LESSON PLAN BASED ON A SEISMIC EVENT

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LESSON PLAN BASED ON A SEISMIC EVENTS AFFECT ON
A SLOPE MADE OF CLAY SOILWILL THE SLOPE
FAIL?ALGEBRA I
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• LESSON PLANS CREATED BY
• DAVID GUTIERREZ
• and
• FRAN HARLOW

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• LESSON PLANS WERE CREATED WITH THE HELP OF
• PROFESSOR GIOVANNA BISCONTIN
• and
• PhD GRADUATE STUDENT
• CASSIE RUTHERFORD

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Submarine Landslide

• Imagine being on an oil rig in the middle of the
  Pacific Ocean and a seismic event causes a
  GIGANTIC landslide of the ocean floor. Will we
  be SWEPT away?

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Submarine Seismic Slope Stability

• Clay soil is weakened by cyclic loading
• Will the slope fail?
• How much displacement during the earthquake?
• Total Stress effective stress water pore
  pressure
• Total stress stays the same (weight on top)
  during the earthquake, effective stress decreases
  but does not 0, and the pore pressure increases

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Will the Slope Fail?

• What is an earthquake?
• How does it affect clay soil on a slope?
• How do you determine if the slope will fail?
• Will a structure built on the slope fail?
• Will a structure built on the slope remain
  undamaged?

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INSTRUMENTATION AND CALIBRATION

• The physical quantities that we need to measure
  when conducting experiments on soils are
• temperatures
• force
• displacement
• pressure

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TRANSDUCERS

• Physical units of force displacement and pressure
  in to electrical signal (sensor) directly related
  to that physical units.

Displacement Transducer
Physical Input
Electrical Signal
Physical Input
Force Transducer
Electrical Signal
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LESSON ONE (45 Minutes)

• Calibration
• Introduce the data
• Set up the chart the students are given
• First Column - Force
• Second Column - Voltage
• Students complete the chart
• Third Column - (Increments in Force)
• Fourth Column - (Increments in Voltage)

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Student HandoutCALIBRATION DATA SHEET (Force)
Weight Added Weight Added Transducer Output (mV) Transducer Output (mV) Incremental Applied Force Incremental Applied Force Change Transducer Output
(kilograms force) Input (kilograms force) Input Output Output (kilograms) - Student Calculations (kilograms) - Student Calculations (mV) - Student Calculations
0.0000   2.47        
10.2311   2.55        
20.2221   2.62        
30.2331   2.69        
40.2391   2.25        
50.1931   2.81        
60.1911   2.89        
70.2131   2.95        
80.2041   3.02        
90.2111   3.09        
100.1820   3.15        
110.1770   3.22        
120.0770   3.28        
130.0700   3.35        
140.0590   3.42        
150.0620   3.48        
160.0760   3.55        
170.0870   3.62        
180.0880   3.68        
190.0420   3.75        
199.9540   3.82        
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Student Work (Lesson One)
Weight Added Weight Added Transducer Output Transducer Output Incremental Applied Incremental Applied Change Transducer
(kilograms force) (kilograms force) (millivolts) (millivolts) Force (Kilograms) Force (Kilograms) Output (millivolts)
Input Input Output Output Student Calculations Student Calculations Student Calculations
0.0000   2.47   0.000   0.00
10.2311   2.55   9.957   0.08
20.2221   2.62   10.001   0.07
30.2331   2.69   10.001   0.06
40.2391   2.25   10.006   0.06
50.1931   2.81   9.954   0.06
60.1911   2.89   9.998   0.07
70.2131   2.95   10.022   0.06
80.2041   3.02   9.991   0.07
90.2111   3.09   10.009   0.07
100.1820   3.15   9.971   0.06
110.1770   3.22   9.965   0.07
120.0770   3.28   9.900   0.06
130.0700   3.35   9.993   0.07
140.0590   3.42   9.989   0.07
150.0620   3.48   10.003   0.06
160.0760   3.55   10.014   0.07
170.0870   3.62   10.011   0.07
180.0880   3.68   10.001   0.06
190.0420   3.75   9.954   0.07
199.9540   3.82   9.912   0.07
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Student HandoutCALIBRATION DATA SHEET (LSCT)
Micrometer Micrometer Transducer Transducer Incremental Incremental Change in
Reading (Input) Reading (Input) Output Output Displacement Displacement Transducer Output
(inches) (inches) (millivolts) (mV) (millivolts) (mV) (inches) (inches) (millivolts) (mV)
(x value) (x value) (y value) (y value) Student Calculations Student Calculations Student Calculations
0.000   -0.92        
0.100   5.65        
0.200   12.53        
0.300   19.41        
0.400   26.28        
0.500   33.19        
0.525   34.91        
0.550   36.62        
0.575   38.34        
0.600   40.06        
0.700   46.93        
0.800   53.76        
0.900   60.60        
1.000   67.45        
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Student Work Key (Lesson One)
Micrometer Micrometer Transducer Transducer Incremental Incremental Change in
Reading (Input) Reading (Input) Output Output Displacement Displacement Transducer Output
(inches) (inches) (millivolts) (millivolts) (inches) (inches) (millivolts)
(x value) (x value) (y value) (y value) Student Calculations Student Calculations Student Calculations
0.000   -0.92   0.000    
0.100   5.65   0.100   6.62
0.200   12.53   0.100   6.88
0.300   19.41   0.100   6.88
0.400   26.28   0.100   6.87
0.500   33.19   0.100   6.91
0.525   34.91   0.025   1.72
0.550   36.62   0.025   1.71
0.575   38.34   0.025   1.72
0.600   40.06   0.025   1.72
0.700   46.93   0.100   6.87
0.800   53.76   0.100   6.83
0.900   60.60   0.100   6.84
1.000   67.45   0.100   6.85
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Lesson Two (45 minutes)

• Review Lesson One
• Furnish students graph paper
• Introduce Linear Relationships
• Students Will
• Determine the maximum and minimum values of the
  independent value (x value)
• Determine the maximum and minimum values of the
  dependent value (y value)

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Lesson Two (Continued)

• Take this information and determine a reasonable
  domain and range
• Graph the x-value and the y-value on the graph
• x-value is column 1 (Force)
• y-value is column 2 (Voltage)
• Determine the best fit by drawing a straight line
• Find the trend for the line after determining the
  best fit

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Student Work CALIBRATION OF LSCT(Linear Strain
Conversion Transducer)Equation y 72.252x
3.8145y is in mV 72.252 is the slope
(calibration factor) (mV/in)-3.8145 is the
y-intercept in mV
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Student WorkCALIBRATIONS OF FORCE
TRANSDUCEREquation y 0.0071x 2.4185y is
in mV 0.0071 is the slope (calibration factor)
(mV/kg)2.4185 is the y-intercept (mV)
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Lesson Three (45 minutes)

• Review lessons One and Two
• With the graph they have created, students will
• Brainstorm
• Determine the 0 value for the graph
• Determine from Lesson One (the chart), the slope
  of the line
• Determine the significance of the slope
• Discuss and apply the relationship between the
  x-values and the y-values
• Write a sentence to describe the above
  relationship
• Formulate an equation from your sentence

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Lesson Three (Continued)

• Predictions
• Be asked to predict how the Voltage will behave
  at different value of force
• What happens when the force increases or
  decreases?
• Discuss predictions of slope failure

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Lesson Four Soil Test

• Introduce the data
• Plot the points on the graph the students are
  given
• First Column Displacement (x-value)
• Second Column Force (y-value)
• Students will discover that the graph is
  nonlinear
• Discussion
• Will the slope fail?
• Students will discover that when the earthquake
  force exceeds the maximum on the y-axis, the
  slope will fail

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SOIL TEST measured in millimeters and newtons
  Displacement Force   Displacement Force   Displacement Force
  (mm) (N)   (mm) (N)   (mm) (N)
1 0.000000 0.0000 18 0.703320 20.2660 35 2.089800 23.6780
2 0.010048 5.9874 19 0.750220 20.5210 36 2.200400 23.7940
3 0.026794 6.9700 20 0.800460 20.7490 37 2.317600 23.8510
4 0.070332 9.2149 21 0.844000 20.9590 38 2.424800 23.7860
5 0.107170 11.3780 22 0.894240 21.1600 39 2.538600 23.7630
6 0.150710 13.2700 23 0.937780 21.3440 40 2.652600 23.8620
7 0.197600 14.5720 24 0.981320 21.5240 41 2.810000 23.6240
8 0.237800 15.5790 25 1.068400 21.8760 42 2.977400 23.5430
9 0.288040 16.4220 26 1.182300 22.2000 43 3.155000 23.3930
10 0.331580 17.1520 27 1.296100 22.5030 44 3.332400 23.3810
11 0.378460 17.7510 28 1.410000 22.7470 45 3.510000 23.2630
12 0.425340 18.2610 29 1.523900 22.8790 46 3.704200 23.1980
13 0.468880 18.7040 30 1.634400 23.0520 47 3.935400 23.2770
14 0.515780 19.0830 31 1.748300 23.2140 48 4.153000 23.1440
15 0.562660 19.4280 32 1.858800 23.3400 49 4.444400 22.9330
16 0.609560 19.7570 33 1.862200 23.4460 50 4.732400 22.6380
17 0.656440 20.0190 34 1.976000 23.5770 51 5.311800 22.1840
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SOIL TEST measured in inches and kilograms of
force
  Displacement Force   Displacement Force   Displacement Force
  (in) (kgf)   (in) (kgf)   (in) (kgf)
1 0.00000 0.000 18 0.00000 0.000 35 0.00000 0.000
2 0.00040 0.610 19 0.00002 0.062 36 0.00000 0.006
3 0.00105 0.710 20 0.00004 0.072 37 0.00000 0.007
4 0.00277 0.939 21 0.00011 0.096 38 0.00000 0.010
5 0.00422 1.160 22 0.00017 0.118 39 0.00001 0.012
6 0.00593 1.353 23 0.00023 0.138 40 0.00001 0.014
7 0.00778 1.485 24 0.00031 0.151 41 0.00001 0.015
8 0.00936 1.588 25 0.00037 0.162 42 0.00001 0.017
9 0.01134 1.674 26 0.00045 0.171 43 0.00002 0.017
10 0.01305 1.748 27 0.00051 0.178 44 0.00002 0.018
11 0.01490 1.809 28 0.00059 0.184 45 0.00002 0.019
12 0.01675 1.861 29 0.00066 0.190 46 0.00003 0.019
13 0.01846 1.907 30 0.00073 0.194 47 0.00003 0.020
14 0.02031 1.945 31 0.00080 0.198 48 0.00003 0.020
15 0.02215 1.980 32 0.00087 0.202 49 0.00003 0.021
16 0.02400 2.014 33 0.00094 0.205 50 0.00004 0.021
17 0.02584 2.041 34 0.00102 0.208 51 0.00004 0.021
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SOIL TEST GRAPH
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Lesson Five (45 minutes)

• From lessons one, two, three, and four, students
  will be asked to write a two page essay on the
  process starting from creating a chart to the end
  result (determining whether the slope will fail).
  The students will be asked to explain the
  connection between these lessons and Civil
  Engineering applications.

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TAKS OBJECTIVES

• Objective 1
• The student describes functional relationships in
  a variety of ways.
• Objective 2
• The student demonstrates an understanding of the
  properties, and attributes of functions.
• Objective 3
• The student will demonstrate an understand-
• ing of linear functions
• Objective 5
• Quadratic and other nonlinear functions

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TEKS OBJECTIVES

• A(b)(1) Foundation for functions.
• The student understands that a function
  represents a dependence of one quantity or
  another and can be described in a variety of
  ways.
• The student describes independent and dependent
  quantities in functional relationships.
• The student gathers or records data, or uses
  data sets, to determine functional (systematic)
  relationships between quantities.
• The student describes functional relationships
  for given problem situations and writes equations
  or inequalities to answer questions arising from
  the situations.
• The student represents relationships among
  quantities using concrete models, tables, graphs,
  diagrams, verbal descriptions, equations, and
  inequalities.
• The student interprets and makes inferences from
  functional relationships.

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TEKS OBJECTIVES (Continued)

• A(c)(2) Linear functions.
• The student understands the meaning of the slope
  and intercepts of linear functions and interprets
  and describes the effect of changes in parameters
  of linear functions in real-world and
  mathematical situations.
• The student develops the concept of slope as a
  rate of chanage and determines slopes from
  graphs.
• A(d)(3) Quadratic and other nonlinear
  functions.
• The student understands there are situations
  modeled by functions that are neither linear nor
  quadratic and models the situations.

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TEKS OBJECTIVES (Continued)

• A(b)(2) Foundations for Functions
• The student demonstrates an understanding of the
  properties and attributes of functions.
• The student identifies, and sketches the
  general forms of linear
• (y x) and quadratics (y x2) parent
  functions.
• For a variety of situations, the student
  identifies the mathematical domains and ranges
  and determines reasonable domain and range values
  for given solutions.
• The student interprets situations in terms of
  given graphs or create situations that fit given
  graphs.
• In solving problems, the student collects and
  organizes data, makes and interprets scatter
  plots, and models, predicts, and makes decisions
  and critical judgments.

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TEKS OBJECTIVES (Continued)

• A(b)(3) Foundation for functions.
• The student understands how algebra can be used
  to express generalizations and recognizes and
  uses power of symbols to represent situations.
• The student uses symbols to represent unknowns
  and variables.
• Given situations, the student looks for patterns
  and represents generalizations algebraically.
• A(b)(4) Linear functions.
• The student understands that linear functions can
  be represented in different ways and translates
  among their various representations.
• The student determines whether or not given
  situations can be presented by linear functions.
• The student translates among and uses algebraic,
  tabular, graphical, or verbal descriptions of
  linear functions.