N umerical analyses such as the finite element method

TUNNELS AND DEEP SPACE P: 80886-7798(98) 00004-2 Lessns Learned frm Field Measurements in Tunnelling S. Sakurai Abstract-- Over the past tw decades, varius numerical methds f analysis have becme ppular in the field f getechnical engineering. Hwever, the accuracy f numerical analyses varies cnsiderably, primarily because f the uncertainties invlved in mdelling cmplex gelgical frmatins ~ith the cmplex gemechanical characteristics f sils and rcks. Field measurements carried ut during cnstructin can be used t vercme this difficulty. The authr reviews ways f using measurement results t imprve numerical analyses, including the determinatin f a "hazard warning level" fr each measurement item prir t the start f cnstructin, the use f back analysis. The imprtance f chsing a prper mdel is als discussed. 1998 Published by Elsevier Science Ltd 1. ntrductin N umerical analyses such as the finite element methd (FEM), bundary element methd (BEM), and distinct element methd (DEM) have becme ppular in the getechnical engineering field. These numerical appraches facilitate the cnsideratin f cmplex gelgical and gemechanical characteristics in the design f gestructures such as tunnels, undergrund caverns, fundatins f structures, slpes, etc., and the mnitring f the stability f the structures during cnstructin. As a result, these numerical analyses make it pssible t achieve a ratinal design f gestructures. t is well knwn, hwever, that the actual behavir f structures quite ften differs frm that predicted by numerical analyses. This difference is due mainly t the fact that many uncertainties are invlved in the mdeling f cmplex gelgical frmatins with the cmplex gemechanical characteristics f sils and rcks. The initial state f stress als causes difficulties in numerical analyses. T btain high accuracy in numerical analyses, input data such as gelgical and gemechanical parameters, initial state f stress, undergrund water table, permeability f the grund, etc., shuld be prperly determined. This, hwever, is nt an easy task, even thugh varius kinds f advanced explratin techniques have been develped and are already available in practice. n rder t vercme this difficulty, field measurements are carried ut during cnstructin. The design parameters used in the riginal design f the structures can then be assessed n the basis f the results f the field measurements, and, if necessary, the riginal design and cnstructin/excavatin methd can be mdified. This design/cnstructin methd is called the "bservatinal methd" Present address: S. Sakurai, Prf. f Rck Mechanics, Department f Civil Engineering, Kbe University, Kbe, Japan. (Terzaghi and Peck 1948). With this methd, hwever, a questin may arise as t hw t interpret the results f field measurements that were made in rder t assess the design parameters used in the riginal design, as well as t mnitr the stability f the structures during cnstructin. As far as mnitring is cncerned, the stability f structures can be assessed by cmparing the measurement results with their allwable values, and it is bvius that the structures are safe if all the measured values remain smaller than the allwable values. These allwable values are ften called "hazard warning levels." Althugh this apprach may be suitable fr mnitring the stability f structures during and/r after the cnstructin perid, it can hardly be used in assessing the adequacy f the design parameters used in the riginal design. This difficulty is simply due t the fact that the design parameters cannt be assessed directly frm the measured values withut ding any analysis f the measured values. The measurement results must be prperly analyzed t assess the design parameters. Fr this prcedure, called "back analysis", the input data are measured values such as displacements, strains, stresses, and pressures, while the utput results are material cnstants, lads, initial state f stresses, permeability, and even bundary cnditins. This is exactly the reverse calculatin prcedure as cmpared t "frward analysis" cmmnly used in structural analyses, in which the input data are material cnstants, lads, initial stresses, and permeability, while the utput results are displacements strains, stresses, and pressures. t is bvius that back analysis is an essential tl in the bservatinal methd fr assessing design parameters. With regard t engineering practices, it is wrth mentining that back analysis shuld be carried ut immediately after taking the measurements s that the riginal design and cnstructin methds can be assessed and mdified if necessary, withut any serius delay during the cnstructin/ excavatin perid. The bservatinal methd fr assessing the adequacy f Tunnelling and Undergrund Space Technlgy, Vl. 12, N. 4, pp. 453-460, 1997 1998 Published by Elsevier Science Ltd Printed in Great Britain, All rights reserved 0886-7798/98 $19.00 +0.00 Pergamn

the design and cnstructin methds, as well as fr mnitring the stability f structures, is shwn as a flw chart in Figure 1. 2. Hazard Warning Level t is recmmended that a hazard warning level be determined fr each measurement item prir t the start f cnstructin. This will make it pssible t assess the stability f the structures immediately aider the taking f measurements simply by cmparing the measured values t the hazard warning level. When the measured values remain smaller than the hazard warning level, the stability f the structures is cnfirmed. Even if the measurement values are still smaller than the hazard warning level, hwever, engineers shuld always pay attentin t what happens after the lapse f a certain perid f time (see Fig. 2). f the measured values are predicted t becme greater than the hazard warning level after a certain perid f time, then the engineers must take sme actin t stabilize the structures and t mdify the riginal design. Field Exp OratiOn ] es' n t" "J- Cnstructin~ [ ~ measurement Back analysis dentificatin f Mechanical mdel and cnstants Mdificatin f Design/ Cnstructin Methds The next questin is, hw is the hazard warning level determined? T answer this questin, the authr has prpsed the critical strain (Sakurai 1981), which can successfully be used fr assessing the results f displacement measurements in tunnels, such as crwn settlement, cnvergence, and extensmeter and inclinmeter measurements. The definitin f the critical strain e is given as fllws: ~c e0 = ~ (1) where ~ is uniaxial cmpressive strength and E is Yung's mdulus. t shuld be nted that the critical strain is always smaller than strain at failure. Varius rcks and sils were tested in the labratry t determine the critical strain. The results are shwn elsewhere (Sakurai 1981). The questin may nw arise as t hw t extend the results btained frm labratry tests n small specimens t large-scale in-situ sils and rcks. As far as sils are cncerned, the critical strain btained frm labratry tests may be almst the same as that fr in-situ sil masses. Hwever, the case f in-situ rck masses requires mre discussin. The critical strain f in-situ rck masses is cnnected t that f intact rcks by the fllwing equatin: (~cr moc where m and n are reductin factrs f uniaxial strength and Yung's mdulus, respectively, in extending the resuits btained frm the labratry t in-situ. Bth uniaxial strength and Yung's mdulus f in-situ rek masses decrease frm the values f intact rcks, because f the existence f jints. Thus, the reductin factrs m and n range between 0 and 1.0. t shuld be nted that bth the reductin factrs m and n fr sils must be apprximately 1.0. This is the reasn why labratry sil tests are ppular in engineering practices. The values f m and n were determined by perating bth labratry tests and in-situ tests (plate bearing tests and direct shear tests). The rati f the tw ranges was fund t be between 1.0 and 3.0, depending n the rck types (Sakurai 1983). This is surprising, in that the critical strain f in-situ rck masses is almst the same rder f magnitude as that f intact rcks, thugh bth uniaxial strength and Yung's mdulus f intact rcks largely differ frm thse f in-situ rck masses. This is because the effects f jints are canceled ut by taking the rati f the tw, althugh the uniaxial strength and Yung's mdulus are bth greatly influenced by the existence f jints. (2) N > qd E g t! ' Hazard Warning Level Time Figure 1. Prcedure f assessing the design and cnstructin methds. Figure 2. Schematic diagram fr measured value in relatin t hazard warning level. 454 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY Vlume 12, Number 4, 1997

n engineering practice, therefre, it may be pssible t use the value f critical strain f intact rcks as a hazard warning level fr mnitring the stability f tunnels. t shuld be nted that if we adpt this warning level, the factr f safety frm 1 t 3 is autmatically included, because the critical strain fin-situ rck masses is always ne t three times greater than that f intact rcks. n additin, it is wrth raentining that labratry tests revealed that the critical strain is nt much influenced by varius aspects f the envirnment, such as misture, temperature, etc. (Sakurai et al. 1994). This is als a great advantage fr the critical strain, when it is used in practice. n rder t verify the applicability f the hazard warning level described abve tbr assessing the stability f tunnels, sme displacement measurements were carried ut. The strains ccurring arund tunnels as a result f excavatin are calculated frm me asured displacements by Eqs. (3) and (4). Uc e0 = W (3) ] -- U 2 e~ = 1 (4) where u c is the measured value f crwn settlement; u, and u 2 are the displacements measured at the measuring pints 1 and 2, respectively, by extensmeters installed inward.,~ frm the tunnel surface; a is the tunnel radius; and l is the length between the tw measunng pints alng the extensmeters. The strains calculated by Eqs. (3) and (4) are pltted in relatin t the uniaxial strength f sils and rcks as shwn in Figures 3 and 4. The tw dtted lines indicate the upper and lwer bunds fr the critical strain btained frm labratry tests (Sakurai 1981). The numbers given beside the data indicate the srt f difficulties encuntered during the excavatin f tunnels, while the data with n numbers are thse fr tunnels excavated with n serius prblems. The types f difficulties are classified as fllws: 1) difficulties in mmntaining tunnel face; 2) failure r cracking in shtcrete; 3) buckling f steel 1ribs; 4) breakage f rck blts; 5) fall-in f rf; 6) swelling at invert:; and 7) miscellaneus. t is seen frm these figures that when the strains ccurring arund the tunnels were smaller than the lwer bund f the critical strain, all the tunnels were stable in such a way that they culd be excavated with n prblems. When the ccurring strains reached the upper bund f the critical strain, many different srts f difficulties ccurred. This evidence is exactly that which we expected frm the characteristics f critical strains. Cnsidering the abve-mentined applicability f critical strain, the authr ]~as previusly prpsed a hazard warning level fr strain and displacement that can be used in mnitring the stability f tunnels. The hazard warning level is classified int three stages in relatin t the degree f stability, as shwn in Figure 5. The hazard warning level f settlement at the tunnel crwn can then be determined frm the crrespnding level f strain by using Eq. (3). As an example, the hazard wa:rning levels fr crwn settlement at a tunnel with a radius f 5 m are als shwn in this figure (Sakurai 1993). 3. Back Analysis and Mdeling The hazard warning level described in the previus sectin can ptentially be used fr mnitring the stability f tunnels. f the strains ccurring arund tunnels tend t crss the warning levels, then back analysis must be carried ut t re-evaluate the design parameters which were used in the riginal design. n the getechnical engineering field, material cnstants such as Yung's mdulus, Pissn's rati, chesin and internal frictin angle are usually determined by back analysis frm the measured values f displacements, strains, stresses and pressures The initial states f stresses are als btained by back analysis. t shuld be nted that these back analyses are cnsidered as parameter identificatins, s that they are adequate nly when the mechanical mdels are well defined and fixed. Hwever, the mechanical characteristics f gematerials such as sils and rcks are s cmplex that it is extremely hard t define the mechanical mdel t represent their behavir. n fact, much research is currently being carried ut, but there still remain many prblems t be slved in the mdeling f gematerials. The authr has already emphasized that in the back analysis f getechnical engineering prblems, the mechanical mdel shuld nt be assumed, but shuld be determined by back analysis (Sakurai and Akutagawa 1995). This means that a back analysis in getechnical engineering practice shuld be capable f identifying nt nly the mechanical cnstants, but als the mechanical mdel itself. n frward analysis, a mechanical mdel is usually assumed r given, such that the grund is represented by a certain mdel such as elastic, elast-plastic, visc-elasticplastic, discrete blck mdels, etc. The values f the mechanical cnstants f the mdels can then be determined Once all the mechanical cnstants are knwn, we can calculate displacements, strains and stresses These results give exact values s that the uniqueness f the slutin is cnfirmed between the input data and utput results, at least fr an assumed mechanical mdel. t is extremely imprtant fr the frward analysis t assume the mst apprpriate mechanical mdel by cnsidering the results f explratins in bth labratry and in-situ. n back analysis, n the ther hand, we first btain displacements, strains, stresses and pressures as a result f field measurements, and the mechanical cnstants are then determined by back analysis by assuming a mechanical mdel. t is n wnder that the values f mechanical cnstants determined by back analysis depend entirely n which mdel we assume in back analysis. Fr instance, if we assume an elastic mdel, then Yung's mdulus can be btained, but if a rigid-plastic mdel is assumed, then Yung's mdulus cannt be btained, thugh the identical values f measured results are used. This means that the results f back analysis are basically a matter f assumptin f the mechanical mdels representing the behavir f gematerials. n ther wrds, in back analysis the uniqueness f the slutin in general cannt be cnfirmed between the input data and utput results (see Fig. 6). We can nw cnclude that back analysis is nt simply a reverse calculatin f the frward analysis. ts cncept shuld be different frm frward analysis in such a way that back analysis can prvide mdelling as well as identify the parameters f the mdel. 4. Difference Between Parameter dentificatin and Back Analyses n a tunnel design, many uncertainties are invlved in evaluating the gelgical and gemechanical characteristics f sils and rcks, as well as initial state f stresses. n Vlume 12, Number 4, ]L997 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY 455

= uc/a u c 1 0.0 ~ ~ ~. ~e,1.2. 2.4 e2.3 2 e4 ~ \ "~~ / ~. "2.3 12 ///'~,~// 7 12 2.3.5 ~.~ 2.3 "~ 1.0 - ~ 2.4.~ 0 ~ '~'-- ~.,,5 8 8 "---...c_ ~ O3 0.1 - ~ 8 ~ 0 0.01 0.01 0.1 1.0 10.0 100 Uniaxial Strength " c (MPa) Figure 3. Relatinship between the measured strain (btained frm crwn settlement) and hazard warning levels. U1-U2 10.0 -- 2.3 2.3 0 2.4 --,...e~6 2.3 2 3.6 ~ 2"3ee 2.3 7 2 4 ~."2.a... /",,~11 ~ 4 ~ v t~.c 1.0 -- 0 ~" 0 O3 0.1 -- 0 ~ 0 0 0 0.01 0.01 0 0, 0.1 1.0 10.0 100 Uniaxial Strength d c (MPa) Figure 4. Relatinship between the measured strain (btained frm extensmeter measurement results) and hazard warning levels. 456 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY Vlume 12, Number 4, 1997

ther wrds, structures like tunnels are designed under cnditins where lads and mechanical prperties are nt well knwn and the), cannt be cntrlled. This is entirely different frm the situatin f bridge-like structures, where lads and mechanical prperties f materials are well knwn since the materials used are all artificial nes like steel and cncrete, such that their material prperties can be easily cntrlled. t is pssible, f curse, t cntrl the strength f sils and rcks, if the strength is nt sufficient enugh t stabilize tunnels, by installing rck blts, shtcrete, as well as thrugh injectins. Hwever, the mechanical behavir f materials strengthened by rckblts and shtcrete becmes mre cmplex, s that further assumptins are needed. Nevertheless, nce mdeling f the materials is achieved, the material prperties such as Yung's mdulus, Pissn's rati, chesin, internal frictin angle, jint stiffness, etc., are determined by cnsidering the results f bth labratry and in-situ experiments. The mechanical behavir f tunnels can then be predicted by a cmputatinal methd such as FEM r BEM, by using these material prperties as input data fr the cmputatin. Hwever, as mentined earlier, the real behavir f the tunnels quite ften differs frm that predicted by the cmputatinal methds. We therefre adpt bservatinal methds t imprve agreement between the real and predicted behaviurs f tunnels, by mdifying the input data that have been used in the cmputatins. This cmputatinal prcedure is called "parameter dentificatin", which shuld be distinguished frm "back analysis." n parameter identificatin, the input data used in the cmputatins are checked after the field measurement results have been analyzed, and can be mdified if needed, but the mdel remains the same the whle time. n back analysis, the mdelling shuld als be checked with field measurements, as well as the [_ ~.., C ~ B,..,.., A 10.0 1.0 0.1 l 1, 1.0 10.0 100 Uniaxialcmpressive strength #c (MPa) A B C 0.3~0.5 0,5~1 1 ~3 11 1 ~1.5 1.5~4 4~9 ]]] 3~4 4~11 11~27 ( U nit : cm) (Radius f tunnel: 5.00m) Figure 5. Hazard warning levels fr assessing the stability f tunnels. 1) Frward analysis Mdelling ~_=Assumptin ~1 = nput data Mechanical parameters E,v,c,~," External frce Uniqueness is guaranteed utput results Frward Stress analysis. Strain - d P 2 ) Back analysis utput results Mechanical parameters E,v,c,," External frce 9~-[[ Back analysis Mdelling nput data Displacement Pressure Stress Strain -~ Assumptin ~} "41--L Uniqueness is nt guaranteed Figure 6. Cmparisn between the prcedures f frward analysis and back analysis. Vlume 12, Number 4, 1997 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY 457

material prperties. Nevertheless, it is cmmn that in the bservatinal methds the input data used in the cmputatin are usually checked during the excavatins, but with the mdelling being fixed. As described earlier, it is extremely imprtant in any getechnical engineering prblem that the mdels shuld nt be assumed, but rather shuld be determined by a back analysis. fa mdel is fixed all the time during bservatinal prcedures, the results are nt nly inadequate, but als misleading in their interpretatin, in that they prvide wrng infrmatin in the decisin making fr mdifying design and cnstructin methds. The example discussed belw demnstrates hw misleading it can be if we assume a mdel f materials in the bservatinal methds in tunnel practices. A duble-track railway tunnel f shallw depth was cnstructed underneath a densely ppulated urban area. The grund in which the tunnel was lcated cnsisted f fine grain sand depsits. Bth the tunnel diameter and the height f verburden are apprximately 10 m. Bth extensmeters and inclinmeters were installed frm the grund surface befre tunnel excavatin s that the ttal displacements due t excavatin culd be measured. The grund surface settlements were als measured by surveying. The measured displacements were interpreted by parameter identificatin t check the material prperties used as the input data in the design analysis. n this parameter identificatin, the mdel f the grund was assumed t cnsist f hmgeneus and istrpic material, s that Yung's mdulus and Pissn's rati were the utput results f the parameter identificatin. The identified material prperties and initial stresses are used t cmpute the displacements arund the tunnel, and the maximum shear strain distributin is then calculated, as shwn in Figure 7. This maximum shear strain is cmpared with the allwable value, perhaps the critical shear strain, t assess the stability f tunnels. t is bvius frm Figure 7 that n lsening zne ccurred in the grund abve the tunnel arch. This is n surprise, hwever, as the mdel assumed the grund t be hmgenus and istrpic. Therefre, the existence f ls- ening has nt been taken int accunt in this calculatin. n back analysis, n the ther hand, we must identify the mdel as well. n this example prblem the nn-elastic strain apprach is used, in which n assumptin are made in mdeling; rather, a cmputer can make a mdel and tell us if sme lsening zne has ccurred. The details f this back analysis prcedure have been presented elsewhere (Sakurai et al. 1993); nly the result f the maximum shear strain distributin is shwn in Figure 8. t is f interest t cmpare the results shwn in Figure 7 and Figure 8. These tw maximum shear strain distibutins were btained frm identical data, but bth are cmpletely different frm ne anther. They depend entirely n which mdel we used. The results shwn in Figure 8 were btained withut assuming any mdel, but the mdeling was dne by a cmputer. Therefre, the results prvided must be clser t the real situatin. This means sme lsening zne in the grund abve the tunnel arch may exist. Hwever, we can say frm Figure 7 that n lsening zne is likely t ccur in the grund abve the tunnel arch. This is a rather dangerus cnclusin in assessing the tunnel stability, althugh Yung's mdulus and Pissn's rati can be identified. t shuld be understd that the back analysis is mre imprtant than the parameter identificatin in tunnelling practices. Mrever, althugh parameter identificatin can prvide material prperties, it smetimes can prvide misleading infrmatin. t is als wrth mentining that in this example case study, rck blts, shtcrete and steel ribs were installed as supprt measures. n the design analysis, these supprt structures were cnsidered as stiff elements installed inward frm the tunnel surface fr rck blts, and placed n the tunnel surface fr shtcrete. Hwever, in back analysis the best agreement between measured and cmputed results were btained fr the case f n stiffness f supprt structures. This fact is demnstrated in Figure 9. n this figure, the errr functin defined in Eq. (5) is pltted as a functin f the rati f Yung's mdulus f supprt structure and that f the grund, E,/E (El: Yung's mdulus f supprt structure; Eg :Yung s mdulus f the grund). " O. 250 O, 500 O. 750. 000. 250 2. 22~ J 5. Om scale Figure 7. Maximum shear strain distributin (istrpic elastic mdel). 458 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY Vlume 12, Number 4, 1997

O. 500. 000. 500 2. 000 2. 500,i, : ' ' ' max= i., r 2.87~ 5. Om scale Figure 8. Maximum s,~ear strain distributin (taking int accunt nn-elastic strain). : = (5) up l=l where u~ and u~ are the measured and cmputed displacements at the measuring pint i, respectively. N is the ttal number f measurements. t is seen frm this figure that the best agreement between measured and cmputed displacements is btained when E/E = 10. This means that the best agreement is achmved m the case f the tunnel being unhned. This is a surprising result in that the tunnel behaves in reality just like an unlined tunnel, thugh supprt structures such as shtcrele, steel ribs and rck blts were installed. Hwever, it shuld bc emphasized that Yung's mdulus f the grund increases bviusly with installatin f stiff supprt structures. This case study demnstrates the difficulty f mdelling the supprt structures,,~uch as shtcrete, steel ribs and rck blts, and that misleading cnclusins can easily be derived if an imprper mdel is adpted. 5. Cnclusins 1) The bservatina:t methd is a very prmising means f achieving the ratinal design f tunnels. With this methd, hwever: a crucial prblem is hw t interpret the results f bservatin and field measurements taken during/after the excavatin. 2) Fr mnitring the stability f tunnels, the hazard warning levels are extremely imprtant, and they must be determined prir t cnstructin, s that the measured values can be assessed immediately after taking them. 3) n rder t determine the hazard warning levels, the critical strain is CLseful. The critical strain f in-situ rck masses can easily be btained by labratry experiments carried ut n a small specimen. The i j /i ij '! " " / 2,0 i ~ ~ - i 1.8... i i i... i... r # t...... i!:i!/---!/--i-i... ~, :!, i i i',il Z i i '~ 1.4 i! i i! i ~ i i,.2. ~: -i-~- '-~-~++i t~ i i i" ii 1.0.......... t":......... : "'"":'""i..., li i i il 10 100 Rati f ung's mdulus f supprt structures and that f the grund (E/Eg) Figure 9. Errr functin pltted as a funtin f E 1E e. 4) critical strain als has an advantage in that it is nt much influenced by varius envirnmental factrs like water cntent, temperature, etc. The stability f tunnels is then assessed by cmparing strain btained frm measured displacements (crwn settlement and extensmeter measurements) with the hazard warning levels evaluated frm the critical strain. Back analyses are very pwerful tls fr interpreting the results f field measurements. n back analysis, the mdel f sils and rcks shuld nt be assumed, but shuld autmatically be btained by a cmputer. Therefre, in back analysis nt nly material prper- Vlume 12, Number 4, 1997 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY 450

ties but als a mechanical mdel f sils and rcks shuld be determined. t shuld be emphasized that back analysis is entirely different frm parameter identificatin, in which nly the material prperties are determined frm the measurement results, while the mdel remains the same all the time. 5) An example case study was discussed t demnstrate the difference between back analysis and parameter identificatin, and t shw that parameter identificatin prvides nt nly less accurate infrmatin, but als misleading infrmatin abut the failure mechanism f tunnels. References Sakurai, S. 1981. Direct strain evaluatin technique in cnstructin f undergrund penings. Prc. 22nd US Syrup. Rck Mech., Cambridge, Massachusetts, M..T., 278-282. Sakurai, S. 1983. Displacement measurements assciated with the design f undergrund penings. Prc. nt. Symp. Field Measurements in Gemechanics, Zurich, Switzerland, 2:1163-1178. Rtterdam: A. A. Balkema. Sakurai, S. 1993. The assessment f tunnel stability n the basis f field measurements. Assciazne Getecnica taliana - XV Cnvegn Nazinale di Getecnica- Rimini, 21-30. Sakurai, S.; Akutagawa, S.; and Kawashima,. 1993. Back analysis f nn-elastic behaviur f sils and heavily jinted rcks. Prc. 2nd Asian-Pacific Cnference n Cmputatinal Mechanics, Sydney, Australia, 465-469. Sakurai, S.; Kawashima,.; and Otani, T. 1994. Envirnmental effects n critical strain f rcks. Prc. Symp. Develpments in Getechnical Engineering, Bangkk, Thailand, 359-363. Rtterdam: A. A. Balkema. Sakurai, S. and Akutagawa, S. 1995. Sme aspects f back analysis in getechnical engineering. EUROCK'93, Lisbn, Prtugal, 1133-1140. Rtterdam: A. A. Balkema. Terzaghi, K. and Peck, R. B. 1948. Sil Mechanics in Engineering Practice,627-632. New Yrk: Jhn Wiley & Sns. 4{;0 TUNNELLNG AND UNDERGROUND SPACE TECHNOLOGY Vlume 12, Number 4, 1997