STUDY ON LOSS OF CONTACT OF RECTANGULAR PLATES RESTING ON COHESIVE SOIL

http://www.iaeme.com/IJCIET/index.asp 488 [email protected]

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

Study On Loss of Contact of Rectangular Plates Resting on Cohesive Soil


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.

Sai Sowmith N and Ch.Hanumantharao


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



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%



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



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%.



Figure 7. CRR vs. ì for particular e in transverse 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



Figure 8. CRR vs. μ for particular e in longitudinal direction



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



Figure 9. CRR vs. μ for particular L/B in transverse 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





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.



REFERENCES

[1] William Thomas Straughan. Analysis of plates on elastic foundation. Ph.D. dissertation Dept. of

Civil Engg, Texas Tech University 1990.

[2] Zekaicelep. Rectangular plates on tensionless winkler foundation. J.Eng. Mech, ASCE. 1988;

144, 2083-2092.

[3] Zekaicelep. Circular plates on tensionless winkler foundation. J.Eng. Mech, ASCE. 1988; 144,

1723-1739.

[4] Bowles J E. Foundation Analysis and Design. The McGraw-Hill Companies, Inc., Fifth Edition,

1997.

[5] Mohammed Y F, Mohammed J H, Sura A A. Behavior of Plate on Elastic Foundation under

Impact Load by The Finite Element Method. Eng. & Tech. Journal. 2014; 32(4), 44-58.

[6] Vallabhan C V G, Straughan W T, Das Y C. Refined model for analysis of plates on elastic

foundation. Journal of Engineering Mechanics. 1991; 117(12), 2830-2844.

[7] Akpila, S. B. and Omunguye, I. W.Derivative of Stress Strain, Deviatoric Stress and Undrained

Cohesion Models Based on Soil Modulus of Cohesive Soils. International Journal of Civil

Engineering and Technology, 6(7), 2015, pp 34-43.

[8] Jeevanantham V, Jayashree J and Magudeaswaran P., Influence of Fly Ash in Strength

Characteristics of Cohesive Soils. International Journal of Civil Engineering and Technology,

7(6), 2016, pp.67 – 72.

[9] Girija C V, Das Y C. Parametric study of the beams on the elastic foundations. Journal of

Engineering Mechanics. 1988; 144, 2072-2082.

[10] Ayse Turhan. Consistent vlasov model for Analysis of plates on elastic foundation using finite

element method” Ph. D dissertator Dept. of civil. Engg, Texas Tech University, 1992.