Download - 2D Analysis - Simplified Methods
Homework Assignment #4
Assume the embankment is 8 m high and has a crest of 12 m. Both side
slopes are constructed on a 1H to 1V slope.
a.
Assume the embankment is constructed of granular material with an
effective stress friction angle of 25 degree, 10 kPa cohesion and a total unit weight of 2 Mg/m^3. The shear wave velocity is 175 m/s.
b.
The foundation soil below the embankment is a clayey soil with an
effective stress friction angle of 20 degrees, 30 kPa cohesion, dry unit weight of 1.2 Mg and a porosity of 0.3.
c.
Given the attached embankment properties and the attached shear modulus
reduction and damping curve and the attached acceleration response spectra, determine the maximum crest acceleration (g) of the embankment.
1.
From this information, calculate the crest acceleration using the design
spectrum attached with these notes.
2.
From this information, calculate the pseudostatic factor of safety against slope
failure using the average acceleration that develops within the critical circle. This may be done use the "Slide" software in conjunction with the Makdisi Seed
method.
3.
Using the Makidisi-Seed approach, make a plot of embankment displacement,
U in meters, as a function of yield acceleration, ky, for a M = 7.5 earthquake.
4.
Using the information given in problem 1 and the "Slide" software, calculate
the yield acceleration of the slope/foundation system.
5.
Use the yield acceleration determined in problem 5 to estimate the
displacement of the embankment/foundation system.
6.
© Steven F. Bartlett, 2014
Lecture Notes○
Pp. 423 - 449 Kramer○
Pp. 286-290 Kramer - Shear Beam Approach○
Makdisi-Seed Analysis (EERC).pdf○
Bray and Travasarou - 2007○
Reading Assignment
None○
Other Materials
http://www.rocscience.com/products/8/feature/87
2D Analysis - Simplified Methods Monday, February 03, 20142:32 PM
2D Analysis - Simplified Methods Page 1
Homework inputs
© Steven F. Bartlett, 2011
0
5
10
15
20
25
30
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.0001 0.001 0.01 0.1 1 10
Dam
pin
g (
%)
G/G
max
shear strain (%)
Sand (Seed and Idriss) Average
2D Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 2
Homework inputs
© Steven F. Bartlett, 2011
2D Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 3
Homework inputs
© Steven F. Bartlett, 2014
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0 0.1 0.2 0.3 0.4 0.5
damping 5 percent
damping 10 percent
damping 15 percent
damping 20 percent
2D Analysis (cont.)Monday, February 03, 20142:32 PM
2D Analysis - Simplified Methods Page 4
© Steven F. Bartlett, 2011
Lower San Fernando Dam - 1971 San Fernando Valley Earthquake, Ca.
Main Issues in Seismic Assessment of Earthen Embankments and Dam:
• Stability: Is embankment stable during and after earthquake? • Deformation: How much deformation will occur in the embankment?
Two general types of analyses needed to answer these questions:
2D Dynamic Response Analysis○
2D Deformation Analysis○
In some approaches, these two analyses are coupled.
2-D Seismic Embankment and Slope Assessment and StabilityWednesday, August 17, 201112:45 PM
2D Analysis - Simplified Methods Page 5
© Steven F. Bartlett, 2011
Pseudostatic Analysis (Stability)○
Makdisi and Seed (1978) used average accelerations computed by the
procedure of Chopra (1966) and sliding block analysis to compute earthquake-induced deformations of earth dams and embankments.
Newmark Sliding Block Analysis (Deformation)○
Quake/W□
Plaxis□
FEM
FLAC□
FDM
Numerically Based Analysis (Deformation)○
This course will focus on Pseudostatic and Newmark Sliding Block Analyses using
the Makdisi-Seed (1978) Method
General Types of 2D Seismic AnalysisSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 6
© Steven F. Bartlett, 2011
If the embankment and foundation materials are not susceptible to
liquefaction or strength reduction due to earthquake shaking, then the embankment will generally he stable and no catastrophic failure is expected
(Seed, 1979).
However, if the embankment or/and foundation comprise liquefiable
materials, it may experience flow failure depending on post-earthquake factor of safety against instability (FOSpe).
For high initial driving stress (steep geometry), the FOS will likely be much less
than unity, and flow failure may occur, as depicted by strain path A-B-C. Example of this is the failure of the Lower San Fernando Dam.
In this lecture we will not address the effects of liquefaction on embankment
stability. This will be discussed later in this course.
from:
Liquefaction EffectsWednesday, August 17, 201112:45 PM
2D Analysis - Simplified Methods Page 7
Pseudostaic apply a static (non-varying) force the centroid of mass to
represent the dynamic earthquake force.
○
Fh = ah W / g = kh W
Fv = av W/ g = kv W (often ignored)
© Steven F. Bartlett, 2011
Guidance on the Selection of Kh
Pseudostatic AnalysisSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 8
Recommendations for implementation of pseudostatic analysis (Bartlett)
General comment: The pseudostatic technique is dated and should only be
used for screening purposes. More elaborate techniques are generally warranted and are rather easy to do with modern computing software.
© Steven F. Bartlett, 2011
Representation of the complex, transient, dynamics of earthquake shaking by
a single, constant, unidirectional pseudostatic acceleration is quite crude.
○
Method has been shown to be unreliable for soils with significant pore
pressure buildup during cycling (i.e., not valid for liquefaction).
○
Some dams have failed with F.S. > 1 from the pseudostatic technique○
Cannot predict deformation.○
Is only a relative index of slope stability○
Limitations of Pseudostatic Technique
Pseudostatic Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 9
© Steven F. Bartlett, 2011
Layer (top to bottom)
(kN/m3)
γ (lb/ft3) E (kPa) v K (kPa) G (kPa) φ c (kPa) Ko Vs (m/s)
1 15.72 100 100000 0.37 128,205 36,496 24.37 0 0.5873 150.9
2 16.51 105 100000 0.37 128,205 36,496 24.37 0 0.5873 147.3
3 17.29 110 150000 0.35 166,667 55,556 27.49 0 0.5385 177.5
4 18.08 115 200000 0.3 166,667 76,923 34.85 0 0.4286 204.3
5 18.08 115 250000 0.3 208,333 96,154 34.85 0 0.4286 228.4
emban 21.22 135 300000 0.3 250,000 115,385 34.85 0 0.4286 230.9
Pasted from <file:///C:\Users\sfbartlett\Documents\GeoSlope\miscdynamic1.xls>
Example Geometry
Example Soil Properties
E = Young's Modulus
= Poisson's ratioK = Bulk modulusG = Shear Modulus
= drained friction anglec = cohesionKo = at-rest earth pressure coefficentVs = shear wave velocity
Pseudostatic Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 10
© Steven F. Bartlett, 2011
Pseudostatic Results
FS = 1.252 (static with no seismic coefficient, Kh)
The analysis has been repeated by selecting only the critical circle. To do this,
only one radius point. This result can then be used with a Kh value to determine the factor of safety, FS.
Pseudostatic Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 11
© Steven F. Bartlett, 2011
Time [sec]
161514131211109876543210
Accele
ratio
n [g]
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
Acceleration time history
Damp. 5.0%
Period [sec]
3210
Response A
ccele
ratio
n [g]
1.4
1.35
1.3
1.25
1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Response Spectrum for acceleration time history
pga = 0.6 gKh = 0.5 * pgaah = 0.3 g (This is applied in the software as a horizontal acceleration).
Pseudostatic Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 12
© Steven F. Bartlett, 2011
Reduce shear strength in stability model for all saturated soils to 80 percent of
peak strength as recommended by the Army Corp of Engineers. This is to account for pore pressure generation during cycling of non-liquefiable soils. (See table
below.) (If liquefaction is expected, this method is not appropriate.)
Layer (top to bottom)
(kN/m3)
γ (lb/ft3) E (kPa) v K (kPa) G (kPa) φ Tan φ
80 percent Tan φ
New phi angle for analysis
1 15.72 100 100000 0.37 128,205 36,496 24.37 0.4530 0.3624 19.92
2 16.51 105 100000 0.37 128,205 36,496 24.37 0.4530 0.3624 19.92
3 17.29 110 150000 0.35 166,667 55,556 27.49 0.5203 0.4162 22.60
4 18.08 115 200000 0.3 166,667 76,923 34.85 0.6963 0.5571 29.12
5 18.08 115 250000 0.3 208,333 96,154 34.85 0.6963 0.5571 29.12
embank 21.22 135 300000 0.3 250,000 115,385 34.85 0.6963 0.5571 29.12
Pasted from <file:///C:\Users\sfbartlett\Documents\GeoSlope\miscdynamic1.xls>
The analysis is redone with Kh = 0.3 and reduced shear strength (see below).
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24 25 2627
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1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106
107108 109 110 111 112
113114115116117118
119120 121 122 123 124
125 126 127 128129 130
131 132 133 134 135136
137 138 139 140 141142
143 144 145 146 147148
149 150 151 152 153154
0.651
1
2 3
4
5678910
111213141516171819202122
23
24 25 2627
2829
3031
3233
34
35
36
The resulting factor of safety is 0.651 (too low). Deformation is expected for this
system and should be calculated using deformation analysis (e.g., Newmark, Makdisi-Seed, FEM, FDM methods.)
Pseudostatic Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 13
Pasted from
<http://pubs.usgs.gov/of/1998/ofr-98-113/
ofr98-113.html>
© Steven F. Bartlett, 2011
Newmark’s method treats the mass as a rigid-plastic body; that is, the
mass does not deform internally, experiences no permanent displacement at accelerations below the critical or yield level, and
deforms plastically along a discrete basal shear surface when the critical acceleration is exceeded. Thus, for slope stability, Newmark’s method is
best applied to translational block slides and rotational slumps. Other limiting assumptions commonly are imposed for simplicity but are not
required by the analysis (Jibson, TRR 1411).
1. The static and dynamic shearing resistance of the soil are assumed to
be the same. (This is not strictly true due to strain rate effects 2. In some soils, the effects of dynamic pore pressure are neglected. This
assumption generally is valid for compacted or overconsolidated clays and very dense or dry sands. This is not valid for loose sands or normally
consolidated, or sensitive soils.3. The critical acceleration is not strain dependent and thus remains
constant throughout the analysis.4. The upslope resistance to sliding is taken to be infinitely large such that
upslope displacement is prohibited. (Jibson, TRR 1411)
Newmark Sliding Block AnalysisSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 14
Steps
Perform a slope stability analysis with a limit equilibrium method and find the
critical slip surface (i.e., surface with the lowest factor of safety) for the given soil conditions with no horizontal acceleration present in the model.
1.
Determine the yield acceleration for the critical slip circle found in step 1 by
applying a horizontal force in the outward direction on the failure mass until a factor of safety of 1 is reached for this surface. This is called the yield
acceleration.
2.
Develop a 2D ground response model and complete 2D response analysis for the
particular geometry. Use this 2D ground response analysis to calculate average horizontal acceleration in potential slide mass.
3.
Consider horizontal displacement is possible for each time interval where the
horizontal acceleration exceeds the yield acceleration (see previous page).
4.
Integrate the velocity and displacement time history for each interval where the
horizontal acceleration exceeds the yield acceleration (see previous page).
5.
The following approach is implemented using the QUAKE/WTM and SLOPE/WTM.
© Steven F. Bartlett, 2011
Acceleration vs. time at base of slope from 2D response analysis in Quake/W.
Newmark Sliding Block Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 15
Analysis perfromed using shear strength = 100 percent of peak value for all soils
(i.e., no shear strength loss during cycling).
© Steven F. Bartlett, 2011
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1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106
107108 109 110 111 112
113114115116117118
119120 121 122 123 124
125 126 127 128129 130
131 132 133 134 135136
137 138 139 140 141142
143 144 145 146 147148
149 150 151 152 153154
1.530
1
2 3
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5678910
111213141516171819202122
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Factor of Safety vs. Time
Fa
cto
r of
Safe
ty
Time
1.0
1.2
1.4
1.6
1.8
2.0
0 5 10 15 20
Note that critical
circle is obtained from the
pseudostatic analysis
Newmark Sliding Block Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 16
Analysis repeated using shear strength = 80 percent of peak value for all soils to
account for some pore pressure generation during cycling.
© Steven F. Bartlett, 2011
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2 3
4
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111213141516171819202122
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1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106
107108 109 110 111 112
113114115116117118
119120 121 122 123 124
125 126 127 128129 130
131 132 133 134 135136
137 138 139 140 141142143 144 145 146 147148
149 150 151 152 153154
1.365
1
2 3
4
5678910
111213141516171819202122
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24 25 2627
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3031
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34
35
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Factor of Safety vs. Time
Fa
cto
r of
Safe
ty
Time
1.0
1.2
1.4
1.6
1.8
0 5 10 15 20
Newmark Sliding Block Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 17
Analysis repeated using shear strength in layer 1 equal to 5 kPa (100 psf) to
represent a very soft clay.
© Steven F. Bartlett, 2011
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1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
101 102 103 104 105 106
107108 109 110 111 112
113114115116117118
119120 121 122 123 124
125 126 127 128129 130
131 132 133 134 135136
137 138 139 140 141142143 144 145 146 147148
149 150 151 152 153154
0.944
1
2 3
4
5678910
111213141516171819202122
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Factor of Safety vs. Time
Fa
cto
r of
Safe
ty
Time
0.8
0.9
1.0
1.1
1.2
0 5 10 15 20
Note FS < 1 for a
significant part of the time history.
Deformation vs. Time
De
form
atio
n
Time
0.0
0.5
1.0
1.5
2.0
2.5
0 5 10 15 20
Note that more than 2 m of
displacement have accumulated.
Newmark Sliding Block Analysis (cont.)Sunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 18
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 19
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 20
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 21
© Steven F. Bartlett, 2011
Eq. 1
Eq. 2
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 22
© Steven F. Bartlett, 2011
Eq. 3
Eq. 3a
Eq. 4
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 23
© Steven F. Bartlett, 2011
Eq. 5
Eq. 6
Eq. 7a
Eq. 7b
Eq. 7c
See p. 533
Kramer
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 24
© Steven F. Bartlett, 2011
Eq. 8
Eq. 9
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 25
© Steven F. Bartlett, 2011
y / h
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 26
© Steven F. Bartlett, 2011
Eq. 10
Makdisi - Seed Analysis - Crest AcceleratiSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 27
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 28
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 29
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 30
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 31
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - Crest AccelerationSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 32
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - DeformationsSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 33
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - DeformationsSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 34
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - DeformationsSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 35
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - DeformationsSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 36
Better chart for previous page
© Steven F. Bartlett, 2011
Interpolation on semi-log plot
If U/kh(max)gT is halfway between 0.01 and 0.1, then the exponent value for this
number is -1.5 (see red arrow on graph above). This can be converted back by 1 x 10-1.5 which is equal to 3.16 x 10-2.
Exponent
Makdisi - Seed Analysis - DeformationsSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 37
Example
Design Spectra
© Steven F. Bartlett, 2011
Values in red must be adjusted until convergenceIs obtained
Makdisi - Seed Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 38
© Steven F. Bartlett, 2011
Shear modulus reduction and damping curves
Calculations
Makdisi - Seed Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 39
© Steven F. Bartlett, 2011
Calculations (cont.)
Charts for deformation analysis
Z = depth to
base of potential
failure plane (i.e., critical
circle from pseudostatic
analysis)
toe circle
Makdisi - Seed Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 40
© Steven F. Bartlett, 2011
(See regression equations on next page for M7.5 and M6.5 events
Makdisi - Seed Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 41
y = 1.7531e-8.401x
R² = 0.988
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
0 0.2 0.4 0.6 0.8 1
U /
(kh
ma
x*g
*T1)
ky/khmax
Deformation versus ky/kymax curve for M = 7.5
y = 0.7469e-7.753x
R² = 0.9613
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0 0.2 0.4 0.6 0.8 1
U /
(kh
ma
x*g
*T1)
ky/khmax
Deformation versus ky/kymax curve for M = 6.5
© Steven F. Bartlett, 2011
Makdisi - Seed Analysis - ExampleSunday, August 14, 20113:32 PM
2D Analysis - Simplified Methods Page 42
© Steven F. Bartlett, 2014
Bray and TravasarouWednesday, February 05, 20142:32 PM
2D Analysis - Simplified Methods Page 43
© Steven F. Bartlett, 2014
Bray and Travasarou (cont.)Wednesday, February 05, 20142:32 PM
2D Analysis - Simplified Methods Page 44
In this application, probabilistic methodologies usually involve three steps:
(I) establishing a model for prediction of seismic slope displacements. where
seismic displacements are conditioned on a number of variables characterizing the important ground motion characteristics and slope properties:
(2) computing the joint hazard of the conditioning ground motion variables,
(3) integrating the above-mentioned two steps to compute the seismic
displacement hazard. Focusing on the first step.
Step 1 - Developing the Model
Compared to the rigid sliding block model, a nonlinear coupled stick-slip
deformable sliding block model offers a more realistic representation of the dynamic response of an earth/waste structure by accounting for (he
deformability of the sliding mass and by considering the simultaneousoccurrence of its nonlinear dynamic response and periodic sliding episodes.
In addition, its validation against shaking table experiments provides confidence in its use (Wartman et al. 2003).
© Steven F. Bartlett, 2014
Bray and Travasarou (cont.)Wednesday, February 05, 20142:32 PM
2D Analysis - Simplified Methods Page 45
Step 1 - Developing the Model (cont.)
The ground motion database used to generate the seismic displacement data
comprises available records from shallow crustal earthquakes (hat occurred in active Plate margins (PEER strong motion database
(http://peer.bcrkeley.edu/smcat/index.html)).
These records conform to the following criteria:
(1) 5.5 < Mw < 7.6
(2) R < 100 km
(3) Simplified Geotechnical Sites B C, or D (4) frequencies in the range of 0.25— 10 Hz have not been filtered out.
Earthquake records totaling 688 from 41 earthquakes comprise the ground
motion database for this study [see Travasarou (2003) for a list of records used]. The two horizontal components of each record were used to calculate
an average seismic displacement for each side of the records, and the maximum of these values was assigned to that record.
The seismic response of the sliding mass is captured by:
1. 1D equivalent-linear viscoelastic modal2. strain-dependent material properties to capture the nonlinear response3. single mode shape. but the effect of including three modes was shown to be
small.
The results from this model have been shown to compare favorably with those
from a fully nonlinear D-MOD-type stick-slip analysis (Rathje and Bray 2000), but this model can be utilized in a more straightforward and transparent manner.
The model used herein is one dimensional (i.e.. a relatively wide vertical column of deformable soil) to allow for the use of a large number ground motions with
wide range of properties of the potential sliding mass in this study. One-dimensional (1D) analysis has been found to provide a reasonably conservative
estimate of the dynamic stresses at the base of two-dimensional (2D) sliding systems
© Steven F. Bartlett, 2014
Bray and Travasarou (cont.)Wednesday, February 05, 20142:32 PM
2D Analysis - Simplified Methods Page 46
© Steven F. Bartlett, 2014
Bray and Travasarou (cont.)Wednesday, February 05, 20142:32 PM
2D Analysis - Simplified Methods Page 47
© Steven F. Bartlett, 2014
This nonlinear coupled stick-slip deformable sliding model can be
characterized by: (1) its strength as represented by its yield coefficient (ky.). and (2) its dynamic stiffness as represented by its initial fundamental period
(Ts). Seismic displacement values were generated by computing the response of the idealized sliding mass model with specified values of its yield
coefficient (i.e., ky=0.02. 0.05, 0.075. 0.1, 0.15. 0.2, 0.25. 0.3, 0.35, and 0.4) and its initial fundamental period (i.e., T=0. 0.2, 0.3. 0.5. 0.7, 1.0. 1.4. and 2.0
s) to the entire set of recorded earthquake motions described previously.
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