experimental study of the engineering mechanical

Research ArticleExperimental Study of the Engineering Mechanical Propertiesof the Foundation Soil for Offshore Wind Power Platforms

Yi Fang 12 Yuejun Lv1 XingYuan Zhou1 and Yanju Peng 1

1National Institute of Natural Hazards Ministry of Emergency Management of China Beijing China2Key Laboratory of Crustal Dynamics China Earthquake Administration Beijing China

Correspondence should be addressed to Yanju Peng pengyj408126com

Received 22 May 2021 Revised 13 September 2021 Accepted 27 September 2021 Published 14 October 2021

Academic Editor Piguang Wang

Copyright copy 2021 Yi Fang et alis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Most of the coastal beach zone in the world is rich in wind energy reserves and has great potential for offshore wind powerdevelopment However the sedimentary environment in the coastal area is complex and changeable and the nature of thefoundation soil of offshore wind power platforms is weak and complex which is quite different from that in the land areas Inorder to systematically study the mechanical properties of marine foundation soils a series of geotechnical tests are carried out onrepresentative undisturbed seabed soils such as basic laboratory geotechnical tests bender element tests undrained triaxial sheartests and resonance column tests e test results show that shear wave velocity (Vs) of marine silt and silty clay increases linearlywith the buried depth the stress-strain relationship curves of silty clay and silt present two different modes of development strainhardening and strain softening the undrained shear strength (Sd) of the two types of marine soils decreases with the increase of thevoid ratio (e) and both present a good single correlation Based on the relationship between Sd and Vs from the laboratory test ofdisturbed seabed soils an undrained strength evaluationmethod of undisturbed seabed soils under the current stratum conditionsincorporating in situ shear wave velocity is establishede dynamic shear modulus (G) in the various strain ranges of undisturbedsilty clay and silt increases regularly with the buried depth (H) Meanwhile the maximum dynamic shear modulus (Gmax) linearlyincreases with the increase ofH whereas the attenuation relationship ofG decreases with the increase ofHe predictionmethodof G based on buried depth is established with high accuracy

1 Introduction

Wind energy is currently one of the fastest-growing re-newable energy sources with the most promising industrialprospects Worldwide onshore wind power started earlierA large number of wind farms have been built successivelyin America Germany China etc In the past decade off-shore wind farms have gradually become the popular de-velopment direction of the global wind power industry emain reason for this development tendency is that electricityconsumption of the coastal areas has increased year by yearand offshore wind power has a large single-unit generatingcapacity moreover the wind energy resources are morestable and abundant In order to satisfy the demand foroffshore wind power transmission and improve the structureand reliability of the structure of urban power grids the

number of wind power platform projects which will beconstructed is increasing annually around the world eoffshore environmental loads and geological conditions aremore complex than their onshore counterparts so that it ismore difficult to build offshore wind power platforms thanonshorersquos In particular the foundation soil of the proposedoffshore wind power platform is deep weak and complexand these problems could be exacerbated by constructiondisturbances erefore it is indispensable to carry out asystematic investigation of the engineering mechanicalproperties of the seabed soil of the foundation of the pro-posed offshore wind power platforms

Compared with onshore drilling expense the cost ofoffshore drilling is rather higher moreover the soil samplesare more difficult to obtain few experimental research hasbeen carried out and in return it has caused a serious lag in

HindawiShock and VibrationVolume 2021 Article ID 1382740 12 pageshttpsdoiorg10115520211382740

basic research on the dynamic characteristics of the seabedsoil Koutsoftas and Fischer [1] found that the stress historyhas a strong influence on the dynamic shear modulus G andthe modulus value of overconsolidated clay is larger thanthat of normally consolidated clay e standardizedmodulus ratio for the undrained shear strength Su is mainlyaffected by the type strain level and overconsolidation ratioOCR of soils e influence of stress history on the dampingratio is not significant Bryan and Stoll [2] conducted res-onance column tests on sand clay and silt taken from thesea about 5 miles from the coast of New Jersey USA andfound that Gmax is mainly related to the void ratio and σrsquomYamamoto et al [3] found that Gmax of marine sediments isproportional to (σrsquom)05 Kagawa [4] discovered that theGmaxof marine soft clay decreases with the increase of void ratio(e) and plasticity index (Ip) and is proportional to the av-erage effective confining pressure (σrsquom) which is basicallyconsistent with the test results of two marine clays byKoutsoftas [1] Vrettos and Savidis [5] conducted resonancecolumn tests on 4 undisturbed clays at 2 sites on the westcoast of Greece and found that Gmax for low plastic clay isproportional to (σrsquom)05 and high plastic clay is proportionalto (σrsquom)05 and the influence of the plasticity index of co-hesive soil should be taken into consideration to predictGmaxe plasticity index and the average effective confiningpressure have a strong influence on the dynamic charac-teristics of the offshore cohesive soil Lanzo et al [6] con-ducted an experimental study on the undisturbed soft clay inthe Adriatic Sea in Italy e results showed that when therelative consolidation ratio and e are close to each other theeffective confining pressure affects the Gmax of marine claysignificantly And the decay curve of the dynamic shearmodulus ratio GGmax-y of marine soil is close to that of theterrestrial soil Kong et al [7] studied the basic properties ofmarine soil from the Qiongzhou Strait of China e testfound that marine soil has unique physical properties and itwas classified as silt based on the soil quality However itscompression deformation characteristics and strength in-dicators are different from those of general silt or silty soiland its shear strength is relatively higher whereas it hascertain structural strength Zhang et al [8] found that thefast-deposited silty soil has a high consolidation rate underits own weight After the normal consolidation is completedthe strength continues increasing with time and there is anonuniform consolidation phenomenon and a pseudo-overconsolidation state similar to those of the primary soilthat occurred with the increase of the depth Liu et al [9]analyzed the advantages and disadvantages of the existingoffshore wind turbine foundations In order to modify theweakness of the existing offshore wind turbine foundationsthey proposed a new umbrella-type suction anchor foun-dation suitable for offshore wind power platforms in theYellow River Delta and its structural advantages and in-stallation method were explained Wu et al [10] presentedan experimental investigation which was conducted throughcomprehensive bender element tests on Gmax of marine siltysand e results indicate that under otherwise similarconditions Gmax decreases with the decrease of e or finescontent (FC) but decreases with the increase of FC Zhao

et al [11] presented an elastoplastic modeling method fordynamic consolidation of the liquefiable seabed around apipeline subjected to ocean environmental loadings Zhanget al [12] proposed a transient seismic structure-water-sediment-rock interactional model to evaluate the seismicresponse of the marine structure in ocean space underobliquely incident earthquakes Wang et al [13] presented asubstructure method for seismic responses of offshore windturbines considering nonlinear pile-soil dynamicinteraction

e above researches show that no systematically ex-perimental researches on the mechanical properties ofgeneral marine engineering have been carried out yetConsequently we carried out this article which is based onthe offshore wind power platform project that is ongoing inthe Yellow Sea of China e representative undisturbedseabed soil was collected from the site to be conducted withbasic laboratory geotechnical tests including bender ele-ment tests undrained triaxial shear tests and resonancecolumn tests to determine the physical and mechanicalproperties of the silt and silty clay e correlations betweenthe basic physical indicators the undrained shear strengthand the shear wave velocity of the primary marine soil areinvestigated Eventually an undrained shear strength eval-uation method is proposed and a predictive model of dy-namic shear modulus and depth is presented is researchcan provide basic scientific data for the design and con-struction of offshore wind power platforms

2 Samples and Resonant Column Test

21 Stratigraphic Information and Basic Physical PropertiesTo study the engineering mechanical properties of typicalmarine foundation soil of offshore wind power platformsexploration works have been carried out in the waters offshoreof the Yellow Sea of China and representative boreholes wereselected Undisturbed silty clay and silt were collected frommultiple depths within the boreholes using open thin-walledsoil samplers e soils were sampled within a depth range of2 to 70m and sulfate sandstone was encountered below 73me natural water content specific gravity natural densityvoid ratio and plasticity index of the samples were tested inaccordance with the ASTM standards Table 1 presents thesoil depths the corresponding physical and mechanicalproperty indices of the undisturbed silty clay and silt samplesfrom the seabed to the bedrock As can be seen from the tablethe silty clay layer and the silt layer each accounted for ap-proximately half of the total core length and they are dis-continuously distributed e upper layer had a relativelylarge water content and the water content remained at ap-proximately 30 at soil depths of greater than 14m especific gravity ranged from 266 to 270 exhibiting only asmall difference e plasticity index of the silty clay wasgreater than 10 and the plasticity index of the silt was less than10 Based on the comprehensive consideration of the drillingexploration data the site engineering geological survey andthe geophysical prospecting data the strata of the site can bedivided into five major layers e lithological characteristicsof the soil layers from top to bottom are as follows

2 Shock and Vibration

Layer I was dominated by very soft bluish-gray plasticsilty clay e soil samples had high water contents and werebasically saturated and the layer was approximately 175mthick

Layer II was dominated by dense light grayish-yellowsilt e soil samples had high water contents and werebasically saturated and the layer was approximately 135mthick

Layer III was dominated by medium-density grayish-yellow silt e soil samples had high water contents andwere basically saturated and the layer was approximately5m thick with a thin (sim25m thick) intercalated silt layer

Layer IV was dominated by medium-soft bluish-grayplastic silty clay e soil samples had high water contentsand were close to saturation and the layer was more than28m thick Layer V was sulfate sandstone

22 Testing Equipment As shown in Figure 1 the undrainedshear tests and shear wave velocity tests were carried out usinga GCTS HCA-300 cyclic loading tester (USA) and a benderelement system at the National Institute of Natural HazardsMinistry of Emergency Management of China e confiningpressure and back pressure of the HCA-300 were loaded andmeasured at up to 1MPa using a standard pressurevolumecontrollere axial force can be independently controlled forstatic and dynamic loading with a maximum of 10 kN and afrequency of 5Hz All of the sensors had a test accuracy ofgreater than 01 of the full scale e soil shear wave velocitywas tested using the bender elements installed at the top andbottom of the HCA-300 pressure chamber

As shown in Figure 2 the modulus and damping testswere conducted using a GCTS TSH-100 high-precisionfixed-free resonant column test system at the out using a

GCTS HCA-300 cyclic loading tester (USA) and a benderelement system at the National Institute of Natural HazardsMinistry of Emergency Management of China e strainresponse curve of soil was recorded at 02ms intervals usingan eight-channel digital acquisition system with an accuracyof 10minus6 for the parameters ie soil resonance frequencymaximum shear strain shear wave velocity and shearmodulus

23 TestingMethod e standard sample accommodated bythe GCTS HCA-300 cyclic loading tester is 50times100mm insize but the field drilled sample was approximately100times 200mm in size erefore it was necessary to man-ufacture the primary soil sample into a standard sample witha diameter of 50mm and a height of 100mm After thestandard-sized samples were obtained they were saturatedusing the vacuum saturation method in accordance with theASTM standards In addition to avoid the impact of thedifferences between the prepared samples on the test resultsthe samples were each saturated in a saturation tank for 10hours

e undrained shear tests and the shear wave velocitytests were carried out as follows After a saturated samplewas mounted on the base of the bender element with its topconnected to the top of the bender element and the dis-placement sensor the pressure chamber was tightly sealedNext the soil sample was uniformly consolidated under anatural stress state according to the depth of the primary soilsample First the consolidated samples were subjected to anondestructive bender element shear wave velocity testfollowed by undrained and drained shear tests with aconstant shear rate of 01min e modulus and dampingtests were carried out as follows e sample was mounted

Table 1 Basic physical properties of undisturbed soil

Depth (H) (m) Lithology Water contents (w) () Specific gravity (Gs) Density (ρ) (gtimes cmminus3) Void ratio (e) Plasticity index (Ip)21ndash23 Silty clay 337 269 189 090 151636ndash38 Silty clay 389 270 178 087 1455104ndash106 Silty clay 362 269 184 099 1254119ndash121 Silt 497 267 161 148 925134ndash136 Silty clay 341 269 190 090 1513138ndash140 Silt 415 268 173 119 956172ndash174 Silty clay 286 270 187 082 1521206ndash208 Silt 305 266 182 098 974257ndash259 Silt 300 266 178 094 768308ndash310 Silt 342 266 188 090 869343ndash345 Silty clay 296 270 190 078 1581357ndash359 Silty clay 322 268 192 076 1739377ndash379 Silt 286 269 189 083 882391ndash393 Silt 286 267 191 080 915395ndash397 Silt 288 268 188 093 915427ndash429 Silt 282 268 184 087 870431ndash433 Silt 272 266 190 078 744441ndash443 Silt 286 267 204 068 825455ndash457 Silt 304 268 188 086 983485ndash487 Silty clay 302 269 191 083 1159549ndash551 Silty clay 318 268 193 083 1110598ndash600 Silty clay 299 268 201 081 1214696ndash698 Silty clay 275 268 190 080 1426

Shock and Vibration 3

on the base of the instrument with its top connected to thesuspension torsion driving device and the displacementsensor the axial displacement data were set to zero and thepressure chamber was sealed en the soil sample wasuniformly consolidated under a natural stress stateaccording to the depth of the primary soil sample e top ofthe consolidated sample was excited using the automaticsuspension torsion device controlled by the WIN-CATS-STD program After the sweep frequency reached the res-onance frequency the soil sample underwent free vibrationBased on the soilrsquos strain response curve which was recordedby the eight-channel digital acquisition system the program

automatically calculated the test values such as the dynamicshear strain c the dynamic shear modulus G and thedamping ratio λ e excitation frequency was increased insteps and Step 4 was repeated until the shear strain am-plitude of the sample was greater than 5times10minus4 at whichpoint the test was completed

3 Test Results and Analysis

31 Variation Law of Shear Wave Velocity and e and H ofUndisturbed Soil In the bender element test Vs was de-termined using the following equation

1 FRM-100-TQ-40 Test Platform 2 PCP-3000-HCA Pressure control cabinet3 Computer 4 SCON-2000 Digital Servo Controller and Acquisition System5 HPS-15-50-380 Hydraulic source 6 Vacuum pump

2

1

34

5

6

Figure 1 GCTS HCA-300 dynamic hollow cylinder apparatus and bender element system

2 Loading frame1 Pressure control panel

4 Computer3 Digital servo controller and acquisition

1

23

4

Figure 2 GCTS TSH-100 type resonant column testing system


Vs d

t (1)

where d is the distance from the transmitting section to thereceiving section of the bender element chip Bai et al [14]showed that when comparing methods of determiningwaveform of t the time domain first arrival method issimpler and more accurate than the frequency domainmethod erefore in the shear wave velocity tests a singlesinusoidal pulse wave was selected as the excitation signalthe excitation frequency was determined based on thespecific stress and the soil density and the time domain firstarrival method was used to determine t A single sinusoidalpulse of 1 to 40 kHz was applied to the sandy soil as theexcitation signal It was found that a clear effective signalwas received at the receiving end of the bender element at anexcitation frequency of 10Hz which is consistent with thetest results of Yang and Liu [15] Figure 3 shows a typicalreceived bender element signal diagram for a sample PointsA B and C in the figure are the first deflection point the firstpeak point and the first arrival point of the received benderelement signal respectively e propagation time t of theshear wave was determined by taking point C as the time ofthe first arrival of the shear wave

Figure 4 shows the relationship between the shear wavevelocityVs and the void ratio e of the primary marine soil Ascan be seen from the figure for the same e Vs of the silt issignificantly greater than that of the silty clay Vs of the siltdecreases linearly with the increase of e whereas Vs of siltyclay tends to decrease with the increase of e but there is noobvious correlation e correlation between Vs and e showsthat for low-plasticity undisturbed seabed silt e can be usedto characterize the particle composition of the soil and theeffect of the consolidation stress on the soilrsquos densityerefore e is an effective physical index that can be used toevaluate the soil shear wave velocity Unlike that of silt e ofsilty clay cannot be used as a single index for the evaluationof the shear wave velocity is is because silty clay has highplasticity and thus characterizing its particle compositionusing only the void ratio fails to consider the effect of thecohesion between the soil particles on the mechanicalproperties of the soil Figure 5 shows the relationship be-tween the shear wave velocity Vs and soil depth H of theprimary seabed soil Vs values of both the silt and silty clayincrease linearly with increasing H e degree of influenceofH onVs of marine silt is apparently greater than that onVsof silty clay In summary an equation for evaluating Vs ofundisturbed seabed soil based on the soil depth can beestablished as follows

Vs a middot H + b (2)

where a and b are fitting parameters a reflects the degree ofinfluence ofH onVs of the primary seabed soil and b is theVsof the primary seabed soil corresponding to the state with noinitial consolidation stress For silty clay a 43 b 694and the coefficient of determination R2 099 as for silta 19 b 1128 and R2 098

Vol

tage

(V)

A B

C

0006 0012 0018 0024 0030 00360Time (s)

-4

-2

0

2

4

Figure 3 Time history of output voltage from the receiver of thebender element testing system

Silty claySilt

Shea

r wav

e velo

city

(ms

)

50

100

150

200

250

300

080 085 090 095 100075Void ratio

Figure 4 Relationship between shear wave velocity Vs and voidratio (e) of undisturbed marine soil

Shea

r wav

e velo

city

(ms

)

Silty ClaySilt

50

100

150

200

250

300

10 20 30 40 50 60 70 800Depth (m)

Figure 5 Relationship between shear wave velocity Vs and depth(H) of undisturbed marine soil


32 Stress-Strain Relationship of Undisturbed SoilFigure 6 shows that the curves depict the relationship be-tween the deviatoric stress σd and the axial strain ε of theundisturbed marine silty clay and silt e stress-strainrelationship curves of the silty clay and silt both exhibit twodifferent development modes strain hardening and strainsoftening For example when the value of e is large thestress-strain relationship is characterized by strain hard-ening that is as ε of the sample increases the pore waterpressure increases and σd gradually increases at a rate thatgradually decreases with increasing ε and gradually tends to0 at which point the sample reaches a critical state Whenthe value of e is small the stress-strain relationship ischaracterized by strain softening that is as ε increases σdinitially increases rapidly and then after reaching the peakdeviatoric stress it decreases rapidly until at a rate thatdecreases with the increase of axial strain and graduallytends to 0 at which point the sample also approaches acritical state During this process the sample volume ex-hibits a significant expansion trend and the pore waterpressure decreases It should be pointed out that when e ofsilty clay is less than 084 the stress-strain relationshipreadily transforms from strain hardening to strain-softeningwhereas the silt sample does not exhibit strain-softeninguntil e reaches 08 erefore compared with that of siltyclay the stress-strain relationship of silt requires a higherdensity to transition from strain hardening to strain-softening

33 Undrained Shear Strength Characteristics of UndisturbedSoil e triaxial undrained shear strength Sd σd2 (thepeak value of the stress-strain curve is taken as Sdwhen thereis a peak in the stress-strain curve otherwise the asymptoticvalue of the deviatoric stress at 15 of the axial strain istaken as Sd) is an important parameter that characterizes thestrength properties of soil e undrained shear strength ofthe primary soil obtained from the laboratory element testswas obtained after the soil sample was unloaded andreconsolidated in the laboratory and it differs from theCoulomb shear strength Soil samples obtained at differentdepths may correspond to different positions on theunloading rebound curve or on the normal compressioncurve erefore the determination of the undrained shearstrength index of the primary soil is affected by complexityfactors e depth can be used to characterize the effectivestress that the soil is subjected to in its natural state and itcan reflect the mechanical properties of the soil to someextent Figure 7 shows the variations in the undrained shearstrengths of the silty clay and silt with depth As can be seenfrom the figure the overall Sd values of both the silty clay andthe silt increase as the depth of the soil layer increases butthere is no clear single correlation which indicates that thedepth or the corresponding consolidation stress is an im-portant factor affecting Sd but it is not the only factor

Figure 8 shows the variation in the undrained shearstrength Sd of the silty clay and silt with increasing void ratioe As can be seen from the figure the Sd values of the silty clayand silt both decrease linearly with increasing e It should be

pointed out that the rate of decrease of Sd of the silty claywith increasing e is significantly higher than that of the siltindicating that the undrained shear characteristics of thesilty clay are more sensitive to soil density Compared withH e can more reasonably characterize Sd of the soil is isbecause e can characterize the soilrsquos structural state under thenatural effective stress conditions to some extent Figure 8also demonstrates that e can reflect the stress-strain devel-opment of the primary soil In summary e can be used as areasonable and effective index for evaluating the undrainedshear strength of the primary soil

Sd A middot eB (3)

where A and B are fitting parameters For the silty clayA 945 B minus83 and R2 089 For the silt A 1359B minus32 and R2 080

Figure 9 shows the relationship between the undrainedshear strength Sd and the shear wave velocityVs of the primarymarine soil As can be seen from the figure Sd increases withincreasing Vs and with the exception of individual silty claysamples there is a correlation between Sd and Vs for the otherdisturbed primary soils erefore the relationship betweenSd andVs can be established based on laboratory element testsconducted on disturbed primary soils and combined with theexisting correction methods for the mechanical parameters ofdisturbed and undisturbed soils the method for evaluatingthe undrained strength properties of the undisturbed primarysoil under the current formation conditions was establishedbased on the field shear wave velocity results is will fa-cilitate the establishment of a preliminary method for pre-dicting the foundation soil strength of offshore wind powerplatforms which will decrease testing costs significantly Itshould be noted that the undrained shear strength evaluationmethod based on shear wave velocity is relatively accurate forlow-plasticity soils but it may underestimate the shearstrengths of high-plasticity soils To obtain the undrainedshear strengths of high-plasticity soils more accurately it isnecessary to carry out more accurate undrained shear testsconsidering the basic physical properties of the soil

34 Variation in G with Soil Depth Figures 10(a) and 10(b)show the variations in the dynamic shear modulus G of theundisturbed silty clay and silt at different depths within thesame borehole with increasing shear strain c e followingcan be seen from the figuree G values of the silty clay andsilt at different depths all decrease with increasing c For verysmall strains (clt 10minus5) the G values of the silty clay and siltbasically remain stable As c increases (cgt 10minus5) the Gvalues of the silty clay and silt begin to decrease rapidly Inaddition a comparison of Figures 10(a) and 10(b) revealsthat at the same strain level the G values of both the siltyclay and the silt increase with increasing soil depth H andthe increase inG with increasingH for the silt is significantlygreater than that for the silty clay erefore G of theprimary soils within each strain range is mainly determinedby the soil type and soil depth H and there may be a patternin the variation in G withH for the same type of primary soilwithin different strain ranges


35 Variation in Gmax with Soil Depth As an importantparameter for evaluating the dynamic properties andcharacterizing the maximum elastic stiffness of a kind of soilthe maximum dynamic shear modulus Gmax is usually de-fined as G when cle 10minus6 Based on the hyperbolic rela-tionship between the soilrsquos dynamic modulus and dynamicstrain under small-amplitude vibration which was proposedby Hardin and Drnevich [16] a linear relationship between1G and c can be obtained (ie 1G a+ bc) and then Gmaxof the silty clay and the silt can be obtained at differentdepths

Figure 11 shows the Gmax values of the silty clay and siltat different depths and the curves demonstrating the

relationship between Gmax and soil depth H As can be seenfrom the figure the Gmax values of the silty clay and silt bothincrease linearly with increasing H but the increase rate ofGmax with H is much higher for silt than for silty clay Basedon this an empirical equation for determining the Gmaxvalues of different types of primary soils based on H (oreffective stress σm

prime) can be established as follows

Gmax A + n times 01Pa timesσmprime

Pa

1113888 1113889 (4)

where A and n are fitting parameters and their specificvalues are given in Table 2 σm

primePa characterizes the soildepth H

σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)

Figure 6 Stress-strain relationship curve of undisturbed marine soil (a) Slit clay (b) Slit

Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500

Figure 7 Relationship between undrained shear strength Sd anddepth (H) of undisturbed marine soil

SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500

Figure 8 Relationship between undrained shear strength Sd andvoid ratio (e) of undisturbed marine soil


36 Comparison of Gmax Obtained by Different Test MethodsAs mentioned above Gmax is an important parameter tocharacterize soil dynamics is paper uses bending elementand resonance column tests to obtainGmax which can promptus to better explore the dynamic characteristics of seabed soil

Figure 12 shows the comparison of the two test results Itcan be seen from the figure that the result of the bendingelement test is generally greater than the result of the reso-nance column test ere is a certain linear relationshipbetween the two which also verifies the reliability of the twotests in this paper

37 Variation in the Dynamic Shear Modulus Ratio (GGmax)with Soil Depth e variation of GGmax against c directlyreflects the nonlinear of the stress-strain relationship of soilsunder dynamic loads [17] To investigate the variations in thedecay characteristics of the G values of the silty clay and siltwith increasing c at different H the normalized dynamicshear modulus G ie GGmax was used to examine the siltyclay and silt at different depths In view of the location of theborehole near the Yellow Sea and the nature of the soft soilwhich has a water content close to that of seabed soft soil thethree-parameter Martin-Davidenkov model was selected to

Strength of siltStrength of silty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500

140 180 220 260100Shear wave velocity (ms)

Figure 9 Relationship between undrained shear strength Sd and shear wave velocity Vs of undisturbed marine soil

Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m

1E-5 1E-4 1E-31E-6 5E-3Shear strain

0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)

Figure 10 Relationship between dynamic shear modulus (G) and shear strain c of each undisturbed soil in the same borehole (a) Silty clayand (b) silt


fit the resonant column test data for the silty clay and silt atdifferent depths in the borehole from the surface to thebedrock [18] e GGmax is defined as [16]

G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)

where α β and c0 are all fitting parameters When α 1 andβ 05 the model simplifies to the H-D hyperbolic model[16] in which c0 is a reference shear strain with a clearphysical meaning and its value is defined as the shear strainamplitude when GGmax 05 [19]

e curves illustrating the variation in GGmax withincreasing c for the silty clay and silt at different depths areshown in Figure 13 As can be seen from the figure therelationship between the normalized shear modulus GGmaxand c for the silty clay and silt at different depths exhibitsstrong nonlinear characteristics at is when clt 10minus5 theGGmax values of the silty clay and silt do not decreasesignificantly with increasing c but when cgt 10minus5 as c in-creases the GGmax values of the silty clay and silt begin torapidly decrease and tend to 0 It should be noted that for thesame strain level the GGmax values of both the silty clay andsilt increase with increasing soil depth (H) which is ac-companied by a decrease in the decay gradient Further-more the overall GGmax-c curve varies from low to highthat is the small-strain dynamic properties of the soilgradually change from nonlinear to linear

To obtain the specific variation pattern of the decaycharacteristics of G of the primary soil with H over the fullstrain range the variations in the fitting parameters α β andc0 of the silty clay and silt with depth H were comparativelyanalyzed α and β are close to 1 and 05 respectively for theundisturbed silty clay at different depths and they are closeto 1 and 042 respectively for the undisturbed silt at dif-ferent depths indicating that soil depth has no significanteffect on fitting parameters α and β of the primary soils

Figure 14 shows the c0 values of the silty clay and silt atdifferent depths and the variation in c0 with soil depthH Forthe silty clay and silt c0 increases linearly with increasing Hbut the rate of increase of c0 with H for the silt is muchgreater than that for the silty clay which is consistent withthe variation pattern of the GGmax-c curve with H for thesilty clay and silt (Figure 11) Based on the variations in c0with H for the silty clay and silt an empirical relationshipbetween c0 andH was established for the silty clay and silt asfollows

c0() B + C timesσmprime

Pa

1113888 1113889 (6)

where B and C are fitting parametersIn summary the MartinndashDavidenkov model can be

further simplified by taking into account the variation in theparameters α β and c0 with H in order to empiricallydescribe the decay of the GGmax values of the silty clay andsilt at different depths

G

Gmax

11 + cc0( 1113857

2β (7)

where the parameters α and β are their average values of 1and 05 respectively for the silty clay and 1 and 042 re-spectively for the silt Table 3 gives the recommended valuesof α β and c0 for the simplified decay models of the GGmaxvalues of the silty clay and silt at different depths

Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)

Figure 11 Variation law of Gmax with soil depth (H) (effectiveconfining pressure σm

prime) of silty clay and silt

Table 2 Parameters A and n and the decision coefficients R2 in theGmax prediction formula

Lithology A n R2

Silty clay 1529 151 0989Silt minus268 423 0981

+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150

50 100 1500Gmax tested by bender element (MPa)

Figure 12 Comparison of Gmax obtained by different testmethods


38 Dynamic Shear Modulus Prediction Model Based on SoilDepth An H-based G prediction method can be establishedby combining equations (4) (6) and (7) to predict the Gvalues of primary soils at different depths and within dif-ferent strain ranges e specific equation is

G A + n times 01Pa times σm

prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)

To investigate the performance of the above predictionmethod in predicting G of the silty clay and silt at differentdepths within each strain range the G values of the silty clayand silt at different depths and different strain levels wereback-calculated using Equation (8) and were compared withthe existing test values at is given the soil depth andstrain level the level of correlation between Gpredict and Gtestwas used to reflect the performance of the G predictionmethod Figure 15 shows the results of the G predictionmethod for the silty clay and silt at different depths anddifferent strain levelse difference between theGpredict andGtest values of the silty clay and silt at different depths anddifferent strain levels is basically within 10 is indicatesthat the proposed method can reasonably predict G of theprimary soils at different depths over the full strain range Inaddition the analysis shows that the standard deviations μ ofequation (8) for the predicted values of the silty clay and siltsoil (GpredictGtest) are 00511 and 0019 respectively Inaddition when the prediction error of GpredictGtest is re-quired to be less than 5 the corresponding predictionaccuracies are 75 and 96 respectively which furtherverifies the validity of the prediction method and meets thereliability requirements of the probability analysis

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)

Figure 13 GGmax-c relationship curve of (a) silty clay and (b) silt at different depths

R2 = 0946

R2 = 0988γ0 () = 25times10-2 +43times10-3 times (σprimemPa)

γ0 () = 16times10-2 +13times10-2 times(σprimemPa)

γ 0 (

)

Silty clay γ0Silt γ0

15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)

Figure 14 Variation of c0 with soil depth (H) (effective confiningpressure σm


Table 3 Recommended values for parameters α β and c0 in asimplified GGmax regression model of silty clay and silt

Lithology α βc0 ()

B CSilty clay 1 05 25times10minus2 43times10minus3

Silt 1 042 16times10minus2 13times10minus2


4 Conclusions

In order to investigate the engineering mechanical prop-erties of marine foundation soils of offshore wind powerplatforms a series of basic physical index tests includingshear wave velocity test undrained triaxial shear test andresonance column test were conducted on the disturbed andundisturbed seabed soils from the surface to the bedrocke relationships between the basic physical indicators theundrained shear strength and shear wave velocity of thedisturbed primary seabed soils were analyzed a method forevaluating undrained shear strength was proposed and therelationship between the dynamic shear modulus and thedepth of the soil layer in the same type of undisturbed soil ineach strain range was investigated e conclusions andrecommendations of this study are as follows

(1) e silty clay layer and the silt layer within the depthrange from the seabed surface to the bedrock eachaccount for approximately half of the total drillingdepth and they are relatively discontinuously dis-tributed e upper layer has a high water contentand the water content of the lower layer is fairlyconstant at approximately 30 e specific gravityranges from 266 to 270 with only a small variatione silty clay has a plasticity index of greater than 10and the silt has a plasticity index of less than 10

(2) e Vs values of the silt and silty clay both increaselinearly with increasing the buried depth H eeffect of H on Vs of the seabed silt is significantlygreater than that on Vs of the silty clay e Sd valuesof the silty clay and silt decrease with increasing ewith both exhibiting a strong correlation e rate ofdecrease of Sd of the silty clay with increasing e is

significantly greater than that of the silty soil eundrained shear properties of the silty clay are moresensitive to the soil density

(3) e stress-strain relationship curves for the siltyclay and silt both exhibit two types of developmentmodes ie strain hardening and strain softeningAs e decreases the stress-strain relationship transitsfrom strain hardening to strain-softening How-ever the silt requires a higher density than the siltyclay to undergo this stress-strain relationshiptransformation

(4) Based on the relationship between Sd and Vsestablished using the results of the laboratory ele-ment tests conducted on the disturbed primary soil amethod for evaluating the undrained strengthproperties of an undisturbed primary soil under thecurrent formation conditions was established basedon the field shear wave velocity results and theexisting methods for correcting the mechanical pa-rameters of disturbed and undisturbed soils How-ever this method may provide slightly conservativeresults for high-plasticity soils

(5) G of the undisturbed soil in each strain range ismainly determined by the soil type and H Gmax ofundisturbed silty clay and silt increased linearly withincreasing H and the attenuation relationship of Galso decreased regularly with increasing H

(6) In the Martin-Davidenkov model H has no signif-icant effect on α and β in the GGmax fitting pa-rameters of undisturbed soil α of the undisturbedsilty clay and silt soil at different depths are bothclose to 1 and β close to 05 and 042 respectively c0shows a linear upward trend with increasing H

G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10

20 40 60 80 1000Gtest of silt (MPa)

20 40 60 80 1000Gtest of silty clay (MPa)

0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100

Figure 15 G predicting effects of (a) silty clay and (b) silt within various strain ranges by an (H)-based G prediction method


(7) e G prediction method based on H is establishedand the accuracy is high which canmeet the needs inactual engineering applications

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the research grant from theNational Institute of Natural Hazards Ministry of Emer-gency Management of China (no ZDJ2017-28) and theNational Key Research and Development Program of China(2017YFC1500403)

References

[1] D C Koutsoftas and J A Fischer ldquoDynamic properties of twomarine claysrdquo Journal of the Geotechnical Engineering Divi-sion vol 106 no 6 pp 645ndash657 1980

[2] G M Bryan and R D Stoll ldquoe dynamic shear modulus ofmarine sedimentsrdquo Journal of the Acoustical Society ofAmerica vol 83 no 6 pp 2159ndash2164 1988

[3] T Yamamoto M V Trevorrow M Badiey and A TurgutldquoDetermination of the seabed porosity and shear modulusprofiles using a gravity wave inversionrdquo Geophysical JournalInternational vol 98 no 1 pp 173ndash182 1989

[4] T Kagawa ldquoModuli and damping factors of soft marineclaysrdquo Journal of Geotechnical Engineering vol 118 no 9pp 1360ndash1375 1992

[5] C Vrettos and S Savidis ldquoShear modulus and damping formediterranean sea clays of medium plasticityrdquo EarthquakeGeotechnical Engineering vol 12 no 6 pp 71ndash76 1999

[6] G Lanzo A Pagliaroli P Tommasi and F L Chiocci ldquoSimpleshear testing of sensitive very soft offshore clay for wide strainrangerdquo Canadian Geotechnical Journal vol 46 no 11pp 1277ndash1288 2009

[7] L W Kong H B Lv R Wang and H Shan ldquoEngineeringproperties and micro-mechanism of structural marine soil inZhanjiang sea areardquo Journal of Hydraulic Engineering vol 33no 9 pp 82ndash88 2002

[8] J M Zhang H X Shan and Y G Jia ldquoAn experimental studyof nonuniform consolidation of rapid sediment seabed soils atYellow River mouth subjected to wave and tide wave loadingrdquoRock and Soil Mechanics vol 7 pp 88ndash94 2007

[9] H J Liu and H J Li ldquoA new suction anchor foundation of theyellow river delta offshore wind powerrdquo Periodical of OceanUniversity of China vol 44 no 7 pp 71ndash76 2014

[10] Q Wu Q Lu Q Guo K Zhao P Chen and G ChenldquoExperimental investigation on small-strain stiffness of ma-rine silty sandrdquo Journal of Marine Science and Engineeringvol 8 no 5 p 360 2020

[11] K Zhao Q Wang S Chen H Zhuang and G ChenldquoDynamic response of pipelines in liquefiable seabed undernature loadings waves and currentsrdquo Ocean Engineeringvol 230 no 1 Article ID 109051 2021

[12] G Zhang P Wang M Zhao X Du and X Zhao ldquoSeismicstructure-water-sediment-rock interaction model and itsapplication to immersed tunnel analysis under obliquely in-cident earthquakerdquo Tunnelling and Underground SpaceTechnology vol 109 no 2 Article ID 103758 2021

[13] P Wang Y Xu X Zhang R Xi and X Du ldquoA substructuremethod for seismic responses of offshore wind turbine con-sidering nonlinear pile-soil dynamic interaction - Science-Directrdquo Soil Dynamics and Earthquake Engineering vol 144Article ID 106684 2021

[14] L D Bai W Xiang A S Savidis and F Rackwitz ldquoResonantcolumn and bender element tests on maximum shear mod-ulus of dry sandrdquo Chinese Journal of Geotechnical Engineeringvol 34 no 1 pp 184ndash188 2012

[15] J Yang and X Liu ldquoShear wave velocity and stiffness of sandthe role of non-plastic finesrdquo Geotechnique vol 66 no 6pp 1ndash15 2016

[16] B O Hardin and V P Drnevich ldquoShear modulus anddamping in soils design equations and curvesrdquo Journal of theSoil Mechanics and Foundations Division vol 98 no 7pp 667ndash692 1972

[17] K Zhao Q Wang Q Chen H Zhuang and G ChenldquoSimplified effective stress simulation of shear wave propa-gation in saturated granular soilsrdquo Geotechnique Lettersvol 11 no 1 pp 1ndash22 2021

[18] P P Martin and H B Seed ldquoOne-dimensional dynamicground response analysesrdquo Journal of the Geotechnical En-gineering Division vol 108 no 7 pp 935ndash952 1982

[19] M B Darendeli Development of a New Family of NormalizedModulus Reduction and Material Damping Curves eUniversity of Texas Austin TX USA 2001


basic research on the dynamic characteristics of the seabedsoil Koutsoftas and Fischer [1] found that the stress historyhas a strong influence on the dynamic shear modulus G andthe modulus value of overconsolidated clay is larger thanthat of normally consolidated clay e standardizedmodulus ratio for the undrained shear strength Su is mainlyaffected by the type strain level and overconsolidation ratioOCR of soils e influence of stress history on the dampingratio is not significant Bryan and Stoll [2] conducted res-onance column tests on sand clay and silt taken from thesea about 5 miles from the coast of New Jersey USA andfound that Gmax is mainly related to the void ratio and σrsquomYamamoto et al [3] found that Gmax of marine sediments isproportional to (σrsquom)05 Kagawa [4] discovered that theGmaxof marine soft clay decreases with the increase of void ratio(e) and plasticity index (Ip) and is proportional to the av-erage effective confining pressure (σrsquom) which is basicallyconsistent with the test results of two marine clays byKoutsoftas [1] Vrettos and Savidis [5] conducted resonancecolumn tests on 4 undisturbed clays at 2 sites on the westcoast of Greece and found that Gmax for low plastic clay isproportional to (σrsquom)05 and high plastic clay is proportionalto (σrsquom)05 and the influence of the plasticity index of co-hesive soil should be taken into consideration to predictGmaxe plasticity index and the average effective confiningpressure have a strong influence on the dynamic charac-teristics of the offshore cohesive soil Lanzo et al [6] con-ducted an experimental study on the undisturbed soft clay inthe Adriatic Sea in Italy e results showed that when therelative consolidation ratio and e are close to each other theeffective confining pressure affects the Gmax of marine claysignificantly And the decay curve of the dynamic shearmodulus ratio GGmax-y of marine soil is close to that of theterrestrial soil Kong et al [7] studied the basic properties ofmarine soil from the Qiongzhou Strait of China e testfound that marine soil has unique physical properties and itwas classified as silt based on the soil quality However itscompression deformation characteristics and strength in-dicators are different from those of general silt or silty soiland its shear strength is relatively higher whereas it hascertain structural strength Zhang et al [8] found that thefast-deposited silty soil has a high consolidation rate underits own weight After the normal consolidation is completedthe strength continues increasing with time and there is anonuniform consolidation phenomenon and a pseudo-overconsolidation state similar to those of the primary soilthat occurred with the increase of the depth Liu et al [9]analyzed the advantages and disadvantages of the existingoffshore wind turbine foundations In order to modify theweakness of the existing offshore wind turbine foundationsthey proposed a new umbrella-type suction anchor foun-dation suitable for offshore wind power platforms in theYellow River Delta and its structural advantages and in-stallation method were explained Wu et al [10] presentedan experimental investigation which was conducted throughcomprehensive bender element tests on Gmax of marine siltysand e results indicate that under otherwise similarconditions Gmax decreases with the decrease of e or finescontent (FC) but decreases with the increase of FC Zhao

et al [11] presented an elastoplastic modeling method fordynamic consolidation of the liquefiable seabed around apipeline subjected to ocean environmental loadings Zhanget al [12] proposed a transient seismic structure-water-sediment-rock interactional model to evaluate the seismicresponse of the marine structure in ocean space underobliquely incident earthquakes Wang et al [13] presented asubstructure method for seismic responses of offshore windturbines considering nonlinear pile-soil dynamicinteraction

e above researches show that no systematically ex-perimental researches on the mechanical properties ofgeneral marine engineering have been carried out yetConsequently we carried out this article which is based onthe offshore wind power platform project that is ongoing inthe Yellow Sea of China e representative undisturbedseabed soil was collected from the site to be conducted withbasic laboratory geotechnical tests including bender ele-ment tests undrained triaxial shear tests and resonancecolumn tests to determine the physical and mechanicalproperties of the silt and silty clay e correlations betweenthe basic physical indicators the undrained shear strengthand the shear wave velocity of the primary marine soil areinvestigated Eventually an undrained shear strength eval-uation method is proposed and a predictive model of dy-namic shear modulus and depth is presented is researchcan provide basic scientific data for the design and con-struction of offshore wind power platforms

2 Samples and Resonant Column Test

21 Stratigraphic Information and Basic Physical PropertiesTo study the engineering mechanical properties of typicalmarine foundation soil of offshore wind power platformsexploration works have been carried out in the waters offshoreof the Yellow Sea of China and representative boreholes wereselected Undisturbed silty clay and silt were collected frommultiple depths within the boreholes using open thin-walledsoil samplers e soils were sampled within a depth range of2 to 70m and sulfate sandstone was encountered below 73me natural water content specific gravity natural densityvoid ratio and plasticity index of the samples were tested inaccordance with the ASTM standards Table 1 presents thesoil depths the corresponding physical and mechanicalproperty indices of the undisturbed silty clay and silt samplesfrom the seabed to the bedrock As can be seen from the tablethe silty clay layer and the silt layer each accounted for ap-proximately half of the total core length and they are dis-continuously distributed e upper layer had a relativelylarge water content and the water content remained at ap-proximately 30 at soil depths of greater than 14m especific gravity ranged from 266 to 270 exhibiting only asmall difference e plasticity index of the silty clay wasgreater than 10 and the plasticity index of the silt was less than10 Based on the comprehensive consideration of the drillingexploration data the site engineering geological survey andthe geophysical prospecting data the strata of the site can bedivided into five major layers e lithological characteristicsof the soil layers from top to bottom are as follows



















2

1

34

5

6




1

23

4



Vs d

t (1)





Vol

tage

(V)

A B

C

0006 0012 0018 0024 0030 00360Time (s)

-4

-2

0

2

4


Silty claySilt

Shea

r wav

e velo

city

(ms

)

50

100

150

200

250

300

080 085 090 095 100075Void ratio


Shea

r wav

e velo

city

(ms

)

Silty ClaySilt

50

100

150

200

250

300

10 20 30 40 50 60 70 800Depth (m)







Sd A middot eB (3)










Pa

1113888 1113889 (4)



σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)


Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500


SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500







S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References






































2

1

34

5

6




1

23

4



Vs d

t (1)





Vol

tage

(V)

A B

C

0006 0012 0018 0024 0030 00360Time (s)

-4

-2

0

2

4


Silty claySilt

Shea

r wav

e velo

city

(ms

)

50

100

150

200

250

300

080 085 090 095 100075Void ratio


Shea

r wav

e velo

city

(ms

)

Silty ClaySilt

50

100

150

200

250

300

10 20 30 40 50 60 70 800Depth (m)







Sd A middot eB (3)










Pa

1113888 1113889 (4)



σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)


Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500


SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500







S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References





















Vs d

t (1)





Vol

tage

(V)

A B

C

0006 0012 0018 0024 0030 00360Time (s)

-4

-2

0

2

4


Silty claySilt

Shea

r wav

e velo

city

(ms

)

50

100

150

200

250

300

080 085 090 095 100075Void ratio


Shea

r wav

e velo

city

(ms

)

Silty ClaySilt

50

100

150

200

250

300

10 20 30 40 50 60 70 800Depth (m)







Sd A middot eB (3)










Pa

1113888 1113889 (4)



σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)


Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500


SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500







S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References

























Sd A middot eB (3)










Pa

1113888 1113889 (4)



σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)


Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500


SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500







S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References


























Pa

1113888 1113889 (4)



σ 1prime-σ

3prime (k

Pa)

22 m (e=090)37 m (e=088)135 m (e=090)173 m (e=082)

358 m (e =084)486 m (e =083)550 m (e =083)697 m (e =080)

5 10 15 20 25 300ε ()

0

200

400

600

800

(a)

120 m (e=148) 139 m (e =119)207 m (e=098)258 m (e=094)

309 m (e=090)392 m (e=080)396 m (e=083)456 m (e =086)

5 10 15 20 25 300ε ()

σ 1prime-σ

3prime (k

Pa)

0

200

400

600

800

(b)


Silty claySilt

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

10 20 30 40 50 60 70 800Depth (m)

0

100

200

300

400

500


SiltSilty clay

S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

08 10 12 14 1606Void ratio

0

100

200

300

400

500







S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References

























S d o

f und

rain

ed sh

ear s

tren

gth

(kPa

)

0

100

200

300

400

500



Dyn

amic

shea

r mod

ulus

(Mpa

)

134-136 m

21-23 m36-38 m 104-106 m

172-174 m 343-345 m

598-600 m

357-359 m485-487 m549-551 m

647-649 m696-698 m


0

20

40

60

80

100

(a)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m


Dyn

amic

shea

r mod

ulus

(Mpa

)

0

20

40

60

80

100

(b)




G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References






















G

Gmax 1 minus

cc0( 11138572β

1 + cc0( 11138572β

⎡⎣ ⎤⎦

α

(5)






Pa

1113888 1113889 (6)



G

Gmax

11 + cc0( 1113857

2β (7)


Silty claySilt

15 30 45 60 750Depth (m)

0

20

40

60

80

100

120

G max

(Mpa

)

0 100 200 300 400 500σprimem (kPa)




Lithology A n R2


+23

G max

teste

d by

reso

nant

colu

mn

Colu

mn

(MPa

)

-23

0

50

100

150






prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References























prime Pa( 11138571113858 1113859

1 + cc0( 11138572β

1113960 1113961 (8)


21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

Shallow

Deep

1E-5 1E-4 1E-3 001 011E-6γ

G (G

max

)

00

02

04

06

08

10

(a)

Shallow

Deep

G (G

max

)

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

1E-5 1E-4 1E-3 001 011E-6γ

00

02

04

06

08

10

(b)


R2 = 0946



γ 0 (

)


15 30 45 60 750Depth (m)

002

003

004

005

0060 100 200 300 400 500

σprimem (kPa)








4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References





















4 Conclusions









G pre

dict

of s

ilt cl

y (M

Pa)

11

21-23 m36-38 m104-106 m134-136 m172-174 m343-345 m

357-359 m485-487 m549-551 m598-600 m647-649 m696-698 m

+10

-10

11

206-208 m257-259 m308-310 m

377-379 m391-393 m431-433 m

+10

-10



0

20

40

60

80

100

Gpr

edic

t of s

ilt (M

Pa)

0

20

40

60

80

100




Data Availability




Acknowledgments


References






















Data Availability




Acknowledgments


References





















experimental study of the engineering mechanical

Documents