1

University of California, DavisDepartment of Civil & Environmental Engineering

Residual shear strengthof liquefied soils

Ross W. BoulangerTRB 2007

Lab testing of field samples:

Frozen sampling techniques (e.g., Robertson et al. 2000)

T b li ith ti ( C t 1975 P l t l 1985)

Evolution of procedures for estimating Sr

Tube sampling with corrections (e.g., Castro 1975, Poulos et al. 1985)

Case history based correlations

Back-analyses of flow slide failures

Initially by Seed (1987); modifications & updates by others (e.g., Seed & Harder 1990, Wride et al. 1999, Olson & Stark 2002)

Void redistribution

Articulated by Whitman (1985); advances by physical & analytical modeling (e.g., Kokusho 2000, Kulasingam et al. 2004, Malvick et al. 2004, Naesgaard et al. 2006)

Seed (1987) noted that case history based correlations implicitly account for void redistribution

2

Recommend relationships for Sr /σ'vo based on reviews of:

Case history studies

This presentation

Laboratory testing studies

Void redistribution studies

Emphasis on providing rational guidance for extrapolation beyond case history data.

Idriss & Boulanger (2007). "Residual shear strength of liquefied th SSsoils," 27th USSD Annual Meeting, March. Preprint at:

http://cee.engr.ucdavis.edu/faculty/boulanger/PDFs/2007/Idriss_Boulanger_USSD_2007_preprint.pdf

Back-analysis

Post-earthquake stability analysis:

Upper bound Sr from undeformed geometry

Lower bound S from final deformed geometryLower bound Sr from final deformed geometry

Interpolated Sr depends on sliding inertia, evolving geometry, intermixing (soils & water), other factors

Example: Olson & Stark (2002) results for LSF dam:

(Sr)upper ≈ 36 kPa

(Sr)lower ≈ 5 kPa

(Sr)best ≈ 19 kPa

(Seed 1987)

3

Group 1: 7 cases with adequate SPT/CPT & geometric details

Case histories

Groups 2 & 3: 11 cases with either adequate SPT/CPT or geometric details, but not both

Group 4: 17 cases with inadequate details

Calaveras dam – CA DSOD

Lower San Fernando dam – CA DSOD

Case History(N1)60cs-Sr *

/ / FC **

Residual Strength, Sr (kPa) published byσ'vo

(kPa)***Number Structure Seed (1987) Seed & Harder (1990) Olson & Stark

(2002)

1 Wachusett Dam – North Dike --/--/7 5–10 / 5 -- -- 16.0 151.2

2 Lower San Fernando Dam 15/13.5/11.5 5–90 / 25 35.9 19.2 18.7 166.7

3 Fort Peck Dam 11/10/8.5 55 / 50 28.7 16.8 27.3 351.5

Published case histories of liquefaction flow failures

4 Calaveras Dam 12/12/8 10–>60 / 60 35.9 31.1 34.5 307.5

5 Hachiro-Gata Road Embankment --/--/4.4 10–20 / 15 -- -- 2.0 32.1

6 Lake Ackerman Highway Embankment† --/--/3 0–5 / 0 -- -- 3.9 51.5

7 Route 272 at Higashiarckinai --/--/6.3 20 / 20 -- -- 4.8 49.3

8 River Bank, Lake Merced 5/6/7.5 1–4 / 3 4.8 4.8 6.9 65.7

9 Kawagishi-cho 4/4/4.4 0–<5 / 3 5.7 5.7 5.3 70.6

10 Mochi-koshi Tailings Dam – Dike 2 6/5/2.7 >60–85 / 85 12.0 12.0 5.4 52.2

11 La Marquesa Dam – U/S Slope †† --/6/4.5 30 /30 -- 9.6 3.1 43.6

12 La Marquesa Dam – D/S Slope ††† --/11/9 20 / 20 -- 19.2 5.3 47.9

13 l /4/3 1 / 1 9 6 4 8 3 813 La Palma Dam †††† --/4/3.5 15 / 15 -- 9.6 4.8 37.8

14 Uetsu Railway Embankment 3/3/3 0–2 / 2 1.7 1.9 1.7 61.3

15 Solfatara Canal Dike 5/4/4 <5–8 / 7 6.2 2.4 2.4 29.9

16 Koda Numa Railway Embankment 3/3/3 13 / 13 2.4 2.4 1.2 23.2

17 Shibecha-cho Embankment --/--/5.6 12–35 / 25 -- -- 5.6 64.7

18 Sheffield Dam 6/6/5 25–48 / 40 2.4 3.6 3.6 68.4

Cases 1 – 7 fit into Group 1, which consists of Case Histories with SPT and/or CPT measurements and reasonably complete geometric details.Cases 8 – 13 fit into Group 2, which consists of Case Histories with SPT and/or CPT measurements, but geometric details are incomplete.Cases 14 – 18 fit into Group 3, which consists of Case Histories with estimated SPT and/or CPT, but geometric details are reasonably complete.

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Values of Δ(N1)60-Sr recommended by Seed (1987)

Fines Content, FC(% passing No. 200 sieve) Δ(N1)60-Sr

10 125 250 475 575 5

0.4

Correlation of Sr /σ'vo to (N1)60cs-Sr

Group 2 & Group 3 (see text for more details)

Group 1 -- Case histories with an adequate amountof in-situ measurements (e.g., SPT, CPT) andreasonably complete geometric details

Seed (1978)

Seed & Harder (1990)

Olson & Stark (2002)

ar S

tren

gth

Rat

io, S

r/ σ' vo

0.2

0.3

Recommended Curvefor conditions where

void redistribution effectsare expected to be negligible

Equivalent Clean Sand SPT Corrected Blowcount, (N1)60cs-Sr

0 5 10 15 20 25 30

Res

idua

l She

a

0.0

0.1

See Figure 4 for Legend

Recommended Curvefor conditions where

void redistribution effectscould be significant

5

120

D = 52%

Vaid & Sivathayalan (1996)Frazer River sand, water pluviated

Undrained direct simple shear testsσ'vc = 200 kPa

Undrained stress-strain behavior

Shea

r Str

ess,

τ (

kPa)

40

80

DR = 52%

DR = 43%

DR = 35%

DR = 31%

Shear Strain (%)0 4 8 12 16 20

0

Shear resistance atphase transformation

R

vc

0.6

Tests with σ'vc = 50, 100, 200 & 400 kPa

Vaid & Sivathayalan (1996); Vaid et al (1996)Frazer River sand, water pluviated

Undrained direct simple shear tests 20% shear strain

Normalized shear resistance

Shea

r Res

ista

nce

Rat

io, τ

/ σ' v

0.2

0.4

At 20% shear strain

At phase transformationAt 10% shear strain

At phase transformationvc , ,

Tests with σ'vc = 200 kPa

10% shear strain

Phase transformation

Relative Density, DR (%)0 20 40 60 80

S

0.0

These & other results suggest undrained DSS strengths will exceed drained strengths (tanφ' ≈ 0.6) at DR ≥ 50 to 60% for σ'vo ≤ 400 kPa

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Sr /σ'vo at QSS relatively independent of σ'vo up to 400 kPa

Effect of confining stress

Yoshimine et al. (1999) – QSS strengths

For σ'vo > 400 kPa, recommend using state corrected N1ξ (Boulanger 2003) rather than N1 in Sr /σ'vocorrelations

yer

θ φ′pk

Void Redistribution

HtConfining Layer

HbLiquefiable Layer

Δu

hd

hc

Impermeable Base Layer

ru,r @ φ′cv

Localization if Vcon > Vdil (Boulanger & Truman 1996, Malvick et al. 2006)

Related studies (Yang and Elgamal 2002, Sento et al. 2004, Yoshimine et al. 2006, Naesgaard et al. 2006)

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NEVADA SAND SILT

Water Surface

Centrifuge model (Malvick et al. 2004)

Nevada sand, DR ≈ 35%; 9-m radius centrifuge

COARSE SAND

SILT

0 100 200 mm

9 m

7.2 m

0 4.5 9.0 m

model scale

prototype scale

Pore Pressure TransducerAccelerometerDisplacement Transducer

SILT

Displacement Transducer

point point A

Midslope PPT array

20

-20

0

0P9

P7

P8

A B C D E

0

0.5

1

1.5

2

Dis

plac

emen

t of

Slid

e M

ass

(m)

FEDC

BA

point C

12

16

arra

y (m

)

PP

Ts

P6P7

P8

P9

Silt

(a) Array 1Δu in an infinite slope, θ = 18.3° and φ′mob = 33°

0

20

0

20

0

cess

Por

e P

ress

ure

(kP

a)

0

20

20P3

P4

P5

P6

P70 400 800

Time After End of Shaking (s)

02000 2800

point D

-10 0 10 20 30 40 50 60Excess Pore Pressure (kPa)

0

4

8

Pos

ition

alo

ng

P1

P2

P3

P4P5P6

AC BDEF

0 400 800 1200 1600Time after end of shaking (s)

Exc

0

0

20

0

20

40

P1

P2

P3

8

Role of DR (Kulasingam et al. 2004)

1-m radius centrifuge tests

6 4 m high slope

1.5

2

Dis

plac

emen

t (m

) Motion AMotion B (after A)Motion C (after A & B)Motion C (alone)

6.4-m high slope (prototype)

Sand initially dense of critical for all models

0 20 40 60 80 100Initial Relative Density (%)

0

0.5

1In

crem

enta

l Hor

iz. D

Void redistribution summary

Degree & timing of void redistribution depend on: pre-earthquake soil state (DR, σv

′) & properties (cyclic resistance, compressibility), physical geometry (stratigraphy, layer thickness, slope height, slope angle), permeability contrasts, ground motion characteristics (level of shaking, duration).

With significant void redistribution:Sr /σ'vo is not uniquely correlated to pre-earthquake stater vo

Sr /σ'vo can be small as the soil shears and progressively loosens under a net inflow of water and a sustained low value of σ'v

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Young NC slightly plastic silts (say PI ≈ 7):

At transition between soils that should be analyzed using procedures developed for clays versus those for sands

Slightly plastic silts

procedures developed for clays versus those for sands (Boulanger and Idriss 2006)

Undrained strengths, su /σ'vo ≈ 0.22 (e.g., Ladd 1991)

Sensitivities, St ≈ 2 to 4 common

Remolded strengths, sur /σ'vo ≈ 0.05 to 0.11

C f fConsistent with findings for slightly plastic silts and sandy silts (e.g., Vasquez-Herrera et al. 1990, Castro and Troncoso 1989, Finn et al. 1991)

S r/ σ' vo

0.4

Recommended Curvefor conditions whereid di t ib ti ff t

Design relationships for Sr /σ'vo

dual

She

ar S

tren

gth

Rat

io, S

0.1

0.2

0.3 void redistribution effectsare expected to be negligible

Recommended Curvefor conditions where

void redistribution effectscould be significant

Equivalent Clean Sand SPT Corrected Blowcount, (N1)60cs-Sr

0 5 10 15 20 25 30

Res

id

0.0See Figure 4 for Legend

If σ'vc > 400 kPa, use N1ξ rather than N1

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Relationships for Sr /σ'vo of nonplastic soils recommended based on reviews of case histories, lab studies, and void redistribution studies.

Summary

redistribution studies.

Comparable to values by other investigators for (N1)60cs-Srless than about 12.

Provides guidance at (N1)60cs-Sr greater than about 14.

Curves for cases with or without void redistribution.

Distinguishing between these two cases may requireDistinguishing between these two cases may require appropriately detailed field and analytical studies.

University of California, DavisDepartment of Civil & Environmental Engineering

Questions?

Ross W. Boulanger

11

0 0.5 1 1.5Cξ

0

State normalization of penetration resistance

N1ξ = Cξ N1

6

4

2

ectiv

e st

ress

, σv′/

P a

(N1)60=40

(N1)60=30

10

8

6

Verti

cal e

ffe (N1)60=20

(N1)60=10

(N1)60=4

60

80

100

ear s

train

(%)

Range estimated by Seed et al. (1985),based on data by Tokimatsu & Yoshimi 1984)

Relation for estimating lateral displacement index (LDI)

Triggering and strain potential

0.4

0.5

0.6

io (C

SR

)

Maximum shear strains, γmax 100% 50% 10%

5%3½%

1%

20%

0

20

40

Lim

iting

she based on data by Tokimatsu & Yoshimi 1984)

and recommendations of Seed (1979).

0 10 20 30 40Modified Standard Penetration - (N1 )60cs

0

0.1

0.2

0.3

Cyc

lic S

tress

Rat

i

CRR recommended by Idriss & Boulanger (2004)

for clean sands

12

, Sr (

kPa)

40

50

Group 2 & Group 3 (see text for more details)

Group 1 -- Case histories with an adequate amountof in-situ measurements (e.g., SPT, CPT) andreasonably complete geometric details

Correlation of Sr to (N1)60cs-Sr

ned

Res

idua

l She

ar S

tren

gth,

10

20

30

Seed (1978)

Seed & Harder (1990)

Olson & Stark (2002)

Relationship for

Equivalent Clean Sand SPT Corrected Blowcount, (N1)60cs-Sr

0 4 8 12 16 20

Und

rain

0

10 pEstimating Residual StrengthUsing Median Measured SPT

Form was consistent with critical state concepts: Sr ⇔ f(e) ⇔ f(N1)

S r/ σ' vo

0.4

Recommended Curvefor conditions where

void redistribution effects

Correlation of Sr /σ'vo to (N1)60cs-Sr

sidu

al S

hear

Str

engt

h R

atio

, S

0.1

0.2

0.3 void redistribution effectsare expected to be negligible

Recommended Curvefor conditions where

void redistribution effectscould be significant

Equivalent Clean Sand SPT Corrected Blowcount, (N1)60cs-Sr

0 5 10 15 20 25 30

Res

0.0See Figure 4 for Legend

Form is guided by lab testing & void redistribution studies

13

σ'vc

0.6

Tests with σ'vc = 50 to 300 kPa

Yoshimine et al (1999)Toyoura sand, dry pluviationUndrained simple shear tests

Normalized shear resistance

Shea

r Res

ista

nce

Rat

io, τ

/ σ

0.2

0.4

At phase transformation

Range for phasetransformation

Relative Density, DR (%)0 20 40 60 80

0.0

transformation

Trends suggest that undrained DSS strengths exceed drained strengths (tanφ' ≈ 0.6) at DR ≥ 50 to 60% and σ'vo ≤ 400 kPa