For the silty soil:
\gamma_{d}=\frac{G_{s} \gamma_{W}}{1+e}=\frac{2.7 \times 9.81}{1.7}=15.6 kN / m ^{3}
\gamma_{\text {sat }}=\frac{\left(G_{s}+e\right) \gamma_{w}}{1+e}=\frac{(2.7+0.7) 9.81}{1.7}=19.62 kN / m ^{3}
\gamma_{b}=\gamma_{ sat }-\gamma_{w}=19.62-9.8 l =9.81 kN / m ^{3}
In the clay stratum:
\gamma_{ sat }=\frac{(2.75+0.8) 9.81}{1.8}=19.35 kN / m ^{3}
\gamma_{b}=19.35-9.81=9.54 kN / m ^{3}
(a) Height of capillary rise
h_{c}=\frac{C}{e D_{10}} per Eq. (9.5)
C_{N}=\left[\frac{95.76}{\rho_{o}^{\prime}}\right]^{1 / 2}
Assume C=0.5 sq \cdot cm.
We have h_{c}=\frac{0.5}{0.7 \times 0.0018}=397 cm \text { or say } 4.0 m
It is clear from h_{c} that the plane of menisci formed by the capillary water coincides with the ground surface as the water table is also at a depth of 4 m from ground level.
(b) Capillary pressure u_{c}
\text { Per Eq. (9.28), } u_{c}=n h_{c} \gamma_{w}=\frac{e}{1+e} h_{c} \gamma_{w}
I_{D}=\frac{p_{z}-p_{1}}{p_{2}-u} (9.28)
or u_{c}=\frac{0.7}{1.7} \times 4 \times 9.81=16.16 kN / m ^{2}
(c) The effective pressure at GL
Since the plane of menisci coincides with the ground surface, the effective pressure at GL is equal to the capillary pressure u_{c}
Total effective pressure at GWT level, \sigma_{\text {sat }}^{\prime}
Per Fig. Ex. 5.15
\sigma_{ sat }^{\prime}=\sigma_{d}^{\prime}+u_{c}=\gamma_{d} h_{c}+u_{c}
\sigma_{\text {sat }}^{\prime}=15.6 \times 4+16.16=78.56 kN / m ^{2}
Total effective pressure at the bottom of the silt layer
The bottom of the silt layer is at a depth of 1 m below GWT level. The effective pressure due to this depth is
\sigma^{\prime}=\gamma_{b} h_{w}=9.81 \times 1=9.81 kN / m ^{2}
Total effective pressure, \sigma_{t}^{\prime}=\sigma_{\text {sat }}^{\prime}+\sigma^{\prime}=78.56+9.81=88.37 kN / m ^{2}
Total effective pressure at a depth of 6m below GL
This point lies in the clay stratum at a depth of 1 m below the bottom of the silty layer.
The increase in effective pressure at this depth is
\sigma^{\prime}=\gamma_{b} h_{w}=9.54 \times 1=9.54 kN / m ^{2}
The total effective pressure \sigma_{t}=88.37+9.54=97.91 kN / m ^{2} \approx 98 kN / m ^{2}
(d) \sigma_{z}^{\prime} \text { at } 2 m below GL
\sigma_{z}^{\prime}=u_{c}+z \gamma_{d}=16.16+2 \times 15.6=47.36 kN / m ^{2}
The pressure distribution diagram is given in Fig. Ex. 5.15.
