Question

A 2.8 m wide reinforced concrete strip footing is situated at 2.5 m below ground level in a thick deposit of a saturated clay. The footing is loaded centrally, and the total vertical line load including the weight of the concrete and backfill is 308 kN/m. The clay has a bulk density (ρ) of 2250 kg/m3 and an undrained shear strength (cu) of 42 kPa.

a) Calculate the factor of safety against bearing capacity failure considering the short term response of the soil.

b) If the strip footing in part a) has to carry an additional horizontal line load of 50 kN/m, calculate the new factor of safety against bearing
capacity failure.

c) Briefly define the terms compression, compaction and consolidation and explain what are the resulting changes in void ratio and moisture content in each of the above cases, assuming a constant total stress is applied onto the soil.

d) A normally consolidated and an over-consolidated clay are subjectedto the same increment of effective stress. Which would result in a higher settlement? Assume the initial void ratio and the height of the soil layer to be the same for both cases. Justify your answers using appropriate plots and/or equations.

Answer 1

(a)

The ultimate bearing capacity equation is as follows

But for , , ,    

So,

= 2250 x 9.81 = 22.07 kN/m3

q = 22.07 x 2.5 = 55.18 kPa

c = 42 kPa

qu = 42 x 5.14 + 55.18 = 271.06 kPa

The stress coming on to the soil qstress = = 110 kPa

Factor of safety = qu/ qstress = 271.06 / 110 = 2.46

(b)

qstress = = 127.857 kPa

Factor of safety = qu/ qstress = 271.06 / 127.857 = 2.12

(c)

Compaction is the densifying of soil by removing air through compactive effort. It is the process of expulsion of air voids. Water content of the soil does not change in this process, however, by compacting at different moisture contents, we can get an optimum moisture content where maximum dry density is achieved. Void ratio decreases during the process as air is removed.

Consolidation is the process of dissipation of pore water pressure which builds when a static load is applied on the soil as the load is initially taken by pore water and not soil grains. When this static load is applied for a long time the pore water pressure dissipates and soil grains start taking the load and the soil gains strength. Void ratio decreases and moisture content also decreases during this process.

Compression or compressibility is the ability of soil to undergo consolidation.

(d)

If the initil void ratio and height of soil layer are same, is the initial pressure, is the pre consolidation pressure, is the stress increment

For over consolidated soil,   if  

if

For normally consolidated soil,

Cs is almost one-fifth to one-tenth of Cc. So we can say that settlement is more in normally consolidated soil than in over consolidated soil. It can be also be inferred from the following graph. It is showed as an example.

As we can see in the graph, for overconsolidated soil i.e. in unload reload loop, decrease in void ratio is very less with increase in pressure but for normally consolidated soil, void ratio decreases drastically with increase in pressure which means larger settlement.