1

DESIGN CONSIDERATIONS

1. Assessment of liquefaction risk and subsequent ground settlement and effects of preloading on them

2. Effects of preloading on seismic motion

3. Computer program implementing 1, 2

4. Conclusions

2

1. Assessment of liquefaction risk and subsequent ground settlement and effects of preloading on them

The liquefaction risk is expressed by the liquefaction factor of safety coefficient FSlique, where: τcyc,N SRN FSlique = -------- = -------- (1) τcyc SRwhere τcyc and SR are the cyclic stress exerted and the respective cyclic stress ratio that is the ratio of the cyclic stress to effective stress at a certain depth, and τcyc,N and SRN are the respective values causing liquefaction in N cycles.Due to uncertainties mainly in the assessment of cyclic soil strength, the Eurocode recommends that the liquefaction safety coefficient should take the value of 1.25.

3

Usually, the liquefaction factor of safety is calculated versus depth. The following equation can be used to estimate the maximum shearing stress versus depth: τmax(z) = αmax rd σν / g (2a)where αmax is the maximum value of the horizontal seismic acceleration exerted at the surface, σν is the total vertical stress and rd is a stress reduction coefficient gradually decreasing with depth z. For the coefficient rd an empirical expression has been proposed by Ishihara (1993):rd = 1 - 0.015z (2b)

4

In an earthquake, the shearing oscillation exerted is not uniform. To use equation (2), the non uniform cycles of the oscillation exerted are converted into uniform cycles as: (a) the value of τcyc and the respective value of SR are determined by the maximum value of the cyclic shearing stress exerted, τcyc-max and SRmax, multiplied times the coefficient 0.65 and (b) the number of equivalent uniform lοading cycles, Ν, is equal to the cycle number of the not uniform excitation with a magnitude 0.65 times the maximum.

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Assessment of cyclic strength Fig. 1 gives the cyclic strength for an earthquake with a magnitude of Μ=7.5, corresponding to about 15 uniform cyclic loading cycles and for sand with or without fine grains, as a function of value (Ν1)60. Coefficient (Ν1)60 that is corrected for depth SPT index is taken from the number of strokes of the standard penetration test (SPT) in the examined depth, Ν, as follows:(Ν1)60 = Ν CN with CN = (Pa/σ΄v)0.5 (3)where σ΄v is the active stress due to the overlying soils, Pa is the atmospheric pressure (=1Kg/cm2).

Fig. 1 Cyclic strength ratio for an earthquake M=7.5 as a function of N1 for sand or silt.

The presence of fine grains in sandy soils affects the number of resistance strokes in a standard penetration (SPT) and the cyclic soil strength and should be taken into account for assessing liquefaction strength. This is done in the diagram of Fig.1 by selecting the curve with the actual fines content. Between curves interpolation is applied.

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For the assessment of cyclic strength in an earthquake with M=7.5R through the CPT test the corrected tip resistance qc1=qc1N defined by: qc1=qc Cq with Cq = (Pa/σ΄v)0.5 (4)is employed. Then the diagrammatic relation shown in Fig.2 is used. Fines content varies between 0 and 35% and between the limiting curves interpolation is applied. Fig. 2 Cyclic strength ratio for an earthquake

M=7.5 as a function of qc1 for pure and silty sand.

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The propagation velocity of shearing waves, Vs, measured through geophysical methods is an additional useful means for assessing cyclic soil strength. To start with, measured speeds Vs are corrected with depth on the basis of the active vertical stress of the overlying soil σ΄v, as follows:Vsl = Vs (Pa/σ΄v) 1/n (5)where Pa is the atmospheric pressure and coefficient n takes, in accordance with the Εurocode, the value of 4.

Fig. 3 Cyclic strength ratio for an earthquake M=7.5 as a function of corrected shear wave velocity Vs1.

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Finally, an earthquake with a magnitude Μ, smaller or greater than 7.5R, gives a cycle number Ν with an acceleration equal to 0.65 times the maximum, which may be greater or smaller than the 15 cycles of an earthquake with M=7.5, and consequently with a different cyclic strength ratio SRN. Corrective coefficients presented by Idriss and Boulanger (2004) for soil cyclic shear stress ratio are given in table 1.

Table 1 Corrective coefficients of cyclic stress ratio for earthquake magnitude

Magnitude of Earthquake Μ 5 5.5 6 6.5 7 7.5 8 8.5 SRM/ SRΜ=7.5R 1.73 1.56 1.38 1.22 1.13 1.0 0.9 0.86

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Prediction of liquefaction-induced settlement

A method for predicting volumetric deformation in saturated sand has been suggested by Ishihara (1993). Volumetric deformation is assessed from (a) the relevant density, in accordance with the value (Ν1)60 in the standard penetration test or the value qc1 in the cone penetration test and (b) the liquefaction factor of safety.

Fig. 4 Chart for determination of the post-liquefaction volumetric strain as a function of factor of safety

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Effects of preloading on liquefaction

Results of the project showed improvement of soil mechanical properties expressed as increase of (N1)60 index value, qc1 and Vs1. This explicitly means that:

PRELOADING INCREASES THE CYCLIC

STRENGTH OF THE SOIL.

In particular, the following equation has been proposed predicting the increase in cyclic liquefaction strength induced by preloading:

SR15-a / SR15-b = PR 0.04/SR15-b (6)

where SR15-a, SR15-b is the cyclic strength after and before preloading respectively and PR is the preloading ratio

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The effects of preloading on the amplification of the seismic motion were studied by an extensive parametric analysis study.The seismic response in free field condition is usually computed by the 1-dimensional equivalent-linear elastic method of analysis. In the present study, the program EERA, which is functioning at environment Windows EXCEL software is used.The seismic response in the free field of soils is affected by: (a) the soil profile defined as the shear wave velocity (Vs) and unit weight (γ) versus depth, (b) the applied seismic motion, (c) the shear velocity of the underlying rock and (d) the change in the shear modulus and the damping coefficient with shear strain.Regarding the soil profile, (i) the soil type and density, (ii) the effective stress level, which at given depth is affected by the depth of the water table, (iii) the depth of the underlying rock and (iv) the overconsolidation ratio of the soil are important parameters.In the present study three types of sands and three types of clays are considered. Regarding the sand types, three relative densities are considered: Dr equal to 0.2, 0.5 and 0.8. Regarding the clay types, the three cases considered are normally-consolidated clays of small, of medium and of high plasticity.Two water table depths were considered: at 2 and 10m.

2. Effects of preloading on seismic motion

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7 different depths of bedrock are considered: db= 5, 10, 15, 20, 30, 45, 60m.

In order to investigate the effect of preloading, preloading is applied, as usually in practice, as an embankment which is placed temporarily at the top of the soil. In addition to the case without preloading, two cases of preloading are assumed with embankment height (h) 5 and 11m.

Fig. 5 gives schematically the cases considered.

bedrock

Sands Dr = 0.2, 0.5, 0.8

Clays WL=15 PI=25, WL=25 PI=50, WL=35 PI=80

water level

Embankment

h=0, 5, 11 m

db = 5, 10, 15, 20, 30,45, 60 m

z = 2, 10 mw

Fig. 5 Embankment – soil cross-section with the full range of values of design parameters.

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For all these 12X7X3=252 cases, the following seismic motions were applied at the bedrock: Aigion 15/6/1995, Friuli-San Rocco 15/9/1976, Kozani 13/5/1995, Umbria and Itea 1997, typical for Europe . To further extend the range of the applied seismic motions, the accelerograms of Aigion 15/6/1995 and Friuli-San Rocco were applied after being multiplied by a factor of 3.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 1.0 10.0

Period (sec)

PS

Ab (

g)

Aigion

Friul i xx

Friul i yy

kozani xx

kozani yy

Umbria xx

Umbria yy

Itea xx

Fig. 6 Response spectra of considered seismic motions.

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The shear wave velocity of the bedrock (Vs-b), according to typical values of rock, was taken equal to 1500m/s and 900m/s.The change in the shear modulus and the damping coefficient with shear strain, was taken according to the largely used and validated curves in terms of the Plasticity Index (PI) by Vucetic and Dobry. Furthermore, considering recent findings where the relationships depend on stress level, the Darendeli equations were applied.

Fig. 8 Shear modulus variation as a function of cyclic shear strain for a range of stresses.

Fig. 7 Shear modulus variation as a function of cyclic shear strain for a range of Plasticity Index values.

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The shear velocity variation with depth for the different soils, as well as the effect of preloading on this variation were estimated using well-known soil mechanics relationships. Performance of the analyses and the study of the results gave the following functional relation for the ratio of maximum acceleration after and before preloading with respect to the embankment height h:

amax-t / amax-t-h=0 = - h Aμd +1 (7)

where h is the height of the preload embankment in [m] and A=APGA is a factor that depends on soil type and depth of the soil layer as indicated in the table below:

Table 2. Proposals for the A for design. Sands Clays db ≤ 7.5m 7.5m< db≤ 30m db > 30m db ≤ 12m 12m < db ≤ 30m db > 30m Mean-Std 0.005 0 0.003 0.008 0.005 0.007

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Furthermore, based on the results of liquefaction analyses, it is proposed that the decrease of amax induced by preloading should vary linearly from

the surface value at depth d=0 to zero at depth d equal to 3.5 m. This is expressed in equ. (7) by the depth coefficient μd given by:

μd = (3.5 - d) / 3.5 d≤3.5m(8)

μd = 0 d>3.5m

It is observed that

PRELOADING REDUCES THE SEISMIC MOTION

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3. Computer program

It is useful to implement the equations (a) assessing the pre-improvement liquefaction risk and subsequent ground settlement and (b) giving the effect of preloading on liquefaction risk and subsequent ground settlement in a computer program easily accessible by the practicing engineer. In order to achieve this, the rules given in graphical form in section 1 were fitted using empirical equations.

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Fig. 9a gives the cyclic strength in terms of fines content and N1 in equation form, assuming an exponential fit. Fig. 9b gives the parameters of the exponential approximation in terms of the fines content (f) assuming linear variation. In particular, the following equations best fit the results SR15=a1exp(a2*N1) (9a)wherea1= 0.051 f +0.068 (9b)a2=0.062 f +0.059 (9c)It can be observed that the coefficient of correlation of all three equations is very close to unity. This indicates good precision of the proposed equations.Fig. 9c gives the response predicted by equations (9) It can be observed that the obtained curves in terms of N1 are reasonable, as they (i) do not cross each other in terms of fines content, and (ii) are equivalent with those of Fig. 1 for the specified fines content.

Fig. 9 Cyclic strength curves as function of N1 with parametric variation of fines content defined on basis of experimental results.

(a) (b) (c)

y = 0.0585e0.0682x

R2 = 0.9941

y = 0.0809e0.086x

R2 = 0.9868

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

N1

SR

15

f=0

f=0.15

f=0.35

Expon. (f=0)

Expon. (f=0.35)

y = 0.0514x + 0.068

R2 = 1

y = 0.0629x + 0.059

R2 = 1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 0.1 0.2 0.3 0.4

f

a1

, a2

a1

a2

Linear (a2)

Linear (a1)

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40

N1

SR

15

f=0 0.1

0.2 0.3

0.35

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(a) (b) (c)

y = 0.0393e0.014x

R2 = 0.9814

y = 0.0434e0.0472x

R2 = 0.9953

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200

qc

SR

15

f=0

f=0.35

Expon. (f=0)

Expon. (f=0.35)

y = 0.0943x + 0.014

R2 = 1

y = 0.0114x + 0.039

R2 = 1

0

0.01

0.02

0.03

0.04

0.05

0 0.1 0.2 0.3 0.4

f

c1

, c2

c1

c2

Linear (c2)

Linear (c1)

0

0.1

0.2

0.3

0.4

0.5

0 50 100 150 200 250

qc1

SR

15

f=0 0.1

0.2 0.3

0.35

Fig. (10a) gives the cyclic strength in terms of fines content and CPT in equation form, assuming an exponential fit. Fig 10b gives the parameters of the exponential approximation in terms of the fines content (f) assuming linear variation. In particular, the following equations best fit the results: SR15=c1exp(c2*qc1) (10a)wherec1= 0.011 f+0.039 (10b)c2=0.094 f+0.014 (10c)It can be observed that the coefficient of correlation of all three equations is very close to unity. This indicates good precision of the proposed equations.Fig. 10c gives the response predicted by equations (10). It can be observed that the obtained curves in terms of f are reasonable, as they (i) do not cross each other in terms of fines content, and (ii) are equivalent with those of Fig. 2 for the specified fines content.

Fig. 10 Cyclic strength curves as function of qc1 with parametric variation of fines content defined on basis of experimental results.

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Fig. 11 gives the cyclic strength in terms of Vs1 in equation form, assuming an exponential fit. It should be noted that this expression does not depend on fines content. In particular, the following equations best fits the results: SR15= 0.02 exp(0.013 * Vs1) (11)It can be observed that the coefficient of correlation is very close to unity. This indicates good precision of the proposed equation.

Fig. 11 Cyclic strength curves as function of Vs1 on basis of experimental results.

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Regarding assessing the ground volumetric change in terms of FS and N1 (or the equivalent qc1 value), according to Fig. 4, the following response is observed: (a) when the factor FS is smaller than a particular value, Fo, εvol/εvol-max equals to unity and (b) when FS is larger than Fo, as FS increases further, the ratio (εvol / εvol-max ) gradually decreases from unity towards zero, forming an S-shape curve (see Fig.12). The shape of this relation can be simulated with the equation:

εvol = εvol-max * 0.5 ( 1 + tanh [ (ln(A/FS))B ] ) (12)

where εvol-max, Α, Β are best-fit parameters.The parameters εvol-max, A, B depend on soil density, or, equivalently on N1 or q1.

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Fig. 12 gives the volumetric strain in terms of safety factor FS and N1 in equation form, for each N1 value separately, assuming the fit described above.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv-

max

Curve NI=3

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliqεv

(%)/

εv-m

ax

Curve NI=6

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv

-max

Curve NI=10

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv

-max

Curve NI=14

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv

-ma

x

Curve NI=20

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv

-ma

x

Curve NI=25

Predicted

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Fig. 12 Parametric with N1 variation of ratio εvol / εvol-max as a function of FSliq.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

FSliq

εv(%

)/εv-

max

Vurve NI=30

Predicted

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Fig. 13 gives εvol-max and A, B that best fit the results in terms of N1 assuming a logarithmic relationship for εvol-max and linear relationships for A and B.In particular, the following equations are proposed for εvol-max, A and B:

εvol-max= -1.84 ln (N1) + 7.65 (13a)

A= -0.0066 N1+1.08 (13b)

B= - 0.2 N1+8.37 (13c)

It can be observed that the coefficient of correlation of all three equations is very close to unity. This indicates good precision of the proposed equations.

Fig. 13 Best fit parameters εvol-max, A,B evaluation as functions of N1, and qc1 variation with N1.

(a) (b)

y = -1.8357Ln(x) + 7.647

R2 = 0.99590

1

2

3

4

5

6

0 10 20 30 40

N1

εvo

l-m

ax (

%)

Curve

Log. (Curve)

y = -0.0066x + 1.0839

R2 = 0.9631

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40N1

A

Values

Linear(Values)

(c) (d)

y = -0.1999x + 8.3692

R2 = 0.942

0

2

4

6

8

10

0 10 20 30 40N1

B

Values

Linear(Values)

y = 30.021e0.0644x

R2 = 0.9919

0

50

100

150

200

250

0 10 20 30 40N1

qc1

Curve

Expon.(Curve)

ln

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Finally, Fig. 14, presents the results of various investigations on the effect of earthquake magnitude on the cyclic shear strength. The ratio SRM/ SRM=7.5 is defined as magnitude scaling factor (MSF). A mathematical approximation of its variation is that based on Idriss results and is given by the equation: MSF = 6.9 exp (-M/4) – 0.058 (14)Values presented in table 1 are only slightly different as an average of results of Seed and Idriss (1982), Idriss (1999) and Seed et al (2003).

Fig. 14 Magnitude scaling factor, MSF, values proposed by various investigators and mathematical approximation of MSF based on Idriss results.

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Description of computer programAll the equations above have been implemented in an excel worksheet predicting the factor of safety against liquefaction risk with depth and the subsequent ground settlement, as well as the effect of preloading on these quantities. The program divides the soil profile in 1m sublayers down to 20m depth. The reason is that liquefaction typically does not occur at depth below 10m and, if it occurs, its effect on the ground surface is minimal. The input needed in the program is: a-max, M, Water table level, Preload height, Preload unit weight, Depth of bedrock. In addition the variation with depth of the following are needed: (a) N1, (b) total unit weight, (c) % of fines, (d) Plasticity Index.The program estimates the pre-improvement and post-improvement liquefaction factor of safety with depth and ground subsidence in terms of NSPT, qCPT and Vs.

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• For the pre-improvement case, the steps performed for these estimates in the case of NSPT are: estimate (1) σv, (2) σ'v, (3) N1 60, (4) f, (5) SRN (M=7.5), (6), SRN (M), (7) rd, (8) SR, (9) FS, (10) εvol, (11) ρtot. The steps performed for these estimates in the case of qc are: estimate (1) σv, (2) σ'v, (3) qc1, N1 60 (4) f , (5) SRN (M=7.5), (6), SRN (M), (7) rd, (8) SR, (9) FS, (10) εvol, (11) ρtot. The steps performed for these estimates in the case of Vs are: estimate (1) σv, (2) σ'v, (3) V1, (4) SRN (M=7.5), (5), SRN (M), (6) rd, (7) SR, (8) FS, (9) N1 60, (10) εvol, (11) ρtot.

• For the post-improvement case, the steps performed for

these estimates in the case of NSPT, qc1, Vs are: estimate (1) σ'v-prel, (2) PR, (3) N1 60new, qc1new, Vs1new, (4) SRN-new, (5) SR-new, (6), Fs-new, (7) ε-vol-new, (8) ρtot-new

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In summing up the program estimates the factor of safety and the ground subsidence using relationships that have been proposed in the bibliography in graphical form developed here in equation form. The program estimates the post-improvement cyclic strength and seismic acceleration based on results of the project.

As an example of application of the program, the field study of the present project is used for both the pre-improvement and post-improvement cases and for different earthquake magnitudes. A validation of the computer program was made by comparison of computed values with the values measured/estimated from the field test (WP2). Good agreement was found to exist.

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4. Conclusions

The basic conclusions established concerning how preloading affects liquefaction seismic risk and therefore design are:(a) It increases the soil’s cyclic strength(b) it dampens the seismic motion

A computer program was developed during the project that can be used for geotechnical design on liquefaction-susceptible soils in terms of both the factor of safety and the ground subsidence. Results were validated with application on the field test.