The cross-sectional area A(x) of a vertical funnel-shape soil specimen of height 2 ft in the2constant-head test (see figure below) varies as A(x) = -sq ft where x (in ft) is measured fromx+1the 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 theunknown 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 and2' 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.▼watersoil2.5'2'← datum

Answer → The 1-D equation of continuity with Darcy's law states q=−kA(x)dx/dh. At x=0,h(0) , is the…

Answered: The cross-sectional area A(x) of a…

Principles of Foundation Engineering (MindTap Course List)

9th Edition

ISBN:9781337705028

Author:Braja M. Das, Nagaratnam Sivakugan

Publisher:Braja M. Das, Nagaratnam Sivakugan

Chapter2: Geotechnical Properties Of Soil

Section: Chapter Questions

Problem 2.13P

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Question 8 (1) - Oedometer test What are the boundary conditions applied to a soil sample tested in an Oedometer? Z H a) Pore water pressure at z = H (top of the sample) is PH = Yw. H b) Ez = Ex c) &z=&v (₂ is the volumetric strain of the sample) d) At time t=0, 4p = 0
The result of falling head permeability test for clay sample having an area of 1500 mm² and a length of 150 mm are as follows: At t=0 min, head difference- 350 mm At t= 4 min, head difference- 150 mm Find the coefficient of permeability of the soil if the area of stand pipe is 75 mm².
Determine the coefficient of permeability of the soil. For a falling- head permeability test, the following are given: re Length of the specimen = 115.5 mm Diameter of soil specimen =104.7 mm Diameter of the stand pipe = 15 mm Head difference at time t=0 is 1360 mr Head difference at timet=78600 sec is 820 mm
Q1/ specimen of the fine-grained soil, 75 mm in diameter and 20 mm thick was tested in an oedometer in a laboratory. At applying pressure (240 kN/m²), the time with dial gauge readings are: Time (min) 0 Settlement (mm) 0 0.25 1 0.22 0.42 Vertical pressure (kPa) 15 Settlement (mm) 0.1 Void ratio 1.88 4 0.6 30 0.11 1.87 9 0.71 16 0.79 And the void ratio and settlement for each load increment is shown in the table below. 60 0.21 1.85 120 1.13 1.72 100 1.04 36 64 0.91 0.86 240 2.17 1.57 480 3.15 1.43 1- Find Coefficient of consolidation in cm²/s using root time and TV90% = 0.848. 2- Find Preconsolidation pressure (oc) and compression index (Cc). Scanned by TapScanner
Permeability tests were performed on a soil sample, under different void ratio and different temperatures and the following results were obtained. Test No. 1 2 Void ratio (e) 0.65 1.02 Temperature °℃ 25° 40⁰ Estimate the coefficient of permeability at a temperature of 20°C for a voids ratio of 0.80. Given the following physical properties of water: At 20°C, n = 10.09 × 10+ and p„ = 0.998 g/cm³ At 25°C, n = 8.95 × 104 g sec/cm² and p k(cm/s) 0.4x10 1.9x10-¹ At 40° C, n = 6.54 × 10-¹ g sec/cm² and p $0.997 g/cm³ = = 0.992 g/cm³
The total volume of a soil specimen is 80,000 mm^3 and has a mass of 152 g. the dry mass of the specimen is 122g, and the density of the soil is 2.65 Mg/m^3. Compute the following index properties: (a) e; (b) n; (c) S; (d) ρt; and (e) ρd. Include phase diagrams.
FUNDAMENTALS OF GEOTECHNICAL ANALYSIS A constant head permeability test is performed on soil that is 2 cm x 2 cm square, and 2.5cm long. The head difference applied during the test is 20 cm and 7 cm3 is collected over a time of 100 sec. Provide step by step solution. a) Compute the permeability based on these test conditions and results. b) A falling head test is conducted on the same soil specimen at the same time (t1 – t2 = 100 sec), and the standpipe diameter is 0.8 cm. If the average head during the test should be 18 cm, what are h1 and h2 values?
In a falling permeameter, the sample used is 20 cm long having a cross-sectional area of 24 cm2. The sample of soil is made of three layers. The thickness of the first layer from the top is 8 cm and has a value of k1 = 2 x 10-4 cm/s, the second layer of thickness 6 cm has k2 = 5 x 10-4 cm/s and the bottom layer of thickness 4 cm has k3 = 7 x 10-4 cm/s. Assume the flow is taking perpendicular to the layers. Estimate the average hydraulic conductivity of soil in the vertical direction. a.3.12 x 10-4 cm/s b.5.69 x 10-4 cm/s c.2.35 x 10-4 cm/s d.4.28 x 10-4 cm/s e.6.69 x 10-4 cm/s
A sand sample in a triaxial test have the following stresses: Cell Pressure 25kpa 34kpa Axial Stress 33kpa 55kpa Pore Water pressure 12kpa 10kpa a. Compute the drained angle of internal friction. b. Determine the cohesion of the soil c. Find the angle of failure in shear
please solve C only. subject: Geotechnical engineering A sample coarse grained soil is 50mm. In diameter and 150mm long was tested in a constant-head apparatus. The soil sample was prepared at a void ratio of 1.5. The total head was kept constant at 300mm and the amount of water is collected in 4 sec. was 50cm^3. The test temperature was 22°Ca.) Compute the temperature correction factor.b.) Compute the corrected coefficient of permeability in cm/sec. c.) Compute the interstitial velocity.
please solve B only. subject: geotechnical Engineering A sample coarse grained soil is 50mm. In diameter and 150mm long was tested in a constant-head apparatus. The soil sample was prepared at a void ratio of 1.5. The total head was kept constant at 300mm and the amount of water is collected in 4 sec. was 50cm^3. The test temperature was 22°Ca.) Compute the temperature correction factor.b.) Compute the corrected coefficient of permeability in cm/sec. c.) Compute the interstitial velocity.
Please solve A only. Subject: Geotechnical engi A sample coarse grained soil is 50mm. In diameter and 150mm long was tested in a constant-head apparatus. The soil sample was prepared at a void ratio of 1.5. The total head was kept constant at 300mm and the amount of water is collected in 4 sec. was 50cm^3. The test temperature was 22°Ca.) Compute the temperature correction factor.b.) Compute the corrected coefficient of permeability in cm/sec. c.) Compute the interstitial velocity.

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