China Ocean Engnering，Vol.24, No.1, pp. 161- 172C 2010 Chinese Ocean Engineering Society, ISSN 0890-5487Characteristics of Pore Water Pressure of Saturated Silt UnderWave LoadingGAO Yu-feng (高玉峰)rb, ZHANG Jian (張健)a,b,SHEN Yang(沈揚)a,b and YAN Jun (閆俊)a,ba Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering,Hohai University, Nanjing 210098，Chinab Geotechnical Research Institute of Hohai Uniersity， Hohai University, Nanjing 210098, China( Received 23 March 2009; received revised form 6 July 2009; accepted 5 November 2009)ABSTRACTThe characteristics of dynamic stress in the seabed under wave loading are constant principal stress and continuousrotation of the principal stress direction. Cyclic triaxial-torsional coupling shear tests were performned on saturated silt bythe hollow cylinder apparatus under different relative densities，deviator stress ratios and vibration frequencies to study thedevelopment of pore water pressure of the saturated silt under wave loading. It was found that the development of porewater pressure fllows the trend of“fast ~ steady ~ drastic"。 The turmning point from fast to steady stage is not affected byrelative density and deviator stress ratio. However, the turning point from steady to drastic stage relies on relative densityand deviator stress ratio. The vibration cycle for the liquefaction of saturated silt decreases with increasing deviator stressratio and increases with relative density . The vibration cycle for the liquefaction of the saturated sit increases with vibra-tion frequency and reaches a peak value, after which it decreases with increasing vibration frequency for the relative den-sity of 70% . But the vibration cycle for the liquefaction of saturated sit increases with vibration frequency for the relativedensity of 30% . The development of pore water pressure of the saturated silt is influenced by relative density and vibra-tion frequency .Key words: sill ; wawe loding; pore water pressure ; ribration frequency; cyclic triaxial-torsional coupling shear; rota-tion of principal stress1. IntroductionMany large- scale marine constructions and facilities were built as a result of the exploitation ofocean resources. Wave loading is the most important load acting upon the marine structures and its fre-quency is normally between 0.05~ 1.0 Hz. The wave loading imposes on the seabed in the form ofcyclic pressure wave which induces the change of pore water pressure and effective stress in the under-lying soil. When the induced shear stress exceeds the strength, significant deformation, shear failureand liquefaction may occur, which can exert damacing influence on nearshore and offshore construc-中國煤化工tions. In the past, many engineering accidents:lynamic characteristics ofmarine soil under wave loading ( Zheng, 1994; GYHc N M H Gand Hong, 2003; Liuet* This work was financially supported by The Key Project of National Natural Science Foundation of China ( Grant Nos.50639010 and 50909039)1 Corresponding author. E mail: yfgao66@ yahoo. com. cn162GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172al., 2005)，for example, the sliding and inclination of platform in the Bohai area during 1970 ~1979，the damage of seawall under construction in the Nigata Port during a storm in 1976, the lique-faction of drill platform foundation in the Shengli Oilfield and Yingge basin in the South China Sea in1994，the sliding and settlement of the semicircle caissons in the Yangtze Estuary under wave loadingin 2002, etc .The stress states of the seabed and the foundation of marine structures under wave loading arevery complex. The stress path in the plane of the magnitude of half cyclic axial stress and cyclic torsionshear stress is a circle based on the facts that the magnitude of the principal stress remains constant andthe principal stress direction rotates continuously. The change in principal stress direction under waveloading is shown in Fig. 1 ( Ishihara and Towhata, 1983).τ一0Fig.1. Change in principal stress direction under wave loading.Previous studies have shown that the rotation of the principal stress direction has a significant im-pact on the strength and deformation characteristics of soil. It has been confirmed in undrained torsion-al shear test (Symes et al., 1984) that the continuous rotation of the principal stress direction leads tothe development of the pore water pressure, and initial anisotropy has the similar effect. A series oftests were carried out for various stress paths of cyclic triaxial test, cyelic torsional shear test and cyclictriaxial-torsional coupling shear test on hollow cylindrical standard sand samples of Japan ( Ishihara andYamazaki，1984; Towhata and Ishihara, 1985). The results showed that the failure vibration cyclemeasured by the cyelic triaxial- torsional coupling shear test is the minimum， while that measured bythe cyclic torsional shear tests is the maximum and that measured by the cyclic triaxial tests is betweenthe above two tests. Under the same vibration cycle, the dynamic strength of the cyclic triaxial-torsion-al coupling shear test is 30% lower than that measuwed hy the rrlic tnreional shear tests. Shen et al .中國煤化工(1996) conducted tests on the same kind of sandEmic strength of the cyclictriaxial-torsional coupling shear test is about 15YHCN M H Ga by the eydlice tosionalshear tests, which is smaller than 30% of Ishihara's results. Wang et al. (1996) also suggested thatthe dynamice strength of the cyclic triaxial-torsional coupling shear test is about 15% lower than that ofthe cyclic torsional shear tests under the equivalent vibration cycles to earthquake between 10 and 30.Undrained dynamic characteristics study on saturated sand by Guo et al. (2005 ) showed that the dy-GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172namic strength of the cyclic triaxial-torsional coupling shear test is the minimum, about 40% lowerthan that of the cyclic torsional shear tests and 20% lower than that of the cyclic triaxial tests. Basedon the undrianed cyclic triaxial-torsional coupling shear test conducted on the saturated sand，Yoshimine et al. (1998) found that the pore water pressure caused by the rotation of the principalstress direction can weaken the soil sample and that the influencing factors are the relative density, de-viator stress and intermediate principal stress. Tests by Yang et al. ( 2007) confimed the conclusionsof Yoshimine. De Gennaro et al. (2004) and Wijewickreme and Vaid (2008) studied the undrianeddynamic characteristics of saturated loose sand with different load paths. Georgiannou et al. ( 2008a,2008b) conducted tests on different sands under drained and undrained conditions to investigate the in-fluence of alteration of the principal stress direction. Lade and Kirkgard ( 2000)，Lin and Penumadu(2005), and Shen (2007) carried out tests on the clays to investigate the influence of alteration of theprincipal stress direction. It is clear that the previous studies have focused on the work about the rota-tion of the principal stress direction for sands and clays, but lttle has been done on silts.The influences of vibration frequency on dynamic characteristics are not conclusive. Yoshimi andOh-oka (1975) and Lee and Focht (1975) suggested that within ordinary seismic frequency (1 ~4Hz) the vibration frequency hardly affects the strength of sands against liquefaction. Zhang and Wang(1990) affirmed the validity of this conclusion for frequency between 1 and 20 Hz. Matsui et al.( 1982) carried out cyclic triaxial tests on Senri clays of Ip= 55 for frequency between 0.02 and 0.5Hz，and showed that under constant cyclic steps lower frequency causes greater pore water pressure.Yasuhara et al. (1982) carried out cyclic triaxial tests on Ariake clay soils of Ip = 58 for frequencybetween0.1 and 1.0 Hz, and showed that higher loading frequency causes greater pore water pres-sure. Chen et al. (2004) suggested that dynamic strength increases with increasing frequency. Zhanget al. (2006) carried out cyclic triaxial tests to study the influence of frequency on dynamic character-istics of clays and showed that for frequency between 0.1 and 4 Hz，the dynamic strength increaseswith increasing frequency，but the tendency reverses at a higher frequency .Cao and Wang (1998) put forward a model for the development of pore water pressure based onthe cyclic triaxial tests and studied the liquefaction characteristics of Shanghai silts, then comparedwith fine sands. Yu and Wang ( 1999) advanced the developing model that the vibration pore waterpressure and vibration cycle satisfy the power function relationship for the dynamic triaxial tests of satu-rated silts, then analyzed the fact that for saturated silts the pore water pressure increases drastically inthe initial stage and finally reaches a steady state. Feng et al. (2002) studied the developing patternand response of the pore water pressure on the silts from _the estuarv of the Yellow River by the cyclic中國煤化工。triaxial test. Zeng et al. (2005) studied the dewater pressure and ad-vanced the developing model that the vibrationMHC N M H Gtion cyle satisfsy the hy-perbola function relationship. Studies with different test conditions were carried out to investigate thedynamic characteristics of silts (Hyde et al., 2006; Sumer et al., 2007). Zhao (2007) consideredthe alteration of the principal stress direction, but neglected the effect of vibration frequency on the dy-namic characteristics of silts.164GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172As stated above , different series of tests and studies about the characteristics of sand and clay soilunder the rotation of principal stress axis were carried out in the past, but the studies of the influenceof wave loading on the pore water pressure development in saturated silts are rare at present. As for the .study on seismic load in the process of dynamic test, in which stress and frequency are high, dynamicresponse of silts under small stress and low frequency of wave loading cannot be demonstrated. In thispaper, a series of cyclic triaxial-torsional coupling shear tests on saturated sils were conducted by theuse of HCA to fulfill the special stress path requirement of the rotation of principal stress axis and de-velopment of pore water pressure by the action of continuous rotation of dynamic principal stress axis，small stress level and low-frequency of wave loading.2. Test Equipment and Procedures2.1 Test EquipmentHCA used in this study has four subsystems for the independent control of axial load, torque, in-ner cell pressure and outer cell pressure so that the continuous rotation of principal stress direction canbe achieved. This manner of rotation can assure that the radial stress is the intermediate principalstress, and the major principal stress and minor principal stress rotate around the axis of radial stress .The coordinate system comprises of major principal stress，intermediate principal stress ，minor princi-pal stress and the orientation of major principal stress relative to the vertical direction of sample, corre-sponding to four loading parameters. So the stress path of continuous rotation of principal stress direc-tion can be simulated by this apparatus . The stress states of the hollow cylinder cyelic triaxial-torsionalcoupling shear test are shown in Fig. 2.W▼M，不lza//dr中國煤化工auth十MYHCNMHGFig. 2. Stress states of the hollow cylinder cyelic triaxial-torsional coupling shear test.GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 1721652.2 Test MaterialThe tests were conducted on an offshore silt and the grain-size distribution is given in Fig. 3.From the figure it can be found that the tested soil has 8.4% of sands, 86.0% of silts, and5.6% ofclays.100ge80 H一.目 60Fig. 3. Grading curve of the silt.營5臺言4020 -230.10.011E-3Soil diameter (mm)The outer and inner radii of the cylindrical samples were 200 mm ( D) and 100 mm (d), respec-tively and the height (H) of the samples was 150 mm. The relative density of samples was controlledto a relative density of 70% according to their natural conditions and a relative density of 30% wasprepared as the control test. The dry deposition method was employed in the sample preparation.Oven-dried silt was weighed and poured into the hollow space between two moulds with a brush and afunnel in 8 layers. Each interface was de- aired when compacted to the corresponding height to ensure aclose contact of each layer. The saturation process of sample was carried out under vacuum- pumpingwhile the voids were flld by de-aired water. A back pressure of 150 kPa was applied to raise the de-gree of saturation of the silt sample to assure the B value exceeds 0. 97. The physical properties of siltused in this study are summarized in Table 1.Table 1Basic physical properties of the siltSpecificLquitPlastic .PlasticityNatural dryMaximum dryMinimum drygravitylimitindexdensityG。WL(%)Wp(%)pρa(g/cm' )Puma(g/cm3 )Pdmin(g/ cm' )2.6833.024.01.451.601.222.3 Test ProgramInitial isotropic consolidation condition was controlled durine the test. Initial mean effective stresswas 100 kPa, relative densities were 70% and 3中國煤化工os were0.1 and 0.125.Mode of stress control was used in the cyclic sMHC N M H Gcic verticalloading andcyclic torsion moment were added simultaneously. Both were harmonic loading. To ensure the circularshape of stress path during the cyclic triaxial-torsional coupling shear test, which accurately simulatesthe real stress state in the seabed due to continuous rotation of the major principal direction under theaction of oceanic wave loading, the cyclic torsion moment was in phase lag of the cyclic vertical loading166GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172by 90°，and it was assured that half of the magnitude of cyclic axial stress was equal to that of cyclictorsion shear stress . The theoretical and measured stress paths plotted in the plane of Ta~(σ.- oσg)/2 are shown in Fig. 4，in which it can be found that the shape of the measured stress path derivedfrom the test is quite close to a circle, thus continuous rotation of the dynamic principal stress directioncan be simulated by this apparatus .15rFo15 rEo5-5t(σ;-σ)12(σ:-σ)12-15-{0.-505-15 -10-515>10-15L-15 l(a)(b)Fig. 4a. Theoretic stress path in τg~(σ.- σp)/2Fig. 4b. Actual stress path in τg~(σ:-σg)/2coordinate system.Tests were carried out in groups. Relative density was fixed first and the development of pore wa-ter pressure under different frequencies and deviator stress ratios was analyzed. Comparative tests onsoils under the same initial effective consolidation stress were carried out, in which the effect inducedby the variation of wave loading frequency，relative density and deviator stress ratio on the developingpattern of pore water pressure was studied. Experimental conditions are summarized in Table 2.Table 2Experimental conditionsRelative densityEffective confiningConsolidationDeviator stressVibration frequencyD,pressure ( kPa)ratio h。ratio ηf(Hz)30%1001.00.10.05, 0.1, 0.2, 0.5，1.070%0.1, 0.1250.05, 0.1, 0.2, 0.5, 1.02.4 Test Termination ConditionIn general, the failure criteria of soil in dynamic condition comorise of“pore water pressure fail-ure criterion”and “strain failure criterion” . TheMYH中國煤化工reching ectite confin-ing pressure was defined as“pore water pressureC N M H Glouble ampltude of axialstrain reaching 5% was defined as“strain failure criterion" . In previous studies, there were many dis-putes about“ strain failure criterion”. So in the present study,“pore water pressure failure criterion”isadopted as the failure criterion and the corresponding vibration cycle is defined as the failure vibrationcycle Nr.GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 1721673. Development Pattern of Pore Water Pressure for the Saturated SiltDeveloping pattem under cyclic triaxial-torsional coupling shear tests of saturated silts are differ-ent from those under dynamic triaxial tests, which are shown in Figs. 5 and 6. The reason for this isthat in former dynamic triaxial tests, pore water pressure of saturated silts cannot reach effective confin-ing pressure, for which the failure criterion is strain failure criterion. But silts employed with strainfailure criterion are not destroyed necessarily. In addition, the measurement criteria are not intuitiveenough. In the tests of this paper, pore water pressure failure criterion is adopted. It can reach the ef-fective confining pressure and thus liquefaction can be observed.1.0r0.8Fig. 5. Development pattern of pore water 6" 0.6pressure for the saturated silt.0.40.2. Test curve in this paper■Test curve achieved by dynamic triaxial test (Zeng 2005)Test curve achieved by dynamic tiaxiad test (Ca,198)0.9.00.40.61.0N/N.1.0 r0.8-D.= 70%D,= 30%η= 0.10.6-0.60.4-0.4 .0.020.00.0 0.2 0.40.6 0.8 1.00.0.20.4 0.6 0.8 1.0(a)D,= 70%, η= 0.1(b) D,= 30%, η= 0.11.0 [D,= 70%η= 0.1250.6 IFig.6. Normalized relationship between vi-中國煤化工bration cycle and pore water pres-MYHCNMHG.sure.y0.20.40.6 .0.8 1.0(C) D,= 70%, η= 0.125168GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172The reason for this trend of“fast-steady-drastic”is that some clay particles are contained in siltssuch that the coefficient of permneability is smaller than fine sands, which explains undissipated anduntransmitted pore pressures. As a result a considerably high volumetric potential is expected and thepore water pressure increases subtantially. With the action of cyclic loading, particle rearrangementand elimination of local instablities occur at the contact points which make the pore water pressure in-crease steadily in the next stage (Takahashi, 1981; Alarcon-Guzman, 1986). The pore water pressurein the final stage increases drastically to the effective confining pressure when the cyclic effective stresspath reaches the instability line (Georgiannou et al.，2008).4. Influence of Relative Density on Pore Water Pressure of Saturated SiltThe development of pore water pressure of the saturated silt is given in Fig. 7, in which relativedensity D,= 70% and D,= 30% and deviator stress ratio η=0.1.1.0 rD, = 30%D,= 70% |1.0pD,= 30% .D,= 70%0.80.8-0.60.4/ u1-0.20.050 100 150 200 250 300 350 400200 400 600 800 1000 1200 1400N(a)f= 0.1 Hz(b)f= 0.2 HzFig.7. Relationship between vibration cycle and pore water pressure for diferent relative densities.It can be observed from Fig. 7 that the vibration cycle for liquefaction of the saturated silt de-creases with decreasing relative density. The turming point from fast to steady is not affected by the vi-bration frequency when the relative density is different, and it appears when excess pore water pressureis equal to 20% of the effctive confining pressure. However, the turming point from steady to drasticis affected by the vibration frequency when the relative density is different. The turming point fromsteady to drastic relies on the relative density.5. Influence of Deviator Stress Ratio中國煤化工of Saturated SiltMHCNMHG_The development of pore water pressure of the saturated SIIt IS given 1n Fig. 8, in which relativedensity D,= 70% and deviator stress ratio η=0.1 and η=0.125.It can be observed from Fig. 8 that the vibration cycle for liquefaction of the saturated silt de-creases with increasing deviator stress ratio. The tumning point from fast to steady is not affected by the :GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172169vibration frequency when the deviator stress ratio is different, and it appears when excess pore waterpressure is equal to 20% of the effective confining pressure. However, the turning point from steady todrastic is affected by the vibration frequency when the deviator stress ratio is different. The turmingpoint from steady to drastic relies on the deviator stress ratio.100 [η= 0.125η=0.1100 rη= 0.1806 60山= 40a 402020 toL50 100 150 200 250 300 350 400200 400 600 800 1000 1200 1400N(a)f= 0.1 Hz(b)f= 0.2 HzFig.8. Relationship between vibration cycle and pore water pressure for diferent deviator stress ratios.6. Infuence of Vibration Frequency on Pore Water Pressure of Saturated SiltThe variations of vibration frequency (f) with failure vibration cycle (N) are shown in Fig. 9,in which relative density D,= 70% and deviator stress ratio η=0.1 or η=0.125.120014001000800z 800z 6006004002000.00.40.60.81.00.2f (Hz)f(Hz)(a)η= 0.1(b) η= 0.125Fig.9. Relationship between vibration. liquefaction.中國煤化工MYHCNMHGIt can be observed from Fig. 9 that, for f ....... ... ... vibration cycle for lique-faction of saturated silt increases with increasing f. But when f is between 0.2~ 1.0 Hz, the vibrationcycle for liquefaction of saturated silt decreases with increasing f. Based on the above discussion, theinfluence of vibration frequency on saturated silts has two aspects. Firstly, part of the pore water pres-sure dissipates because of the decrease of vibration frequency and longer interval of action duration.170GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172Thus the pore water pressure increases slowly with decreasing vibration in some frequency range. Onthe other hand, silts are fully vibrated under lower vibration frequency because of the existence of siltgranules and clay granules in offshore silts, which leads to soil' s internal resistance to consume moredynamic energy. Consequently, more energy has to be absorbed to make full destroy of the soil struc-tures and that produces a substantial increase of pore water pressure in some frequency range .The variations of vibration frequency (f) with failure vibration cycle (NL) are shown in Fig. 10,in which relative density D, = 30% and deviator stress ratio η=0.1.250200η= 0.1150Fig. 10. Relationship between vibration fre-z100quency and vibration cycle for liq-uefaction.50 F0.00.20.60.81.0f(Hz)It can be observed from Fig. 10 that the vibration cycle for liquefaction of the saturated silt in-creases with increasing vibration frequency for D,= 30% . The reason is that the development of porewater pressure and deformation is restricted because of the inhomogeneous distribution of pore waterpressure and delay development of deformation with the increasing of vibration frequency .7. ConclusionsExperimental investigations are performed in this paper to study the development of pore waterpressure for saturated silt under wave loading， which provide basis for safety evaluation and stabilitycalculation of ocean engineering.(1) Cyclic triaxial-torsional coupling shear tests are performed on saturated silt under differentrelative densities ，deviator stress ratios and vibration frequencies to study the development of pore waterpressure of the saturated silt under wave loading. It can be found that the development of pore waterpressure follows the trend of“fast ~ steady ~ drastic" . The turming point from fast to steady stage is notaffected by relative density and deviator stress ratio. However. the turming noint from steady to drastic中國煤化工stage relies on relative density and deviator stres(2) The vibration cycle for the liquefactionMYHCNMHGwith increasing deviatorstress ratio but increases with relative density.(3) The vibration cycle for the liquefaction of saturated silt increases with vibration frequency andreaches a peak value, after which it decreases with increasing vibration frequency for the relative den-sity of 70%. But the vibration cycle for the liquefaction of saturated silt increases with vibration fre-GA0 Yur-feng et al . / China Ocean Enginering, 24(1), 2010, 161- 172171quency for the relative density of 30% . The development of pore water pressure of the saturated silt isinfluenced by relative density and vibration frequency.Acknowledgements- The authors wish to express their sincere thanks to the assistances provided by Associate ProfessorC.F. Chiu of Hohai university, Professor CHEN Guoxing, Associate Professor ZHU Dinghua, Ph. 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