Question

1. three storey structure having a square footprint of 225 m² is constructed on a clayey deposit. The structure is planned to be supported by square isolated footings having a width of 2m and spaced at 5m center to center. typical borehole indicates that the soil consists of 2m fill layer at the top (g=17KN/m³) followed by a very stiff clay layer 2m thick (gsat=18.5KN/m³) underlain by a normally consolidated soft clay layer of 4.5m thickness (gsat=17KN/m³) followed by a rock layer extending down to the bottom of borehole. The foundations are laid on top of the stiff clay layer. Water table is located at the top of the stiff clay layer. Undisturbed samples were taken from the middle of each clay layer and consolidation tests done on undisturbed samples indicated the following:

 Stiff Clay: Cc=0.15; Cs = 0.02; P_c = 120 kPa; e₀=0.9

 Soft Normally Consolidated Clay: Cc=0.38; Cs = 0.06; e₀=1.0

a) The isolated foundations are subjected to a stress of 140 kPa. Calculate the consolidation settlement. Consider the very stiff clay as one layer and divide soft clay layer into two equal sub-layers. Calculate settlement under one typical foundation.

b) What would be the maximum additional stress applied on a central foundation from two neighboring foundations (situated at the left and right sides of the central foundation). Is it necessary to consider the additional stresses from neighboring foundations in the settlement calculations?

c) A concern is the differential settlement between isolated adjacent footings. It was decided to change the design to have the structure founded on a raft foundation subjected to a stress of 45 kPa. Compute the consolidation settlement and comment on the results.

Answer 1

Given datas,

Building structural footprint = 225 m2

Isolated footing size = 2x2 m

Spacing = 5m

g = 17 KN/m3

g (sat) = 18.5 KN/m3

Thickness of clay by each layer = 2m , 2m , 4.5m

( Foundation is on the top of stiff clay layer 2m thick and water table is located on the top of stiff clay layer)

For Stiff clay layer given ,
Cc = 0.15, Cs = 0.02 Pc = 120 Kpa e0 = 0.9

For soft normally consolidated clay,
Cc= 0.38 , Cs = 0.06 e0 = 1.0

a) Stress = 140 KPa

Consolidation settlement ,  

where Cc = Compression index of clay layer = 0.15

e0 = void ratio = 0.9

H = thickness of clay layer = 8.5 m
= Increase of stress at midpoint = 140/8.5*8.5 Kpa

Po' = effective stress at layer

Po' = 17 *1.5 + (17-9.87)*2.5 + (18.5- 987.)*5

= 25.5+17.825+ 43.15

=86. 47 KN

Consolidation settlement = 8.5 * 0.15/ 1+0.9 * Log (86.47+1.93)/ 86.47

= 0.67* Log (1.022)

= 0.0063 m