Test 2 – Rock Mechanics, Earth Structures and Earthquakes
1) Compare and Contrast (note: give and explain defining equations or discuss significance where pertinent) (24pts)
a. Normal stress vs. shear stress
b. Tensile failure vs. Coulomb failure vs. frictional sliding
c. Viscous vs. Elastic deformation
d. focus vs. epicenter
e. P-wave vs. S-wave
f. Magnitude (i.e., Richter Scale) vs. Intensity (i.e., Mercalli Scale)
Figure 1.Stress-strain graph from a rock deformation experiment. Note that stress here is given in kiloPascal (kPa) rather than MegaPascal.
2) With reference to the stress-strain graph above, answer or complete the following: (5 pts)
a. Label the following on the curve:
The elastic segment of the curve The plastic segment of the curve
The yield point The point of failure
b. Based on this graph, what is the modulus of elasticity (E) for this material?
3) One of the rock formations that figures prominently in the foundation at our proposed dam site is the Kope Formation. Fleming and Johnson (1994) report the results of residual shear tests on weatheredKope Formation that yielded and angle of internal friction (?f) of 16o and a cohesion (C) of 10 kPa (note – that’s kilopascal, not MegaPascal).
a. Imagine that you needed to excavate a vertical road cut 3 m high through weathered Kope Formation. Assuming a density of 2450 kg/m3 for the Kope Formation, what would be the vertical stress at the base of your 3 m high cut? (2 pts)
b. On the graph paper at the end of this test, plot a Mohr diagram showing the Coulomb failure envelope for weathered Kope Formation based on the values of cohesion and internal friction given above. Then add a Mohr circle to the diagram based on the state of stress calculated for the base of the cut as determined in pt (a). Is weathered Kope Formation strong enough to support a vertical face 3 m high? (5 pts)
4) McFadden (2008) reports unconfined compressive strengths (UCS) for unweatheredKope formation from fresh core in the range of
UCS = 400 ± 400 ksf (kilopounds per sq. ft).
In addition, Oldfield reports values for the Modulus of Elasticity in the range
E = 8 ± 4 GPa (GigaPascal)
a. Noting that 1 ksf = 0.49 kg/cm2 and 1 GPa = 1.02 x 104 kg/cm2, plot and label the KopeFm on the diagram at right. (3 pts)
b. Briefly describe the Kope Formation’s strength and stiffness properties. (3 pts)
c. See Figure 7.29 – 7.31 in your text. How does the Kope shale compare with the range of values for the above parameters reported for typical rocks in your text? In particular, how does it compare with the range of shale values for typical sedimentary rocks illustrated Figure 7.30? Are you comfortable with the idea of building a major, heavy structure such as a dam with this material as a foundation? (3 pts)
5) What is Elastic Rebound Theory and how does it related to the concept of the earthquake cycle and earthquake forecasting? (3 pts)
6) How does the type of faulting (thrust vs. strike-slip vs. normal) relate to the magnitude of earthquakes produced? (2 pts)
7) We recently had a great earthquake offshore of Iquique, Chile (pictured above). Briefly describe the plate tectonic setting of this earthquake (i.e., what kind of plate boundary did it occur along? What type of fault ruptured?). Was an earthquake of this magnitude at this locality surprising or would it be more accurate to say that it was not unexpected? (3 pts)
8) What is liquefaction and why does it occur? (2 pts)
9) California is presently following the lead of Japan by installing an earthquake warning system. How does this system work? (2 pts)
10) List and briefly describe 3 strategies or principles that could be applied to improve the survivability of buildings and other infrastructure during earthquakes (6 pts)
11) List and briefly describe 3 strategies or principles other than better structural design that have been or could be applied to avoid or minimize the risks associated with earthquake hazards: (6 pts)
12) Contrast the concept of long-term earthquake forecasting with that of short-term earthquake prediction. Which approach has been most successful? What are the basic principles on which each is based? (4 pts)
Part 2 – Ohio River Reservoir-Induced Seismic Risk Analysis
Background and Given Information
The purpose of this exercise is to evaluate whether there would be any reasonable risk of reservoir-induced seismicity due to our imaginary dam construction project on the Ohio River. Forthe state of stress beneath Ohio we will use the samein situ stress measurement that we used for the in-class exercise on the Youngstown seismicity, as detailed below: derived from hydraulic fracturing at a depth of 808 m in Hocking County (from the World Stress Mapdatabase, Heidbach et al., 2008):
Hocking County, Ohio
(based on hydraulic fracturing at 808 m depth):
azimuth of ??: 064°
plunge of ??: 0°
azimuth of ??: 064°
plunge of ??: 90°
azimuth of ??: 334°
plunge of ??: 0°
Magnitude ??: 24 MPa
Magnitude of ??: 14 MPa
Magnitude of ??: 11.3 MPa
Since we have no way of predicting at what depth a possible earthquake might be triggered, so for convenience we will use a depth of 808 m (i.e., we will simply use the state of stress given above for our Mohr construction).
Recall also that the failure criterion for frictional sliding on a pre-existing fracture is given by “Byerlee’s Law” (Byerlee, 1978):
For ?n< 200 MPa: ?s = 0.85?n
1) Based on the state of stress given above, what type of faults would you expect to find most commonly in Ohio and why? (Normal, Reverse, thrust, or strike-slip?) (2 pts
2) Begin by studying the map of historical earthquake epicenters in Ohio overlain on the map of known Ohio faults. In the table on the following page, list the names of three faults that you believe could be at risk of reservoir-induced seismicity in the table below. Determine the angle ?f that each fault makes relative to the ?? principal plane for the state of stress given above. Assume all faults are vertical. Finally, for each fault indicate whether you would expect a left-lateral (positive) or right-lateral (negative) sense of slip. (Note that for your convenience in measuring angles I have labeled the ??principal stress direction in northern Hocking County. If you would like a clearer view of either figure I am also attaching pdf’s for both maps). (6 pts)
Fault Name Angle to ?? principal plane (?f) Expected sense-of-slip on fault if active
3) Based on your comparison between the fault map and the epicenter map, do you see any evidence that any of these faults may actually have been active in historical times? Which faults, and when do you think they could have been active? (3 pts)
4) On the last page of this document you will find a graph paper grid. Plot a Mohr circle using the state of stress given on the previous page. Clearly Label the points on the Mohr circle that correspond to each of the potentially active fault planes you identified in question 2.1 above. (Note: You may find it easier to use MS Words drawing tools rather than a compass to complete this drafting, but if you prefer to print it out and complete by hand with a compass that is also acceptable). (12pts)
a. What is the mean normal stress for this state of stress?
b. What is the differential stress?
c. Indicate the normal and shear stresses on each of the three fault planes (Make sure you get your signs right on the shear stresses)
Fault Name Mean Normal Stress (?n) Differential Stress (?d) Maximum shear stress (?max)
5) Calculate the pore fluid pressure assuming hydrostatic stress at a depth of 800 m and on your Mohr diagram plot a new Mohr Circle for the effective normal stress taking fluid pressure into account. (4 pts)
6) Assume a pool depth of 50 m (150 ft) for the reservoir. How much would this increase fluid pressures at depth? Are any of your faults close enough to failure that this seemingly minute increase in fluid pressure could actually be enough to trigger an earthquake? Discuss. (5pts)
Figure 2. Map of known bedrock fault systems in Ohio with semitransparent overlay of historical earthquake epicenters (Ohio Dept. Nat. Res. Div. of Geol. Surv.)
The major is Organizational Learning, Performance, and Change
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