Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 6, Problem 6.16P
To determine
Find the volume of water flowing into the ditch every day (V).
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2. A confined aquifer is recharged by a continuous supply of water from the certain source. The average thickness of the aquifer was determined to be 25 m and the average width is 4 km. The hydraulic conductivity of the aquifer was obtained at 40 m/day and its void ratio is 0.3333. The piezometer heads in two wells 1.325 km apart are 65 meters and 60 meters from a common reference datum. Determine the rate of flow in cubic meters per day.
Determine:
•compute the rate of flow through the aquifer in m3/day
•compute the seepage velocity in m/day
•compute the time of travel from the head of the aquifer to a point 8 km downstream in days
1. (30 pts) The soil profile shown below consists of 10 meters of sandy silt overlying gravel.
The pore water pressure at the top surface of the silty sand is zero and can be assumed to
remain zero.
a) Calculate the level to which water would rise in a piezometer tube inserted into the top
of the gravel if the silty sand is just stable? Use submerged unit weights and seepage forces
to arrive at your answer (do not calculate total stresses and pore water pressures). Express
your answer as an elevation, e.g. "Elev. 130". (Note: Elevations are in meters) (10 pts)
b) Using the piezometric elevation calculated in part (a), calculate the pore water pressure
at the bottom of the silty sand if the silty sand is just stable (10 pts).
c) Calculate the total stress at the base of the silty sand and show that it is equal to the pore
water pressure calculated in part (b) (10 pts)
Elev. 120 m.
Elev. 110 m.
Sandy Silt (saturated)
Void ratio, e = 0.68
G = 2.65
Gravel
From the figure shown, the thickness of permeable layer is 1.1m making an
angle of 14 degrees with the horizontal. K= 4.87x10^-12 cm/sec. If the
vertical thickness depth of the aquifer at point of the first piezometer (left)
is 1.5m and the other point at second piezometer is 1.1m, determine the
area of flow.
h=1.4 m
Direction
impervious
layer
of seepage
3 m
14
1.1 m
impervious layer
14
-36 m-
Chapter 6 Solutions
Fundamentals of Geotechnical Engineering (MindTap Course List)
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- A canal is cut into a soil with a stratigraphy shown in Figure A. Assuming flow takes place laterally and vertically through the sides of the canal and vertically below the canal, determine the equivalent hydraulic conductivity in the horizontal and vertical directions. The vertical and horizontal hydraulic conductivities for each layer are assumed to be the same. Calculate the ratio of the equivalent horizontal hydraulic conductivity to the equivalent vertical hydraulic conductivity for flow through the sides of the canal. 1.1 m k = 2.0 × 10-6 cm/sec 1.4 m k = 4.5 × 10-6 cm/sec Canal 3.2 m 2.0 m k = 3.2 × 10-5 cm/sec 1.3 m k = 0.5 × 10-3 cm/sec 3.2 m k = 0.7 × 10-4 cm/secarrow_forwardGiven the following: H1 = 1.5 m H2 = 3.0 m H3 = 2.0 m K1 = 0.001 cm/sec K2 = 0.032 cm/sec K3 = 0.000041 cm/sec 1. Find the effective average permeability of the deposit in the horizontal direction. (in cm/s) 2. Find the effective average permeability of the deposit in the vertical direction. (in cm/s) 3. What is the ratio of the equivalent hydraulic conductivity?arrow_forward1. A confined aquifer is recharged by a continuous supply of water from the certain source. The average thickness of the aquifer was determined to be 18 m and the average width is 8 km. The hydraulic conductivity of the aquifer was obtained at 60 m/day and its void ratio is 0.1586. The piezometer heads in two wells 2,145m apart are 128 meters and 188 meters from a common reference datum. Determine: •compute the rate of flow through the aquifer in m3/day •compute the seepage velocity in m/day •compute the time of travel from the head of the aquifer to a point 8 km downstream in daysarrow_forward
- (Situation 3) Determine the equivalent hydraulic conductivity of the soil strata given in the figure considering direction of flow of water parallel and perpendicular to the layers. k = 2.3 x 102 cm/s k, = 8 x 102 cm/s k, = 5.7 x 10 cm/s, k, = 25.5 x 104 cm/s 10 m 2 m! = 9.2 x 10 cm/s k, = 27 x 107 cm/s 10 m %3!arrow_forwardFrom the figure shown, H₁ = 0.60, H₂ = 0.90 m. and h = 0.45 m. The sand has a saturated unit weight of 18.65 KN/m³. Hydraulic conductivity of sand K= 0.12 cm/sec. If the cross sectional area of tank = 0.46 m², determine the rate of upward seepage of water in liters /sec. h=0.45m T H₂=0.60 m H₂-0.90 m Direction of flow H₂O Sand ILGS G valve openarrow_forwardFrom the figure shown, an unconfined non homogenous aquifer between two water bodies at a depth of t1 = 96 m and t2 = 75 m respectively. Take K1 = 36 m/s, K2 = 48 m/s, H1 = 1470 m and H2 = 1230 m. K, K2 t2 H1 H2 a. Compute the average coefficient of permeability of the aquifer in m/s. (2 DECIMAL PLACES) b. Compute the rate of flow in m^3/s. (2 DECIMAL PLACES) c. Compute the time in seconds required for the water to pass through the soil if it has a void ratio of 0.36. (2 DECIMAL PLACES)arrow_forward
- A 500 m long levee made of compacted clay impoundswater in a reservoir as shown in attached Figure There is a 1 mthick (measured in the direction perpendicular to the seam)sand seam continuing along the entire length of the levee, at10° inclination to the horizontal, which connects the reservoirand the ditch. The hydraulic conductivity of the sand is2.6 X 10-3 cm/s. Determine the volume of water that flowsinto the ditch every day.arrow_forwardA confined aquifer shown has hydraulic conductivity of 52 m/day with void ratio of 0.282. The average thickness is 30 m and the average width is 4 km. el = 85 m el = 55 m 30 m aquifer 1400 m Determine the nearest value of the time of travel from the head of aquifer to a point 5.2 km downstream in days (in a whole day).arrow_forwardA layered soil is shown in Figure B. Estimate the ratio of equivalent horizontal and vertical hydraulic conductivity. 1.5 m 1m 1.5 m I m k = 2 × 10-3 cm/sec (top layer) k = 2 × 10-4 cm/sec k = 10-4 cm/sec %3D k = 3 × 10-4 cm/sec (bottom layer)arrow_forward
- A confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure. Piezometer P Piezometer Q Piezometric Surface Aquiclude 34.1 m Aquiclude. L= 2500 m Reference Datum The heads indicated by two piezometers P and Q are 55.2 m and 34.1 m, respectively. The aquifer has a hydraulic conductivity of 80 m/day and its effective porosity is 0.25. If the distance between the piezometers is 2500 m, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) IS_ 55.2 m Aquiferarrow_forwardTwo soil layers are shown in the figure. The soils have the same cross section area of 0.2 m2; and hydraulic conductivity of soils K, = 3 x 106 m/s, and K, = 6 x 106 m/s. Calculate flow rate q, and pore 1. pressures at A, B, and C. Controlled inflow Upper reservoir 5m 6m A Lower reservoir Soil 1 Discharge 3m B Soil 2 1.5m 4m 2marrow_forwardA confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale) Piezometer P 55.2 m Piezometric Surface Aquiclude Aquifier: Piezometer Q Aquiclude 34.1 m L = 2500m The heads indicated by two piezometers P and Q are 55.2 m and 34.1 m, respectively. The aquifer has a hydraulic conductivity of 80 m/day and its effective porosity is 0.25. If the distance between the piezometers is 2500 m, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) isarrow_forward
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