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Derek Gay 2015-09-16 COEM 6012 Coursework #2
COEM 6012 CONSTRUCTION GEOTECHNICS
Coursework #2 2015-09-16
1. Develop a computer solution (Excel, MATLAB, Fortran95, C/C++,
or other) to implement the numerical
finite difference solution for the 1D consolidation of a
compressible soil layer 12 m thick subjected to a
uniform surface loading of 100 kN/m2over its depth (site fill).
The computer solution must be capable of
modelling both doubly and singly drained layers. In this
algorithm the value of R must be a variable, where
R = cv*t/z2
cv= coefficient of consolidation, m2/month
z = depth increment length (m)
t = time step in months = (R*z2/cv)
For this problem, assume a single uniform layer, with a
uniformly distributed stress change with depth, where
cv= 0.15 m2/month and R = 0.5.
(i)
Create a 1D finite difference grid, for z = 3.0, 2.0, 1.0, 0.5
m. For each grid spacing
determine t calculate and compute and plot pore pressures vs
depth at times, t = 8, 16, 32, 64,128 months for a doubly and
singly drained soil [to do this you must first determine the
number of time-steps to be executed in each case, using the
stability condition at R=0.5]. In
the numerical solution the number of time-steps would not yield
the exact times indicated.
Round the number of steps up.
(ii) Using Equation 1.18 (Consolidation notes) determine the
theoretical pore pressure distributions
over depth, for the actual times (rounded up) and compare these
to the numerical solutions;
calculating the % error at each node point. Change the value of
R = 0.505 and comment on the
stability and accuracy of the solution for part (i).
(iii) For z = 0.5 m determine the average degree of
consolidation U%over the full depth of the
layer, at the times t = 4, 8, 16, 32, 64, 128, 256 months using
the area approximation method
(Trapezoidal Rule) and plot the graphs of Time Factor vs U%
Consolidation, for both the
double and single drainage conditions. Using Equation 1.21
(Consolidation notes 2015)
determine the theoretical %U and Time Factor values and compare
these to the numerically
computed values.
(iv) For z = 0.5 m and for both the double and single drainage
conditions, determine the average
degree of consolidation U%over a depth of 3.5 m at the times
indicated in (iii) above using the
area approximation method (Trapezoidal Rule). Plot the
relationships of Time Factor vs U%
Consolidation for this condition. Compare these
relationships/graphs with those obtained in
part (iii) above [where the U% Consolidation values were
averaged over the full layer depth].
(v) If the average mvfor the layer varies from, mv= 1.8 x
10-3
m2/kN at the top and mv= 1.0 x
10-3
m2/kN at the bottom, plot thelog10(time) vs settlementcurves for
conditions encountered
in (iii) and (iv) above.
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Derek Gay 2015-09-16 COEM 6012 Coursework #2
2. (a) Develop a MATLAB, Python, Fortran95, C/C++,
algorithm/script to determine the average stress
distribution zand x, under the
(i) centreline of an Embankment,
(ii)
centreline of a Tank foundation.The program must treat
embankment height, width, side slopes, tank radius, loading and
soil
parameters as input variables.
(b) Continue this algorithm to include the numerical solution of
1D consolidation. Using this algorithm,
redo question (1) part (iv) using the non-linear mean stress
distribution, (z+x)/2, at the centreline of
both the (i) embankment (ii) tank. Use (i) the maximum
embankment height is 6 m, = 21 kN/m3,
embankment top width 10 m and a 1:3 side slopes and for (ii)
tank radius = 5 m, filled with water to 10
m.
Submission Date: Qu.1 September 25
th
2015, 4:30 pmSubmission Date: Qu.2 October 1st2015, 4:30 pm
Late Submissions would be penalised by 2.5%/day up to a maximum
of 25% after which,
submissions would attract an F
