## Question:

Soft compressible soils are often a problem for foundation engineers.

A soil profile with a silty-sand (?=15kN/m3??sat=17kN/m3) overlain by high?plasticity Clay (?sat=17kN/m3) and then a peat layer (16kN/m3). Then, dense sand.

A 2?m?thick layer of fill material, compacted at 19 kN/m3, will then be added on top of the silty soil layer to speed consolidation and minimize settlement.

The fill will have a plan area of 10 m X10 m. After that, construction will begin.

These properties were obtained from undisturbed samples taken from clay and organic layers.

The total settlement due to the action of thefill load is estimated.

Normally, consider both clay and peat layers.

The time required for primary consolidation at 99% in each layer is estimated.

Is each layer single- or double-drained?

Determine the secondary compression of each layer.

What will the total settlement be after 2 years of existence?

Three months after application of the fillload, calculate the effective stress point A.

## Answer:

Hydraulic conductivity

Kv =

Substitution of H = 600mm H1 = H2= H3 = 200mm K1 = 5/10-3 K2 = 4.2*10-2 K3 = 3.99 * 10-4

The hourly flow of water through the sample should be determined.

Kv =

Water flow through the sample

i = hydraulic gradient; A = soil cross section.

Substitute 47/60 in place of I and d =15 cm

The water flow through the sample at an hour is 536.04 cm3/hr

Calculate when the x value is 0.

Because there is no water pressure below the datum line (Y – Y), the pressure head is 0.

Z’s value is 220 mm

The equation calculates the head at entry and exit for each layer.

h =

The elevation head is Z and the pressure head is

h = 0. + 470

= 470 mm

Thus, the total head is 470mm

Calculate when 200 mm = x

Because there is no water pressure below the datum line (Y – Y), the pressure head is 0.

Z’s value is 220 mm

The equation calculates the head at entry and exit for each layer.

h =

Here, pressure head (altitude head) is Z.

You can also use the discharge velocity to your advantage

Kv = K1 *i1

h = 475 – 33.7

= 436.29 mm

Calculate the price of

656.29mm

The total head is 656.29mm

Calculate when the X = 400mm

Because the datum line is Y, there is no water pressure, the pressure head is 0.

Z’s value is 220 mm

Equip the discharge velocity

Kv = K1 *i1

h = 436.29 – 4

= 432.29mm

Calculate the price of

652.29mm

The total head is 652.29mm

Calculate when 600 mm = x

Because the datum line is Y, there is no water pressure, the pressure head is 0.

Z’s value is 220 mm

Equip the discharge velocity

Kv = K1 *i1

h = 436.29 – 432.24

= 0mm

Calculate the price of

200 mm

The head total is 200 mm

k = hydraulic conductivity in the soil, and I = hydraulic gradient

k = 0.001076

v = 0.017676 * 47/60

The equation can be used to calculate the seepage speed.

Vs =V/n

V = 0.000843; n = 1.5

Vs = 0.99433/0.5

V = 0.000843; n =0.6

Vs = 0.000043/0.6

V = 0.000843; n = 0.33

Vs = 0.09433/0.33

Calculation of the height at A

Height = (pressure at X)200mm

= 656.29 mm

Thus, A has a height of 656.29 mm.

Calculate B’s water elevation

Height = (pressure at X)400 mm

= 652.29mm

Accordingly, A has a height of 652.29 mm.

The plane stress in the XY plane is z = 0 or ZX = ZY =YZ=0

Sum forces in the x1 direction

Sum forces in the y1 directions

Simplified version of xy =yx

Trigonometric identities can be used

Sin

1face, replacement of

Substituting R for rearranging

Principles with a larger scope

Settlement of clay layer by one-dimensional consolidation

Cc compression index

0 is the effective pressure of overburden.

Clay clay bearing capacity

Where

Calculation of m1

L = B = ten m

Calculation of the value b

b = b/2

B = 10m

b = 10/2 = 5m

Consider a clay layer of different thicknesses from the fill load = Z

b = 5m and 4 = 4.

Calculate the effective stress increase by tabulating the value of different z

Z (m)

b = b/2

q

Calculate the settlement rate of clay layers due to one-dimensional consolidation

e0 = 1.1,, Cc = 0.36

= 0.096 m

Calculation for the settlement of the peat layer

Cc compression index

0 is the effective pressure of overburden.

Clay clay bearing capacity

Where

Calculation of m1

L = 10 m

Calculation of the value b

b = b/2

B = 10m

b = 10/2 = 5m

Consider a clay layer of different thicknesses from the fill load = Z

b = 5m; z = 8

Calculate the effective stress increase by tabulating the value of different z

Z (m)

b = b/2

q

Calculate the settlement rate of the peat layer because of one-dimensional consolidation

e0 = 5,9,, Cc=6.6, H = 2.m

0.136 m

Sc = Scclay + Scpeat

Sc = 0.096 + 0.386

0.232 m

Total consolidation settlement = 0.232m

The formula calculates the time needed to consolidate 99% of primary debt.

Here, the maximum drainage path is Hdr. T99 is the time factor. Cv is the coefficient of consolidation.

Since the clay layer has silty-sand at the top and a peat layer at the bottom, both have high permeability and high void ratios, it is assumed that there is a drainage condition.

For 99% of the degree of consolidation

Variation of Tv with U.T99=1.781

Substitute 200cm in place of Hdr.

1.781 for the T99.

Cv.

=275 days

Thus, the time needed for 99% priming consolidation of clay is 275 Days

Calculation of time 99% primary consolidation

One drainage is necessary for the peat layer.

Substitute 200cm in place of Hdr.

1.781 to T99.

Cv.

=33 days

The time it takes to consolidate 99% of the clay is therefore 33 days

Secondary compression in clay

C’a secondary compress index, t1 = initial and t2 = final.

primary = C*log

Cc = 0.36 and 0 = 60.76 KN/m2.

primary =0.36*log

Calculation of clay’s void percentage

Substitution e0 1.1, primary =0.0506.

ep = 1.1 + 0.0506

Calculation for the primary compression index

Ca = 0, ep = 1,049

Substitution of H = 4 m and C’a = 0.0246, H = 365 days

Calculation of secondary compression in peat layers

C’a secondary compress index, t1 = initial and t2 = final.

primary = C*log

Cc = 6, 0 = 833.33 kN/m2,, e0= 5.9

primary =6.6*log

Calculation of the void ratio of clay

Substitution e0 5,9, primary =0.468

ep = 0.568 – 5.9

Calculation for the primary compression index

Ca = 0.263, ep= 5.432

Substitution of H = 2m, C’a = 0.0408, H = 365 Days, t2= 33 Days

S = Sc+ Sc-clay+ Sc-peat

Sc = 0.232; Sc-clay= 0.0247 and Sk-peat= 0.109

0.365 m

e) Calculation of the Time Factor in Three Months

Tv =

Time = t. Cv = coefficient de consolidation. Hdr = maximum drainage route.

t = 3 month, Cv= 0.003 cm2/sec., Hdr=200 cm

Tv =

Hdr = 4/2 =2 m. The clay layer is a double drainage.

= 200 cm

Calculation of the degree consolidation

Calculate the ratio = Z/Hdr

Variation of Uz – Tv or z/Hdr

Extra pore water pressure calculation at point A

Calculate the rise in stress levels after 3 months

0 – uz

z = 3.4875kN/m2 & u0 = 23.25kN/m2

0 – uz

Clay layer: Effective stress at A

End of the effective stress after three months

Q = 200 kips

10 ft =3

100 pcf = 14.72

120 pcf = 1887

110 pcf = 17,3

Z = from the footing to center of clay layer

= 2 +3 +2 = 7m

Settlement

Ss =

H = 3m

Ss =

= 2.164 *10-3m

Trial no.

N. Weight of moist earth

Moist unit weight

Substituting = 16.48*10-3 kN fW and 953.3*10-6m3

Calculation of dry unit weight = D

Table of wet and dry unit weight values

V in cm3

N. Weight of moist earth

d in N/m3

You can see the graph.

Maximum dry unit weight = 16.64 KN/m3.

The dry unit weight is used to calculate the void rate EUR

s is soil’s specific gravity

e = 0.58

Finding the level of saturation (S).

Substitute 15.0% in place of W, Gs= 2.68, and e = 0.58

S = *100