Study on permanent ground displacement induced by seismic liquefaction

Computers and Geotechnics 4 (1987) 197 220

STUDY ON PERMANENT GROUND DISPLACEMENT INDUCED BY SEISMIC LIQUEFACTION

M.Hamada Department of Civil Engineering Tokai University Shlmizu, Shizuoka, Japan l. Towhata Division of Geotechnical Engineering Asian Institute of Technology Bangkok, Thailand S.Yasuda Department of Civil Engineering Kyushu Institute of Technology Kita-Kyushu, Fukuoka, Japan and

Nihon

R. Isoyama Gidyutsu Kaihatsu Tokyo, Japan

ABSTRACT Permanent ground displacement as induced by seismic liquefaction was measured in the area which was recently hit by an earthquake. The m e a s u r e m e n t was carried out by comparing two aerophotographs of the area which were taken before and after the tremor. Using the measured data an empirical equation was derived which can calculate the magnitude of the displacement briefly. Furthermore, a flnite-element technique was developed in order to predict the magnitude and the direction of the displacement in more precise manners.

INTRODUCTION During serious earthquakes, the liquefaction of sandy ground is one of the main causes of damage to structures such as bridges, embankments, lifelines, and so on. This damage includes the settlement and tilting of structures due to the reduction of the bearing capacity of the foundations, the floating of embedded structures caused by buoyancy in the liquefied soils, the failure of retaining structures under increased dynamic earth pressures,

197 Computers and Geotechnics 0266-352X/87/$03.50 @ 1 987 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain

1 98 and slope instability

resulting from loss of shear, strength of soil.

The types of damage mentioned here are more or less related to failure or large shear deformation of liquefied soils. There are also cases in which displacement of structures caused by ground liquefaction leads to loss of function or structural failure, even when the ground soil does not totally fail. Typical examples of this were shown in reference [ 1 ] , which attributed the loss of bridge functions to the permanent displacement of abutments. The permanent displacement of ground induced by earthquakes is not a new topic for geotechnical investigation. When Alaska was shaken by the disastrous earthquake of 1964, the sea coast of Valdez City slld into the water [2] . Moreover, a gentle slope in the vicinity of the Upper Van Norman Lake, California, moved two to three meters towards the lake when the area was hit by the San Fernando earthquake in 1971 (references [3] and [4]). The seismic resistance of pipelines has been attracting recent engineering concern. Buried lifeline networks for water, electricity, communication etc. have to survive earthquakes because their functions are crucially important for restoration as well as rescue. Although the seismic reinforcement of the whole networks of buried pipeline seems to be the best precaution to be taken, it is practically impossible because of the vast extent of such networks. Hence, it is appropriate that the possible locations of pipeline failure during future earthquakes should be predicted so that effective countermeasures may be taken at these critical locations. This study focuses on the permanent displacement of the ground induced by liquefaction as one of the most important causes of failure of buried pipelines. So far, the lack of quantitative data has been a barrier to adequate research into permanent displacement. With this in mind, the writers use measurements of displacement to facilitate statistical studies as well as numerical predictions [5].

MEASUREMENT OF PERMANENT GROUND DISPLACEMENT INDUCED BY THE EARTHQUAKE OF 1983 Noshiro City is located close to the northern tip of Honshu Island, Japan, and was hit by a strong earthquake on May 26, 1983 (Fig. I). The earthquake, magnitude 7.7, occurred some 90 km to the west of the city, and caused substantial damages in the area. As indicated in Fig. i, the maximum acceleration recorded in Aklta City was over 200 gals, suggesting similar intensity of motion in nearby Noshiro City. Noshiro City, lying on the alluvial plain and sand dunes along the seashore, suffered substantial damage to its buildings. Failures of lifeline facilities were also significant. In the areas of heaviest damage, a large number of sand boilings were detected, suggesting the total liquefaction of subsoils. Cracks, subsidences, and heavlngs were also common (references [6] and [7]).

Method of ~easurement

of Permanent Displacement

of the Ground

Permanent horizontal ground displacements induced by the earthquake were measured from aerial photographs which were taken under identical conditions before and after the tremor. The pre-earthquake photos were taken in 1981, the post-earthquake photos seven days after the event. The scale in both cases was 1:8000.

199 In order to measure the permanent ground displacement from the aerial photos, it was necessary to identify datum points which were considered to have suffered no permanent displacement in the course of the earthquake. Most of the datum points in the survey were selected from triangulation points in the periphery of the study area. All the selected points were located on seismically stable hilltops or sand dunes, uninfluenced by ground failures or liquefaction. Thus, displacement at the selected datum points was negligible. The measurement of permanent ground displacement had to be carried out at fixed points on the ground surface in both pre- and post-earthquake photographs. Manholes, cadastral boundary stones, the bases of lamp-posts, corners of drainage channels were preferred. Where such points were not available, roofs of houses surviving the quake were used. The total number of measurement points was around 2,000. Photo 1 shows an example of an aeropboto with measurement points indicated by the circles. The accuracy of displacement measurement may be affected by the reduced scale of the photographs, human error in reading the coordinates and so on. As is described in detail in Appendix I, the possible error was estimated at not more than 20 cm in a horizontal direction for Noshiro City. To verify this estimation, traverse and plane table surveys were carried out on a small area, independent of aerophoto measurements. Displacement measured by the two different methods was found to be in good agreement (see Fig. A-2).

! Af~rs~ ~:25 • 6,9

~

4I-

S

:

,,u 72

J

J / r39

140

A Maximum Hor~zont@l Accelenttlon in ~ Observed by Strong Motion Se~smollr@gh (SMA¢ T),lpe)

Figure 1 Epicentre and maximum horizontal acceleration during the 1983 earthquake.

Photo I Aerial photograph of the northern slope of Maeyama Hill.

200 Measured Ground Displacements

for Noshiro City

Fig. 2 shows Noshlro City with the two areas where the permanent ground displacements were studied. Figs. 3 and 4 illustrate ground failure and permanent displacements in the north and south study areas, respectively. It can be seen that substantial displacement occurred along gentle slopes of sand dune. In the north area (Fig. 3), ground failure the Noshiro-Oga Road. Crack, subsidence, and as sand boillngs, as proof of liquefaction. between sand dunes and alluvial plains, has approximately 0.3 percent. The predominance of subsoils liquefied throughout the area.

was significant to the west of heaving were reported, as well This part of area, located an inclination as small as sand boiling suggests that the

The permanent displacements were notably large in the same area as ground failure was significant. Their orientation was parallel to the slope and perpendicular to the cracks. The maximum displacement was around 3 m near the top of the slope. On the other hand, displacement decreased to a negligible magnitude at the bottom of the slope and in the flat plain to the east of the Noshiro-Oga Road. In the south study area (Fig. 4), ground failure was also prevalent. In particular, numerous cracks occurred around the top of a small hill, Maeyama Hill. Sand boilings were apparent everywhere, suggesting that the subsoil liquefied totally at the seismic event. The permanent displacement vectors around Maeyama Hill were oriented parallel to the slope and perpendicular to the cracks. A maximum displacement of 5 m was detected on the north slope close to the hill top. Down the gentle north slope of the hill, which inclines at an average of only one degree, the magnitude of the displacement diminished almost to zero at the lowest elevation near the Santoh Swamp. Further north, the elevation again rises slightly orbour Rive ~ towards No. 7 Road, where the slope showed cracks and downslope displacements.

Y°neshlr°

In the south study area, several well pipes were extracted after the earthquake. Originally the pipes had been straight and vertical. However, on extraction, they were revealed to be distorted as seen in Fig. 5. The pipe bending occurred at the level of the ground water, which may be indicative of the permanent movement of the surface layer.

No.7 Noshiro

N City

/

Figure 2 Areas of measurement permanent ground displacement Noshiro.

of in

~ig.3 Permanent horizontal displacement in the part of Noshiro City.

ground northern

~ig.4 Permanent horizontal displacement in the part of Noshiro City.

ground southern

2O2 PERMANENT DISPLACEMENT

INDUCED BY THE 1964 NIIGATA EARTHQUAKE

On June 16, 1964, an earthquake of magnitude 7.5 hit Niigata City. It reported that liquefaction occurred in the reclaimed channels of rivers [6]. In this section, permanent ground displacements from aerial photograph surveys of Niigata City are described. was

Method of Measurement The method employed for Niigata is more or less the same as for Noshiro. Fig. 6 shows the area in which the permanent ground displacements were investigated. The pre-earthquake photograph was taken in 1962, two years prior to the seismic event, the post-earthquake one four hours after the tremor. The scales of the photos were I:ii,000 and 1:12,500, respectively. Datum points were the tops of the stable sand dunes in the northwest of the city (Fig. 6). No ground failure was detected in the vicinity of the datum points during or after the earthquake. Hence, it can be assumed that no permanent displacement occurred at those points. The permanent ground displacements were measured at about 400 points; manholes, corners of drainage channels, and so on. The measurement accuracy was estimated by almost the same procedure as that for the Noshiro case (Appendix I), i.e. +72 cm horizontally and +66 cm vertically.

Disp|ocernent of Q well

• Datum points [ ] Area' of study on ground displacement A: Showa Bridge /~J rB : Yachiyo Bridge / / ~ f /

~'-'1 ~ 6 c m Ground waterlevel. ,~"~"~ /7

Figure 5 Distortion of a well damaged during the earthquake.

,k 2 " Nlig,gta \

";" ' """ Nli~lata

Stotion city

\

Figure 6 Area of measurement of ground displacement and datum points in Niigata City.

203 Permanent Ground Displacement Fig. 7 indicates the vectors of permanent ground displacement along with ground failures such as sand boilings, cracks, subsidences, which were reported by the reference [8]. The permanent displacement was very large on the left bank of the Shlnano River, between the Showa Bridge and the Hakusan power substation in Kawaglshi-Cho area, and also on both banks between the Bandai Bridge and the Yachiyo Bridge. It was particularly large in the vicinity of the river. The maximum displacement was 8.5 m in the proximity of the Rakusan power substation and 8.8 m on the left bank near the Bandal Bridge. The directions of the horizontal vectors of the displacement was almost perpendicular to the river bank. On the other hand, the permanent ground displacements on the right bank between the railway bridge and Showa Bridge were very small and random in direction. No sand boillngs or cracks were reported in this area. Fig. 8 illustrates the front water lines of the Shinano River and the coast circa 1600. It can be seen the the locations of the former river channel mostly coincide wlth the areas where large displacements occurred. Namely, the left bank between Showa Bridge and Kawagishi-Cho and both banks between Yachiyo and Bandai Bridges lie on the former river channel. The areas of small displacements, on the other hand, are located outside the former channel.

)

Figure 7

Permanent horizontal ground displacement the 1964 Niigata earthquake.

in Niigata City caused

by

204 The magnitude of permanent ground displacement in the area near the Niigata Railway Station was 2 to 3 m, less than along the Shlnano River. It is, however, notable that the orientation of the displacement vectors here is opposite to that of the river. This area is also located on the former river channel (Fig. 8). When the piles of the foundation of a building near the Niigata Station were extracted at the time of reconstruction in 1985, about twenty years after the earthquake, RC piles of 350 mm diameter and Ii to 12 m length were found to be broken [ 9 ] . As shown in Fig. 9, the piles were damaged at two elevations; 2.5 m to 3.5 m from the head and also 2.0 to 3.0 m from the tlp. Investigation was made of seventy-four out of the total of 304 piles, and most of the piles were found to have been damaged in this manner. From this observation, the lateral displacements of the plle heads were estimated at 1.0 to 1.2 m, as suggested in Fig. 9. The directions and magnitudes of the displacement of the pile head thus derived are in agreement with those derived from aerial surveys in their vicinity.

STUDIES ON THE CAUSES OF PERMANENT GROUND DISPLACEMENTS Noshiro City A large number of sand boilings were found out in the areas of Noshiro Clty where large ground displacements occurred (Figs. 3 and 4). Hence, it can be inferred that the subsoil of those areas liquefied significantly. A subsurface exploration program was carried out throughout the liquefied area of Noshiro in order to identify the liquefied layers in the ground. This program included 12 standard penetration tests and 134 Swedish penetration tests, the results of which were subsequently converted to SPT blow counts. With

the

subsurface

data thus derived,

the factor of

safety

against

Southeast

1o 2o 30 N.Value

.....

Old Water Front circa 1600 ~

3

$

4

~

5

•

?

11

Figure 8

Waterfront line of City circa 1600.

Niigata

Figure 9

13

19

Broken RC pile and conditions [9].

soil

205 liquefaction, FI, was calculated, following reference surface acceleration was assumed to be roughly 250 gals.

[lO|.

The

maximum

Fig. I0 is a soll profile of the north slope of Maeyama Hill. This soil cross section is parallel to the direction of the permanent displacement vectors. The shading indicates the layers which probably liquefied during the earthquake. It can be seen that the layers immediately below the groundwater table (Asd) liquefied and lost their shear strength and shear stiffness considerably. As already mentioned, the direction of the permanent ground displacement was more or less parallel to that of the slope. Moreover, the displacement was greater near the top of the slopes where the slope gradient was also high. Many ground cracks were detected at high elevations (Fig. 3 and 4). On the other hand, displacement was less at lower elevations where the slope was gentle or non-exlstent. Thus, it can be claimed that ground topography definitely has an effect on the magnitude of permanent displacement. The thickness of the liquefied layers is also likely to influence the magnitude of the displacement. It seems that liquefaction in significantly thick layers may result in greater displacement than that in thin layers.

Niilata Fig. 11 shows the ground profiles and the permanent displacement along the line A-A' in Kawagishi-Cho area on the left bank, and the llne B-B' from Hakusan Park to the Showa Bridge. The estimated liquefied layers are illustrated by shades. As indicated in Fig. 11a, the area between the Echlgo Railway Line and around I00 m distance from the bank of the Shinano River had permanent displacement of only about i m towards the river. The displacement then suddenly increased to as large as 7 m near the bank. Although the ground surface and the upper surface of the liquefied layer in this area were flat, the bottom of the liquefied layer was inclined gently towards the river. It

J~Liquefied soil. tayer L A : Al.Luvial.

~u

/ Ac-2"x, -sJ-

Ac - 3

--=~.=" As-2~

~

i0

Ac-3

d : Dune | Ts : Surface I sol t J /

J

--

- ".--. ~s-~

ofMaeyama HiLL

1.0 m displacement

Figure

s: Sand c : Cl.ay P : Peat

~

Cross section of the north slope of Maeyama Hill.

206 can be assumed that besides the inclination of the liquefied layer, the thickness of the liquefied layer, more than i0 m, and the collapse of the retaining structure of the river played a great role to increase the magnitude of the displacement which occurred along the river. In section B-B' in Fig. llb, the ground displacement in the area near Hakusan park was small and the direction was random as illustrated in Fig. 7. The displacement increased up to 2 to 5 m in the area of the left bank. On the right bank of the river, no large ground displacement was found. From the soil layer profile, it can be seen that the estimated liquefied layer was not thick near the Hakusan Park and was mostly horizontal. On the other hand, the liquefied layer was very thick, more than I0 m near the left bank and the bottom of the liquefied layer was inclined towards the river. In this case also, it can be assumed that the collapse of the retaining structure of the river had a great influence on the magnitude of the displacement. The thickness of the liquefied layer on the right bank was very thin.

A 10-

Niigato Kotsu Rai tway

Echigo Rai tway

A' Ts r" Shinano

--7

0--

.iv,r

-lO

~

-20

As-3

-30 .~ 6

Figure lla

Liquefaction \

1

Permanent

Soil layer profile and estimated liquefied layers in section A-A' in Niigata.

B Hakusan Park

Showa Bridge

B'

°_10 As- 3

~Liquetaction

'~ -30 E 4

Figure llb

disptacement

Soil layer profile and estimated liquefied layers in section B-B' in Niigata°

207 Showa Bridge failed completely due to differential displacement of its piers. It has been suggested hitherto that the collapse of the bridge was induced by dynamic motion differences among its piers during the earthquake. However, reliable eyewitnesses have said that the collapse started a short time, presumably about one minute, after the seismic motion had ceased [ 1 1 ] . The distortion of the piers of the bridge is illustrated in Fig. 12, which suggests that the river bed suffered permanent ground displacements similar to those on shore near the station (Fig. 9). Apparently the displacement in the river bed is related to the inclined bottom of the liquefied layer (Fig. llb) rather than the collapse of the retaining structures.

,o

"~

Niagara

if

"

"'o o

ooo L e f t Bank -

~

Right Bank 0

5

I0

Gradient of C
Figure 13 Relationship between the gradient of ground surface and the magnitude of permanent displacement. d

LEGENO

--

Noshi¢o

NiJgato

i/'

c

C~

oo4

o o

Ioo E o • o • oo

Gradient of Lower Boundary Face of Liquefied Layer (%)

Figure 12 Damage to steel pipe piles of pier P4 of Showa Bridge 6 .

Figure 14 Relationship between the gradient of the bottom of the liquefied layer and the magnitude of permanent displacement.

208 REGRESSION ANALYSIS OF FACTORS RELATING TO MAGNITUDE OF PERMANENT GROUND DISPLACEMENTS Correlation between measured permanent displacement and various were investigated. The factors investigated were: (1) (ll) (Ill) (iv) (v)

factors

slope of ground surface, gradient of bottom of liquefied layer, higher values out of (1) and (ii), gradient of upper surface of liquefied layer, gradient of ground surface averaged over whole slope,

LEGEND

LEGEND

Noshiro

Noshiro

Ni(goro

Niigofo

i

31 2 ~°o oO o

°o e

i~o o:

L," "o:o I ooo

o

5 ~0 Gradient of Upper Boundary Face of Liquefied Layer (%)

Figure 15 Relationship between the gradient of the top of the liquefied layer and the magnitude of permanent displacement.

IO

LEGEND Noshiro N~Jgoto

il

°

~ l o Meon Gradient AlonQ Section Line [%)

Figure 16 Relationship between the mean gradient of the ground surface and the magnitude of permanent displacement.

LEGENO Noshi~o

• "

i ~

%0 ~

o o eo

o

Larger Gradient (%)

Figure 17 Relationship between the higher value of the ground surface gradient and the bottom gradient of the liquefied layer, and the magnitude of permanent displacement.

5 Thickness of Liquefied Loyer (m)

I0

Figure 18 Relationship between the thickness of the liquefied layer and the magnitude of permanent displacement.

209 (vi) (vii)

t h i c k n e s s of l i q u e f i e d l a y e r , minimum v a l u e of s a f e t y f a c t o r

against

liquefaction

(F1) a t

each

boring site, (viii) index of liquefaction potential, PI. The index, PI, direction [12].

was

derived from the variation of FI value

in

a

vertical

The data used were not only from Noshiro and Nilgata but also from the San Fernando area in California, where permanent ground displacements were detected after the earthquake in 1971 (references [3], [4], [13], and [14]).

i EGpND

Noshiro

k. i::

}O

o

o

. . . .

~

•

Noshlro

•

$

E

i ,. i :°°°

o

FL

iiii I/ o ii o

4

iii

~,~3 w 2

~0

//o/I /o

I

/ ~

oa/"

2

o

~/~'~ ~'

~

3

4

0

o

oOoO

oj

iQ I0

oo

°I 20

Liquefaction Potential

Figure 19 Relationship between the minimum value of factor of safety against liquefaction, FI, and the magnitude of permanent displacement.

5

Oo

%°~;° ~°O~Oo o ° LO

Minimum

6

: O:o

•

~ : ~ : ~ ° 05

5

Nilgafo

6

Displacement Calculated by Re~iression Formula

Figure 21 Comparison between the permanent displacement estimated by regression formula and the observed displacement.

30

Pt

Figure 20 Relationship between the index of liquefaction potential and the magnitude of permanent displacement.

210 Figs. 13 to 20 show the concerned correlation, among which the thickness of the liquefied layer (Fig. 18), and the higher value out of surface slope, and the gradient of the bottom of the liquefied layer (Fig. 17) were considered to have significant correlation with the displacement. Employing the two factors mentioned above, an empirical equation was obtained.

D = 0.75

D

where

H 8

2~

3F

(I)

ffi permanent ground displacement in the horizontal direction (m), thickness of the liquefied layer (m), = the higher of the surface slope and the gradient of the bottom of the liquefied layer (%).

The predicted and the measured displacements were compared in Fig. 21. Although a discrepancy is seen between the predictions and measurements, this simple equation can give an indication of the magnitude of the displacement. It should be noted that most of the data employed in the regression analysis are from Noshlro. Thus, care is necessary, if the equation is applied to different sites with different soll properties.

FINITE ELEMENT PREDICTION OF PERMANENT DISPLACEMENT Basic Principles An attempt was made to predict the permanent displacement which was detected around Maeyama Hill in the south of Noshlro City. In the course of this attempt, the following observed facts were taken into account:

(1) (ll) (ill) (iv) (v)

total liquefaction in the subsoil, deflection of the extracted well pipes, directions of permanent displacements parallel to the slope, ground cracks at the top of the slopes, the magnitude of the displacements, which is large at elevations, and small or negligible on low and level plains.

high

It is also emphasized that the technique of prediction has to be as simple as possible, because the area of analysis, as shown in Fig. 4, was too large for a sophisticated but complicated analysis to be carried out at a reasonable cost. This point can be understood if the difficulty of a three-dimensional nonlinear dynamic finite element analysis of that vast area is contemplated. Fig. 22 illustrates the proposed method. The surface soil layer, Ts, above the ground water table is analyzed. Under normal conditions, there is sufficient frictional resistance between the surface layer and the subsoil to prevent free movement of the surface layer. Once the subsoil llquefles, the effective stress diminishes, thereby reducing the frictional resistance to zero. Consequently, the surface layer can move freely, llke a board floating on water. The movement of the surface layer is controlled by two factors. The first is gravity. The small element of surface soll in Fig. 22 is under the action of gravity force, Yt A X , in which Y is the unit weight of soil, t is the thickness, and ~x is the length of the element. When an analysis is made of the force equilibrium after the liquefaction of subsoil, the shear stress at the bottom of the element can reasonably be neglected, as mentioned

211 above.

Hence, using the axial stress =

tAo

o

,

~t sin8 Ax

(2)

in which 8 stands for the slope inclination. Note that g is positive in compression. When the coordinate is measured from the top of the slope towards the bottom, and when the downslope displacement is denoted by u, the axial strain, positive in compression, is expressed by ~u ~x

(Axial strain)

By combining

Eq. 3 through Young modulus,

~u ~x

-- E

=

(Axial

in which C is a constant.

u

=

(3)

-

~

x2

2E

stress)

E, with Eq. 2,

= y sinSx

+ C

By further integrating

C

--I/-

(4)

Eq. 4,

(5)

x+D

where D is also an unknown constant. The second controlling factor is the boundary conditions. At the top of the slopes, many cracks occurred (Fig. 4). Hence, the axial stress is equal to zero at x - 0. By substituting x = 0 and axial stress equal to zero in Eq. 4, the constant C is found also to be zero. At the bottom of the slopes (x = L), the measured displacements normally negligible. Using Eq. 5 along with x = L and C = 0,

O :

s_I_~!~_ 2E

L 2

/'X ~

Fixed end

Nagasaki

t '~

x-L-s~o,. ¢=

As layer

were

Hitttop

=:~ =~

I

Gravltatlanal force i component parallet ( to lhe gr~md surface

J ~ g 1-".--~ Gravity force y tAX

y:Unlt weight of soi!

Figure 22 Force equilibrium in the one-dlmenslonal surface layer,

Figure 23 Gravitational loads two-dlmenslonal computation.

in

212 Consequently,

u = ~

(L 2 - x 2)

(6)

Eq. 6 was applied to the north slope of Maeyama Hill, where standard penetration test results suggested E = ii0 kg/cm 2. Also, Y = 1.6 g/cm 3 , L = 550 m, and Y = arctan(5/550) were assumed. The calculated displacement at the top (x = O) was 2.0 m. Although this value is smaller than the measured maximum displacement of 5 m, it is promising in spite of the highly approximated nature of analysis.

Two-Dimensional Analysis The basic principles of analysis described above were immediately expanded to a two-dimensional case. Fig. 23, which is an aerial view, presents its concepts. The slope is divided into finite elements. Each element has a thickness equal to the depth of the ground water table. Since there is no shear stress between the surface layer and the liquefied subsoil, a conventional plane-stress analysis is reasonable. The elements are subject to the action of gravity, which is oriented in the direction of the slope. Two types of boundary conditions are available. The top of the slope had cracks, and therefore is modeled by free end. The flat plains which experienced only small displacements are amenable to fixed ends. The unliquefied area is replaced by fixed end as well. Accordingly, the area surrounded by tops of slopes, low plains, and unliquefied sites are analyzed by a linear elastic finite element technique. The gravitational force component in the direction of the slope evaluated by the procedure below. In a triangular element, the elevation, is expressed by a linear function of horizontal coordinated, x and y. z = ax + by + c

is z,

(7)

Since the elevations at three nodal points of a triangular element can be easily derived from a map, the three constants, a, b, and c, in Eq. 7 can be determined. The linear plane of element surface (Eq. 7) is illustrated in

.p G~t~tl~t

Figure 24

f~r~e G

Conceptual view of triangular element plane.

Figure 25 Quadrilateral an addition of elements.

element as triangular

213 Fig. 24. The direction of the steepest slope in the element plane agrees with that of the vector K~.

K% : (a, b, ~

+ # )

(8)

When the area of the triangular element is denoted gravitational force acting on it is expressed by a vector, 2. = (0, 0, - y t s )

by

S,

the

(9)

in which Y is the %nit weight of the surface soil, and t is the thickness of the element which is equal to the depth of the ground water. The magnitude of the gravitational component parallel obtained as equal to a dot multiplication.

to the

slope

is

( ~. ~/,K%, ) Its x and y components are given by

- ( ~. K-~/~K-~i ) Fy

(io) kS in e )

in which the angle e is equal to the angle MKQ in Fig. 24. cos e = a/ ~ a 2 + b 2 c-sin a = b/ Ja z + b z Substituting

Fy

(11)

Eqs. 8 and II in Eq. 10,

il+~ +~

(I2)

Eq. 12 gives the gravitational load on a triangular element, which is equally distributed as lumped forces among three nodes on the element. When a quadrilateral element is employed, it is divided into triangles one of the two diagonals (Fig. 25). For each of the triangles gravitational loads are calculated using Eq. 12. Since the two diagonals equally significant, this procedure is repeated twice for each diagonal. gravitational nodal loads are derived thus twice, added, and divided by for further analysis.

by the are The two

CASE STUDY IN NOSHIRO CITY A finite element analysis was made of the area around the Maeyama Hill in Noshiro City. The Swedish Penetration Tests conducted in this area gave an average result of Nsw = 100. This value was converted to SPT blow counts N 8, and was substituted in Schultze and Menzenbach's empirical equation [15] for Young modulus, E.

214 E = 71 + 4.9~ (kg/cmz) Thus E = ll0 kg/°mz was derived. Poisson ratio of 0.3 finite element model is illustrated in Fig. 26.

was

assumed.

The

In the course of the analysis, many elements were detected as under tensile stress. Since the surface layer consists of sandy soil, this tensile stress is not realistic. The tensile behavior of finite elements is normally eliminated from the analysis by introducing nonlinear stress-strain relationships. However, this apparently requires substantial computation time. From this reason, it was decided to take a simpler alternative. The finite element analysis explained above calculates the increments which were induced by liquefaction in the subsoil. components were added to the initial static stress, i -i-K0 ytm/t

= +KoY

stress Those

t

in which K is the coefficient of earth pressure at rest, and a value of 0.5 was assumed. The added values gave the true stress components after the subsoil liquefaction. The tensile behavior was eliminated by detecting those elements in which both major and minor principal values of true stress were tensile, and then reducing their Young modulus to I% of the normal value. Using the revised Young modulus, the analysis was carried out once more. The calculated displacements are indicated in Fig. 27. A maximum displacement of 5 m was obtained on the north slope of Maeyama Hill, and is in a good agreement with the measured value. The following features of the measured displacements were also seen in the calculated behaviors:

Ym

N

'[ ¢

N High [o~dfFree end) Y.n'~ _.!:..

1

___I i

I

~Nottiqu,fi,d

/ r soo -

/

I. ~#~',~f~L.~

~ O f~: ~ .1. .~1;;.;;; 7 . , ' 1~:I

IJ

~ ....

~;~. M." ;':.,?-::':i L:*.(/~:.~. ;~.~.i,::i ::. ,..~,;<,:,!<~.~4. ...>.:, ,;::.~..~<~..~.

t,"";"..,~.';(Kb; "i

I

•~

I

t:~

I

ot-

/ o' ....

:5m displacement)

~ ,, :,,<:,.

i i;::"t"~'.7.~:~:.-.,~:_..i.._..i

/ • ~ l)l+fPh/l

S

(~

logo x.'''

0

/

. .......... ! .... v :,,,:.,.~. . . . . .,,,: ~~....... ~~"r-."

r !.7:-'~:..~;: ":.~:.~.:.PS:..::i::Tf ~

500

1000 ×,'n °

J Figure 26 Finite element the southern study Noshlro.

model area

of in

Figure 27 Calculated permanent displacements after elimination of tensile stresses.

215 (i) (li) (ill) (iv)

the direction of displacement parallel to the slope, large displacement at high elevations and small displacement low areas, negligible displacement in the Santoh Swamp area in the middle the analyzed area, south-bound displacements near the No. 7 Road.

in of

The proposed method of analysis is a linearly elastic analysis, and can be carried out in any flnlte-element package program. Hence, its computation cost is significantly lower than that of nonlinear analyses and it avoids the necessity of mastering a new program.

CONCLUSIONS The permanent ground displacements induced by liquefaction were measured by aerial photographs of Noshiro and Nilgata Cities before and after the earthquakes. The occurrence of permanent displacement was confirmed by traverse and plane table surveys as well as by distortion of well pipes and piled foundations. Through an investigation of the displacements, the following conclusions were drawn. (i)

(il)

(ill)

(iv) (v)

In the Noshiro area, where the ground surface was inclined, the magnitude of the displacement was greater at high elevations, decreasing to negligible values on low or level plains. The direction of the displacement was downward, parallel to the slope. Thus, ground inclination was apparently the cause of the permanent displacement in the Noshiro area. The direction of the displacement was perpendicular to ground cracks. In Nilg~ta, where the ground surface was almost level, displacement as high as 8 m occurred near the Shinano River. The inclination of the bottom of the liquefied layers seems to be the cause of this displacement. However, translation of retaining structures played at least a partial role, inducing large displacements near the walls, as suggested by the significant displacement in their vicinity. A regression analysis was carried out to obtain a simplified equation to predict permanent displacement. A finite element method of analysis was developed to calculate permanent displacement. This analysis was conducted in an elastic manner.

ACKNOWLEDGEMENT The research presented in this paper was conducted by the research committee organized by the Association for the Development of Earthquake Predication in Japan for a "Study on Liquefaction-Resistant Design of Buried Pipes." Deepest appreciation is owed to Prof. K.Kubo of Saitama University, the chairman of the committee, for his excellent leadership and strong support of the research. Appreciation is also extended to other members of the committee for their helpful discussion during committee meetings as well as for their germane recommendations on how to carry out the research. The authors are of the opinion that the successful achievement of this research project would not have been possible without their cooperation. Furthermore, sincere thanks are expressed to Mr, J.Ikeda, the secretariat of the association, who contributed greatly to the management of the committee.

216 LIST OF REFERENCES I.

2.

3.

4.

5.

6. 7.

8. 9.

i0.

Ii. 12.

13.

14.

15.

Seed, H.B. and Whitman, R.V., Design of Earth Structures for Dynamic Loads, Lateral Stresses in the Ground and Desisn of Earth-Retaining Structures, ASCE (1970) 103-147. Coulter, H.W. and Migliacio, R.R., Effects of the Earthquake of March 27, 1964 at Valdez, Alaska, US Geolo$ical Survey Professional Paper 542-C (1966). Youd, T.L., Landslides in the Vicinity of the Van Norman Lakes, U.S.Department of Commerce, The San Fernando, California, Earthquake of February 9, 1971, US Geological Survey Professional Paper 733 (1971). O'Rourke, T.D. and Tawfik, M.S., Effects of Lateral Spreading on Buried Pipelines during the 1971 San Fernando Earthquake, PVP-Vol.77, Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, ASME, 1983. Hamada, M., Yasuda, S., Isoyama, R., and Emoto, K., Study on Liquefaction Induced Permanent Ground Displacements, Association for the Development of Earthquake Prediction, Tokyo (1986). Japanese Society of Civil Engineers, Report on The 1964 Nii~ata Earthquake (in Japanese) (1966). Noshiro Municipal Government, The 1983 (May 26) Nihonkai-Chubu Earthquake, a Document of the Hazard Experienced in the Noshiro City (in Japanese) (1984). Niigata University et al., Map of Ground Failure during the 1964 Niisata Earthquake (1964). Kawamura, S., Nishizawa, T. and Wada, H., Liquefaction-lnduced Damage to Piles Found by Excavation Twenty Years after an Earthquake, Nikkei Architecture (in Japanese) (1985). Tatsuoka, F., lwasaki, T., Tokida, K., Yasuda, S., Hirose, M., Imai, T., and Kon-no, M., A Method for Estimating Undrained Cyclic Strength of Sandy Soils Using Standard Penetration Resistances, Soils and Foundations, Vol.18, No.3, (1978) 43-58. Waseda University, Special Issue on Niigata Earthquake, Bulletin of Science and En$ineerin$ Research Institute, No.34 (1966). Tatsuoka, F., lwasaki, T., Tokida, K., Yasuda, S., Hirose, M., Imai, T., and Kon-no, M., (1980) Standard Penetration Tests and Soil Liquefaction Potential Evaluation, Soils and Foundations, Vol.20, No.4, (1980) 95-111. Smith, J.L. and Fallgren, R.B., Ground Displacement at San Fernando Valley Juvenile Hall and the Sylmar Converter Station, San Fernando Earthquake - Geology and Geophysics (Chapter 12), California Division of Mines and Geology Bull., 196 (1974). FUGRO Inc., Geotechnical Investigation for Stabilization and Reconstruction at the San Fernando Valley Juvenile Hall Site in Sylmar, California, Project No. 71-082-EG, Jan. 24 (1975). Schultze, E. and Menzenbach, E., Standard Penetration Test and Compressibility of Soils, Proc. 5th Int. Conf. Soil Mech. Found. E n ~ . , Vol.l (1961) 527-532.

APPENDIX I The accuracy of the measurement of the permanent ground displacements was examined using the following procedures: Step 1 : Several datum points were selected in the area of the measurement, including triangulation points. Fig. A-I shows one example of the locations of the datum points in the northern area of the city in the pre-earthquake survey.

217 Step 2 : The coordinates of the datum points were measured independently by two methods; a survey on the ground surface using a transit and geodlmeter, and an aerial photographic survey. Step 3 : Under the assumption that the coordinates measured by the onground survey were correct, errors in the coordinates derived by aerial survey were distributed to each datum point so that the mean value of the sqaares of errors might be minimized. This distribution of errors was achieved by an adjustment of the location and the angle of the aerial photographs. Step 4 : The accuracy of the aerial survey was determined as a standard deviation of the differences between the coordinates from the on-ground survey and the corrected coordinates of the aerial survey. Step 5 : The accuracy of the measurement of the permanent ground displacements caused by the earthquake was calculated as the square root of the sum of squared accuracy of two aerial surveys before and after the earthquake. The accuracy of the permanent ground displacements in Noshiro City, estimated taking these five steps, is shown in Tables A-I and A-2. In the northern area of the city, the accuracy is +17 cm and 28 cm in horizontal and vertical directions, respectively. As a matter of course, the accuracy of the permanent ground displacements estimated by the procedure depends heavily on the accuracy of the on-ground survey. However, in the present case, the accuracy of the on-ground survey was higher, +8.1 cm in a horizontal direction, than those of aerial surveys and, hence, its effect was neglected. In addition to the examination of the measurement accuracy of the permanent ground displacements mentioned above, the traverse and the plane table survey were conducted in a part of the southern area of Noshlro City in order to verify the results of the aerial survey. The accuracy of the traverse survey was controlled within i/i0,000 and the error was estimated as less than +i0 cm in the measured area. The error of the plane table survey itself was estimated as +I0 cm mainly because of the 1/500 reduction scale for the mapping. Thus, the total error is considered to be within +20 cm, somewhat larger than the error of the aerial survey shown in Table A-2. Fig. A-2 shows a comparison between the results by aerial survey and those by the traverse and plane table survey. The pre-earthquake map shown in the figure was made in 1977, six years before the earthquake, also by traverse and plane table survey.

Figure A-I Datum points for aerial survey in northern area of Noshlro City.

218 Since then, changed.

it has been revised several times,

whenever land boundaries were

As can be seen from the figure, the magnitudes and the directions of the permanent groun4 displacements measured by the aerial survey mostly coincide with those by the traverse and plane table surveys.

TABLE A-I Accuracy of Measurement of the Permanent Displacement in North Area of Noshiro City.

Aerial Survey

Total Number of Datum Points

Accuracy of Aerial Survey (Standard deviation of differences of coordinates by on-ground and aerial surveys)

Accuracy

of Measurement of

Permanent Ground Displacement

Pre-earthquake

Post-earthquake

8

9

(m) +0.14 (Hori.) +0.26 (Vert.)

(m) +0.I0 (Hori.) ~0.12 (Vert.)

(m) ~4(0.14~+(0.10)2 = ~0.17 (Hori.) ~4(0.26~ +(0.12) 2 = ~0.28 (Vert.)

TABLE A-2 Accuracy of Measurement of the Permanent Displacement in South Area of Noshiro City.

Aerial Survey

Total Number of Datum Points

Accuracy of Aerial Survey (Standard deviation of differences of coordinates by on-ground and aerial surveys)

Pre-earthquake

21

(m) +0.08 (Hori,) $0.16 (Vert.)

Post-earthquake

5

(m) +0.14 (Hori.) ~0.12 (Vert.)

Accuracy of Measurement of

(m) ±J(0.08)2+(0.14) ~ : t0.16 (Hori.)

Permanent Ground Displacement

t J(0.16)z+(0.12) ~ = t 0"20 (Vert.)

219

e Plane/ md

Aerial 'rey

0 t

Figure A-2

I0 .

I

20 30m .

I

.

I

Comparison

between

the aerial survey and

plane

table

survey

220 APPENDIX II An attempt was made with the help of M.S. Islam, a research associate of Asian Institute of Technology, to predict the permanent displacement in Niigata using an elastic finite element method. The main difference between the Noshiro and Niigata cases lies in the slope of the ground surface. In Noshiro the ground was inclined, and the gravity force induced permanent displacement, while in Nilgata the ground was reasonably level and the mechanism of the displacement is not yet known clearly. In the present analysis, a study was made of the contribution to the permanent ground displacement made by the substantial translation of the retaining structures along the Shinano River, An analysis was made of the north bank of the Shinano River. The surface soll layer above the groundwater table was divided into finite elements in a manner similar to that for the Noshiro analysis. The Young modulus and Poisson ratio were set at ii0 kg/om z and 0.3, respectively. Boundaries of the finite-element mesh at a distance from the river were fixed because only small displacements occurred. The displacement in the unliquefied area was also set to zero. Along the boundary on the riverside, a prescribed displacement of 7.0 m was given in a direction normal to the shore. After the first computer run, those elements which had tensile stress states were picked up, and their Young modulus was reduced to only 5% of the original value. The second run was carried out using the modified modulus, and the results are given in Fig. A-3. It may be seen that the overall trend is in agreement with the measured displacement.

Predicted permanent displacement in Niigata ~,N Unliguefied / ,~,. area ar. ,a ,~, ~ . . ~ . . _ . ~ _ _ ~ . ~ ' ~~''".': ~jq.

\\\

Figure A-3

5di lac

Permanent horizontal ground displacement in Niigata calculated by finite element method.

Received 30 March 1987; revised version received 20 May 1987; accepted 27 May 1987