Question

4. A soil deposit consists of three horizontal layers of soil: an upper stratum A (lm thick), a middle stratum B (2m thick) and a lower stratum C (3 m thick). Permeability tests gave the following values: Soil A, k = 0.3 mm/sec; Soil B, k= 0.2 mm/sec; Soil C: k=0.1 mm/sec. a) Determine the ratio of the average coefficients of permeability of the soil deposit (all three layers) in the horizontal and vertical direction. b) Beneath the deposit there is a gravel layer subjected to artesian pressure, the surface of the deposit coinciding with the ground water level. Standpipes show that the fall in head across soil A is 150 mm. Determine the value of the water pressure at the top of the gravel. -1 I 150 mm Soil A, 1m Soil B,2m Soil C, 3m Gravel Figure 4

Answer 1

150mm Soil A is I'm thick Hi = lm Permeability of Scil A = k, = 0-3 mm/s For soil B - H₂ = 2m Hirim Soil A ki= 0.3 mils_ K2 = 0.2mmls for soil C K2= 0.2 mmis Hz = 3m H2=3m/ Soul K2=0.1mm's K3= 0.1 mm/ s ha (1) average coefficient of permeability in Horizontal direction is given by C KH= K,Hit K₂ H₂ + K₃ H3 B Hit H₂ + H₂ * KH= (x 0.3 + b^2x2+ o|x3 1+ 2+3 KH= 5 = 0.166 mmis Kr= 0.166 mm/s average coefficient of Permeability in direction is given by Ku = H, +H2 +H3 Vertical Kv 1+2+3 o'z + O2 + oi 03 0.2 l

Ku = 0.138 mmis soil cepoliet Ratio In 1. of average coeffe cent of permeability of Horizontal and vertical direction KH = 0.166 1. ku 0.138 KH = 12036 150mm 11 ammis 0.2 mmls . (b) het xx is taken ces A datium . Total Head Elevation Pressure at loveel zz = Head 't Head (H)22 - 5+ (1+0:15) * Total Head - Elevation + pressure at level AA - Head Head (HAA = 6 + 0 ¥ © K3=0.1 mm/s 3 m X Datum (GRAVEL) r I level AA is oph to atmosphere ferice Pressure Head ir o Head cet level zz is greater than Head at level AA. This mean Seepage is in upward direction Head loss - (Hzz - (HJAA in Soil A conda = 5+ (1+0.15 ) - 6 coma = 0.15m

direction * Discharge is taking plac Charge in upward Q = kill ( James (@J= ki bun - H orge is taking place Normal to Beddrig plame means Diescharge is same through all layers sut loss of head in dieberent layers of soil is different *As the Area (A) of all Beddring plane is same. That means Descharge per unit Area (a) will also be some through all layers. ..( = kilowa.. -- [from ezo] J = 0.3X10-3X0-15 To 3 mms L = 0:3X10 @= 4.5X105 This value of (a) is same for all layers. Applying equation ② for second soil (8) ( = kz Ohje 4,5X10-5 = 0·2x10-3xCong) Fo.2mmis, 1 = 0.2x10 3 m/s AhB = 0.225 m as she represents loss of Head by upward seepage through sail B. DhB = Total Head at yy - Total Head at 22

we haud initially calculated total Head at level ZZ » H₂z=6.15m 0.225 = (Hlyy -(6:15) (Hey) = 6.375m Applyng eq@ for Third Soil (C) (a) = Kz (Ahle 4.5 x 10-5 = 0·1X 103x Concl .. (Ahlc = 0.45m as ohle represent loss of Head through soil (C). Total Head at xx - Total Head at YY phc= -0.45 = (H)xx - 6.375 (H)xx = 6-825m as xx layer represent the top of Grand layer xx line is top of graud layer. (Hxx) = Total Head at xx layer Now we have assamed xx layer as datum. . So, election Head of xx layer=0 (Hxx) = Elevation Head & Pressure Head 6.825 = o + Pressure read Pressure Head at xx = 6.825m pressure Head at Top of gravel = 6.825m Water pressure at top of graud = (Pressure head) x Yw Water pressure at top of gravel = 6.825 89:81 = 66.953 kN/m²