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Simplified Prediction Method for Behavior of Sheet Pile Quay Wall on Liqufied Ground

Kenji HayashiChuo Fukken Consultants Co. Ltd., Japan

Tamotsu Matsui and Kazuhiro OdaOsaka University, Japan

ABSTRACT

The 1995 Hyogoken-Nambu Earthquake had caused severe

damages to many structures in the bay area. The damage of the shore

structures were due to the occurrence of the liquefaction. In this paper,

focusing on the sheet pile quay wall, which is a typical type of shore

structures, the seismic behavior of the structures is discussed when the

liquefaction occurs, by applying the dynamic response analysis and the

simplified prediction method which was proposed by the authors.

Firstly, based on the case study by the dynamic response analysis, the

influence of the input earthquake motion on the residual deformation

of sheet pile quay wall is discussed. As a result, It is confirmed that the

residual horizontal displacement of top of sheet pile depends on the

maximum horizontal acceleration and the degree of stiffness of back

fill. Secondly, the applicability limit of the simplified prediction

method were discussed by comparing with the dynamic response

analysis. The simplified analysis is applicable as a prediction method

for seismic behavior of sheet pile quay wall by considering the

influence of the semi-liquefaction.

KEY WORDS: aseismic design; dynamic response analysis;liquefaction; shore structure; sheet pile quay wall

INTRODUCTION

The 1995 Hyogoken-Nambu Earthquake had caused severe

damages to many structures. Especially, the damage of the caisson

quay walls and sheet pile quay walls were very heavy in ports and

harbors. The damage were due to the occurrence of the liquefaction

and the earthquake motion over the design seismic coefficient. In this

paper, focusing on the sheet pile quay wall, which is a typical type of

shore structures, the seismic behavior of the structures is discussed

when the liquefaction occurs, by applying the dynamic response

analysis and the simplified prediction method which is proposed by the

authors.

SEISMIC BEHAVIOR OF SHORE STRUCTURES

DURING EARTHQUAKE

There are several types of structure in the sheet pile quay wall.

In this study, the counterfort sheet pile quay wall as the typical type of

sheet pile quay wall is focused. The typical damage of the sheet pile

quay wall is the leaning of the top of sheet pile, the settlement of back

ground and the crack of apron. Fig. 1 shows the typical damage of the

sheet pile quay wall. Three factors (the inertial force, the earth pressure

and the liquefaction) are sought to be the causes of damage to the sheet

pile quay wall during earthquake. Each factor is explained below.

Inertial Force Whenever any earthquake produces a certain

acceleration, the inertial force acts on a structure both in vertical and

horizontal directions. Assuming that the vertical motion of earthquake

has rather small influence on the structures, the inertial force by

horizontal motion has been adopted generally for the aseismic design

of structures. The larger the dead weight of the structure, the larger theinertial force acting thereon becomes. Therefore, the inertial force is a

factor that greatly contributes to the seismic damage of the gravity type

shore structures, especially.

Earth Pressure The lateral earth pressure acting on the structures is

usually the earth pressure at rest under the static condition. During

earthquakes, however, it becomes a seismic earth pressure that is larger

than the earth pressure at rest. When the liquefaction occurs, it will

become much larger, because the ground is changed to liquefied

condition. Since, in particular, the gravity type quay wall and sheet pile

quay wall must stand against the earth pressure, the earth pressure mayFigure 1 Typical damage of sheet pile quay wall

536

Proceedings of The Twelfth (2002) International Offshore and Polar Engineering Conference

Kitakyushu, Japan, May 2631, 2002

Copyright 2002 by The International Society of Offshore and Polar Engineers

ISBN 1-880653-58-3 (Set); ISSN 1098-6189 (Set)

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become a significant factor of seismic damage to these structures.

Liquefaction The liquefaction is closely related to the seismic

damage to shore structures. Most of the seismic deformation of shore

structures in the bay area is attributed to the liquefaction, either

directly or indirectly. The liquefaction generates excess pore water

pressure in the ground, which will cause the shear strength reduction of

the foundation ground, followed by occurring the damage of structures

by settlement of structures or lateral flow of ground. Because the

liquefaction continues after the earthquake, it should also be

considered as a factor that keeps deformation or damage to structuresfor a longer time. The damage of structures cannot be ignored even in

the case of semi- liquefaction where excess pore water pressure ratio is

less than the unity.

SIMPLIFIED ANALYTICAL METHOD

In the dynamic response analysis, it is possible to express the

seismic behavior of structure during earthquakes appropriately.

However, it is complicated and cannot be used frequently in the

conventional aseismic design. Therefore, a simplified and reasonable

method for predicting the seismic behavior of structure during

earthquakes is required. The simplified analytical method for the

gravity type quay wall was already proposed by the authors (Matsui et

al. [1998]). In this paper, the applicability of simplified analysis for

seismic behavior of sheet pile quay wall on liquefied ground isdiscussed.

In the proposed analytical method, the structure is replaced by a

simplified model, and the ground contacting the structure by a

subgrade spring. The simplified analysis consists of three phases:

phase 1 (before the earthquake), phase 2 (during the time submitting to

inertial force by earthquake motion) and phase 3 (during liquefaction).

The deformation of structure in each phase is analyzed under the

conditions of appropriate loads and subgrade springs of ground,

followed by calculating the final residual deformation by summing up

the deformation in three phases. Table 1 and Fig. 2 show the analytical

conditions and schematic models for the three phases.

As shown in Table 1, the load conditions are dead weight and

earth pressure at rest in phase 1, seismic earth pressure during

earthquakes and inertial force in phase 2, and liquefaction earth

pressure (when back fill is liquefied) in phase 3. The inertial force iscalculated from the horizontal seismic coefficient obtained based on

the maximum acceleration of the horizontal earthquake motion. It is

assumed that the liquefaction earth pressure by the back fill acts only

after the main earthquake motion. This means that the liquefaction

earth pressure and inertial force do not act at the same phase. There aretwo types of subgrade springs employed elasto-plastic spring and

liquefied soil spring. The bilinear type subgrade spring for

elasto-plastic condition is used in the non-liquefied ground (phases 1

and 2), while the liquefied soil spring is used in the phase 3. The

rigidity of ground is reduced due to liquefaction to have the reduced

spring constant, which is assumed to be equivalent in the vertical and

horizontal directions.

Table 1. Analytical conditions in simplified analysis

Phase External force Subgrade spring1

Dead weight

Earth pressure at restElasto-plastic spring

2

Inertial force

Dead weight

Seismic earth pressure

Elasto-plastic spring

3Dead weight

Earth pressure of liquefied soilLiquefied soil spring

The constants of subgrade spring are represented as follows:

Spring constant for plastic condition Kp=pKe (1)

Spring constant of liquefaction ground K1=1Ke (2)

In which, Ke: Constant of subgrade spring for elastic conditioning,

p: Reduction ratio of subgrade spring due to yielding

1: Reduction ratio of subgrade spring due to liquefaction

APPLICABILITY OF SIMPLIFIED ANALYTICAL

METHOD

In this chapter, firstly, through the case study by the dynamic

response analysis, the seismic behavior of sheet pile quay wall in

liquefied ground is evaluated. Secondly, in order to confirm the

applicability of the proposed simplified analytical method, the case

study is performed to compare the results of the simplified analysis and

the dynamic response analysis. The dynamic response analysis is

carried out by FLIP, which is the prediction program of damage due to

liquefaction ( Iai et al. [1992]). It has been elucidated that the seismic

behavior of sheet pile quay wall during earthquake can be expressed

with high accuracy by the dynamic response analysis (Iai et al. [1993]).

The objective structure for evaluating the seismic behavior is asheet pile quay wall that showed a large residual deformation in the

1995 Hyogoken-Nambu Earthquake. Table 2 and Fig. 3 show the

analytical model and the used parameters, respectively. As for the

ground condition, the back fill of sheet pile is assumed as

homogeneous sand layer. The parameter of ground stiffness is varied

from loose condition as N value equal to 10 to dense condition as N

value equal to 40. The input earthquake motion are used as the

irregular seismic waves for about twelve seconds, which is modified

the maximum acceleration of observed seismic waves at location of

Figure 2 Schematic models for three phases

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Table 2. Analytical parameter for dynamic response analysis

N-Value

Unit

weight

(kN/m3)

Poissons

Ratio

Initial shear

modulus

G0(kN/m2)

Damping

constant

h max

10 18 0.33 78,000 0.24

15 18 0.33 90,800 0.24

22 20 0.33 118,000 0.24

28 20 0.33 139,000 0.24

35 20 0.33 162,000 0.2440 20 0.33 195,000 0.24

Port island in the 1995 Hyogoken-Nambu Earthquake. The maximum

acceleration of input earthquake motion is varied from 100 gal to 600

gal.

Fig. 4 shows the variation of horizontal and vertical

displacements of the top of sheet pile with the elapsed time, in the case

that the seismic wave having the maximum horizontal acceleration of

500gal at the basement and N value equal to 10. The horizontal

displacement of structure increases greatly during earthquake, while

the settlement of structure increases at the beginning of earthquake

motion till the elapsed time of about 10 seconds, then the rate of

increasing of the settlement is weakened during earthquake. It is clear

that the duration of earthquake motion is closely related to the residual

horizontal displacement.

Fig. 5 shows the variation of the excess pore water pressure at

the back ground of sheet pile with the elapsed time, for the same case

of Fig.4. The excess pore water pressure is increasing after the value is

beginning of earthquake, then becomes constant of about 0.8, which

the condition of semi-liquefaction. The structures caused major

damage in the condition of semi-liquefaction generally.

Figure 3 Analytical model for dynamic response analysis

Figure 5 Variation of excess pore water pressure

Figure 4 Variation of displacement of structure with elapsed time

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Fig. 6 shows the deformation of sheet pile and ground in the

case of the maximum horizontal acceleration of 500gal and the N value

of 10. As shown in Fig. 6, the top of sheet pile is leaning forward and

the bottom of sea is rising, then the settlement occurs at the back of

sheet pile. The mode of deformation is similar to the real disaster

instance.

Fig. 7 shows the relationships between the horizontal

acceleration at basement and the residual horizontal displacement of

the top of sheet pile. As shown in Fig. 7, the larger the maximum

acceleration of input earthquake motion, the larger the residual

horizontal displacement of the top of sheet pile.

Fig. 8 shows the relationships between the N value and the

residual horizontal displacement of top of the sheet pile. As shown in

Fig. 8, the greater the N value (ground stiffness), the smaller theresidual horizontal displacement of the top of sheet pile.

Next, in order to confirm the applicability of the proposed

simplified analytical method, a case study is performed to compare the

results of the simplified analysis with that of the dynamic response

analysis. The sheet pile quay wall as shown in Fig. 3, which was used

in the dynamic response analysis, is selected as the simplified

analytical model. Table 3 gives the analytical parameters for the

simplified analysis, in which the subgrade spring constant is calculated

as a coefficient of subgrade reaction. The reduced spring constants

both for the elasto-plastic and liquefied soil springs are decided based

on the results of the back analysis of the dynamic response analysis.

Fig. 9 shows the relationships between the N value (ground

stiffness) and the residual horizontal displacement of top of the sheet

pile, in the case of the maximum horizontal acceleration of 100gal. Inthe simplified analysis, the residual horizontal displacement of the top

of sheet pile is predicted in assuming only inertial force by earthquake

Figure 6 Deformation of sheet pile and back ground

Figure 7 Relationships between horizontal acceleration at basement

and residual horizontal displacement

Table 3. Analytical parameter for simplified analysis

N-Value

Constant of subgrade

spring for elastic condition

Kp (vertical) (kN/m3

)

Constant of subgrad

spring for elastic condi

Kp (horizontal) (kN/

10 11,400 37,800

15 17,000 56,800

22 25,000 83,200

28 31,800 106,000

35 39,700 132,000

40 45,400 151,000

Figure 8 Relationships between N value and residual horizontal

displacement (see Table 2 for G value)

Figure 9 Relationships between N value and residual horizontal

displacement (100 gal case)

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motion. The reduction ratio of subgrade spring due to yielding is

p=0.0021 in the simplified analysis, and this is calculated by the

back analysis for the dynamic response analysis, in the case of the N

value of 40, in which case the liquefaction does not occur. As shown in

Fig. 9, the results of the simplified analysis are same as the results of

the dynamic response analysis. Fig. 10 and 11 show the relationships

between the N value (ground stiffness) and the residual horizontal

displacement of the top of sheet pile in the case of the maximum

horizontal acceleration of 300 gal and 500 gal respectively. The

agreement between the two method in these figures is as same as the

above mentioned.Fig. 12 shows the relationships between the acceleration and

the residual horizontal displacement of the top of sheet pile based on

the simplified analysis and the dynamic response analysis. In Fig. 12,

the case A of the simplified analysis represents complete liquefaction,

while the case B without liquefaction. The reduction ratio of subgrade

spring due to liquefaction is l=0.062 in the simplified analysis, and

this is calculated by the back analysis for the dynamic response

analysis with the maximum horizontal acceleration of 600gal to have a

complete liquefaction. In the case A of the simplified analysis, the

residual horizontal displacement of structure is larger than that of the

dynamic response analysis at the small range of horizontal acceleration.

The difference is due to the difference of expressing the liquefaction

between the simplified analysis and the dynamic response analysis at

the case of small horizontal acceleration. That is, the dynamic response

analysis express the actual behavior of seismic structures with good

accuracy prior to the semi-liquefaction condition, that is the

intermediate condition between non-liquefaction and completeliquefaction at the saturated ground. Therefore, in order to match the

result of the simplified analysis with that of the dynamic response

analysis, consideration of semi-liquefaction state will be necessary in

the simplified analysis. The agreement may be easily obtained by

adjusting the reduction ratio of subgrade spring prior to the

liquefaction adequately.

Figure 12 Relationships between acceleration at basement and

residual horizontal displacementFigure 10 Relationships between N value and residual horizontaldisplacement (300 gal case)

Figure 13 Relationship between horizontal acceleration and

logarithmic reduction ratio of liquefied springFigure 11 Relationships between N value and residual horizontaldis lacement 500 al case

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Fig. 13 shows the relationship between the horizontal

acceleration and the logarithmic reduction ratio of the liquefied spring

ladjusted for this case study. As shown in Fig. 13, the reduction ratio

of liquefied spring l is changed from 0.4 to 0.05 between

non-liquefaction and complete liquefaction conditions. The similar

results are obtained in the study of the reduction ratio of liquefied

spring lfor the gravity type structures [ Hayashi et al. (2001)].

Since the simplified analysis includes the same static model of

the seismic intensity method, the external force of the earthquake

motion is obtained by the horizontal seismic coefficient multiplied by

the dead weight usually. It is not easy to simulate the dynamic response

of structures by the static inertial force. However, the simplification of

analytical method for shore structures on liquefied ground is possible

based on the above mentioned results.

CONCLUSIONS

In this paper, in order to confirm the applicability of the

proposed simplified analytical method, the seismic behavior of sheet

pile quay wall in liquefied ground is evaluated firstly, through the case

study with the dynamic response analysis. Secondly, case studies are

performed to compare the results of the simplified analysis and the

dynamic response analysis.

The conclusions based on the results of the dynamic response

analysis are summarized as follows:

(1) The excess pore water pressure generates greatly at the back of

sheet pile in the case that the back ground is loose.

(2) The results of the dynamic response analysis can express the real

disaster of sheet pile. That is the top of sheet pile quay wall leaning

forward, the bottom of sea rising and the settlement at the back of

sheet pile.

(3) The larger the input earthquake motion, the larger the residual

horizontal displacement of the top of sheet pile.

(4) The greater the ground stiffness, the smaller the residual horizontal

displacement of the top of sheet pile.

(5) Horizontal displacement is increasing during earthquake. It is clear

that the duration of earthquake motion is closely related to the residual

horizontal displacement.

The conclusions based on the comparison both the dynamic

response analysis and the simplified prediction method are

summarized as follows:

(1) In the results of the simplified analysis, the greater the ground

stiffness, the smaller the residual horizontal displacement of the top of

sheet pile, as same as the result of the dynamic response analysis.

(2) Both in the simplified analysis and the dynamic response analysis,

the larger the maximum acceleration of input earthquake motion, thelarger the residual horizontal displacement of the top of sheet pile.

(3) The dynamic response analysis can express the behavior of sheet

pile quay wall in the condition of semi-liquefaction. While, the

simplified prediction method can express the behavior of sheet pile

quay wall in the condition of semi-liquefaction to adjust the reduction

ratio of subgrade spring due to liquefaction adequately.

REFERENCES

Hayashi K., Matsui T., Oda K., Imono T. and Miyamoto H. (2001).

"Analytical evaluation for behavior of shore structures on liquefied

area during earthquakes,"Proceedings of 4th International

Conference on Recent Advances in Geotechnical Earthquake

Engineering and Soil Dynamics, Paper Number 7.13Iai, S., Matsunaga, Y. amd Kameoka, T. (1992). "Strain space plasticity

for cyclic mobility, Soils and Foundations," Vol.32, No.2, pp.1-15

Iai, S. and Kameoka, T. (1993). "Finite element analysis of earthquake

inducede damage to anchored sheet pile quay walls," Soils and

Foundations, Vol.33, No.1, pp.71-91

Matsui, T., Akakuma, M., Hayashi, K., Ishikawa, T., Nakano, T. and

Imono, T. (1998). "Aseismic evaluation against rare big earthquake

for shore structures," Proc. 8th International Offshore and Polar

Engineering Conference, Vol. I, pp. 610-614

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