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The shear and normal forces affecting Materials A and B are graphed on the right. It is clear from this graph that Material B is cohesive. Material B's intrinsic strength at zero normal stress is much higher than that of Material A. In order to determine the cohesion value for Material B, a linear trendline was fit to the dataset. The intercept value of the model and therefore the cohesion value of Material B is about 3948 pascals.
Given a normal force of 4000 N, the shear strength of Material A is 2843 pascals and the shear strength of Material B is 6816 pascals. Calculations are shown on the right.
As shown in the predictive calculations at right, the relationships graphed above can be generalized using linear equations. The general form of the equation for shear strength is S = C + σtanϕ , which is adapted below for materials A and B. In this equation, C refers to cohesion, sigma to normal force and phi to the internal angle of friction.
Material A: y = 0.696x + 59.054
Material B: y = 0.7171x + 3947.8
Calculations for the internal friction angles of Materials A & B
Material A: 34.84 degrees, Material B: 35.64 degrees
Examples of outputs given by the model
Dry density = 1800 kg/m3
Wet density = 2200 kg/m3
Gravity = 9.8 m/s2
Phi angle = 30 degrees
slab thickness = 1, 2, 3, 10 m
failure plane angle = 10, 20, 30, 40 degrees
cohesion = 1000, 5000, 10000 pascals
saturation depth = 1, 2, 5 m
The provided Excel model was used to perform a sensitivity analysis for the Riverside Ave slope. Inputting different values for slab thickness, failure plane angle, cohesion and saturation depth was helpful for understanding the conditions that lead to the landslide in 2019. The Halloween storm saturated the slope with rainfall and the impervious surfaces above the area of the landslide likely led to even more water entering the slope from runoff. The failure plane angle was estimated from field observations and my own photos, so it's entirely possible that this angle is not as accurate as it could be. The material that slid was mainly fill from previous landslides and road expansions and other junk, so it was not cohesive. Tree roots probably provided some amount of cohesion at the site of the landslide, since it is forested.
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