Stiffness Characteristics of Very Soft Offshore Clay for Wide Strain Range

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1 of 8 Stiffness Charateristis of Very Soft Offshore Clay for Wide Strain Range B. D Elia,. Lanzo, A. Pagliaroli, P. Toasi, F.L. Chioi 3 Departent of Strutural and eotehnial Engineering, University of Roe La Sapienza, Roe, Italy Institute for Environental eology and eo-engineering, National Researh Counil, Roe, Italy 3 Departent of Earth Sienes, University of Roe La Sapienza, Roe, Italy Abstrat Stiffness harateristis of very soft lay sedients of the Italian Adriati ontinental shelf are presented. A siple shear devie apable of investigating yli properties of soils in a wide range of shear strains was eployed for the experiental study. The dependene of sall-strain and seant shear oduli on a nuber of fators suh as strain aplitude, vertial onsolidation stress, stress history and loading yles is analyzed and disussed. Keywords Soft offshore lay, stiffness, siple shear INTRODUCTION The solution to a nuber of arine geotehnial probles (foundation of offshore strutures, stability of subarine slopes subjeted to earthquake exitation and wave ation, et.) requires the knowledge of the stiffness properties of very soft offshore lays under yli loading. Over the past three deades a wealth of experiental results fro laboratory investigations have highlighted that stiffness properties of onshore soils are a funtion of several variables suh as shear strain aplitude, onfining stress, stress history, nuber of yli loading and strain rate [,,3,4]. In partiular, yli behavior of soft lays have been studied by a nuber of researhers [e.g. ] and, ore reently, have gained inreasing attention [6,7,8]. On the other hand, researh on stiffness of very soft arine lay sedients is extreely sare, exept for large strains [e.g. 9,]. Reent works on soft arine lay sedients are essentially devoted to the study of opressibility and undrained strength and, to a liited extent, to the easureent of the sall-strain stiffness fro in situ and laboratory tests [e.g. ]. In this paper, the results of an experiental investigation eploying a yli siple shear apparatus for undisturbed speiens sapled fro very soft lay sedients fro the Italian Adriati shelf are presented. Ephasis is given to the easureent of the stiffness properties in a wide strain range, i.e. the sall-strain stiffness expressed by the axiu shear odulus ( ) and the ediu-to-large stiffness expressed by the seant shear odulus ( s ) and its variation with the yli shear strain aplitude (γ ). The influene of fators suh as vertial stress, void ratio and stress history on and s is exained and disussed. Further, at ediu and large strains the effet of loading yles is also evaluated. EOLOICAL OUTLINES The study area is loated in the entral-southern Adriati sea, off the eastern oast of Italian Peninsula. The area is part of the broad (4 k) entral Adriati ontinental shelf, gently sloping towards the basin whih extends between the Meso-Adriati depression and the Treiti Islands high (Fig. ). The irulation of the area is doinated by shallow and interediate water asses whih ove geostrophially ounterlokwise along the Adriati Italian oast []. Suh irulation disperses towards south-west the peliti sedients disharged by the Po River (. 7 Mg/year) and by the inor rivers draining the Apennini hain (.4 7 Mg/year). The Po sedients were in fat found along the oast for hundreds of kiloetres to the south that is even further south of the study area. Core 9 Punta Penna k Core Vasto ROME Fig. : Loation of study area and sapling sites. Study area All over the Adriati shelf [3] a well-defined erosional unonfority fored during the last glaial sea level lowstand (soe years b.p.) divides the overonsolidated Quaternary sequenes fro the overlying sedient deposited during last sea level yle, fored by transgressive silty sand units (-8 years) and a peliti highstand unit (8 years b.p. to the present). The latter, whih is the target of the geotehnial haraterization, has a axiu thikness up to in the iddle shelf (4- water depth) and dereases towards the basin beoing a drape -3 thik at the shelf break.

2 of 8 SAMPLIN AND EOTECHNICAL PROPERTIES.8 Two ores were reovered in the upperost part of the peliti unit lying on the Quaternary substratu, 4 k offshore Punta Penna, south to the town of Vasto (Fig. ). Core #9 is 6. long and was taken at a water depth of 4 where the peliti unit is 6 thik. Core # is long and was taken at a water depth of 7 where the peliti unit is 6 thik. Cores were reovered by using a 9 diaeter vibroorer whih penetrated the sedient under the sole stati load due to its own weight as to produe a very low saple disturb. Siple shear tests were perfored on speiens fro ore #. The sedient reovered in the two ores, whih is siilar in stratigraphy and struture, is a lay and silt of ediu plastiity (CF=47%-%, PI=9-) having a grain density of.7 Mg/ 3. The natural water ontent is lose or slightly above the liquid liit. The aterial is rather hoogeneous as indiated by the slight variability of plastiity and grain size as well as by the sare variations of x-ray absorption in digital radiographs. A typial log of geotehnial properties easured on saples fro ore #9 is shown in Fig.. In the shallower layer the undrained strength u, easured by eans of a laboratory vane test, regularly dereases fro soe 4 kpa at seafloor down to.7 kpa at below the seafloor. Below this depth, u inreases linearly down to a depth of aording to the expeted ratio u /σ v, alulated fro the expression by [4] assuing the effetive vertial in situ stress (σ v ) be equal to the preonsolidation pressure (σ p ). Conventional oedoeter tests were onduted on saples retrieved fro ore # at three different depths, naely.,. and.. The e-logσ v relationship referred to the saple taken at. depth is plotted in Fig. 3. The preonsolidation pressure σ p is not learly identified beause the e-logσ v urve does not exhibit a lear bending point. However, the deterination of σ p Undrained strength, C u (kpa) Void ratio, e saple depth =.... Vertial effetive stress, σ' v Fig. 3: Measured e-log σ v relationship in oedoeter test. using Casagrande s proedure yields a value of about. MPa. The shape of the e-logσ v urve shows soe non-linearity even in the norally onsolidated range. Average values of the opression index, C, and swelling index, C s, are.47 and.7 respetively. Note that the value of C evaluated fro the urve is lose to that obtained fro the well-known relationship proposed by Terzaghi C =.9(w L -), whih yields C =.4. Intrinsi opression line (ICL) and sedientation opression line (SCL) were plotted in Fig. 4 []. These two urves an be used as referenes for evaluating the degree of struturation of natural lays. In the sae plot the noralised oedoeter opression urves are also reported, showing differenes between shallow and deeper saples. These urves progressively depart fro the sedientation line (SCL) as sapling depth inreases and only at the highest onsolidation stresses onverge towards the intrinsi opression line (ICL). This behavior ould be related to a progressive hange of soil fabri with depth (less open struture). Bulk density, γ (Mg/ 3 ) Water ontent, w Peak Depth below seafloor () reoulded. Fig. : eotehnial profiles fro ore #9.

3 3 of 8 Void index I v, I v 3 - (a) ICL initial void index, I vo depth. ". ". SCL Vertial effetive stress, σ' v (kpa) Fig. 4: Noralized oedoeter opression urves and initial void ratio index at different depths. EXPERIMENTAL APPARATUS AND TESTIN PROCEDURE The Double Speien Diret Siple Shear (DSDSS) devie was eployed for the study. This apparatus was reently onstruted at the University of Roe La Sapienza [6], based on the prototype designed and built at the University of California at Los Angeles [7]. The basi onfiguration and the ain features of the original devie were aintained in onstruting the new version and only inor odifiations have been ade. The DSDSS devie is extensively desribed elsewhere [7] and therefore only soe relevant harateristis are provided hereafter. In partiular, it is worth entioning its peuliar two-speiens onfiguration, whih enabled to overoe probles typial of a standard diret siple shear (DSS) devie (i.e., false deforations, syste opliane and frition). The DSDSS devie is unique in the aspet that it is apable of investigating, in a single test, the yli properties of soils in a very wide range of strains, fro about.4% to in exess of % [8, 9]. Tests were onduted on saturated speiens, 66 in diaeter and high, sapled fro ore # at a depth of.. The test progra inluded two series of tests. In the first series the average natural water ontent (w ) and initial void ratio (e ) were 6.% and.63, respetively, and in the seond series were 8.4% and.3, respetively. The experiental proedure suggested by [] was followed for testing, i.e. the onstant-volue equivalent-undrained siple shear testing proedure. The test results obtained with the onstant-volue proedure desribe the undrained behavior of Vasto lay sedients []. The speiens were first onsolidated under onstant vertial stress σ v. At the opletion of priary onsolidation, the speiens were subjeted to several steps of yli strain-ontrolled tests gradually inreasing the agnitude of the yli shear strain aplitude, γ, overing a wide range of shear strains. TESTIN PRORAM As already entioned, the test progra inluded two series of tests, hereafter referred as A and B respetively, oposed eah of several stages of vertial effetive stress σ v (Table I). For the tests in series A, a total of stages were exeuted. The test sequene onsisted of a loading phase, with σ v fro kpa (~σ v ) to 3 kpa, an unloading phase, with σ v fro 3 to kpa, a reloading phase with σ v up to 64 kpa and, finally, a seond unloading phase with σ v down to 4 kpa. In Table I the values of overonsolidation ratio (OCR) and void ratio at the end of priary onsolidation (e ) for eah stage are reported. The yli shear strain aplitude γ varied between.4% and.4%, i.e. slightly below the voluetri threshold shear strain that for soils of siilar plastiity is about.4% []. No ore than yles were applied in eah test. For the tests in series B, stages were arried out. The test sequene onsisted of a loading phase only, with σ v ranging fro kpa to 6 kpa (Table I). The γ values overed a wide range of strains, fro very sall of about.4%, to very large, up to %. The nuber of yles applied in eah step of onstant γ >.% was 3. In both series of tests, the shape of yli straining was approxiately sinusoidal with a frequeny between. and.3 Hz. Typial test results are reported in Fig. where s easureents are plotted as a funtion of γ at σ v =6 kpa. In this figure lusters of data points orresponding to the values of s and γ pertaining to the different steps of inreasing γ are plotted. The s data are onneted by a solid line to obtain the urve representing the redution of s with γ. This urve is then extrapolated by a dashed line to γ =.% to estiate the axiu shear odulus. TABLE I: SUMMARY OF CYCLIC TESTIN CONDITIONS Series Stage# Loading σ v sequene a (kpa) e OCR A L.69 A L.3 A 3 L 4.43 A 4 L 8.36 A L 6. A 6 L 3.8 A 7 U 6.9 A 8 U A 9 U A U.49 6 A R A R 3.9 A 3 R A 4 U A U B L. B L.479 B 3 L 4.4 B 4 L 8.98 B L 6.9 a L=Loading, U=Unloading, R=Reloading, U= nd Unloading

4 4 of 8 Seant shear odulus, s 3 Fig. : Typial redution of s with yli shear stain aplitude. TEST RESULTS AND DISCUSSIONS Test results are presented hereafter in ters of the stiffness paraeters, s and s /. The effets of γ, σ v, e and OCR in the sall to ediu strain range on the stiffness paraeters will be dealt with. At larger strains the effet of the nuber of yles on s will be also investigated. Results at sall strains It is well established that sall-strain stiffness is influened by ean effetive onfining stress σ, overonsolidation ratio OCR as well as void ratio e. Many attepts have been ade to desribe the dependeny of on the above entioned paraeters, ost of the expressed by relationships in the for: n n r = S F(e) σ' σ OCR () where F(e) is a void ratio funtion, S, n, and k are adiensional stiffness paraeters aounting for the nature of soil, σ r is a referene stress usually taken as the atospheri pressure p a. The ain differene aong the various relationships depends on the hoie of the void ratio funtion [e.g. 3, 4]. In partiular [] showed that by using the following void ratio funtion:.3 F(e) = e () the effet of OCR ay be onsidered negligible (i.e. k~ in Eq. ()) for a wide spetru of soils and thus Eq. () ay be rewritten in a sipler for: n n S F(e) σ' σ r Series B Stage # σ' v = 6 kpa OCR=.... = (3) For soft natural lays it is worth realling the epirial orrelation proposed for by [] based on test results on alluvial lays with void ratio ranging fro.9 to 4: k.6 = A [(7.3 e) ( + e)] σ' (4) where A is equal to 9 and 7 for norally and overonsolidated soils respetively and F(e)=(7.3- e) /(+e). More reently [6] based on the analysis of norally onsolidated soils with void ratio ranging fro to expressed by :.4. v = 4 (+ e) σ' () where the void ratio funtion is F(e)=(+e) -.4. In both Eqs. (4) and (), and σ (or σ v ) are expressed in kpa. An alternative way to take into aount the dependeny of on state and stress history under isotropi ondition of onfineent was proposed by [6]. The Authors expressed only as a funtion of two independent variables, the isotropi ean effetive stress p and the isotropi overonsolidation ratio R. In fat, the influene of void ratio e (or speifi volue v) is taken into aount by the opressibility relationship between e and p, uniquely deterined for norally onsolidated states and aounted for by R for overonsolidated states. Under these hypotheses they proposed the following equation: n n S p' p r R = (6) where S, n and are adiensional stiffness paraeters siilar to S, n and k and p r is a referene stress. It an be deonstrated that Eq. (6) an also be written: n pr S (p' pr ) (p' e p' ) = (7) where p e is the equivalent pressure, =/Λ where Λ=(λ - k)/λ, λ and k being the slopes of the noral opression and swelling lines in the lnp'-v plane. A siilar approah ay be applied to desribe the effet of stress level and history on the sall-strain stiffness of a soil opressed in oedoeter onditions by using the following expression: It ust be onsidered that : n n r = S σ' σ OCR (8) Λ p σ' v = (σ' ve σ' v) OCR = σ' (9) where σ ve is the equivalent vertial onsolidation stress defined as : σ' (e r e)/c ve σr = () e r being the void ratio at σ v =σ r = kpa. In eq. (9) the quantity Λ, previously introdued for isotropi

5 of 8 onsolidation, an be used to a good approxiation also for K onsolidation. So that, beause λ=.434c and k~.434c s, Λ = (λ k) λ (C C ) C () Taking into aount Eq. (9), it is possible to write Eq. (8) as: or n n S σ' σ r (σ' ve σ' v ) s = () n σr S (σ' σr ) (σ' ve σ' v ) = (3) where = /Λ. The values estiated fro test results an be used to verify the appliability of the above relationships. To this purpose values fro the tests in series A are plotted in Fig. 6 as a funtion of σ v in a log-log sale. Different sybols refer to different values of overonsolidation ratio, i.e. losed sybols for norally onsolidated states (OCR=) and open sybols for overonsolidated states (OCR>). The data points with OCR= have been qualitatively interpolated by a solid line while those with OCR> have been interpolated by broken lines averaging the unloading-reloading branhes. For both norally and overonsolidated states inreases alost linearly with σ v. However, it ust be observed that the values orresponding to norally onsolidated states plot on a straight line that is steeper than the lines orresponding to the overonsolidated states, i.e. inreases with OCR at a given σ v. In Fig. 7 the sae set of data is plotted versus the ean effetive stress σ =(σ v +σ h )/3, where σ h =K σ v is the horizontal effetive stress and K is the oeffiient of earth pressure at rest. The values of K for the loadingunloading-reloading sequene were evaluated using the relationships proposed by [7], assuing the angle of shearing resistane ϕ =3 based on the epirial orrelation between ϕ and PI. In Fig. 7 the values Maxiu shear odulus,.. Vertial effetive stress, σ' v Fig. 6: Values of versus vertial effetive stress. Loading OCR = Unloading-Reloading OCR > nd Unloading OCR > Maxiu shear odulus, Loading OCR = Unloading-Reloading OCR > nd Unloading OCR >... Mean effetive stress, σ' Fig. 7: Values of versus ean effetive stress. pertaining to overonsolidated states plot slightly higher than those referring to norally onsolidated ones. In order to redue the influene of void ratio, the noralized axiu shear odulus, that is divided by a void ratio funtion F(e), is plotted versus σ in Fig. 8. In this plot distintion is siply between norally and overonsolidated data points. The void ratio funtions F(e) proposed by [] and [], reported in the Eqs. () and (4) respetively, have been used. This noralization proedure further redue the satter between the data points whih are approxiately distributed along straight lines. This irustane is onfired by the value of the oeffiient of regression r fro a best fit of the overall data, equal to.9 and.98 using the void ratio funtions in equations () and (4), respetively. In Fig. 9 a oparison between estiated fro tests results and predited by the epirial orrelations given in Eqs. (4) and () has been ade. A good agreeent between the values alulated by Eq. (4) and those estiated an be observed only a high vertial stresses. The values predited by Eq. () onsistently overestiate the estiated at all onfining stresses. Noralized axiu shear odulus, / F(e). Jaiolkowski et al. (994) r =.9 Kokusho et al. (98) r =.98, + OCR = OCR >.. Mean effetive stress, σ' Fig. 8: Values of /F(e) versus ean effetive stress.

6 6 of 8 Results at ediu and large strains predited Fig. 9: Predited versus easured values. The alternative approah, in whih is expressed only as a funtion of ean effetive stress σ and overonsolidation ratio OCR, was also adopted to redue the data aording to Eq. (3). To apply Eq. (3) two paraeters are needed, i.e. the opressibility index C, whose value is.47 as already entioned, and the referene void ratio e r equal to.6; as referene stress was assued σ r = kpa. By a linear regression analysis of the data, the paraeters S, n and were deterined and the resulting values are 33,, and., respetively. A value of Λ=.87 was deterined for this soil and, aordingly, a value of =.8 was obtained. The data were therefore noralized with respet to the ratio σ ve /σ v raised to the power of (or, analogously, to OCR raised to power of ) and plotted versus the ean effetive stress σ in Fig.. A lear trend an be reognized with all the data plotting around a straight line irrespetive of their overonsolidation ratio. The oeffiient of regression r is.99, thus iplying that norally and overonsolidated data an be approxiated with very satisfatory auray by Eq. (3). / (σ'v,e /σ' v ) estiated, + OCR = OCR > Kokusho et al. (98) Shibuya et al. (997), OCR = + OCR > OCR = r = Mean effetive stress, σ' Fig. : Values of /(σ ve /σ v ) versus the ean effetive stress In Fig. the plots showing the redution of s with γ are presented. Fig. a displays soe representative s - γ relationships orresponding to the loading and first unloading stages for the tests in series A. The plots show that the odulus s dereases as γ inreases at all onfining stresses. In general this redution starts to appear at γ below.% and beoes appreiable as γ inreases above.%. Further, under the sae σ v, the s -γ urves pertaining to the overonsolidated states plot higher than the orresponding urves pertaining to norally onsolidated ones. It is worth noting the very low values of s of about MPa at very low σ v = kpa, orresponding to the approxiately zero vertial loading with ere top and ediu aps weight. In Fig. b, typial s -γ relationships for the tests in series B are presented, showing the apability of the DSDSS devie to investigate the whole range of shear strains fro.4% to slightly above %. The redution of s with γ an also be portrayed in a ore standard for, i.e. by plotting the noralized shear odulus, s /, as a funtion of γ. To this purpose, at eah γ, an average value of the lusters of data points displayed in Fig. was onsidered. These average s Seant shear odulus, s Seant shear odulus, s (a) (b) Unloading Series B Series A σ Stage v ' (kpa) σ Stage v ' (kpa).... Fig. : Values of s versus yli shear strain aplitude: results fro the tests in (a) series A and (b) series B

7 7 of 8 values were therefore divided by the estiated to obtain s /. The variation of s / with γ is presented for the tests in series B in Fig.. In the sae figure the s / -γ urves suggested by [8] for sands and by [9] for lays for PI= and PI=3, drawn as dashed lines and solid line respetively, were reprodued as referene. As σ v inreases between and 4 kpa, a strong nonlinearity is apparent. In fat, the s / -γ data points plot between the [8] lower and average boundaries. As σ v inreases above 4 kpa, the s / -γ data points plot between or above the Vueti & Dobry urves, thus indiating a ore linear behavior. At high γ between.% and % the s / -γ data points onverge to the sae values irrespetive of the vertial onfining stress. A oparison between the norally and overonsolidated data for the tests in series A is shown in Fig. 3. The oparison is ade at σ v =4 kpa and OCR variable between and 6. As OCR inreases (and void ratio dereases) the s / -γ data points shift towards right, i.e. at a given γ the s / values of overonsolidated states are higher than the orresponding ones pertaining to the norally onsolidated ones. This. Seed et al. (986) Series B σ v ' Stage (kpa).8 Noralized shear odulus, s / Fig. : Values of s / versus yli shear strain aplitude. Noralized shear odulus, s / PI= PI=3 Vueti & Dobry (99) Series A σ v ' (kpa) = 4 kpa Loading Unloading nd Unloading OCR Fig. 3: Coparison between s / γ data points at different OCR and void ratio values. 8 6 e inrease of the noralized shear odulus at inreasing OCR and dereasing void ratio has already been douented on onshore soils. The effet of nuber of yles N on the shear odulus is displayed in Fig. 4. In this figure the ratio s,n / s,, that is s at yle N noralised with respet to s at N=, is plotted versus N at σ v =8 kpa and for three values of γ, naely γ ~.%, γ ~.% and γ ~%. It an be seen that s is hardly affeted by the nuber of yles at γ ~.% while exhibits a progressive redution as γ inreases. At γ ~% the ratio s,n / s, reahes a stable value of about.7 after around yles. Based on these results, the degradation paraeter t=-log( s,n / s, )/logn [3,3] was also deterined and plotted versus γ in Fig.. The t values, qualitatively interpolated by a bold line in the figure, plot onsistently with literature data for different lays of various PI.. s,n / s,. Degradation paraeter, t Fig. 4: Variation of s,n / s, with the nuber of yles N at different yli shear strain aplitudes Nuber of yles, N Series B AL CLAY (PI = -) Vasto lay (PI=9-) σ' v = 8 kpa PI = 8-3 VTCB (PI=-3) 3 Fig. : Effet of plastiity index on degradation paraeter of norally onsolidate lays ([3], siplified). CONCLUSIONS γ ~. % γ ~. % γ ~. % VOR (PI=3-33) VNP (PI=38-3) Shear odulus of very soft offshore lay fro the Italian Adriati ontinental shelf was investigated by

8 8 of 8 eans of yli siple shear tests over a wide range of shear strain aplitudes, vertial stresses and stress histories. The sall-strain shear odulus was exained in relation to the dependene on stress and history paraeters (σ, e and OCR). A standard noralization proedure was first adopted, naely was divided by soe void ratio funtion F(e) and plotted versus σ. The F(e) was seleted suh that the effet of OCR ould be onsidered negligible. An alternative proedure was also used, in whih was divided by a funtion of OCR, i.e. OCR, and plotted versus σ. In this proedure the ontribution of void ratio is ipliitly taken into aount by onsidering the relationship between e and σ v, uniquely deterined for norally onsolidated states and aounted for by OCR for overonsolidated ones. Both proedures provided onsistent results, i.e. the noralized values plotted versus σ were distributed along straight lines with no signifiant satter. The strain-dependent urves of the noralized shear odulus s / lie in the region between lay and sand. This iplies a rearkable dependeny on vertial effetive stress of the s / -γ urves, whih shift signifiantly towards right as σ v inreases. As for sandy soils, an apparent non-linearity is observed at very low onsolidation stresses oparable to the in-situ vertial stress. At higher onsolidation stresses, the s / -γ urves are in agreeent with those of ohesive soils of siilar plastiity. Aording to literature data, the plastiity index of the soft lay was also found to affet its degradation harateristis due to loading yles. The strong non-linearity at low σ v ould be related to the sedient struture, whose influene will be larified by further investigation aied at oparing reonstituted and natural soil behavior. REFERENCES [] R. Dobry and M. Vueti, Dynai properties and response of soft lay deposits, Pro. Int. Syp. eoteh. Eng. Soft Soils, Mexio City, vol., pp. -87, 987. [] K.H. Stokoe, S.K. Hwang and J.N.K. Lee, Effets of various paraeters on the stiffness and daping of soils at sall to ediu strains, in Prefailure Deforation of eoaterials, Eds. Shibuya, Mitahi and Miura, Vol.., pp , 994. [3] F. Tatsuoka, D.C.F. Lo Presti and Y. Kohata, Deforation harateristis of soils and soft roks under onotoni and yli loding and their relationships, 3rd Int. Conf. Reent Adv. eote. Earth. Eng. & Soil Dyn., SOA, vol., pp , 99. [4] K.H. Stokoe, II, M.B Darendeli, R.D. Andrus and L.T. Brown, Dynai Soil Properties: Laboratory, Field and Correlation Studies, Thee Leture, nd Int. Conf. Earth. eotehnial Eng., Vol. 3, Lisbon, Portugal, June, pp. 8-84, 999. [] T. Kokusho, Y. Yoshida, and Y. Esashi, Dynai properties of soft lays for wide strain range, Soils and Foundations, vol., no. 4, pp. -8, 98. [6] S. Shibuya, S.C. Hwang and T. Mitahi, Elasti shear odulus of soft lays fro shear wave veloity easureent, éotehnique, vol. 47, no. 3, pp. 93-6, 997. [7] S. Shibuya and S.B. 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