2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow LESSON PLAN BASED ON A SEISMIC EVENT’S AFFECT ON A SLOPE MADE OF CLAY SOIL WILL THE SLOPE FAIL? ALGEBRA I

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow LESSON PLANS CREATED BY DAVID GUTIERREZ and FRAN HARLOW

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow LESSON PLANS WERE CREATED WITH THE HELP OF PROFESSOR GIOVANNA BISCONTIN and PhD GRADUATE STUDENT CASSIE RUTHERFORD

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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?

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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?

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow INSTRUMENTATION AND CALIBRATION The physical quantities that we need to measure when conducting experiments on soils are: –temperatures –force –displacement –pressure

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow TRANSDUCERS Physical units of force displacement and pressure in to electrical signal (sensor) directly related to that physical units. Physical Input Electrical Signal Displacement Transducer Force Transducer Electrical Signal Physical Input

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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)

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow Student Handout: CALIBRATION DATA SHEET (Force ) Weight AddedTransducer Output (mV)Incremental Applied ForceChange Transducer Output (kilograms force) – InputOutput(kilograms) - Student Calculations(mV) - Student Calculations

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow Student Work (Lesson One) Weight AddedTransducer OutputIncremental AppliedChange Transducer (kilograms force)(millivolts)Force (Kilograms)Output (millivolts) InputOutputStudent Calculations

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow Student Handout: CALIBRATION DATA SHEET (LSCT) MicrometerTransducerIncrementalChange in Reading (Input)OutputDisplacementTransducer Output (inches)(millivolts) (mV)(inches)(millivolts) (mV) (x value)(y value)Student Calculations

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow Student Work Key (Lesson One) MicrometerTransducerIncrementalChange in Reading (Input)OutputDisplacementTransducer Output (inches)(millivolts)(inches)(millivolts) (x value)(y value)Student Calculations

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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)

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

Student Work: CALIBRATION OF LSCT (Linear Strain Conversion Transducer) Equation: y = x – y is in mV; is the slope (calibration factor) (mV/in); is the y-intercept in mV

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow Student Work: CALIBRATIONS OF FORCE TRANSDUCER Equation: y = x y is in mV; is the slope (calibration factor) (mV/kg); is the y-intercept (mV) Student Work: CALIBRATIONS OF FORCE TRANSDUCER Equation: y = x y is in mV; is the slope (calibration factor) (mV/kg); is the y-intercept (mV)

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow SOIL TEST measured in millimeters and newtons DisplacementForce DisplacementForce DisplacementForce (mm)(N) (mm)(N) (mm)(N)

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow SOIL TEST measured in inches and kilograms of force DisplacementForce DisplacementForce DisplacementForce (in)(kgf) (in)(kgf) (in)(kgf)

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow SOIL TEST GRAPH

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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.

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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.

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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.

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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 = x 2 ) 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.

2006 E 3 Teacher Summer Research ProgramDavid Gutierrez and Fran Harlow 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.