PSEUDO-STATIC ANALYSIS OF PILES IN LIQUEFIABLE SOILS: PARAMETRIC EVALUATION OF LIQUEFIED LAYER PROPERTIES Hayden J. Bowen 1 and Misko Cubrinovski 2

Transcription

1 234 PSEUDO-STATIC ANALYSIS OF PILES IN LIQUEFIABLE SOILS: PARAMETRIC EVALUATION OF LIQUEFIED LAYER PROPERTIES Hayden J. Bowen 1 and Misko Cubrinovski 2 SUMMARY In this aer, seudo-static analysis of iles in liquefying soils is alied to a case study of a bridge foundation. The resonse of iles is searately evaluated for the cyclic hase during the intense shaking and develoment of liquefaction, and for the subsequent lateral sreading hase. With regard to the considerable uncertainties involved in redicting liquefaction and lateral sreading henomena the effects of key arameters influencing the ile resonse are examined through arametric analyses. Particular attention is given to the variation in stiffness and residual strength of the liquefied soil, the magnitude of lateral ground dislacement and the magnitude of inertial loads from the suerstructure. The results shed light on the relative imortance of key arameters for different combination of loads and ground conditions, and allow comarative evaluation between loads on the ile exerted by the crust layer and the liquefied layer. INTRODUCTION Pile foundations are rimarily designed to transfer vertical loads from the suerstructure to the bearing stratum. For this reason, iles are relatively vulnerable to lateral loads such as those imosed by ground shaking during strong earthquakes. In the case of soil liquefaction, this vulnerability is articularly ronounced since the loss of strength and stiffness in the liquefied soil results in a significant loss of lateral suort for the embedded iles. Soil liquefaction has caused major damage to ile foundations in revious earthquakes, articularly the 1964 Niigata (Hamada and O'Rourke 1992) and 199 Kobe (Cubrinovski et al. 21; Ishihara and Cubrinovski 1998; Ishihara and Cubrinovski 24; Jaanese Geotechnical Society 1998; Tokimatsu and Asaka 1998; Yasuda and Berrill 2) events. Two hases in the seismic resonse of iles in liquefied soil have been recognised: firstly a cyclic hase during the ground shaking and develoment of liquefaction, and secondly lateral sreading following the liquefaction. The soil-ile interaction in the cyclic hase is characterised by dynamic loads on the ile from both ground movements and inertial loads from the suerstructure. The lateral sreading hase rimarily occurs after the liquefaction has develoed and is characterised by large unilateral ground dislacements and relatively small inertial effects. During this hase the stiffness and strength of liquefied soils are very low, reflecting features of a comletely liquefied soil. The henomenon of soil liquefaction and lateral sreading is comlex and redictions of the seismic resonse of iles in liquefied soil are subject to a high level of aleatoric uncertainty. This suggests that when simlified analysis is erformed, the key consideration is not the modelling technique itself; rather it is dealing with the uncertainties in a sensible manner. Many simlified design orientated aroaches are available to analyse the seismic resonse of ile foundations (Cubrinovski and Ishihara 24; Cubrinovski and Ishihara 26; Cubrinovski et al. 26a; Liyanaathirana and Poulos 2; O'Rourke et al. 1994; Tokimatsu et al. 2; Wang and Reese 1998). In this aer a seudo-static analysis rocedure roosed in Cubrinovski et al. (26a) is examined, somewhat in detail. This analysis uses a beam sring model and can be erformed using common site investigation data such as the SPT blow count, yet it catures the basic mechanism of ile behaviour. Presented here are details of the adoted modelling technique and its alication to a case study of a bridge foundation in liquefiable soil. The key inut arameters of the model, namely the magnitude of alied free field ground dislacement, the degradation of soil stiffness and strength due to liquefaction and the magnitude of inertial load from the suerstructure are varied arametrically to identify imortant features of the resonse. The objectives of the aer are to determine how variations in these key arameters affect the soil-ile interaction and to emhasise the need to consider a wide range of values of inut arameters when simlified analysis is erformed. BEAM-SPRING MODEL Analytical Model The analytical model used in this aer is based on a simlified three layer model described in Cubrinovski and Ishihara (24) that consists of a non liquefiable crust layer, liquefied layers and a non-liquefied base layer. The original model used a closed form solution to solve a three layer roblem; here a more rigorous model was adoted where a finite element (FE) beam-sring model is used to incororate more comlex soil layering. Figure 1 shows the analytical model: the ile is modelled as a beam connected to a series of srings reresenting the lateral stiffness of the soil. The effects of liquefaction on the soil are accounted for by degrading the stiffness of the soil srings and limiting the lateral force in the liquefied layers. 1 Geotechnical Engineer, Tonkin and Taylor Ltd., Christchurch (Member). 2 Associate Professor, Deartment of Civil Engineering, University of Canterbury, Christchurch (Member). BULLETIN OF THE NEW ZEALAND SOCIETY FOR EARTHQUAKE ENGINEERING, Vol. 41, No. 4, December 28

2 23 a) Cross section b) Soil-ile model c) Numerical scheme Uer foundation U G U P Non-liquefied crust layer Lateral load Liquefied layers Degraded stiffness & strength Pile Free field ground dislacement Deformed ile Non-liquefied base layers Soil sring Pile The comlex dynamic forces alied to iles in liquefied soil are aroximated by the sum of two static loads alied to the ile: (1) Kinematic loads from the soil movement are alied through free field ground dislacements acting on a series of soil srings, as shown in Figure 1. These dislacements can reresent either cyclic ground dislacements or lateral sreading dislacements of liquefied soils. Note that these are free field ground dislacements unaffected by the resence or resonse of the ile foundation. (2) Inertial loads from the suerstructure are modelled as a lateral oint load alied at the ile head. It was adoted in the analysis that this load acts in the same direction as the alied ground dislacement. In the seudo-static analyses, the cyclic hase of the loading and subsequent lateral sreading hase were considered searately since the loads and soil conditions (stiffness and strength) are greatly different between these two hases. Inut Parameters The inut arameters of the model are summarized in Figure 2 for a three layer model configuration. Soil srings are reresented using bi-linear - relationshis, with an initial stiffness k and ultimate ressure max. Here reresents the relative dislacement between the ile and the soil. In liquefied soil layers the loss of stiffness is reresented by a degradation factor, β. The ile is modelled as a beam with diameter D o and a tri-linear moment-curvature (M-φ ) relationshi. The three oints on the M-φ curve corresond to the cracking, yielding and ultimate moments of the ile. The FE model allows comlex soil layering to be taken into account; changes in soil stiffness between layers and different ile diameters throughout the deth can be incororated easily into the model. The external loads on the ile are modelled using a lateral ground dislacement U G and an inertial load F. The ground dislacement alied to the ile can take any form throughout the soil rofile; U G reresents the maximum lateral ground dislacement at the to of the liquefied soil layer and also reresents the movement of the crust layer in the free field. Figure 1. Adoted model for simlified seudo-static analysis. Key Parameters and Uncertainties Cubrinovski and Ishihara (24) identified the following key arameters affecting the ile resonse: The stiffness and strength of the liquefied soils, β and 2-max The ultimate ressure exerted by the crust layer, 1- max The magnitude of the lateral ground dislacement, U G The inertial load alied, F The intrinsic uncertainties associated with iles in liquefiable ground are directly reflected on these key arameters. Therefore for the analysis of iles in liquefiable soil these arameters should not be uniquely determined; rather a range of values should be considered. For this reason a arametric study was erformed on a case study to examine how variations in these four key arameters affect the ile resonse. Surface layer Inertial load, F Liquefied layer(s) M Base layer(s) C Y Footing φ D o U Pile U G Ground dislacement k 1 β 2 k 2 1-max 3-max Figure 2. Inut arameters and characterisation of nonlinear behaviour for seudo-static analysis. k 3 2-max

3 236 + CPT * SPT North West N = 12-4 m thick liquefiable layer + Fitzgerald Avenue NORTH BANK + North East N = - 3 1m thick liquefiable layer * * ++ N River Road South West N = m thick liquefiable layer Kilmore Street ** + New ile + SOUTH BANK + * South East N = 17 - No liquefaction AVON RIVER Avonside Drive Figure 3. Plan view of the bridge site, showing site investigation locations and summary of enetration resistance results. CASE STUDY To illustrate the effects of variation in key arameters on the ile erformance, arametric studies were conducted on a case study of twin bridges crossing the Avon River in Christchurch, New Zealand. The Fitzgerald Avenue Twin Bridges cross the Avon River, carrying three lanes of southbound traffic on the east bridge and two lanes of northbound traffic on the west bridge. Both bridges are suorted by iled abutments on the banks with a central iled ier at the mid-san. According to the initial investigations, the existing iles were founded on otentially liquefiable soils. The bridges have been identified as an imortant lifeline for ost-disaster emergency services and recovery oerations. To avoid structural failure of the foundations or significant damage causing loss of function of the bridge in an anticiated earthquake event, a structural retrofit has been roosed by the Christchurch City Council. In conjunction with bridge widening, this retrofit involves strengthening of the foundation with new large diameter bored iles to be installed; the location of the new iles are shown schematically by the solid circles in Figure 3. The new iles will be connected rigidly to the existing foundation and suerstructure, and founded into deeer strata consisting of non-liquefiable soils. Soil Conditions Detailed investigations were conducted at several locations at the site using SPT and CPT, as indicated in Figure 3. The results of these field tests reveal the highly variable stratigrahy and enetration resistance of the investigated locations. Testing was conducted on the north and south banks of the river, at locations on both the east and west sides of the bridge and in between the two bridges. The site investigation data is summarised in Figure 3, showing the inferred range of SPT blow counts at the four corners of the bridge. The occurrence of liquefaction at the site was assessed based on the results of the in situ testing and by considering the ground shaking hazard. In general the soil on the north bank is looser and more suscetible to liquefaction than the soil on the south bank. 1 1 SPT MA2 SPT DT2 Assumed Footing Pile N= Sandy SILT Sandy N=12 GRAVEL N=14 SAND Silty N=8 SAND Silty N=1 SAND 2 N=3 SAND SPT blow count Liquefied layers Figure 4. Soil rofile, CPT and SPT results for the north east corner.

4 237 This is consistent with the assumed nature of soil deosition at the site; the north bank is on the inside of a bend in the river while the south bank is on the outside. As the river has rogressed soil has been eroded from the outside of bends and deosited on the insides, thus the soil on the inside of a bend is likely to have been laterally accreted in a low energy environment. The worst soil conditions were encountered at the North-East corner; the analysis in this aer is based on the soil roerties at this corner and hence reresents a conservative assessment. Here the soil between 2. m and 17. m is considered to be liquefiable, with layers of silty sand, sandy gravel, sandy silt and sand, with a dense sand base layer below 17. m deth. Figure 4 shows the results of SPT and CPT testing; the assumed soil rofile and SPT blow counts used in the analysis are also shown. From the CPT results at the north east corner, a fines content of aroximately 1% was inferred for the liquefiable soil. magnitude event on the strike-sli Porters Pass fault, which is located at a distance of about 4-6 km from the site. Stirling et al. (21) give the following eak ground acceleration values for Christchurch:.2g in a 1 year event.37g in a 47 year event and.47g in a 1 year event. With regard to the imortance level of the bridge as a lifeline, the loadings standard NZS117. requires an ultimate limit state (ULS) design seismic event with an annual robability of exceedance of 1/2, i.e. a 2 year event. This corresonds to a eak ground acceleration of.44g, as calculated in NZS117. based on the soil conditions and eriod of the structure. This is roughly in agreement with the above mentioned eak ground acceleration from Stirling et al. (21). BRIDGE FOUNDATION Figure shows a cross section of the east bridge; the abutments and iers are suorted by driven reinforced concrete iles connected to a reinforced concrete ile-ca at the river level. The existing iles are aroximately 1-11 m in length and.3 m in diameter. The central ier is suorted by 8 existing iles at D sacing; the abutments are suorted by four vertical iles and five raked iles at 4D sacing. The two bridges have identical foundations and the river level is aroximately 2. m below the road level. The roosed new iles will be founded at a deth below the exected deth of liquefaction and installed outside the existing ile ca. In conjunction with roosed widening of the bridge the ile ca will be extended and the new iles will be rigidly connected to the suerstructure. The new iles will be steel-encased reinforced concrete iles designed to carry the entire load from the existing bridge and any additional loads from the bridge widening. Shown in Figure are the roosed iles; they are 1.2 m in diameter under the abutments and 1. m in diameter under the central ier. Seismic Hazard Previous seismic hazard studies for Christchurch (Dowrick et al. 1998; Stirling et al. 21) indicate that the most significant contribution to the ground shaking hazard arises from a Determination of Material Parameters As the rocedure is a simlified, design orientated aroach, all inut arameters can be determined using emirical correlations with common site investigation data. The inut arameters can be divided into the four categories; soil roerties (k, max ), effects of liquefaction on the soil stiffness and strength (β, S u ), ile roerties (D, M-φ curve) and external loads (U G and F). Soil roerties The stiffness and ultimate ressure of the soil srings were evaluated using correlations with the SPT blow count, N. The stiffness was calculated by first evaluating the subgrade reaction coefficient, κ, using an emirical formula (Architectural Institute of Jaan 21): -3/4 κ = 6 (N 78 ) D o [MN/m 3 ] (1) where N 78 is the SPT blow count corresonding to 78% of the theoretical free fall energy and D o is the ile diameter in cm. The stiffness, k, is then evaluated by the formula k = κ D l (2) where l is the sacing between nodes or the length of the beam element used in the FE analytical model. The ultimate ressure, max, exerted by the soil on the ile in non-liquefied soil is given by the exression Bridge deck 2m 2.m River level Existing reinforced concrete iles D =.3m 1-11m Proosed new iles D = 1.2m D = 1.m Not to scale Figure. Bridge cross section showing existing iles and roosed new iles.

5 238 max = α u (z) (3) where (z) is the Rankine assive ressure as a function of deth and α u is a factor introduced to account for the difference in lateral ressure between a single ile and an equivalent wall. Note that α u may take a value as high as 4. in the non-liquefied crust. The Rankine assive ressure is calculated as ( z) = σ ' (4) K v where σ v is the vertical effective stress and K is Rankine assive earth ressure coefficient calculated as (Hatanka and Uchida, 1996) K = tan 2 (4 + φ 2) () where φ can be estimated, for examle as φ = 2 + (2N (6). 1 (78) ) The SPT blow count normalised to an effective overburden stress of 98 kpa ( N ) can be calculated using the exression 1 of Liao and Whitman (1986) N 1 98 = N ' σ v. Note that the SPT blow count corresonding to 78% energy of the theoretical free fall energy is given by (7) 6 N 78 = N (8) 6 78 Here N 1(6) is an SPT blow count normalised for the effective overburden stress corresonding to 6% energy of the theoretical free fall energy, where N (6) is an SPT blow count corresonding to 6% of the theoretical free fall energy. Effects of liquefaction on soil stiffness and strength In liquefied soil the stiffness k is degraded by a factor β which is less than one. With reference to case studies and exerimental tests (Cubrinovski et al. 26b; Ishihara and Cubrinovski 1998; O'Rourke et al. 1994; Orense et al. 2; Tokimatsu et al. 2; Yasuda and Berrill 2), the stiffness degradation of liquefied soils can be assumed to vary between β = 1/1 and 1/ for the cyclic hase cases, and between β = 1/ and 1/1 for lateral sreading cases. The rediction of the liquefied soil stiffness is very difficult and deends on many factors, including the density of the soil, develoment of excess ore ressures, the magnitude and rate of ground dislacement and the drainage conditions. Furthermore, full scale shake table tests (Cubrinovski et al. 26b) show that the stiffness of liquefied soils varies considerably during the course of both the cyclic and lateral sreading hases. The ultimate ressure exerted on the iles from the liquefied soil is also subject to uncertainty. The interaction in the liquefied layer can be treated in a simlified manner by an equivalent linear - relationshi with a degraded stiffness and no limiting ultimate ressure. Alternatively and more rigorously, a limit can be laced on the ressure exerted by the liquefied soil. The aroach used herein is to define the ultimate ressure from the liquefied layers, 2-max, using the undrained or residual strength of the sandy soils, S u. Here S u is evaluated from emirical correlation with SPT value originally roosed by Seed and Harder (199) as shown in Figure 6. The data in this figure were back calculated from case history observations during revious earthquakes in which flow slides occurred. Post-earthquake static stability analyses were conducted by many researchers (Idriss and Boulanger 27; Olson and Stark 22; Seed 1987; Seed and Harder 199) investigating liquefaction flow slides; the undrained shear strength was estimated by back calculating a value of S u based on the deformed geometry after the event. Hence in this lot, each oint reresents the estimate of S u for one case history. Since the scatter of the data is quite significant, an uer (S u-ub ) and lower bound ( ) values as indicted in Figure 8 were used to cover the range of values. Table 1 summarises the soil roerties used in the analysis of cyclic and lateral sreading cases, as calculated according to the exressions and rocedures outlined above. Pile roerties The yielding, cracking and ultimate oints of the ile were calculated by assuming that the concrete and reinforcing steel are elastic-erfectly lastic materials with bi-linear stress strain relationshis. By secifying the ile cross section and characteristics (dimensions, area and osition of reinforcement, Young s modulus and strengths of materials, restress level, axial force) the tri-linear moment curvature relationshi of the ile was calculated. The three oints are defined as follows: Table 1. Soil roerties used in arametric study Descrition Stiffness, k (kn/m) Cyclic hase Lateral sreading β lb =1/1 β ub =1/ β lb =1/ β ub =1/1 Ultimate ressure, 2-max (kpa) 1 Crust layer 183 K = Sandy SILT Sandy GRAVEL SAND Silty SAND Silty SAND SAND S u-ub

6 239 Residual strength of liquefied soil, S u (kpa) Seed (1987) Seed and Harder (199) Olson and Stark (22) Uer bound S u-ub 1 Lower bound Figure 6. Equivalent clean sand corrected SPT blowcount, (N 1 ) 6cs Emirical chart used to evaluate ultimate ressure exerted by liquefied soil through undrained shear strength (after Idriss and Boulanger 27). (1) Cracking is the oint where the tensile stress in the concrete exceeds the concrete tensile strength. (2) Yielding is the oint where the stress in the reinforcement exceeds the yield level. (3) Ultimate is the oint where comressive strain in the concrete exceeds the ultimate concrete comressive strain level, usually in the range between.2 and.3. The moment curvature relationshi for the new 1.2m diameter ile was calculated assuming 3 MPa concrete, MPa steel reinforcement at a.8% longitudinal reinforcement ratio and a 1 mm thick steel casing with a strength of 2 MPa. The axial loads on the iles are reliminary estimates; Figure 7 shows the calculated M-φ relationshis for both the serviceability limit state (SLS) and the ultimate limit state (ULS) axial loads to give an indication of the effect of increasing axial load on the ile bending caacity. For consideration of the seismic resonse an axial load of 16 kn was used. This axial load is a reliminary estimate only, based on the likely bridge weight and traffic loading. External loads Two external loads are alied to the ile: an inertial force at the ile head and a ground dislacement. The level of inertial load alied at the ile head can be calculated as the ground acceleration times the tributary mass of the suerstructure taken by the ile. The level of acceleration can either be the eak ground acceleration or a lesser value. For the ile at the north east corner, the maximum inertial load considered was calculated as the tributary suerstructure mass of 16 kn multilied by the eak ground acceleration of.44g giving a maximum inertial load of 74 kn. In the analysis the lateral ground dislacement can reresent either cyclic dislacements during the shaking hase or a ermanent dislacement at the end of the sreading hase. Lateral sreading dislacements were modelled as having a cosine distribution throughout the liquefied layers, with a dislacement at the ground surface, U G, describing the magnitude of the ground movement. Many emirical methods exist for redicting this dislacement (e.g. Ishihara et al. 1997; Bending moment, M (MN-m) Figure Axial load = 14kN Axial load = 28kN D = 1.2m ile C Y Axial load = 16kN M (MN-m) Curvature, φ U φ Cracking Yielding Ultimate Moment curvature relationshi for the new 1.2 m ile. Tokimatsu and Asaka 1998; Youd et al. 22) however it is very difficult to make an accurate rediction. The magnitude of lateral sreading at the north east corner was redicted using the method of Youd et al. (22). A free face height of 2. m was assumed, and a dislacement of 2.2 m was calculated at the riverbank. Due to the considerable uncertainty in redicting the ground dislacement Youd et al. suggest a factor of 2 be used for dislacements redicted using their model to cover the range of exected values. With this in mind, and considering the large differences between different emirical methods, a wide range of values were considered in the arametric study. Maximum cyclic ground dislacements in liquefied soils during the cyclic hase were estimated using a simlified rocedure described in Tokimatsu and Asaka (1998). The rocedure is based on observations from revious earthquakes, where cyclic shear strains in liquefied soil layers were evaluated from analysis of strong motion records and detailed surveys of iles in level ground and then lotted against SPT value, as shown in Figure 8. The chart is essentially equivalent to the conventional SPT-based charts for evaluation of liquefaction; the cyclic stress ratio τ av σ ' on the y-axis is vo calculated using the standard method of Seed and Idriss (Youd et al. 21). To estimate the cyclic ground dislacement, for each liquefied soil layer the cyclic shear strain is first evaluated using the chart. Then, these strains are integrated throughout the soil rofile to obtain a cyclic ground dislacement rofile. Shown in Figure 8 is the calculation of the induced cyclic shear strain for a soil layer with a corrected SPT blow count for clean sand of N 1(6)cs =14 and a cyclic stress ratio of τ av σ ' vo =.43. Note that the SPT blow count in Figure 8 imlicitly corresonds to 78% of the theoretical free fall energy, even though data from 6-78% have been used in the derivation of the lot. In view of the differences in the correction of the blow count for the effects of fines and highly aroximate nature of the lot, it is considered aroriate to use this lot without correcting the blow count with the energy ratio. For the North-East corner soil rofile, Figure 9 shows the maximum shear strains and corresonding maximum cyclic horizontal ground dislacements calculated using the rocedure described above.

7 24.6 Stress ratio, τ av /σ vo ' γ cy = 4% 2% 1%.% Deth (m) (a) (b) Figure Corrected SPT blow count N 1-cs Emirical chart used to evaluate cyclic ground dislacements through induced shear strains (after Tokimatsu and Asaka 1998). Shown is the shear strain evaluated for a soil layer with (N 1 ) 6cs =14 and τ av / σ vo =.43. PARAMETRIC STUDY Shear strain (%) Ground dis. (m) Figure 9. Liquefaction induced cyclic ground deformation: (a) maximum cyclic shear strains, (b) maximum cyclic ground dislacement rofile. roerties of the ile were used in the lateral sreading analysis. Overview The seismic resonse of the roosed 1.2 m diameter ile at the north-east corner is evaluated using the seudo static aroach described reviously. The identified key arameters are varied to account for uncertainties in the analysis; this is to gain insight into how variations in these arameters affect the analysis results. In all analyses the roerties of the ile, the crust and base soil layers were ket constant. The two hases in the resonse, the cyclic hase and lateral sreading, were treated searately. In cyclic hase analyses, an inertial load was alied at the ile head in addition to the ground dislacement shown in Figure 9b. In contrast, the lateral sreading cases have no inertial load and the ground dislacement has a cosine rofile throughout the liquefied layers with a magnitude U G at the to of the liquefied layer. Lateral sreading cases with reduced inertial loads were also considered but are not discussed herein. Note that a otential damage to the ile caused during the cyclic hase was not considered in the analysis of the subsequent lateral sreading hase. In other words, in this simlified interretation, intact Tyical Results In order to demonstrate key features of the ile resonse, one analysis case is described in detail. Figure 1 shows the results of a lateral sreading analysis, where the magnitude of free field ground dislacement was one metre, and relatively high degradation of stiffness and strength was used with β = 1/1 and 2-max = (which corresonds to a range of 2-17kPa throughout the liquefied layers). Figure 1a shows the comuted bending moment distribution with reference to the cracking, yielding and ultimate moments of the ile. It can be seen that the maximum moments occur at the ile head and at the interface between the liquefied and base layers, and that the bending moment exceeds the yield level at the ile head. Figure 1b shows the ile dislacement comared to the free field ground dislacement. The ile exhibits behaviour tyical of stiff iles, and resists the large lateral movement of the surrounding soils. The resulting relative dislacement between the soil and the ile is therefore quite large as shown in Figure 1c. Deth (m) 1 1 M c M y M u (a) 2 M u M y M c Bending moment (MN-m) 1 1 (b) 2 Pile Ground Dislacement (m) 1 1 Soil yielding (c) 2 Rel. dis. Yield dis Dislacement (m) Figure 1. Results of tyical analysis showing the ile resonse to a lateral sreading dislacement of one metre: (a) bending moment versus deth lot; (b) ile and ground dislacements; and (c) relative dislacement between the soil and ile comared to the soil yield dislacement.

8 241 Figure 11. Deth (m) 1 1 Flexible ile behaviour (a) Uer 2 Lower Ground Dis. (m) Inertial load.44g (b) Distributed load (kn/m) 1 1 (c) 2 M umym M c M y M u 2 c Bending moment (MN-m) Uer bound β ub =1/1 (d) Lower bound β =1/ lb Variation of ile resonse due to liquefied layer roerties for a cyclic hase case with a large inertial load, showing ile dislacement, distributed load on the ile and ile bending moment. S u-ub Figure 12. Deth (m) 1 1 Stiff ile behaviour (a) Uer 2 Lower Ground Dis. (m) (b) Dist. load (kn/m) Uer bound M β =1/ (c) u ub S M u-ub y 1 M c (d) 1 Lower bound 2 M β =1/1 S u lb u-lb M y M 2 c Bending moment (MN-m) Variation of ile resonse due to liquefied layer roerties for a lateral sreading case with U G = 1 m, showing ile dislacement, distributed load on the ile and ile bending moment. The dashed line in this figure indicates the relative dislacement y at which yielding occurs in the soil or the dislacement at which 2-max has been reached in the bi-linear relationshi. Hence the shaded areas indicate arts of the soil rofile where the relative dislacement exceeds the yield level of the soil; here the ressure acting on the ile has reached the maximum level as defined by the - relationshi. Degradation of Liquefied Soil Stiffness and Strength Due to the uncertainty of the effect of liquefaction on the soil stiffness and strength, analyses were conducted using two - relationshis, an uer bound and lower bound - curve. In this way two extremes of liquefied soil stiffness and strength were considered, with the uer bound - curve combining, for lateral sreading cases, a stiffness degradation of β = 1/ and 2-max = S u-ub. Conversely, the lower bound - curve was defined by β = 1/1 and 2-max =. For the cyclic cases the uer bound - curve was defined using β = 1/1 and 2- max = S u-ub ; the cyclic lower bound - curve used β = 1/ and 2-max =. Effects on stiff and flexible iles For both cyclic and lateral sreading hases the ile behaviour deends on the stiffness of the ile relative to the liquefied or dislacing soil. Relatively flexible iles move together with the lateral ground dislacement; whereas relatively stiff iles resist the movement of the surrounding ground. Therefore to evaluate the effects of different liquefied soil roerties on the ile resonse two cases need to be analysed corresonding to the stiff and flexible behaviour resectively. Needless to say, the stiff ile behaviour is more relevant to design, because the flexible ile behaviour often rovides unaccetable erformance due to the excessive lateral dislacements of the ile and hence the suerstructure. Figure 11 shows the ile resonse for a cyclic hase analysis where a large inertial load corresonding to.44g was alied at the ile head in addition to the maximum cyclic ground dislacement shown in Figure 9b. Two cases are shown corresonding to the uer bound and lower bound bi-linear - curves, shown in Figure 11d. Figure 11a shows that for both cases of degradation the ile acts in a flexible manner with little relative dislacement between the ile and the soil. It can be seen that desite differences in the forces acting on the ile from the liquefied layers the bending moments and ile dislacements are very similar. This suggests that for this flexible ile behaviour the liquefied layer does not have a large bearing on the ile resonse as the ile behaviour is governed by the large inertial load. Note that due to the small relative dislacement between the soil and the ile, the full assive ressure of the crust layer has not been mobilised in this case.

9 242 Deth (m) Su-ub Su-lb Ground Dis. (m) Figure M c M y M u 2 M u M y M 2 c -1-1 Bending moment (MN-m) Pile resonse for a lateral sreading case with U G =.m and β = 1/, showing the effects of ultimate ressure from the liquefied soil. Deth (m) = S 2-max u-ub Dis. (m) Soil yielding max = S u-lb Dis. (m) Rel. dis. Yield dis. Figure 14. Comarison of relative and yield dislacements comuted in analyses with 2- max = and 2-max = S u-ub In contrast, Figure 12 shows the results of a lateral sreading analysis with different liquefied soil roerties and no inertial load. Here, both cases of uer bound and lower bound - curves show stiff ile behaviour, as such the large relative dislacements between the ile and the soil result in the liquefied soil roerties having a significant effect on the ile resonse. For the uer bound liquefied - relationshi the forces from the liquefied soil are larger, resulting in larger ile dislacements and bending moments than those observed for the lower bound - curve. Because of the large relative dislacements, in both cases stiff ile behaviour was observed, resulting in full mobilisation of the assive load from the nonliquefied crust soil. In the absence of a large inertial load, the ile exhibited stiffer behaviour and the loads from the crust and liquefied layers had a larger effect on the ile resonse. Effect of ultimate ressure, 2-max To examine how the ultimate ressure exerted by the liquefied soil on the ile affects the ile resonse, two analyses were conducted on a lateral sreading case with U G =. m and β at 1/. Figure 13 shows the comuted ile resonse for cases where (a) the ultimate ressure was limited to 2-max = (in the range of 2 17 kpa), and (b) 2-max = S u-ub (28 43 kpa). It can be seen that adoting 2-max = S u-ub for the ultimate ressure in the liquefied soil results in more flexible behaviour and higher bending moments than the 2-max = case. These observations can be exlained by considering the relative dislacements between the soil and the ile for both cases. Figure 14 shows the relative dislacement between the soil and the ile lotted with the soil yield dislacement for the two cases. It can be seen that the lower bound S u case has low yield dislacements and high relative dislacements, whereas the uer bound S u case has higher yield dislacements and lower relative dislacements. A large art of the soil rofile has yielded with the lower bound case of 2-max =, thus the ressure is limited to for a large length of the ile in this case. Forces from the crust soil and liquefied soil In the case of stiff ile behaviour, the soil ressure from the crust and liquefied layers rovide a driving force, while the non-liquefied base layer rovides a resisting force. With changes in the liquefied soil stiffness and strength the forces alied to the ile from both the crust and liquefied layers change. To quantify these changes lateral sreading analyses were conducted using U G =. m with the ultimate ressure in the liquefied layer given by 2-max = S u-ub or 2-max =. In both cases the stiffness degradation β varied from 1/ to 1/1 and the total force on the ile, including contributions from the crust and liquefied layers, was calculated and lotted against β as shown in Figure 1. It was observed that all cases exhibited stiff ile behaviour; the iles in general resisted the ground movement and the bending moments exceeded the yield level at the ile head. It was observed that the total load from the crust layer remained the same regardless of β or S u. This is because the large relative dislacements between the stiff ile and the soil caused the entire crust layer to yield. For the 2-max = S u-ub case shown in Figure 1a the load from the liquefied layer increases with increasing β, when β = 1/ (.2) the load from the liquefied layer is as large as the load from the crust layer. Figure 1b shows the case where 2-max = was used; here the load from the liquefied layer is limited by the lower bound ultimate ressure from the liquefied soil. The same analysis was reeated for a ile with a diameter of.6 m to examine the interaction between the crust and liquefied layer loads for more flexible iles. For all these cases flexible behaviour was observed and the ile moved together with the ground; the bending moment reached the ultimate level at the ile head. Figure 16 shows the contribution of loads for the flexible ile cases. Here the load from the crust layer is much smaller than that for the stiff ile cases, and decreases with increasing β. This is because a large β value results in smaller relative dislacement between the ile and the soil and hence a lower load from the crust layer. The load from the liquefied layer increases with increasing β, and the combined loads from the crust and liquefied soil result in an increase in the total load as β increases. Effect of horizontal ground dislacement For stiff iles undergoing lateral sreading, it is interesting to determine how the magnitude of horizontal ground dislacement alied, U G, affects the ile resonse. As the rediction of lateral sreading dislacement is very difficult, and considering the variation in emirical rediction methods, the aroach taken here is to consider a wide range of lateral sreading dislacements. Figure 17 shows the comuted maximum ile dislacements for cases with β = 1/ and U G =., 1, 2 and 3 m.

10 243 Figure 1. Force (kn) U G =.m, S u-ub D = 1.2m Liquefied layer Crust layer β Force (kn) U G =.m, D = 1.2m Liqufied layer Crust layer β.1.2 Force alied to stiff iles from the crust and liquefied layers as a function of the stiffness degradation due to liquefaction, β. Force (kn) U G =.m, S u-ub D =.6m Crust layer Liquefied layer β.1.2 Force (kn) U G =.m, D =.6m Crust layer Liquefied layer β.1.2 Figure 16. Max. ile dislacement (m) Figure Force alied to flexible iles from the crust and liquefied layers as a function of the stiffness degradation due to liquefaction, β Equivalent linear analysis β = 1/ Analysis with S u-ub.m 1m 2m 3m Analysis with Variation of maximum ile dislacements with alied lateral ground dislacement for different values of ultimate ressure from the liquefied soil. Results are calculated using three different - curves for the liquefied soil; one without ultimate ressure in the liquefied soil (equivalent linear case), while the other two cases use 2- max = S u-ub and 2-max = to limit the ultimate ressure. For the equivalent linear case the ile dislacement increases with increasing ground dislacement and the ile exhibits flexible behaviour. The equivalent linear cases redicted flexible behaviour and very large values of ile bending moment; at U G = 3 m the bending moment is well in excess of the ultimate moment of the ile. This result is unrealistic because the ultimate load from the liquefied soil exceeded any reasonable limit. Therefore the more rigorous - curves with a limit on the ultimate ressure are necessary for cases with large relative dislacements between the soil and the ile. In contrast, when limits are laced on the ultimate ressure in the liquefied soil, stiff ile behaviour is observed, and the magnitude of ground dislacement has virtually no effect on the ile resonse. This observation is hardly surrising given that in these cases the alied ground dislacement is sufficient to cause the vast majority of the soil rofile to yield, thus for these cases the same lateral load corresonding to the limiting ressure is being exerted on the ile. The above behaviour suggests that for a given ile a critical magnitude of U G exists above which any increase in lateral ground dislacement will have no effect on the ile resonse. In order to scrutinise this, a series of analyses were conducted with different values of alied ground dislacement U G using different values of β and 2-max.The results of these analyses are shown in Figure 18, which lots the calculated ile dislacement against the value of U G alied in the analysis. Figure 18 shows that this threshold ground dislacement exists; as the alied lateral ground dislacement is increased a certain level is reached above which any further increase in the dislacement has no effect on the ile resonse. It is also aarent that this critical value deends on the stiffness degradation constant β and the ultimate ressure 2-max. Figure 19 lots this threshold value against β, where U G-threshold is defined as the alied ground dislacement that results in a ile dislacement which is 9% of the ile dislacement calculated using a very large ground dislacement. Quantitatively, for the 2-max = S u-ub case, this is defined as.37m, which corresonds to 9% of.39 m, the ile dislacement calculated using a U G value of m. The critical value decreases as β is increased and is U G-threshold =.6 m and 2.3 m for β = 1/ and 1/ resectively. It is aarent from Figure 18 that U G-threshold is much smaller in the 2-max = cases.

11 244 Pile dislacement (m) β=1/ (a) β=1/ β=1/1 β=1/2.12 β=1/1 = S 2-max u-ub Alied lateral ground dis., U G (m) Pile dislacement (m) β=1/ 2-max = S u-lb (b).12 β=1/ β=1/1 β=1/2 β=1/ Alied lateral ground dis., U G (m) Figure 18. Plot of maximum bending moment versus alied ground dislacement for different values of β. Figure 19. Threshold ground dis., U G-threshold (m) /1 1/ 2-max = S u-ub 1/2 1/1 1/ Stiffness degradation constant, β Critical ground dislacement above which any further increases in U G have no effect on the ile resonse lotted against stiffness degradation in the liquefied soil. To illustrate the imlications of Figure 19, suose a β value of 1/1 was assumed. Figure 19 indicates that for any value of ground dislacement greater than.8 ractically the same ile resonse will be obtained when 2-max = S u-ub is used. In other words, the accuracy in evaluating U G is not relevant if the value of.8 m could be exceeded. Effect of loads at the ile head In the seudo static analysis rocedure two loads are alied at the to of the ile; a oint load reresenting the inertial loads from the suerstructure, and a distributed load from the assive ressure exerted by the crust layer on the footing. Both these loads can vary in magnitude. The assive ressure exerted on the ile by the non-liquefied crust is generally only fully mobilised once a certain yield dislacement in the soil is reached. Consequently flexible iles with small relative dislacements will exerience a smaller load when comared with a stiff ile where the full assive ressure has been mobilised in the crust layer. The level of inertial load alied at the ile head is generally calculated using the eak ground acceleration and tributary mass for the ile. Analysis during the cyclic hase considers the ile resonse when the ground dislacement is at a maximum; however the maximum inertial load is not necessarily being alied at the same time. Large-scale shaking table tests (Tokimatsu et al. 2) and dynamic finite element analyses (Chang et al. 2) have indicated that inertial loads and cyclic ground dislacements act in hase when the natural eriod of the suerstructure is less than that of the ground. Nevertheless there is a need to examine how variations in the combination of the inertial and crust loads affect the ile resonse. The effects of loads at the ile head have a large effect on the ile resonse; large loads can cause the ile to act in a flexible manner, while stiffer behaviour can be observed with no inertial load alied. Thus, it is interesting to examine the effect that loads alied at the ile head have on the resonse of iles. The combination of inertial and crust layer loads can be discussed with reference to the total load alied at the ile head, as both loads act at ractically the same location they roduce similar effects on the ile resonse. Cyclic hase analyses with different loads at the ile head were conducted to determine how the addition of these two loads affects the ile behaviour. Six combinations of loads were analysed, corresonding to Three cases with inertial loads equivalent to eak ground accelerations of.44g,.22g and g using the original soil rofile, and Three cases with the same inertial loads as above but using a soil rofile without a crust layer. As before, analyses with uer and lower bounds of - relationshis for the liquefied soil were conducted, the loads from the crust layer and the inertial loads for all twelve analysis cases are summarised in Table 2. The maximum load from the crust layer is 49 kn; this is observed in cases where the relative dislacement between the soil and the ile is large enough to cause all of the crust layer to yield. Figure 2 shows the results of these analyses, where the eak ile dislacements and bending moments were lotted against the total load at the ile head for both uer and lower bounds of liquefied soil stiffness and strength. Table 2. Combinations of loads alied at the ile head Acc (g) Crust load (kn) Total load (kn) Crust layer No crust Inertial load (kn) Uer bound β=1/1 S u-ub Lower bound β=1/ Uer bound β=1/1 S u-ub Lower bound β=1/ * 49* *corresonds to the maximum load from the crust layer

12 24 Figure 2. Max. ile dis. / Max. ground dis Flexible ile behaviour Stiff ile behaviour.2 Uer bound Lower bound Combined load at the ile head (kn) Max. ile bending moment (MN-m) M u Combined load at the ile head (kn) Effect of total load alied at the ile head on the eak ile dislacements and bending moments for different combinations of inertial and crust layer loads, considering both relatively stiff and relatively soft liquefied soils. Figure 2a shows the ratio of maximum ile dislacement to the maximum free field ground dislacement lotted against the total load at the ile head for both the uer and lower bound cases. It can be seen that both cases show flexible ile behaviour (ratio aroaches one) when large loads are alied and stiff ile behaviour (ratio aroaches zero) when relatively small load is alied. However the transition between stiff and flexible differs between the uer and lower bound cases adoted in the analysis. For cases with the uer bound liquefied stiffness and strength, flexible behaviour occurs at loads that are aroximately 3% less than the lower bound cases; in other words, stiffer liquefied soil results in more flexible behaviour of the ile. For the case where no inertial load is alied (the total ile load is the 49 kn from the crust layer), the uer bound case has a ile dislacement twice as large as the lower bound case. These features are also observed in the maximum ile bending moments shown in Figure 2b. When considering lateral sreading cases stiff ile behaviour is redominately observed. This is reasonable as the liquefied soil must have relatively low stiffness and strength in order for lateral sreading to occur. Due to this stiff behaviour, the relative dislacement in the crust layer is likely to be large; thus the crust soil will be yielding and the maximum ressure from the crust layer will always be alied. As inertial loads during this hase are likely to be small, when evaluating the total load at the ile head attention should be focussed to considerations of variations in the assive load from the crust layer. CONCLUDING REMARKS Simlified analysis of ile foundations in liquefied soil is burdened by many uncertainties. In this aer a case study is resented where a arametric study was conducted to determine the effects of these uncertainties on the ile resonse. Key findings include: The effect that the stiffness and ultimate strength of liquefied soil have on ile resonse deends on the behaviour of the ile under loading; flexible iles have small relative dislacements hence the liquefied soil roerties and ultimate ressure from the crust layer have little effect, in contrast to stiff iles with large relative dislacements. For stiff iles, the level of stiffness and strength degradation due to liquefaction adoted in the analysis had a large effect on the ile resonse. When lower bound values of stiffness and strength were adoted the ile showed smaller lateral dislacements and bending moments as comared to those obtained in the analysis with uer bound values. Using equivalent linear - relationshis in the liquefied layers have been shown to redict overly conservative bending moments in cases where the liquefied soil is relatively stiff and the relative dislacements are large. A more aroriate aroach is to use a bi-linear - relationshi for the liquefied soil where the ultimate ressure is limited to the undrained residual strength of the soil. For stiff iles undergoing lateral sreading, there exists a threshold magnitude of lateral ground dislacement above which any further increase in the ground dislacement has no effect on the ile resonse. This threshold value deends on the stiffness and strength of the liquefied soil. Increasing the load at the ile head may lead into a transition from stiff to flexible ile behaviour. This transition occurs earlier in relatively stiff liquefied soils. In the design of ile foundations in liquefiable soil, stiff ile behaviour is desired. Flexible iles suffer large ile dislacements and often fail in bending, thus the arameters that are most imortant for design are those that affect stiff iles. The arametric study described in this aer suggests that the choice of liquefied soil roerties adoted in design have a large bearing on the comuted resonse for stiff iles. In contrast it was shown that once a certain magnitude of ground dislacement has been reached further increases in ground dislacement have no effect. Therefore in design threshold ground dislacement needs to be evaluated first and then accordingly attention should be aid to the effects of the crust layer and the liquefied soil roerties. The study also showed the imortance of inertial loads, as the magnitude of inertial load alied has a large effect on the relative ile dislacements and hence resonse of the ile. REFERENCES Architectural Institute of Jaan. (21). Recommendations for the Design of Building Foundations. Chang, D., Boulanger, R. W., Brandenberg, S. J. and Kutter, B. L. (2). "Dynamic analysis of soil-ile-structure interaction in laterally sreading ground during earthquake shaking." ASCE Geotechnical Secial Publication 14,