Question

A 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. A 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) Draw a sketch representing the various problem components.

b) 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.

c) 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?

d) 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

a). the diagram is shown below

b).

c). Yes, there will be additional stresses and due to that stresses, settlement in central foundation takes place

In the elastic settlement estimation of footings, interactions between adjacent footings are not taken into account in the conventional approach. However, it is noted that shallow foundations for typical buildings consist of multiple footings that are generally in close proximity.

four configurations that could be possible in practice and have been considered: a) only main footing, b) one adjacent footing c) two adjacent footings d) three adjacent footings d) four adjacent footings.

here the case is 2 adjacent footings

A MATLAB code has been generated to calculate the settlement under the footing by Schmertmann’s Method for the four cases mentioned. In order to simplify the problem, it is assumed that all of the footings have identical contact pressure and their bases are square with a width of B.

Depend on the number of adjacent footings, all the stress increments are superimposed under the main foundation at the depth of B/2.

The percentages of settlement increments can be estimated by the following equation

?? = 0.3843? − 0.0002

where Sp= percentage of settlement increment,

n= number of adjacent footings

Therefore Sp = (0.3843*2)-0.0002

Sp = 0.7684 %

c).