PERFORMANCE-BASED DESIGN OF BRIDGE FOUNDATION ON PARTIALLY IMPROVED LIQUEFIABLE SOIL

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1 Paper No. 1.1 SECOND INTERNATIONAL CONFERENCE ON PERFORMANCE-BASED DESIGN IN EARTHQUAKE GEOTECHNICAL ENGINEERING May 28-3, TAORMINA (ITALY) PERFORMANCE-BASED DESIGN OF BRIDGE FOUNDATION ON PARTIALLY IMPROVED LIQUEFIABLE SOIL Dimitris K. KARAMITROS 1, George D. BOUCKOVALAS 2, Yannis K. CHALOULOS 3 ABSTRACT According to currently applicable seismic codes, the foundation of a typical highway bridge pier on liquefiable soil would require the use of a pile group, combined with ground improvement measures to mitigate liquefaction-induced large bending moments and shear forces in the piles. This paper examines whether the performance-based design criteria may be also fulfilled if the bridge pier loads are undertaken by a shallow footing and the ground improvement measures are applied to a smaller zone, only in the upper part of the liquefiable layer. A sophisticated numerical methodology is utilized for this purpose and parametric analyses are performed, in order to determine the required plan size and depth of the improved zone. The analyses are 3D dynamic, with coupled excess pore pressure build up and dissipation in the liquefied soil, while the overall accuracy of the numerical methodology has been verified through comparison with a number of relevant centrifuge tests. It is thus demonstrated that such a solution may efficiently ensure foundation safety and operation requirements, at reduced cost compared to the use of a pile group. Furthermore, it is shown that the proposed partial improvement of the liquefiable subsoil may prove beneficial to the superstructure s performance, as the seismic accelerations that reach the ground surface are drastically de-amplified. Keywords: Liquefaction, shallow foundation, settlements, bearing capacity, numerical analyses, ground improvement, stone columns, liquefaction mitigation. INTRODUCTION Liquefiable soils are treated by all currently available seismic codes as extreme ground conditions, where the construction of shallow footings is essentially allowed only after proper soil treatment. This has been based on numerous case studies (e.g. Yoshimi & Tokimatsu, 1977, Ishihara et al, 1993, Sancio et al, 22), as well as on centrifuge and large scale experiments (e.g. Acacio et al, 21, Adalier et al, 23, Coelho et al, 24, Kawasaki et al, 1998, Liu & Dobry, 1997), which have indicated that liquefactioninduced shear strength degradation of the foundation subsoil may result in post-shaking static bearing capacity failure, while excessive seismic settlements may also accumulate. Thus, it is recommended to ensure foundation safety through one or more of the following methods: 1 Civil Engineer, PhD, National Technical University of Athens, School of Civil Engineering, Geotechnical Department, dimkaram@gmail.com, web: 2 Civil Engineer, Professor, National Technical University of Athens, School of Civil Engineering, Geotechnical Department, gbouck@central.ntua.gr, web: 3 Civil Engineer, MSc, PhD Candidate, National Technical University of Athens, School of Civil Engineering, Geotechnical Department, ioannischaloulos@gmail.com

2 Ground improvement, in order to densify the soil and increase its liquefaction resistance beyond the dangerous range. Use of drainage, to reduce the excess pore-water pressure generated by ground shaking. Construction of pile foundations, transferring loads to layers not susceptible to liquefaction. Still, recent studies (e.g. Bouckovalas & Dakoulas, 27, Karamitros, 21, Karamitros et al, 211) have indicated that the presence of a sufficiently thick and shear resistant non-liquefiable clay crust between the foundation and the liquefiable subsoil, could potentially ensure a viable performance-based design. In this case, it is of cornerstone importance to be able to estimate: the post-shaking bearing capacity of the foundation, as well as the relevant degraded static factor of safety FS deg, and the accumulating dynamic settlements ρ dyn, and to ensure that they remain within the allowable limits. Note that the degraded static factor of safety refers to a rather short-living threat, which will no longer exist when earthquake-induced excess pore pressures have dissipated. Therefore, its design value may be well below the conventional values for static loads, and close to unity, i.e. FS deg =1. to 1.5 (instead of FS=2. to 3. used in conventional practice). On the other hand, the allowable dynamic settlements are a function of both safety and serviceability requirements, and should be thus specified by superstructure owners or code provisions, depending upon the type of structure and the return period of the design seismic actions. Following a similar logic, it is examined, herein, whether the above performance-based design principles may also be applied to cases where there is no clay crust between the foundation and the liquefiable subsoil and consequently it has to be artificially replaced by a crust of improved soil. Thus, a typical highway bridge foundation is analyzed, resting on top of a relatively thick liquefiable sand layer. The beneficial role of the clay crust is now played by an artificially created non-liquefiable zone, formed by the application of gravel piles-drains within the upper part of the liquefiable sand layer. A sophisticated numerical methodology is utilized for the simulation of the combined foundation-soil response and parametric analyses are performed, in order to determine the required plan size and depth of the zone where the liquefaction mitigation measures should be applied in order to fulfill specific performancebased design criteria. Furthermore, it is demonstrated that the proposed partial with depth improvement of the liquefiable subsoil may reduce drastically the seismic loads applied to the superstructure, as compared to the case where liquefaction mitigation measures are applied to the whole thickness of the liquefiable layer. OUTLINE OF CASE STUDY The soil profile and the characteristics of the foundation considered herein, correspond to a typical bridge pier foundation of the Egnatia Highway, in northern Greece. As shown in Figure 1, the examined foundation supports the self-weight of a 12.5m high pier, as well as the self-weight and applied loads of two simply supported bridge decks, each featuring a length of 45m. The corresponding vertical loads are presented in Figure 1, together with the applied horizontal force and overturning moment, which were computed through a conventional pseudo-static analysis of the superstructure, for a maximum acceleration of a max =.36g (effective acceleration a eff =.24g).

3 L = 45m L = 45m ρ Vertical loads Deck Load : 65kN Pillar Load: 38kN Seismic Loading: a max =.36g a eff =(2/3)a max =.24g V = 13 kn H=8 kn M=95 knm Silty Sand Figure 1. Schematic profile of the examined highway bridge foundation. Bedrock W.T. N SPT f (%) (N 1 ) 6CS FS L SM-GM ML SP SM-SC 5 1 non-improved soil improved soil Depth (m) 15 I p = % 2 SM 25 SM-CL 3 Figure 2. Soil profile characteristics: Soil classification, standard penetration resistance N SPT, fines content f, corrected SPT number (N 1 ) 6,cs and safety factor against liquefaction FS L. The soil profile characteristics are shown in Figure 2, in terms of soil classification, SPT number N SPT and fines content f. Observe that the foundation subsoil mainly consists of loose silty sands, down to a depth of 3m, where the bedrock is encountered. Furthermore, Figure 2 presents the corrected SPT values (N 1 ) 6,cs, computed according to Youd et al (21), as well as the corresponding factors of safety against liquefaction FS L. These safety factors remain well below unity in the upper 18m of the silty sand layer, indicating high liquefaction susceptibility. Note that the bridge pier is located within a river basin where the water table remains well above the ground surface. The actual foundation for the above bridge and soil profile was conventionally designed, according to the currently available seismic codes, and consisted of a combination of a group of bored piles, as well as ground improvement of the entire liquefiable sand layer through stone columns. The latter were used to

4 mitigate liquefaction and ensure that the applied vertical and horizontal forces may be safely undertaken by the pile foundation. It is stressed out, herein, that, in case that no ground improvement measures were applied, subsoil liquefaction would result in a significant degradation of the piles shaft resistance, while excessive bending moments and shear forces would also develop. Therefore, foundation safety requirements would result in larger pile diameters, pile lengths and reinforcement, increasing further the overall cost of the foundation. The stone-columns used with the conventional design to mitigate liquefaction had a diameter of.8m and they were placed on a rectangular grid, at axial distances of 2.m, as shown in Figure 3. The replacement ratio of a s =.125 and the distance ratio of D/S=.8/(2./1.77) were selected by taking into account both the compaction of the foundation subsoil (Mizuno et al, 1987) and the associated increase of the SPT resistance (Figure 2), as well as the beneficial effect of drainage (Seed & Booker, 1977). As shown in Figure 2, the proposed ground improvement measures successfully increase the factor of safety against liquefaction to FS L >1, while it was estimated that the corresponding excess pore pressure ratios are expected to remain below r u =.4. Taking into account the high costs of the conventional construction, the above case-study is re-examined, herein, in order to evaluate the feasibility of a performance-based design of the pier foundation using the concept of partial with depth improvement of the liquefiable subsoil. Hence, a shallow footing was designed for the bridge pier, as shown in Figure 3. More specifically, a 9m wide and 17m long footing was found sufficient to undertake the applied vertical and horizontal forces, as well as the overturning moments presented in the above, in the case where no liquefaction occurs in the foundation subsoil. It must be noted that the above dimensions were selected considering that the foundation would rest on top of a 1m thick gravel layer, and assuming a uniform stress distribution through this layer, at an angle of 45. The underlying improved ground was considered to have a friction angle of φ=38, estimated by taking into account the initial soil properties, the effects of sand densification during the construction of the stone columns, as well as the gravel properties and the soil replacement ratio (a s =.125). It is important to note, that the design loads that were considered conservatively ignore the acceleration deamplification that is expected to occur at the ground surface, due to the shear strength degradation of the liquefied subsoil. 17.m +2m m L imp Z imp Φ8 Z liq 9.m Βimp -18m 2.m -3m Figure 3. 2.m 17.m Cross section and plan view of the examined foundation and the proposed grid of stone columns, used for liquefaction mitigation.

5 NUMERICAL SIMULATION Numerical Methodology The liquefaction performance of the examined foundation was investigated through fully-coupled effective-stress dynamic analyses, using the numerical methodology developed by Andrianopoulos (26) and Karamitros (21). This methodology is based on the implementation of a modified version of the bounding surface critical state constitutive model proposed by Papadimitriou & Bouckovalas (22), into the commercial finite difference code FLAC3d. The constitutive model predictions have been evaluated against experimental data (Arulmoli et al, 1992), indicating that the model allows the accurate prediction of the most important aspects of the dynamic behavior of sands, such as shear strength degradation and damping increase with increasing cyclic shear strain amplitude, as well as excess pore pressure build-up towards liquefaction. Furthermore, the accuracy of the numerical algorithm has been verified against the results of various centrifuge experiments, including Model #12 of the research program VELACS (Arulmoli et al, 1992), which refers to the problem examined herein. Details on the equations of the employed constitutive model, named NTUA-SAND, the adopted integration scheme, its calibration process and the numerical methodology s verification against experimental data, may be found in Andrianopoulos et al (21a,b). The above described algorithm was applied to perform twelve (12) parametric analyses, considering different thicknesses Z imp and widths B imp of the improved zone underneath the foundation (see Figure 3). The selected values are shown in Table 1, normalized against the thickness Z liq of the liquefiable layer and the width B of the foundation, respectively. In each case, the length L imp of the improved zone was taken as equal to: imp with L being the length of the foundation. ( imp ) L = L+ B B (1) The model configuration considered for the analyses is presented in Figure 4a. Note that only the upper 18m of the sand layer were modeled, as the lower part was not found susceptible to liquefaction and is therefore expected to have a significantly higher shear wave velocity, essentially behaving as the seismic bedrock. The implemented NTUA-SAND constitutive model was used to model the behavior of the liquefiable soil, calibrated against Nevada Sand, at an initial relative density of D r =5%, which corresponds to the shear strength of the foundation subsoil encountered in the present case-study. The Mohr-Coulomb model was used for the improved ground, considering a friction angle of φ imp =38. The water table was assumed to be located at 1m above the ground surface, while, in order to simulate free field conditions at the side boundaries of the model, the corresponding opposite nodes were tied rigidly to each other, thus being forced to exhibit the same horizontal displacements during shaking. Finally, it is noted that the footing was rigid and massless, with an average bearing pressure of 115kPa. Table 1. Examined normalized thicknesses Z imp /Z liq and normalized widths B imp /B of the improved zone. Z imp / Z liq = B imp / B = 1 x x 2 x x x x 3 x 5 x x x x x

6 46.5m a. b. Static Load (Q) a ρ st b 18m ρ dyn static loading to failure Figure m tied node boundaries Non-improved Soil NTUA-Sand Dr=5% B=9m, L/2=8.5m q=115kpa Improved Soil Mphr-Coulomb φ=38 ο (a) Numerical model used for the parametric analyses and (b) typical load-settlement curve. Settlement (ρ) c Q ult deg d d' Each numerical analysis was performed in three (3) steps: Initial, pre-seismic, static loading (part a-b of the load-settlement curve of Figure 4b). It was performed under drained conditions. Dynamic loading (part b-c of the load-settlement curve). It consisted of N=7 sinusoidal cycles, of amplitude a eff =.24g and a period equal to T=.25sec, applied at the model s base. Note that, since a sinusoidal excitation was considered, its amplitude was taken as an effective ratio of 2/3 of the design peak ground acceleration a max =.36g. The dynamic analysis was performed under partially drained conditions. A permeability of k=5 1-3 cm/sec was considered for the liquefiable sand, while the permeability of the improved ground was assumed to bed 1 times larger, in order to account for drainage through the stone columns. Post-seismic static loading to failure (part c-d of the load-settlement curve). It was performed under drained conditions, starting with the effective stresses and the excess pore pressures attained at the end of shaking. Typical Results Aiming to highlight the basic characteristics of the foundation s liquefaction performance, Figures 5 and 6 present typical results from the performed numerical analyses, namely from the case where Z imp /Z liq =.4 and B imp /B=. More specifically, Figures 5a and 5b show the deformed mesh at the end of shaking, in combination with the corresponding contours of excess pore pressure ratios r u = u/σ v,o and dynamic settlements ρ dyn, respectively. In the sequel, Figure 6 presents time-histories of the accelerations at the base of the model and at the soil surface, the foundation settlements ρ, as well as the excess pore pressure ratios r u, developing at different depths below the footing s axis. Focusing first upon Figure 5a, observe that excess pore pressures in the region below the foundation remain lower than the ones developing in the free-field. More specifically, Figure 6c indicates that excess pores pressures underneath the footing s axis tend to decrease for shallower depths, while they do not exceed a maximum value of.8. It must be noted, that this observation is in accordance with the results of numerous centrifuge and large-scale experiments (Acacio et al, 21, Adalier et al, 23, Coelho et al, 24, Kawasaki et al, 1998, Liu & Dobry, 1997). According to Karamitros et al (212), this behavior may be attributed to the persistent deviatoric stresses applied by the foundation, as well as to shear-induced dilation, associated with dynamic settlement accumulation. Furthermore, Karamitros et al (212) have shown that the fact that the foundation subsoil does not reach complete liquefaction may act as a natural

7 restraining mechanism to foundation settlement accumulation and bearing capacity degradation, thus allowing performance-based design criteria to be fulfilled without the need to apply soil improvement measures over the whole liquefiable foundation subsoil. Focusing next upon foundation settlements, it may be observed that, in accordance with experimental evidence, they accumulate more or less linearly with time and that they mostly develop during shaking, with only a small portion developing due to the post-shaking excess-pore pressure dissipation (Figures 5b and 6b). It may be therefore deduced that they are mainly associated to inertia-induced failure of the foundation subsoil and not to volume densification (Karamitros et al, 212). This implies that increasing the size of the improved zone would reduce the shear stresses applied by the foundation to the liquefiable subsoil, thus decreasing the earthquake-induced foundation settlements. Finally, Figure 6a indicates that the accelerations at the ground surface are significantly de-amplified, as compared to the excitation applied at the model s base. This effect may be attributed to the previously described failure of the foundation subsoil, as well as to the liquefaction-induced soil softening and the associated increase of the equivalent eigen-period of the soil column. Therefore, it becomes essentially evident that allowing excess pore pressures to develop in a region underneath the foundation may create a zone of natural seismic isolation, which acts beneficially for the dynamic performance of the superstructure. (a) r u = u / σ' vo (b) settlement, ρ (m) Figure 5. Typical results from the numerical analyses: Deformed mesh at the end of shaking and contrours of (a) excess pore pressure ratios and (b) dynamic settlements.

8 acceleration (g) Figure 6..5 (a) base (b) (c) footing time (sec) settlement, ρ (m) time (sec) ru = u / σ'vo z=1.7b z=1.3b time (sec) Typical results from the numerical analyses: Time-histories of (a) acceleration at the base of the model and at the soil surface, (b) dynamic settlements of the foundation and (c) excess pore pressure ratios at depths Z=1.3B and 1.7B underneath the footing s axis..15 (a) 5 (b) ρ dyn (m) B imp / B FS deg Figure Z imp / Z liq Z imp / Z liq Variation of (a) the dynamic settlements ρ dyn and (b) the post-shaking degraded factor of safety FS deg of the foundation, with the increasing nomalized thickness Z imp /Z liq of the improved zone. RESULTS OF PARAMETRIC ANALYSES The results of the parametric analyses that were performed in this study are summarized in Figure 7. More specifically, Figure 7a presents the variation, with the normalized thickness of the improved zone Z imp /Z liq of the dynamic settlements ρ dyn of the foundation, for the various examined normalized widths B imp /B of the improved zone. Furthermore, Figure 7b shows the variation of the post-shaking degraded factor of safety FS deg, with the normalized thickness of the improved zone Z imp /Z liq, for B imp /B=2.. In Figure 7a, it is observed that increasing the thickness of the improved non-liquefiable zone significantly decreases the developing dynamic settlements, for the given seismic excitation. This observation is in accordance with the findings of Bouckovalas and Dakoulas (27) and Karamitros et al (211), for the case of a physical cohesive non-liquefiable crust. As thoroughly explained by Karamitros et al (212), settlement accumulation is associated with the development of a composite failure mode, which comprises of punching of the foundation through the surfacial non-liquefiable crust and evolution of the failure mechanism within the underlying liquefiable layer. Hence, it becomes obvious that

9 increasing the thickness or the shear resistance of this crust would prohibit the development of this mechanism, thus decreasing the accumulating settlements, as is the case herein. Following the same logic, it is reasonable to expect that a minimum width of this superficial crust is required, for the punch-through failure mechanism to develop. This is in agreement with the numerical results for the case study examined herein, which indicates that increasing the width of the improved zone from B imp /B=1. to 2. has a significant beneficial effect, with respect to dynamic settlements. Namely, observe that a width of B imp /B=2. proves adequate for the punch-through shearing resistance to develop, thus larger values of B imp /B have only minor effects on dynamic settlements. Furthermore, focusing on the case of B imp /B=2. in Figure 7b, observe that the post-shaking degraded factor of safety FS deg remains larger than 1.25 for the whole range of examined thicknesses of the improved zone. As a result, the degraded factor of safety is not the key performance-based design criterion, in the case examined herein. Nevertheless, this conclusion should not be readily generalized, since, for weaker applied excitations, dynamic settlements are expected to be lower than in the present case-study (e.g. Bouckovalas & Dakoulas, 27, Karamitros et al, 211, Karamitros et al, 212), thus the foundation safety may be primarily controlled by its post-shaking degraded bearing capacity. Focusing on the accumulating dynamic settlements, an allowable value should be defined, in order to proceed to the selection the minimum required thickness of the non-liquefiable zone. Numerous performance-based design criteria have been proposed and may be found in the literature, for this purpose, with the ones corresponding to bridge foundations being summarized in Table 2. It is reasonable that the allowable settlement of bridge foundations is associated to the allowable extent of structural damage and the driving disturbance. Taking into account that subsoil liquefaction is an extreme loading case, the criterion of ρ<1cm proposed by Grover (1978), Bozozuk (1978) and Walhs (199) is conservatively adopted herein. According to this criterion, damage will occur on the superstructure, though it will remain within tolerable levels, resulting in minor driving disturbance along the bridge. According to the initial static design of the foundation, pre-shaking settlements are expected to remain below ρ st =2cm. Therefore, an additional allowable dynamic settlement of ρ dyn =8cm is considered, herein, resulting in a required normalized thickness of the improved zone, equal to Z imp /Z liq =.45. This corresponds to an absolute thickness of the improved zone Z imp =8m. The corresponding degraded factor of safety in this case becomes equal to FS deg =1.8, thus satisfying the performance-based design requirements. Table 2. Allowable settlements for bridge foundations. Allowable Settlement Performance Criterion Reference (cm) 5 No driving disturbance or structural damage Bozozuk (1978) 6.5 Driving disturbance Walkinshaw (1978) >6.5 Structural Damage Walkinshaw (1978) 1 Tolerable driving disturbance and structural damage Grover (1978), Bozozuk (1978) >1 Intolerable driving disturbance and structural damage Walhs (199) >.4L Intolerable for multiply supported structures Moulton et al. (1986) >.8L Intolerable for simply supported structures Duncan & Tan (TRB, 1981)

10 CONCLUDING REMARKS The conventional design practice for geotechnical structures in a liquefaction regime may result in highly overpriced foundation systems, which may include ground improvement measures, drainage and use of pile foundations. A similar case-study of a typical highway bridge pier was examined herein, where a combination of all three of the above techniques was used in the actual construction site. Aiming to provide an alternative, cost-effective solution, a sophisticated numerical methodology was utilized and the performance-based design feasibility of a surface footing resting on partially (with depth) improved foundation subsoil was examined. More specifically, the application of liquefaction mitigation measures was considered, not on the whole thickness of the liquefiable sand layer, but only within its upper zone. Parametric analyses were consequently performed, for different normalized widths B imp /B and normalized thicknesses Z imp /Z liq of this zone, in order to determine its required dimensions. The numerical analyses indicated that the application of liquefaction mitigation measures at an area wider than B imp >2.B has only minor effects to the liquefaction performance of the foundation, while, focusing on the case where B imp /B=2., it was shown that increasing the thickness of the improved zone results in a significant reduction of the expected dynamic settlements, while also increasing the post-shaking degraded bearing capacity. As a result, a feasible solution was eventually obtained, that may ensure foundation safety and minimize operational disturbance, at a fraction of the initial cost of the conventionally designed foundation. It must be noted, herein, that the design criteria in similar cases should be defined in terms of the allowable dynamic footing settlements, while also taking into account the post-shaking bearing capacity degradation due to the liquefaction-induced shear strength reduction of the foundation subsoil. Furthermore, it is stressed that allowing excess pore pressures to develop in a region underneath the foundation essentially creates a zone of natural seismic isolation, which significantly de-amplifies the accelerations reaching the ground surface, and may thus prove beneficial for the dynamic performance of the superstructure. Finally, note that the research on this topic is continued at the Foundation Engineering Laboratory of NTUA, focusing on the following main directions: Come up with an analytical design methodology which will eventually replace the numerical analyses and may also be included to seismic code provisions, Define the requirements for considering a liquefied soil layer as "natural seismic isolation" so that inertia effects on the superstructures may be efficiently reduced, and Define the performance-based design criteria for surface foundations settlements, subjected to seismic and not only to static loads. ACKNOWLEDGEMENTS The presented study was funded by the General Secretariat for Research and Technology (Γ.Γ.E.T.) of Greece, through research project EΠΑN- Π23 ( X-SOILS ), as well as by the Basic Research Fund Π.Ε.Β.Ε. of N.T.U.A. (Grant no. 65/186). Furthermore, in support of our research, Itasca Inc. has granted free use of FLAC3D (version 3.1) through Educational Loan S/N The above contributions are gratefully acknowledged.

11 REFERENCES Acacio, A.A., Kobayashi, Y., Towhata, I., Bautista, R.T., Ishihara, K. (21): Subsidence of building foundation resting upon liquefied subsoil case studies and assessment, Soils and Found., 41(6), pp Adalier, K., Elgamal, A., Meneses, J., Baez, J.I. (23): Stone columns as liquefaction countermeasure in non-plastic silty soils, Soil Dynamics and Earthquake Engineering, 23 (7), pp Andrianopoulos, K. (26): Numerical simulation of static and dynamic loading on elastoplastic soils, PhD Thesis, National Technical University of Athens, School of Civil Engineering, Geotechnical Division. Andrianopoulos K.I., Papadimitriou A. G., Bouckovalas G. D. (21a): Bounding surface plasticity model for the seismic liquefaction analysis of geostructures, Soil Dynamics and Earthquake Engineering. 3(1): Andrianopoulos K. I., Papadimitriou A. G., Bouckovalas G.D. (21b): Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction, International Journal for Numerical and Analytical Methods in Geomechanics. DOI: 1.12/nag Arulmoli, K., Muraleetharan, K.K., Hossain, M.M., Fruth, L.S. (1992): VELACS: Verification of Liquefaction Analyses by Centrifuge Studies; Laboratory Testing Soil Data Report, Research Report, The Earth Technology Corporation Bouckovalas, G., Dakoulas P. (27): Liquefaction Performance of Shallow Foundations in Presence of a Soil Crust, Invited Lectures of the 4th International Conference on Earthquake Geotechnical Engineering (4ICEGE), Volume 6, Bozozuk, M. (1978): Bridge foundations move, Transportation Research Record, 678, pp Coelho, P.A.L.F., Haigh, S.K., Madabhushi, S.P.G. (24): Centrifuge modelling of the effects of earthquake-induced liquefaction on bridge foundations, Proc. of the 11th ICSDEE, University of California, Berkeley. Grover, R.A. (1978): Movements of bridge abutments and settlements of approach pavements in Ohio, Transportation Research Record, 678, pp Ishihara, K., Acacio, A., Towhata, I. (1993): Liquefaction-induced ground damage in Dagupan in the July 16, 199 Luzon earthquake, Soils and Found,33(1),pp Karamitros D. (21): Development of a numerical algorithm for the dynamic elastoplastic analysis of geotechnical structures in two (2) and three (3) dimensions, PhD Thesis, National Technical University of Athens, School of Civil Engineering, Geotechnical Division. Karamitros D.K., Bouckovalas G.D., Chaloulos I. (211): Effect of Clay Crust on Seismic Liquefaction Performance of Surface Foundations, XV European Conference on Soil Mechanics & Geotechnical Engineering, Technical Workshop: ERTC-12 Geotechnical Evaluation and Application of the Seismic Eurocode EC-8, September 12-15, Athens. Karamitros D.K., Bouckovalas G.D. & Chaloulos Y.C. (212): Insight to the Seismic Liquefaction Performance of Shallow Foundations, ASCE Journal of Geotechnical and Geoenvironmental Engineering (submitted for review). Kawasaki, K., Sakai, T., Yasuda, S., Satoh, M. (1998): Earthquake-induced settlement of an isolated footing for power transmission tower, Centrifuge 98, pp Liu, L., Dobry, R. (1997): Seismic response of shallow foundation on liquefiable sand, Journal of Geotechnical and Geoenvironmental Engineering, 123 (6), pp Moulton, L.K. (1986): Tolerable movement criteria for highway bridges, 86 pp. Report No. FHWA-TS , Federal Highway Administration, Washington D.C. Papadimitriou, A.G., Bouckovalas, G.D. (22): Plasticity model for sand under small and large cyclic strains: a multiaxial formulation, Soil Dynamics and Earthquake Engineering, 22 (3), pp

12 Sancio, R.B., Bray, J.D., Stewart, J.P., Youd, T.L., Durgunoglu, H.T., Onalp, A., Seed, R.B., Christensen, C., Baturay, M.B., Karadayilar, T. (22): Correlation between ground failure and soil conditions in Adapazari, Turkey, Soil Dyn. and Earthquake Eng., 22 (9-12), pp Seed, H.B. & Booker, J.R. (1977): STABILIZATION OF POTENTIALLY LIQUEFIABLE SAND DEPOSITS, ASCE Journal of the Geotechnical Engineering Division, 13 (7), pp Wahls, H.E. (1986): ISSMFE Technical subcommittee on allowable deformations of buildings and damages, General report, 14 pp, 4 tables & 7 figs. Walkinshaw (1978): Survey of bridge movements in the Western United States, Transportation Research Record, 678, pp Yoshimi, Y., Tokimatsu, K. (1997): Settlement of buildings on saturated sand during earthquakes, Soils and Foundations, 17 (1), pp Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G., Christian, J.T., Dobry, R., Liam Finn, W.D., Harder L.F., Jr., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson III, W.F., Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., Stokoe II, K.H. (21): Liquefaction resistance of soils: Summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils, Journal of Geotechnical and Geoenvironmental Engineering, 127 (1), pp