Dynamic Earth Pressures - Simplified Methods

Transcription

1 Dynamic Earth Pressure - Simplifed Methods Page 1 Dynamic Earth Pressures - Simplified Methods Reading Assignment Lecture Notes Other Materials Ostadan and White paper Wu and Finn paper Homework Assignment # 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) Use the Wu-Finn method to calculate the dynamic thrust against the same buried rigid wall in problem 1. (20 points) 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.

2 Dynamic Earth Pressure - Simplifed Methods Page 2 Coulomb Theory Note Eq of Kramer has an error.

3 Dynamic Earth Pressure - Simplifed Methods Page 3 Mononobe - Okabe - Active Case

4 Dynamic Earth Pressure - Simplifed Methods Page 4 Mononobe - Okabe - Active Case (cont.)

5 Dynamic Earth Pressure - Simplifed Methods Page 5 Mononobe - Okabe Passive Case

6 Dynamic Earth Pressure - Simplifed Methods Page 6 Mononobe - Okabe Application Wednesday, February 12, :32 PM (from AASHTO LRFD Bridge Design Specifications, 2012) Steven F. Bartlett, 2014

7 Dynamic Earth Pressure - Simplifed Methods Page 7 Mononobe - Okabe Application (cont.) Wednesday, February 12, :32 PM (from AASHTO LRFD Bridge Design Specifications, 2012) Steven F. Bartlett, 2014

8 Dynamic Earth Pressure - Simplifed Methods Page 8 Other Methods Allowed within AASHTO Wednesday, February 12, :32 PM (from AASHTO LRFD Bridge Design Specifications, 2012) Steven F. Bartlett, 2014

9 Dynamic Earth Pressure - Simplifed Methods Page 9 Gravity Wall Example

10 Dynamic Earth Pressure - Simplifed Methods Page 10 Gravity Wall Example (cont.)

11 Dynamic Earth Pressure - Simplifed Methods Page 11 Cantilevered Wall Example

12 Dynamic Earth Pressure - Simplifed Methods Page 12 Cantilevered Wall Example (cont.)

13 Dynamic Earth Pressure - Simplifed Methods Page 13 Cantilevered Wall Example (cont.) Summary Results static dynamic F.S. Sliding = FS static 1.25 to 2 F.S. Overturning = FS static 2 to 3 Pasted from <file:///c:\users\sfbartlett\documents\my%20courses\7330\spreadsheets \CantileveredWall.xls>

14 Dynamic Earth Pressure - Simplifed Methods Page 14 Seed and Whitman - Simplified Method the base.

15 Dynamic Earth Pressure - Simplifed Methods Page 15 Choudhury et al. 2006

16 Dynamic Earth Pressure - Simplifed Methods Page 16 Choudhury et al (cont.)

17 Dynamic Earth Pressure - Simplifed Methods Page 17 Choudhury et al (cont.) horizontal acceleration vertical acceleration mass of wedge weight of wedge

18 Dynamic Earth Pressure - Simplifed Methods Page 18 Choudhury et al (cont.) T = period of wave active

19 Dynamic Earth Pressure - Simplifed Methods Page 19 Choudhury et al (cont.) passive

20 Dynamic Earth Pressure - Simplifed Methods Page 20 Choudhury et al (cont.) Results - Active case Static case kh and kv = 0

21 Dynamic Earth Pressure - Simplifed Methods Page 21 Choudhury et al (cont.) kv = 0

22 Dynamic Earth Pressure - Simplifed Methods Page 22 Choudhury et al (cont.) kv = 0.5 kh

23 Dynamic Earth Pressure - Simplifed Methods Page 23 Choudhury et al (cont.) Results - Passive Case Static case kh and kv = 0

24 Dynamic Earth Pressure - Simplifed Methods Page 24 Choudhury et al (cont.) kv = 0

25 Dynamic Earth Pressure - Simplifed Methods Page 25 Choudhury et al (cont.) kv = 0.5 kh

26 Dynamic Earth Pressure - Simplifed Methods Page 26 Choudhury et al (cont.) Comparison with Mononobe-Okabe Method

27 Dynamic Earth Pressure - Simplifed Methods Page 27 Choudhury et al (cont.) Comparison with Mononobe-Okabe Method

28 Dynamic Earth Pressure - Simplifed Methods Page 28 Non-Yielding Walls

29 Dynamic Earth Pressure - Simplifed Methods Page 29 Non-Yielding Walls (cont.)

30 Dynamic Earth Pressure - Simplifed Methods Page 30 Non-Yielding Walls -Observations from Earthquakes

31 Dynamic Earth Pressure - Simplifed Methods Page 31 Non-Yielding Walls - Ostadan and White L

32 Dynamic Earth Pressure - Simplifed Methods Page 32 Non-Yielding Walls - Ostadan and White (cont.) Amplitude at low frequency

33 Dynamic Earth Pressure - Simplifed Methods Page 33 Non-Yielding Walls - Ostadan and White (cont.)

34 Dynamic Earth Pressure - Simplifed Methods Page 34 Non-Yielding Walls - Ostadan and White (cont.) 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).

35 Dynamic Earth Pressure - Simplifed Methods Page 35 Non-Yielding Walls - Ostadan and White (cont.) L = infinite

36 Dynamic Earth Pressure - Simplifed Methods Page 36 Non-Yielding Walls - Ostadan and White (cont.)

37 Dynamic Earth Pressure - Simplifed Methods Page 37 Ostadan and White (Steps) 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. Obtain the total mass using: m = 0.50 ρ H 2 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 S a 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 maximum lateral earth pressure (ground surface) by dividing the results for step 3 by the area under the normal soil pressure curve (normalized area = H) Calculate the lateral pressure distribution verses depth by multiply the max. lateral earth pressure by the p(y) function below. p(y) = y y y y y 5 where y is the normalized height (Y/H) measured from the base of the wall.

38 Dynamic Earth Pressure - Simplifed Methods Page 38 Ostadan and White (Summary) 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 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!

39 Dynamic Earth Pressure - Simplifed Methods Page 39 Wu and Finn (1999)

40 Dynamic Earth Pressure - Simplifed Methods Page 40 Analytical Solution - Homogenous Backfill - Shear Beam Theory

41 Dynamic Earth Pressure - Simplifed Methods Page 41 Analytical Solution (cont.)

42 Dynamic Earth Pressure - Simplifed Methods Page 42 Analytical Solution (cont.)

43 Dynamic Earth Pressure - Simplifed Methods Page 43 Wu and Finn - Numerical Model Finite element model by Wu and Fin

44 Dynamic Earth Pressure - Simplifed Methods Page 44 Comparison of Analytical Solution with FE Modeling - Homogeneous Backfill - Non Harmonic Motion

45 Dynamic Earth Pressure - Simplifed Methods Page 45 Solutions for Non-homogeneous backfill Solution for simple harmonic motion

46 Dynamic Earth Pressure - Simplifed Methods Page 46 Non Harmonic Motion

47 Dynamic Earth Pressure - Simplifed Methods Page 47 Blank