Dynamic Earth Pressures - Simplified Methods Sunday, August 14, 2011 3:32 PM
Reading Assignment ○ Lecture Notes Other Materials ○ Ostadan and White paper ○ Wu and Finn paper Homework Assignment #5 1. Use an 1D EQL ground response model and acceleration time history developed in the previous homework assignment to do the following: a. Calculate the dynamic thrust against a buried rigid wall using the Ostadan-White method for a buried structure that is 10 m below the ground surface. (20 points) b. 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) 2. Use the Wu-Finn method to calculate the dynamic thrust against the same buried rigid wall in problem 1. (20 points) 3. 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 homework assignment 3. (20 points)
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.
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Coulomb Theory Sunday, August 14, 2011 3:32 PM
Note Eq. 11.13 of Kramer has an error.
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Mononobe - Okabe - Active Case Sunday, August 14, 2011 3:32 PM
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Mononobe - Okabe - Active Case (cont.) Sunday, August 14, 2011 3:32 PM
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Mononobe - Okabe Passive Case Sunday, August 14, 2011 3:32 PM
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Mononobe - Okabe Application Wednesday, February 12, 2014 2:32 PM
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(from AASHTO LRFD Bridge Design Specifications, 2012)
Mononobe - Okabe Application (cont.) Wednesday, February 12, 2014 2:32 PM
(from AASHTO LRFD Bridge Design Specifications, 2012) © Steven F. Bartlett, 2014
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Other Methods Allowed within AASHTO Wednesday, February 12, 2014 2:32 PM
(from AASHTO LRFD Bridge Design Specifications, 2012)
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Gravity Wall Example Sunday, August 14, 2011 3:32 PM
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Gravity Wall Example (cont.) Sunday, August 14, 2011 3:32 PM
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Cantilevered Wall Example Sunday, August 14, 2011 3:32 PM
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Cantilevered Wall Example (cont.) Sunday, August 14, 2011 3:32 PM
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Cantilevered Wall Example (cont.) Sunday, August 14, 2011 3:32 PM
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
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Seed and Whitman - Simplified Method Sunday, August 14, 2011 3:32 PM
the base.
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Choudhury et al. 2006 Sunday, August 14, 2011 3:32 PM
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
horizontal acceleration vertical acceleration
mass of wedge
weight of wedge
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
T = period of wave
active
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
passive
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
Results - Active case
Static case kh and kv = 0
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
kv = 0
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
kv = 0.5 kh
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
Results - Passive Case
Static case kh and kv = 0
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
kv = 0
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
kv = 0.5 kh
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
Comparison with Mononobe-Okabe Method
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Choudhury et al. 2006 (cont.) Sunday, August 14, 2011 3:32 PM
Comparison with Mononobe-Okabe Method
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Non-Yielding Walls Sunday, August 14, 2011 3:32 PM
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Non-Yielding Walls (cont.) Sunday, August 14, 2011 3:32 PM
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Non-Yielding Walls -Observations from Earthquakes Sunday, August 14, 2011 3:32 PM
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Non-Yielding Walls - Ostadan and White Sunday, August 14, 2011 3:32 PM
L
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Non-Yielding Walls - Ostadan and White (cont.) Sunday, August 14, 2011 3:32 PM
Amplitude at low frequency
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Non-Yielding Walls - Ostadan and White (cont.) Sunday, August 14, 2011 3:32 PM
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Non-Yielding Walls - Ostadan and White (cont.) Sunday, August 14, 2011 3:32 PM
Recall that M-O method is only valid for yielding wall; 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).
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Non-Yielding Walls - Ostadan and White (cont.) Sunday, August 14, 2011 3:32 PM
L = infinite
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Non-Yielding Walls - Ostadan and White (cont.) Sunday, August 14, 2011 3:32 PM
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Ostadan and White (Steps) Sunday, August 14, 2011 3:32 PM
1. 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.
2. Obtain the total mass using: m = 0.50 ρ H2 Ψν 3. 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 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. 4. Calculate the maximum 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) 5. Calculate the lateral pressure distribution verses depth by multiply the max. lateral earth pressure by the p(y) function below. 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.
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Ostadan and White (Summary) Sunday, August 14, 2011 3:32 PM
• 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!
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Wu and Finn (1999) Sunday, August 14, 2011 3:32 PM
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Analytical Solution - Homogenous Backfill - Shear Beam Theory Sunday, August 14, 2011 3:32 PM
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Analytical Solution (cont.) Sunday, August 14, 2011 3:32 PM
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Analytical Solution (cont.) Sunday, August 14, 2011 3:32 PM
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Wu and Finn - Numerical Model Sunday, August 14, 2011 3:32 PM
Finite element model by Wu and Fin
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Comparison of Analytical Solution with FE Modeling Homogeneous Backfill - Non Harmonic Motion Sunday, August 14, 2011 3:32 PM
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Solutions for Non-homogeneous backfill Sunday, August 14, 2011 3:32 PM
Solution for simple harmonic motion
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Non Harmonic Motion Sunday, August 14, 2011 3:32 PM
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Blank Sunday, August 14, 2011 3:32 PM
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