Calculate vertical stress under an embankment

In this problem, we need to calculate the vertical stress at three points, A, B, and C, under an embankment that is three meters high with a unit weight of nineteen kilonewtons per cubic meter.

For an embankment loading, the vertical stress at a point below the surface can be calculated using the influence factor approach for a trapezoidal load.

Wait, let's use the standard influence factor chart method. The formula is the surface pressure times the influence factor I. First, let's calculate the surface pressure q nought. It is the height of the embankment times the unit weight of the soil.

Substituting the given values, three meters and nineteen kilonewtons per cubic meter gives us fifty seven kilonewtons per square meter.

To find the stress at point A, we notice it's under the center of the symmetrical trapezoid. We can split the trapezoid into two identical halves.

For one half, the top width b is three meters, and the horizontal projection of the slope a is also three meters since the slope is one to one. The depth z is three meters.

Using the influence chart for a trapezoidal load, for a ratio of one and one, the value of the influence factor is zero point four seven nine. Since Point A is in the center, we multiply by two.