Stress Increase Under a Foundation
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A (1.83 m x 1.83 m) foundation shown in figure below. Using the procedure outlined in Section 8.9, determine the average stress increase in the clay layer below the center of the foundation due to the net foundation load of 500 kN. Use the common corner, Eq. (8.25).
This question includes visual content: A cross-sectional diagram showing a square foundation (1.83 m x 1.83 m) subjected to a net load of 500 kN. The soil strata depicted are: an upper sand layer (depth 1.52 m, $\gamma = 15.7 \text{ kN/m}^3$), a lower sand layer (thickness 1.22 m, $\gamma_{sat} = 19.24 \text{ kN/m}^3$), and a clay layer (thickness 3.05 m). Groundwater table (GWT) is shown at the base of the foundation. The clay layer properties are given as $\gamma_{sat} = 19.24 \text{ kN/m}^3$, $e_o = 0.8$, $C_c = 0.25$, $C_s = 0.06$, and preconsolidation pressure = 100 kN/m².
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In this problem, we need to calculate the average stress increase in a clay layer under the center of a square foundation. We are given the net load, the foundation dimensions, and the soil profile depths.
Average Stress Increase in Clay Layer
Let's list our given values first. The foundation is one point eight three meters by one point eight three meters. The net load, P, is five hundred kilo Newtons.
First, we calculate the net pressure applied by the foundation, which is the load divided by the area.
Calculating that gives us approximately one hundred forty-nine point two nine kilo Newtons per square meter.
To find the average stress increase in the clay layer, we use Simpson's rule, which requires the stress at the top, middle, and bottom of the layer.
Simpson's Rule Method
The problem asks for the stress below the center of the foundation. We can calculate this by dividing the area into four equal corners. Each corner has dimensions B prime and L prime equal to half of the total width and length.
The total stress increase is then four times the stress caused by one of these small corner areas. We use the influence factor I sub z to find this.
Now, let's determine the depths from the foundation base to each point in the clay layer. The top of the clay is one point two two meters below the base.
Calculating Depths (z)
The middle of the three point zero five meter clay layer is half its thickness added to the top depth, which is two point seven four five meters.
The bottom of the clay layer is at a total depth of four point two seven meters from the foundation base.
For each depth, we calculate the ratios m and n to find the influence factor from the standard chart or tables.
Influence Factors (I_z)
For the top of the layer, z equals one point two two. Dividing our sub-dimension by this depth, m and n are zero point seven five.
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