Assignment03

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School

Florida International University *

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Course

4012

Subject

Civil Engineering

Date

Dec 6, 2023

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pdf

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2

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FLORIDA INTERNATIONAL UNIVERSITY NAME: ______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING DATE: _______________ 1 CEG 4012 Fall 2023 ASSIGNMENT #3 Due: Nov. 14, 2023 at 1:59 PM PLEASE ADHERE TO THE HOMEWORK GUIDELINES POSTED ON CANVAS AND IN THE SYLLABUS. PLEASE REMEMBER TO SHOW ALL WORK FOR EACH PROBLEM. PROVIDE YOUR FINAL ANSWERS IN THE BOXES PROVIDED A series of direct shear tests are carried out on Wabash River sand. Two normal (effective vertical) stresses (10 psi and 20 psi) will be considered. There are one loose and one dense sample for each normal stress (i.e., 4 test in total). A square shaped box of 6 cm × 6 cm (2.36 in × 2.36 in) will be used. During the test, the area of the shearing plane keeps changing and the corrected area Ac can be easily obtained by Ac = Ao b × δ , where Ao is the original area, b is the width of the box normal to the direction of shear and δ is the shear displacement. The obtained lab test data in Excel spreadsheet (similar to the table shown below) is also posted in the Canvas website. Please download, fill up the columns with your own calculation to answer the following problems. Example calculations are shown in red below for your information. Test No. 1 Sample Loose Wabash River Sand Normal Load 55.73 lb Effective vertical stress: 10 psi Area 2.36 x 2.36 in 2 Proving Ring Constant (PRC) 0.204 lb/division Shear Rate 0.015 in/min ③ = ② - 897 = × PRC = / Ac = - 1019 Shear Proving Ring Corr. Shear Shear Vertical Vertical Remarks Displ. Dial P.R. Force Stress Dial Deform. (in) (Division) (Division) (lb) (psi) (in) (in) x 10 -3 x 10 -4 x 10 -4 0 897 0 0.000 0.000 1019 0 (-) Contraction 3 960 63 12.852 2.310 1004 -15 (+) Dilation 6 976 79 16.116 2.901 997 -22
FLORIDA INTERNATIONAL UNIVERSITY NAME: ______________ DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING DATE: _______________ 2 1. Plot shear stress ( τ ) vs. shear displacement ( δ ), and vertical deformation ( H) vs. shear displacement ( δ ) for all the 4 tests (i.e., under different densities and normal stresses). An example is shown below. 2. Plot maximum shear stress ( τ max ) vs. normal stress ( σ n ) for all tests in the same σ - τ space. Plot two envelops in the σ - τ space, one for the loose samples and the other one for the dense samples. Measure ϕ in degrees for loose and dense specimens. (Note that the shear stress and normal stress must be plotted in the same scale so that you can graphically determine the ϕ from the plots.) Use different symbols, lines and legend to identify different tests. 3. Comment on the relative shape of the shear stress ( τ ) vs. shear displacement ( δ ) curves for the loose and dense samples at the same normal stress. 4. Similarly as in Problem 3, how does the behavior reflect the volume change tendencies of each sample during various states of shear?
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