Paper No. TS-1-2
Yield Strength Approach to Evaluate the Triggering of Liquefaction for Sloping
GroundAlfonso Cerna-Díaz1
ABSTRACT:The yield strength ratio concept, Su(yield)/σ’vo (Olson & Stark, 2003) and the cyclic
strength ratio CRR (Seed et al, 1984) remain the main approaches of assessing
triggering of liquefaction resistance for sloping ground. The Kα correction factor(Seed, 1983) has been extensively studied for considering the effect of the initialstatic stress on the triggering of liquefaction of sloping ground. Based on a suite ofliquefaction triggering analyses, these most-commonly used cyclic stress methods,Seed et al. (2003)/Cetin et al. (2004) and Idriss and Boulanger (2008), are comparedto the yield strength ratio approach (Olson and Stark 2003; Olson et al. 2006; Mesri
2007; and Olson and Zitny 2012), and the efficacy of the yield strength ratio isdemonstrated. For validation of the comparison, one Mw 7.0 Haiti (2010) earthquake
flow failures cases (North River near Dechapelle), (Olson et al., 2010) was selected toestimate the triggering of liquefaction and post-liquefaction resistance.
INTRODUCTION
Methods to evaluate the triggering of liquefaction in sloping ground (i.e., groundsubjected to a static driving shear stress) were first proposed nearly three decadesago. Because of the limited number of well-documented case histories of liquefaction
in sloping ground, the majority of these methods were based on extending the widelyused cyclic stress approach (Seed and Idriss 1971; Whitman 1971) used to evaluate
the triggering of liquefaction under level ground. Olson and Stark (2003), Olson et al.
(2006), Mesri (2007), and Olson and Zitny (2012) proposed an alternate approach toevaluate sloping ground liquefaction using a yield strength ratio. The yield strength
ratio, su(yield)/σ'vo is a function of the static shear stress ratio [where su(yield) is thepeak, or yield, shear strength mobilized under undrained conditions in contractive
soils and σ'vo is the prefailure vertical effective stress]. If liquefaction is triggered insloping ground, a post-triggering stability analysis is performed using either theliquefied shear strength, su(liq), or the liquefied shear strength ratio, su(liq)/σ'vo for theliquefied soils. Seed and Harder (1990) proposed a widely-used correlations forliquefied (or undrained residual) shear strength, while Terzaghi et al. (1996), Olsonand Stark (2002), Mesri (2007), and Idriss and Boulanger (2008) have proposedcorrelations for su(liq)/σ'vo.

1

Graduate Research Assistant, Civil and Environmental Engineering Department, University ofIllinois at Urbana-Champaign, 205 N. Mathews Ave., Urbana, IL, 61801, email: cernadi2@illinois.edu

The 12 January 2010 Mw 7.0 Haiti earthquake triggered extensive liquefaction
failures (i.e. lateral spreads, bank slumps) along the Gulf of Gonave coastline andalong rivers north of Port-au-Prince, causing considerable damage. Based on tworeconnaissance missions after the earthquake (January/February 2010 and April2010), Olson et al. (2010) documented eight liquefaction case histories. The
geotechnical reconnaissance effort involved surface mapping, dynamic cone
penetration tests (DCPT), hand auger borings, and laboratory index test.
In this study, the methods above to evaluate the triggering of liquefaction insloping ground and post-triggering slope stability are compared using twoliquefaction-induced slope failures triggered by the 2010 Haiti earthquake.
APPROACHES TO EVALUATE LIQUEFACTION OF SLOPING GROUND
The widely-used cyclic stress approach relates the seismic shear stress ratio,τseismic/σ'vo, required to trigger liquefaction (or cyclic resistance ratio, CRR) with theoverburden stress-normalized standard penetration test (SPT) resistance, (N1)60. From
its original form (i.e.,Seed and Idriss 1971; Whitman 1971), numerous updates havebeen published as new field case histories become available. In addition, recentstudies have proposed modifications to estimating τseismic/σ'vo, e.g., revisions to themagnitude scaling factor (MSF) and depth reduction factor (rd), and have introduced
probabilistic tools (e.g., Cetin et al. 2004; Idriss and Boulanger 2008). As this method
was developed for level ground, additional corrections have been proposed to apply
the approach to sloping ground, including a high overburden stress (Kσ; Youd et al.
2001; Seed et al. 2003; Idriss and Boulanger 2008) and static shear stresses correction(Kα; Seed 1983; Rollins and Seed 1990; Seed and Harder 1990; Harder andBoulanger 1997; and Boulanger 2003). Using this approach, the sloping-groundliquefaction resistance, or yield strength ratio, can be estimated as:(1)௦ೠ (௬௜௘௟ௗ)ఙᇱೡ೚ఛ= ೞ೟ೌ೟೔೎ + ‫ܭ‬ఈ ‫ܭ‬ఙ ‫ܴܴܥ‬ఙᇱೡ೚As an alternative, Olson and Stark (2003) back-analyzed 10 static loading- anddeformation-induced liquefaction flow failures case histories to evaluate the yieldstrength ratio [su(yield)/σ'vo] mobilized at the time of failure. Olson et al. (2006)
collected a large database of published isotropically- and anisotropically-consolidatedundrained triaxial compression tests, as well as direct simple shear and rotational
shear tests with a monotonically-applied drained shear stress prior to undrainedloading. Based on these laboratory data, Olson et al. (2006) proposed a family ofyield strength ratio correlations related to the static shear stress ratio, τstatic/σ'vo.
Recently, Olson and Zitny (2012) performed a suite of ring shear tests with amonotonically-applied drained shear stress prior to constant volume loading.
Combining these data with those from Olson et al (2006), Olson and Zitny (2012)
proposed the following relationship among (N1)60, su(yield)/σ'vo, and τstatic/σ'vo (aswell as a similar relationship based on cone penetration test tip resistance).

࢙࢛ (࢟࢏ࢋ࢒ࢊ)

(2)

࣌ᇱ࢜࢕࣎

૙.૙૙૛

= ࢙࢚ࢇ࢚࢏ࢉ + ቆ ࢙࢚࣎ࢇ࢚࢏ࢉ ቇ (ࡺ૚ )૟૙
࣌ᇱ࢜࢕

࣌ᇲ࢜࢕

Terzaghi et al. (1996) and Mesri (2007) approximated the level-groundliquefaction resistance relationship [defined as su(yield)/σ'vo for level ground]proposed by Seed et al. (1985) as a linear function of SPT blow count up to (N1)60 =20. Incorporating the Kα correction for sloping ground proposed by Rollins and Seed(1990), Terzaghi et al. (1996)/Mesri (2007) proposed the following relationshipamong (N1)60, su(yield)/σ'vo, and τstatic/σ'vo.
௦ೠ (௬௜௘௟ௗ)

(3)

ఙᇱೡ೚ఛ

ఛ

ೞ೟ೌ೟೔೎= ఙᇱ+ (0.011)(1 − 2 ೞ೟ೌ೟೔೎)(ܰଵ )଺଴
ఙᇱ
ೡ೚

ೡ೚

SLOPE FAILURE TRIGGERED BY 2010 HAITI EARTHQUAKE
Case 1. Slope failure near Dechapelle
Case 1 involved the failure of a 7-m high riverbank. Figure 1 presents the prefailure geometry, approximate phreatic surface, and dynamic cone penetration test
resistance, (N1)60,DCPT profiles, reproduced from Olson et al. (2010). The soil consists
chiefly of a fairly homogeneous brown and gray, fine- to medium- grained sand withtrace non-plastic silt (D50 ~ 0.3 mm), although zones of stiff fine-grained soil wereencountered above the watertable. As discussed by Olson et al. (2010), below thewatertable, (N1)60,DCPT in the sand are on the order of 7 to 15, suggesting that thislayer liquefied during the earthquake.
(N1)60,DCPT
Banana tree grove

0Approximate
pre-earthquake
geometry

10102030

40

501

Approximate
post-earthquake
geometry

66o05Brown and gray, fine- to mediumgrained SAND with trace silt

DECH-2

DECH-1-10(N1)60,DCPT
050-2-501020Distance (m)30DECH-1
DECH-2-3Figure 1 - Profile of slope failure at North River near Dechapelle (Case 1) and (N1)60 profile(from Olson et al. 2010)

COMPARISON OF SLOPING GROUND TRIGGERING ANALYSESThe authors performed liquefaction triggering analyses for the the slope failure
described above. The approaches are as follows.
Method 1. Level-ground cyclic stress method with Kα and Kσ corrections using aprobability of liquefaction of 20% (Seed et al. 2003; Cetin et al. 2004; Harder andBoulanger 1997).
Method 2. Level-ground cyclic stress method with Kα and Kσ corrections (Idrissand Boulanger 2008).
Method 3. Yield strength ratio method (Olson and Stark 2003; Olson et al. 2006;
Olson and Zitny 2012).
Method 4. Yield strength ratio method (Terzaghi et al. 1996; Mesri 2007).

Elevation (ft)Elevation (m)Triggering analyses were performed for the slip surfaces shown in Figure 2 forCase 1. Strengths associated with non-liquefiable soils were selected as the fullymobilized drained or undrained estimated from SPT-based empirical correlations.
Table 1 summarizes the parameters for the triggering analyses.

Figure 2 - Failure surfaces analyzed for Case 1.
Table 1. Average parameters for analysis of slope failures (seismological parametersfrom Olson et al. 2010).

Case(N1)60
FC (%) D50 (mm)τstatic/σ'vo σ'vo (kPa) Mw pga (g)
110
<50.3
0.38
56
70.17
For Case 1, Methods (1), (3), and (4) predict that liquefaction would be triggered
along the entire sliding surface (Fig. 3), while Method (2) predicts that liquefaction isnot triggered, but the factors of safety against liquefaction are not much above unity.
Table 2. Factors of safety against liquefaction (FSliq) using average input parametersfrom Table 1.
FSliq
Case
(1)
(2)
(3)
(4)
1
0.90 – 1.00 1.08 – 1.21 0.83 – 0.93 0.77 – 0.86
COMPARISON OF POST-TRIGGERING STABILITY ANALYSESThe authors performed post-triggering analyses for the slope failure describedabove as each case had several segments of the critical slip surface with FSliq < 1. Theapproaches are as follows.
Method 1. Liquefied segments were assigned liquefied shear strengths (residualundrained shear strength) from Seed and Harder (1990). The lowerbound, 33rd
percentile, and average of the Seed and Harder (1990) were considered. Nonliquefied segments within the estimated liquefiable layer were assigned a fraction of
the drained strength (Seed and Harder 1990). For FSliq ≤ 1.1, the soil was assigned theresidual strength. For FSliq ≥ 1.4, the soil was assigned 75% of the drained shearstrength. For 1.1 ≤ FSliq ≤ 1.4, the soil strength was interpolated between the residual
strength and 75% of the drained strength.
Method 2. Liquefied segments were assigned liquefied shear strengths based on
the liquefied shear strength ratio correlations from Idriss and Boulanger (2008). The
correlations considering some void redistribution (upperbound) and no void
redistribution (lowerbound) were considered. No guidance was provided for soils in
the liquefied zone that were not predicted to liquefy. Therefore, the authors employed
the approach in Method (1) for these segments.
Method 3. Liquefied segments were assigned liquefied shear strengths based on
the average liquefied shear strength ratio correlations from Olson and Stark (2002).
Nonliquefied segments within the liquefiable zone were assigned their yield shear
strength ratios (Olson and Stark 2003).
Method 4. Liquefied segments were assigned liquefied shear strengths based on
the liquefied shear strength ratio correlations from Mesri (2007). Nonliquefied
segments within the liquefiable zone were assigned their mobilized yield shear
strength ratios (Mesri 2007).

For Case 1, Methods (3) and (4) yielded similar factors of safety against slope
stability (FSFlow) of approximately 0.885 and 0.88, respectively. Method (1) yielded awider range of FSFlow, with FSFlow = 0.85, 0.92, and 0.96 for the lowerbound, 33rd
percentile, and average residual strength correlations, respectively. Only Method (2)predicts FSFlow greater than unity, with FSFlow = 1.03 and 1.17 for the lowerbound andupperbound correlations, respectively.

CONCLUSIONS AND RECOMMENDATIONSThis study tested four methods to evaluate triggering of liquefaction and post
triggering stability using one flow failures where the seismic/dynamic demand
induced liquefaction of the sandy soils below the water table. From the analysis, it isverified that Olson and Zitny (2012), Mesri (2007) and Seed et al. (2003),
successfully predict liquefaction triggering in each case, being Mesri (2007) moreconservative than Olson and Zitny (2012) and Seed et al. (2003). Idriss andBoulanger (2008) appeared to be the least conservative method as it does not predict
the triggering of liquefaction for all variations between potential failure surfaces andpenetration resistance in both cases.
Based on post-triggering stability analyses, Olson and Stark (2002) and Mesri (2007)
successfully predicts the flow failure in each case, being Mesri (2007) the lessconservative since it includes the effect of the initial static shear stress in its liquefied
correlation. Seed and Harder (1990) does not predict the flow failure for both cases
and turned out to give the most unconservative result for the flow failure caseassociated with the lowest prefailure vertical stress (23kPa) by a factor of two,
considering its lower bound recommendation. Idriss and Boulanger (2008) does notpredict the flow failure for each analyzed case. However, it seems to predict
reasonably well the flow failure for the case with the highest prefailure vertical stress(56kPa). On the other hand, Idriss and Boulanger (2008) Sr/σ’vc lower and upperbound for considering the significance of void redistribution, was found to be criticalin the estimation of the flow failure factor of safety for (N1)60≥14, as its flow failure
prediction gives values of factors of safety less and more than one, depending if theSr/σ’vc lower or upper bound is used, respectively.
From the study, it is observed that:(1) Olson and Zitny (2012), Mesri (2007) and Seed et al. (2003) approaches
provide better estimates to evaluate the triggering of liquefaction.
(2) Olson and Stark (2002) and Mesri (2007) approaches provide better estimatesto evaluate the post-triggering stability. Seed and Harder (1990) should not be
used for projects involving relatively low confining stress (i.e. σ’o<50kPa),
and its use for higher confining stresses should be limited to its lower boundrecommendation. Analogously, Idriss and Boulanger (2008) residual shear
strengths are not conservative for moderate confining stress (i.e. σ’o>50kPa)
and its used for lower confining stresses should be limited to its lower bound.

Table 3. Factors of safety against flow failure
MethodSeed & Harder (1990)
Case1

FailureSurface

Circular

Lower Boundary(N1)60710
130.81 0.85 0.94

1/3(N1)60710130.86 0.92 1.02

Average(N1)60710130.89 0.96 1.07

Olson & Stark(2002)

Mesri (2007)(N1)60710130.84 0.85 0.86

(N1)60710130.87 0.88 0.89

Idriss & Boulanger (2008)
Lower Boundary(N1)60710130.84 1.03 1.17

Upper Boundary(N1)60
710131.17 1.18

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