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Lecture Notes○
Reading Assignment
Ostadan and White paper○
Wu and Finn paper○
Other Materials
© Steven F. Bartlett, 2011
Homework Assignment
Calculate the dynamic thrust against a buried rigid wall using the Ostadan-White method for the new Orson-Spencer Hall structure that is 10 m below the ground surface, assuming site class C. Use Vs values consistent with the mid-range of the site class (20 points).
a.
Calculate the dynamic pressure distribution to be applied against the buried structure using the Ostadan-White method for the same structure. Show this distribution versus depth on a depth plot. (10 points)
b.
Use an 1D EQL ground response model and acceleration time history developed in homework assignment #3 (Matahina Dam - scaled to the fundamental period of the surrounding soil) to do the following:
1.
Use the M-O method to estimate the factor of safety against sliding and overturning for a gravity wall using the acceleration time history from the previous homework assignment 3. (20 points)
2.
The wall is a yielding wall retaining wall and is 4 m high and is 1 m thick at the base and tapers to 0.6 m at the top. The retained backfill behind the is flat (i.e., horizontal) and has a unit weight of 22 kN/m^3 with a drained friction angle of 35 degrees and the backfill is unsaturated. Also, the base of the wall rests on backfill material and is embedded 0.6 m in this material at its base.
Assume that the horizontal acceleration used in the design is 50 percent of the peak ground acceleration. You may also neglect the vertical component of acceleration.
Dynamic Earth Pressures - Simplified MethodsSunday, August 14, 2011 3:32 PM
Dynamic Earth Pressure - Simplifed Methods Page 1
© Steven F. Bartlett, 2011
Note Eq. 11.13 of Kramer has an error.
Coulomb TheorySunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Mononobe - Okabe - Active CaseSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Mononobe - Okabe - Active Case (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Mononobe - Okabe Passive CaseSunday, August 14, 2011 3:32 PM
Dynamic Earth Pressure - Simplifed Methods Page 5
© Steven F. Bartlett, 2014
(from AASHTO LRFD Bridge Design Specifications, 2012)
Mononobe - Okabe ApplicationWednesday, February 12, 2014 2:32 PM
Dynamic Earth Pressure - Simplifed Methods Page 6
© Steven F. Bartlett, 2014
(from AASHTO LRFD Bridge Design Specifications, 2012)
Mononobe - Okabe Application (cont.)Wednesday, February 12, 2014 2:32 PM
Dynamic Earth Pressure - Simplifed Methods Page 7
© Steven F. Bartlett, 2014
(from AASHTO LRFD Bridge Design Specifications, 2012)
Other Methods Allowed within AASHTOWednesday, February 12, 2014 2:32 PM
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© Steven F. Bartlett, 2011
Gravity Wall ExampleSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Cantilevered Wall ExampleSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Cantilevered Wall Example (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Summary Results
static dynamic
F.S. Sliding = 2.29 1.36 FS static 1.25 to 2
F.S. Overturning = 2.97 1.51 FS static 2 to 3
Pasted from <file:///C:\Users\sfbartlett\Documents\My%20Courses\7330\Spreadsheets\CantileveredWall.xls>
Cantilevered Wall Example (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
the base.
Seed and Whitman - Simplified MethodSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Choudhury et al. 2006Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Rigid Case
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
mass of wedge
weight of wedge
horizontal acceleration
verticalacceleration
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
T = period of wave
active
Q = total inertial force
Pae = static +s ismic active thrust
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
passive
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Results - Active case
Static casekh and kv = 0
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
kv = 0
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
kv = 0.5 kh
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Results - Passive Case
Static casekh and kv = 0
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
kv = 0
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
kv = 0.5 kh
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Comparison with Mononobe-Okabe Method
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Comparison with Mononobe-Okabe Method
Choudhury et al. 2006 (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Non-Yielding WallsSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Non-Yielding Walls (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Non-Yielding Walls -Observations from EarthquakesSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
L
Assumptions and Method • Assume the building basemat is founded on rock. • Input ground motion at basemat elevation. • The walls of the building are effectively rigid. • 30 foot-embedment considered • 5 percent material damping of soil • Poisson’s ratio of soil = 1/3 • Kinematic SSI is considered. • Inertial SSI is not considered. • The solution is derived from SSI analyses using SASSI.
Non-Yielding Walls - Ostadan and WhiteSunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Amplitude at low frequency
Non-Yielding Walls - Ostadan and White (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Non-Yielding Walls - Ostadan and White (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Recall that M-O methodis only valid for yieldingwall; hence it forms a lower bound
The use of the low frequency (i.e., long period) amplitude is based on the findings of the Lotung experiment site (see previous).
Non-Yielding Walls - Ostadan and White (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
L = infinite
Non-Yielding Walls - Ostadan and White (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Non-Yielding Walls - Ostadan and White (cont.)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
Perform seismic ground response analysis (using SHAKE) and obtain the acceleration response spectrum at the base mat level in the free-field at 30% damping.
1.
Obtain the total mass using:2.
m = 0.50 ρ H2 Ψν
Obtain the total seismic lateral force by multiplying the mass from Step 2 by the spectral amplitude of the free-field response (Step 1) at the soil
3.
column frequency.
F = m Sa
where Sa is the spectral acceleration at the base mat level for the free field at the fundamental frequency of the soil column with 30 percent damping.
Calculate the max. lateral earth pressure (ground surface) by dividing the results for step 3 by the area under the normal soil pressure curve (normalized area = 0.744 H)
4.
Calculate the lateral pressure distribution verses depth by multiply the max. lateral earth pressure by the p(y) function below.
5.
p(y) = - .0015 + 5.05y - 15.84y2 + 28.25y3 - 24.59y4 + 8.14y5
where y is the normalized height (Y/H) measured from the base of the wall.
Ostadan and White (Steps)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
The method was verified by comparing the results of the simple computational steps with the direct solution from SASSI.
•
The verification included 4 different wall heights, 6 different input time histories and 4 different soil properties.
•
The method is very simple and only involves free-field (e.g. SHAKE) analysis and a number of hand computational steps.
•
The method has been adopted by building code (NEHRP 2000) and will be included in the next version of ASCE 4-98.
•
The Ostadan-White method is by no means a complete solution to the seismic soil pressure problem. It is merely a step forward at this time.
•
Solution! Perfect isolation!
Ostadan and White (Summary)Sunday, August 14, 2011 3:32 PM
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© Steven F. Bartlett, 2011
BlankSunday, August 14, 2011 3:32 PM
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