COMPRESSIBILITY OF SOIL
Settlement of Foundations
Total Settlement:
St = Sc + Ss + Se
Where:
St = total settlement
Sc = primary consolidation settlement
Ss = secondary consolidation settlement
Se = immediate or elastic settlement
A. Primary Consolidation Settlement
1. Normally Consolidated Clays
Normally consolidated clays are those whose present effective
overburden pressure is the maximum pressure that the soil was
subjected to in the past. The maximum effective past pressure is called
the preconsolidation pressure.
Sc =
Cc H
Po + ∆ P
log
1+e o
Po
(
)
Sc = primary consolidation settlement
Cc = compression index
Cc = 0.009 (LL – 10)
eo = in situ void ratio
H = thickness of clay layer
∆ P = average increase of effective stress on clay layer
Po = average effective stress at the mid-height of clay layer.
2. Over Consolidated Clay:
Over consolidated clays are those whose present effective overburden
pressure is less than that which the soil experienced in the past.
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1. when Po + ∆ P< P c
Pc = preconsolidation pressure
Sc =
Cs H
P o+ ∆ P
lo g
1+e o
Po
(
)
Cs = swell index
1 1
(ranges from 5 ¿ 10 of Cc)
2. when Po + ∆ P> P c
Pc = preconsolidation pressure
Sc =
Cs H
Pc c c H
Po + ∆ P
log +
log
1+e o
P o 1+e o
Pc
(
)
B. Secondary Settlement
Ss =
Ca H
T2
lo g
1+ e p
T1
( )
Ss = secondary settlement
Ca = secondary compression index
T2 = time after completion of primary settlement
T1 = time for completion of primary settlement
ep = void ratio at the end of primary consolidation
ep = eo - ∆ e
∆ e=Cc log
(
Po +∆ P
Po
)
eo = in situ void ratio
C. Immediate or Elastic Settlement
1.
Se ¿C s q B(
1−μ2
)
Es
2.
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Se =q B
1−μ 2
lp
Es
( )
where:
Cs = shape and foundation rigidity factor
B = width of foundation or diameter of circular foundation
q=
P
B 2 (net vertical pressure applied)
μ = Poissons ratio of soil
Es = modulus of elasticity of soil
Ip = influence factor
Compression Index:
1. Skempton’s Equation (1944)
Cc = 0.009 (LL – 10)
LL = liquid limit
2. Rendon-Herrero (1983)
1.2
C c =0.141G s
1+ eo
Gs
( )
2.38
3. Naagaraj and Murty (1985)
C c =0.2343
( 100¿ ) G
s
LL = liquid limit of soil
Gs = specific gravity of soil
4. Park and Koumoto (2004)
C c=
no
371.747−4.275n o
Swell index:
1. Nagaraj and Morty (1985)
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C s=
0.0463(¿)
Gs
100
1 1
2. C s= 5 ¿ 10 C c
Cc = compression index
Time Rate of Consolidation (Theory of Consolidation)
1. Compression Index (Cc)
Cc = compression index
e1 −e 2
C c=
log
P2
P1
( )
e1 = void ratio at a pressure P1
e2 = void ratio at a pressure P2
2. Coefficient of Compressibility:
It is the ratio between the change in void ratio and the change in
effective stress for the given increment.
av = coeff. of compressibility in m2/kN
a v=
e1−¿ e
¿
P 2−P1
2
3. Coefficient of volume Compressibility:
mv = coefficient of volume compressibility
mv =
( e ¿ ¿ 1−e 2)
¿
(1+ eav e )( P ¿ ¿ 2−P1) ¿
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e ave
e 1 +e 2
2
mv =
av
(1+ e¿¿ ave )¿
4. Coefficient of Consolidation (Cv)
Cv = coeff. of consolidation
C v=
K
mv γ w
K = coefficient of permeability
mv = coefficient of volume compressibility
γ w = unit weight of water
Time Factor (Tv)
C t
T v = ¿ ¿v ¿
Cv = coeff. of consolidation
t = time corresponding to degree of consolidation
Hdr = half the thickness of the sample if drained on both sides
Hdr = thickness of the sample if drained on one side only.
5. Degree of consolidation for the entire depth of clay layer at anytime
“t”.
U=
Sct
Sc
U = degree of consolidation
Sct = settlement of the layer at time “t”
Sc = ultimate settlement of the layer from primary consolidation
6. Degree of consolidation at a distance “z” at anytime “t”.
U=
Uz
Uo
U = degree of consolidation
Uz = excess pore pressure at time “t”
Uo = initial excess pore water pressure
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7. Relation of time and degree of consolidation
t 1 U 21
=
t 2 U 22
U1 = degree of consolidation at time t1.
U2 = degree of consolidation at time t2.
8. Preconsolidation Pressure Pc ‘ for overconsolidation clay:
Nagaraj and Murthy (1985)
1.22−(
log Pc ' =
eo
)−0.0463 log P o '
eL
0.188
Pc’ = preconsolidaation pressure in kPa.
eo = in situ void ration
eL = void ratio of the soil at liquid limit
e L=
( 100¿ ) G
s
Gs = sp.gr. of soil
Po = in situ average overburden pressure.
10. Over Consolidation Radio (OCR)
OCR=
Pc
Po
Pc = preconsolidation pressure
Po = present effective vertical pressure.
11. For normally consolidated clay:
Nagaraj and Morthy (1985)
e
=1.122−0.2343 log P o
eL
e L=
( 100¿ ) G
s
Po = overburden pressure
12. Surcharge needed to eliminate the entire primary settlement for a
period of time “t” by precompression.
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Precompression:
Precompression of soil is used to minimize post construction
settlement for highly compressible normally consolidated clay which
produces depth and large consolidation settlements as a result of
construction of dams, highways embankments and large bldgs. If the
temporary total surcharge load ∆P + ∆Pf when applied on the ground
surface will produce a settlement equal to that if ∆P is only applied, that is
if ∆Pf is removed and only ∆P is acting, no appreciable settlement will
occur, the process is known as precompression.
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Degree of Consolidation:
U=
Sc 1 if only ∆ P is acting
S c2 ∆ P+∆ P f is acting
Sc 1 =
Cc H
∆ P+ P o
log
1+ e
Po
Sc 2=
Cc H
( ∆ P+ ∆ P f ) + Po
log
1+ e
Po
(
[
log
U=
log
[
[
∆ P+ Po
Po
Po
(
]
)
∆ Pf
∆P
1+
Po
∆P
[ (
log 1+
∆P
Po
]
]
( ∆ P+ ∆ Pf ) + P o
log 1+
U=
)
)]
U = Degree of consolidation
∆Pf = additional surcharge needed to eliminate settlement for a period of
time “t” by precompression.
∆P = surcharge (average increase of effective stress on clay layer)
1. Problem:
At a planned construction site, a 2 m. thick buried clay layer lies beneath
a surficial stratum of free draining soil. Free draining granular soil also
underlies the clay layer. Double drainage from the clay layer can
therefore occur when construction loads cause consolidation. The
coefficient of consolidation for the clay is 0.001 m2/day. Settlement
calculations indicate that the clay layer will eventually compress 4 cm.
(primary compression or consolidation) due to the effect of bldg. loads.
1. How long a time period is required for 90% of the estimated
settlement to occur?
2. How much settlement occurs in the first 12 months?
3. What time period is required for a settlement of 2 cm?
2. Problem:
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A normally consolidated clay layer is 4 m. (one-way drainage). From the
application of a given pressure, the total anticipated primary consolidation
settlement will be 80 mm.
1. What is the average degree of consolidation for the clay layer when
the settlement is 30 mm?
2. If the average value of Cv for the pressure range is 0.003 cm2/sec.,
how long will it take for 50% settlement to occur?
3. How long will it take for 50% consolidation to occur if the clay layer
is drained at both top and bottom?
3. Problem:
The estimated primary consolidation settlement of a clay layer
having a thickness of 4.5 m. is 300 mm. The clay layer is drained
at the top only.
1. Compute the average degree of consolidation for the clay layer when
the settlement is 75 mm.
2. How long will it take for 50% consolidation to occur if the coefficient of
consolidation is 0.004 cm2/sec.
3. If the 4.5 m. clay layer is drained on both sides, how long will it take
for 50% consolidation to occur?
4. Problem:
The soil shown has its properties. A surcharge of 140 kPa is applied at the
ground surface.
1. Estimate the primary
consolidation settlement
of the clay layer
assuming that it is
normally consolidated.
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2. Estimate the primary consolidation settlement if the preconsolidation
1
pressure is 160 kPa, Assume C s= 5 cc ∙
3. Estimate the settlement after 300 days if the preconsolidation
pressure is 160 kPa and the coeff. of consolidation is C v = 0.002
cm2/sec.
5. Problem:
For a normally consolidated clay, the following are given.
Thickness of clay = 4 m.
Po = 50 kPa
∆P + Po = 120 kPa
Hydraulic conductivity K of the clay = 3.1 x 10 -7 m/sec.
1. In how many days will it take for a 4 m. thick clay layer (drained on
both sides) in the field to reach 50% consolidation?
2. Compute the primary consolidation settlement of the clay layer.
3. What is the settlement when it reaches 50% consolidation?
6. Problem:
It will take 150 sec. for a 25 mm. thick clay layer (drained at both top and
bottom) to reach 50% consolidation.
1. Compute the coefficient of consolidation in mm/sec.
2. How long in days will it take for 3 m. thick layer of the same clay in
the field under the same increment to reach 50% consolidation if
there is a rock layer at the bottom of the clay field.
3. If the primary consolidation settlement of the 3 m. thick layer of clay
with same condition in “b” is 120 mm, how long will it take for the
settlement to become 84 mm.
7. Problem:
An 8 m. thick layer of saturated clay under a surcharge loading
underwent 80% primary consolidation in 70 days. The clay layer is
drained both top and bottom.
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1. Find the coefficient of consolidation of clay for the pressure range.
2. How long in minutes will it take to undergo 80% consolidation in the
laboratory for a similar consolidation range of a 60 mm. thick
saturated clay under surcharge loading. The saturated clay is drained
both top and bottom.
3. If the 8 m. thick clay layer in the field under a given surcharge will
undergo 175 mm. of total primary consolidation settlement, estimate
the time required for the first 50 mm. of settlement if the first 80 mm.
of settlement takes 120 days.
8. Problem:
Given the following data for a normally consolidated clay specimen on both
sides.
P1 = 144 kPa
P2 = 288 kPa
e1 = 1.10
e2 = 0.9
Thickness of clay = 30
Time for 50% consolidation = 2 min.
1. Compute the coefficient of compressibility.
2. Compute the coefficient of consolidation of clay for 50% consolidation
in m2/min.
3. Determine the hydraulic conductivity in m/min of the clay for the
loading range.
4. How long days will it take for a 1.8 m. clay layer in the field (drained
on one side) to reach 60% consolidation?
9. Problem:
The footing shown in the figure supports a
load of 224 kN (including the
weight of the footing). The footing is 1.5
m. x 1.5 m. in plan.
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1. Determine the settlement of the soft clay.
2. Find the number of days for the consolidation of the clay to reach
80%.
3. Find the settlement after 20 days.
10. Problem:
A tank 12 m. high with a 45 m.
radius filled with oil is to be built
on a site. The existing soil profile
consists of a 3 m. sand layer
underlain by 14 m. clay layer.
Another sand layer is under the
clay. The water table is at the
surface. The clay has an initial
void ratio of 1.27 and unit weight
of soil is 9.4 kN/m3. From a
consolidation test on a 25 mm
laboratory sample of the clay
with drainage on both ends, 50%
consolidation is achieved after
6.5 minutes. The compression
indexis 0.40. Assume the
foundation is very flexible.
Neglect weight of tank.
1. Find the ultimate differential settlement of the tank if the influence
coefficient under the center and the edge of the tank are 1.0 and 0.48
respectively.
2. Find the time for 70% consolidation. Use the time factor table.
3. Find the depth in the ground to which the tank must be placed in
order to minimize settlement.
12. Problem:
The soil profile shown is a section of
the proposed construction of
highway bridge. A permanent
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surcharge ∆P = 50 kPa is applied at the ground surface. Thickness of clay
layer is 6 m. The clay is normally consolidated. Coefficient of consolidation
is 0.40 m2/month.
1. Compute the primary consolidation settlement of the bridge without
precompression.
2. Compute the degree of consolidation if the entire primary
consolidation settlement will be eliminated by precompression in 8
months.
3. Compute the surcharge needed to eliminate the entire primary
consolidation settlement in 8 months by precompression.
13. Problem:
The coordinate of two points on a virgin compression curve are as follows.
e1 = 1.2
e2 = 0.95
P1 = 110 kPa.
P2 = 220 kPa.
1. Compute the void ratio that corresponds to a pressure of 350 kPa.
2. Compute the value of coefficient of volume compressibility.
3. Compute the hydraulic conductivity in cm/sec. if the coefficient of
consolidation is 0.0036 cm2/sec.
14. Problem:
The laboratory consolidation data for an undisturbed clay specimen are as
follows:
e1 = 1.12
e2 = 0.90
P1 = 90 kPa
P2 = 450 kPa
1. Compute the value of the compression index.
2. Compute the value of the swell index assuming it is equal to 1/6 the
value of the compression index.
3. Compute the void ratio for a pressure of 600 kPa.
4. Compute the coefficient of compressibility.
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5. Compute the value of the coefficient of volume compressibility.
15. Problem:
When the total pressure acting at midheight of a consolidating clay layer is
200 kN/m2, the corresponding void ratio of the clay is 0.98.When the total
pressure acting at the same location is 500 kN/m 2, the corresponding void
ratio decreases to 0.81.
1. Compute the compression index.
2. Compute the void ratio of the clay if the total pressure acting at
midheight of the consolidation clay layer is 1000 kPa?
3. Compute the coefficient of compressibility.
16. Problem:
The time required for a 50% consolidation of 25 mm thick layer (drained at
both top and bottom) in the laboratory is 2 min. 20 sec.
1. How long in days will it take for a 3 m. thick clay layer of the same
clay in the field under the same pressure increment to reach 50%
consolidation? In the field there is a rock layer at the bottom of the
clay.
2. How long in days will it take in the field for 30% primary consolidation
to occur?
3. From the application of given pressure the anticipated primary
consolidation settlement is 0.064 mm. What is the average degree of
consolidation for the clay layer when the settlement is 0.02 mm?
17. Problem:
A civil engineer made a preliminary settlement analysis for a foundation of
an office bldg., which is to be constructed at a location where the soil strata
experienced a consolidation settlement of 60 mm. The bldg. will impose an
average vertical stress of 160 kPa. In the clay layer.
1. As often happens in design practice, design changes are required. In
this case the actual thickness of the clay is 30% more than the
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original soil profile indicated. Estimate the new primary consolidation
settlement due to the increase in thickness.
2. During the construction the ground water table is lowered by 2 m.
Compute the total primary consolidation settlement from vertical
stress increase due to lowering of the ground water level.
3. If the thickness of the clay layer used in the final calculation is equal
to 2.8 m, compute the modulus of volume compressibility of the soil.
18. Problem:
A soil profile shown is subjected to a
surcharge load of 120 kPa on the
ground surface.
1. Compute the value of “h” after
the load is applied.
2. Compute the degree of
consolidation at A when h = 6
m.
3. Compute the value of h when
the degree of consolidation at
A is 80%.
19. Problem:
From the figure shows a soil profile
with the corresponding properties.
The soil is acted upon by a
uniformly distributed load ∆P = 60
kPa. at the ground surface.
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1. Compute the settlement of the clay layer caused by primary
consolidation if the soil is normally consolidated.
2. Compute the settlement of the clay layer caused by primary
consolidation if the preconsolidation pressure of clay is 230 kPa.
1
Use C s= 5 C c ∙
3. Compute the settlement of the clay layer caused by primary
consolidation if the preconsolidation pressure of clay is 200 kPa.
1
Use C s= 5 C c ∙
20. Problem:
A soil formation shown in the
figure has its ground water table
located at 2 m. below the ground
surface. The ground surface is
subjected to a uniformly distributed
load of 40 kPa.
1. Compute the primary
compression index.
2. Compute the primary
consolidation settlement of
the normally consolidated
clay layer.
3. Compute the secondary settlement of the clay layer 5 yrs. After the
completion of primary consolidation settlement. Time for completion
of primary settlement is 1.5 years. Secondary compression index is C a
= 0.02.
21. Problem:
A normally consolidated clay layer 3 m. thick has a void ratio of 1.10 Liquid
limit is equal to 40 and the average effective stress on the clay layer was
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80 kPa. The average stress on it is increased to 120 kPa. as a result of the
construction of a foundation. Cc = 114 Cc
1. Compute the consolidation settlement that the clay layer undergo.
2. If the clay layer is preconsolidated, compute the consolidation
settlement if the preconsolidation pressure is 96 kPa.
3. Compute the consolidation settlement if the preconsolidation
pressure is 130 kPa.
22. Problem:
From the given soil profile:
1. Compute the effective stress at the
mid-height of the clay layer.
2. Compute the void ratio at the end of
primary consolidation.
3. Compute the primary settlement of
the normally consolidated clay
layer.
23. Problem:
From the given soil profile shown, the ground surface is subjected to a
uniformly distributed load of 80 kPa.
1. Compute the compression index.
2. Compute the present overburden
Po at mid-height of the
compressible clay layer.
3. Compute the total settlement due
to primary consolidation.
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24. Problem:
From the given soil profile shown, the ground surface is subjected to a
uniform increase in vertical pressure of 12 N/cm 2.
1. Compute the buoyant unit weight
of clay.
2. Compute the overburden pressure
Po of mid-height of the
compressible clay layer.
3. Compute the total settlement due
to primary consolidation.
25. Problem:
At a planned construction site, a 2 m. thick stratum of normally
consolidated clay underlies a surface layer of compact granular soil 3 m.
deep. The unit weight for the compact granular soil is 20.2 kN/m 3. The clay
material has a unit weight of 17.6 kN/m3. The ground water table is very
deep. Laboratory testing of the clay indicated an in place void ratio of 1.35
and a compression index of 0.42. The bldg.. planned for the site will create
a stress increase of 24.5 kN/m2 at the center of the clay layer.
1. Assume that the foundation for
the bldg.. will be situated near
the surface of the upper compact
granular soil layer. Determine the
foundation settlement due to
primary compression occurring in
the clay layer because of the
stress increase.
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2. Calculate the settlement to be expected if the ground water table
were at the soil surface, assuming saturated unit wt. of granular soil is
20.2 kN/m3.
3. Determine the compression occurring in the clay layer if the clay is
over consolidated, Cs = 0.09 and the preconsolidation pressure is 120
kPa.
26. Problem:
From the soil profile shown, the ground surface is subjected to a uniformly
distributed load of 40 kPa. The thickness of the over consolidaaetd clay is
2.5 m. The institu void ratio of the clay is eo = 0.80 with liquid limit of 45%.
Specific gravity of clay is 2.71. Assume
1
swell factor C s= 6 C c ∙
The institu effective burden pressure
P'o =120 kPa
1. Compute the pre consolidation
pressure (Pc’).
2. Compute the primary
consolidation settlement of the
clay layer.
3. Compute the secondary
consolidation settlement 6
years after the completion of
primary consolidation
settlement. Time for completion
of primary settlement is 1.8
years. Secondary compression
index C α =0.3 .
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27. Problem:
A soil profile shown in the figure. A uniformly distributed load of 50 kPa is
applied at the ground surface. The clay is normally consolidated.
1. Compute the compression
index.
2. Compute the primary
consolidation settlement.
3. Compute the secondary
settlement 8 years after the
completion of primary
consolidation settlement. Time
for completion of primary
settlement is 2 years. Assume
secondary compression index
C α =0.025
28. Problem:
From the figure shown, the clay is normally consolidated. A laboratory
consolidation test on the clay gave the following results.
Pressure (kPa)
100
200
void ratio
0.905
0.815
1. Calculate the average effective
stress on the mid height of clay
layer.
2. Determine the compression
index Cc.
3. If the average effective stress
on the clay layer is increased
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(Po + ∆P) to 115 kPa, what would be the total consolidation
settlement?
29. Problem:
A proposed site for a large warehouse is underlain by a 2.4 m. thick of soft
clay that would be subject to severe settlement under the loadings that
would apply as shown in the soil profile. A decision has been made to
consolidate the clay layer prior to site development by pre loading with a
sand layer 3 m. thick and by lowering the water table by 1.5 m. by
improving site drainage. The silty sand has a unit weight of 15.74 kN/m 3
above the water table and a saturated unit weight of 16.52 kN/m 2 below the
water table. The sand fill will have a unit weight of 17.30 kN/m 3. Soil tests
on undisturbed samples indicate that the clay layer is normally consolidated
and the clay has a void ratio of 1.6, water content of 59.26% and a liquid
limit of 48%.
1. Compute the initial state of
effective stress at center of clay
layer prior to placement of sand
fill and lowering of water table.
2. Compute the final state of
effective stress at center of clay
layer after placement of fill and
lowering of water table.
3. Compute the total settlement
that would occur in the clay
layer near the center of the site
in response to the sand layer
preloading and lowering of the
ground water table.
30. Problem:
A proposed site for large industrial complex is underlain by 3.6 m. thick
layer of soft clay that would be subject to severe settlement under the
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loadings that would be applied. A decision has been made to consolidate
the clay layer prior to site development by preloading with a sand layer 2.4
m. thick. The sand fill will have a unit weight of 16.5 kN/m 3. The clay layer
is normally consolidated and tests have determined that the water content
of clay is 44% and a void ratio of 1.20.
1. Compute the effective stress at
mid point of clay layer prior to
preloading.
2. Compute the effective stress at
mid point of clay layer after
preload is applied.
3. Compute the total settlement
that would be expected to occur
in the clay layer in response to
the sand layer loading if the
compression index of the clay is
0.44.
31. Problem:
A manufacturing plant was constructed on a silty soil 12 m. thick which is
underlain by sand and gravel. Several years later, after all settlement of the
building had stopped, water wells and rate of pumping was such that the
water table was lowered from 3 m. below the ground surface to 6 m. below
ground surface over an extensive area. The unit weight of the soil above
the water table is 15.74 kN/m3 and below the water table is 18..88 kN/m3
(saturated unit weight). The compression index C c for the clay is 0.32 and
the void ratio of the soil before the water table was lowered was 0.6. The
bldg.. floor load is 24 kPa.
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1. Compute the final stress at a point 4.5 m. below the ground surface
when the water table lowers by 3 m.
2. Compute the final stress at a point 9 m. below the ground surface
after the water table lowers by 3 m.
3. Approximately how much will the center of the bldg.. settle as a result
of lowering the water table.
32. Problem:
From the given soil profile
shown in the figure.
1. Compute the
compression index.
2. Compute the effective
stress increase the water
table lowered by 5 m.
3. Compute the settlement.
33. Problem:
A soil profile shown is underlain by a 2.4 m. thick of soft clay that would be
subject to severe settlement when the water table is lowered to improve the
site drainage. The silty sand has a unit weight of 15.60 kN/m 3 above the
water table and a saturated unit weight of 16.58 kN/m 3 below the water
table. The clay layer is normally consolidated having a void ratio of 1.20
and a water content of 44% liquidity index of 0.80 and a plastic limit of 20%.
1. Determine the compression index.
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LECTURER: MAVIE CABALAG
23
2. Determine the effective
stress increase with the
ground water table lowered
by 1.5 m. to improve the
site drainage to
consolidate the clay layer
prior to site development.
3. Compute the settlement
that would occur in the clay
layer in response to the
lowering of the ground
water table.
34. Problem:
The profile of a given soil formation shown consists of a 5 m. layer of sand
having a dry unit weight of 14.72 kN/m3 and a saturated unit weight of
19.075 kN/m3. Beneath the layer of sand lies a layer of clay 17 m. thick
having a saturated unit weight of 20.48 kN/m 3/ Ground water table is
located 2 m. below the ground surface. Sp.gr. of clay is 2.7 having a
plasticity index of 22% and a plastic limit of 30%.
1. Compute the compression
index.
2. Compute the settlement if a
surcharge of 60 kPa is
applied at the ground
surface.
3. Compute the effective stress
at the bottom.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
24
35. Problem:
For a large construction project, the general subsoil condition is shown. If a
3 m. thick fill is placed over the existing ground surface with a unit weight of
17.31 kN/m3.
1. Compute the increase in the
vertical pressure ∆P.
2. Compute the overburden
pressure at the mid height of
clay.
3. Compute the consolidation
settlement of the soft clay
layer.
36. Problem:
A tank 12 m. high filled with oil having a unit weight of 9.4 kN/m 3 is to be
built on a site. The existing soil profile consists of a 3.6 m. sand layer
underlain by a 16 m. clay layer. The water table is on the ground surface.
Neglecting the weight of the tank.
1. Compute the compression
index of clay.
2. Compute the settlement
under the center of the tank.
3. Find the minimum depth in
the ground to which the
tank must be placed in
order to minimize
settlement.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
25
37. Problem:
Assume a buried stratum of clay 1.83 m. thick will be subjected to a stress
increase of 33.6 kPa at the center of clay. The magnitude of the pre
construction soil overburden pressure Po = 48 kPa at the center of the clay
layer. A laboratory compression test indicates that the clay has a pre
consolidation pressure of 72 kPa. Compression index is 0.30 and the value
of swell index is 0.05. Void ratio of clay is 1.50.
1. Compute the settlement due to primary compression of clay.
2. If full consolidation settlement (primary compression settlement) will
require approximately 8 years, compute the settlement due to
secondary compression of clay ever a period of 20 year time span.
Assume secondary compression index = 0.008.
3. Estimate the total settlement to be expected over a 20 year time span
considering the effects of secondary compression.
38. Problem:
From the soil profile shown, given B = 1.5 m. and L = 2.5 m. The footing
carries a load of 120 kN.
1. Compute the average effective
pressure at mid-height of clay
layer.
2. Compute the average increase
of effective pressure in the
clay layer using 2:1 method.
3. Compute the primary
consolidation settlement of the
foundation.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
26
39. Problem:
A foundation shown is 1 m x 2 m in plan has a net stress increase qo = 150
kN/m2 at its bottom section. The unit weight of sand is 16.5 kN/m 3 and its
saturated unit weight is 17.5 kN/m3. The ground water table is located 2.5
m. below the ground surface with Df = 1 m. The normally consolidated clay
has a thickness of 2.5 m., located 3 m., below the ground surface. The clay
has a compression index of 0.32 m., and a void ratio of 0.80. Saturated unit
weight of clay is 16 kN/m3.
1. Compute the overburden
pressure at the mid height
of the clay.
2. Compute the average
vertical stress increase.
3. Compute the
consolidation settlement.
40. Problem:
A rigid square footing shown 2 m x 2m. carries an axial load of 2400 kN.
1. The footing has a shape
and foundation rigidity factor
Cs = 0.82, a modulus of
elasticity of clay = 50000
kPa., Poissons ratio of 0.5
for saturated clays.
Compute the settlement
under the center of the rigid
foundation due to volume
distortions occurring in a
saturated clay stratum.
2. Compute the settlement due
to primary compression of
clay having a compression
index of Cc = 0.32.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
27
3. Estimate the total settlement to be expected over a 15 year time
span, considering the effects of secondary compression. Full
consolidation settlement (primary compression settlement) will
require approximately 5 years. Compression index for secondary
compression Ca = 0.0128.
41. Problem:
A rigid 3 m. square footing is constructed over a loose sand layer as shown
on the figure. It carries a total load of 710 kN.
1. Compute the elastic settlement of
the 3 m. footing if the Poisson’s
ratio ( μs ¿ of soil is 0.32, modulus
of elasticity of soil Es = 16000
kPa, influence factor Ip = 0.88.
2. Compute the primary
consolidation settlement of the
clay layer if It is normally
consolidated.
3. Compute the total consolidation
settlement of the clay 5 yrs. after
the completion of primary
consolidation settlement. Time
for completion of primary
settlement is 2.0 yrs. Secondary
compression index Ca = 0.02.
42. Problem:
A soil profile is shown in the figure. A uniformly distribute load of 50 kPa is
applied at the ground surface, what is the settlement of the clay layer
caused by primary consolidation if.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
28
a) The clay is normally
consolidated.
b) The preconsolidation
pressure
(Pc) 190 kPa.
c) The preconsolidation
pressure
Pc = 170 kPa.
43. Problem:
For a given over consolidated clay.
Sp.gr. = 2.71
Liquid limit = 45
In situ average effective over burden pressure = 120 kPa.
In situ void ratio = 0.80
Thickness of clay layer = 4 m.
∆P = 4- kPa.
Effective pressure at the mid-height of clay layer = 60 kPa.
1
Swell index (C ¿¿ s)= 5 Cc ¿
a) Compute the compression index.
b) Compute the pre consolidation pressure.
c) Compute the primary consolidation settlement.
44. Problem:
From the figure shown, the water table is located 2 m. below the ground
surface. A uniform load ∆P = 120 kPa is acting at the top of the water
surface.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
29
a) Compute the saturated unit
weight of sand.
b) Compute the overburden
pressure at the mid-height of
clay.
c) Compute the primary
consolidation settlement.
45. Problem:
Given the following data for a normally consolidated clay layer in the field.
Thickness of clay layer = 2.6 m.
Primary compression index Cc = 0.30
Void ratio = 0.80
Ave. effective pressure at the mid height of the clay layer P o = 127 kPa
∆P = 46 kPa (increase in vertical pressure)
Secondary compression index Ca = 0.02
a) Compute the primary consolidation settlement.
b) Compute the secondary settlement of the clay layer five years after
the completion of primary settlement. Time for completion of primary
settlement is 1.5 yrs.
c) Compute the total consolidation settlement.
46. Problem:
For a laboratory consolidation test on a clay specimen (drained on both
sides) the following results were obtained.
Thickness of the clay soil = 25 mm
P1 = 50 kPa
P2 = 120 kPa
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
e1 = 0.92
e2 = 0.78
30
Time for 50% consolidation = 2.5 min.
Tv = 0.197
a) Determine the coeff. of compressibility.
b) Determine the coeff. of consolidation.
c) Determine the hydraulic conductivity of the clay for the loading range.
47. Problem:
The square footing having a dimension of 3 m x 3m. is resting on a soil
having the given properties as shown on the figure. It carries a
concentrated load of 1800 kN. The undrained elastic modulus of clay is
estimated to be 40 MPA with a Poissons ratio of 0.5.
a) Compute the expected immediate
settlement beneath the center of
the footing. If the footing has a
shape and foundation rigidity
factor
Cs = 0.82.
b) Compute the settlement due to
primary consolidation of clay if
the clay has a void ratio of 0.80
and a liquid limit of 47%. Use the
weighted average method of
computing the average increase
in pressure.
c) Compute the total settlement
expected over a 20 year time
span assuming full primary
consolidation of the clay requires
approximately 5 years.
Compression index for secondary
compression is equal to 0.0136.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
31
48. Problem:
The coordinates of two points on a given compression curve are as follows:
e1 = 1.82
e2 = 1.54
P1 = 200 kPa
P2 = 400 kPa
a) Compute the coefficient of compressibility.
b) Compute the coefficient of volume compressibility for the pressure
range stated above.
c) Given the coefficient of consolidation Cv = 0.003 cm2/sec., determine
the hydraulic conductivity (k) in cm/sec. corresponding to the average
void ratio.
49. Problem:
A square footing having a dimension of 3 m. x 3 m. carries an axial load of
15000 kN. The bottom of the footing is 2 m. from the ground surface
consisting of a layer of sand overlying a 4 m. layer of clay. The water table
is located 2 m. below the ground surface.
Dry unit weight of sand = 16.5 kN/m3
Saturated unit weight of clay is = 20 kN/m3
Void ratio of clay = 0.80
Liquid limit of clay = 50%
a) Compute the increase in the
vertical pressure.
b) Compute the overburden
pressure at the midpoint of
clay.
c) Compute the primary
consolidation settlement.
GEOTECHNICAL ENGINEERING
CE-161P-2_1Q2021
LECTURER: MAVIE CABALAG
32