A 3 m high embankment is to be constructed as shown in Fig. Ex. 6. 11. If the unit weight of soil used in the embankment is 19.0 kN / m ^{3}, calculate the vertical stress due to the embankment loading at points P_{1}, P_{2} \text {, and } P_{3}.
Question 6.11: A 3 m high embankment is to be constructed as shown in Fig. ...
q=\gamma H=19 \times 3=57 kN / m ^{2}, z=3 m
The embankment is divided into blocks as shown in Fig. Ex. 6.11 for making use of the graph given in Fig. 6. 15. The calculations are arranged as follows:
| Point | Block | b | a | b/z | a/z | I |
| (m) | (m) | |||||
| P_{1} | ACEF | 1.5 | 3 | 0.5 | 1 | 0.39 |
| EDBF | 4.5 | 3 | 1.5 | 1 | 0.477 | |
| P_{2} | AGH | 0 | 1.5 | 0 | 0.5 | 0.15 |
| GKDB | 7.5 | 3 | 2.5 | 1 | 0.493 | |
| HKC | 0 | 1.5 | 0 | 0.5 | 0.15 | |
| P_{3} | MLDB | 10.5 | 3 | 3.5 | 1 | 0.498 |
| MACL | 1.5 | 3 | 0.5 | 1 | 0.39 | |
Vertical stress \sigma_{z}
At point P_{1}, \quad \sigma_{z}=\quad (0.39+0.477) \times 57=49.4 kN / m ^{2}
At point P_{2}, \quad \sigma_{z}=\quad 0.15 \times(57 / 2)+0.493 \times 57-0.15 \times(57 / 2)=28.1 kN / m ^{2}
At point P_{3}, \quad \sigma_{z}=\quad (0.498-0.39) 57=6.2 kN / m ^{2}
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