Evaluation of Seismic Performance of Geotechnical Structures

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provided by UC Research Repository Evaluation of seismic performance of geotechnical structures

M. Cubrinovski University of Canterbury, Christchurch, New Zealand B. Bradley University of Canterbury, Christchurch, New Zealand

ABSTRACT: Three different approaches for assessment of seismic performance of earth structures and soil- structure systems are discussed in this paper. These approaches use different models, analysis procedures and are of vastly different complexity. All three methods are consistent with the performance-based design philosophy according to which the seismic performance is assessed using deformational criteria and associated damage. Even though the methods nominally have the same objective, it is shown that they focus on different aspects in the assessment and provide alternative performance measures. Key features of the approaches and their specific contribution in the assessment of geotechnical structures are illustrated using a case study.

1 INTRODUCTION The assessment of seismic performance of geo- Methods for assessment of the seismic performance technical structures is further complicated by uncer- of earth structures and soil-structure systems have tainties and unknowns in the seismic analysis. Par- evolved significantly over the past couple of dec- ticularly significant are the uncertainties associated ades. This involves improvement of both practical with the characterization of deformational behaviour design-oriented approaches and advanced numerical of soils and ground motion itself. Namely, the com- procedures for a rigorous dynamic analysis. In paral- monly encountered lack of geotechnical data for lel with the improved understanding of the physical adequate characterization of the soil profile, in-situ phenomena and overall computational capability, soil conditions and stress-strain behaviour of soils new design concepts have been also developed. In results in uncertainties in the modelling and predic- particular, the Performance Based Earthquake Engi- tion of ground deformation. Even more pronounced neering (PBEE) concept has emerged. In broad are the uncertainties regarding the ground motion terms, this general framework implies engineering (earthquake excitation to be used in the analysis) evaluation and design of structures whose seismic arising from the inability to predict the actual ground performance meets the objectives of the modern so- motion that will occur at the site in the future. ciety. In engineering terms, PBEE specifically re- The above uncertainties affect key elements in quires evaluation of deformations and associated the analysis, the input load (ground motion or earth- damage to structures in seismic events. Thus, the quake load) and constitutive model (stress-strain key objective in the evaluation of the seismic per- curve or load-deformation relationship). Clearly, the formance is to assess the level of damage and this in output of the analysis will be adversely affected by turn requires detailed evaluation of the seismic re- these uncertainties and would therefore require care- sponse of earth structures and soil-structure systems. ful interpretation. One may argue that, strictly Clearly this is an onerous task since the stress-strain speaking, a prediction of the seismic response is not behaviour of soils under earthquake loading is very possible under these circumstances; instead, the aim complex involving effects of excess pore-water pres- should be an assessment of the seismic performance. sures and significant nonlinearity. The ground re- This argument is not in the realm of semantics, but it sponse usually involves other complex features such rather implies difference in philosophy. It alludes to as: the importance of the process and engineering inter- - Modification of the ground motion (earth- pretation rather than the outcome alone, which is in quake excitation for engineering structures) agreement with the traditional role that engineering - Large ground deformation and excessive per- judgement has played in geotechnical engineering. manent ground displacements In this paper, three approaches for assessment of - A significant loss of strength, instability and seismic performance are applied to a case study of a ground failure, and bridge on pile foundations. Conventional methods of - Soil-structure interaction effects. seismic analysis are used in the assessment and comparatively examined. Key features in the imple- Simple Advanced Other methods SEISMIC EFFECTIVE PSEUDO-STATIC ANALYSIS STRESS ANALYSIS - Equivalent static analysis - Dynamic time-history analysis

Figure 1. Methods for seismic analysis of earth structures and soil-structure systems mentation of the methods, their advantages and dis- Despite its complexity, the seismic effective stress advantages are discussed. It is demonstrated that the analysis is now frequently used in geotechnical prac- examined approaches focus on different aspects and tice for assessment of the seismic performance of make different contribution in the assessment. important structures. As indicated in Figure 1, a large number of alternative analysis methods are available in the range between these two benchmark 2 METHODS FOR ASSESSMENT OF SEISMIC approaches. PERFORMANCE 2.1 Analysis methods 2.2 Deterministic versus probabilistic approaches There are various approaches for seismic analysis of Generally speaking, the seismic response can be earth structures and soil-structure systems ranging evaluated either deterministically or probabilisti- from relatively simple approximate methods to very cally. Figure 2 illustrates the three approaches scru- rigorous but complex analysis procedures. These tinized in this study in this regard: (i) Deterministic approaches differ significantly in the theoretical ba- approach (DA) in which a single scenario is consid- sis, models they use, required geotechnical data and ered; in this case, only one analysis is conducted and overall complexity. The simplest methods are based respectively a single response of the system is com- on the pseudo-static approach in which an equiva- puted; (ii) Deterministic approach (DAP) in which a lent static analysis is used to estimate the dynamic series of analyses are conducted in a parametric response induced by the earthquake. The pseudo- manner in order to account for the uncertainties and static analysis is based on routine computations and unknowns in the analysis; as indicated in Figure 2, use of relatively simple models, and hence is easy to this approach results in a range of different re- implement in practice. For this reason, it is the com- sponses for the analyzed system; (iii) Probabilistic monly adopted approach in seismic design codes. approach (PA) in which “all possible” earthquake On the other hand, the most rigorous analysis proce- scenarios are considered for the site in question; this dure currently available for evaluation of the seismic approach also results in a range of different re- response of soil deposits and earth structures is the sponses for the system and, in addition, provides an seismic effective stress analysis. This analysis per- estimate for the likelihood of each response. mits detailed evaluation of the seismic response The key difference between these three ap- while considering the complex effects of excess pore proaches is in the treatment of the uncertainties. The water pressures and highly nonlinear behaviour of deterministic approach with a single scenario (DA) soils in a rigorous dynamic (time history) analysis. effectively ignores the uncertainties in the analysis

DETERMINISTIC (DA) Single scenario Single response APPROACH

DETERMINISTIC Range of (DAp ) Parametric analyses APPROACH responses

Likelihood PROBABILISTIC "All possible" scenarios Range of (PA) & of their APPROACH are considered responses occurence

Figure 2. General approaches for assessment of seismic performance of geotechnical structures (a) Bridge deck (b) Pier Footing 0 m N =10 2.0 m 1

N =15 1

8.5 m Existing RC piles D = 0.3m 0 N =10 1

West 15.0 m pile East N =25 pile 1 New steel encased RC (non liquefiable) piles D = 1.5m 0 20.0 m

Figure 3. Central pier of the bridge: (a) cross section; (b) simplified soil profile used in seismic effective stress analyses (Bo- wen and Cubrinovski, 2008) while the probabilistic approach (PA) offers the Figure 4 depicts the SPT blow count and soil pro- most rigorous treatment of uncertainties and quanti- file at the northeast corner of the bridge. This soil fies their effects on the computed seismic response. profile was adopted in the pseudo-static analyses. The soil deposit consists of relatively loose liquefiable sandy soils with a thickness of about 15 m over- 2.3 Adopted approaches lying a denser sand layer. The sand layers have low This paper examines three approaches for assess- fines content predominantly in the range between ment of the seismic performance in the context out- 3% and 15% by weight. Detailed SPT and CPT in- lined above as follows: vestigations revealed a large spatial variability of the (1) Pseudo-static analysis within a deterministic penetration resistance at the site. Hence, a rigorous approach incorporating parametric evaluation investigation of the seismic response of the bridge (DAp) and its foundation would require consideration of (2) Seismic effective stress analysis using a sin- 3-D effects and spatial variability of soils. These gle scenario (DA) complexities are beyond the scope of this paper, (3) Probabilistic approach based on the so-called however, and rather a simplified scenario will be PEER framework (Cornell and Krawinkler, 2000) using the seismic effective stress analysis as a computational method (PA) 0 These assessment approaches can be applied to vari- Sandy ous earth structures and soil-structure systems, but N=7 SILT here they are applied to the assessment of seismic 5 N=12 Sandy performance of pile foundations in liquefiable soils. GRAVEL 10 N=14 SAND 2.4 Case study Silty N=8 Assumed SAND The Fitzgerald Avenue Bridge over the Avon River 15

Depth(m) Silty in Christchurch, New Zealand, will be used as a case N=15 SAND study. It is a small-span twin-bridge that has been identified as an important lifeline for post-disaster 20 emergency services. Hence, the bridge has to remain N=30 SAND operational in the event of a strong earthquake. To this goal, a structural retrofit has been considered 25 0 20406080 Liquefieable involving widening of the bridge and strengthening SPT blow count, N soil of the foundation with new large diameter piles. A cross section at the mid span of one of the bridges is Figure 4. SPT blow count and soil profile at the north-east shown in Figure 3 where both existing piles and new abutment piles are shown. considered herein with the principal objective being mic performance of the new piles of Fitzgerald to examine the response of the pile foundation Bridge. Key features of the simplified analysis and shown in Figure 3. Here, we will focus on the cyclic effects of uncertainties on the pile response are dis- response of the foundation during the intense ground cussed. shaking; effects of lateral spreading are beyond the scope of this study. 3.2 Computational model and input parameters Although in principle the pseudo-static analysis 3 PSEUDO-STATIC ANALYSIS could be applied to a pile group, typically it is applied to a single-pile model. This is consistent with 3.1 Objectives the overall philosophy for a gross simplification As a practical approach, the pseudo-static analysis adopted in this approach. A typical beam-spring should be relatively simple, based on conventional model representing the soil-pile system in the sim- geotechnical data and applicable without requiring plified pseudo-static analysis is shown in Figure 5. significant computational resources. In addition, in The model can easily incorporate a stratified soil order to satisfy the PBEE objectives in the seismic profile (multi-layer deposit) with different thickness performance assessment, the pseudo-static analysis of liquefied layers and a crust of non-liquefiable soil of piles should: at the ground surface. Since one of the key require- - Capture the relevant deformational mechanism ments of the analysis is to estimate the inelastic defor piles in liquefying soils formation and damage to the pile, in the proposed - Permit estimation of the inelastic response and model simple but non-linear load-deformation rela- damage to piles, and tionships are adopted for the soil-pile system. The - Address the uncertainties associated with seis- soil is represented by bilinear springs in which de- mic behaviour of piles in liquefying soils. graded stiffness and strength of the soil are used to Not all available methods for simplified analysis account for effects of nonlinear behaviour and lique- satisfy these requirements. In particular, in the cur- faction. The pile is modelled using a series of beam rent practice the treatment of uncertainties in the elements with a tri-linear moment-curvature rela- simplified analysis is often inadequate; commonly, tionship. Parameters of the model are illustrated in the uncertainties are either ignored or poorly ad- Figure 5 for a typical three-layer configuration in dressed in the analysis. In what follows, a recently which a liquefied layer is sandwiched between a sur- developed method for pseudo-static analysis of piles face layer and a base layer of non-liquefiable soils. in liquefying soils (Cubrinovski and Ishihara, 2004; All model parameters are based on conventional Cubrinovski et al., 2009) is used to assess the seis- geotechnical data (SPT blow count) and concepts

a) Cross section b) Numerical scheme

UG UP

p Lateral load, F Non-liquefied kC pC-max HHC crust layer δ

M Y U

Free field ground C displacement φ Liquefied HL layers p p β kL L-max δ

Deformed pile Pile H Non-liquefied B base layer p p kB B-max Soil spring δ

Figure 5. Beam-spring model for pseudo-static analysis of piles (model parameters and characterization of nonlinear behav- (subgrade reaction coefficient, Rankine passive 60 Range of data pressure). In the model, two equivalent static loads p S presented by 50 r-UB Seed & Harder (1991) are applied to the pile: a lateral force at the pile-head (kPa) r S (F) representing the inertial load due to vibration of r-LB S 40 δ r-UB the superstructure, and a horizontal ground dis- Upper bound placement (UG) applied at the free end of the soil 30 springs (Fig. 5b) representing the kinematic load on Used for RM the pile due to lateral movement of the free field 20 soils. S 10 r-LB Lower bound

3.3 Uncertainties in the parameters of the model Residual shear strength, S 00 5 10 15 20 The pseudo-static analysis aims at estimating the Equivalent clean sand SPT blow count, (N ) 1 60cs maximum response of the pile under the assumption Figure 6. Residual shear strength of liquefied sandy soils that dynamic loads can be idealized as static actions. (after Seed and Harder, 1991) Since behaviour of piles in liquefying soils is ex- tremely complex involving very large and rapid changes in soil stiffness, strength and lateral loads of UG = 0.36 m was estimated for the maximum cy- on the pile, the key question in the implementation clic ground displacement at Fitzgerald Bridge site. of the pseudo-static analysis is how to select appro- Note that since UG is an estimate for the free field priate values for the soil stiffness, strength and lat- response at the site, it is reasonable to expect a con- eral loads on the pile for the equivalent static analy- siderable variation in the value of UG around the sis. In other words, what are the appropriate values above estimate based on an empirical model. , p , U and F in the model shown in Figure for β L-max G As mentioned earlier, the objective of the pseudo- 5? The following discussion illustrates that this static analysis is to estimate the peak response of the choice is not straightforward and that all these pa- pile that will occur during an earthquake. The peak rameters may vary within a wide range of values. loads on the pile due to ground movement and vibra- In the adopted model, effects of liquefaction on tion of the superstructure do not necessarily occur at stiffness of the soil are taken into account through the same time, and hence, there is no clear and sim- the degradation parameter . Observations from full- β ple strategy how to combine these loads in a static size experiments and back-calculations from case analysis. Recently, Boulanger et al. (2007) sug- histories indicate that for cyclic liquefaction (exclud- gested that the maximum ground displacement ing lateral spreading), typically takes values in the β should be combined with an inertial load from the range between 1/10 and 1/50 (Cubrinovski et al., vibration of the superstructure proportional to the 2006). peak ground acceleration a using the following Similar uncertainty exists regarding the ultimate max expression: F = Icmsamax. Here, ms is the mass of pressure from the liquefied soil on the pile or the the superstructure whereas I is a factor that depends in the model. The ultimate lateral c value of pL-max on the period of the earthquake motion and practi- pressure p can be approximated using the resid- L-max cally provides a rule for combining the kinematic ual strength of liquefied soils (S ) as p = S . r L-max αL r (U ) and inertial (F) loads on the pile. Again, a wide G There are significant uncertainties regarding both αL range of values have been suggested for this parame- and Sr values. The latter is illustrated by the scatter ter: Ic = 0.4, 0.6 and 0.8 for a short, medium and of the data in the empirical correlation between the long period ground motions respectively (Boulanger residual strength of liquefied soils and normalized et al., 2007). SPT blow count (N1)60cs (Seed and Harder, 1991) shown in Figure 6. For example, for a normalized equivalent-sand blow count of (N1)60cs = 10, the re- 3.4 Computed response for a reference model (RM) sidual strength varies approximately between 5 kPa Based on the procedures outlined above, a so-called and 25 kPa. reference model (RM) was defined for the pile foun- The selection of appropriate equivalent static dation of Fitzgerald Bridge. RM is a single pile loads is probably the most difficult task in the model for the new piles (1.5m in diameter) in which pseudo-static analysis. This is because both input a ‘mid range’ values were adopted for the parame- loads in the pseudo-static analysis (UG and F) are in ters of the model, as summarized in Table 1. Here, effect estimates for the seismic responses of the free the Sr values of 14 and 36 were derived using the field ground and soil-pile-structure system respec- broken line in Figure 6 and normalized blow counts tively. The magnitude of lateral ground displacement of (N1)60cs = 10 and 15 respectively, for the liquefi- UG can be estimated using simple empirical models able layers. The pile was subjected to a free field based on SPT charts such as that proposed by Toki- ground displacement with a peak value at the ground matsu and Asaka (1998). Using this method, a value Variation in pile displacement Variation in bending moment due to properties due to properties of liquefied soils of liquefied soils Sr-LB Sr-LB Sr-UB S r-UB 0 0 (a) (b) Mc 5 5 M RM My u Pile 10 displacement 10 My Applied free field

ground displacement (m) Depth Depth (m) Depth 15 15 RM

Mu Mc 20 20

25 25 0 0.1 0.2 0.3 0.4 0.5 -10 -5 0 5 10 Horizontal displacement (m) Bending moment, M (MN-m) PH Figure 7. Effects of properties of liquefied soils on the pile response computed in the pseudo-static analysis: (a) pile displacements; (b) bending moments

surface of UG = 0.36m, indicated in Figure 7a, and a fied soil, for which instead the lower bound or lateral load at the pile head corresponding to a peak minimum values of β = 1/50, Sr = 6 kPa (N1 = 10) ground acceleration of amax = 0.4g and an inertial and Sr = 24 kPa (N1 = 15) were used. Similarly, an- coefficient of Ic = 0.6. The computed pile displace- other analysis was conducted in which the upper ment and bending moment for the reference model bound or maximum values of β = 1/10, Sr = 22 kPa (RM) are shown with solid lines in Figures 7a and (N1 = 10) and Sr = 48 kPa (N1 = 15) were used in 7b respectively. A pile head displacement of 0.21m conjunction with the RM values for all other pa- and a peak bending moment at the pile head of 9.6 rameters. Results of these two analyses are shown in MN-m were computed. The bending moment ex- Figure 7 indicating significant effects of the spring ceeded the yield level both at the pile head and at the properties for the liquefied soil on the pile response. interface between the liquefied layer and underlying Figure 8 shows results from a similar pair of base layer. analyses in which the value for the applied ground displacement was either decreased (UG = 0.29m) or increased (UG = 0.43m) for 20% with respect to the ______Table 1. Characteristic values of model parameters RM displacement of 0.36m. Again, a large differ- Parameter RM Range______of values ence in the pile response is seen resulting from a relatively small variation in the ground displacement ______LB* UB** β - 1/20 1/50 - 1/10 applied to the pile. Sr (N1=10) (kPa) 14 6 - 22 Results of the parametric analyses are summa- Sr (N1=15) (kPa) 36 24 - 48 rized in Table 2 and are depicted in tornado charts Ic - 0.6 0.4 - 0.8 for the pile head displacement and bending moment U______G (m) 0.36 0.29 - 0.43 (at the pile head) respectively in Figures 9a and 9b. * Lower Bound (minimum value) The response of the reference model (RM) is also ** Upper Bound (maximum value) indicated in these plots for comparison purpose. The results clearly indicate that the pile response is significantly affected by the adopted values for stiffness 3.5 Effects of uncertainties on the pile response and strength of the liquefied soil, and to a lesser ex- tent by the adopted values for loads, U and F (due To examine the effects of uncertainties associated G to variation of I between 0.4 and 0.8). Note that the with the liquefied soil and lateral loads on the pile, c size of these effects will change with the properties parametric analyses were carried out in which the of the soil-pile system (especially with the stiffness above parameters were varied within the relevant of the pile relative to that of the soil), degree of range of values listed in Table 1. For example, an yielding in the soil and pile, and the size of lateral analysis was conducted in which RM values were loads from a non-liquefied crust at the ground sur- used for all parameters except for the stiffness deg- face. radation (β) and residual strength (Sr) of the lique- Variation in pile displacement Variation in bending moment due to applied U due to applied U G G UG = 0.29m UG = 0.43m UG = 0.43m UG = 0.29m 0 0 (a) (b) Mc 5 5 (U = 0.36m) M RM G My u

10 10 My Applied free field RM (UG = 0.36m)

Depth (m)Depth 15 ground displacement (m)Depth 15

Mu Mc 20 20

25 25 0 0.1 0.2 0.3 0.4 0.5 -10 -5 0 5 10 Horizontal displacement (m) Bending moment, M (MN-m) PH Figure 8. Effects of applied lateral ground displacement on the pile response computed in the pseudo-static analysis: (a) pile displacements; (b) bending moments

(a) (b) ______Table 2. Results of parametric analyses Model Pile response S , β S , β ______r r ______UPH* MPH** RM with Sr-LB and β2-LB 0.10 7.8 U U G LB UB G LB UB RM with UG = 0.29m 0.16 8.9 RM with Is-LB = 0.4 0.18 8.9 RM - 0.21 9.5 F(I ) F(I ) RM with UG = 0.43m 0.25 9.9 s s RM with Is-UB = 0.8 0.23 10.0 RM with S and β 0.27 10.3 ______r-UB 2-UB RM RM * Pile-head displacement ** Bending moment at pile head 0.1 0.2 0.3 7891011

Pile head displacement, Bending moment, U (m) M (MNm) PH H 3.6 Discussion The above results clearly illustrate a high sensitivity Figure 9. Tornado charts depicting pile response computed in parametric pseudo-static analyses: (a) pile-head displacement; of the pile response on the parameters of the simpli- (b) bending moment at pile head fied model. This sensitivity is not specific to the adopted approach in this study, but rather is a com- mon feature of simplified methods of analysis. It simply reflects the significant uncertainties associ- have distinct modelling features and use different ated with the complex phenomena considered and load-deformation relationships, geotechnical data their gross simplification in the pseudo-static and empirical correlations. For this reason, they all method of analysis. The results also clearly empha- require an independent process of ‘calibration’ in size the need for a parametric evaluation of the which model parameters will be rigorously exam- seismic response when using simplified methods of ined and their relevant range of values identified. analysis. In terms of the previously introduced as- Note that this calibration is both model-specific and sessment approaches, a deterministic approach in- problem-specific. For example, the pseudo-static analysis method presented herein when applied to cluding parametric analyses (DAP) would be required when using simplified methods of analysis the assessment of piles subjected to lateral spreading for seismic performance assessment. will need different set of reference values for the In the current practice, various methods for sim- model parameters, e.g. magnitude of UG, load com- plified (pseudo-static) analysis are used. These bination rule for UG and F, and stiffness degradation methods are similar in principle however they all factor β. 4 SEISMIC EFFECTIVE STRESS ANALYSIS propriate boundary conditions along end-boundaries and soil-foundation-structure interfaces are critically 4.1 Implementation steps important in order to allow unconstrained response Unlike the simplified analysis procedure where the and development of relevant deformation modes. response of the pile is evaluated using a beam-spring Similarly, stress-strain behaviour of soils and lique- model and equivalent static loads as input, the seis- faction resistance are strongly affected by the initial mic effective stress analysis incorporates the soil, stress state of the soil, and therefore, an initial stress foundation and superstructure in a single model and analysis is required to determine gravity-induced uses an acceleration time history as a base excitation stresses in all elements of the model resembling for this model. This analysis aims at a very detailed those in the field. modelling of the ground response and soil-structure In the final step, an acceleration time history system in a rigorous dynamic analysis. The seismic (ground motion) is selected which is used as a base effective stress analysis is difficult to implement in excitation for the model. Considering the geometry practice because it requires significant computa- of the problem and anticipated behaviour, numerical tional resources and specialists knowledge from the parameters such as computational time increment, user. In concept, the effective stress analysis could integration scheme and numerical damping are be considered as the opposite approach to that of the adopted, and the dynamic effective stress analysis is practical pseudo-static analysis. then executed. The analysis is quite demanding on The implementation of the effective stress analy- the user in all steps including the final stages of sis generally involves three steps (Fig. 10): post-processing and interpretation of results since it (1) Determination of the parameters of the consti- requires an in-depth understanding of the phenom- tutive model ena considered, constitutive model used and particu- (2) Definition of the numerical model lar numerical procedures adopted in the analysis. (3) Dynamic analysis and interpretation of results Benchmarking exercises imply that these rigorous In the first step, parameters of the constitutive requirements are not always satisfied in the profes- model for the soil are determined using results from sion even when dealing with static problems (Potts, laboratory tests on soil samples and data from in-situ 2003). investigations. The required types of laboratory tests In cases when the analysis is used for a rigorous are model-specific and are generally used for deter- assessment of the seismic performance of important mination of stress-strain relationships and effects of structures, high-quality geotechnical data from field excess pore pressures on the soil response (liquefac- investigations and laboratory tests are needed in or- tion tests). Whereas most of the constitutive model der to model the particular deformational character- parameters can be directly evaluated from data ob- istics (stress-strain relationships) of the soils in ques- tained from laboratory tests and in-situ investigations. Such data are rarely available, however, and tions, some parameters are determined through a this has been often used as an excuse to avoid using calibration process in which best-fit values for the the seismic effective stress analysis in geotechnical parameters are identified in simulations of labora- practice. However, even when conventional data is tory tests (so-called element test simulations). used as input, this analysis still provides an impor- In the second step, the numerical model is de- tant and unique contribution in the seismic perform- fined by selecting appropriate element types, dimen- ance assessment of earth structures and soil- sions of the model, mesh size, boundary conditions foundation-structure systems, as illustrated below. and initial stress state. The last two requirements often receive less attention, even though they have 4.2 Numerical model pivotal influence on the performance of the constitutive model and numerical analysis. Namely, one of The 2-D finite element model adopted for the effec- the key advantages of the advanced numerical analy- tive stress analysis of the pile foundation of Fitzger- sis is that no postulated failure and deformation ald Bridge is shown in Figure 11. The model in- modes are required, as these are predicted by the cludes the soil, pile foundation (both existing piles analysis itself. In this context, the selection of ap- and new piles) and the superstructure. Four-node

STEP 1 STEP 2 STEP 3 Determination of parameters Definition of numerical model Dynamic analysis of the constitutive model - Element types and FE mesh - Ground motion (input) - Laboratory tests - Boundary conditions - Numerical parameters - In-situ investigations - Modelling of interfaces - Postprocessing - Element test simulations - Initial stress state - Interpretation of results

Figure 10. Key steps in the implementation of seismic effective stress analysis Bridge superstructure Piles Elastic solid elements with Non-linear beam elements appropriate tributary mass with hyperbolic M-φ relationship

Soil elements (Two-phase solid elements; elasti-plastic constitutive model for sand)

Figure 11. Numerical model used in the seismic effective stress analysis of Fitzgerald Bridge solid elements were employed for modelling the soil hara, 1998a) and modifying the dilatancy parameters and bridge superstructure while beam elements were as described below. used for the piles and pile cap. Lateral boundaries of Borelogs, penetration resistance data from CPTs the model were tied to share identical displacements and SPTs and conventional physical property tests in order to simulate a free field ground motion near were the only geotechnical data available for the the boundaries. Along the soil-pile interface, the soils at Fitzgerald Bridge site. A rudimentary model- piles and the adjacent soil were connected at the ling of stress-strain behaviour of soils considering nodes and were forced to share identical horizontal liquefaction would require knowledge or assumption displacements. of the initial stiffness of the soil, strength of the soil The footing, bridge deck and pier were all mod- and liquefaction resistance. Since none of these were elled as linear elastic materials with an appropriate directly available for the soils at this site they were tributary mass to simulate inertial effects from the inferred based on the measured penetration resis- superstructure. Nonlinear behaviour of the piles was tance. The liquefaction resistance was determined modelled with a hyperbolic moment-curvature (M-φ) using the conventional procedure for liquefaction relationship while the soil was modelled using an evaluation based on empirical SPT charts (Youd et elastic-plastic constitutive model developed specifi- al., 2001). After an appropriate correction for the cally for modelling sand behaviour and liquefaction fines content and the magnitude of the earthquake problems (Cubrinovski and Ishihara, 1998a; 1998b). (using magnitude scaling factor), these charts pro- Details of the constitutive law and numerical proce- vided the cyclic stress ratios required to cause lique- dures will not be discussed herein, but rather model- faction in 15 cycles, which are shown by the solid ling of the liquefaction resistance based on conven- symbols in Figure 12. Using these values as a target tional geotechnical data will be demonstrated. liquefaction resistance, the dilatancy parameters of The model shown in Figure 11 was subjected to the model were determined and the liquefaction re- an earthquake excitation with similar general attrib- sistance was simulated for the two layers, as indi- utes (magnitude, distance and PGA) to those rele- cated with the lines in Figure 12. These two lines vant for the seismic hazard of Christchurch. An ac- represent the simulated liquefaction resistance celeration record obtained during the 1995 Kobe curves for the soils with N1 = 10 and N1 = 15 respec- earthquake (M=7.2) was scaled to a peak accelera- tively. To illustrate better this process, results of tion of 0.4g and used as a base input motion. Need- element test simulations for the sand with N1 = 10 less to say, the adopted input motion is neither rep- are shown in Figure 13 where effective stress paths resentative of the source mechanism nor path effects and stress-strain curves are shown for three different specific to Canterbury, but rather it was considered a cyclic stress ratios of 0.12, 0.18 and 0.30 respec- relevant excitation typical for the size of the earth- tively. The number of cycles required to cause lique- quake event considered in the analysis. faction in these simulations and the corresponding stress ratios are indicated with open symbols in Fig- ure 12, depicting the simulated liquefaction resis- 4.3 Modelling of liquefaction resistance tance. Thus, only conventional data were used for For a rigorous determination of parameters of the determination of model parameters. While this employed constitutive model, about 15 to 20 labora- choice of material parameters practically eliminates tory tests are required including monotonic and cy- the possibility for a rigorous quantification of the clic, drained and undrained shear tests. In the ab- seismic response of the soil-pile-structure system, sence of laboratory tests for the soils at the one may argue that the parameters of the model de- Fitzgerald Bridge site, the constitutive model pa- fined as above are at least as consistent and credible rameters were determined by largely adopting the as those used in a conventional liquefaction evalua- parameters of Toyoura sand (Cubrinovski and Ishi- tion. 0.5 ' vo

τ/σ 0.4 Based on conventional liquefaction evaluation N = 15 0.3 1 C 0.2 N = 10 1 B 0.1 A Cyclic stress ratio, 0 110100 Number of cycles, N c Figure 12. Liquefaction resistance curves adopted in the seismic effective stress analysis (curves represent model simulations)

30 30 CSR=0.12 CSR=0.12 20 20 (kPa) (kPa)

τ 10 τ 10 Point A: CSR=0.12 0 0 40 cycles -10 -10 -20 40 cycles to liquefaction -20 -30 Shear stress, Shear stress, -30 020406080100 -4 -2 0 2 4 Mean effective stress , p' (kPa) Shear strain, γ (%)

30 30 CSR=0.18 CSR=0.18 20 20 (kPa) (kPa)

τ 10 τ 10 Point B: CSR=0.18 0 0 -10 -10 10 cycles -20 -20 -30 10 cycles to liquefaction Shear stress, Shear stress, -30 020406080100 -4 -2 0 2 4 Mean effective stress , p' (kPa) Shear strain, γ (%)

30 CSR=0.30 30 20 2 cycles to CSR=0.30 liquefaction 20 (kPa) (kPa)

τ 10 τ 10 Point C: CSR=0.30 0 0 -10 -10 2 cycles -20 -20 -30 Shear stress, Shear stress, -30 020406080100 -4 -2 0 2 4 Mean effective stress , p' (kPa) Shear strain, γ (%)

Figure 13. Effective stress paths and stress-strain curves obtained in element test simulations for the soil layer with N1 = 10

4.4 Computed ground response isolation” effects and curtailed the development of Figure 14a shows time histories of excess pore water liquefaction in the overlying denser layer. Figure pressure computed at two depths corresponding to 14b further illustrates the development of the excess pore water pressure throughout the depth of the de- the mid depth of layers with N1 = 10 and N1 = 15 (z = 13.2m and 7.0m respectively). In the weaker layer, posit with time. Note that part of the steady build up = 15) is the pore water pressure builds-up rapidly in only one of the pore pressure in the upper layer (N1 caused by “progressive liquefaction” or upward flow or two stress cycles until a complete liquefaction of of water from the underlying liquefied layer. Need- this layer was reached at approximately 15 seconds. less to say, the pore pressure characteristics outlined In the denser layer (N1 = 15), the pore water pressure build up is slower and affected by the liquefaction in in Figure 14 will be reflected in the development of the underlying looser layer. The latter is apparent in transient deformation and permanent displacements the reduced rate of pore pressure increase after 15 of the ground. The seismic effective stress analysis seconds on the time scale. Clearly, the liquefaction can simulate these complex features of the ground of the loose layer at greater depth produced “base- response and their effects on structures. Pore water pressure ratio (u/σ' ) ) 1.2 vo vo ' z = 13.2m (a) 0 0.25 0.5 0.75 1 σ 1 0 t=40s End 0.8 10 0.6 5 z = 7.0m 15 0.4 t=25s 10 t=15s N =10 0.2 1

0 (m)Depth 15 -0.2 Pore water pressure ratio (u/ 20 (b) -0.4 0 102030405060 Time (s) 25

Figure 14. Computed excess pore water pressure in the free field soil: (a) time histories at mid-depths of layers with N1 = 10 and N1 = 15; (b) distribution of excess pore water pressures throughout the depth of the deposit and time

4.5 Computed pile response tained at the pile head (MH) with values slightly The computed time history of horizontal dis- below the yield level (Figure 15b). This time history placement of the pile is shown in Figure 15a to- indicates not only the peak level of the response but gether with the corresponding displacement of the also the number of significant peaks exceeding ground in the free field. The peak pile displacement cracking level which in turn provides additional in- reached about 0.18m at the pile head, which is sig- formation on the damage to the pile. Similar level of nificantly smaller than the peak free field displace- detail is available for other components of the nu- ment at the ground surface of 0.30m indicating rela- merical model including the foundation soil, old and tively stiff pile behaviour (the pile is resisting the new piles, and response of the superstructure. ground movement). The response shown in Figure 15a indicates that the peak displacements of the pile 4.6 Discussion and free field soil occurred at different times, at ap- As illustrated in the above application, the seismic proximately 19 seconds and 32 seconds, respec- effective stress analysis allows realistic and detailed tively. The peak bending moment of the pile was at-

0.4 (a) Free-field displacement 0.2 (at ground surface)

(m) 0 Horizontal displacement -0.2 Pile-head displacment -0.4 0 102030405060

H M P (b) y

M 5 M 0 c M -5 c Bending moment at pile head, (MN-m) M -10 y 0 102030405060 Time (s)

Figure 15. Computed response of the pile in seismic effective stress analysis: (a) horizontal displacement at pile head; (b) bending moment at pile head simulation of the seismic response of geotechnical employs an integrated probabilistic treatment of all structures induced by strong earthquakes. Effects of uncertainties that apply to the prediction of ground soil-structure interaction are easily included in the motion and evaluation of system response and asso- analysis, in which sophisticated nonlinear models ciated damage (uncertainties associated with charac- can be used both for soils and for structural mem- teristics of ground motion, material properties, mod- bers. The analysis permits a rigorous assessment of elling approximations, seismic response and the seismic performance of the soil-structure system associated physical damage for a given response as a whole and each of its components. measure). Hence, it provides an alternative and more Effects of excess pore water pressure are often a rigorous way for assessment of seismic performance key factor in the seismic response of ground and of engineering structures. Recently, attempts have earth structures. Hence, the ability of this analysis to been made to expand the application of this ap- capture details of pore pressure build-up, develop- proach to geotechnical problems (Kramer, 2008; Le- ment of liquefaction and consequent loss of strength dezma and Bray, 2007; Bradley at. al., 2008). De- and stiffness in the soil is of great value. The method tails of the probabilistic PBEE assessment are simulates the most salient features of seismic behav- beyond the scope of this paper, and instead key fea- iour of soils including peculiar effects from individ- tures and implementation of this procedure will be ual layers and cross interaction amongst them such outlined in the following using the case study con- as “base-isolation effects” or progressive liquefac- sidered. tion due to upward flow of water. Because of its complexity and high-demands on 5.2 Analysis procedure the user, the seismic effective stress analysis is typically applied in a deterministic fashion using a sin- Christchurch is located in a region of relatively high gle scenario (DA) or input ground motion. However, seismicity and Fitzgerald Bridge is expected to be this analysis also provides an excellent tool for as- excited by a number of earthquakes during its life- sessment of alternative design solutions, effective- span. Considering all possible earthquake scenarios, ness of structural strengthening and soil remediation the response of the bridge and its pile foundation (countermeasures against liquefaction) on a com- needs to be evaluated for earthquakes with different parative basis by quantifying their effects on the intensities ranging from very weak and frequent ground deformation, structural response and reduc- earthquakes to very strong but rare earthquakes. tion (control) of damage. Characteristics of ground motions caused by these earthquakes are very difficult to predict because of the complex and poorly understood source mecha- 5 PROBABILISTIC APPROACH nism, propagation paths of seismic waves and surface-soil effects. In order to account for these uncer-

5.1 Background tainties in the ground motion characteristics, the A probabilistic approach (PEER framework) for Per- following procedure was adopted. formance-Based Earthquake Engineering (PBEE) A suite of 40 ground motions recorded during has been recently developed for a robust assessment strong earthquakes was first selected, as indicated in of seismic performance of structures (Cornell and Figure 16a. Next, each of these records was scaled Krawinkler, 2000; Krawinkler 1999). This approach to ten different peak amplitude levels, i.e. peak

(a) 40 Earthquake Records (b) 400 Ground Motions (c) 400 Time History Analyses EQ1: Northridge 1994 GM1: EQ1, a = 0.1 g EQ2: Imperial Valley 1979 max GM2: EQ1, a = 0.2 g max

EQ40: Kobe 1995 GM10: EQ1, a = 1.0 g max Input motion GM11: EQ2, a = 0.1 g max

GM399: EQ40, a = 0.9 g max GM400: EQ40, a = 1.0 g max Figure 16. Schematic illustration of multiple effective stress analyses used in the probabilistic approach 0.8 0.8 (m) (m) PH PH 0.7 (a) 0.7 (b) U U 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 Peak pile-head displacment, Peak pile-head displacment,Peak pile-head 0 0 00.250.50.7511.25 0 200 400 600 800 Peak ground acceleration, a (g) Velocity spetrum intensity, VSI (cm/s) max

Figure 17. Computed pile-head displacements (UPH) in 400 effective stress analyses: (a) correlation between (UPH) and amax of input motion; (b) correlation between (UPH) and velocity spectrum intensity (VSI) of input motion

ground accelerations of amax = 0.1, 0.2, 0.3, 0.4, 0.5, ing the size of the response (EDP) with the in- 0.6, 0.7, 0.8, 0.9 and 1.0 g. Thus, 400 different tensity of the ground motion (IM). ground motions were generated in this way, as indi- For example, one way of presenting the results cated in Figure 16b, having very different ampli- from the 400 analyses with respect to the pile re- tudes, frequency content and duration. Using each of sponse for Fitzgerald Bridge is shown in Figure 17a these time histories as a base input motion, 400 ef- where the peak displacement at the pile head (UPH) fective stress analyses were conducted using the computed in the analysis is plotted against the peak model shown in Figure 11 and procedures outlined acceleration of the input motion (amax). Here, UPH earlier, as schematically depicted in Figure 16c. represents a measure for the size of the pile response (EDP) while amax is a measure for the intensity of the ground motion (IM). Each open symbol in Fig- 5.3 Computed response ure 17a represents the result (peak response of the The next challenge to overcome is how to present pile) from one of the 400 seismic effective stress results from 400 time history analyses in a meaning- analyses while the solid line is an approximation of ful way. Obviously, some relaxation in the rigorous the trend from a regression analysis. treatment of time histories and evaluation of the re- The scatter of the data in Figure 17a is quite large sponse is needed here. In the probabilistic PBEE ap- indicating a significant uncertainty in the prediction proach, this is achieved through the following rea- of the peak response of the pile based on the peak soning: acceleration of the ground motion (input PGA). (1) First, the object of assessment is identified. Clearly one issue in this approach is the need to Thus, instead of examining the entire soil-pile- identify an efficient intensity measure that reduces structure system, for example, the attention is the uncertainty and hence improves the predictabil- focused on the response of the pile. ity of the pile response. However, there is no wide- (2) Next, a representative measure for the re- ranging intensity measure that is appropriate for all sponse of the pile is identified, i.e. a parameter problems but rather the intensity measure is prob- that describes and quantifies the pile response lem-dependent and is affected by the particular de- efficiently (“Engineering Demand Parameter”, formational mechanism and features of the phenom- EDP in the PBEE terminology). Hence, in- ena considered. Based on detailed numerical studies, stead of using the entire time history of the Bradley et al. (2008) have identified that velocity- pile response, the peak value of the response based intensity measures correlate the best with the parameter (EDP) is used as a measure for the seismic response of piles, and that in particular the size of the response. velocity spectrum intensity (VSI) is the most effi- (3) Similarly, a single parameter is used to de- cient intensity measure for piles. This is illustrated scribe the input motion or measure the inten- in Figure 17b where the same results for UPH from sity of the ground motion (“Intensity Meas- the 400 analyses shown in Figure 17a are re-plotted ure”, IM). using VSI as the intensity measure for the employed (4) Finally, the results of the analyses are pre- input motions. The improved efficiency and predict- sented by correlating the parameter represent- ability of the pile response is evident in the reduced 100 100 (a) (b) 10-1 10-1

-2 -2 Existing foundation 10 10 DBE (1/475yr) 10-3 10-3 Strengthened foundation MCE (1/2475yr) 10-4 10-4

10-5 10-5

Mean annual rate of exceedance of rate annual Mean exceedance of rate annual Mean U at yielding 10-6 10-6 PH 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 Peak ground acceleration, a (g) Peak pile-head displacement, U (m) max PH

Figure 18. Probabilistic assessment of seismic performance of pile foundation: (a) seismic hazard curve for Christchurch; (b) Demand hazard curve for piles of Fitzgerald Bridge

uncertainty as depicted by the smaller dispersion of In the above interpretation, the peak pile dis- the data. The plots shown in Figure 17 provide placement was adopted as a measure for the size of means for estimating the peak response of the piles the pile response because it is a good indicator of the of Fitzgerald Bridge for all levels of earthquake ex- peak deformation and damage to the pile (Bradley et citation, from elastic response to failure. al., 2008). Thus, UPH can be converted to a parameter directly correlating with the damage to the pile (the peak curvature of the pile), and then the demand 5.4 Assessment of seismic performance: Demand hazard curve can be easily expressed in terms of a hazard curve damage measure, thus providing likelihood of char- A conventional output from Probabilistic Seismic acteristic damage levels for the pile (cracking, yield- Hazard Analysis (PSHA) is the so-called seismic ing, failure). Furthermore, the physical damage of hazard curve which expresses the aggregate seismic the pile foundation will lead to losses, and hence, the hazard at a given site by considering all relevant demand hazard curve can be also used to quantify earthquake sources contributing to the hazard. A the seismic performance in terms of economic meas- seismic hazard curve for Christchurch (Stirling et ures (dollars). This in turn will provide an economic al., 2001) is shown in Figure 18a where a relation- basis for decisions on seismic design, repair and ret- ship between the peak ground acceleration (amax) rofit, and will facilitate communication of the design and mean annual rate of exceedance of a given amax outside the profession. Clearly, the probabilistic as- is shown. For example, this hazard curve indicates sessment provides alternative measures of the seis- that an earthquake event generating an amax = 0.28g mic performance of the pile while rigorously ac- in Christchurch has a recurrence interval or return counting for the uncertainties associated with the period of 475 years (or 10% probability of ex- seismic hazard and phenomena considered. This ap- ceedance in 50 years). proach can be applied to seismic performance as- By combining the seismic hazard curve expressed sessment of any other component of the soil-pile- in terms of amax (Fig. 18a) and the correlation be- structure system and to the bridge as a whole. Also, tween the peak pile response (UPH) and amax estab- other sources of uncertainty such as those related to lished from the results of the effective stress analy- modelling, soil and site characterization can be eas- ses (Fig. 17a), a so-called “Demand Hazard Curve” ily incorporated in the analysis and their effects on was produced, shown in Figure 18b for the existing the response can be quantified. and new piles respectively. In this way, the probability for exceedance of a certain level of peak pile displacement in any given year (annual rate of ex- 6 SUMMARY AND CONCLUSIONS ceedance) could be estimated for the piles of Three different approaches for assessment of the Fitzgerald Bridge. A unique feature of the demand seismic performance of earth structures and soil- hazard curve is that it provides an assessment of the structure systems have been presented. These ap- seismic performance of the pile foundation by con- proaches use different models, analysis procedures sidering all earthquake scenarios for the site in ques- and are of vastly different complexity. All are con- tion and associated uncertainties in the characteriza- sistent with the performance-based design philoso- tion of the ground motion. phy according to which the seismic performance is realistic simulation of the seismic behaviour of earth assessed using deformational criteria and associated structures and soil-structure systems. It incorporates damage; however, they focus on different aspects sophisticated nonlinear models for the soil, founda- and make different contribution in the assessment. tion and structure in a rigorous dynamic analysis. Key features of the examined approaches and their The key contribution of this analysis is that it allows specific contribution in the seismic performance as- examining in detail the performance of the soil- sessment are summarized in Table 3. structure system under a strong earthquake excitation. Even results from a single analysis (such as that presented herein) illustrate the benefit of a detailed 6.1 Pseudo-static analysis soil-pile-structure analysis. The pseudo-static analysis is a practical approach The experience from recent strong earthquakes based on conventional geotechnical data, engineer- suggests that design concepts in which pile founda- ing concepts and relatively simple computational tions are considered to remain within the elastic models. It postulates a specific deformational range of deformation during strong earthquakes are mechanism and aims at estimating the peak response not economical. The PBEE philosophy also suggests of the pile due to an earthquake under the assump- accepting damage in seismic events, if this proves tion that dynamic loads can be represented as static the most economic solution (Krawinkler, 1999). actions. The method is easy to implement in practice Hence, there is a need to consider inelastic deforma- and provides a suitable tool for evaluation of the tion concurrently in both the superstructure and pile seismic response of piles and associated damage to foundation, and to assess the performance both on a piles. This approach focuses on the pile itself (en- system level and at a component level (Gazetas and hances foundation design) while it ignores the re- Mylonakis, 1998). Advanced numerical analyses sponse of the system and other components of the provide this capability and methods based on the ef- system. fective stress principle further permit consideration In addition to the uncertainties associated with of important ground response features such as ef- the complex seismic behaviour and ground motion, fects of excess pore pressures and liquefaction. there are significant uncertainties related to model- Since this approach focuses on a detailed evalua- ling arising from unknown variables and inaccurate tion of the seismic response, it is not appropriate for model form. These modelling uncertainties are very parametric evaluation including large number of pronounced in the simplified analysis because of the analyses. In this context, the selection of an appro- significant approximations and gross simplification priate input motion is problematic in cases when rig- of the problem adopted in this approach. Thus, when orous assessment and quantification of the seismic using simplified methods of analysis in the assess- performance of important structures is needed. ment, it is critically important to address these uncertainties through systematic parametric studies. 6.3 Probabilistic approach The probabilistic approach offers a unique perspec- 6.2 Seismic effective stress analysis tive in the assessment of seismic performance, first The seismic effective stress analysis aims at a very through a rigorous treatment of the single most im-

Table 3. Methods for seismic performance assessment of soil-structure systems: Key features and contributions in the assessment Method of assessment Key features Specific contributions in the assessment Shortcomings • Simple • Evaluates the response and damage level for the pile • Does not consider Pseudo-static • Conventional data (parametric evaluation is needed) the response of the analysis and engineering soil-foundation- • Enhances foundation design concepts structure system • Detailed assessment of seismic response of pile foun- • Ignores uncertain- Realistic simulation dations including effects of liquefaction and SSI ties in the ground

Seismic effective of ground response & • Integral assessment of inelastic behaviour of soil- motion stress analysis seismic soil- foundation-structure systems foundation-structure interaction • Enhances communication of design concepts between geotechnical and structural engineers • Addresses uncertainties associated with ground mo- • Ignores details of • Considers all earth- tion characteristics on a site specific basis the seismic re-

Probabilistic quake scenarios • Provides engineering measures (response and damage) sponse PBEE framework • Quantifies seismic and economic measures (losses) of performance

risk • Enhances communication of design outside profession portant source of uncertainty in seismic studies, the tion,” Bulletin of the NZ Society for Earthquake Engineer- ground motion, and then by providing alternative ing, 41(4): 247-262. Cornell, C.A. & Krawinkler, H 2000. Progress and challenges performance measures in the assessment, engineer- in seismic performance assessment. PEER Center News, ing and economic ones. It allows us to combine geo- 3(2):1-4. technical and structural design aspects and to evalu- Cubrinovski, M. & Ishihara, K. 1998a. Modelling of sand be- ate their effects on the performance of the entire haviour based on state concept. Soils and Foundations system (soil-foundation-structure system) and each 38(3): 115-127. of its components. It is worth noting that in spite of Cubrinovski, M. & Ishihara, K. 1998b. State concept and modified elastoplasticity for sand modelling. Soils and the use of an effective stress analysis as a basic com- Foundations 38(4): 213-225 putational tool in the probabilistic approach em- Cubrinovski, M. & Ishihara, K. 2004. Simplified method for ployed herein, details of the response were not con- analysis of piles undergoing lateral spreading in liquefied sidered in the seismic performance assessment. soils. Soils and Foundations, 44(25): 119-133. Cubrinovski, M., Kokusho, T. & Ishihara, K. 2006. Interpreta- tion from large-scale shake table tests on piles undergoing 6.4 Future needs lateral spreading in liquefied soils. Soil Dynamics and Earthquake Engineering, 26: 275-286. The examined approaches address different as- Cubrinovski, M., Ishihara, K. & Poulos, H. 2009. Pseudostatic pects in the assessment and, in essence, are compli- analysis of piles subjected to lateral spreading. Special Is- mentary in nature. It is envisioned that these ap- sue, Bulletin of NZ Society for Earthquake Engineering, proaches will be used in parallel in the future, and 42(1): (in print). Gazetas G. & Mylonakis, G. 1998. Seismic soil-structure inter- hence, they all require further development and im- action: new evidence and emerging issues. ASCE Geotech- provement. The pseudo-static approach requires es- nical Special Publication 75: 1119-1174. tablishment of improved models depicting multiple Kramer, S.L. 2008. Performance-Based Earthquake Engineer- deformational mechanisms and in particular more ing: opportunities and implications for geotechnical engi- rigorous and systematic procedures for parametric neering practice. ASCE Geotechnical Special Publication 181: 1-32. evaluation of the seismic response. Methods based Krawinkler, H. 1999. Challenges and progress in performance- on seismic effective stress analysis require im- based earthquake engineering. Int. seminar on seismic en- provement in the simulation of large ground defor- gineering for Tomorrow – In Honour of Professor Hiroshi mation and more emphasis on use of sophisticated Akiyama Tokyo, Japan, November 26, 1999:1-10. nonlinear models for an integrated analysis of the Ledezma, C. & Bray, J. 2007. Performance-based earthquake engineering design evaluation procedure for bridge founda- soil-foundation-structure system. Finally, further de- tions undergoing liquefaction-induced lateral spreading, velopment of the probabilistic approach is needed PEER Report 2007: 1-136. including efforts towards simplification of proce- Potts, D.M. 2003. Numerical analysis: a virtual dream or prac- dures and identification of representative response tical reality? The 42nd Rankine Lecture, Geotechnique measures (EDPs) and ground motion measures 53(6): 535-573. (IMs) for various specific problems. Seed, R.B. & Harder, L.F. 1991. SPT-based analysis of cyclic pore pressure generation and undrained residual strength. All of these analysis procedures improve our un- H. Bolton Seed Memorial Symposium Proc., 2: 351-376. derstanding of complex seismic behaviour and en- Stirling, M.W., Pettinga, J., Berryman, K.R. & Yetton, M. hance engineering judgement, which is probably one 2001. Probabilistic seismic hazard assessment of the Can- of the most significant contributions that one can terbury region, Bulletin of NZ Society for Earthquake Engi- expect from such an exercise. neering 34: 318-334. Tokimatsu K. & Asaka Y. 1998. Effects of liquefaction- induced ground displacements on pile performance in the 1995 Hyogoken-Nambu earthquake. Special Issue of Soils ACKNOWLEDGEMENTS and Foundations, September 1998: 163-177. Youd, T.L. & Idriss, I.M. 2001. Liquefaction resistance of The authors would like to acknowledge the finan- soils: summary report from the 1996 NCEER and 1998 cial support provided by the Earthquake Commis- NCEER/NSF workshops on evaluation of liquefaction resistance of soils, Journal of Geotechnical and Geoenviron- sion (EQC), New Zealand. mental Engineering, 127(4): 297-313.

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