Email: aghasemi@ut.ac.ir * نوينسده مسئول

*

][

][

][

][][

][

][

][

][

c-φ

c φ

][][

DEM

][

][ ][

][

.

][

][

α1

α2(II)

(I)(III)

α3

θ1θ2

Z

(I)N1

N2N3

Shear spring (t)

knormal

.

.

Tension

Compression

k

k'

F

(

k k'

knormalkshear

(E)

(G)

kshear)

(knormal

G

E

k

k

shear

normal

)1(2

G

E

(ν)

kshear)

(knormal

(X,Y,Z)

NN

Normal spring (n)

Shear spring (s)

)( normalk

)66(4,43,42,41,4

4,33,32,31,3

4,23,22,21,2

4,13,12,11,1

NNKKKK

KKKK

KKKK

KKKK

K

({U} = [K] -1

{Fext})

.

σn (P) =Kn x ΔPn

(ΔPn)

(ΔPn)

ΔPn

n

tmaxn

maxn

tn

k

F)P(

)P(

Fk

tnnn FPPP )()( max

nnnmaxnn Pk)P()P(P

k

n

tnmaxnn

P

Fk)P(P

(δP)

shearshearshearPshear Pk)P()P(P

shear

PP

P

Pshear

k

)P()P(

)P(

)P(k

)P()P()P(P PshearPshear

k

shear

Pshear

P

)P(k

DEM

.

{FMINT}{FMEXT}

{ FMEXT}

{FMINT}

iiiniP

cPP tan)()(

R

Rmean

AA

CACAC

21

R

Rmean

VV

VV

21

V

VRV

γ1

2γ

meanγ

C1

C2

A

ARA

φ

R

Rmean

AA

AA

21 tantan

tan

1φ

2φ

-0.2 -0.17 -0.15 -0.13 0 m Fist layer depth

2 2 2 2 2 t/m3 Fist layer specific gravity

1.2 1.2 1.2 1.2 1.2 t/m3 Second layer specific gravity

1.58 1.53 1.49 1.34 1.2 t/m3 Equivalent layer specific gravity

0 0 0 0 0 t/m2 Fist layer cohesion

8 8 8 8 8 t/m2 Second layer cohesion

3.49 3.57 3.62 3.74 8 t/m2 Equivalent layer cohesion

26 26 26 26 26 degree Fist layer friction angle

0 0 0 0 0 degree Second layer friction angle

14.65 14.40 14.22 13.82 0 degree Equivalent layer friction angle

φ c γ Soil

parameters

degree t/m2 t/m

3 unit

0 3 1.5 First layer

26 0 2 Second

layer

][

Bearing

capacity

HANSEN

(t/m2)

Bearing

capacity

DEM

(t/m2)

Ground water

depth (m)

15.88 15.01 0.2

18.40 25.03 0.4

20.45 26.41 0.6

22.78 29.56 0.8

- 34.86 1.0

- 34.87 1.2

DEM

][][

][

DEM

DEM

DEM

DEM

DEM

Bearing capacity

MEYERHOF

(t/m2)

Bearing

capacity

DEM

(t/m2)

Depth

of sand

layer

(m)

41.1252.330.0

41.3175.05 0.2

41.9075.05 0.4

42.8784.61 0.6

44.2492.66 0.8

-

][

DEM

Bearing

capacity

MEYERHOF

(t/m2)

Bearing capacity

DEM

(t/m2)

Depth of

clay

layer

(m)

30.8439.88 0.0

37.1160.78 0.2

43.3865.61 0.4

49.3467.54 0.6

49.3472.90 0.8

DEM

ca

α

α

˚

][ tan-1

(1/2)][ ˚

˚]['φ

][

α

DEM

α

][

kp

kp

DEM

DEM

DEM

DEM

Depth equal

to 0.3 m

Depth

equal to 0.1

m

Bearing capacity

(t/m2)

34.81 26.11

Projected Area

Method

(Strip footing)

26.02 23.62 Okamura Method

(Strip footing)

42.50 41.11 DEM

(L/B=8)

Ks

ca

1-

2-

1 - Fellenius, B. H. (1999). Bearing capacity of footings and piles-a delusion? DFI Annual meeting, October 14-

16, Dearborn, Michigan.

2 - Prandtl, L. (1920). Uber die harte plasticher korper, Nachr.kgl. Ges.Wiss.Gottingen, Math.Phus.Klasse.

3 - Terzaghi, K. and Peck R. B. (1967). Soils Mechanics in Engineering Practice, John Wiley, New York.

4 - Meyerhof, G. G. (1963). “Some recent research on bearing capacity of foundations.” Canadian Geotechnical

Journal, Vol. 1, No. 1, PP. 16-26.

5 - Hansen, B. and Christensen, N. H. (1969). “Discussion of theoretical bearing capacity of very shallow

foundations.” by A. L. Larkins, Journal Of The Soil Mechanics And Foundation Divisions, ASCE, Vol. 95,

Paper No. SM6, PP. 1568-1572.

6 - Brown, J. D. and Meyerhof, G. G. (1969). “Experimental study of bearing capacity in layered clays.”

Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 2, PP.

45-51.

7 - Meyerhof, G. G. (1978). “Ultimate bearing capacity of footings on sand layer overlying clay.” Canadian

Geotechnical Journal, Vol. 15, No. 4, PP. 565-572.

8 - Okamura, M., Takemura. J. and Kimura. T. (1998). “Bearing capacity predictions of sand overlying clay

based on limit equilibrium methods.” Soils and Foundations, Vol. 38, No.1, PP. 181-194.

9 - Purushothamaraj, P., Ramiah, B. K. and Rao, K. N. V. (1973). “Bearing capacity of strip footing in two

layered cohesive-friction soil,” Canadian Geotechnical Journal, Vol. 11, PP. 32–45.

10 - .Majidi, A. R., Mirghasemi, A. A. (2008). "Seismic 3D bearing capacity analysis of shallow foundations.”

Iranian Journal of Science & Technology, Transaction B, Engineering, Vol. 32, No. B2, PP. 107-124.

11 - Majidi, A. R. (2007). Three Dimensional Analysis of Bearing Capacity of Foundations in Discrete Element

Method, Ph.D. thesis, University of Tehran

12 - Cundall, P. A. and Strack, O. D. L. (1979). “A discrete numerical modeling for granular assemblies.”

Geotechnique, Vol. 29, PP. 45-47.

13 - Chang, C. S. (1971). “Discrete element method for bearing capacity analysis.” Computer and Geotechnics,

Vol. 12, PP. 273-288.

14 - Chang, C. S. (1992). “Discrete element method for slope stability analysis.” J. of Geotechnics. Eng, Vol.

118, No. 12, PP. 1889-1905.

15 - Chang, C. S. (1994). “Discrete element analysis for active and passive pressure distribution on retaining

wall.” Computer and Geotechnics, Vol. 16, PP. 291-310.

16 - Bowles, J. E. (1996). Foundation analysis and design, 5th edition, McGraw-Hill, New York.

17 - Das, B. M., “Principles of foundation engineering.” Second edition, PWS-KENT publishing company

Boston.

18 - Hanna, A. M. and Meyerhoff, G. G. (1980). “Design chart for ultimate bearing capacity of foundations on

sand overlying soft clay.” Canadian Geotechnical Journal, Vol. 17, PP. 300–303.

19 - Yamaguchi, H. and Terashi, M. (1971). “Ultimate bearing capacity of the multilayered ground, Proc.” 4th

Asian Regional Conf on SMFE, Bangkok, Thailand, Vol. 1, PP. 99–105.

20 - Kraft, L. M. and Helfrich (1983). “Bearing capacity of shallow footing, sand over clay.” Canadian

Geotechnical Journal, Vol. 20, PP. 182-185.

21 - Myslivec, A. and Kysela, Z. (1978). the Bearing Capacity of Building Foundations, Elsevier Sc. Publ.

Comp. Amsterdam, PP. 134-8.

22 - Baglioni, V. P., Chow, G. S. and Endley, S. N. (1982). “Fugro Gulf, Inc. Jack-Up Rig foundation stability

in stratified soil profiles.” Offshore Technology Conference, 3-6 May, Houston, Texas.

1 - Finite Element Method

2 - Discrete Element Method

3 - Winkler Springs

4 - Secant Stiffness

5 - Young’s Modulus

6 - Isotropic Elastic

7 - Assemble

8 - Convergent

9 - Divergent

10 - Iterations

11 - Projected Area Method