Stress calculation in Soil
The following example shows the stress calculation at different level within the soil.
Problem 1: Calculate total, effective stress and pore water pressure at different level of the soil as shown in Figure 5.2.
Fig. 5.2. (a) Soil profile (b) Stress diagrams
Solution:
The bulk unit weight of the partially saturated sand
\[{\gamma _{t(sand)}}={{{G_s} + Se} \over {1 + e}}{\gamma _w}={{2.6 + 0.5 \times 0.65} \over {1 + 0.65}} \times 10=17.72\;kN/{m^3}\]
The unit weight of the water is taken as 10 kN/m3. The saturated unit weight of sand is
\[{\gamma _{sat(sand)}}={{{G_s} + e} \over {1 + e}}{\gamma _w}={{2.6 + 0.65} \over {1 + 0.65}} \times 10=19.7\;kN/{m^3}\]
The saturated unit weight of the clay-I is.
\[{\gamma _{sat(clay - I)}}={{{G_s} + e} \over {1 + e}}{\gamma _w}={{{G_s} + {G_s}w} \over {1 + {G_s}w}}{\gamma _w}={{2.65 + 2.65 \times 0.55} \over {1 + 2.65 \times 0.55}} \times 10=16.71\;kN/{m^3}\]
[Se = Gsw and for fully saturated soil S =1]
The saturated unit weight of the clay-II is
\[{\gamma _{sat(clay - II)}}={{{G_s} + e} \over {1 + e}}{\gamma _w}={{{G_s} + {G_s}w} \over {1 + {G_s}w}}{\gamma _w}={{2.7 + 2.7 \times 0.6} \over {1 + 2.7 \times 0.6}} \times 10=16.49\;kN/{m^3}\]
At elevation -2.5 m
Total stress (σ) = 17.72 ´ 2.5 = 44.3 kN/m2
Pore water pressure (u) = 0
Effective stress () = 44.3 - 0 = 44.3 kN/m2
At elevation -6 m
Total stress (σ) = 17.72 ´ 2.5 + 19.7 ´ 3.5 = 113.25 kN/m2
Pore water pressure (u) = 10 ´ 3.5 = 35 kN/m2
Effective stress ( \[\sigma '\] ) = 113.25 - 35 = 78.25 kN/m2
At elevation -10 m
Total stress (σ) = 17.72 ´ 2.5 + 19.7 ´ 3.5 + 16.71 ´ 4 = 180.1 kN/m2
Pore water pressure (u) = 10 ´ 7.5 = 75 kN/m2
Effective stress ( \[\sigma '\] ) = 180.1 - 75 = 105.1 kN/m2
At elevation -14 m
Total stress (σ) = 17.72 ´ 2.5 + 19.7 ´ 3.5 + 16.71 ´ 4 + 16.49 ´ 4 = 246.1 kN/m2
Pore water pressure (u) = 10 ´ 11.5 = 115 kN/m2
Effective stress ( \[\sigma '\] ) = 246.1 - 115 = 131.1 kN/m2
1. What is stress calculation in soil? |
2. How is stress in soil measured? |
3. What factors affect stress distribution in soil? |
4. Why is stress calculation important in agricultural engineering? |
5. How does stress calculation help in soil mechanics? |
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