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A Borehole Stress-strainMeasurement System byEmploying Electronic SpecklePattern Interferometry

Hirabayashi, Jun; Takemoto, Shuzo

Hirabayashi, Jun ...[et al]. A Borehole Stress-strain Measurement System by Employing Electronic Speckle PatternInterferometry. Memoirs of the Faculty of Science, Kyoto University. Series of physics, astrophysics, geophysics andchemistry 1995, 39(2): 177-196

1995-03

http://hdl.handle.net/2433/257631

Memoirs of the Faculty of Science, Kyoto University, Series of Physics, Astrophysics, Geophysics ancl Chemistry, Vol. XXXIX, No. 2, Article 1, 1995

A BorehoRe Stress-sSraige MeasaxremaieKit System hy EgxpEoyiitg

Egectroitic Speckle Pattern Enterferometry

By

Jun E{KRABAYASffIrk• and Shuze TAKEM8TO

Department of Geophysics, Faculty of Science, Kyeto University Kyoto 606-el, Japan

(Received November 17, 1994)

Abstract

A borehole stress-strain measurement system based on Electrenic Speckle PatternInterferometry (ESPI) was developed and emp}oyed for rneasuring crustal stresses andstrains. The system was designed to be smali in size and iight in weight, and to be able to

rneasure quantitative}y out-of-p}ane deformations (radial deformations) of the cylinclrical

area in a borehole in terms ofa wavelength ofthe laser light. Laboratoy tests confirmed that

the system could be avaiiable for preclse stress-strain measurements. We have carried outfield experiments employing the system at Hiraki mine in Hyogo Prefecture. As a result,some problems to be solved for employing the system in field experiments have been ciarified.

Based oR these experiments, a measurement module has been improvecl to measure out-of-plane displacements not on}y in the surrounding cylindrical area but in the bottom area. It

will also be possible to measure in-piane dispiacements in both side and bottom areas ofa

borehole by medifying an optical arrangement of the moclule. Using a new system,laboratory tests were performed. Consequently, it was confirmed that the new system was

able to measure quantitatively a small deformation of the object in terms of fringedisplacements in speckle patterns. However, there rernain some problems to be solved to

apply the system for measurements of crustal deformatioR in borehoies: that is, thewaterproofdesign of the system and the introduction of the small semi-conductor la$er source

Snstead of the He-Ne gas laser and optical fiber system used ln this study. As aRotherappllcation of the ESPI system in geophysicai sciences, we propose to employ it in precise

measurements of tunnel deformation.

Contents

Is Introduction ...m...m...."."...."."....h"........"."."."."."........."..-.".-...-..-..,."

Design aRd ConstrucÅíioR of an ESPI Stress-strainMeasurement System ".....-..-...H..".HH.............-......".-.-"..............-..."-

Results of Laboratory [rests............."..........................."....."....m...H.......".w..

Field Experiments at Hiraki Mine ..........-...•h•--"•..••.••.-••-•-••••••••••••-••••••

Improvement of the Measurement Module ...................................................

Discussion"....-...........".""....."."•H•..--..•-•••••••••-••••••-••-••••-•••••t••••••••••-••••••••

Concluding Remarks.e.-••.••-•-•--t-•••-•-•••••••••••-••-•••••-••••••••-•--••••••••-••••-•••'•''"

I78

179

l86

}88

190

192

194

* Present address: Canon Co., Ltd., Shimomaruko 3-30-2, Ota-ku, Tokyo l46, Japan.

178 J. HIRABAYASHI and S. TAKEMo"ro

i. gn{reduction

Knowledge oÅí the state of crustal stresses and strains plays an important ro}e in

understanding the driving rnechaRism of tectonic processes. It is alse important to

know their regioRal distributions as wel} as time variations to promoÅíe earthquake

prediction studies. Stress measurements have thus been carried out in various regions

in Japan (e.g., :lrANAKA, I987; [lrANAKA et a}., 1990).

Methods to measure crustal stresses are classlfied inte the hydrofracturlng method,

the stress-relief method by using strain-gauges, the breakout method and so on(KAMEoKA, 1978). [lrhe hydrofracturlng method can determine the state of crustalstress from fractures which appear in a borehole wail due to a hydropressure. In case

of the stress-relief method, the crL}stal stress ls determined from measurements of

defermation of a borehole wheR the stress is relieved by means of overcorlng.Deformation measurements are combined with the e}astic property of rocks to estlmate

the state of s{resses. The radial deformation o'f a borehole is usual}y measured by

determining a crustal stress tensor. In sorne cases, the crustal stress tensor ls

determined by measuring the de{brmation of tke bottom of the boreho}e. A deviceusing a l6 element-gauge was deve}oped for such a purpose (OKA et al., 1979). In the

breakout method, directions ofa principal stress are determined frem breakeuts that are

zones of spal}ing aRd ft-acturing appeared on side wa}ls of a borehole (e.g., MAstriN,

l988).

A itBique ins{rumenÅí for measuring in sittt stress fieids in crustal rocks was

develeped by a gyoup at the Caiifornla lnsti{ute ofTechnoiogy (BAss et al., l986). The

instrument is ca}led a `holographic stressmeter' and is able to measure a smal} dis-

placement around a borehole in teyms of an iRterference fringe pattern on a ho}ogram.

The state ofstress fields around the bore}iole caR be determined by tke same procedure

as that commonly used in the stress-relief method.

On the other hand, extensometeys, which empioy length standards in ferms ofquartz tubes or supey-invar bars, kave been widely usecl in many observatories to searchfor crustal deformations. Ifwe measure tida} strains on an order of }O-8 by means of

an extensometer, re}ative disp}acements between the fixed and free ends of an exten-someter wi{h a Iength of 10 m are fotmd to be O.1 jum or se. A resolution of 1 Å~ 10ww iO is

required to observe tidal sÅírains with a precisioR of10/o. As for t}ie other devices,

crustal strain measurements usiRg resis{ive strain gauges (YANAGis.xwtx, l984) and

multi-compoRent smal} borehole strainmeters (lsHii et al., 1992) have been reported.

In any case, absolute calibyation ofthese lnstrurnents is diff7icult. One solut!on to

overcome this di{ficulty is the use of laser extensometers which caR measure sinal}

strains quantitatively in terms of the wave}ength of Iight (TAKew{o'}'o, l979). As

mentioned above, optica} interferoirietric devices have beeB eff)ectSvely used in stress and

strain measurements in geophysical sciences. XNJe tkus intend to improve the inter-

ferometric measurement system of crustal stress and strain.

Among the optical interferometric methods, Speckle Pattern Ixaterferometry (SPI)

is a teclmique that can measure the sma}1 deformation ofan object w2thouÅí teuching it

in terms ef the wavelength of the Iaser iight. The speckle pattem is caused by Åíhe

A BOREHOLE STRESS-STRAIN MEASUREMETSTT SYS"i"EM l79

random interfereRce ofscattered waves from a diffusely refiecting surface ofan object.

SPI wkich uses photographs as recording devices involves difficulties in continuottsly

automatlc operatlon. EIectronic Speckle ?atterR Interferometry (ÅíSPI), which obtains !mages by usiRg

e}ectroRic devices such as a video camera and an image-processor, was developed iR the

l970's and has been app12ed to various purposes since Åíhen. As an exampie ofapractica} applicatioB of ESPI to laboraÅíory mesurernents of small disp}acements,

YAMAGucm (}98}) deve}oped a }aser speckle strain gauge. In solid eartl} sclences,

iaser speck}e interferometry is used to study the process of the fractuye zoRe in rocks

(CHENGyoNG et al., l990). ' The applicability ofESPI to crustal stress aRd strain measurements is described in

this paper. Flrst, design aRd constructlon ofthe ÅíSPI boreho}e measurement system is

described. Secoond, problems Åío be solved through laboratory tests and fieldexperiments are clarfied.

2. Design and Constructkon of aen ESPK Stress-strain tw{easurement System

2.1. Proeedure of Crustal Stress Measecrement by Strain-relief Method T}ie principle of measurements of crusÅía} stress by means of the strain--relief

(overcoring) method is i}}ustrated in Figure 1. A rock rnass is first assumed to be

subjected to two dimensioRal stresses . A pi}ot hole ls drilled into the rock at the po!nt

where the sÅíress shotild be measured. After Åíhe drilling, the hole skould be deformed

by the pre-existing crustal stress. The measuremeRt module ef the system is thenattached in the borehole. The borehole is sea}ed by means ofa borehole p}ug tewaterproof the system. TheB {he pilot borehole is overcored and separated from tke

surrouncling rock mass. As a resu}t, radial disp}acements of the pilot borehole should

be measured. Crttstal styesses in rocks, in which {he measurernent module is set up,

caB be determined from the resultaBt displacements, if elastic properties of rocks are

known. The present system is designed to rneasure the radial displacements ofthe borehole

wa}1 (cylindrica} area whose height is 5 cm). The system is required to have not oR}y

lkigh accuracy but mobility.

2.2. Analysis ofEgastic Deformations InJapan, early contribution to analyze the relation between a radial displacement

of a circu}ar borehole and a crustal stress was made by NiRAMA'i'su aRd OKA (i962).

AB analysis of e}astic deformations by munerical ca}culatioRs is described iR thefollowing.

One of the coordinate systems reÅíerred to in this analysis has the z-axis along the

borehele axis (positive in the Åíorwayd direction of boring) and the x- and y-axes

perpendicu}ar Åío the z-axis to ferm a right-handed system. Another system usingcy}indrical coordinates (r, 0, c) with the z-axis coincident with that of the Cartesian

coordinates is introduced and e is measured from the x-axis. The rock is assumed to

be isotropic. Ifwe deltote components ofstress tensors by 6x, 5J,, oj, Trvo T.-x and Tx])

l80 J. HIRABAYASHIand S. TAKEMOTO

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(a) A rock mass subjected to the horizontal stresses.

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sealed by means of a borehole plug for the purpose of waterproof.

(e)

Fig

s' :;F."Nv .e .:n-.,

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Radial displacements of

. 1. Principle of crustal

the pilot borehole to

stress measurements

be measured.

by bvercoring.

a radial displacement d, is

d,= 2 EO ifi f2 f3 fi)

glven Ox

ol

Txl

dz

by the

'

following form J

(1)

where,and,

ro is the radius ofthe borehole , E is the Young's modulus, v is the Poisson's ratio '

fi =(1- v2)(1 +2 cos 20) + v2,

f2=(1- v2)(1 '2 cos 20) + v2,

f3 =4(1- v2) sin 2 0, and,

f4=-V.

(2)

(3)

(4)

(5)

A BOREHOLE STRESS-STRAIN MEASUREMENT SYSTEM181

Equation (1) shows that three measurements in independent directions arerequired at least to determine the whole stress tensors

2.3. Construction of the ESPI Measurement System Figure 2 shows a schematic diagram of the measurement module of the crustal

stress measurement system employing electronic speckle pattern mterferometry Theheight of the measurement module is 40 cm and its diameter is 10 cm The weight ofthe module is about 5 kg The module is fixed by three legs (J) at the upper side ofthe

module as well as by three legs (J) near the bottom The legs are able to be expanded

and tightly contract to the borehole wall by compressed air

The laser beam is supplied from a He-Ne laser of I5mW and fed to a beamexpander (A) through an optical fiber (1), and then split by a beam sphtter (B) to two

waves,one is the reference wave toward a reference plane (C) and the other is the obJect

wave toward a borehole wall (G) The object wave is distributed m all directions(3600) surroudmg the borehole wall by a cone mirror (F). Two waves reflected by both

the object wall and the reference plane interfere with each other, and the interference

image is recorded by a video camera (H). Speckle patterns arise in the images The

speckle pattern is caused by the random mterference ofscattered waves from the surface

of a diffusing object and reference plane illuminated by the coherent light of the laser.

The images obtamed are processed by a personal computer (NEC PC9801VX) and

(a)

231 Optical fiber

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Fig 2 (a) Schematic diagram of the borehole module of the ESPI stress measurement system (b) View of the borehole module

182 J. HIRABAYASHI and S. TAKEMOTO

[IlilllllllEIbi

- - st-Videomon1tor

Computer

Sd-•

Picturedevice

.:

::

f':"

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Fig. 3. Setup of the ESPI stress measurementsystern.

Fig. 4. An example of estimation of radial displacements which should be detected by the measurement system.

A BOREHOLE STRESS-Srl"RAIN MEASUREMENrr SYS'I'EM 183

an image processor (EDEC IMAGE-MAX). The radial displacement of the boreholewall caR be estlmated by tke image processing in terms ofa halfof the wave}eng{h of the

laser iight. The video camera is a KM-80 image sensor camera unit in whicl} CCD has

5l2 Å~ 582 pixels. A rininimum i}lumination needed by tke camera is 5 lux. The image

processor has 512Å~480 pixels. Therefore, pixels to be processed in the system are

512Å~480. Figure 3 shows the setup of the whole system. Figure 4 shows an example of theoretical results for radia} expansions. Thetheoretical image was calcttlated to represent a stored image after overcorlng.

Maximum aBd minimum radial dispiacemeRts are shown ln Figure 4.

2.4. Calculation of ESPI Image in the System The theory of out-of-plane ESPI (reference light method) measurement by which

the out-of-plane deformatioRs are measured is described in {his subsection.

Let a coordinate on the CCD and that on the object piane be (x,]J) and (X, n,respective}y. (sc,],) can be expressed as a function related to (X, Y),

(x,)) ==AX, n. (6)At Åíhe poiRt (x,7) on the CCD of the video camera, the object wave A, (x,!) refiected

from (IY, Y) on the object plane and reference wave A, (sc,7) refiected Åírom (l\,, Y,) are

g!ven in the form of the fo}lowing equations, respectively.

Object wave A,(x,")==a.(I\,y,z,)exp[ik(vXti}'ir-iP+y+(zi+z)-l-vftiiViiRfiIIFMiZilln2S--t- 2y-t-(z+z,))],

Reference wave Ar(x,2)=:ar(i\r,Yr)Zr)exp[ik("ftif;I6]Jii"IFniZFZ5'-i- iYr+(Zi+Zr)+rmt-+Yr+(Zr+Zc))],(7)

where,

Zi: the length ofthe optical path from the focal point of the fiber }ens to the center of

the beam sp}itter,Z. : the length ofthe optical path from the center oÅíthe beam sp}itter to the center ofthe

object plane (Y :O, Y=O),Z, : the }ength ofthe optical path from the center ofthe beam splitter to the cenÅíer ofthe

reference plaRe,

Z, : the length ofthe optica} path Åírom the ceRter ofthe beam splitter to the center ofthe

CCD (x=:O, ],=O),a. (X, Y, Z,): the distribution of the light intensity (the object wave),

a, (IV,, Y,, Z,) : tl}e dlstribution of the light intensity (the reference wave), aRd

k : a wave number (=ur2n!Z)[A: the wavelength of the Iaser light].Usin.cr the proporÅíional relation,

x; y: (zt+z,) :x,: :y,.: (zt+z,.),

Xr and Y, are expressed by, X,=(.Z,i.'.Zi)X

l84 J. HIRABAYASNI ancl S. TAKEMOTO

where,

Yr : ( Zi + Zo

==RY,

= ex,

Zt+z,.y)

Zi+ Z,. R= Zt+Ze 'Then Equation (7) is transformed into the following form,

Ar(X,])=:ar(Xr) Yr, Zr)'eXP [ik(Rir+Rcr)], (8)where,

Rtr="vQ(il61VIZiMiFMFfii2;iiiHRX)+(Ry)+(zt+z),and,

R,,=vQ(EIij'ii"iFi7EYili}'ii-ilZiii-Z5-i-R.\)+(Ry)-i-(z.+z,).

Since the image intensity I(x,?) on the CCD is given by IA,(x,")+A,(x,7)I2, it is

expressed in the foIIwing form.

I(x,7) rm IA.(x,])+A,(x,")i2 ==a,2(x\, Y, Zo) -l-ar2(x\r, Yr, Zr)

-F2ao(X, Y, Zo)ar(Xr, Yr, Zr) ' CeS [k((Li+L2)ww (Rir+Rcr))], (9)

where,

L}==os1\+Y+(Zi+Z,),and, L,=vftgll"i-iYl}-IZIi2;iliE-+y+(za-z,).

Ifthe object plane (the berehole wa}1) is deformed by (S.y, Sy, 5z) and k is changed to k',

two waves should be changed. Then,

I'(x,") rm IA'o(x,s) -lwwA'r(sc,s)12

==a2o(X+ 5K, Y+ 6y, Ze ww 6z) +a2r(Xr, Yr, Zr)

wwF 2a.(X+ Sx, Ynvim Sy, Zo- Sz)ar(Xr) Yr, Zr)

'COS [k'((Li'+L2')-(Rgr -i- Rcr))]) (}O)where,

Li' : (X+ Sx)2+ (Ymelma 5y)2+ (Zi -i- Z, ww Sz)2 , and,

L,'== V7(-ifaI-Jil--a\) +(y+6}r) -f-(Z,+Z,-6z) .

Since 5.y, 6y ancl 5z are very small,

a.(.iY-lww S.y, Y+ 8y, Z, -lww 6z)s'a,(X, Y, Z,). (}1)

Then,

I'(sc,r) ==a,2(X, Y, Zo) +ar2(Xr7 Yr, Zr)

+2a,2(tY, Y, Zo)ar2(X,•, Yr, Zr) 'Cos[k'((Li+L2)-(Rir+Rcr))]• (12)

The image intensity obtained by subtracting the image before deformation from

A BOREHOLE STRESS-STRAIN At{EASURE)vfENT SYSTEIYi 185

tl}at after deformatlon is,

Isttb(X)vJ)) =ur I' ( c,r) nv I(x,vy)

=: ww4ao(X, Y, Zo)ar(1\lr, Yr7 Zr)

' sin [-ll-(k'(VLi2+2Li"2+ SL2 + L22m}-2L2"2+ 6L2 ww (]Rlr+Rcr))

.,,:Xl,`itlvl2il)IliR,ti•t'L+RC31.l']+paL,+2L2+on-(Rir"Rcr)'

Mk((Li+L2) ww (Rir+Rcr)))]) (l3)

where J 8L2=: 6.y2 + Sy2 -i- 6i

L"i2==.\6x+Y6}rww(Zt+Z,)Sz, and, L" 22 =:XS.y -tnv YSym (Zo -l- Zc) Sz• '

6L is very small, and Li aRd L2 are much larger than Li" and L{2", respectively. I,,,b(x,

),) is approximated to Åíhe foIIowing form,

Isttb(X)vJ') SS ww4ao(X, Y, Ze) ar(tYr, Yr, Zr)

' Si" [-iir(k' wwE- k) ((Li +L2)- (Rtr+R,,))+k'( LX'2 + Liil'2 ))]

sin[-Sm(k'( LSi'2 -I- Liill'`2 )+(k'-k)((Li+L2) ww (Rt,-l" Rc,))] (14)

A macroscopic average of li(x,],)(""(I,.b(x,])2) is given by the followiRg form,

<Ii(x,v7))> =8ao2(X, Y, Ze)a,2(Xr, Yr, Zr) 'sin2 [-ilrP(X, Y, Z,, 6x, 6y, 6z)], (15)

where, k' k" =w, and Ll tt2 L2u2 L, -l- L2 ) P(X, Y, Z,, 6.y, 6y, 6z)=k"(

+(k"MI)((Li+L2) ww (Rir+RLr))• (16)

<li(x,.),)> is dark in areas where p(X, IY, Z,, S.y, 6y, 67..) =mk (A =O, 1, 2, ''') is satisfied,

while <Ii(x,))> is bright in areas wlterepO=:(m+-S)ft (m==O, l,2, ''') is satisfied. In

the extreme case when the laser }ight is approximated to be parallei (X, Y f=O), and k"==

1, then pO is expressed by,

faO == -26z. (1 7)Equation (l7) holds to a fairly good approximatien in this measurerneBt system. Ifthe

wavelength ofthe laser iight was to chaB.ae (k \= }), coaxial clrcttlar fringes would occur.

But, it is assumed that tkermal changes in tke borehole are small and that thewac veleBgth does not change. IB this case, the system can measure quantitatively the

displacement of the borehole wall in terms of tke wavelength of the Iaser lighÅí. The

sensitivity of the system will increase to measure 1/IO of the wavelength by detaHed

186 J. HIRABAYASHI and S. TAKEMOTO

analysis. Thus, it will be able to measure displacements smaller than O.1ptm.

3. Results of Laboratory Tests

Laboratory tests of the system have been carried out at a basement room of the

Iaboratory in Kyoto University.

An aluminum cylinder (inner diameter : 100 mm, thickness : 1 mm) was used as a

dummy borehole. After the system was fixed in the cylinder, one surface side of the

cylinder was fixed to a rigid wall in the laboratory and the opposite side was pushed by a

micrometer (Figure 5(a)). The cylinder was thus deformed. The micrometer wasthan retracted from the cylinder surface, and the reference image of the cylinder was

taken by the video camera. Subsequent images were stored in memories by using the

image processor at every1second. An example ofimages processed by theimage pro-cessor is shown in Figure 6. Because 'the object plane of the cylindrical area was taken

(a)

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1

:::::::

:.:,:.:

::

.

t:tt

.-

:,:,:.: 1:" N.--:t:t:. -

(b)

xg o

x+T

)`8

r; T}

Fig. T5. (a) Layout ofa laboratory test. An aluminum cylinder is employed to

be a dummy berehole. Tests were performed by measuring displacements of the cylinder surface. The star denotes the point on which the micrometer was attached to push the cylinder. (b) Illustration of the cylindrical area in a borehole to be measured by the ESPI irnage

precessing system. (c) A circular image to be taken by a video eamera.

A BOREHOLE STRESS-STRAIN MEASUREMENT SYSTEM187

` l

n,•

"s.t ••si

- lj}

"k.

Fig. 6. An Example 'of speckle pattern.

by the video camera through a cone mirror (Figure 5(b)), the object plane is presented

by a circle, in which the upper end of the measured area is located at the center of the

circle and the lower one is the circumference ofthe image (Figure 5(c)). Three pillars

ofthe measurement unit are represented by dark radial lines on the image. Therefore,

the areas shadowed with the pillars could not be measured by this system. Figure 7 shows images indicating an absolute value of the differences between the

reference image and respective ones after 1, 2, 3 and 4 seconds. The mark "B" denotes

the point that had been pushed by the micrometer. Patterns corresponding to thedeformations of the cylindrical wall indicate that the largest deformation of the

cylindrical wall occurred at B. Three dark lines indicated as the mark "A" in Figure 7

correspond to three pillars. These lines don't show the deformation of the wall. In

Figure 8, images representing cylindrical deformations are shown in the same way as

those in Figures 5(b) and 7. In the procedure to transform the circular image into the

cylindrical one, the laser light is assumed to be parallel. In Figure 8, arrows on the top

of the cylindrical wall show the directions of the deformation. In shaded areas, the

radial displacement dr is, ,R. -'l2-<dr<o.In the areas that are covered with coarse oblique lines, dr is,

,1 O< dr<-. 2In the areas that are covered with fine oblique lines, dr is,

188 J. HIRABAYASHI andS. TAKEMOTO

i.

'

l

iB .•b

t 't ec-t '-

x

,

-.

"l

gf'

4

l

-

(a) An image obtained from the between the reference image after 1 seconds.

difference

and that

I

(b) An image obtained from the between the reference image after 2 seconds.

'

T

.

tt

t'

-

`

'} t'

difference

and that

(c) An image obtained from the diff;erence (d) An irnage obtained frorn the difference between the reference image and that between the reference image and that

after3seconds. after4seconds. Fig. 7. Examples ofresults obtained from laboratory tests. A fringe corresponding to the deformation of the inner wall of the cylinder was obtained from the difference between the reference image (t=Osec.) and respective images taken after 1, 2, 3

and 4 seconds. Three dark lines indicated by the mark CA' correspond to three pillars where the displacement could not be detected. The mark `B' denotes the

point that had been pushed by the rnicrometer.

c< dr< 1.

4. Field Experiments at Hiraki Mine

Field experiments using this measurement system were carried out at Hiraki mine

inJanuary 1993. The purposes of the experiments were to evaluate the mechanism of

fixing the measurement module to a borehole wall and to check the performance of the

total system. Before the start ofexperiments, it became clear that the diameter ofthe

module (104 mm) was too large to be used in the overcoring procedure with a diameter

of 150 mm. Moreover, the module was not waterproof. Because of these two reasons

the overcoring experiment was not carried out.

A BOREHOLE

iils$s

STRESS-STRAIN

(a) The deformation during 1

the reference image was secondtaken.

A/2 A

o

after

#

MEASUREMENTSYSTEM

k

,". ifeips' ff

o

189

(b) The deformation during 2 second after the reference image was taken.

A/2A p

(a) The deformation during 3 second after (b) The deformation during 4 second after the reference image was taken. the reference image was taken. ew -Z12<dr<O, ssO<dr<A12, pa A12<dr<2A12

Fig. 8. Images representing cylindrical deformations in cases shown in Fig. (a)-(d). (A=O.633ptm).

Fig. 9.

<'i,,'

,,i

C':sa2ihlrerere""":'su /,)ifee.ewTlirw':i.g,,,wa,,,`x,,.Sii

v,tat:

')t:-

''r:-"ptielLLeeewt S2sij

View of the experiment field at Hirali mine.

the first and second boreholes were drilled,

,i-./Lsii,,tst,e'ii ,.i'ii..

`A' and `B' denote the points where

respectively.

190 J. HIIMBAYASHI and S. TAKEMOTO

•k',,

` Fig. 10. An example of fringe patterns obtained by field experiments at Hiraki mine.

Figure 9 shows a Iayout of the experiments. A borehole with a diameter of 110mm was first drilled into the rock's wall at the point (A) and the module was set up in

this borehole. Next, a borehole B with the same diameter was drilled at the point (B)

about 80mm apart from the borehole A. Using the measurement system, radialdisplacements caused by the effect of drilling a new borehole were investigated.

While the boring was in progress, images were taken by the video camera andrecorded every minute on a hard disk through a personal computer. After the drilling,

images were recorded over the rest 12 hours. While it was possible in the laboratory to obtain fringes over a period of24 hours

from the same reference image, continuous fringes could not be obtained in this field

experiments. The reason for this failure may be twofold : Slight motions of the optical

fiber would lead to loss ofcoherence and that the intensity ofthe images was very weak.

Figure 10 shows an example of the images representing the radial displacementobtained in field experiments at Hiraki mine.

Consequently, we must solve some problems before the system can become field

worthy, e.g. waterproofing, solving optical fiber problem, and using a very highquality video camera to enhance fringe contrast.

5. Improvement of the Measurement Module

Under the necessity ofminiaturization, the measurement module was improved and a

new one was manufactured. Figure 11(a) shows a schematic diagram of the newborehole module and Figure 1 1 (b) is the view of this module. The video camera (A) is

a BELL TEX 902 CCD camera unit which has 512Å~582 pixels. The minimumillumination required to get images through the camera is O.2 lux. The plate (G) is the

reference plane. The lens (B) is fastened with a C mount, and easily be replaced if

desired. Arrangements ofthe video camera and the beam expander (C) are modified.

The

A BOREHOLE STRESS-STRAIN MEASUREMENT siYSTEM 191

legs (D) are interchangeable and can be set at an arbitrary length.Modifications and features of the module are as follows. The module is divided

(a) (b)

Fig. 11. (a) Schematic diagram ofan improved module ofthe measurement system View of the module.

. (b)

Fig. 12. An example of images measured with the improved module.

l92 J. HIRABAYASHI and S. TAKEMOTO

(a) An image obtained from the between the reference image after 1 second.

difference

and that

K

(b) An image obtained from the ditierence between the reference image and that after 2 seconds.

(c) An image obtained from the diflrerence (d) An image obtained from the difference between the reference image and that between the reference irnage and that

after3seconds. after4seconds. Fig. 13. Examples of laboratory tests by employing the improved module.

into two pieces;an upper and lower pieces (E). The cone mirror (F) is fixed on the

lower piece. The height of the upper piece is 160mm and its diameter is 70mm,whereas the height of the lower piece is 70 mm. The weights ofboth pieces are 1.9 kg

and O.5 kg, respectively. The module is capable to measure deformation ofa borehole

with a diameter larger than 75mm. Although the original module could only be used to measure radial displacement of

the surrounding cylindrical area, the improved module can also be used to measure the

deformation of the bottom of the borehole.

Figure 12 shows an example ofimages measured in the bottom area. Figure 13shows examples of the laboratory experiments with the improved measurement module.

It shows thermal deformations of a chloroethylene cylinder (inner diameter : 78 mm,

thickness: 6mm) in the direction of the radius of the cylinder.

6. Discussion

A He-Ne laser source is too large to be used within the measurement module of the

A BOREHOLE STRESS-STRAIN MEASUREMENT SYSTEM 193

ESPI borehole stressmeter. It is inevitable to adopt an optical fiber in the present

system when using a He-Ne laser. In this case, the fiber must be long enough so as to

transmit a laser beam from the source to the measurement module. It is diMcult tokeep the long optical fiber at a constant state fora long time.during and after boring.

It is thus difficult to measure displacements because of the instability of the optical

system. In extreme cases, the fringes do not occur, and it is almost impossible toanalyze the images. Ifthe images were taken closely in time, it could be possible to be

solved to some extent. However, when the images are taken at very short intervals, the

measurements are inaccurate, since the displacements are too small to cause welldefined fringes. A small-sized semicQnductor laser can generate higher power than a

He-Ne laser. Ifa semiconductor laser is used as the light source, it is not necessary to

use an optical fiber. But the problem in employing a semiconductor Iaser as the Iight

source in an ESPI system is that the stability of a semiconductor laser is much worse

than that ofthe He-Ne laser at this time. It needs to be kept at a constant temperature

and the electric current must be well regulated in order to stabilize the wavelength.

This problem will be solved in the near future if frequency-stabilized semiconductor

lasers can be used. In measurements of the surrounding cylindrical area, the occurrence ofdark Iines,

which are not clearly distinguishable from fringes, can't be avoided in the present

design. When many fringes occur in one image, it is difficult to analyze thedisplacements. If images are taken frequently in a short interval and fringes arerecognized in the images, displacements will be obtained from the following equation,

2 . <Ii(x,.J,)> tm8o(X,Y)Zo)ar(X,Y,z.)'(l8) p(X, Y, Z,, Sx, 6y, 6z)- k arcsin

Values of PO are discontinuous because they are obtained by an inversetrigonometric function. It is necessar ?r to connect them continuously.

interval of wavelength) within the time If displacements are small (<<-IE-

Fig. 14. An optical arrangement for measurement of in-plane displacements.

l94 J. HIRABAYASHI aRd S. TAKEMOTO

Ll L2 +(k"-i)(Li-L2) (19) Li==vlt?iFM(i7ntSiirzPi+(yf,+y)+z.,and,

Li==vftvaiTiFSEM+(yytb+z,

Equation ( 19) is approximated with the following equation in the same way as Eqwation

(17).

PO==-vlLllillili}]y.,2,,2Y+z,2) (2o)

where, Z, is tke distance from a focai point of the fiber lens (A) to the object plaBe, and

Yf, is a sum of the distance from the center of the focal point of the fiber lens (A) to a

mirror (B) and the distance from the center of tlie object to the mirror (B) in the

direction of Y-axis.

measurements, phase-shifting ESPI can be utilized, and tke semiconductor laserprovided can keep the wavelength under contro}. The pkase-shifting ESPI uses three

or more interference fringe patterns tkat are in the same deformation state but at

different interference phases. A phase value at each pixel point can be determined

from intensities of the different phase-shifted interference fringe patÅíerns at the same

location. The deformation ofan object surface is estimated from the phase value. A

measurement of the deformation is independent of the dark lines in this estimation.

It will also be possible to measure in-plane d!splacements by modifying the optica}

aryangernent of the module. Figure 14 shows an optical arrangement for measure-ments ofin-plane dispiacements. In this arrangement, displacements in Åíke direction

ofthe Y-axis can be measured, and Equatlon (16) is rewritten as the following equatien,

pormkt,(-YS+(Y+b5yZ6 XS.r(YfowwDSv-Z,5z)

7. Concludlng Remarks

The Electronic Speckle Pattern Interferometry (ESPI) technique was introduced to

crustal stress and strain measurements. We developed the borehoie stress-strainmeasurement system employing ÅíSPI. The system was designed te be able to measure

out-ef-plane dispacements ofthe wall and bottom areas ofa borehole. It would also be

possib}e to measure in-plane clisplacements in both areas by modifying the optica}

arrangement of the measgrement module. The system is small-sized in dueconsideration ef mobility and easiness of seÅíting up. At this stage, it is difEcult to

measure continuosly the deformaÅíion by using the opticai fibers. By employing afrequency stabilized semiconductor laser, this difliculty will be overcome.

As another application of ESPI system in geophysical sciences, we propose to

empioy the ESPI system in precise measurernents of tunne} deformation.Measurements ofcrustal deformation using a laser holographic method in a deep tunnel

have been carried out (TAKEMoTo, l986, TAKEMoTo and YAMADA, 1989). In thesimilar manner as those, by using ESPI system, measurements oftunne} deformation in

terms of the wavelength of the }aser lighÅí system should be posslble.

The improved module is able to measure the deformation of a tunnel without

A BOREHOLE STRESS-STRAIN MEASUREMENT SYSTEM195

(a) (b)

Fig. 15. Layout ofprecise measurerrients of tunnel deformations. (a) Measurement of vertical deformation. (b) Measurement of difference between vertical and horizontal deformations.

modification (Figure 15(a)). Differences between out-of-plane displacement on a side

wall and the displacement on a ceiling could be measured by modifying the reference

plane (Figure 15(b)). In this case, the deformation is able to be measured with high

resolution because of a phase difference between the deformation in the horizontal

direction and that in the vertical direction.

Acknowledgements

The authos would like to express sincere thanks for encouragement of Professors

Yutaka TANAKA and Ichiro NAKAGAwA of Kyoto University. The authors are alsogratefu1 to Professor Hartmut SpETzLER ofUniversity of Colorado at Boulder and Dr.

Koji TENJiNBAyAsm of Mechanical Engineering Laboratory for. many criticalcomments. The authors were favored to have the cooperation ofMr. Tsutomu Io oflo

Mamufactory and Mr. Uzaburo MAGARi of Kyoto University who contributed theirexperimental skill to manufacture the measurement module. This research was partially supported by the Grant-in-Aid for Scientific Research

from the Ministry ofEducation, Science and Culture ofJapan (No. 03554010) and the

19th Nissan Science Foundation.

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