![Page 1: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/1.jpg)
Applying Slope Stability -Exercises
![Page 2: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/2.jpg)
Spreadsheet Calculations
• Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses.• All are very simple, but instructive.• These are intended for educational purposes ONLY!• We will work through a series of examples together.
![Page 3: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/3.jpg)
Infinite Slope
![Page 4: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/4.jpg)
Application
• Reasonable for shallow surficial failures.• Shallow is relative, might apply to cases where a long,
continuous translational failure might occur.• Assumes that surface and groundwater is parallel to failure
plane.
![Page 5: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/5.jpg)
Influence of Slope Angle
• Depth of Slide Plane=5 feet• Water Table Height=0 feet (dry)• Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=0• Other Properties all set to 0.• Determine FS for Slope Angles of 10, 20, and 30°.• The steeper the slope, the less stable a slope is.
![Page 6: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/6.jpg)
Influence of Slope Angle
Influence of Slope AngleSlope FS
10 3.2715 2.1520 1.5925 1.2430 1
0
0.5
1
1.5
2
2.5
3
3.5
10 15 20 25 30
Fact
or o
f Saf
ety
Slope Angle (Degrees)
![Page 7: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/7.jpg)
Influence of Shear Strength
• Slope Angle is 20°.• Depth of Slide Plane=5 feet• Water Table Height=0 feet (dry)• Unit Weight=100 pcf• Other Properties all set to 0.• Determine FS for:
• Friction angle=20°, Cohesion =0 psf• Friction angle=20°, Cohesion =100 psf (trace of cohesion)
• A tiny bit of cohesion goes a long way – be careful…
![Page 8: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/8.jpg)
Influence of Shear Strength
Influence of CohesionCohesion FS
0 1.5920 1.7140 1.8460 1.9680 2.08100 2.21
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100
Fact
or o
f Saf
ety
Cohesion (psf)
![Page 9: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/9.jpg)
Influence of Water• Slope Angle is 20°.• Depth of Slide Plane=5 feet• Friction Angle=30 degrees• Cohesion=0• Unit Weight=100 pcf• Other Properties all set to 0.• Determine FS for:
• Water Table Height=0 feet (dry)• Water Table Height=2.5 feet • Water Table Height=5 feet (saturated)
• Water has major destabilizing influence on stability (reduced effective stress)
![Page 10: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/10.jpg)
Influence of Water
Influence of Water - No CohesionWater FS
0 1.591 1.382 1.163 0.954 0.745 0.53
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5
Fact
or o
f Saf
ety
Water Level (Feet)
![Page 11: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/11.jpg)
Influence of Water• Slope Angle is 20°.• Depth of Slide Plane=5 feet• Friction Angle=30 degrees• Cohesion=100 psf• Unit Weight=100 pcf• Other Properties all set to 0.• Determine FS for:
• Water Table Height=0 feet (dry)• Water Table Height=2.5 feet • Water Table Height=5 feet (saturated)
• When cohesion is present (if real), less sensitive to changes in water.
![Page 12: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/12.jpg)
Influence of Water
Influence of Water - CohesionWater FS
0 2.211 22 1.793 1.584 1.375 1.160
0.5
1
1.5
2
2.5
0 1 2 3 4 5
Fact
or o
f Saf
ety
Water Level (Feet)
![Page 13: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/13.jpg)
Influence of Seismicity• Slope angle = 20°• Depth of Slide Plane=5 feet• Water Table Height=0 feet (dry)• Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=0• Other Properties all set to 0.• Determine FS for Horizontal accelerations of 0.1, 0.2 g’s• The higher the seismicity, the less stable a slope is.
![Page 14: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/14.jpg)
Influence of Seismicity
Influence of Seismicitykh FS0 1.59
0.1 1.20.2 0.950.3 0.770.4 0.65
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.1 0.2 0.3 0.4
Fact
or o
f Saf
ety
Seismic Coeffecient (g's)
![Page 15: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/15.jpg)
Influence of Vegetation – Shallow Soils• Slope angle = 20°• Depth of Slide Plane=5 feet• Water Table Height=0 feet (dry)• Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=0• Other Properties all set to 0.• Determine FS for:
• Root reinforcement = 160 psf, Tree Surcharge= 120 psf (old growth)• Root reinforcement = 160 psf, Tree Surcharge= 0 psf (harvest)• Root reinforcement = 0 psf, Tree Surcharge= 0 psf (fallow)
• Roots matter for shallow soils. Surcharge effect of trees may be rather small.
![Page 16: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/16.jpg)
Influence of Vegetation – Shallow Soils
Influence of Vegetation - ShallowRoot Reinf. Tree Surch. FS
0 0 1.59160 0 2.58160 120 2.39
![Page 17: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/17.jpg)
Influence of Vegetation – Deeper Soils• Slope angle = 20°• Depth of Slide Plane=25 feet• Water Table Height=0 feet (dry)• Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=0• Other Properties all set to 0.• Determine FS for:
• Root reinforcement = 0 psf, Tree Surcharge= 120 psf (old growth)• Root reinforcement = 0 psf, Tree Surcharge= 0 psf (harvest)
• Vegetation makes no mechanical difference for moderately deep slides.
![Page 18: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/18.jpg)
Influence of Vegetation – Deeper Soils
Influence of Vegetation - DeepRoot Reinf. Tree Surch. FS
0 0 1.590 120 1.59
![Page 19: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/19.jpg)
Forensics
• A translational landslide has occurred on 30° slope.• The depth of failure is approximately 15 feet. Seeps and springs
are found 5 feet above the shear plane.• Unit weight of soil is 100 pcf. The failure occurred after heavy
rainfall (drained conditions, c’=0 psf).• Find the drained friction angle of the soil.
![Page 20: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/20.jpg)
Planar Wedge
![Page 21: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/21.jpg)
Application
• Common for Road Cuts and Fills.• May be underconservative for gentle slopes. • Good “rule-of-thumb” for stability.
![Page 22: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/22.jpg)
Stability and Right-of-Way
• Slope Height = 20 feet• Backslope Angle = 10°• Water Table Elevation = 10 feet • Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=100 psf• Other Properties all set to 0.• Determine maximum slope angle for FS=1.3.
![Page 23: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/23.jpg)
Stability and Right-of-Way
• Max slope is 46°.
![Page 24: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/24.jpg)
Stability and Right-of-Way• Let’s consider a big rainstorm. The slope is now saturated.• Slope Height = 20 feet• Backslope Angle = 10°• Water Table Elevation = 20 feet • Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=100 psf• Other Properties all set to 0.• Determine maximum slope angle for FS=1.3.
![Page 25: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/25.jpg)
Stability and Right-of-Way
• Max slope is 31°.• Water makes a big difference. What will you design to?
![Page 26: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/26.jpg)
Loading from Heavy Equipment• Slope Height = 20 feet• Slope Angle = 45°• Backslope Angle = 0°• Water Table Elevation = 10 feet • Unit Weight=100 pcf• Friction Angle=30 degrees• Cohesion=100 psf• Other Properties all set to 0.• Equipment weights 50,000 lbs• Determine FS for:
• Surcharge clearance of 5, 10, 20, 30, 40 feet• There is a range of influence for a surcharge. The closer to the slope, the more
dangerous.
![Page 27: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/27.jpg)
Loading from Heavy Equipment
Equipment ExampleSurcharge Distance FS
0 0.685 0.81
10 0.9515 1.1120 1.2525 1.3530 1.3535 1.3540 1.35
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25 30 35 40
Fact
or o
f Saf
ety
Distance from Edge (feet)
![Page 28: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/28.jpg)
Method of Slices
![Page 29: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/29.jpg)
Ordinary Method of Slices
• Considers rotational (circular) failure geometry.• Allows consideration of water, multiple soil types.• Can use approach to size a rock buttress.
![Page 30: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/30.jpg)
Forensics• A slope failure occurs in winter months after heavy rainfall.• The headscarp daylights at approximately 120 feet from the toe.• Slope height is 50 feet with angle of 30°, backslope angle of 10°.• Water seeps and springs noted at 15 feet of elevation at slope face.• Unit weight of soil is 100 pcf. Drained conditions (c’=0 psf).• Determine the drained friction angle. It is necessary for repair.
![Page 31: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/31.jpg)
Forensics
• Drained conditions, natural soil that is not overconsolidated or cemented, so cohesion is 0, find friction angle.
• Slope is failing, so Factor of Safety is 1.• For FS=1, friction angle is 33 degrees.
![Page 32: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/32.jpg)
Repair• We need to size a rock buttress for repair. • Rockfill has unit weight of 130 pcf. It’s friction is 45° with no cohesion. • How wide of a buttress is necessary?• How many cubic yards of rockfill are required per foot of length of the
landslide?
![Page 33: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/33.jpg)
Repair
RepairFS Width Volume1.2 25 feet 7 cy/ft1.3 30.5 feet 10 cy/ft1.4 36.5 feet 14 cy/ft1.5 42 feet 19 cy/ft
0
2
4
6
8
10
12
14
16
18
20
0
5
10
15
20
25
30
35
40
45
1.2 1.3 1.4 1.5
Roc
kfill/
Exca
vatio
n Vo
lum
e (y
ds/ft
)
Buttr
ess
Wid
th (f
fet)
Drained Factor of Safety
![Page 34: Applying Slope Stability - Exercises...2019/04/10 · • Open MS Excel-based Slope Stability calculator. • Note that there are three basis slope stability analyses. • All are](https://reader030.vdocument.in/reader030/viewer/2022040604/5ea6f4ba66d7de5b2c394c8d/html5/thumbnails/34.jpg)
Questions?