Keywords: pile, liquefaction, lateral spreading, analysis ABSTRACT

Transcription

1 Key arameters in seudo-static analysis of iles in liquefying sand Misko Cubrinovski Deartment of Civil Engineering, University of Canterbury, Christchurch 814, New Zealand Keywords: ile, liquefaction, lateral sreading, analysis ABSTRACT Soil-ile interaction in liquefying soils is very comlex and involves raid changes in soil characteristics and loads on iles. Thus, when analyzing the behaviour of iles with a simlified seudo-static aroach, the key issue is how to determine aroriate values for the arameters of the model while considering the inherent uncertainties associated with liquefaction. This aer identifies key arameters in the seudo-static analysis of iles in liquefying soils and rovides guidance for their determination based on observations from case histories and full-size tests. 1 INTRODUCTION There are several methods available for analysis of iles in liquefying soils including sohisticated finite element analysis based on the effective stress rincile and simlified methods using the seudo-static aroach. Irresective of the adoted analytical method, however, the analysis of iles in liquefying soils is burdened by unknowns and uncertainties associated with liquefaction and lateral sreading in articular. For examle, it is very difficult to estimate the strength and stiffness of liquefied soils or redict the magnitude and satial distribution of lateral sreading dislacements. One of the key asects of the simlified analysis is therefore to roerly address these uncertainties through arametric studies using a relatively simle model with conventional engineering arameters. This aer examines the use of the seudo-static analysis of iles in liquefying soils and identifies key arameters influencing the ile resonse. CYCLIC LIQUEFACTION AND LATERAL SPREADING When analyzing the behaviour of iles in liquefied soils, it is useful to distinguish between two different hases in the soil-ile interaction: a cyclic hase in the course of the intense ground shaking and consequent develoment of liquefaction, and a lateral sreading hase following the liquefaction. During the cyclic hase, the iles are subjected to cyclic horizontal loads due to ground movement (kinematic loads) and inertial loads from the suerstructure, as illustrated schematically in Figure 1a. The combination of these oscillatory kinematic and inertial loads determines the critical load for the integrity of the ile during the shaking. Lateral sreading, on the Cyclic ground dislacement Inertial force Unilateral ground dislacement soil soil Figure 1. Cyclic hase and lateral sreading hase

2 other hand, is rimarily a ost-liquefaction henomenon that is characterized by very large unilateral ground dislacements and relatively small inertial effects (Figure 1b). Thus, both liquefaction characteristics and lateral loads on iles are quite different between the cyclic hase and the subsequent lateral sreading hase, and therefore, these two hases should be considered searately in the simlified seudo-static analysis of iles. 3 PSEUDO-STATIC APPROACH FOR SIMPLIFIED ANALYSIS The most frequently encountered soil rofile for iles in liquefied deosits consists of three distinct layers, as illustrated in Figure where the liquefied layer is sandwiched between a non-liquefied crust layer at the ground surface and non-liquefied base layer. Liquefaction during strong ground shaking results in almost a comlete loss of strength and stiffness of the liquefied soil, and consequent large lateral ground dislacements. Particularly large and damaging for iles are ostliquefaction dislacements due to lateral sreading of the ground. During sreading, the nonliquefied surface layer is carried along with the underlying sreading soil, and when driven against embedded iles, the crust layer is envisioned to exert large lateral loads on the iles. Thus, the excessive lateral movement of the liquefied soil, lateral loads from the surface layer and significant stiffness reduction in the liquefied layer, are key features that need to be considered when evaluating the ile resonse to lateral sreading. Based on the characteristics and kinematic mechanism as described above, a three-layer soil model was adoted for a simlified seudo-static analysis of iles in a revious study (Cubrinovski and Ishihara, 4). As indicated in Figure 3, in this model the ile is reresented by a continuous beam while the interaction between the liquefied soil and the ile (- relationshi) is secified by an equivalent linear sring (β k ). Here, k is the subgrade reaction coefficient while β is a scaling factor reresenting the degradation of stiffness due to liquefaction. In the analysis, cyclic or sreading ground movement is reresented by a horizontal free-field dislacement of the liquefied soil while effects of the surface layer are modelled by an earth ressure and lateral force at the ile head. Note that the lateral force at the ile head may also include inertial loads from the suerstructure. Needless to say, one may use an FEM beam-sring model instead of the above closed-form solution and conduct even more rigorous analysis, because it will ermit consideration of multile load-deformation relationshis along the ile length. In rincile, however, the following discussion alies to the seudo-static analysis of iles, in general. Inut arameters of the comutational model and adoted load-deformation relationshis for the soil and the ile are shown in Figure 3. Three bilinear - relationshis are adoted for the resective soil layers while tri-linear moment-curvature relationshi (M-φ) is used for the ile. The Non-liquefied surface layer Lateral Earth force ressure U G 1-max layer β k Non-liquefied base layer Free field dislacement of liquefied soil Figure. Simlified mechanism of lateral sreading

3 H f Surface layer Footing H 1 M Y U U G k 1 1-max H layer C φ β k -max Ground dislacement H 3 Base layer D o k 3 3-max Figure 3. Characterization of nonlinear behaviour and inut arameters for the simlified analysis subgrade reaction coefficients in the bilinear - relationshis can be evaluated using emirical correlations based on the elastic roerty or SPT blow count of the soil, as described in Cubrinovski and Ishihara (4). In the analysis of a given ile, it is envisioned that β will serve as a arameter that will be varied over a relevant range of values, thus ermitting evaluation of the ile resonse by assuming different stiffness characteristics of the liquefied soil. max defines the ultimate lateral ressure that can be alied by the soil to the ile in the course of cyclic liquefaction and lateral sreading. In the following section, key arameters in the adoted model are identified and selection of their most aroriate values is discussed based on results from large-scale exeriments and back-calculations from case histories. 4 KEY PARAMETERS IN THE PSEUDO-STATIC ANALYSIS 4.1 Lateral ground dislacement In both cases of cyclic dislacements and sreading dislacements, the lateral ground dislacement that is used as an inut in the simlified analysis is a free field ground dislacement which is unaffected by the ile foundation. Cyclic ground dislacements can be estimated relatively accurately by means of an effective stress analysis, but the use of an advanced analysis for defining the inut in a simlified analysis is not ractical. Hence, it seems more aroriate for the seudo-static analysis to estimate the eak cyclic dislacements by using simlified charts correlating the maximum cyclic shear strain that will develo in the liquefied layer with the cyclic stress ratio and SPT blow count, as suggested by Tokimatsu and Asaka (1998), for examle. The horizontal cyclic dislacement rofile can be then easily obtained by integrating the shear strains throughout the deth of the liquefied layer. The lateral dislacement of the sreading soil can be evaluated using emirical correlations for ground dislacements of lateral sreads (Ishihara et al., 1997; Tokimatsu and Asaka, 1998; Youd et al., ). It is imortant to recognize, however, that in most cases it would be very difficult to make a reliable rediction for sreading dislacements, and therefore it would be necessary to vary the magnitude of the sreading dislacement within the estimated range of values. 4. Lateral ressure from the crust layer The lateral load from the unliquefied crust layer may often be the critical load for the integrity of the ile because of its large magnitude and unfavourable osition as a to-heavy load acting above

4 Measured resultant ressure α = Rankine assive ressure P = P α u Steel ile PHC ile Relative dislacement between soil and ile, = U (z) - U (z) (cm) g Figure 4. Lateral ressure from the crust layer on a single ile (full-size test on iles) above a laterally unsuorted ortion of the ile in the liquefied soil. For the adoted bilinear - relationshi for the crust layer, the key inut arameter is the ultimate lateral ressure, 1-max. The ultimate soil ressure from the surface layer er unit width of the ile can be estimated using a simlified exression such as, 1-max = α u, where (z 1 ) is the Rankine assive ressure while α u is a scaling factor to account for the difference in the lateral ressure between a single ile and an equivalent wall. Figure 4 shows the variation of α u with the relative dislacement observed in a lateral sreading exeriment on full-size iles (Cubrinovski et al., 6) with the maximum lateral ressure on the single ile being about 4.5 times the Rankine assive ressure. Note that α u can be also used for considering a ossible reduction in the mobilized ressure from the crust layer due to sand-boils, fissuring of the ground or imediment of ground deformation by adjacent foundations. 4.3 Stiffness and strength of the liquefied layer The factor β, which secifies the reduction of stiffness due to liquefaction (β k ) is affected by a number of factors including the density of sand, excess ore ressures, magnitude and rate of ground dislacements, and drainage conditions. Tyically, β takes values in the range between 1/5 and 1/1 for cyclic liquefaction and between 1/1 and 1/5 in the case of lateral sreading. Because of this large variation in β, it is recommended to examine the effects of stiffness reduction on the ile resonse through arametric studies, by varying β in the relevant range of values. The ultimate soil ressure in the bilinear - relationshi for the liquefied layer can be aroximated with the undrained residual strength of the soil. The emirical correlation between the undrained strength and SPT blow count roosed by Seed and Harder (1991) can be used for this urose (Figure 5). Since the scatter of the data is quite large and hence the value of S u may vary significantly for a given SPT blow count, the two bounding values for the residual strength might be used, i.e. the uer bound value S u-ub and the lower bound value S u-lb resectively, as indicated in Figure 5. Whereas a relatively wide range of values has to be considered for the arameters introduced above, it is imortant to adot a consistent aroach in the selection of the values where, for examle, a relatively small ground dislacement will be associated with higher stiffness (β value) and higher ultimate ressure (S u value) for the liquefied soil. Alication of the method to a case study and effects of the selected of S u on the ile resonse are discussed in the comanion aer Bowen et al. (7). 4.4 grou effects s in a grou are almost invariably rigidly connected at the ile head, and therefore, when subjected to lateral loads, all iles will share nearly identical horizontal dislacements at the ile head. During lateral sreading of liquefied soils in a waterfront area, each of the iles will be subjected to a different lateral load from the surrounding soils, deending uon its articular location within the grou and the satial distribution of the sreading dislacements. Consequently, both the interaction force at the ile head and the lateral soil ressure along the length of the ile

5 6 5 S u-ub 4 S u-lb S u-ub S u (kpa) 3 1 S u-lb (N ) 1 6cs Figure 5. Undrained residual strength (S u ) from case histories (after Seed and Harder, 199) will be different for each ile, thus leading to a develoment of distinct atterns of deformation and stresses along the length of individual iles in the grou. In addition to the cross-interaction effects discussed above, iles in a grou may affect the value of key arameters such as the magnitude and distribution of ground dislacements, stiffness characteristics of sreading soils and ultimate soil ressure. Figure 6, for examle, shows ile-grou effects on the ultimate lateral ressure from the crust layer where decrease in max is seen with increasing number of iles with sacing of.5 to 3 diameters. Exerimental data on ile grous in liquefiable soils is scarce and not conclusive, and therefore further evidence for the ile-grou effects on key arameters such as U G, β, 1-max and -max is urgently needed. 5 STIFF VERSUS FLEXIBLE PILE BEHAVIOUR When iles are subjected to large lateral ground dislacements, they generally behave either as flexible or stiff iles. Flexible iles follow the ground movement, and hence the relative dislacement between the ile and the soil is small, as shown in Figure 7. Consequently, the ultimate lateral ressures from the crust layer and liquefied layer may never be mobilized. The magnitude of the ground dislacement is the key arameter controlling the resonse of flexible iles since it ractically defines the maximum deflection of the ile. Stiff iles show strong lateral resistance and do not follow the ground movement. Consequently, the relative dislacement between the ile and sreading soil is very large, with the ultimate lateral u (ile in grou) u (single ile) d =.5D o or 3D o 3x3 Active iles Meyerhof (198) McVay (1995) Brown (1988) Ruesta 1997) Passive iles Pan () Poulos (1995) 4x4 grou Number of iles Figure 6. grou effects on the ultimate soil ressure

6 Horizontal dislacement (cm) Yielding Failure Flexible ile Stiff ile Alied ground dislacement Time (sec) Figure 7. Measured lateral dislacements of stiff and flexible iles during sreading soil ressure being alied by the crust layer and liquefied layer to the ile. Hence, for stiff iles, the ultimate soil ressure is the key arameter in the analysis while the magnitude of ground dislacement is not critically imortant. Note that the stiffness degradation arameter β affects the relative stiffness of the ile, and that the ile resonse is most sensitive to β when the change in the value of β changes the behaviour from flexible to stiff ile behaviour and vice versa. 6 CONCLUSIONS A simlified method for analysis of iles in liquefying soils based on the seudo-static aroach has been resented. The method uses a relatively simle model with a set of conventional engineering arameters for simulating the soil-ile interaction in liquefying soils. Because of the gross simlification of the roblem and significant uncertainties associated with liquefaction and lateral sreading, the key arameters in the analysis are not uniquely defined, but rather they may vary over a wide range of values. Methods for determination of the arameters and range of relevant values for the stiffness degradation β and ultimate soil ressures from the crust layer and liquefied layer, 1-max and -max resectively, have been resented. The relative significance of the arameters deends on the ile behaviour and is quite different for flexible iles and stiff iles. grous effects on key arameters need to be accounted for esecially because these effects are significant and the seudo-static analysis is commonly erformed using a single-ile model. REFERENCES Bowen, H., Cubrinovski, M. and Jacka, M. (7). Pseudo-static analysis of iles in liquefiable sand: a case study of a bridge foundation. Proc. 1 th Australia New Zealand Conference on Geomechanics. Cubrinovski, M. and Ishihara, K. (4). Simlified method for analysis of iles undergoing lateral sreading in liquefied soils. Soils and Foundations, 44(5) Cubrinovski, M., Kokusho, T. and Ishihara, K. (6). Interretation from large-scale shake table tests on iles undergoing lateral sreading in liquefied soils, Soil Dynamics and Earthquake Engineering, 6, Cubrinovski, M., Ishihara, K. and Poulos, H. (7). Pseudostatic analysis of iles subjected to lateral sreading, Secial Issue Bulletin of NZ Society for Earthquake Engineering (to be ublished). Ishihara, K, Yoshida, K. and Kato, M. (1997). Characteristics of lateral sreading in liquefied deosits during the 1995 Hanshin-Awaji earthquake, Journal of Earthquake Engineering, 1(1), Seed, R.B. and Harder, L.F. (1991). SPT-based analysis of cyclic ore ressure generation and undrained residual strength, H. Bolton Seed Memorial Symosium Proc., Vol., Tokimatsu, K. and Asaka, Y. (1998). Effects of liquefaction-induced ground dislacements on ile erformance in the 1995 Hyogoken-Nambu earthquake, Secial Issue of Soils and Foundations, Setember 1998: Youd, T.L., Hansen, M.C. and Bartlett, F.S. (). Revised multilinear regression equations for rediction of lateral sread dislacement, ASCE J. Geotech. & Geoenv. Engrg., 18(1),