Question

4- It is known that a particular normally consolidated soil layer was deposited under a lake. The situation that existed a long time ago is shown in Figure 1. Consider a point x in this soil deposit. The Point x was 20m beneath the water level and at a depth of z below the top of the soil deposit. At this point in time the climate of the area changed and the lake dried up and the soil deposit gradually eroded to give the present situation shown in Figure 2 Water table Lake 20m 8m Point x o Point x o In Figure 1: Past situation Figure 2: Present situation The soil at the point x is now sampled and tested giving the following properties 20kN/m3, Determine a) The maximum depth of soil which existed above x, i.e., z. b) The void ratio at x when this maximum existed. c) If the site is now subjected to a surcharge of 200kPa over the surface what total final C.-05, Cr-0.1, σ,pc-150kPa e 0.84 settlement of the clay layer will occur? Answers: Q: 166, 0.9949 02: er 1.047; Cr0.1 Q3: 80mm Q4: 14.7m, 0.8136, 1.42m

Answer 1

Answer a) since the soil was normally consolidated hence effective stress at X = 150 KPa ( pre consolidation pressure)

Effective stress at X = 9.81*(20-z) + 20*z -(9.81*20)

Thus 150 =( 20-9.81) z thus z = 14.72 m

Answer b) In position 2 effective stress at X =( 20-9.81)*8 = 81.52 KPa and Cr = 0.1 = change in void ratio / log(change in effective stress)

Thus change in void ratio = 0.1* log( 150-81.52) = 0.1*1.835 = 0.1835

Thus void ratio at past situation = 0.84-0.1835 = 0.6565

Answer c) Change in effective stress due to surcharge and soil = 200 KPa

Final settlement =[ Cc Ho /(1+e) ]* log( Increased or decreased effective stress / initial effective stress) +[ Cr Ho/(1+e)]* log( 150/ initial effective stress) =[ 0.5*16/(1+0.84)]*log(81.52+200/81.52) + [ 0.1*16/(1+0.84)] log(150/81.52) = 2.57 m