Civil Engineering Reference
In-Depth Information
10. A rectangle of saturated soil has an
-dimension of 2
units. If drainage is allowed from all four faces of the rectangle and the initial excess
pore pressure is set at all points to
x
-dimension of 4 units and a
y
u
=
1
.
0, use a single finite element and assume
symmetry, to estimate the variation of
u
with time at the centre of the rectangle if
c
x
=
10 and
c
y
=
1.
u
=
e
−
21
t/
2
)
(Ans: Analytical,
11. A layer of saturated clay of Depth
is drained at
its top surface only. The layer is subjected to a sudden excess pore pressure which
varies linearly from zero at the surface to
D
and coefficient of consolidation
c
v
at the base. Using two 1D elements
across the soil depth and a dimensionless time step of
U
o
T
=
0
.
1, estimate the average
degree of consolidation when
T
=
0
.
2.
(Ans: Using consistent “mass”,
U
=
0
.
4)
References
Carslaw HS and Jaeger JC 1959
Conduction of Heat in Solids
. Clarendon Press, Oxford.
Dobbins WE 1944 Effect of turbulence on sedimentation.
Trans Am Soc Civil Eng
109
, 629-656.
Smith IM 1976 Integration in time of diffusion and diffusion-convection equations.
Finite Elements
in Water Resources
, vol. 1. Pentech Press, Plymouth, pp. 3-20.
Smith IM 1979 The diffusion-convection equation.
Summary of Numerical Methods for Partial Dif-
ferential Equations
. Oxford University Press. Chapter 11, pp. 195-211.
Smith IM, Farraday RV and O'Connor BA 1973 Rayleigh-Ritz and Galerkin finite elements for
diffusion-convection problems.
Water Resour Res
9
(3), 593-606.
