Soil Mechanics (civl2410) – Report Question E

Soil Mechanics (CIVL2410) – Report Question E

The construction of any structure on soil requires considerable thought regarding settlement. If the foundations of a particular structure settle differing amounts, the foundation will experience shear forces that may ultimately lead to the failure of a structure. Therefore it is imperative to have a way to calculate the settlement of a soil with the ability to change variables to apply to each unique problem.

Since the final settlement is unique to the soil substructure, a number of assumptions are made in order to simplify the problem to attain a numerical solution. It is assumed there are no lateral strains, thus settlement only occurs in the vertical direction. This assumption allows the formula  to be used to calculate vertical strain. It is also assumed the soil behaves linearly elastic and layers are homogenous. [pic 1]

The problem to be solved is a circular oil tank is to be constructed on a site where the soil profile consists of 3m of clay with an over-consolidation ratio that varies from 5 at the surface to 2 at 3m overlying a 5m thick clay layer with an over-consolidation ratio of 2, which overlies rock. The soil properties are Cc = 0.5, Cr = 0.05 and γsat = 19 kN/m3 for both clays, and the water table is 1 m below the soil surface. Determine the settlements when a stress of 80 kPa is applied by the tank which is 10 m in diameter.

To calculate settlement, the stress increase at each depth of the soil due to loading must be calculated. Furthermore, it is important to compare the settlement difference between the centre and circumference of the structure, as this will impose further stresses. Calculating stress in the centre is done using the formula: . For the circumference, a formula was obtained using the trendline function after recreating the vertical stress below a circle on half-space in excel. For r/a value = 1, the formula obtained was:[pic 2]

 [pic 3]

Figure 1 shows the maximum stress experienced at each depth:

[pic 4]

Figure 1 also shows the difference dividing the soil into more sub-layers has on the maximum stress values – the stress under the centre of the structure. When 128 sub-layers are used, a defined curve forms that is more accurate than using the linear relationship resulting from 2 sub-layers. Therefore preferred to use a greater number of sub-layers for calculations.

The change in void ratio due to loading can then be calculated using  since the entire substructure is over-consolidated. Once this is calculated settlement is calculated through: , where D is the depth of the soil substructure. [pic 5][pic 6]