フィルダムの地震時における水理破壊現象に関する研究

愛総研・研究報告 第2号 平 成 12年

63

Hydraulic Fracturing in Fill-type Darns during Earthquake

フィルダムの地震時における水理破壊現象に関する研究

Yoshio OHNE.)

，

Kunitomo NARITA吋

Yoshio NAKAMURA吋 'and Yuji MURASE仲.)

r

大根義男，成田国朝，中村吉男，村瀬裕司

ABSTRACT: In addition to the safety against sliding failure of embankment slopes， saf巴，ty against

internal erosion caus巴dby hydraulic fracturing has b巴巴nanother important issues to be discussed in the

seismic resistant design of fill~type dams. This paper conc巴rns the m巴chanismand its possibi1ity of

occurr巴nceof hydraulic fracturing in巴arthand rock fill dams during巴arthquak巴 Laboratoryseepage

fracture tests wer巴conductedon erosive soils under various conditions of water pressure and confining

stresses to know what are to b巴 influ巴nti且1factors on seepage failur巴， and FEM dynamic response

analysis was made for different cases of embankment configuration to study the ext巴ntof damages and

dev巴lopmentproc巴S8of hydraulic fracturing during earthquak巴a

Key words: hydraulic fracturing/ earthquake/ hydraulic gradient/ dynamic analysis/ stress ratio

1.INTRODUCTION

Stability evaluation of fill-type dams during

悶rthquake has mostly focu8ed on the sliding

failure of embankrnent slopesー FEM' dynamic response analysis has been an巴ffective and

us巴ful to01 commonly appli巴d in the study of

seismic b巴haviorof dam body during earthquake司

In the First司US-JapanWorkshop on Advanced

Research on Earthquake Engin巴巴ring for Dams

(Nov. 1996)，' the authors have proposed a practically us巴fulmethod of stability evaluation

of embankment， by taking into account response shear strain as a failure criterion.1) Because the propos巴dmethod necessarily does not r巴quireth巴

dynamic shear s住巴ngthof construction mat巴rials，

lt s巴巴msto be applicab1e with high accuracy in the evaluation of slope stability of earth and rock 白11dams. In the earthquake resistant d巴signof fill-typ巴 勺Professor，Aichi Jr山ituteof Technology 村)Chief Engヮ AJCOConsulting co， ltd.

*域本) Chief Eng司，DAJME Eng. Service co. ltd.

dams， however， not only st旦bilityagainst sliding

failure of embankrnent slope but also that against int巴malerosion and water leakage through the

core is necessary to ensure wh巴n the res巴rvoir

water is filled during dam operation. Cut司off

wall tr巴nchconstruction and sev巴rese1ection of

core and filter zone materials are for instanc巴to b巴 己 貸'ectivem阻suresto prevent such， hydraulic fracturing damages. In this study， laboratory seepage fracture tests were conducted to investigate failure criterion of hydraulic fracturing by paying attention on the relationship between出e confining stress and hydraulic gradient in the core zone. FEM dynarnic response analysis was then made on the 10ngitudinal section of embankrnent dams to find stress distribution and hydraulic gradient in the core. The computed values w巴recompared with

thos巴 bytests to examin巴 thepossibility of the

occu訂巴nce of hydraulic fracturing. Th巴 results

presented the fact that hydraulic fracturing tends to occur in the upper part of the sharp abutment and near th巴turningpoint of the abutm巴ntslope.

64

愛知工業大学総合技術研究所研究報告，第2号，平成12年，Vo1.2， Mar.2000

B

(a) Plan View of Rock Fill Dam

Sliding Plane Sliding Plane (b) A-A Section (c) B-B Section

(d) Cracking and Sliding in Earth Dam

Hydraulic Frac加ringin Fill-type Dams during Earthquake

6

5

2. DAMAGE OF FILL-TYPE DAMS CAUSED BY EARTHQUAKE According to th巴r巴centinv巴stigationreports on the damages of fill-type dams caused by big 巴arthquak巴s

，

seismic damag巴scan be classified into two categories; (1) the transverse cracking at the crest of a dam near th巴 abutment foundation

，

as shown in Figs.2.1(a) and (b)

，

and (2) th巴 longitudinal cracking to cause sliding failure of embankment slopes

，

as shown in Figs.2.1(c) and (d).2) The forrner type of cracking could lead leakage of the reservoir water and intemal巴rosionthrough the core. 3. MECHANISM OF HYDRAULIC FRACTURING J).) Hydraulic fracturing takes place due to the (a)

トー→

l

Shear.deformation (b) r C'， ，/， 〆"、、、

午-(大山

fill σ3 σ3 σ1 σ Fig.3.1 Str巴ss Change du巴 to Differential Settlement decrease in confining stress acting on the soil， which in turn is caused by the differ叩 tial settlement in the core. In Fig.3.1(a)

，

for instance

，

differential settl巴ment is induced by the earthquake force near the abutment foundation

，

and it causes r巴ductionin the lateral confining pressure (CJ3).In Fig.3.2(a)， settlement near出巴 turning point of the core width induces arching action and decrease in the vertical confining pressure(a 1)， which must be the cause of hydraulic企acturing. Fig.3.1 (b) and Fig.3.2(b)， respectively， repres巴nts these stress conditions with Mohr's str回scircles.As indicated by the dotted lines

，

reduction in出econfining pressur巴 may shift the stress circle left and get it closer to the failure envelope to lead a stat巴 ofhydraulic fracturing. (a) (b) τ C'， q，' σ Fig.3.2 Stress Change du巴toArch Action

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愛知工業大学総合技術研究所研究報告，第2号，平成12年，Vo1.2，M町田2000

3.1 Laboratory tests on hydraulic fracturing

In ord巴rto discuss the possibility of hydraulic

fracturing for diff巴r巴nt situations mention巴司

above， th巴 following two series of tests were

caπi巴dout in this study. Test-l: from the initial uniform stress state of 0"1 =0"3inth巴tri-axialcompression apparatus， the minor principal stress0"3 on the sp巴cimenis decr巴ased gradually， und巴ra seepage condition of constant hydraulic gradient， to produce th巴 final state of seepage fracture， which realizes the stress states shown in Fig.3.1. T巴st-2: se巴pag巴 fractut巴 tests are conducted under a constant effectiv巴verticalstress .((Jゆ， by increasing the hydrau日cgradient st巴Pby st巴p to obtain th巴finalvalue (if) at fracture， which r巴alizesth巴stressstates in present巴dFig.3.2.

3.2 Apparatus and soil samples

Sch巴matical illustrations of the apparatus for

Test-l and Test-2 series are shown in Fig.3.3 and Fig.3.4， respectively. The water flows from one side to th巴 other in Fig.3.3回 d from the

印 刷erto the two end points inFig.3.4， with a

head di百巴renc巴

L

J

h.

Grain size distributions of the mat巴rialsused

in the t巴stsare shown in Fig.3.5， in which the material of a) SM and b) SC are used for Test-l and Test・2，respectiv巴ly.Th巴 specimens ar巴 prepared in th巴 laboratory to satis勾 the specified Proctor compaction conditions of dry density and water content， as shown inFig.3

ム

of points B， C and D in Test-l and the point E in Test-2 series. D巴tailsof the test conditions are surnmarized in Table-3.1. 3.3 Test resu[ts in Test-1 series The r巴sults of Test-l series are summarized in Figs.3.7 and 3.8. The relationship b巴 同'een th巴 discharge (q)and the e妊巴ctiv巴 stress ratio (ob!oc) defined in. th巴 column is shown in Fig.3.8. It is cl巴arlys巴巴n in the figure that the

discharg巴fromthe specimen increases due to the

incr巴 丘 町 in the str巴ssratio， showing an abrupt 一ー-Q Fig.3.3 Se巴page Test Apparatus forTest-l Series Fig.3.4 Se巴page Test Apparatus for Test-2 Series 100 ( ポ ) ﹄ ω c c E H C ω U ﹂ 由 仏 a) b) ρs(g/cm') 2.67 2.67 Sand c.(%) 84 83 Siltc.(%) 10 5 Clay c.(%) 6 12 80 ! 日 60 40 20 O 0.001 0.1 Grain Size (mm) Fig.3.5 Grain Size Distribution of Fill Mat巴rials used in Tests

Hydraulic Fracturing in Fill-type Dams during E紅白quake 67 可 巴礼 ρdmax. c

、

、

n X 0 3子

、 川 弘 、

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戸 巳 告 書 W

Fig.3.6 Compaction Conditions of Test Specim巴ns Table-3.1 Summary of Seepage Tf.;st Conditions Tcst-l Tcst-2 Initial Stalc: a 1=C 2 a...= 0.5 (kgf!1ロザ} 5l悶S5and Sc巴pagc σ1宮 1，，23 (kgf/cm')σ.'= 0.1， 0.2， 0.4 Conditions i = 5，10.20 σョ grad u a 1"ly i gradually dc四 国siog incrcasing Tesl Point B C D E

E

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= 1.85g1cm') Watcr Contcnt W (略〉 9.4 13.7 16.8 17.6 Dcg・of5a" 5r(喝} 49.1 71.6 87.8 90.0

一一

change at a certain condition.The values of the critical stress ratio (Ob/OC)f defined by the point are plotted against the value of the，hydraulic gradient at failure(if)in Fig.3.8 for different compaction conditions.It is recognized in the figure that for sampl巴s having the same dηr densiザ ahigher resistance can be expected to achieve against hydraulic fracturing as the material is compacted in the， wet side of出e optlmum. 3.4 The test results in Test-2 series A representative tes't result of CJ'v=O.4kgf/cm' iS: shown in Fig.3.9， taking the discharge(Q) from the sp巴cimenon the ordinate and the hydraulic 160

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Fig.3.8 Stress Ratio at Failure σest-1) gradient (i) on the abscissa， in which solid lin巴s are drawn in reference to the constant coefficient of ，permeability， which satisfies 'the Darcy's law of v=ki for the state， of出邑 laminarflow. It is seen that solid circle plots move along these s traigh t lin目 ofconstant k-value in the early stage of the test， showing however an abrupt ch阻gein the discharge(Q)in the vicinity of i キ 40. The critical value of the hydraulic gradient(u)can then be defined at the po泊tof if=40 for the case of CJ'v=0.4kgf!cm'. Th巴 relation. between the values of if and σ'v is summarized in Fig.3.10， for the results of the present study by solid circles and for other tests on SM to CL materials by open circles.

愛知工業大学総合技術研究所研究報告，第2号，平成12年，Vol.2， Mar.2000

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8

1) The analysis is done for a standard type of rock fill dam with a c巴ntrallylocated core of 100m in height， as presented in Fig.4.1， by changing abutment configurationinfour cases. 2) Two-dimensional叩alysismay be r巴asonable as a first step to understand dynamic b巴haviorof fill-type dams and to evaluate their possibility of hydraulic fracturing during earthquake. Analysis is therefore made for harmonic excitation of acceleration with a frequency of 1Hz. 3)τn巴 阻alytical proc巴dure adopt巴d

basically the same as theQUAD・4 program

，

where non linear material properties of dynamic behaviorむerepresented by the HardirトDrnevich mod巴1in the following forms. here is D-yalue思 95% 5r=9口%

v

a.'=0.4kgl/ロn' :

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v d

H Hydraulic Discharge vers国 Relation (Test-2) Fig.3.9 1) Dynamic response of embankment ln Table-4.1， values of the input and response acceleration calculated at the base and the crest 釘e compared， with the natural frequency obtain巴dfor the primary mode of vibration of the embankrnent. It is clear that出e response acceleration鉱 山ecrest is about 3.5to 4.0 times larger出 血thebase acceleration.

Primary mode of vibration and distribution of th巴 response accelerationinembankrnent are drawn加 Fig.4.2for a representative case of the abutment slope of 1 to 1.5 (case司2).Such results for others cas巴sas case-l， 3， 4 and 5 are alrnost same as that of case・20ne's. 2) Evaluation of hydraulic fracturing Possibility of the hydraulic fracturing during earthquake is exarnined here by applying the following two criteria. 1 1 +(γ/ 'Yr)γ G 0

=

510 a "." γr = 4.8 X 10'] a

，

'.75 4.2 Results 01 dynamic response analysis γ/γr 1 +(γ/γ

。

G/Go= h/ho= wher巴 Presen

.

t study 匡 Other

。

tests

，

1=40口{σ').... /

F

500 100 』 担 c 由

B

_.... 0 U = コ_帽 』 セコ 』 コ ご 1 0.5 5口 ! 日 Ekgf/cm2) Hydraulic Gradient at Failure (T巴st・2) ロ.05 0.1 日.5 E仔'ectiveStress σ' Fig.3.10

4. FEM DYNAMIC RESPONSE ANALYSIS

4.1Analysis procedure

τne aim of this study is to examine possibility of hydraulic fracturing in fill司typ巴

dams when earthquak巴forcesact upon the cor巴 with the‘reservoir fiUed with wat巴r. FEM dyn白 羽icresponse analysis is now conducted on simple embankrnent models for different typ巴sof

harmonic巴xcitation. Analysis procedur巴s and conditions employed here are summariz巴dbelow.

Case No. Case-1 Case-2 Case-3 Case-4 Case-5

Hydraulic Fracturing in Fill-type Dams during

E

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Table 4.1 Response Acceleration at Dam Crest Base Accel巴ration ( 1Hz) Cas巴No. 50 gal 100gal 200 gal Case-1 214.3 414.5 754.9 (1.05) (1.02) (0.97) Case-2 ₍218_0.95.4_{) (}407.8 _{0.93) (}7₀0_.7₉.₀6₎ Case-3 200.9 373.1 667.7 (0.90) (0.89) (0.86) Case-4 200.9 372.6 666.1 (0.90) (0.89) (0.86) Case-5 201.9 373.6 666.7 (0.91) (0.89) (0.86) ( ) shows natural fr叫uency(Hz) at the first mode

7

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Hydraulic Fracturing in Fill勾peDams during Earthquake

(a)

号

afetyevaluation proposed in this paper Evaluation of saf巴，ty factor against hydraulic

fracturing is explained in Fig.4.3， which is redrawn from Fig.3.8 in a more precise form. In this figure， the stress ratio which leads to hydraulic合acture is obtained co汀esponding to the value of the hydraulic gradient at failure(ir)， and the safety factor can be evaluated as the ratio of the value of也estress ratio at failure to that at the present state. Assuming that if = 2.0 for the soil compacted in the state of B， for example， the value of出巴 stressratio at failure can be deteロninedfrom the upper solid line as (ob/高)f= 0.95.百th巴 叫ueof the stress ratio calculated in the dynamic response analysis is tak巴n as (ob/oc)= 0.93， the safety factor (Fs) becomes to be Fs=0.95/0.93今1.02

，

suggesting a little safety against hydraulic fracturing. (b) Safety evaluation by SeedS)，的

Seed et al.(1976) have presented the fol1owing crit巴ria to evaluate possibiliザ of hydraulic

fracturing in the Teton dam failure. a 3'話 u

where a 3'and u are the minor principal stress and pore water pr巴ssure

，

respectively

，

at a certain point. 1.0

( 喧

陪 )

・ ﹄

( 目

問

)

。 一 日 伺 ﹄ 回 目 ∞ ﹄ 干 の 0.8a 2 Hydraulic Gradient(if) 4 Fig.4.3 Safety Evaluation with Stress Ratio

7

1

5. DISCUSSIONS O N POSSIBILITY OF HYDRAULIC FRACTURING Possibility of hydraulic fracturing in the core zone is discussed now by comparing the results from two methods of safety evaluation presented above; one is the criterion proposed in this paper and the oth巴rby Seed et al.

5.1 Safety evaluation proposば inthis paper Distributions of the response acceleration釘ldthe safety factor against hydraulic fracturing in the embankment are pres巴nted in Fig.5.1 through Fig.5.10 for allロsesof abutment configuration. Discussions are summarized in th巴following. (a) In the embankment with abutment slope of 1:1.5

，

hydraulic fracture app巴 むsinitially inぬe upper part near the abutment foundation， and it develops to the lower part as the respons巴 acceleration increases. (b) Possibi1ity of企acturing becomes lower as the abutment slope is gentle. (c) In th巴 casethe abutment foundation has a turning point of slop巴 inclination， hydraulic fracture tak巴splace first near the point and it extends widely upwards. (d)Inthe c出E出eabutment slope is st巴eperin 出eupper part than the lower CU-shaped valley)， fracture starts near the turning point of slope and it巴xtendsupwards and much more widely出an

the above case along the upper st巴巴p.abutment.

τhis result is not a matter of worrying about

，

because the confming s位essin the core is much high巴rthan the above case in the static state. 5.2 Safety evaluatioれbySeed method Distributions of出eminor pri且cipalstress a 3 and the pore water pressure u in embankment are giv巴nin Fig.5.ll through Fig.5.15. Tendency of hydraulic fracturing is almost the same as present巴dabove except th巴shapeand extent of th巴 rapture zone.It is clear that the criterion present巴dby Seed is rather loose as compared

72 愛知工業大学総合技術研究所研究報告，第2号，平成12年，VoI.2，M低2000 ιSUM民1ARIES Possibility of hydraulic fracturing during earthquake was discussed in this pap巴rthrough laboratory seepage fracture tests and FEM dynamic response analysis. Focus of the present study is placed on to know the threshold of the hydraulic fracturing， and satisfactory results were obtained to discuss on the safety evaluation of embankment against hydraulic仕acture. It is

nec巴ssary

，

however

，

much more follow-up study to apply the proposed method for the actual dam design: i.e.

，

more rigorous 3D dynamic analysis and s巴巴page fracture tests und巴rvibration are

required for a future precise stlldy on hydraulic fracture.

REFERENCES

1) Ohne， Y.巴tal (Nov. 1996). Evaluation of

seismic slope stab出tyof earth and rock fil1 dams

，

First U.S明Japan Workshop on

Advanced Research on Earthquake Eng. [or Dams.

2) Ohne， Y. (1985) . Seismic behavior of MAKIO dam， A report o[ specialty session o[ NAGANO・KENSEIB U Earthquake

，

the 20th

JSSMFE annual meeting. (in Japanese) 3) Ohne

，

Y. & Narita

，

K. (1978). Some

considerations of the Teton Dam failure. Technical r宅porto[ Aichi Inst. o[ Technology

，

No.13: pp.217・229.

4) Murase， Y.巴tal (Aug. 1995). Study on hydraulic fracturing of core-type rock fill dams. The 1¥θ弘4International Con

f

.

on Dam Engineering， pp.363-371.

5) Teton Dam Failure Interior Review Group. 1976a. First interim report on the Teton Dam [ailure.

6) Teton Dam Failure Interior Review Group. 1976b. Second interim report on the Teton Dam [ailure. 7) Narita， K. et al (1997). Centrifuge mod巴l tests on hydraulic企acturing in巴arth and rockfill dams. Proc. 9th Int. Con

f

.

o[ IACJo.る4G，voL3， pp.2291・2294.

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