Q3

A rigid strip footing with a width of B isconstructed above the ground on a clay deposit, overlying bedrock.The depth of clay layer is H and the water levelis at the natural ground surface. Before construction of thefooting, laboratory tests on a saturated clay sample, taken at adepth of H/2 below the ground surface, providedthe following properties:

Compression Index = Cc ,Recompression Index = Cr ,Consolidation Coefficient =cv

Over Consolidation Ratio = OCR, Water Content =w% and Specific Gravity =Gs

Assume the vertical uniform surcharge stress on the footingincluding the weight of footing and column = q

(a) Calculate the initial saturated unit weight of claydeposit.

(b) Based on the elastic theory (Boussinesq’s equation),calculate the excess pore water pressures at the depth ofH/2 immediately after applying the surcharge load.Assume the vertical stress (q) is appliedinstantaneously.

(c) Using theory of 1-D consolidation, calculate the totalaverage settlement of this rigid footing due to consolidation ofthe clay layer, long time after applying the total load.

(d) Determine the average settlement of this rigid footing aftern days of applying the total load due toconsolidation of clay deposit. Assume the bedrock is permeable(i.e. Drainage path = H/2)

(e) Plot the graph of settlement versus time (in log scale) forthis footing