•
Lecture-8
SOIL MECHANICS
AND FOUNDATION ENGINEERING-I (CE-210)
CONSOLIDATION
• Degree of consolidation (U): The ratio, expressed as a percentage, of the
amount of consolidation (r) at a given time within a soil mass, to the total
amount of consolidation (rf) obtainable under a given stress condition.
𝑈 % =
𝜌
𝜌𝑓
×100
• TIME REQUIRED TO CONSOLIDATE A CLAY LAYER
• 𝑡=
𝑑2
𝑐𝑣
𝑇𝑣
where, cv= coefficient of consolidation, d = drainage path and
Tv is:
• Time Factor, 𝑇𝑣 =
𝜋 𝑈 2
4 100
when U<60%
𝑇𝑣 = −0.9332 𝑙𝑜𝑔10 1 −
𝑈
100
− 0.0851 when U>60%
Consolidation Settlement of Clay layer
𝐻𝐶𝑐
𝜎1
𝜌𝑓 =
𝑙𝑜𝑔10
1 + 𝑒𝑜
𝜎0
H = Thickness of clay layer
eo = Initial void ratio
Cc = Compression Index
𝜎0 = Initial Effective Stress
𝜎1 = Final Effective Stress
PROBLEMS
1. An undisturbed sample of clay, 24mm thick, consolidated 50% in 20 minutes,
when tested in the laboratory with drainage allowed at top and bottom. The
clay layer, from which the sample was obtained, is 4m thick in the field. How
much time will it take to consolidate 50% with double drainage? If the clay
stratum has only single drainage, calculate the time to consolidate 50%.
Assume uniform distribution of consolidation pressure.
2. An undisturbed sample of clay stratum, 2m thick, was tested in the laboratory
and the average value of coefficient of consolidation was found to be 2 × 10-4
cm2/sec. If a structure is built on the clay stratum, how long will it take to
attain half the ultimate settlement under the load of the structure? Assume
double drainage.
3. A clay layer, whose total settlement under a given loading is expected to be
12cm settles 3cm at the end of 1 month after the application of load
increment. How many months will be required to reach a settlement of 6cm?
How much settlement would occur in 10 months? Assume the layer to have
double drainage.
PROBLEMS
4. A 6m of sand is underlain by 3m thick layer of clay. There is another
layer of dense sand below the clay layer. The water table is upto the
ground surface. The submerged unit weight of sand 10kN/m 3. The
clay layer has a compression index of 0.35, water content = 40% and
specific gravity 2.7. If a square footing of size 2mx2m is placed at
1.5m below the ground level, Calculate the ultimate settlement of
clay layer. The foundation is carrying a load of 1000kN.
5. A 20mm thick undisturbed sample of a saturated clay is tested in the
laboratory with drainage being allowed both through the top and
bottom faces. The sample reaches 50% degree of consolidation in 60
minutes. If clay layer from which the sample was obtained is 4m thick
and is free to drain through both top and bottom surface, calculate the
time required by the clay layer to undergo the same degree of
consolidation. What would have been the time of consolidation if the
clay layer were free to drain only through its top surface? Assume
uniform distribution of consolidating pressure.