An Investigation on the Variation of Mechanical Properties of Saturated Sand During Liquefaction

Transcription

1 6 th Internatonal Conference on Earthquake Geotechncal Engneerng -4 November 25 Chrstchurch, New Zealand An Investgaton on the Varaton of Mechancal Propertes of Saturated Sand Durng Lquefacton Y-Y.Ko, C-H. Chen 2, T-S. Ueng 3, C-H. Chen 4 ABSTRACT Sol lquefacton not only nduces settlement and lateral spreadng of the ground, but also lowers the stffness and strength of the sol body. In order to nvestgate the varaton of sol mechancal propertes durng lquefacton, data of the shakng table tests on saturated sand usng a large lamnar shear box conducted n Natonal Center for Research on Earthquake Engneerng were analyzed. Frstly, the excted responses of saturate sol durng lquefacton were characterzed. Furthermore, one-dmensonal shear beam dealzaton was adopted to establsh the smplfed sol profle model, and system dentfcaton of the sol body can thus be conducted to examne the varaton of mechancal propertes of saturated sand, such as the shear modulus and the dampng rato, wth respect to the development of shear stran and excess pore water pressure. Results of ths study wll be helpful to assess the real sesmc behavor of lquefed sol. Introducton Tawan locates n the sesmc actve west Pacfc Rm, and therefore earthquake dsasters are nevtable. In Tawan, populaton are concentrated n alluval plans, and thus sol lquefacton s the threat that people n Tawan have to face. Sol lquefacton causes not only the settlement and lateral spreadng of sandy ground, but also the reducton of the stffness and strength of the sandy sol. Consequently, the sesmc behavor and the asesmc capacty of the foundaton and other engneerng structures restng on lquefed sol wll be nfluenced. Therefore, the weakenng of sol nduced by lquefacton should be approprately consdered n sesmc desgn. In Tawan, the reducton factors for the mechancal parameters of lquefed sol proposed n JRA (996) and n AIJ (998) are wdely used n foundaton desgn. However, these reducton factors are not based on sold theores and are nconsstent. Because exstng related studes are qute lmted, conservatve consderatons are usually adopted n engneerng practce, causng uneconomcal desgns. Therefore, t s necessary to nvestgate the varaton of sol mechancal propertes durng lquefacton for a real assessment of the sesmc behavor of lquefed sol and for more reasonable sesmc desgn. In order to effectvely smulate the sesmc response of layered sol, Natonal Center for Research on Earthquake Engneerng (NCREE) developed a large baxal lamnar shear box wth Assocate Researcher, Nat'l Center for Research on Earthquake Engng., Tape, Tawan, yyko@ncree.narl.org.tw 2 Assstant Researcher, Nat'l Center for Research on Earthquake Engng., Tape, Tawan, chaham@ncree.narl.org.tw 3 Professor Emertus, Department of Cvl Engng., Natonal Tawan Unversty, Tape, Tawan, ueng@ntu.edu.tw 4 Professor, Department of Cvl Engng., Natonal Tawan Unversty, Tape, Tawan, chchen2@ntu.edu.tw

2 a nner dmenson of.88 m (L).88 m (W).52 m (H) (Ueng et al., 26a), as shown n Fgure (a). To allow baxal moton, each layer conssts of an nner and an outer frames able to move n two orthogonal drectons respectvely n the horzontal plane, as shown n Fgure (b), and each layer can move ndependently so that the box can provde a lamnar flexble boundary to mnmze the boundary effect. Along wth the large shakng table of NCREE, large scale geotechncal physcal model tests can be performed, makng the sesmc response of the sol specmen be more smlar to the real stuaton. In order to study the characterstcs of lquefacton behavor of saturated sand, a seres of physcal model shakng table test were conducted n NCREE n 22~27 usng ths shear box (Ueng et al., 26b; Ueng et al., 28). In ths research, these expermental data were utlzed o nvestgate the varaton of mechancal propertes of saturated sand durng the process of lquefacton. Frstly, the excted responses of saturate sol were characterzed n each stage of lquefacton. In addton, one-dmensonal shear beam dealzaton was adopted to establsh the smplfed sol profle model for the system dentfcaton of the sol body, and then the varaton of sol mechancal propertes wth respect to the development of shear stran and excess pore water pressure can thus be examned. (a) (b) Fgure. NCREE lamnar shear box: (a) top vew (b) movable frame scheme (Ueng et al., 26b) Lterature Revew of Influence of Lquefacton on Mechancal Propertes of Sol Kostadnov and Towhata (22) performed tme-frequency analyss on the earthquake records of several lquefed stes usng short-tme Fourer transform (STFT) to nvestgate the change of the mean nstantaneous frequency (MIF) of the ground sesmc response. The MIF of each ste was sgnfcantly lowered after lquefacton. Kramer et al. (2) also conducted tme-frequency analyss on earthquake records of lquefed stes usng STFT, wavelet transform and Stockwell transform. Dramatc reducton n acceleraton ampltude and predomnant frequency were observed, showng that the lquefacton nduced the quck softenng of sol. In order to study the dynamc behavor of sol n a well controlled envronment, small scale laboratory tests are often adopted. Seed and Lee (966) were the poneers usng the cyclc traxal test to nvestgate the lquefacton of saturated sand, and ndcated that effectve stresses

3 of sol wll be nearly zero. Martn et al. (975) depcted that the shear stress, as well as the shear modulus of sol, s proportonal to the square root of vertcal effectve stress based on laboratory tests to characterze the volumetrc change of sand subjected to cyclc shear. Hence, decrease of vertcal effectve stress wll degrade the shear modulus. Ths s conformable to the observatons from the earthquake records of lquefed stes. Kokusho (98) also verfed that the dea of Martn et al. (975) was vald n small strans usng draned cyclc traxal tests. If the varaton of sol mechancal propertes can be estmated accordng to actual earthquake records, the real sesmc behavor of sol n feld can be more authentcally reflected. A smple dea of one-dmensonal (-D) shear beam dealzaton proposed by Koga and Matsuo (99) was utlzed by Zeghal and Elgamel (994) to obtan shear stress-stran hstores wthn the ground profle n 987 Superstton Hlls Earthquake based on the data of the downhole accelerometer array at Wldlfe Refuge, Calforna. Ths earthquake caused a sgnfcant ncrease of excess pore water pressure, and evdences of lquefacton such as sand bols and mnor lateral spreadng were observed n feld nvestgatons. Accordng to the analyss results, the shear wave velocty was obvously reduced as the sharp rse of excess pore water pressure occurred. System Identfcaton Usng -D Shear Beam Idealzaton Consderng the case that shear horzontal (SH) waves propagate vertcally n horzontally layered sol, the -D shear beam theory can be used for the dealzaton of the sol profle. Then, usng the dea proposed by Koga and Matsuo (99), the shear stress-stran hstores of the sol body can be calculated from the measured ground response (dsplacement or acceleraton), and the sol mechancal propertes can be accordngly estmated. As shown n Fgure 2, the sol profle s dealzed as a -D shear beam and s dscretzed. Then the shear stress tme hstory of the sol body at a depth of h can be expressed va the mass densty of sol, ρ, and the sol h acceleraton at a depth of x, u (x ), as t ( h, = ρ u ( x) dx. Then, If the acceleratons at the black ponts n Fgure 2 are known, the shear stress at the -th pont (at a depth of x ) can be calculated: u + u t ( = t ( + ρ ( x x ) () 2 where t ( = t ( x,, and u = u ( x,. In addton, the shear stran at a depth of x can be calculated n the fnte dfference form: x [ ] + [ ] x γ ( = u + ( u ( u ( u ( (2) x + x x x where x = x + x. Thus, because τ () = (free surface condton), the shear stresses at dfferent depths can be calculated subsequently usng Equaton from the acceleratons at dfferent depths. Also, the shear strans can be calculated usng Equaton 2 from the drectly measured dsplacements or the double tme ntegraton of acceleratons. Consequently, the hysteretc loop of the stress-stran tme hstores can be obtaned, and the equvalent lnear shear modulus G eq and hysteretc dampng rato β can be accordngly estmated, as shown n Fgure 3.

4 x u( h t (h, y 2 3 a a 2 a 3 W D t t a G max W S G eq x - a - a γ a γ + a + β WD = = 4π W S tdγ 8π t γ a a Fgure 2. D shear beam dealzaton. Fgure 3. Stress-stran hysteretc loop. Case Study- Snusodal Exctaton Test of Saturated Sand The large shakng table tests of NCREE on saturated Vetnam sand (Ueng et al., 26b), whch s often regarded as clean sand, was utlzed for case study. In order to clearly characterze the sesmc behavor of the sol, one of the horzontal unaxal snusodal exctaton test was adopted. The nput moton was a 2-Hz snusodal wave wth an ampltude of.75 g. An accelerometer was nstalled wthn the sol body at a depth of 556 mm below the sol surface and about at the center horzontally. At the same locaton a pezometer was nstalled. Accelerometers and varable dfferental transformers (LVDTs) were also nstalled on movable frames of the shear box. Thus, the method mentoned n the prevous secton can be appled to analyze the test data. Characterstcs of Excted Responses of Saturate Sand Fgure 4 shows the measured acceleratons of the sol body at a depth of 556 mm and the frame of the shear box at the same elevaton, and excess pore water pressure. The pore water pressure ncreased sharply durng 2~4 sec, and reached a upper bound at 5 sec. At about 4 sec the response of the sol body started to change, mplyng the ntal lquefacton had occurred. After the ntaton of lquefacton (4~5 sec), the acceleraton showed a sgnfcant spke and then exhbted a response wth a longer perod. Afterwards, the acceleraton ampltude reduced obvously and showed a mult-frequency curve, representng complete lquefacton. Concernng the frame, a hgh frequency response was observed after lquefacton, whch could be related to the sgnfcant stffness decrease of lquefed sol, whch not only altered the vbraton characterstcs of sol body, but also nduced the hgh frequency vbraton of frames due to the loss of lateral resstance. Stress-Stran Hysteretc Loop of Sol Response Accordng to the prevous secton, spectral analyss can exhbt the degradaton of f pre of sol response durng lquefacton, and can also clarfy the unexpected response resulted from test setup. However, due to the resoluton of spectrum and envronmental condtons, spectral analyss s more approprate for qualtatve nvestgaton of the sesmc behavor of lquefed sol rather than quanttatve descrpton. Hence, the -D shear beam dealzaton (Koga and Matsuo,

5 99) mentoned prevously was further ntroduced to deduce the tme hstores of the shear stress and shear stran of the sol body durng exctaton. Thus, the stress-stran hysteretc loop can be obtaned, and the shear modulus and dampng rato can be estmated based on Fgure 3. Utlzng Equaton and Equaton 2, the tme hstory of shear stress and shear stran of the sol body can be calculated from the data of the accelerometer wthn the sol body and the data of LVDT at the frames near the observed elevaton. Accordngly, the stress-stran hysteretc loop of the sol body was obtaned. Fgure 5(a) depcts the hysteretc loops before lquefacton (~4 sec), n whch t can be observed that the slope declned and the area enlarged sgnfcantly, mplyng the degradaton of the sol stffness and the ncrease of the dampng rato. From the hysteretc loops after lquefacton (4~8 sec), as shown n Fgure 5(b), t s found that the slope dropped to a very low value after the maxmum of shear stress was reached, ndcatng that the sol had scarce any stffness. However, the sol stll had the capablty of energy dsspaton because the hysteretc loops had consderable area. In addton, t should be mentoned that the shear stran developed rapdly between 2~4 sec (as excess pore water pressure ncreased quckly) and reached a maxmum at 4. sec. Acceleraton (g) Acc. of Frame Acc. of Sol Excess pore pressure Tme (sec) Pressure head (mm) Fgure 4. Acceleratons of sol body and frame and excess pore water pressure (depth = 556 mm). Shear Stress (kn/m 2 ) ~4 sec Shear Stress (kn/m 2 ) ~8 sec - - (a) Shear Stran (%) (b) Shear Stran (%) Fgure 5. Stress-stran hysteretc loop of the sol body: (a) ~4 sec; (b) 4~8 sec.

6 Varaton of Mechancal Propertes of Saturated Sand Durng Lquefacton From Fgure 5, t s notced that the varaton of sol mechancal propertes durng lquefacton occurred prmarly n the process of the generaton of excess pore water pressure and the development of shear stran. Therefore, the stress-stran hysteretc loops n the duraton when excess pore water pressure and shear stran changed most sgnfcantly (2.~4. sec) were used to estmate the shear modul and compare them to the correspondng excess pore water pressures, as shown n Fgure 6. The equvalent shear modulus G eq generally decreased as the excess pore water pressure rato (r u, rato of excess pore water pressure to vertcal effectve stress) ncreased, and was nearly zero when r u was over.8, ndcatng that completely lquefed sol can be consdered havng no stffness. It s also found that G eq showed an exponental decay wth respect to r u. However, r u was actually dependent on shear stran ampltude (γ amp) and showed a logarthmc relatonshp, as shown n Fgure 7. Consequently, the degradaton of shear modulus was actually nfluenced by shear stran and excess pore water pressure smultaneously. G eq (kn/m 2 ) y = 298.e -4.56x R² = r u r u y =.236ln(x) R² = γ amp (%) Fgure 6. Relatonshp between G eq and r u. Fgure 7. Relatonshp between r u and γ amp. The relatonshp between the normalzed shear modulus rato (G eq /G, where G denotes the shear modulus correspondng to a shear stran of -6 ) and the effectve stran γ eff (γ eff =.65γ amp) obtaned n ths study s gven n Fgure 8. It was compared wth the shear modulus degradaton curve proposed by Seed and Idrss (97), whch was manly based on expermental data on clean sand, has been consdered representatve and was specfed as the default for sand n the ground response analyss code SHAKE 9 (Idrss and Sun, 992). It should be mentoned that the G eq /G value related to the mnmum γ eff of ths study (when r u was nearly zero) was assumed to be dentcal of the G eq /G value of Seed and Idrss (97) at the same γ eff value. It s noted that both decreased wth respect to γ eff wth a smlar decayng tendency, yet consderable dfference was observed when the stran level was hgher. G eq /G of ths study was smaller, probably due to the nfluence of the excess pore water pressure. In addton, Fgure 9 exhbts relatonshp between the dampng rato β and γ eff, and t was compared wth that proposed by Idrss (99) for clean sand, whch was also used as the default for sand n SHAKE 9. Both dampng rato curves ncreased wth respect to γ eff yet the data n the one of ths study were much more dspersed, and were larger due to the effect of excess pore water pressure.

7 Because Fgure 8 can be consdered for the draned condton, t can be used to elmnate the effect of shear stran n Fgure 6 by ntroducng the relatonshp gven n Fgure 7. Thus, the relatonshp between G eq and r u wthout the nfluence of shear stran can be obtaned, as gven n Fgure (a), whch stll showed an exponental decay trend as n Fgure 6. In a smlar way, the relatonshp between β and r u wth the effect of shear stran elmnated can be acqured, as shown n Fgure (b), whch was roughly a logarthmc relatonshp yet was rather fluctuated. However, t can stll be noted that the excess pore water pressure due to the snusodal exctaton to the sol caused a consderable rse of the dampng rato ranged between %~3%. G eq / G Ths Study Seed & Idrss (97) Dampng rato β (%) Ths Study Idrss (99).... γ eff (%).... γ eff (%) Fgure 8. Shear modulus vs. shear stran. Fgure 9. Dampng rato vs. shear stran. G eq / G y =.498e -.943x R² = Dampng rato β (%) y = 6.63ln(x) R² = (a) r u (b) r u Fgure. Relatonshps wth the effect of shear stran elmnated: (a) G eq /G vs. r u ; (b) β vs. r u. Conclusons. The softenng of sol after lquefacton due to the decrease of effectve stresses can be noted from the acceleratons of sol body and the frame of shear box n the snusodal exctaton test. 2. Stress-stran hysteretc loops of the sol n the snusodal exctaton test can be obtaned usng the -D shear beam dealzaton, and the decrease of stffness and the ncrease of dampng durng the development of lquefacton can be accordngly observed. 3. Based on the system dentfcaton of the sol body usng ts stress-stran hysteretc loops, the relatonshps of declne of shear modulus and the rse of hysteretc dampng rato wth respect

8 to the shear stran can be obtaned. Comparng these relatonshps to the often used curves of sol mechancal propertes versus shear stran, the nfluence of excess pore water pressure on the decrease of shear modulus and the ncrease of dampng rato can be exhbted. 4. Usng the change of excess pore water pressure versus the shear stran, the effect of shear stran can be elmnated to obtan the varaton curves of shear modulus and dampng rato wth respect to the excess pore water pressure rato, whch can serve as the reference of sesmc desgn and analyss n engneerng practce. Acknowledgments The authors express ther grattude for the fnancal support provded by Mnstry of Scence and Technology, Executve Yuan, Tawan. References Archtectural Insttute of Japan (AIJ). Recommendatons for Desgn of Buldng Foundatons. Archtectural Insttute of Japan: Tokyo, 988 (n Japanese). Idrss IM. Response of soft sol stes durng earthquakes. Proceedngs of Symposum to Honor Professor H.B. Seed. Unversty of Calforna: Berkeley, CA, 99: Idrss, IM, Sun, JI, User's Manual for SHAKE9. Unversty of Calforna, Davs: Davs, CA, 992. Japan Road Assocaton (JRA). Desgn Specfcatons for Hghway Brdges. Japan Road Assocaton: Tokyo, 996 (n Japanese). Koga Y, Matsuo O. Shakng table tests of embankments restng on lquefable sandy ground. Sols and Foundatons 99; 3(4): Kokusho, T. Cyclc traxal test of dynamc sol propertes for wde stran range. Sols and Foundatons 98, 2 (2): Kostadnova MV, Towhata I. Assessment of lquefacton-nducng peak ground velocty and frequency of horzontal ground shakng at onset of phenomenon. Sol Dynamcs and Earthquake Engneerng 22; 22(4): Kramer SL, Hartvgsen AJ, Sderas SS, Ozener PT. Ste response modelng n lquefable sol deposts. 4th IASPEI / IAEE Internatonal Symposum: Effects of Surface Geology on Sesmc Moton 2: Santa Barbara, CA. Martn, GR, Fnn WDL, Seed HB. Fundamentals of lquefacton under cyclc loadng. Journal of the Geotechncal Engneerng Dvson, ASCE 975; (5): Seed HB, Idrss IM. Sol Modul and Dampng Factors for Dynamc Response Analyss. Report No. EERC 7-. Earthquake Engneerng Research Center: Berkeley, CA, 97. Seed HB, Lee KL. Lquefacton of saturated sands durng cyclc loadng. Journal of the Sol Mechancs and Foundatons Dvson 966; 92(6): Ueng TS, Wang MH, Chen MH, Chen CH, and Peng LH. A large baxal shear box for shakng table tests on saturated sand. Geotechncal Testng Journal 26, 29 ():-8. Ueng TS, Chen CH, Cheng HW, Wu CW. Large-Scale Shear Box Sol Lquefacton Tests on Shakng Table (III) - Settlement of Saturated Vetnam Sand Specmen n Shakng Table Tests. Research Report NCREE-6-9. Natonal Center for Research on Earthquake Engneerng: Tape, 26. Ueng TS, Chen CH, Tsou CF, Chen YC. Large-Scale Shear Box Sol Lquefacton Tests on Shakng Table (IV) - Behavors of Saturated Malao Sand Specmen n Shakng Table Tests. Research Report NCREE-8-. Natonal Center for Research on Earthquake Engneerng: Tape, 28. Zeghal M, Elgamel AW. Analyss of ste lquefacton usng earthquake records. Journal of Geotechncal Engneerng, ASCE 994; 2(6):