Smith's Elements of Soil Mechanics. Ian Smith

k in m/s.

      Answer 1.05 × 10⁻² m/s

      Exercise 2.3

      To determine the average permeability of a bed of sand 12.5 m thick overlying an impermeable stratum, a well was sunk through the sand and a pumping test carried out. After some time, the discharge was 850 kg/min and the drawdowns in observation wells 15.2 and 30.4 m from the pump were 1.625 and 1.360 m, respectively. If the original water table was at a depth of 1.95 m below ground level, find the permeability of the sand (in m/s) and an approximate value for the effective grain size.

      Answer k = 6.7 × 10⁻⁴ m/s, D₁₀ ≈ 0.26 mm

Exercise 2.4

A cylinder of cross‐sectional area 2500 mm² is filled with sand of permeability 5.0 mm/s. Water is caused to flow through sand under a constant head using the arrangement shown in Fig. 2.34.

      Determine the quantity of water discharged in 10 minutes.

      Answer 9 × 10⁶ mm³

Fig. 2.34 Exercise 2.4.

      Exercise 2.5

      The specific gravity of particles of a sand is 2.54 and their porosity is 45% in the loose state and 37% in the dense state. What are the critical hydraulic gradients for these two states?

      Answer 0.85, 0.97

      Exercise 2.6

      A large open excavation was made into a stratum of clay with a saturated unit weight of 17.6 kN/m³. When the depth of the excavation reached 7.63 m the bottom rose, gradually cracked, and was flooded from below with a mixture of sand and water. Subsequent borings showed that the clay was underlain by a bed of sand with its surface at a depth of 11.3 m.

      Determine the elevation to which water would have risen from the sand into a drill hole before excavation was started.

      Answer 6.45 m above top of sand

      Exercise 2.7

      A soil deposit consists of three horizontal layers of soil: an upper stratum A (1 m thick), a middle stratum B (2 m thick), and a lower stratum C (3 m thick). Permeability tests gave the following values:

       Soil A 3 × 10−1 mm/s

       Soil B 2 × 10−1 mm/s

       Soil C 1 × 10−1 mm/s

       Determine the ratio of the average permeabilities in the horizontal and vertical directions.

      Answer 1.22

      Beneath the deposit there is a gravel layer subjected to artesian pressure, the surface of the deposit coinciding with the groundwater level. Standpipes show that the fall in head across soil A is 150 mm. Determine the value of the water pressure in the gravel.

      Answer 80 kPa