A layer of silty soil of thickness 5 m lies below the ground surface at a particular site and below the silt layer lies a clay stratum. The ground water table is at a depth of 4 m below the ground surface. The following data are available for both the silt and clay layers of soil. Silt layer:

Question

A layer of silty soil of thickness 5 m lies below the ground surface at a particular site and below the silt layer lies a clay stratum. The ground water table is at a depth of 4 m below the ground surface. The following data are available for both the silt and clay layers of soil.

Silt layer: [latex]D_{10}=0.018 mm , e=0.7, ext { and } G_{s}=2.7[/latex]

Clay layer: [latex]e=0.8 ext { and } G_{s}=2.75[/latex]

Required: (a) Height of capillary rise, (b) capillary pressure, (c) the effective pressure at the ground surface, at GWT level, at the bottom of the silt layer and at a depth of H = 6 m below ground level, and (d) at a depth 2 m below ground level.

Accepted Answer

For the silty soil:

[latex]\gamma_{d}=\frac{G_{s} \gamma_{W}}{1+e}=\frac{2.7 imes 9.81}{1.7}=15.6 kN / m ^{3}[/latex]

[latex]\gamma_{ ext {sat }}=\frac{\left(G_{s}+e ight) \gamma_{w}}{1+e}=\frac{(2.7+0.7) 9.81}{1.7}=19.62 kN / m ^{3}[/latex]

[latex]\gamma_{b}=\gamma_{ sat }-\gamma_{w}=19.62-9.8 l =9.81 kN / m ^{3}[/latex]

In the clay stratum:

[latex]\gamma_{ sat }=\frac{(2.75+0.8) 9.81}{1.8}=19.35 kN / m ^{3}[/latex]

[latex]\gamma_{b}=19.35-9.81=9.54 kN / m ^{3}[/latex]

(a) Height of capillary rise

[latex]h_{c}=\frac{C}{e D_{10}}[/latex] per Eq. (9.5)

[latex]C_{N}=\left[\frac{95.76}{ ho_{o}^{\prime}} ight]^{1 / 2}[/latex]

Assume [latex]C=0.5 sq \cdot cm[/latex].

We have [latex]h_{c}=\frac{0.5}{0.7 imes 0.0018}=397 cm ext { or say } 4.0 m[/latex]

It is clear from [latex]h_{c}[/latex] 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 [latex]u_{c}[/latex]

[latex] ext { Per Eq. (9.28), } u_{c}=n h_{c} \gamma_{w}=\frac{e}{1+e} h_{c} \gamma_{w}[/latex]

[latex]I_{D}=\frac{p_{z}-p_{1}}{p_{2}-u}[/latex] (9.28)

or [latex]u_{c}=\frac{0.7}{1.7} imes 4 imes 9.81=16.16 kN / m ^{2}[/latex]

(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 [latex]u_{c}[/latex]

Total effective pressure at GWT level, [latex]\sigma_{ ext {sat }}^{\prime}[/latex]

Per Fig. Ex. 5.15

[latex]\sigma_{ sat }^{\prime}=\sigma_{d}^{\prime}+u_{c}=\gamma_{d} h_{c}+u_{c}[/latex]

[latex]\sigma_{ ext {sat }}^{\prime}=15.6 imes 4+16.16=78.56 kN / m ^{2}[/latex]

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

[latex]\sigma^{\prime}=\gamma_{b} h_{w}=9.81 imes 1=9.81 kN / m ^{2}[/latex]

Total effective pressure, [latex]\sigma_{t}^{\prime}=\sigma_{ ext {sat }}^{\prime}+\sigma^{\prime}=78.56+9.81=88.37 kN / m ^{2}[/latex]

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

[latex]\sigma^{\prime}=\gamma_{b} h_{w}=9.54 imes 1=9.54 kN / m ^{2}[/latex]

The total effective pressure [latex]\sigma_{t}=88.37+9.54=97.91 kN / m ^{2} \approx 98 kN / m ^{2}[/latex]

(d) [latex]\sigma_{z}^{\prime} ext { at } 2[/latex] m below GL

[latex]\sigma_{z}^{\prime}=u_{c}+z \gamma_{d}=16.16+2 imes 15.6=47.36 kN / m ^{2}[/latex]

The pressure distribution diagram is given in Fig. Ex. 5.15.

Question 5.15: A layer of silty soil of thickness 5 m lies below the ground...

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