Unified Correlation between SPT-N and Shear Wave Velocity for all Soil Types

Transcription

1 6 th International Conference on Earthquake Geotechnical Engineering 1-4 ovember 15 Chritchurch, ew Zealand Unified Correlation between SPT- and Shear Wave Velocity for all Soil Type C.-C. Tai 1 and T. Kihida ABSTRACT The hear wave velocity (V) of ediment play a key role in eimic wave amplification and i required in ite repone analyi. Such information i uually lacking during field exploration, but tandard penetration tet blow count () i motly obtained. Therefore, everal tudie have etablihed empirical correlation between and V for engineering ue. Thee empirical correlation, however, vary ignificantly in term of model form and parameter. A unified empirical correlation i developed in thi tudy through the ue of the Engineering Geological Databae for the Taiwan Strong Motion Intrumentation Program, which contain grain-ize ditribution, void ratio, water content, pecific gravity, unit weight, liquid limit, and platicity index (PI) in addition to the V and of trata. The influence of overburden preure, fine content (FC), PI, and oil type on mall-train behavior (i.e., V) and large-train behavior (i.e., ) i dicued. A unified correlation between V and that i dependent on overburden preure, FC, and PI i propoed through the conditional prediction approach. Introduction A key property required to effectively etimate the eimic repone of a ite i mall-train hear modulu Go, which i often computed by meauring hear wave velocity V and ma denity ρ a follow: Go= ρv. (1) Geophyical invetigation are typically performed to meaure the V profile. However, thee meaurement are not alway common becaue of the additional cot of the field invetigation. Correlation between V and tandard penetration tet (SPT) blow count (), conditioned on the geologic etting and ite tratigraphy, are potentially ueful for the above ituation. umerou relation between and V for Taiwan region have been etablihed in the previou tudy (Kuo et al., 11). Thee empirical correlation, however, vary ignificantly in term of model form and are limited to a pecific oil type (e.g., and or clay). The development of thee correlation alo lack theoretical upport. Therefore, with a theoretical bai, thi tudy aim to etablih a unified correlation between and V that can be applied to and, ilt, and clay. The Engineering Geological Databae for the Taiwan Strong Motion Intrumentation Program 1 Aitant Profeor, Department of Civil Engineering, ational Chung Hing Univerity, Taiwan, taicc@nchu.edu.tw Pot-Doctoral Reearcher, Pacific Earthquake Engineering Reearch Center (PEER), Univerity of California, Berkeley, USA, kihidapple@gmail.com

2 (EGDT) (Kuo et al., 11) i utilized in the analyi. The factor that can change the mall-train propertie Go are reviewed. Baed on a previou tudy on laboratory tet data, a model form that decribe mall-train propertie (i.e., V) and large-train meaurement (i.e., ) i propoed. The influence of effective overburden preure (σ o ), fine content (FC), platicity index (PI), and over conolidation ratio (OCR) on mall-train propertie and large-train meaurement i dicued baed on the regreion analyi reult. Latly, a unified correlation between V and that i dependent of thee parameter i propoed through the conditional prediction approach. Fundamental Functional Form Theoretical Form of V and The mot common functional form for the relation of Go propoed in literature i Go = AF(e)(σ ) nn, () where σ i the effective confining (or vertical) tre, F(e) i the function of void ratio, and contant A and n are determined by tatitical regreion of a data et. A ummary by Ihihara (1996) indicate that n i motly.5 for both and and variou type of clay (i.e., n =.5 for V according to Eq. (1)). However, a train amplitude increae, n increae according to laboratory tet data from 1/3 to 1. a hear train γ < 1 4 % increae to γ = 1 % (i.e., the exponent term of σ change from 1/6 to.5 a γ increae from 1 4 % to 1 % for V). The change in n indicate that confining tre influence mall- and large-train oil propertie differently. Therefore, the exponent n i train-dependent, which implie that mall-train property (e.g., V or Go) and large-train meaurement (e.g., ) need to be corrected by confined preure differently. A a reult, confined preure hould be included when etablihing the correlation between and V, a uggeted by Brandenberg et al. (1). Other Factor that Influence Functional Form Hardin and Black (1968) dicued the model form of Go for normally conolidated (C) and overly conolidated (OC) clay and uggeted that Go = AF(e)OCR PPPP/16 (σ ) nn. (3) The equation implie the following. Firt, for a non-platic or low-pi oil (e.g., and or ilt), Go i independent of OCR. Second, given OCR = 1 (C clay), Eq. (3) yield Eq. () and exponent n i a fixed number regardle of PI. Viggiani and Atkinon (1996) reported that impact of confined tre on Go i uncoupled with OCR a Go = B(σ ) nn OCR mm. (4) However, B, n, and m are dependent on PI a revealed by laboratory tet reult. Kawaguchi and Tanaka (8) recently propoed a theoretical form of Go a follow:

3 Go = w.8 LL ( 3 OOOOOO). ( 1+OOOOOO.5 ).6 (σ 3 ).8, (5) where w L i the liquid limit, which i correlated to PI. Equation (5) indicate that the effect of OCR and PI (or w L ) on Go i uncoupled unlike that in Eq. (3) where the influence of OCR and PI on Go i coupled. Propoed Model Form Baed on the review of previou tudie, two poible regreion model of Go are propoed a follow: Model 1: Go = A PI mm OCR ll (σ ) nn, (6) Model : Go = A OCR (a PI) (σ ) nn. (7) The effect of PI and OCR on Go i uncoupled in Model 1, wherea it i coupled in Model. Conidering that the coupling effect between PI and OCR i till under debate, thi tudy adopt Model 1 for the development of the correlation between and V becaue of it implicity. Meanwhile, FC can alo change the blowout, and it effect i uually accounted for when performing liquefaction analyi. Therefore, the propoed general model for V and i further modified a V = cc (σ ) cc 1 FFFF cc PI cc 3 OCR cc 4, (8) = bb (σ ) bb 1 FFFF bb PI bb 3 OCR bb 4. (9) A dicued earlier, confining tre influence mall- and large-train oil propertie differently (i.e., c 1 and b 1 are different). Similarly, the influence of FC, PI, and OCR on mall- and largetrain behavior may alo be different. Thi iue will be dicued later baed on the regreion analyi. Conditional Prediction Approach The regreion analyi of V with conditional meaurement of baed on Kihida and Tai (15) i decribed in thi ection. Firt, regreion analye are performed eparately to determine the coefficient in Eq. (8) and (9). Second, the relationhip between V and (V conditional on ) i etablihed baed on the correlation of the reidual in Eq. (8) and (9). A a imple example to illutrate the conditional prediction approach, we ue the following two regreion model that only include the confined tre term. ln = b + b σ 1 ln + ε o, lnv = c c + 1 ln o + ε V, (1) (11) where ε and ε V are the reidual after regreion analyi and follow the normal ditribution with mean = and tandard deviation of σσ and σσ VVVV, repectively. The correlation between ε and ε V i ρ V. Conditional prediction of lnv given ln i expreed a follow:

4 ε E ln 1 1 V V V [ V ln ] = E[ lnv] + V ρ V = c b ρ V + ρ V ln + c b ρ V ln o ( ρ ) V = 1 V V. (1) (13) Therefore, the following equation i obtained. [ V ln ] = β + β ln + β ln o E ln 1, (14a) where c b ρ V b = V, V β 1 = ρv, V b = c1 b1 ρ V. (14a) (14a) (14a) The propoed conditional approach can be extended in a imilar manner when more term (e.g., FC, PI, and OCR in Eq. (8) and (9)) are added to Eq. (1) and (11). Databae for Regreion Analyi The baic data provided in EGDT include tratum decription, reult of oil phyical property tet (uch a grain-ize ditribution, uniformity coefficient, coefficient of gradation, void ratio, water content, pecific gravity, unit weight, liquid limit, and PI), oil claification, P- and S- wave velocitie, and SPT- value. EGDT provide ufficient information for the regreion analyi in addition to the meaurement of and V. However, OCR i unavailable in EGDT. Therefore, OCR i approximately etimated by Eq. (5) in thi tudy. The influence of thi aumption will be explored later in the paper. Effective vertical tree are calculated with the given depth, unit weight, and water table elevation. Groundwater elevation i ometime not recorded for ome boring. In uch a cae, the p-wave velocity profile i utilized to identify the approximate elevation of the groundwater table. An abrupt tranition from p-wave velocity lower than 5 m/ to higher than 15 m/ i typically apparent in boring log, clearly indicating the poition of the groundwater table. In EGDT, SPT- i meaured by an automatic hammer falling ytem every 1.5 m (every 3 m to 5 m for gravel layer) or at the depth of notable dicontinuity during drilling. The i corrected to 6 by auming the meaured energy ratio of 7%. Only SPT- le than 5 i utilized for the regreion analyi. P- and S-wave velocitie are meaured with a upenion PS logger ytem. Velocity meaurement i generally performed every.5 m, except for everal drilling in the firt and econd year, in which velocity i meaured for every 1 m. A total of 3684 data et from 334 ite that include V, (<5), σ o, FC, PI, and etimated OCR are utilized for regreion. The ditribution of data i preented in Figure 1. For non-platic oil, PI i et a a

5 unit; for oil without FC, FC i alo et a a unit. A hown in Figure, V i approximately linear againt the model parameter in log log pace, which indicate that modeling by Eq. (8) and (9) i ufficient. Figure 1. Ditribution of data et Small- and Large-Strain Behavior Figure. V againt model parameter in log log pace Regreion Analyi Reult Table 1 provide a ummary of the regreion reult obtained with Eq. (8) and (9). The exponent term of FC and PI i negative, wherea that of σ o and OCR i poitive. The poitive value indicate that or V increae a OCR and σ o increae, and the negative value indicate that or V decreae a FC and PI increae. However, the value of the exponent term i different for and V. The exponent term of σ o for V (mall-train property) i approximately.5, wherea that for (large-train meaurement) i approximately.5. Thi reult i conitent with that of everal previou laboratory tudie ummarized in Ihihara (1996), that i, a train amplitude increae, the exponent of σ o change from 1/6 to.5. Different exponent value of predictor variable mean different degree of influence by thee variable on and V. The degree of variou influence can be quantified by the exponent ratio between and V, in which a high value implie the mot different effect on large- and malltrain behavior. Therefore, a hown in Table 1, FC influence and V mot differently followed by σ o, PI, and OCR. Such difference hould be conidered when developing the correlation between and V. With σ o a an example, the obtained exponent ratio i approximately. Therefore, if V i conditioned on (or i normalized by V imilar to the modulu reduction curve where hear modulu G i normalized by Gmax at mall train), the

6 influence of σ o i not negligible. In other word, the prediction model of V baed on hould include the σ o term, a reported by Brandenberg et al. (1). Similarly, FC and PI hould be included in the model becaue they alo influence mall- and large-train behavior differently. Only the ratio of OCR i approximately 1. Thu, the prediction model of V baed on can poibly ignore the OCR term. Table 1. Reult of the regreion analyi of model 1 Intercept Exponent R ρ VS σ o FC PI OCR V Ratio Influence of FC The developed correlation between and FC and V and FC can alo be utilized to evaluate the impact of FC on V and. The exponent of FC for i higher than that for V, indicating that FC ha more influence on. In liquefaction potential analyi, and V require correction to conider the impact of FC. Corrected (or equivalent) or V i typically higher than meaured or V for oil with certain FC becaue high FC reult in low meaured and V or can increae the reitance of liquefaction. The negative exponent of FC obtained in thi tudy i conitent with the concept of correction for FC in the liquefaction analyi. We alo quantitatively compare FC correction from our regreion analyi with that propoed by previou tudie. Figure 3(a) how a comparion of FC-corrected (c) by Idri and Boulanger (8), Seed et al., (3), and Youd et al. (1) for variou FC given meaured = 5, 1, 15. c in thi tudy i calculated a follow: c=/fc (15) Given meaured = 5 and 1, the c in thi tudy i in the range of the c obtained by the other tudie. For = 15, the c in thi tudy i lightly larger than the c in the other tudie. The previou tudie motly corrected with FC up to 35% to 4%. By contrat, the reult of thi tudy indicate that may be further corrected for a higher FC by conidering mechanical correction during meauring (a)-1 Meaured =5 (a)- Meaured =1 (a)-3 Meaured = (b) C,S V, CS FC(%) FC(%) FC(%) FC(%) Figure 3. Comparion of (a) corrected for variou FC given meaured = 5, 1, 15 and (b) corrected V for variou FC given meaured V = 15,, 5 m/

7 We alo compare FC-corrected V (V, CS ) in thi tudy with that corrected by Andru et al. (4) for variou FC given three meaured V. A hown in Figure 3(b), the V, CS in thi tudy i lightly higher than that in Andru et al. (4) for low meaured V but agree well with that in Andru et al. (4) for meaured V = 5 m/. Similar to the impact of FC on, V may be further corrected for a high FC, a indicated by our regreion model. Unified Model A unified empirical model i propoed according to the previouly decribed conditional prediction procedure (Eq. (1) to (14a)) by uing the regreion reult lited in Table 1, that i, lnv = ln +.17lnσ.4lnFFFF.1lnPI +.6lnOCR. (16) The tandard deviation of σ lnv/ i.6, which i approximated a σ v/ = 63 m/ given mean V = 7 m/. In Kuo et al. (11), the data et imilar to the one ued in thi tudy wa grouped into clay and and for regreion analyi, and the obtained σ of individual V- model wa 67 and 77 m/, repectively. σ in the preent tudy i lower than that by Kuo although we ued the entire dataet in the regreion analyi. The model that include additional prediction parameter uch a FC and PI ignificantly improve prediction accuracy. The model can alo be applied to more general condition for etimating V by and i not limited to a pecific oil type. Conidering that OCR i not directly provided in the databae and i etimated indirectly, we alo evaluate model performance if OCR i excluded from the model. The reult how that removing OCR from the model ha a limited effect becaue σ i lightly increaed from 63 m/ to 68 m/ given mean V = 7m/. The model baed on σ o, FC, and PI can ufficiently predict V although OCR i typically unavailable in practice. Thi reult may be due to the fact that the impact of OCR on mall- and large-train behavior i imilar, a dicued earlier. Therefore, the following equation can be adopted if OCR i unavailable. lnv = ln +.11lnσ.3lnFFFF +.lnpi (17) If the model form only include σ o a typically modeled by other, σ become high (V = 94 m/). everthele, it i till lower than the σ obtained by Kuo et al. (11) (approximately 18 m/). Thi reult may be attributed to the fact that we adopted a conditional prediction approach and ued σ o intead of depth in the model. Concluion umerou relation between and V have been propoed for practical purpoe in earthquake engineering. Thee empirical correlation, however, vary ignificantly in term of model form and parameter. Without a theoretical or experimental bai, they are developed only for a pecific ite and oil type. V and repreent mall- and large-train behavior, repectively. Such difference hould be conidered when a model i developed. Therefore, a unified empirical correlation model wa developed in thi tudy uing a conditional prediction approach to

8 correlate mall- and large-train behavior. The developed model can be applied to clay, ilt, and and. EGDT with 3684 data et wa utilized to develop the model. The main factor that can change the mall-train property include σ o, FC, PI, and OCR according to a previou tudy on laboratory tet data. Therefore, we developed a imple model form that include thee parameter to etimate mall-train property and applied it to large-train meaurement imilarly. The influence of thee parameter on mall-train propertie (i.e., V) and large-train meaurement (i.e., ) wa dicued according to the regreion reult. Different exponent value of predictor variable mean different degree of influence by thee parameter on large- and mall-train behavior. A indicated by the exponent ratio between and V, FC influence and V mot differently, followed by σ o, PI, and OCR. The exponent ratio of σ o between and V i approximately, which i conitent with that in previou tudie. The change in and V by FC in the regreion reult agree well with the fine correction recommended in the liquefaction potential analyi. Latly, a unified correlation model between V and that i dependent on σ o, FC, PI, and OCR wa etablihed through a conditional prediction approach. The model include additional prediction parameter, uch a FC, OCR, and PI, which ignificantly improve prediction accuracy according to the reduction in tandard deviation. The propoed model can be applied to more general condition and i not limited to a pecific oil type. However, the correlation ha only been teted for oil in Taiwan and ha yet to be verified for other oil in other region. Acknowledgment We would like to thank the CREE for providing the EGDT. We alo thank Hu, H. Y. and Wen, C. L. for managing the databae. Reference Andru, R. D., Piratheepan, P., Elli, B. S., Zhang, J., and Hein, C. (4). Comparing liquefaction evaluation method uing penetration-vs relationhip. Soil Dynamic and Earthquake Engineering, 4, Brandenberg, Scott J., Bellana, areh, and Shantz, Thoma. (1). Shear wave velocity a function of tandard penetration tet reitance and vertical effective tre at California bridge ite. Soil Dynamic and Earthquake Engineering, 3(1), Hardin, B.O., and Black, W. L. (1968). Vibration modulu of normally conolidated caly. Journal of Soil Mechanic and Foundation Diviion, American Society of Civil Engineer, 94(SM), Idri, I. M., and Boulanger, R. W.. (8). Soil Liquefaction during Earthquake: EERI. Ihihara, K. (1996). Soil behavior in earthquake geotechnique: Clrendon Pre, Oxford. Kawaguchi, T., and Tanaka, H. (8). Formulation of Gmax from recontituted clayey oil it application to meaured Gmax in the field. Soil and Foundation, 48(6), Kihida, T., and Tai, C.-C. (15). Prediction model of hear wave velocity by uing SPT blow count baed on the conditional probability framework. Submitted to Journal of Geotechincal and Geoenvironmental Engineering. Kuo, C.-H., Wen, K.-L., Hieh, H.-H., Chang, T.-M., Lin, C.-M., and Chen, C.-T. (11). Evaluating empirical regreion equation for V and etimating V3 in northeatern Taiwan. Soil Dynamic and Earthquake Engineering, 31(3), Seed, R.B., Cetin, K. O., Mo, R. E. S., Kammerer, A. M., Wu, J., Petana, J. M.,Fari, A.. (3). Recent advance in oil liquefaction engineering: a unified and conitent framework. Paper preented at the 6th Annual

9 Geotechnical Spring Seminar, Lo Angele Section of the GeoIntitute, American Society of Civil Engineer, Queen Mary, Long Beach, CA. Viggiani, G., and Atkinon, J. H. (1996). Stiffne of fine-grained oil at very mall train. Geotechinique, 45(), Youd, T. L., Idri, I. M., Andru, R. D., Arango, I., Catro, G., Chritian, J. T., Stokoe, K. H. (1). Liquefaction reitance of oil: ummary report from the 1996 CEER and 1998 CEER/SF Workhop on evaluation of liquefaction reitance of oil. Journal of Geotechnical and Geoenvironmental Engineering, 17(1),