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TRB Webinar: Load and Resistance Factor Design

Analysis for Seismic Design of Slopes and Retaining Walls

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Today’s Presenters and ModeratorMike Keever, California Department of Transportation, [email protected]

Edward Kavazanjian, Arizona State University, [email protected]

Donald Anderson, CH2MHill, [email protected]

Geoffrey Martin, University of Southern California, [email protected]

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11

Load and Resistance Factor Designfor

Seismic Design of Slopes and Retaining Walls

sponsored by

TRB Committee AFF50Seismic Design of Bridges

February 17, 2010

TRB Webinar

22

Overview of Presentation

Presenters Facilitator

Mike Keever/Caltrans Speakers

Ed Kavazanjian/ASUDon Anderson/CH2M HILL Geoff Martin/USC

Reference documents NCHRP Report 611 (Volumes 1 and 2)

Seismic Analysis and Design of Retaining Walls, Slopes & Embankments, and Buried Structures

NHI Course 130094 (in preparation)LRFD Seismic Design of Geotechnical Transportation Structures and Foundations

33

Overview

NCHRP 12-70 Projecthttp://www.trb.org/Main/Blurbs/Seismic_Analysis_and_Design_of_Retaining_Walls_Bur_160387.aspx

or type “NCHRP 611” into Google or Bing

http://www.trb.org/Main/Blurbs/Seismic_Analysis_and_Design_of_Retaining_Walls_Bur_160387.aspx�

44

Overview

Objectives of NCHRP 12-70 Project

Develop methods for LRFD seismic design of retaining walls, buried structures, slopes, and embankmentsDevelop recommended specifications compatible and consistent with AASHTO LRFD Bridge Design Specifications

Ref: NCHRP Research Project Statement Project 12-70, FY 2004

55

Overview

Need for NCHRP 12-70 Project

Difficulties with retaining wall seismic design M-O method “blows up” with high back slopes,

high PGA’s, not appropriate for passive Appropriate seismic coefficient Soldier pile, tieback, soil nail, and MSE walls

Lack of guidance for slope stability Pseudo-static versus deformation approach Appropriate seismic coefficient Ground motion amplification Liquefaction effects

66

Outline of Presentation

Background for methodology - Kavazanjian

Seismic slope stability - Anderson

Retaining wall design - Martin

77


Background for methodology AASHTO seismic damage philosophy Load and resistance factor design principles Design ground motions

Seismic slope stability Factor of safety (C/D) approach Displacement-based approach Liquefaction issues Mitigation

Retaining wall design Earth pressure determination External, internal, and global stability Guidance on AASHTO wall design

88

Prescriptive Approach Explicit (quantified): Sustain damage without

loss of life or collapse in a large, rare earthquake♦ 7% probability of occurrence in 75 yr

(1000 yr Rp)

Implicit (not quantified): Withstand smaller, more frequent seismic events♦ Without significant damage or ♦ With repairable damage

AASHTO Background

Seismic Design Philosophy

99

Alternative approaches (Owner’s discretion) More rigorous performance standard

♦ e.g., 3% probability of occurrence in 75 yr

Multi-level (performance-based) design standard♦ Upper level event for “No Collapse”♦ Lower level event for “No Damage”

Often applied to facilities of high importance♦ Critical bridges♦ Lifelines routes

AASHTO Background

Seismic Design Philosophy

1010

ηi = load modifier for load component iγi = load factor for load component iQi = nominal value of load component iφi = resistance factor for resistance component iRi = nominal value of resistance component i

∑∑ ϕ≤γη iiiii RQ

AASHTO Background

LRFD Design Principle

1111

Factored C/D ratio:(Must be > 1)

Unfactored C/D ratio:(Analogous to FS) ∑

∑i

i

QR

∑∑

iii

ii

QR

γηϕ

AASHTO Background

Capacity/Demand Ratio

(Not an AASHTO Term)

1212

LRFD and soil mechanics use the same symbols

φ (phi) = soil friction angle & LRFD resistance factor

γ (gamma) = soil unit weight & LRFD load factor

Use subscripts and check context to differentiate

AASHTO Background

Note on Notation

1313

Regardless of the method, the following condition must be satisfied

Load Effects ≤ ResistanceDifference in methods is based on how uncertainties in loads and resistances are accounted forLRFD is here to stay

Load and resistance factors will be refined with time

Confirm with ASD checks where necessary

AASHTO Background

LRFD versus ASD

1414

AASHTO (2007) LIMIT STATES FOR BRIDGE DESIGN Limit State Type Case Load Combination

I Normal vehicular use of the bridge without wind

II Use of the bridge by Owner-specified special vehicles, evaluation permit vehicles, or both, without wind

III Bridge exposed to wind velocity exceeding 55 mph

IV Very high dead load to live load force effect ratios

Strength

V Normal vehicular use of the bridge with wind of 55 mph

I Load combination including earthquake Extreme Event

II Ice load, collision by vessels and vehicles, and certain hydraulic events with a reduced live load other than that which is part of the vehicular collision load, CT

I Normal operational use of the bridge with a 55 mph wind and all loads taken at their nominal values

II Intended to control yielding of steel structures and slip of slip-critical connections due to vehicular live load

III Longitudinal analysis relating to tension in prestressed concrete superstructures with the objective of crack control and to principal tension in the webs of segmental concrete girders

Service

IV Tension in prestressed concrete columns with the objective of crack control

Fatigue Repetitive gravitational vehicular live load and dynamic responses under the effects of a single design truck

AASHTO Background

Limit States for Earthquake Design

1515

(AFTER AASHTO 2007, TABLE 3.4.1-1) Use one of these at a time Load

Combination Limit State PL LL WA WS WL FR TCS TG SE EQ IC CT CV

Strength I γp 1.75 1.00 - - 1.00 0.50/1.20 γTG γSE - - - - Strength II γp 1.35 1.00 - - 1.00 0.50/1.20 γTG γSE - - - - Strength III γp - 1.00 1.40 - 1.00 0.50/1.20 γTG γSE - - - - Strength IV γp - 1.00 - - 1.00 0.50/1.20 - - - - - - Strength V γp 1.35 1.00 0.40 1.00 1.00 0.50/1.20 γTG γSE - - - - Extreme Event I γp γEQ 1.00 - - 1.00 - - - 1.00 - - - Extreme Event II γp 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00 Service I 1.00 1.00 1.00 0.30 1.00 1.00 1.00/1.20 γTG γSE - - - - Service II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - - Service III 1.00 0.80 1.00 - - 1.00 1.00/1.20 γTG γSE - - - - Service IV 1.00 - 1.00 0.70 - 1.00 1.00/1.20 - 1.00 - - - - Fatigue - 0.75 - - - - - - - - - - -

PL permanent load WL wind on live load EQ earthquake LL live load FR friction IC ice load WA water load and stream pressure TG temperature gradient CT vehicular collision force WS wind load on structure SE settlement CV vessel collision force

TCS uniform temperature, creep, and shrinkage

AASHTO Background

Load Combinations and Load Factors

1616

Retaining walls & slopes Set permanent load load-factor, γp = 1

♦ Use best-estimate unit weight for soil, concrete, etc.♦ Use best-estimate seasonal average groundwater

location

Set live load load-factor, γEQ = 0 or 0.5 x LL based on ADTT

♦ γEQ = 0 for low volume, non-critical roadways♦ (γEQ)max= 0.5 for high volume, critical roadways

AASHTO Background

Load Factors for Seismic Design

1717

Extreme Event 1 (earthquake loading) resistance factors (φ ) equal 1 except for: Undrained shear strength of clay when M>7.5

♦ φ = 0.9

Bearing resistance of retaining wall footings♦ φ = 0.67

Deep foundation design♦ φ = 0.8 for axial uplift & lateral resistance in

pushover analysis

AASHTO Background

Resistance Factors

1818

AASHTO Background

Design Ground Motions

Two key ground motion parameters Peak Ground Acceleration (PGA)

♦ Proportional to design seismic inertial force (seismic coefficient)

Spectral Acceleration at 1 sec (S1)♦ Defines seismic environment ♦ Used to calculate seismic displacement potential

PGA and S1 must be adjusted for local site conditions Accounts for amplification or de-amplification Typically based on shear wave velocity in top 100

ft (30 m), (Vs)30

1919

AASHTO Background

Design Ground Motions

AASHTO employs 2002 USGS seismic hazard map for PGA & S1 for reference site condition CD provides search by latitude and longitude Reference condition is soft rock (Site Class B)

Adjust for local site effects if not Site Class B Using site factors based upon (Vs)30 or Alternatives

♦ (Vs)30 – dependent maps (2008 USGS Maps)♦ Site-specific hazard analysis w/ NGA relationships♦ Site-specific response analysis (e.g., SHAKE)

2020

7% probability of exceedance in 75 yrs (nominal 1000 year return period)

AASHTO National Seismic Hazard Map

2121

AASHTO Background

Site Classification System

Site class based on (VS)30 (or other geotech characteristics) in top 100 ft (30 m) Site Class F: soft clay, sensitive clay

Site Class (VS)30 SPT Su

A > 5000 ft/s N.A. N.A.B 2500 - 5000 ft/s N.A. N.A.C 1200 - 2500 ft/s > 50 > 2 ksfD 600 - 1200 ft/s 15 - 50 1 -2 ksfE < 600 ft/s <15 < 1 ksfF (Special Study Sites)

2222

AASHTO Background

PGA Site Factor, FPGA

Site Class

Mapped Spectral Response Acceleration at Short Periods

PGA ≤ 0.10 g

PGA = 0.20 g

PGA = 0.30 g

PGA = 0.40 g

PGA ≥ 0.50 g

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C 1.2 1.2 1.1 1.0 1.0

D 1.6 1.4 1.2 1.1 1.0

E 2.5 1.7 1.2 0.9 0.9

F a a a a a

Table notes:

Use straight line interpolation for intermediate values of PGA, where PGA is the peak ground acceleration obtained from the ground motion maps.

a Site-specific geotechnical investigation and dynamic site response analyses shall be performed (Article 3.4.3).

2323

AASHTO Background

PGA Amplification Plot

2424

AASHTO Background

Long-Period Site Factor, FV

Site Class

Mapped Spectral Response Acceleration at 1 Sec Periods

S1 ≤ 0.10 g

S1 = 0.20 g

S1 = 0.30 g

S1 = 0.40 g

S1 ≥ 0.50 g

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C 1.7 1.6 1.5 1.4 1.3

D 2.4 2.0 1.8 1.6 1.5

E 3.5 3.2 2.8 2.4 2.4

F a a a a a

Table notes:

Use straight line interpolation for intermediate values of S1, where S1

is the spectral acceleration at 1.0 seconds obtained from the ground motion maps.

a Site-specific geotechnical investigation and dynamic site response analyses shall be performed (Article 3.4.3).

25




Retaining wall design Earth pressure determination External, internal, and global stability Guidance on AASHTO walls

26

Overview of Slope Discussions Types of slopes Performance

expectations Current practice Proposed design

methodology Special considerations Design specifications

Slopes and Embankments

General

27


GeneralTwo categories Engineered slopes and embankments Constructed of imported material Typically 1.5H:1V and flatter Properties generally well defined and controlled Groundwater location often known and below

embankment

Natural slopes Wide range of soil conditions Range from flat to very steep (1H:1V) Properties can be highly variable May be comprised of many different layers Groundwater location can be erratic and within slope

28

Performance expectation needs to be defined Non-critical slopes and embankments Accept potential for failure

Minimum risk to public Repair cost less than mitigation Requires Owner approval

Critical slopes and embankments Failure could have significant consequence

High risk to public Damage to bridge structure Closure of lifeline roadway

Define Owner’s performance expectations Minimum acceptable C/D ratio (i.e., FS) Minimum acceptable displacements


General

29

Current practice involves either of two approaches Limit-equilibrium, pseudo-static method Conduct conventional stability analysis Apply horizontal seismic coefficient Accept if C/D > approved value (typ. 1.1 to 1.3)

Displacement-based approach Simplified Newmark-type analysis

Direct integration of EQ records Charts

Numerical modeling (e.g., FLAC, PLAXIS, etc.)

Overview of each approach follows


General

30


Limit-Equilibrium Method

Method of analysis Conventional stability

program used (UTexas, SlopeW, SLIDE, etc.)

Vertical acceleration = 0 Undrained total

stress/static strength parameters

Seismic coefficient (kav) describes horizontal force

31



Strength of non-liquefiable soils Use total stress properties (c & φ) if >5% fines Proposed maximum values of apparent cohesion

as follows:

Reduce strength of clays by 0.9 factor if M > 7.5 Test “special soils” → sensitive clays, silts, ??

Liquefiable soils covered later

% < #200 sieve Max. Apparent Cohesion (psf)

5-15 50

15-25 100

25-50 200

32



Need seismic coefficient Start with maximum seismic coefficient (kmax)

kmax = (FPGA)(PGA)where PGA = USGS mapped acceleration coefficient for Site

Class B FPGA = acceleration adjustment factor for AASHTO Site

Class Next, adjust to average seismic coefficient (kav)

kav = (α)(kmax)where α = slope height reduction factor

33


Limit-Equilibrium Methodα factor accounts for wave scattering Evaluated using

QUAD 4M modeling Slopes and retaining

walls Range of EQ records,

slope & wall heights, and soil properties

Important for slopes with H > 20 ft

34



α factor for Site Classes C, D, and Eα = 1 + 0.01H [0.5β - 1]whereH = depth of failure surface β = FvS1/PGA

α = 1.0 if H ≤ 20 ft

α factor for Site Classes A and B –increase computed value by 20%

35



Next, apply displacement (ductility) factor, r kav = r α kmax

reduces kmax for allowable permanent displacement

Values of r = 1.0 to 0.5 For r =1.0, kav = α kmax

C/D (FS) > 1 – Negligibly small permanent displacement Very conservative design criteria

For r = 0.5, kav = 0.5 α kmax

C/D (FS) = 1.0 => 1–2 inches permanent displacement C/D (FS) > 1.1 => minimal permanent displacement Recommended for most design

36



Notes r can be < 0.5 Displacement analysis to support Owner approval needed

May need to check more than one failure surface

37

Pseudo-static analysis procedure – summary1. Find PGA and S1 from AASHTO hazard maps2. Find Site Class adjustment factors, FPGA & Fv

3. Find kmax = PGA x FPGA

4. Find β = S1FV/kmax = (SD1/kmax)5. Find scattering factor, α

If H < 20 ft, α = 1 If H ≥ 20 ft,

α = 1 + 0.01 H (0.5β – 1) Check H – iterate if necessary Limit H in α determination to 100 ft



38

Pseudo-static analysis procedure – summary (cont.)5.Find kav = r α kmax

If ∆permissible = 1 to 2 in. or more, set r = 0.5 If ∆permissible < 1 to 2 in., set r = 1.0

6.Conduct pseudo-static stability analysis with kav If C/D (FS) ≥ 1.1, slope meets requirements If C/D (FS) ≤ 1.1

Implement mitigation Perform displacement analysis



39


Simplified Displacement MethodMethod of analysis Limit-equilibrium method

used to define yield acceleration, ky

Deformations estimated using Newmark method Failure mass assumed rigid Accelerations are average

values of sliding mass Slope deforms when PGA >

ky

Vertical acceleration ignored

40

Earthquake records can be integrated Determine ky, where ky = kav at C/D (FS) = 1.0 Integrate EQ acceleration record above ky


Simplified Displacement Method

41

Charts and equations commonly used Methodology Permanent

displacement = f (ky / kmax, M)

Based on analysis of EQ records

Various methods available

NCHRP 12-70 analyses show same relationship for slopes & retaining walls



42

NCHRP 12-70 Project (2008) equations for slopes and retaining walls in

Displacement in inches for western United States (WUS)log (d) = -1.51 – 0.74 log (ky / α kmax) + 3.27

log (1– ky /α kmax) – 0.80 log (α kmax) + 1.59 log PGV)

[Note: no magnitude term]

Slightly different form of equation for Central and Eastern United States (CEUS) rock sites (Site Classes A and B) – See NCHRP 611 Report



43

PGV required for NCHRP 12-70 displacement equation Simplified method developed during NCHRP 12-70

Project Values of mean PGV (in/sec)

PGV = 38 (Fv S1)where

S1 = spectral acceleration at 1 secondFv = site class adjustment factor

Values of mean + one std dev PGV (in/sec)

PGV = 55 (Fv S1)



44

Comparison between AASHTO (2007) and NCHRP (2008) equations for PGV = 30 kmax (in/sec)



45

Simplified displacement procedure – summary 1. Find PGA and S1 from AASHTO hazard maps2. Find Site Class adjustment factors, FPGA & Fv

3. Find kmax = PGA x FPGA

4. Find β = S1FV/kmax = (SD1/kmax)

5. Find scattering factor, α If H < 20 ft, α = 1

If H ≥ 20 ft,

α = 1 + 0.01 H (0.5β – 1) Check H – iterate if necessary. Limit H to 100 ft



46

Simplified displacement analysis procedure – summary (cont.)

6. Find ky from pseudo-static stability analysis

7. Estimate displacement potential using NCHRP 12-70 equation (or charts in NCHRP Report 611)

8. Evaluate acceptability of displacement based on performance criteria established by Owner



47


Example

Seismic stability of fill embankment example in Vol. 2 of NCHRP 12-70 Report Slope angle = 1.5H:1V and 2H:1V Slope height = 15 to 45 ft Soil strengths variable (c & φ)

48

Results for embankment in Los Angeles (as shown in previous slide) Values from AASHTO hazard map PGA = 0.6g S1 = 0.52g

Site Class evaluation (at bottom of embankment) Site Class D Fpga = 1 Fv = 1.5

Site-adjusted parameters for design PGA = 0.6 SD1 = 0.78


Example

49

Results of limit-equilibrium and displacement analyses C/D ratio (FS) = 0.94 (for r = 0.5) Displacement = 6 in.

Influence of project location

Location Rock PGA C/D ∆ (inches)

Seattle 0.4 1.05 1

Charleston 0.2 1.21 0


Example

50

Calculated displacements show Even for cohesionless fills and very strong

earthquakes, small lateral slope deformations (and settlement) expected; i.e., well-compacted fills perform well in earthquakes

Pseudo-static C/D > 1.0 using a seismic coefficient = 0.5 kav is consistent with small deformations

Added complexities for natural slopes –though methodology is the same


Example

51


Special Consideration – Liquefaction

Slopes with or on liquefiable soils Several methodologies available Empirical correlations based upon field data

Newmark-type analyses

Numerical modeling (FLAC or similar effective stress methods)

Significant uncertainty with each approach and no consensus within profession

52

Example of lateral spreading using simplified Newmark-displacement approach



53

Simplified displacement approach Residual strength (Su)liq from residual strength

ratio, (Su)liq/σ’vo Olson and Johnson (2008) Idriss and Boulanger (2007) Kramer Wang Hybrid (2008)

Confirm that C/D > 1.0 (no flow slide) kav = 0

Estimate ky using (Su)liq. k @ C/D = 1.0

Use charts or equation to obtain displacement



54

Simplified displacement approach –limitations Uncertainties in residual strength

determination Lateral spreading versus flow failure

Lateral spreading is not correctly modeled Does not account for dilation at large incremental

displacements May not account for static shearing stress Residual strength assumed from first cycle of

loading Effects of pore-water pressure on ground

motions not addressed Thought to be conservative and provides a

basis for design, but use with caution!



55

Proposed liquefaction design procedure –summary1. Find residual strength using SPT or CPT method2. Find C/D for post-EQ flow condition

Use residual strength of liquefied soil and kmax = 0 C/D needs to be > 1.0. If C/D < 1.0, mitigate

conditions

3. Find yield acceleration, ky, by conducting pseudo-static stability analysis using (Su)liq

4. Find ratio of ky/kmax

5. Find displacement using NCHRP equation



56


Special Considerations – Mitigation

Factors influencing acceptable C/D ratio (FS value) or calculated displacement Slope location and function/ traffic density/

public safety Types of soil/geologic conditions and

uncertainties Implications of movement/ facilities in

proximityApply mitigation for unacceptable conditions

57

Alternatives available to designer Highway decision-makers Accept risk Avoid problem by relocation of highway

Geotechnical engineer Reduction of driving force

Flatten or bench slope Drainage Lightweight fills for embankments

Increase resisting force Buttress fills Structural retention systems/retaining walls/soil nailing Drainage to increase soil strength


Special Considerations – Mitigation

58


Design GuidelinesNCHRP 12-70 Specifications (Volume 2) has proposed specifications and commentary Screening criteria used to decide whether to

conduct analyses (sites not involving liquefaction)

Example problems provided

Slope Angle Fpga PGA3H:1V 0.3

2H:1V 0.2

59

Flow chart for analysis approach in Fig. Y-2 of Vol. 2


Design Guidelines

60




Retaining wall design Earth pressure determination External, internal, and global stability Guidance on AASHTO walls

61

Retaining Walls

Types of Walls

Section 11, AASHTO LRFD Bridge Design Specifications Conventional Gravity and Semi-Gravity Walls Mechanically Stabilized Earth (MSE) Walls Metallic Strips Polymeric Reinforcement

Non-gravity Cantilever / Anchored Walls Discrete Elements (drilled shafts) with lagging Continuous Wall Elements (e.g., sheetpiles or tangent

piles)

Soil Nailed Walls not addressed

62

Retaining Walls

Types of Walls

Gravity and Semi-Gravity Walls

Non-Gravity Walls Soil Nailed Walls

63

Mechanically Stabilized Earth (MSE) Walls

Retaining Walls

Types of Walls

64

Retaining Walls

Gravity Walls – AASHTO LRFD M-O Equations

65

Retaining Walls

AASHTO LRFD M-O Equations

Example of M-O limitations Steep backfill

slope high kh

Granular fill with φ = 35

KAE » 0.6

66

Retaining Walls

AASHTO LRFD M-O Equations

Problems and knowledge gaps with M-O Equations Non-homogenous backfill and presence of

groundwater Sloping ground behind can give unrealistically

large seismic active pressure coefficients Rigid block sliding assumption – may not be

appropriate for wall heights > 30 ft Wall sliding assumption / displacement-based

design – not well understood & rotational displacement not considered

Existing charts do not consider seismic setting (e.g., WUS vs. CEUS)

67

Retaining Walls

M-O Application in Homogenous Backfill

If failure plane angle αAE1 < α1/2,M-O solution for PAE1 OKIf αAE1 > α1/2, calculate PAE1and PAE1/2

, use larger value

68

Retaining Walls

Active Earth Pressures with CohesionM-O equations don’t account for cohesion Even small

cohesion (50 psf) give significant reductions in PAE

Charts have been developed based upon c/γH Apply with caution

in design practice due to uncertainties on c

69

Retaining Walls

Active Pressure in Non-homogenous Soil

Use generalized limit equilibrium (GLE) method Standard slope

stability program Handles layers of

soil Handles surface

loads Handles

groundwater

70

Retaining Walls

Passive Earth Pressure

M-O not reliableDeveloped charts using log spiral method Use static passive

pressures for H < 5 ft For H > 5 ft, use charts

from Shamsabadi et al. (2007) δ = φ/2 kpe = f(c/γH)

71

Retaining Walls

Displacement Based DesignSame Newmark approach as for slopes Reduce PGA for wave scattering to define kav

Determine ky

Integrate area under acceleration record above ky

72

Retaining Walls

Wave Scattering Effects

Accounts for spatial incoherency of ground motions Important for taller

walls (H > 20 ft) Conducted QUAD 4M

modeling Different wall heights Range of soil properties Three different seismic

environments

73

Retaining Walls

Types of Seismic Environment

Developed spectral curve shapes to define seismic environments

74

Retaining Walls

Height-Dependent Wave ScatteringDescribed by α factor: kav = α x PGA Use PGA corrected for

site class For Site Class C, D, and

Eα = 1 + 0.01H [0.5β - 1]

whereH = depth of failure surface β = FvS1/PGAα = 1.0 if H ≤ 20 ft

For Site Class A and B –increase computed α by 20%

75

Retaining Walls


NCHRP 12-70 Project (2008) equations for slopes and retaining walls in WUS

log (d) = -1.51 – 0.74 log (ky / α kmax) + 3.27 log (1– ky /α kmax) – 0.80 log (α kmax) + 1.59 log (PGV)[d in inches]

Different though similar equation for CEUS rock sites. See NCHRP 611 report.

Use 0.5 kmax for 1-2 inches of estimated displacement

76

Retaining Walls


Revised NCHRP 12-70 displacement equations & charts

d = f(ky/ α kmax, PGA, PGV)

PGV = 38 FvS1 (mean) or 55 FvS1 (m + σ)

Comparison to existing AASHTO equation

d = 0.087(PGV)2 / kmax g (ky/ kmax)-4

where PGV = peak ground velocity (in/sec)

77

Retaining Walls

MSE Walls : AASHTO 2007

Note: Am = (1.45 - A) APAE = 0.375 Am γs H2

78

Retaining Walls

Design Approach / External Stability

79

Retaining Walls

Design Approach / External Stability

1. Establish initial static design

2. Determine kmax

For AASHTO, use 1000-yr maps for PGA

Adjust PGA for site conditions: kmax = PGAAASHTO x site factor

3. Determine kav

Use α factor to adjust for height: kav = α x kmax

4. Determine PAE assuming kav / 2 (M-O or GLE) Assumes 1-2 inches displacement OK

80

Retaining Walls

Design Approach / External Stability5. Check overturning

e/w ≤ 1/3 C/D for toe bearing pressure ≥ 1 (φ = 0.67)

6. If criteria not met, revise footing dimensions7. If criteria met, check for sliding

C/D ≥ 1 (φ = 1.0)8. If sliding criteria not met, determine ky and

sliding/displacement potential9. Is displacement acceptable or is a redesign

necessary?

Design examples provided in NCHRP Reports

81

Retaining Walls

Acceptable Displacement Strategy

NCHRP 12-70 Specifications1. Allow 50% reduction in kav if 1-2 in. acceptable, or2. Use Newmark methodology to estimate sliding

displacementOwner should evaluate acceptability of estimated displacementFactors to be considered1. Wall location and function2. Wall type3. Wall geometry4. Type of soil5. Implications of wall movement

82

Retaining Walls

Design Approach

Screening for “no seismic analysis” at nonliquefiable sites for retaining walls Sufficient reserve capacity in static design to

preclude need for seismic check – particularly in CEUS

“No seismic analysis” decision depends on slope above wall and level of ground shaking

Backslope Angle Above Wall PGAFlat 0.3g

3:1 0.2g

2:1 0.1g

83

Retaining Walls

Design ApproachSoil property characterization – same as for slope; i.e., Use total stress strength parameters for seismic

loading Include cohesion in estimates where appropriate

% < #200 sieve Max. Apparent Cohesion (psf)

5-15 50

15-25 100

25-50 200

84

Retaining Walls

Design Approach

Seismic earth pressure determination Include wave scattering where appropriate

Reduce seismic coefficient to 0.5kmax for walls that can undergo several inches of permanent movement

Apply seismic active pressure as total uniform pressure load. Don’t use incremental seismic pressure approach

♦ Static earth pressures use effective stress strength parameters versus total stress for seismic loading

♦ Different load and resistance factors for static and seismic loading

85

Retaining Walls

Design Approach

Points of note Gravity and semi-gravity walls Use GLE method to compute active earth pressure load in

complex soil profiles and where groundwater encountered

Determine passive pressure using log spiral method

Nongravity cantilever and anchored walls Use seismic active earth pressure for most cases – sufficient

displacement occurs to develop active pressures

Consider alternate beam column approach to define wall performance Software available (P-Y Wall, L-Pile, COM624, BMCOL)

P- and y-multipliers developed in NCHRP 12-70

86

Retaining Walls

Design ApproachPoints of note (cont.) MSE walls Replace “Am = (1.45 –A) x A” in current AASHTO with

height-dependent scattering factors Restrict inertial force to 0.7H

Soil nail walls No AASHTO provisions

Currently, design follows guidelines in FHWA GEC No. 7 2005 NCHRP Project 24-21 Report may form future

specification section

Two computer codes, GOLDNAIL and SNAIL, are standard-of-practice – both handle seismic case. Use 0.5 α kmax for most designs

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Retaining Walls

Design ApproachFlow chart for analysis approach in Fig. X-2 of Vol. 2

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Slopes, Embankments & Retaining Walls

Concluding CommentsNCHRP Report 611 provides framework for update to AASHTO LRFD Bridge Design Specifications More design checks needed

Are screening levels appropriate? Are proposed methodologies consistent with other numerical

results, model testing, and field experiments?

Further studies and development required in some areas Does shear banding occur in cohesionless soils? How should inertial force in MSE wall be defined? Will soil-structure interaction affect ground motions adjacent to

nongravity cantilever and anchored walls? What is total seismic pressure distribution behind gravity,

cantilever, and anchored walls?

Seismic Hazard Levels - onlinepubs.trb.org

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