Question

Related to (( SOIL MECHANICS )) subject:-

Please i need a correct answer of this question, only correct one!!!

Please Make A), B), C) too clear.

A 7 feet layer of clay is buried beneath a 10 feet stratum of very compact granular soil. Compact
sand underlies the clay. The layer of granular soil is composed of material having a unit weight
of 130 pcf. The clay unit weight is 105 pcf. A laboratory compression test on a sample of the
clay indicates a compression index of 0.40 and a natural void ratio of 1.30. A planned building
loading will cause a 550 psf of stress increase at the middle of the clay layer.

a) What amount of primary compression occurs in the clay layer for the indicated
conditions?

b) How much primary compression of the clay layer would result if the groundwater table
was at the ground surface (all other conditions remain the same)?

c) How much clay layer compression would occur if the clay was an overconsolidated
material, the past maximum pressure was 2,000 psf, and the Cr value was 0.10?
Assume a deep water table.

Answer 1

a) Initial effective overburden pressure at middle of clay layer i.e at a depth of 13.5 ft from surface is

q'_i = Y_sH_s + Y_ch

where Y_s and Y_c are unit wt of sand and clay

q_i' = 130x10 + 105x3.5

= 1667.5 lb/ft²

Increase in stress at middle of clay layer due to building is

dq' = 550 lb/ft²

Final effective stress at middle of clay layer is

q'_f = 1667.5 + 550

= 2217.5 lb/ft²

Settlement is given by

S = (C_cH/1 + e₀)xlog(q'_f/q'_i)

where H = height of clay layer = 7 ft

C_c = 0.4

e_o= 1.3

S = (0.4x7/1+1.30) log(2217.5/1667.5)

= 0.1507 ft

= 1.81 in

b) When the ground water table is at surface

Initial effective overburden pressure at middle of clay layer i.e at a depth of 13.5 ft from surface is

q'_i = (Y_s - Y_w)H_s + (Y_c - Y_w)xh

where Y_s , Y_c , Y_w are unit wt of sand, clay and water respectively

H_s = height of sand layer

q'_i = (130 - 62.4)x10 + (105 - 62.4)x3.5

= 825.1 lb/ft²

dq' = 550 lb/ft²

q'_f= 825.1 + 550 = 1375.1 lb/ft²

Settlement is given by

S = (C_cH/1 + e₀)xlog(q'_f/q'_i)

= (0.4x7/1+1.30)xlog(1375.1/825.1)

= 0.270 ft

= 3.24 in

c) If the clay is overconsolidated

From part (a)

q'_i = 1667.5 lb/ft²

q'_f = 2217.5 lb/ft²

Also

Preconsolidation pressure = q'_p = 2000 lb/ft²

Since

q'_i < q'_p < q'_f

Settlement is given by

S = (C_rxH/1+e_o)log(q'_p/q'_i) + (C_cH/1+e_o)xlog(q'_f/q'_p)

= (0.10x7/1+1.3)xlog(2000/1667.5) + (0.4x7/1+1.3) xlog(2217.5/2000)

= 0.024 + 0.0545

= 0.0785 ft

= 0.942 in