Smith's Elements of Soil Mechanics. Ian Smith

pressure of 155 kPa. The surface of the sand is flooded with water to a depth of 1 m.

Determine the quantity of flow per unit area in mm³/s, and the excess hydraulic heads at the sand/coarse silt and the coarse silt/fine silt interfaces.

       Solution:

      Taking the top of the gravel as datum:

      Head of water due to artesian pressure = 15.5 m

      Head of water due to groundwater = 3 × 4 + 1 = 13 m

      Therefore, excess head causing flow = 15.5 − 13 = 2.5 m.

      This quantity of flow is the same through each layer.

      Excess head loss through fine silt:

      Therefore,

      Excess head loss through coarse silt:

      Excess head loss through fine sand:

      Excess head at interface between fine and coarse silt

      Excess head at interface between fine sand and coarse silt

Fig. 2.30 Example 2.11.

      2.15.4 Seepage through soils of different permeabilities

      When water seeps from a soil of permeability k₁ into a soil of permeability k₂, the principle of the square flow net is no longer valid. If we consider a flow net in which the head drop across each figure, Δh, is a constant then, as has been shown, the flow through each figure is given by the expression:

      (2.36)

      If Δq is to remain the same when k is varied, then b/l must also vary. As an illustration of this effect, consider the case of two soils with k₁ = k₂/3.

      Then

      and

      (2.37)

      i.e.

      If the portion of the flow net in the soil of permeability k₁ is square, then:

The effect on a flow net is illustrated in Fig. 2.31.

Fig. 2.31 Effect of variation of permeability on a flow net. (a) k₂ > k₁. (b) k₂ < k_1.

Fig. 2.32 Flow across an interface when the flow lines are at an angle to it.

      2.15.5 Refraction of flow lines at interfaces

      An interface is the surface or boundary between two soils. If the flow lines across an interface are normal to it, then there will be no refraction and the flow net appears as shown in Fig. 2.31. When the flow lines meet the interface at some acute angle to the normal, then the lines are bent as they pass into the second soil.

In Fig. 2.32, let RR be the interface of two soils of permeabilities, k₁ and k₂. Consider two flow lines, f₁ and f₂, making angles to the normal of α₁ and α₂ in soils 1 and 2, respectively.

      Let f₁ cut RR in B and f₂ cut RR in A.

      Let h₁ and h₂ be the equipotentials passing through A and B, respectively, and let the head drop between them be Δh.

      With uniform flow conditions, the flow into the interface will equal the flow out. Consider flow normal to the interface.

      In soil (1):

Fig. 2.33 Flow net for seepage through two soils of different permeabilities.

      Similarly, it can be shown that, in soil (2):

      Now q₁ = q₂,

      (2.38)

A flow net which illustrates the effect is shown in Fig. 2.33.

      Exercises

      Exercise 2.1

      In a falling head permeameter test on a fine sand, the sample had a diameter of 76 mm and a length of 152 mm with a standpipe of 12.7 mm diameter. A stopwatch was started when h was 508 mm and read 19.6 s when h was 254 mm. The test was repeated for a drop from 254 to 127 mm and the time was 19.4 s.

      Determine an average value for k in m/s.

      Answer 1.5 × 10⁻⁴ m/s

      Exercise