Disaster Mitigation Geotechnology 2012
Assignment 2 (due 18 Jan 2013)
A wide embankment of 10-m height and V:H=0.6:1.0 slope is to be constructed on a level ground
consisting of soft clay. The construction needs to be completed within 18 months. The properties of the
foundation clay layer and the embankment are shown in the illustration. Firstly, confirm that the
embankment cannot be safely constructed (i.e. Factor of safety, Fs <1) without ground improvement or
multi-stage, long-term construction. Secondly, design, optimise and prove the ‘best’ ground improvement
method and its specification for the foundation clay layer base on cost and stability. You may choose
from (i) multi-stage construction aided by vertical drains, (ii) sand compaction pile method and (iii)
cement-treating. Stability analysis may be performed based on total-stress-based circular slip analysis
(Swedish method; an Excel spreadsheet for calculation is provided). For simplicity, it may be assumed
that the embankment always fails along a circular mechanism regardless of the adopted improvement
technique. Finally, describe the reason why you chose the method and what advantages it has over the
other methods.
1.0
10 m
0.6
Embankment:
Total unit weight: gt = 18 kN/m3
Friction angle: f = 40o ,
Cohesion: c = 0
Original foundation layer (clay):
Total unit weight: gt = 15 kN/m3,
Friction angle: f = 0o ,
Initial cohesion (undrained shear strength): c0 (kN/m3) = 20+3z (z: Depth in [m])
Horizontal coefficient of consolidation: ch = 1.0×10-7 m2/sec
- Vertical drains and multi-stage construction:
Imaginary cost: ¥500/m (i.e. per length of plastic board drain, including execution)
Properties after improvement: The unit weight, gt, may be assumed to be unchanged and the friction
angle, f, remains 0o. Determine the cohesion, c (=cu, the undrained shear strength), as c0+0.3×Uh×
v (kN/m 2). The degree of consolidation, Uh, is time-dependent and calculated from the diagram
provided separately. The vertical stress increment, v, may be calculated by using an integrated form
of Boussinesq’s elastic solution (see Appendix). For the effective diameter of the drains, use de =
50mm.
- Improvement by sand compaction pile method:
Imaginary cost: ¥8,000/m 3 (volume after installation: assume that the clay is all replaced by sand: In
other words, the replacement ratio as = 100%)
Properties after improvement: gt =18 kN/m 3, c =0 kN/m 2, f=40o
- Improvement by cement-treating
Imaginary cost: ¥15,000/m 3 (volume after execution)
Properties after improvement: gt =16 kN/m 3, c =300 kN/m 2, f=0o
Appendix: Vertical stress under strip load
A
q=1
0
q

  sin  cos 
1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2
Z
z 
3
4
5
-5
-4
-3
-2
-1
0
X
1
2
3
4
5
In this problem with a ‘wide’ embankment (the right edge of the strip load is at infinite distance),  /2=/2
and  = /2 - 1 (if you use Osterberg’s chart, it is of course more rigorous, but you may find it less easy
to implement when you work with Excel).
You may approximate a trapezoidal load by stacking layers of a strip load, as illustrated above.