Slopes
1.
A)
Units:pascals kg/(m*s2)
B)
C)
D)
E)
F)
G)
H)
Which material is cohesive?
Material B is cohesive.
How do you know?
The y-intercept of material B is not zero. Material A is not cohesive because has it has no shear strength with no normal force.
What is the cohesion value for the cohesive material?
Material B: y = 0.7171 x + 3947.8
Cohesion Value: 3947.8 Pa
Given a normal force of 4000 pascals what will be the shear strengths of the two materials? s = c + σ tan ϕ σ = 4000 Pa
Material A: s = 59.054 + 0.696 σ
s = 59.054 + 0.696*4000 => s = 2843.054 Pa
Material B: s = 3947.8 + 0.7171 σ
s = 3947.8 + 0.7171*4000 => s = 6816.2 Pa
Generalize the relationships that you graphed above using a mathematical formulation.
What do the data define?
The data for each given materials, defines the relationship between shear strength and normal force and the resulting cohesion value and angle of internal friction.
What is the general formula for this pattern?
The terms in the y = mx +b, slope equation calculated on the graph, can be substituded for the following equation: s = σ tan ϕ + c
s - shear strength, σ - normal force, ϕ - angle of internal friction, c - cohesion value
What is the specific formula for Material A?
y = 0.696 x + 59.054
What is the specific formula for Material B?
y = 0.7171 x + 3947.8
What is the friction angle for Material A? (show work)
y = 0.696 x + 59.054
tan ϕ = 0.696
ϕ = tan-1 (0.696)
ϕ = 34.84°
What is the friction angle for Material B? (show work)
y = 0.7171 x + 3947.8
tan ϕ = 0.7171
ϕ = tan-1 (0.7171)
ϕ = 35.64°
2. Slope Failure Conditions
The model results indicate that slope stability increases with slopes with greater cohesion values. A slope with zero cohesion is very vulnerable to landslides. Slope stability decreases as the failure angle (alpha) increases. A larger slab thickness will have a greater factor of safety, but the higher the water table, the less stable the slope and the smaller factor of safety.
These results are consistent with the land use changes. This area is very prone to slope failure due to the continuous expansion and development of the boulevard, as well as poor remediation of the land after landslides. As early as 1933, extensive work has been done to Riverside Ave, including deforestation and paving. In the following decades urbanization continued, street work was done to expand and improve the area and dumping occurred. Once permeable surfaces were transformed into impermeable streets, lots, sidewalks, and buildings. As a result, run-off increased and slope stability decreased. Due to the removal of trees, the cohesion values of the slope decreased. As numerous slides have occurred, there have been a variety of remediation efforts of filling in the slides with sand, gravel, concrete, large rocks, and landfill debris such as old appliances and cars. This fill has low cohesion and is not compacted. These slopes become very vulnerable during high rainfall events, because water table will rise quicker from the increase in run-off, so the bouyancy force reduces the effective normal force, therefore there will be less frictional strength opposing the driving shear stress. Also, the river expands the bank, and decrease the supporting mass at the toe of the slope, while, humans continually expand to the edges and exceed safe loads at the head of the slope. All of this is cause for an unstable slope, that if not enough evidence of this from the repeated landslides in the past, the slope shows evidence of active deformation in the tilted trees and curving of the tree trunks, or pistol butt trees.