# LAB 4 SLOPE STABILITY by rja46630

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E&ES 222                                     Geomorphology Laboratory

LAB 4: SLOPE STABILITY

Due October 3, 2006

Equipment: calculator, Abney level, plastic bags, scales, tape measure, trowels

The stability of a slope can be expressed as a Factor of Safety, F, where

F=          sum of resisting forces
sum of driving forces
on the plane of failure.

When F > 1 a slope is stable, F < 1 a slope is unstable, F=1 slope is critical.

In this lab we will examine the equation for failure of a shallow translational slide on an infinite
slope:

c'+hgcos2 " ( # r \$ # w m)tan %
F=
# r hgsin " cos "

where:
c’ is the effective cohesion
!
h is thickness of potential slide
g is the acceleration of gravity on Earth
θ is dip angle of potential failure plane
ρr is density of rock in potential slide
ρw is density of water
m is the portion of thickness that is saturated (m = 1 for a fully saturated slide (water table at the
surface), m = 0 for dry slide (water table beneath slide thickness))
φ is the angle of internal friction

See attached sheet for values for these parameters.

Using this equation, answer the following questions. Show your work. If you use an excel

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You are a contractor assigned to assess slope stability for a region in Los Angeles to determine if
stilt houses should be built on the land. You examine the hillslope and observe that it is made of
clayey soil, you measure the slope and find it to be 17°. Cohesion is 11900kg/ms2

1. If the 10 m thick mass is unsaturated above a potential failure surface, is it safe?

2. If a 10 m thick slide mass is 50% saturated above a potential failure surface is it safe?

3. What saturation is the maximum to have a safe slope?

After your analysis, the homeowners change their mind and decide to move to the beach. They
have selected a spot in the sand dunes.

4. What is the steepest sand dune they can safely build upon?

President Bush has implemented a new Vision for Space Exploration that is preparing to send
humans to the Moon and Mars. It will be necessary to build bases there. Assume 10 m plane of
failure.

5. What is the steepest slope one can build safely upon in the lunar regolith (gMoon =
1.624m/s2)?

6. What is the steepest slope one can build safely upon on the martian regolith (gMars
=3.711m/s2)?

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The above figure shows a plot of F versus theta for the general parameters (ρr, c’ , φ and slide
thickness of 5 m) specified on the previous page given saturations of m = 1 and m = 0.1. Use this
chart for the following 2 questions.

7. If this is in Oregon or Washington where the hill is completely saturated in the winter,
what is the maximum stable slope (FS = 1) if the thickness of the potential slide mass is 5
m?

8. If the slide is in Arizona where the maximum saturation of the hill is only 10% of the
slide thickness (again, h = 5 m), what is the maximum stable slope?

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FIELD ANALYSIS

Purpose: Measure slope and soil density in the field.
Site: Slope behind Ravine Ave

Measurement of slope:
With your field partner, measure a topographic profile of the slope using an Abney level
and a tape measure. Detailed instructions for measuring a slope profile will be given in the field.

Measurement of soil bulk density.
a. Expose the soil by clearing grass and other plants with your trowel
b. Prepare a flat surface by scraping the soil
c. Dig a small hole (~10cm x 10cm x 10cm) with your trowel or knife. Carefully place all of the
excavated soil into a sandwich bag.
d. Line the hole with another sandwich bag. Fill the hole with water. Carefully make sure that the
water completely fills the hole.
e. Weigh the mass of the soil sample and the mass of the water using the portable electronic
balance. Note: To a close approximation, 1 g H2O = 1 mL H2 O.
f. Soil density = mass/volume.
g. If time permits, repeat your measurements across the hillslope 5 times. Average and take a
standard deviation.

Assessment of soil properties.
Note color, composition, grain size, stickiness.

Using the parameters measured in the field, answer the following:

9. At failure, F = 1. Does your computed FS indicate that the slope may be subject to failure? Or
is it safe?

10. Are there any circumstances under which this hill could become unstable?

11. Describe the role that water plays in creating slope failures. What additional parameters
would we have to measure in the field and/or lab to improve our estimate. Hint: Look at
your notes on the Coulomb equation for shear stress.

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Some Useful Numbers on the Engineering Properties of Materials (Geologic and Otherwise)
GEOL 615

Coefficient of sliding friction (m)
For most rocks, m varies between 0.8 and 0.5. A value of 0.60 would be a good number for
general use.
Glass on glass        0.4
Rubber on concrete 0.75
Steel on steel        0.55

Angle of internal friction (f
Rock                        30°
Sand                        30-40°
Gravel                      35°
Silt                        34°
Clay                        20°
Loose sand                  30-35°
Medium sand                 40°
Dense sand                  35-45°
Gravel with some sand 34-48°
Silt                        26-35°
Because the angle of internal friction, f, is typically around 25-35°, the coefficient of internal
friction (tanf is 0.5 to 0.7

Cohesive strength (t0)
Rock            10,000 kPa
Silt            75 kPa
Clay            10-20 kPa
Very soft clay 0- 48 kPa
Soft clay        48-96 kPa
Medium clay 96-192 kPa
Stiff clay      192-384 kPa
Very stiff clay 384-766 kPa
Hard clay        >766 kPa

Density (ρ)
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Sandy soil             1800 kg/m
Limestone 2700 kg/m3
Gravel soil            2000 kg/m3
Chalk      2100 kg/m3
Silty soil             2100 kg/m3
Shale     2500 kg/m3
Clay soil              1900 kg/m3
Sandstone 2000 kg/m3
Mafic igneous rocks    3000 kg/m3
Steel      8000 kg/m3
Felsic igneous rocks   2700 kg/m3
Concrete 1680-3000 kg/m3
Metamorphic rocks      2700 kg/m3
Water      1000 kg/m3
Sedimentary rocks      2600 kg/m3
Granite                2700 kg/m3

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