The cross-sectional area A(x) of a vertical funnel-shape soil specimen of height 2 ft in the 2 constant-head test (see figure below) varies as A(x) = - sq ft where x (in ft) is measured from x+1 the top of the soil region. Knowing the downward flow rate q must be constant at any soil cross- section and the soil's average permeability coefficient k is 0.3ft/sec, obtain (a) the 1-D equation of continuity with Darcy's law in terms of the total head h(x) and the unknown steady flow rate q, (b) the hydraulic boundary conditions on h(x) at the top (x=0) and bottom (x=2') of the soil, (c) the complete solution for h(x) in the soil zone by applying its boundary conditions at .x=0 and 2' in (b), and check that the solution satisfies the conditions of (b). Plot it over the range of 0 ≤ x ≤2' of the soil region. (d) the pressure elevation head he(x) over 0 ≤ x ≤ 2' in the soil and plot it. (e) the pressure head hp(x) in the soil and plot it. ▼ water soil 2.5' 2' ← datum
The cross-sectional area A(x) of a vertical funnel-shape soil specimen of height 2 ft in the 2 constant-head test (see figure below) varies as A(x) = - sq ft where x (in ft) is measured from x+1 the top of the soil region. Knowing the downward flow rate q must be constant at any soil cross- section and the soil's average permeability coefficient k is 0.3ft/sec, obtain (a) the 1-D equation of continuity with Darcy's law in terms of the total head h(x) and the unknown steady flow rate q, (b) the hydraulic boundary conditions on h(x) at the top (x=0) and bottom (x=2') of the soil, (c) the complete solution for h(x) in the soil zone by applying its boundary conditions at .x=0 and 2' in (b), and check that the solution satisfies the conditions of (b). Plot it over the range of 0 ≤ x ≤2' of the soil region. (d) the pressure elevation head he(x) over 0 ≤ x ≤ 2' in the soil and plot it. (e) the pressure head hp(x) in the soil and plot it. ▼ water soil 2.5' 2' ← datum
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The cross-sectional area A(x) of a vertical funnel-shape soil specimen of height 2 ft in the
2
constant-head test (see figure below) varies as A(x) = -
sq ft where x (in ft) is measured from
x+1
the top of the soil region. Knowing the downward flow rate q must be constant at any soil cross-
section and the soil's average permeability coefficient k is 0.3ft/sec, obtain
(a) the 1-D equation of continuity with Darcy's law in terms of the total head h(x) and the
unknown steady flow rate q,
(b) the hydraulic boundary conditions on h(x) at the top (x=0) and bottom (x=2') of the soil,
(c) the complete solution for h(x) in the soil zone by applying its boundary conditions at .x=0 and
2' in (b), and check that the solution satisfies the conditions of (b). Plot it over the range of 0 ≤ x
≤2' of the soil region.
(d) the pressure elevation head he(x) over 0 ≤ x ≤ 2' in the soil and plot it.
(e) the pressure head hp(x) in the soil and plot it.
▼
water
soil
2.5'
2'
← datum
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