Francisco Pineda Corey Negrete Giancarlo Cozzi

Acknowledgements Thank you to Dr. Jon Stewart, Dr. Bob Nigbor, and the laboratory Thank you to Sherry Hormozi, Audrey Pool O'Neal, and Rick Ainsworth

Slopes All Over the World All over Los Angeles and the rest of world, we are faced with soil slope problems due to earthquakes, landslides, and erosion Civil Engineers attempt to solve these problems in a number of ways Our project conveys one of the ways we solve these problems and how significant it can be.

Soil Slopes A critical slope is the maximum angle with the horizontal at which a sloped bank of soil of a given height will remain undeformed without some form of support. Different types of soil have different critical slopes The particular soil that we used in our experiment was sand which had a critical slope of around 40 degrees

Reinforced Slopes Another one of the ways Civil Engineers attempt to solve slope problems is by using reinforced slopes. A reinforced slope is a series of layers of soil secured by fabric or mesh which form a secured slope A few of the reasons why reinforced slopes are used: Allows construction at slope angle greater than that of the friction angle of the soil Improves the seismic stability of the slope

Project Overview In order to demonstrate how soil slopes behave during an earthquake, we needed to build a chamber and fill it with sand to represent a real slope in nature. Tasks completed  Built a box (chamber)  Secured chamber to a shake table  Constructed slopes and performed tests  Analyzed data Giancarlo creates the slope inside the chamber

Building the Chamber We first drew design drawings on Microsoft Visio After calculating dimensions and gathering materials, we began building our box. Dimensions: 36” x 12” x 12” Side View Sketch of Chamber Top View Sketch of Chamber

Unreinforced Slope Tests Test #1 and #2 We placed the chamber full of sand with a critical slope onto a shake table The test was then conducted by shaking the chamber at a frequency of 1 and 2 Hz and we steadily increased the amplitude We then recorded at which amplitude the slope failed

Reinforced Slope Tests Test #3 and #4 We arranged the sand into 8 layers separated by tissue paper (the tissue paper simulated “geomembrane” that would be used in real installation) The test was then conducted by shaking the chamber at a frequency of 1 and 6 Hz and we steadily increased the amplitude We then recorded at which amplitude the reinforced slope failed

Calculating Acceleration From Measured Displacement Given the frequency (Hz) and the amplitude (inches), we can model the displacement as: s(t) = A sin (ωt) We can then calculate its acceleration by differentiating the displacement function twice. Acceleration = a(t) = -(A)(ω²) sin (ωt)

Real Life Comparison If we compare the results from our test to actual measurements of recent earthquakes, such as the 1994 Northridge Quake, we can see that our unreinforced slope would have failed almost all across the Los Angeles Area However, our reinforced slope, which is able to withstand a higher acceleration, would only have failed just around the epicenter of the earthquake.

What does it all mean? As predicted, the reinforced slope withstood a higher amplitude and higher frequency before collapsing than did the unreinforced slope Even the very weak reinforcement used in this case was effective at providing slope reinforcement We have developed lognormal fragility functions for reinforced and unreinforced sand slopes. Fragility functions like these are used in probabilistic seismic design.

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