Geostatic Stess & Strain: General Example

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I. Calculating the geostatic stress at a point, P, below the ground. Use Figure 3 as a reference.



Figure 3.
There are four different layers (strata) of soil in Figure 3. Each one is labled individualy, i, ii, iii, iv. Table 1 will give the neseccary information for each of the soil layers.
The location of P is 3m below layer iii.
Layer
 Unit Weight (kN/m^3)
 Thickness (m)
i
 18.1
 5
ii 17.8
 5
iii 17.4
 5
iv 17.6
 5

With the given information the stress at P is equal to 18.1*5 + 17.8*5 + 17.4*5 + 17.6*(5-2) [(kN/m^3)(m)].
Calculating this out, σ1 = 319.9kPa.


II. After lab testing of a core sample of P, σ3 was set to 100kPa, which yeilded a failure plane with an angle β = 68 degrees from the horizontal.
We can now calculate the shear and normal stress of the failure plane.

The normal stress will be equal to .5[(319.9+100)+(319.9-100)cos(2*68)] = 130.9kPa.
The shear on the failure plane will be equal to .5(319.9-100)sin(2*68) = 76kPa.