Interference of Continuous Foundations in Granular Soils

7/28/2019 Interference of Continuous Foundations in Granular Soils

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68 Shallow Foundations: Bearing Capacity and Settlement

l ll

cd qd

qd

c dN= -

-= - - =

11 308

1 1 308

12 5 17 31

tan.

.

. tan ..

tan ( sin ) ( )(tan

387

1 2 1 1 2 12l qd d d fD

B= + -

= + 7 3 1 17 3 0 6

0 61 308

1

2. )( sin . ).

..-

=

=ld

From equation (2.111)

q c N qN BN d c cs cd q qs qd sall(shear) gross

= + +l l l l l 12 lld

= +( )( . )( . )( . ) ( . )( )( . )( .32 12 5 1 192 1 387 0 6 18 4 8 1 1156 1 308

18 0 6 3 6 0 8 1

661 3 7

12

)( . )

( )( . )( . )( . )( )

.

+

= + 8 4 15 6 755 3. . .+ = kN/m2

From equation (2.112):

q qall(shear) net

= - = - 761 5 755 3 0 6 18. . ( . )( ) 744.5 kN/m2

2.13 interFerenCe oF ContinuouS

FoundationS in Granular Soil

In earlier sections o this chapter, theories relating to the ultimate bearing capacity

o single rough continuous oundations supported by a homogeneous soil medium

extending to a great depth were discussed. However, i oundations are placed close

to each other with similar soil conditions, the ultimate bearing capacity o each oun-

dation may change due to the intererence eect o the ailure surace in the soil. This

was theoretically investigated by Stuart35 or granular soils. The results o this studyare summarized in this section. Stuart35 assumed the geometry o the rupture surace

in the soil mass to be the same as that assumed by Terzaghi (Figure 2.1). According

to Stuart, the ollowing conditions may arise (Figure 2.37):

Case 1 (figURe 2.37)

I the center-to-center spacing o the two oundations isxx1, the rupture surace in

the soil under each oundation will not overlap. So the ultimate bearing capacity oeach continuous oundation can be given by Terzaghis equation [equation (2.31)].

For c= 0,

q qN BN u q= + 12

(2.113)


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Ultimate Bearing CapacityTheoriesCentric Vertical Loading 69

FiGure2.3

7

Assumptionsforthefailuresurfaceingra

nularsoilundertwocloselyspacedroughcontinuous

foundations.Note:a

1=f,a

2=4

5f/2,a

3=1

80f.

2

2

2

2

2

2

2

(a)

(b)

2

2

2

2

2

2

2

1

1

1

1

qu

qu

B

qu

q=

Df

q=

Df

B

B

B

x=x1

x=x2

qu


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2

3

(c

)

(d)

3

2

g1

d1

d2

g2

e

B

B

B

B

x

=x3

x=x4

qu

qu

qu

qu

q=

Df

q=

Df

FiGure2.3

7

(Continued).


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where

Nq,Ng= Terzaghis bearing capacity actors (Table 2.1)

Case 2 (figURe 2.37b)

I the center-to-center spacing o the two oundations (x=x2


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the load is applied. When the two oundations touch, the zone o arching disappears

and the system behaves as a single oundation with a width equal to 2B. The ultimate

bearing capacity or this case can be given by equation (2.113), withB being replaced

by 2B in the third term.Das and Larbi-Cheri36 conducted laboratory model tests to determine the inter-

erence efciency ratios xq and xgo two rough continuous oundations resting onsand extending to a great depth. The sand used in the model tests was highly

angular, and the tests were conducted at a relative density o about 60%. The angle

o riction f at this relative density o compaction was 39. Load-displacementcurves obtained rom the model tests were o the local shear type. The experi-

mental variations oxq and xg obtained rom these tests are given in Figures 2.40and 2.41. From these fgures it may be seen that, although the general trend o the

experimental efciency ratio variations is similar to those predicted by theory,there is a large variation in the magnitudes between the theory and experimen-

tal results. Figure 2.42 shows the experimental variations o Su/B with x/B (Su=settlement at ultimate load). The elastic settlement o the oundation decreases

with the increase in the center-to-center spacing o the oundation and remains

constant atx> about 4B.

3.5

3.0

2.5

1.5

1.0 1 2 3 4

x/B

5

2.0

= 40

Rough base

Along this line, two footingsact as one

3937

35

32

30

FiGure 2.39 Stuarts intererence actor xg.


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2.0

1.5

1.0

0.5

TeoryStuart[35]

ExperimentDas and Larbi-Cherif[36]

0 21 3 4 5 6

x/B

q

= 39

FiGure 2.40 Comparison o experimental and theoretical xq.

2.5

1.5

0.5

00 2 3 4 5

x/B6

2.0

1.0TeoryStuart[35]

ExperimentDas andLarbi-Cherif[36]

= 39

FiGure 2.41 Comparison o experimental and theoretical xg.


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reFerenCeS

1. Terzaghi, K. 1943. Theoretical soil mechanics. New York: John Wiley.

2. Kumbhojkar, A. S. 1993. Numerical evaluation o TerzaghisNg. J. Geotech. Eng.,ASCE, 119(3): 598.

3. Krizek, R. J. 1965. Approximation or Terzaghis bearing capacity. J. Soil Mech.

Found. Div., ASCE, 91(2): 146.

4. Vesic, A. S. 1973. Analysis o ultimate loads o shallow oundations. J. Soil Mech.

Found. Div., ASCE, 99(1): 45.

5. Meyerho, G. G. 1951. The ultimate bearing capacity o oundations. Geotechnique.

2: 301.

6. Reissner, H. 1924. Zum erddruckproblem, in Proc., First Intl. Conf. Appl. Mech.,

Delt, The Netherlands, 295.

7. Prandtl, L. 1921. Uber die eindringungs-estigkeit plastisher baustoe und die estig-keit von schneiden.Z. Ang. Math. Mech. 1(1): 15.

8. Meyerho, G. G. 1963. Some recent research on the bearing capacity o oundations.

Canadian Geotech. J. 1(1): 16.

9. Hansen, J. B. 1970.A revised and extended formula for bearing capacity. Bulletin No.

28, Danish Geotechnical Institute, Copenhagen.

10. Caquot, A., and J. Kerisel. 1953. Sue le terme de surace dans le calcul des onda-

tions en milieu pulverulent, in Proc., III Intl. Conf. Soil Mech. Found. Eng., Zurich,

Switzerland, 1: 336.

11. Lundgren, H., and K. Mortensen. 1953. Determination by the theory o plasticity o

the bearing capacity o continuous ootings on sand, in Proc., III Intl. Conf. Mech.Found. Eng., Zurich, Switzerland, 1: 409.

12. Chen, W. F. 1975.Limit analysis and soil plasticity. New York: Elsevier Publishing

Co.

13. Drucker, D. C., and W. Prager. 1952. Soil mechanics and plastic analysis o limit

design. Q. Appl. Math. 10: 157.

80

60

40

20

Average plot

Df/B = 0

Df/B = 1

x/B

Su

/B(

%)

0

0 2 3 4 5 6

= 39

FiGure 2.42 Variation o experimental elastic settlement (Su/B) with center-to-center spac-

ing o two continuous rough oundations.

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Interference of Continuous Foundations in Granular Soils