ceij.ut.ac.ir€ computer and geotechnics, vol. 16, pp. 291-310. 16 - bowles, j. e. (1996)....
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Email: aghasemi@ut.ac.ir * نوينسده مسئول
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][
][
][
][][
][
][
][
][
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
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