. L/B ratio
3.3.1. Transverse direction
From Figure 5. it is observed that for a particular eccentricity as L/B ratio is increasing the CRR
value also increased. The percentage increase of the CRR values for e/B ratios varying from 0 to
0.1334 for the L/B Ratio varying from 1.2 to 2.0 as shown in Table 3. This is because as the L/B
ratio increases the rigidity of footing also increases hence to have loss of contact the soil RR should
be increased so the CRR is increasing.
Figure 5. CRR vs. L/B ratio for a particular e/B Ratio in transverse direction

6. Study On Loss of Contact of Rectangular Plates Resting on Cohesive Soil
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Table 3. Percentage Increase in CRR with Increase in L/B Ratio
e/B 0 0.0334 0.0667 0.1 0.1334
L/B(1.2 to
2.0) 51.45% 28.94% 27.86% 19.51% 21.42%
3.3.2. Longitudinal direction
From Figure 6. it is observed that for a particular eccentricity as L/B ratio is increasing the
CRR value also increased. The percentage increase of the CRR values for e/B ratios varying from 0
to 0.1334 for the L/B Ratio varying from 1.2 to 2.0 are as shown in Table 4. This is because as the
L/B ratio increases the rigidity of footing also increases hence to have loss of contact the soil RR
should be increased so the CRR is increasing.
Table 4. Percentage Increase in CRR with Increase in L/B Ratio
Eccentricity
0 0.028 0.055 0.083 0.0111 0.139
L/B(1.2 to
2.0)
51.45% 48.23% 42.1% 27.81% 46.05% 58.53%
Figure 6. CRR vs. L/B ratio for a particular e/L ratio in longitudinal direction
3.4. CRR vs. μ for particular e
3.4.1. Transverse direction:
From Figure 7. it is observed that for a particular eccentricity of all L/B ratios as the value of poisons
ratio increases the value of CRR decreased this is because as the poisons ratio increases the modulus
of subgrade reaction decreases which in turn results in a decrease of CRR values. Here it is observed
that in the transverse direction the decrease in CRR value is up to 22%-25%.

7. Sai Sowmith N and Ch.Hanumantharao
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Figure 7. CRR vs. ì for particular e in transverse direction
3.4.2. Longitudinal direction
From Figure 8. it is observed that for a particular eccentricity of all L/B ratios as the poisons ratios
value increases the value of CRR decreased this is because as the poisons ratio increases the modulus
of subgrade reaction decreases which in turn results in a decrease of CRR values. Here it is observed
that in the transverse direction the decrease in CRR value is up to 20%-25%.
Figure 8. CRR vs. μ for particular e in longitudinal direction

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3.5. CRR vs. μ for particular L/B
3.5.1. Transverse direction
From Figure 9. it is observed that for a particular L/B ratio for all eccentricities as the value of poisons
ratio increases the value of CRR decreased this is because as the poisons ratio increases the modulus
of subgrade reaction decreases which in turn results in a decrease of CRR values. Here it is observed
that in the transverse direction the decrease in CRR value is up to 23%-26%.
Figure 9. CRR vs. μ for particular L/B in transverse direction
3.5.2. Longitudinal direction
From Figure 10. it is observed that for a particular L/B ratio of all eccentricities as the poisons ratios
value increases the value of CRR decreased this is because as the poisons ratio increases the modulus
of subgrade reaction decreases which in turn results in a decrease of CRR values. Here it is observed
that in the transverse direction the decrease in CRR value is up to 24%-26%.

9. Sai Sowmith N and Ch.Hanumantharao
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Figure 10. CRR vs. μ for particular L/B in longitudinal direction
3.6. The advantage of Determining CRR
By determining the CRR for various conditions helps in the design of footing by altering dimensions
of the footing of the footing and thickness of the footing such that the CRR is always greater than
the RR for all conditions.
4. CONCLUSIONS
• As eccentricity of the concentrated load in the longitudinal direction increases for a poisons ratio, the
CRR decreases from 77% to 81%, for a particular L/B Ratio of footing.
• As the eccentricity of the concentrated load in the transverse direction increases for a poisons ratio,
the CRR decreases from 79% to 85%, for a particular L/B Ratio of footing.
• For a particular eccentricity of the concentrated load in the longitudinal direction as the L/B Ratio of
the footing increases the CRR value increases from 27% to 60%.
• For a particular eccentricity of the concentrated load in the transverse direction as the L/B Ratio of
the footing increases the CRR value increases from 20% to 52%.
• For a particular eccentricity in the longitudinal direction as the poisons ratio µ increases the CRR
value decreases up to 20%-25%, for a particular L/B ratio of footing.
• For a particular eccentricity in the transverse direction as the poisons ratio µ increases the CRR value
decreases up to 22%-25%, for a particular L/B ratio of footing.
• For an L/B ratio as the poisons ratio µ increases for a particular eccentricity in the longitudinal
direction, the CRR value decreases up to 24%-27%.
• For an L/B ratio as the poisons ratio µ increases for a particular eccentricity in the transverse direction,
the CRR value decreases upto23%-26%.
• When eccentric concentrated load in the longitudinal direction is applied at the middle one-third of
its longer and shorter span dimension always a loss of contact will occur.

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