HW05

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School

University of Illinois, Urbana Champaign *

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Course

380

Subject

Mechanical Engineering

Date

Dec 6, 2023

Type

pdf

Pages

8

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CEE 380 Fall 2022 HOMEWORK # 5 DUE DATE: Oct 5-2022 (5.00 PM) NAME: ________________________ NOTE: PLEASE SHOW ALL YOUR CALCULATIONS IN A CLEAR FORM. REMEMBER TO INCLUDE UNITS IN YOUR CALCULATIONS. 1. (25 points) The soil conditions at a site consists of 5 meters of sand underlain by 6 meters of clay over a thick silt deposit. The water surface is located 2 meters below the ground surface. Three piezometers have been installed at the site: one in the clay layer and two in the silt layer. The soil profile, piezometer locations, and porewater pressure measurements are shown in the figure below. Assume steady-state flow within the soil profile and use γ water = 10 kN/m 3 for your calculations. (a) Assigning the datum at a depth of 17 meters below the ground surface (i.e., the elevation of the lowest piezometer), plot the elevation head, pressure head, and total head with depth (you can use Excel to create your plot). (b) What is the direction of flow? What is the direction of flow? zhi yun Shi upwards
154 60 94 063 solution la Emin nn.mnhe io 2 17 5 5 5 5 0 15 15 14 12 15.005 13 3 005 n in ni my 7 10 16.27 no no n.si 6188 ji 6 in limp 4 y hp 60zo.to 5 4 4 3 2 ht it 1 2 3 4 5 6 7 8 gonna ne 5 on b The direction is upwards because hp decreases a 6r n.at V2 2okwlm3 int 8kNlm3 3m 154kPacd nrw.lZztZD 1okN1m3 bmilokpa.ie o a M 94kPa If i 06325
At mid-depth of the clay layer (point A): (c) Calculate the total vertical stress. (d) Calculate the porewater pressure. (e) Calculate the effective vertical stress. (f) What is the hydraulic gradient, i, in the clay layer? Total vertical stress, σ v (kPa) Porewater pressure, u (kPa) Effective vertical stress, σ’ v (kPa) Hydraulic gradient, i 2. (20 points) A soil profile consisting of sand and clay is shown below. The sand has a total and saturated unit weight ࠵? = 112 ࠵?࠵?࠵? , and a permeability ࠵? = 9 ࠵?࠵?/࠵?࠵?࠵? . The clay has a saturated unit weight ࠵? = 102 ࠵?࠵?࠵?, and ࠵? = 3 × 10 −2 ࠵?࠵?/࠵?࠵?࠵? . Use the piezometer conditions shown below and γ water = 62.4 lb/ft 3 to determine the following. a. Location of the water surface in the sand layer (reported in feet above the top of the clay layer), assuming zero total head loss in the sand layer b. Porewater pressure at point A c. Total vertical stress at point A (use same unit weight for the sand above and below water surface) d. Effective vertical stress at point A e. Rate of flow through the clay in ft 3 /day/ft 2 54 60 94 0035
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