Civil Engineering Reference
In-Depth Information
δσ
a
=
δσ
r
=
During the increment
10 kPa,
0 and, from Eqs. (3.3) to (3.6),
q
=
δ
a
−
δσ
r
=
δ
10 kPa
p
=
1
3
(
1
3
δσ
a
+
σ
r
)
δ
2
=
×
10
=
3.3 kPa
2
3
(
2
3
(0.05
δε
s
=
δε
a
−
δε
r
)
=
+
0.01)
=
0.04%
δε
v
=
δε
a
+
2
δε
r
=
0.05
−
0.02
=
0.03%
Example 3.2: Calculation of shear and bulk modulus
The soil in Example 3.1 is
isotropic and elastic (i.e. shearing and volumetric effects are decoupled). For the
increment,
q
Shear modulus
G
=
δ
10
=
1000
=
8.3MPa
3
δε
3
×
0.04/100
×
s
p
δε
bulk modulus
K
=
δ
3.3
0.03/100
v
=
1000
=
11.1MPa
×
Young's modulus
E
=
δσ
a
δε
10
0.05/100
a
=
1000
=
20MPa
×
ν
=−
δε
a
=−
−
0.01
0.05
=
r
δε
Poisson's ratio
0.2
From Eqs. (3.24) and (3.25), substituting for
E
and
ν
,
E
20
G
=
+
ν
)
=
0.2)
=
8.3MPa
2(1
2(1
+
E
20
K
=
ν
)
=
0.4)
=
11.1MPa
3(1
−
2
3(1
−
Further reading
Atkinson, J. H. (1981)
Foundations and Slopes
, McGraw-Hill, London.
Calladine, C. R. (1969)
Engineering Plasticity
, Pergamon Press, London.
Case, J., A. H. Chilver and C. T. F. Ross (1999)
Strength of Materials and Structures
, Edward
Arnold, London.
Heyman, J. (1972)
Coulomb's Memoir on Statics
, Cambridge University Press.
Jaeger, J. C. (1969)
Elasticity, Fracture and Flow
, Methuen, London.
Palmer, A. C. (1976)
Structural Mechanics
, Oxford University Press.
Timoshenko, S. P. and J. N. Goodier (1969)
Theory of Elasticity
, McGraw-Hill, New York.
