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Gazetas G., (2015).“4th Ishihara Lecture: Soil-Foundation-Structure Systems Beyond Conventional Seismic Failure Thresholds”, Soils Dynamics and Earthquake Engineering, Vol. 68, pp. 23-39, 2015 .
A new paradigm has now emerged in performance–based seismic design of soils foundations structure systems. Instead of imposing strict safety limits on forces and moments transmitted from the foundation onto the soil (aiming at avoiding pseudo-static failure), the new dynamic approach “invites” the creation of two simultaneous “failure” mechanisms: substantial foundation uplifting and ultimate-bearing-capacity slippage, while ensuring that peak and residual deformations are acceptable. The paper shows that allowing the foundation to work at such extreme conditions not only may not lead to system collapse, but it would help protect (save) the structure from seismic damage. A potential price to pay: residual settlement and rotation, which could be abated with a number of foundation and soil improvements. Numerical studies and experiments demonstrate that the consequences of such daring foundation design would likely be quite beneficial to bridge piers, building frames, and simple frames retrofitted with a shear wall. It is shown that system collapse could be avoided even under seismic shaking far beyond the design ground motion. Three key phenomena are identified as the prime sources of the success; they are illustrated for a bridge pier: (i) the constraining of the transmitted accelerations by the reduced ultimate moment capacity of the foundation, to levels of about one-half of those developing in a conventional design; (ii) the beneficial action of the static vertical load of the structure which pushes down to “re-center” the leaning (due to uplifting and soil yielding) footing, instead of further distressing the plastic hinge of the column of the conventional design; and (iii) the substantial increase of the fundamental natural period of the system as uplifting takes place, which brings the structure beyond the significant period range of a ground motion, and hence leads to the abatement of its severe shaking. (Full Text)
Garini E., Makris N., Gazetas G. (2014).”Elastic and Inelastic Systems under Near-Fault Seismic Shaking : Acceleration Records versus Optimally-Fitted Wavelets”, Bulletin of Earthquake Engineering, DOI : 10.1007/s10518-014-9631-z
Four idealised dynamic systems, which are used as analogues in earthquake and geotechnical engineering, are studied: an elastic single-degree-of-freedom (sdof) oscillator; an elastic–perfectly-plastic sdof oscillator; a rigid block resting in simple frictional contact on a horizontal base; and a rigid block resting on a sloping plane. They are subjected to several near-fault-recorded ground motions bearing the effects of ‘forward-rupture directivity’and fault surface dislocation (‘fling-step’) phenomena—long-period acceleration pulses and large velocity or displacement steps. Two types of idealized wavelets (the Mavroeidis & Papageorgiou and the Ricker wavelets) are optimally-fitted to each record, applying the matching procedure presented by Vassiliou and Makris (Bull Seismol Soc Am 101(2):596–618, 2011). Extensive comparisons between the accelerogram response and the corresponding fitted wavelets response show if and when the destructive pulse-like part of the records is indeed their most deleterious component, and if and when this destructiveness can be captured with the particular fitted wavelets. For the two purely inelastic systems, in particular, the comparison elucidates the role of the contained pulses in the size of sliding displacements. The results reveal that while the response of elastic and elasto plastic sdof systems to the wavelets is usually reasonably similar with the response to the actual records, this is not usually the case for the two purely inelastic (sliding) systems. The unpredictable consequences of seismic shaking on such systems, even if the shaking intensity and frequency content were precisely known, is best demonstrated with the sensitivity of the size of sliding displacement to the polarity (+ or−), the sequence and number of cycles, and even the details of the excitation. (Full Text)
Loli M., Knappett J.M., Brown M.J., Anastasopoulos I. & Gazetas G (2014). “Centrifuge Modeling of Rocking-Isolated Inelastic RC Bridge Piers”, Earthquake Engineering &Structural Dynamics, DOI : 10.1002/eqe.2451
Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately under designing shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil-footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking-isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self-centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. (Full Text)
Karapiperis K., Gerolymos N. (2014). “Combined Loading of Caisson Foundation in Cohesive : Finite Element versus Winkler Modeling”, Computers and Geotechnics, Vol. 56, pp. 100-120.
The undrained response of massive caisson foundations to combined horizontal, vertical and moment loading is parametrically investigated through a series of 3D finite element analyses. The parameters are: (a) the embedment ratio (D/B), (b) the factor of safety against initial vertical loading (FSV) and (c) the ratio of the overturning moment to the horizontal force applied at the top of the caisson (M/Q). Emphasis is given on: (i) the identification of all possible failure mechanisms in M–Q–N space, (ii) the developed stress distributions along the caisson walls for various load levels up to complete failure conditions. The results are then used as a feedback for calibrating the parameters of a generalized four-type spring model, originally proposed by Gerolymos and Gazetas (2006), through a genetic algorithm-based optimization procedure. The predictions of the Winkler model compare very well with the FE results, not only at the local response level (in terms of stress distributions along the caisson shafts), but at a global response level (in terms of force–displacement curves and M–Q–N failure envelopes at the top of the caisson) as well. Contrary to established lateral soil resistance theories, it is shown that both the ultimate horizontal soil reaction and resisting moment per unit depth do not solely depend on the strength properties of soil and geometry of the caisson but are also functions of the applied load ratio M/Q and initial soil yielding due to vertical loading. Interesting conclusions are also drawn regarding the transition from the elastic to the ultimate limit state (hardening). Quantifying through analytical expressions the contribution of each of the two basic lateral resisting mechanisms to the response of the caisson, a classification method for embedded foundations is then proposed. The capabilities of the Winkler model are further demonstrated through comparison with FE analysis of the caisson cyclic lateral response. (Full Text)
Gazetas G., Anastasopoulos I., Garini Ev. (2014). “Geotechnical Design with Apparent Seismic Safety Factors Well-Bellow 1”, Soil Dynamics and Earthquake Engineering, Vol. 57, pp. 37-45.
The paper demonstrates that whereas often in seismic geotechnical design it is not realistically feasible to design with ample factor of safety against failure as is done in static design, an “engineering” apparent seismic factor of safety less than 1 does not imply failure. Examples from slope stability and foundation rocking illustrate the concept. It is also shown that in many cases it may be beneficial to under-design the foundation by accepting substantial uplifting and/or full mobilization of bearing capacity failure mechanisms. (Full Text)
Drosos V. and Anastasopoulos I. (2014). “Experimental Investigation of the Seismic Response of Classical Temple Columns”, Earthquake Engineering and Structural Dynamics, DOI 10.1007/s10518-014-9608-y.
Remnants of Greek Temples are found all over the Mediterranean, surviving in most cases in the form of free-standing columns. The drums are resting on top of each other without any connection, being considered susceptible to strong seismic shaking. Their seismic response is complex, comprising a variety of mechanisms, such as rocking of sliding of the drums relative to each other. This paper studies experimentally the seismic performance of such structures, aiming to derive insights on the key factors affecting the response. Physical models of such multi-drum columns were constructed at reduced scale and tested at the shaking table of the NTUA Laboratory of Soil Mechanics. The marble specimens were excited by idealized Ricker wavelets and real seismic records. The tested multi-drum columns were proven to be very earthquake-resistant. Even when subjected to the strongest motions ever recorded in Greece, their permanent deformation was minimal. (Full Text)
Anastasopoulos I. Kontoroupi Th. (2014). “Simplified Approximate Method for Analysis of Rocking Systems accounting for Soil Inelasticity and Foundation Uplifting”, Soil Dynamics and Earthquake Engineering, Vol. 56, pp. 28-43.
A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil in elasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element(FE)analyses,employing at horoughly – validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation(CR–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation(Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing itspredictionswiththeresultsof3DFEanalyses.The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means,be considered a substitute for more sophisticated analysis methods. However,despite its limitations, it may be utilized for (at least preliminary) design purposes. (Full Text)
Kourkoulis R., Lekkakis P., Gelagoti F., Kaynia A. (2014).”Suction caisson foundations for offshore wind turbines subjected to wave and earthquake loading : effect of soil-foundation interface”, Geotechnique, Vol. 63, pp. 1-15.
The response of wind turbines founded on suction caissons and subjected to lateral monotonic, cyclic and earthquake loading is studied with due consideration of the role of soil–sidewall adhesion, using non-linear three-dimensional finite-element analyses. In the case of monotonic and slow cyclic lateral loading it is shown that imperfect interface bonding could reduce the moment capacity and may lead to foundation detachment or even uplifting in the case of shallowly embedded caissons. A preliminary comparison of two caisson alternatives has shown that increasing the caisson diameter while maintaining the embedment ratio is more efficient in terms of material resources than increasing the skirt length while keeping the diameter constant. The second part of the study evaluates the response of a soil–foundation–wind turbine interacting system subjected to earthquake shaking. Contrary to an often prevailing impression that seismic effects are insignificant, apparently originating from evaluating the seismic behaviour on the basis of spectral characteristics, it is illustrated that the system kinematics may prove crucial for the response of large wind turbines subjected to simultaneous environmental and seismic loads. Although not instantly catastrophic, the accumulation of foundation rotation could lead to the turbine reaching serviceability limits early during its operation . (Full Text)
Anastasopoulos I., Gelagoti F., Spyridaki, A. Sideri Tz., and Gazetas G. (2014). “Seismic Rocking Isolation of Asymmetric Frame on Spread Footings”, Journal of Geotechnical and Geoenvironmental Engineering, Vol.140(1), pp. 133-151.
“Rocking−isolation” is a relatively new design paradigm advocating the intense rocking response of the superstructure as a whole, instead of flexural column deformation. This is accomplished through intentionally under-designing the foundation in order to guide plastic “hinging” below the ground surface, rather than in the columns. A two-storey two-bay asymmetric frame is used to explore the effectiveness of this novel design approach. Finite element dynamic analyses are performed using as seismic excitation idealized pulses and 20 real accelerograms, taking into account material (soil and superstructure) and geometric (uplifting and P–Δ effects) nonlinearities. A conventionally Eurocode–designed frame and its foundation are compared with a design featuring the same frame, but with substantially under–designed (“unconventional”) footings. It is found that the performance of the unconventional system is advantageous, as not only does it escape collapse, but as it also suffers repairable damage. Despite their reduced width, the residual settlements of the under-designed footings are comparable to those of the conventional ones. However, the analyses also reveal that residual rotation and differential settlement of the under-designed footings may be unavoidable and must be critically evaluated – a need exaggerated from the asymmetry of the examined frame. Three possible ways of improvement at the foundation level are examined: (a) a single conventional tie beam, monolithically connected to the footings ; (b) two separate tie beams hinged at each footing (allowing rotation, but resisting axial deformation) ; and (c) a hybrid system, comprising a single continuous tie beam connecting the three footings, but “externally” hinged to each of them. The first solution hardly offers improvement, as it hinders rocking ; and the second fails to reduce differential settlements. The “hybrid” solution provides encouraging results in terms of residual rotation and differential settlement, while it does not hinder the development of beneficial rocking isolation mechanisms, and fully restrains horizontal differential movements. (Full Text)
Adamidis O., Gazetas G., Anastasopoulos I., and Argyrou Ch. (2014). “Equivalent- Linear Stiffness and Damping in Rocking of Circular and Strip Foundations”, Bulletin of Earthquake Engineering, Vol. 12(3), 1177-1200. DOI: 10.1007/s10518-013-9554-0.
An approximation is developed for obtaining the nonlinear stiffness KR and damping CR of a shallow circular or strip footing undergoing rocking oscillation on a homogeneous but inelastic undrained clayey stratum. Based on the parametric results of 3-D and 2-D finite-element analyses, equivalent–linear KR and CR are expressed in readily usable dimensionless forms. KR, normalized by its linear elastic value, is shown to be a unique function of: (i) the vertical factor of safety Fs against static bearing capacity failure, and (ii) the angle of rotation θ normalized by a characteristic angle θs. The latter is approximately the angle for which uplifting usually initiates at one edge of the foundation. Three sources contribute to the value of the dimensionless damping ratio ξR (derived from CR): wave radiation, which is a function of frequency but is shown to amount to less than 3%; soil inelasticity (hysteresis), for which graphs are developed in terms of θ/θs and Fs; and energy loss due to impact and the collateral vertical motion when severe uplifting takes place, which is tentatively determined from dynamic M : θ loops. Comparative parametric seismic time-history analyses provide an adequate validation of the iterative equivalent-linear approximation which implements the developed equivalent ΚR and ξR , but they also highlight its limitations. (Full Text)
Anastasopoulos I., Loli M., Georgarakos T., and Drosos V. (2013), “Shaking Table Testing of Rocking−isolated Bridge Pier on Sand”, Journal of Earthquake Engineering, Vol.17(1), pp.1-32.
This paper studies the seismic performance of a rocking-isolated bridge pier. A series of reduced-scale shaking table tests are conducted, comparing the performance of the rocking-isolated system to conventional capacity design. The two design alternatives are subjected to a variety of shaking events, comprising real records and artificial motions of varying intensity. In an effort to explore system performance in successive seismic events, three different shaking sequences are performed. Rocking isolation is proven quite effective in reducing the inertia forces transmitted onto the superstructure. The rocking-isolated pier is effectively protected, surviving all seismic excitations without structural damage, at the cost of increased foundation settlement. In contrast, the conventionally-designed system is subjected to inertia forces in excess of the capacity of the RC pier, and, hence, a certain degree of structural damage is unavoidable. The rocking-isolated system is proven remarkably resistant to cumulative cyclic loading, exhibiting limited strength degradation even when subjected to cyclic drift ratio in excess of 5.5 %. Due to soil densification, the rate of settlement accumulation is found to decrease with repeating seismic excitations. The rotational response is practically insensitive to the shaking history when the preceding seismic events are symmetric. In stark contrast, when the preceding seismic events are non-symmetric (such as the directivity-affected records of this study), the system tends to accumulate rotation after each event, progressively worsening its performance. Nevertheless, the rocking-isolated system survives toppling collapse, even when subjected to a highly improbable, unrealistically harsh, sequence of seismic events. (Full Text)
Anastasopoulos I., Kourkoulis R., Gazetas G., Tsatsis A. (2013). “Interaction of Piled Foundation with a Rupturing Normal Fault”, Vol. 63(12), pp. 1042-1059, Géotechnique.
Post-seismic observations in the 1999 Kocaeli earthquake in Turkey have indicated that piled foundations may be less suitable than stiff mat foundations in defending a structure against a major normal fault rupturing underneath. This paper explores the interplay of such a rupture, as it propagates in a moderately dense sand stratum, with an embedded two by four pile foundation (typical of common highway overpass bridges). An experimentally validated numerical scheme and constitutive law for sand are utilised in the analysis, with due attention to realistically modelling the non-linear pile–soil interface and the structural inelasticity of the piles. Parametric results identify and elucidate the development of different rupture mechanisms as a function of the exact location of the group relative to the fault and of the magnitude of the tectonic displacement (the fault offset). It is shown that even for a moderate fault offset (less than 0•5 m), lightly reinforced piles will fail structurally, while also forcing the pile cap and the bridge pier on top to undergo substantial rotation and displacement. Even heavy reinforcement might not prevent potentially disastrous displacements. Pile inelasticity is unavoidable and should be acceptable as part of a ductility-based design. However, despite the possible survival of the piles themselves, letting them reach the limit of their ductility capacity may lead to large cap rotation and displacements, which are likely to impose severe demands on the superstructure. Piled foundations may indeed be inferior to rigid raft foundations in protecting a structure straddling an active seismic fault, but with few notable exceptions. (Full Text)
Fadaee M., Anastasopoulos I., Gazetas G., Jafari M.K., Kamalian M. (2013). “Soil Bentonite Wall Protects Foundation from Thrust Faulting : Analyses and Experiment”, Earthquake Engineering and Engineering Vibration, Vol. 12(3), pp.473-486.
When seismic thrust faults emerge on the ground surface, they are particularly damaging to buildings, bridges and lifelines that lie on the rupture path. To protect a structure founded on a rigid raft, a thick diaphragm-type soil bentonite wall (SBW) is installed in front of and near the foundation, at sufficient depth to intercept the propagating fault rupture. Extensive numerical analyses, verified against reduced–scale (1 g) split box physical model tests, reveal that such a wall, thanks to its high deformability and low shear resistance, “absorbs” the compressive thrust of the fault and forces the rupture to deviate upwards along its length. As a consequence, the foundation is left essentially intact. The effectiveness of SBW is demonstrated to depend on the exact location of the emerging fault and the magnitude of the fault offset. When the latter is large, the unprotected foundation experiences intolerable rigid-body rotation even if the foundation structural distress is not substantial. (Full Text)
Tasiopoulou P., Gerolymos N., Tazoh T., and Gazetas G. (2013) “Pile – Group Response to Large Soil Displacements and Liquefaction : Centrifuge Experiments Versus a Physically Simplified Analysis”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 139(2), pp.223-233.
The paper presents a physically simplified method for computing displacements and structural forces on piles under conditions of lateral spreading triggered by the large seaward displacement of a harbor quay‐wall. The method avoids the empirical selection of stiffness‐reduction factors and the associated use of p ‐ y curves that current state‐of‐the‐art methods employ. Instead, the 3D highly nonlinear problem is approximated in two steps, both involving 2D plane‐strain analyses. The first step involves a vertical (representative) slice in which the pile group has been omitted and which, shaken at its base, gives the permanent deformation of the quay‐wall and of the liquefiable soil. It is an effective stress analysis. In the second step, a horizontal (representative) slice taken from the middle of the liquefiable zone is subjected to an outward quay‐wall displacement; the goal is to evaluate the reduction of the pile displacement over the free‐field one, and the ensuing pile group distress. The pile resistance to ground deformation depends heavily on the constraints imposed by the superstructure, as well on the exact stiffness of the soil layers. Thus, the interplay between soil‐piles‐quaywall under soil flow conditions is captured in a physically meaningful way. The predictions compare well with results from two centrifuge tests. (Full Text)
Zafeirakos A., Gerolymos N., Drosos V. (2013). “Incremental Dynamic Analysis of Caisson–Pier Interaction”, Soil Dynamics and Earthquake Engineering 48, 71–88.
This paper presents a 3D finite element Incremental Dynamic Analysis (IDA) study of caisson foundations carrying single-degree-of freedom (SDOF) structures on clayey soil. The emphasis is given to the interplay between the nonlinearities developed above (superstructure) and, mainly, below ground surface, either of material (soil plasticity) or of geometric (caisson–soil interface gap in g and slippage) origin. The study is performed with respect to the static (FS) and the seismic(FE) safety factor of the foundation and involves SDOF oscillators of varying mass (to account for vertical loading, FS) and height (relating to moment loading, FE) founded on similar I rigid cubic caissons. Structural nonlinearity is considered through a simplified moment-curvature law and the yield strength is deliberately chosen so that the following three configurations are obtained:(a) a lightly loaded (FS=5) seismically under-designed (as compared to the superstructure) caisson, (b) a lightly loaded seismically over-designed caisson, and (c) a heavily loaded (FS=2.5) seismically under-designed caisson. The analysis is performed with several earthquake records, each scaled to multiple levels of intensity. IDA curves are produced for a single intensity measure, (peak ground acceleration, PGA), and appropriate engineering demand parameters (EDP) describing both the maximum and the residual response of the system. The results emphasize a potentially beneficial role of foundation nonlinearities in reducing the seismic demands on the superstructure, but at the cost of residual foundation settlements and rotations. (Full Text)
Zafeirakos A., Gerolymos N. (2013). “On the Seismic Response of Under-Designed Caisson Foundations”, Bulletin of Earthquake Engineering, Vol. 11, pp. 1337-1372.
The seismic behaviour of caisson foundations supporting typical bridge piers is analysed with 3D finite elements, with due consideration to soil and interface nonlinearities. Single-degree-of freedom (SDOF) oscillators of varying mass and height, simulating heavily and lightly loaded bridge piers, founded on similar caissons are studied. Four different combinations of the static (FSV) and seismic (FSE) factors of safety are examined: (a) a lightly loaded (FSV = 5) seismically under-designed (FSE < 1) caisson, (b) ) a lightly loaded seismically over-designed (FSE >1) caisson, (c) a heavily loaded (FSV = 2.5) seismically under-designed (FSE < 1) caisson and (d) a heavily loaded seismically over-designed caisson. The analysis is performed with use of seismic records appropriately modified so that the effective response periods (due to soil-structure-interaction effects) of the studied systems correspond to the same spectral acceleration, thus allowing their inelastic seismic performance to be compared on a fair basis. Key performance measures of the systems are then contrasted, such as: accelerations, displacements, rotations and settlements. It is shown that the performance of the lightly loaded seismically under-designed caisson is advantageous: not only does it reduce significantly the seismic load to the superstructure, but it also produces minimal residual displacements of the foundation. For heavily loaded foundations, however (FSV = 2.5), the performance of the two systems (over and under designed) is similar. (Full Text)
Gazetas G., Anastasopoulos I., Adamidis O., Kontoroupi Th.(2013). “Nonlinear Rocking Stiffness of Foundations”, Soil Dynamics & Earthquake Engineering, Vol. 47, pp.83-91.
The response of surface foundations to large over turning moments is studied under undrained conditions. Rigid circular, strip, and rectangular footings of various aspect ratios are considered, with the soil modeled as an inelastic homogeneous deposit, characterized by an elastic (small-strain) shear modulus Go, an undrained shear strength Su, and a G/Go versus c curve appropriate for medium- plasticity clays. Three stages of foundation performance, ranging from the initial elastic fully-bonded response, to the nearly-elastic but nonlinear response with the foundation partially detaching and uplifting from the soil, and finally to the ultimate stage where full mobilization of soil bearing failure mechanisms develop. Simple to use formulas or charts are developed for all stages of response in terms of dimensionless parameters, prominent among which is the static factor of safety against bearing- capacity failure under purely-vertical loading. (Full Text)
Sapountzakis E.J. and Kampitsis A.E.(2013). “Inelastic Analysis of Beams on Two-Parameter Tensionless Elastoplastic Foundation”, Engineering Structures,Vol.48, pp.389-401.
In this paper a boundary element method is developed for the inelastic analysis of Euler–Bernoulli beams of simply or multiply connected constant cross-section having at least one axis of symmetry, resting on two-parameter tensionless elastoplastic foundation. The beam is subjected to arbitrarily distributed or concentrated vertical loading along its length, while its edges are subjected to the most general boundary conditions. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed plasticity model exploiting material constitutive laws and numerical integration over the cross-sections. An incremental–iterative solution strategy along with an efficient iterative process are employed, while the arising boundary value problem is solved employing the boundary element method. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy. (Full Text)
Sapountzakis E.J. and Kampitsis A.E.(2013). “Nonlinear Dynamic Analysis of Shear Deformable Beam-Columns on Nonlinear Three-Parameter Viscoelastic Foundation.II:Applications and Validation”, Journal of Engineering Mechanics, Vol. 139(7), pp.897-902.
The nonlinear dynamic analysis of beam-columns undergoing moderate large deflections and partially supported on a nonlinear three-parameter viscoelastic foundation is presented, taking into account the effects of shear deformation and rotary inertia and employing the boundary element method (BEM). The beam’s constant cross section is an arbitrarily shaped, doubly symmetric simply or multiply connected one, while its edges are supported by the most general boundary conditions. In Part I the governing equations have been derived, leading to five boundary-value problems with respect to the transverse displacements, to the axial displacement, and to two stress functions. These problems are numerically solved using the analog equation method, a BEM-based method. In Part II the numerical applications are worked out to illustrate the efficiency, and wherever possible the accuracy and range of applications of the proposed method. Thus, the results obtained from the developed method are presented compared with those obtained from the literature and from finite-element software. More specifically, the linear analysis of a simply supported beam-column on a Pasternak-viscoelastic foundation, the nonlinear analysis of a clamped beam-column on a viscoelastic or nonlinear three-parameter viscoelastic foundation, and the nonlinear analysis of a partially embedded column-pile in a nonlinear three-parameter viscoelastic foundation are presented and discussed through applications of particular interest. (Full Text)
Sapountzakis E.J. and Kampitsis A.E.(2013). “Nonlinear Dynamic Analysis of Shear Deformable Beam-Columns on Nonlinear Three-Parameter Viscoelastic Foundation.I:Theory and Numerical Implementation”, Journal of Engineering Mechanics, Vol. 139(7), pp. 886-896.
A boundary element method is developed for the nonlinear dynamic analysis of beam-columns of an arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on a nonlinear three-parameter viscoelastic foundation, undergoing moderate large deflections under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical development and numerical implementation of the method, while Part II discusses the examined numerical applications illustrating the efficiency (wherever possible), the accuracy, and the range of applications of the proposed method. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions, as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary-value problems are formulated with respect to the transverse displacements, axial displacement, and two stress functions, and solved using the analog equation method, a boundary element-based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution to this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton-Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of the bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. (Full Text)
Psycharis I., Fragiadakis M., Stefanou I.(2013). “Seismic reliability assessment of classical columns subjected to near-fault ground motions”, Earthquake Engineering & Structural Dynamics, Vol.42, pp. 2061-2079.
A methodology for the performance-based seismic risk assessment of classical columns is presented. Despite their apparent instability, classical columns are, in general, earthquake resistant, as proven from the fact that many classical monuments have survived many strong earthquakes over the centuries. Nevertheless, the quantitative assessment of their reliability and the understanding of their dynamic behaviour are not easy, due to the fundamental non-linear character and the sensitivity of their response. In this paper, a seismic risk assessment is performed for a multidrum column using Monte Carlo simulation with synthetic ground motions. The ground motions adopted contain a high and a low frequency component, combining the stochastic method and a simple analytical pulse model to simulate the directivity pulse contained in near source ground motions. The deterministic model for the numerical analysis of the system is three dimensional and is based on the Discrete Element Method (3D DEM). Fragility curves are produced conditional on magnitude and distance from the fault and also on scalar intensity measures for two engineering demand parameters (EDPs), one concerning the intensity of the response during the ground shaking and the other the residual deformation of the column. Three performance levels are assigned to each EDP. Fragility analysis demonstrated some of the salient features of these spinal systems under near-fault seismic excitations, as for example their decreased vulnerability for very strong earthquakes of magnitude 7 or larger. The analysis provides useful results regarding the seismic reliability of classical monuments and decision making during restoration process. (Full Text)
Kampitsis A., Sapountzakis E., Giannakos S., Gerolymos N. (2013) “Seismic Soil-Pile-Structure Kinematic and Inertia Interaction – A New Beam Approach”, Soil Dynamics and Earthquake Engineering, Vol.55, pp.211-224.
The main purpose of this study is to investigate the accuracy of an advanced beam model for the soil–pile–structure kinematic and inertia interaction and demonstrate its efficiency and advantages compared to other commonly used beam or solid models. Within this context, a beam on nonlinear Winkler foundation model is adopted based on the Boundary Element Method (BEM), accounting for the effects induced by geometrical nonlinearity, rotary inertia and shear deformation, employing the concept of shear deformation coefficients. The soil nonlinearity is taken into consideration by means of a hybrid spring configuration consisting of a nonlinear (p-y) spring connected in series to an elastic spring–damper model. The nonlinear spring captures the near–field plastification of the soil while the spring–damper system (Kelvin–Voigt element) represents the far–field viscoelastic character of the soil. An extensive case study is carried out on a pile–column–deck system of a bridge, founded in two cohesive layers of sharply different stiffness and subjected in various earthquake excitations, providing insight to several phenomena. The results of the proposed model are compared with those obtained from a Beam–FE solution as well as from a rigorous fully three-dimensional (3–D) continuum FE scheme. (Full Text)
Makris, N. and G. Kampas (2013). “The Engineering Merit of the “Effective Period” of Bilinear Isolation Systems”, Earthquakes and Structures, Vol 4, No 4, 2013, pp 397-428.
This paper examines whether the ―effective period‖ of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulse like excitations, the paper shows that the ―effective period‖ = Teff of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system = T2 is an even better approximation regardless the value of the dimensionless strength, Q/(K2 uy) = 1/α – 1, of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a ―linear‖ vibration period has a marginal engineering merit. (Full Text)
Alexakis, H. and N. Makris (2013). “Structural Stability and Bearing Capacity Analysis of the Tunnel-Entrance to the Stadium of Ancient Nemea”,International Journal of Architectural Heritage, Vol. 7(6), pp. 673-692.
In the archaeological site of Ancient Nemea, Greece, southeast of the Temple of Zeus, is an ancient stadium in which the athletes of the past entered through a 36-m tunnel—a cut-and– cover vaulted structure, constructed of limestone. The tunnel was buried with earth until it was discovered in 1978. At present, some limestone blocks of the tunnel show appreciable damage mainly due to the humidity fluctuation within the tunnel. This study presents a comprehensive structural analysis of the tunnel, ranging from the thrust line limit analysis and the discrete element method to a three-dimensional finite-element analysis of the tunnel and its surrounding soil. The study concludes that the tunnel with its overburden-surrounding soil is structurally stable and has ample bearing capacity. The study also shows that the stones that suffer the most noticeable exfoliation due to the humidity fluctuation are those for which their visible surface from the inside of the tunnel is in compression. In conclusion, selective stones of the structure need to be retrofitted in order to avoid further local failures, while the humidity fluctuation inside the tunnel needs to be minimized. (Full Text)
Makris, N. and M.F. Vassiliou, (2012). “Sizing the Slenderness of Free-Standing Rocking Columns to Withstand Earthquake Shaking”,Archive of Applied Mechanics, Vol. 82, pp. 1497-1511
This paper investigates the problem of sizing the width of tall free-standing columns with a given height which are intended to rock, yet shall remain stable during the maximum expected earthquake shaking. The motivation for this study is the emerging seismic design concept of allowing tall rigid structures to uplift and rock in order to limit base moments and shears. The paper first discusses the mathematical characterization of pulse-like ground motions and the dimensionless products that govern the dynamics of the rocking response of a free-standing block and subsequently, using basic principles of dynamics, derives a closed-form expression that offers the minimum design slenderness that is sufficient for a free-standing column with a given size to survive a pulse-like motion with known acceleration amplitude and duration. (Full Text)
Gelagoti F., Kourkoulis R., Anastasopoulos I., and Gazetas I. (2012). “Nonlinear Dimensional Analysis of Trapezoidal Valleys Subjected to Vertically Propagating SV Waves”, Bulletin of the Seismological Society of America, Vol. 102, No. 3, pp. 999–1017.
This paper studies the seismic response of soil basins emphasizing the sensitivity of 2D dynamic response to geometric and material properties. This is accomplished through a formal dimensional analysis accounting for fully inelastic soil response thus augmenting the generalization potential of the results, and providing a novel framework for future research on the subject. It is shown that 2D valley response may be described through the following key dimensionless parameters: (1) the valley shape factor s, expressing the slope inclination; (2) the impedance ratio i, which expresses the stiffness of the soil relative to the bedrock; (3) the wavelength ratio λS, which is a function of soil stiffness and seismic excitation frequency; (4) the rigidity ratio v, expressing the stiffness of the soil relative to its strength; and (5) the resistance ratio r, which expresses the degree of soil nonlinearity. The effectiveness of the dimensional formulation is verified through the numerical analysis of equivalent valleys, assuming elastic and nonlinear soil response. Finally, a parametric study is conducted to gain insight on the effects of the introduced dimensionless parameters on the dynamic response of trapezoidal alleys. It is shown that decreasing the valley slope or the wavelength ratio promotes wave reflections within the wedge, thus enhancing the possibility of wave interferences and subsequently leading to 2D aggravation on the valley surface. On the other hand, the geometry-dependent parasitic vertical acceleration increases as the valley slope becomes steeper. As the degree of soil nonlinearity increases, 2D phenomena tend to become localized close to the valley edges. (Full Text)
Kourkoulis R., Gelagoti F., I. Anastasopoulos (2012). “Rocking Isolation of Frames on Isolated Footings : Design Insights and Limitations”, Journal of Earthquake Engineering, Vol. 16, pp. 374-400.
To date, a significant research effort has been devoted attempting to introduce novel seismic protection schemes, taking advantage of mobilization of inelastic foundation response. According to such an emerging seismic design concept, termed “rocking isolation,” instead of over-designing the footings of a frame (as in conventional capacity design), they are intentionally under-designed to promote uplifting and respond to strong seismic shaking through rocking, thus bounding the inertia forces transmitted to the superstructure. Recent research has demonstrated the potential effectiveness of rocking isolation for the seismic protection of frame structures, using a simple 1-bay frame as an illustrative example. This article: (a) sheds light in the possible limitations of rocking isolation, especially in view of the unavoidable uncertainties regarding the estimation of soil properties; (b) investigates the potential detrimental effects of ground motion characteristics; and (c) assesses the effectiveness of rocking isolation to more complex structures. It is shown that the concept may be generalized to 2-bay frames, and that even when foundation rocking is limited, the positive effect of foundation under-design remains, especially when it comes to very strong seismic shaking. In contrast, its effectiveness may belimited when the frame is subjected to combined horizontal and synchronous vertical acceleration components — a possible scenario on the surface of alluvial basins. (Full Text)
Panagiotidou A.I., Gazetas G., N. Gerolymos. (2012) “Pushover and Seismic Response of Foundations on Stiff Clay: Analysis with P-Δ Effects”, Earthquake Spectra , Vol. 28(4), pp.1589-1618.
Finite-element analyses are performed for the response to lateral monotonic, slow-cyclic, and seismic loading of rigid footings carrying tall slender structures and supported on stiff clay. The response involves mainly footing rotation under the action of overturning moments from the horizontal external force on, or the developing inertia at, the mass of the structure, as well as from the aggravating contribution of its weight (P-Δ effect). Emphasis is given to the conditions for collapse of the soil–foundation–structure system. Two interconnected mechanisms of nonlinearity are considered: detachment from the soil with subsequent uplifting of the foundation (geometric nonlinearity) and formation of bearing-capacity failure surfaces (material inelasticity). The relation between monotonic behavior (static “pushover”), slow-cyclic behavior, and seismic response is explored parametrically. We show that with “light” structures uplifting is the dominant mechanism that may lead to collapse by dynamic instability (overturning), whereas “very heavy” structures mobilize soil failure mechanisms, leading to accumulation of settlement, residual rotation, and ultimately collapse. (Full Text)
Anastasopoulos I., Kourkoulis R., Gelagoti F., Papadopoulos E. (2012), “ Rocking Response of SDOF Systems on Shallow Improved Sand : an Experimental Study”, Soil Dynamics and Earthquake Engineering, Vol. 40, pp. 15-33.
Recent studies have highlighted the potential advantages of allowing inelastic foundation response during strong seismic shaking. Such an alternative seismic design philosophy, in which soil failure used as a ‘‘fuse’’ for the superstructure has recently been proposed, in the form of ‘‘rocking isolation. Within this context, foundation rocking may be desirable as a means of bounding the inertia force transmitted onto the superstructure, but incorporates the peril of unacceptable settlements in case of low static factor of safety FS. Hence, to ensure that rocking is materialized through uplifting rather than sinking, an adequately large FSv is required. Although this is feasible in theory, soil properties are not always well-known in engineering practice. However, since rocking-induced soil yielding is only mobilized within a shallow layer underneath the footing, ‘‘shallow soil improvement’’ is considered as an alternative approach to release the design from the jeopardy of unforeseen inadequate FSv. For this purpose, this paper studies the rocking response of relatively slender SDOF structures (h/B ratio equals 3 and rocking dominates over sliding), with emphasis on the effectiveness of shallow soil improvement stretching to various depths below the foundation. A series of reduced-scale monotonic and slow-cyclic pushover tests are conducted on SDOF systems lying on a square surface foundation. It is shown that shallow soil improvement may, indeed, be quite effective provided that its depth is equal to the width of the foundation. For lightly-loaded systems, an even shallower soil improvement may also be considered effective, depending on design requirements. The effectiveness of shallow soil improvement is ameliorated with the increase of cyclic rotation amplitude, and with repeating cycles of loading. (Full Text)
Giannakos S., Gerolymos N., Gazetas G. (2012), “Cyclic Lateral Response of Piles in Dry Sand : Finite Element Modelling and Validation”, Computers and Geotechnics, Vol. 14, pp.116-131, 2012.
The response of a vertical pile embedded in a dry dense sand when subjected to cyclic lateral loading is studied numerically. Three-dimensional ﬁnite element analyses with a new constitutive model of cyclic behavior of sand reproduce published centrifuge tests results. Three types of cyclic loading, two asymmetric and one symmetric are applied. Performance measure parameters (the normalized tangent and secant stiffnesses with respect to the ﬁrst cycle of loading and the relative pile head displacement between two consecutive loading-unloading reversal points) are introduced to evaluate the results of the overall response of the pile–soil system. The results replicate the plastic shakedown response of the pile -soil system during cyclic loading, a response which is attributed to two mechanisms (a) soil densiﬁcation and (b) ‘‘system’’ densiﬁcation due to the gradual enlargement of the resisting soil mass to greater depths with cyclic loading. It is shown that the hardening mechanism of ‘‘system’’ densiﬁcation dominates upon soil densiﬁcation in cyclic loading. The response of a 1 x 2 pile group under cyclic lateral loading is also numerically investigated, emphasizing the role of cyclic loading on (a) the pile-to-pile interaction, (b) the additional pile distress due to the group effect, and (c) the shadow effect. (Full Text)
Gazetas G., Garini E., Berill J.B., Apostolou M. (2012), “ Sliding and Overturning Potential of the Christchurch 2011 Earthquake Records”, Earthquake Engineering and Structural Dynamics, Vol.41, pp. 1921-1944.
The 22 February 2011 Mw 6.3 earthquake produced a number of unique accelerograms in the city of Christchurch and the port of Lyttelton. Four of these records are analyzed in this paper. The two are from the Christchurch Catholic Cathedral College and Christchurch Hospital stations in the center of the city, which were placed on top of loose sandy soils that suffered softening due to liquefaction; one is from the Lyttelton station, Lyttelton Port Company, on a rock outcrop; and one is from the station at the Heathcote Valley Primary School, on stiff colluvial silts and sands near the edge of a steep and stiff sedimentary basin. The (elastic) response spectra are discussed and related to some salient characteristics of the motions. Symmetric and asymmetric sliding of a block resting through Coulomb friction on horizontal or inclined planes and rocking–overturning of rigid blocks, when excited at their base by these records, offer a strong indication of their ‘destructiveness potential’. The corresponding sliding and overturning spectra of the 2011 records are compared with those of some historic accelerograms to get an understanding of the severity of ground shaking that caused 170 deaths and heavy geotechnical and structural damage in the city of Christchurch. The possible role played by the unusually large vertical accelerations is also explored. (Full Text)
Kourkoulis R., Gelagoti F., Anastasopoulos I., Gazetas G. (2012), “Hybrid Method for Analysis and Design of Slope Stabilizing Piles”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 138(1), pp. 1–14.
Piles are extensively used as a means of slope stabilization. Despite the rapid advances in computing and software power, the design of such piles may still include a high degree of conservatism stemming from the use of simplified easy to apply methodologies. This paper develops a hybrid method for designing slope stabilizing piles, combining the accuracy of rigorous 3D finite element (FE) simulation with the simplicity of widely accepted analytical techniques. It comprises two steps : (a) evaluation of the lateral resisting force RF needed to increase the safety factor of the precarious slope to the desired value, and (b) estimation of the optimum pile configuration offering the required RF for a prescribed deformation level. The first step utilizes the results of conventional slope stability analysis. A novel approach is proposed for the second step. This consists of the decoupling of the slope geometry from the computation of pile lateral capacity, which allows numerical simulation of only a limited region of soil around the piles. A comprehensive validation is presented against published experimental, field, and theoretical results from fully coupled 3D non‐linear FE analyses. It is shown that the proposed method provides a useful computationally efficient tool for parametric analyses and design of slope stabilizing piles. (Full Text)
Kourkoulis R., Anastasopoulos I., Gelagoti F., Kokkali P. (2012), “Dimensional Analysis of SDOF Systems Rocking on Inelastic Soil”, Journal of Earthquake Engineering, Vol.16(7), pp. 995-1022.
Aiming to derive results of generalized applicability and provide a generalization framework for future research on the subject, this article performs a dimensional analysis of SDOF systems rocking on compliant soil, taking account of soil inelasticity, foundation uplifting, and P–δ effects. The effectiveness of the proposed formulation, under static and dynamic conditions, is verified through numerical analyses of self-similar “equivalent” systems. Then, a parametric study is conducted to gain further insights on the key factors affecting the performance, with emphasis on metaplastic ductility and toppling rotation. It is shown that P–δ effects may lead to a substantial reduction of (monotonic) moment capacity, especially in the case of slender and heavily loaded structures. Interestingly, this reduction in moment capacity is compensated (to some extent) by an overstrength that develops during cyclic loading. Asymmetric (near-field) seismic excitations tend to produce larger maximum and permanent rotation, compared to symmetric multi-cycle (far-field) excitations, which are critical in terms of settlement. The dimensionless toppling rotation θ ult /θ c (where θ c is the toppling rotation of the equivalent rigid block) is shown to be a function of the factor of safety against vertical loads FS v and the slenderness ratio h/B. In the case of lightly loaded systems (FS v → ∞), soil plastification is limited and the metaplastic response approaches that of the equivalent rigid block : θ ult /θ c → 1. The toppling rotation θ ult /θc is shown to decrease with FS v : θ ult /θ c → 0 for FS v → 1. The role of the h/B becomes increasingly important when the response is governed by soil nonlinearity (FS v → 1). Finally, an approximate simplified “empirical” equation is proposed, correlating θ ult /θ c with h/B and FS v . (Full Text)
Gelagoti F., Kourkoulis R., Anastasopoulos I., and Gazetas G. (2012) “Rocking isolation of low-rise frame structures founded on isolated footings”, Earthquake Engineering and Structural Dynamics, Vol.41(7), pp.1177-1197.
This paper explores the effectiveness of a new approach to foundation seismic design. Instead of the present practice of over-design, the foundations are intentionally under-dimensioned so as to uplift and mobilize the strength of the supporting (stiff) soil, in the hope that they will thus act as a rocking–isolation mechanism, limiting the inertia transmitted to the superstructure, and guiding plastic ‘hinging’ into soil and the foundation–soil interface. An idealized simple but realistic one-bay two-story reinforced concrete moment resisting frame serves as an example to compare the two alternatives. The problem is analyzed employing the finite element method, taking account of material (soil and superstructure) and geometric (uplifting and P–Δ effects) nonlinearities. The response is first investigated through static pushover analysis. It is shown that the axial forces N acting on the footings and the moment to shear (M/Q) ratio fluctuate substantially during shaking, leading to significant changes in footing moment-rotation response. The seismic performance is explored through dynamic time history analyses, using a wide range of unscaled seismic records as excitation. It is shown that although the performance of both alternatives is acceptable for moderate seismic shaking, for very strong seismic shaking exceeding the design, the performance of the rocking-isolated system is advantageous: it survives with no damage to the columns, sustaining non-negligible but repairable damage to its beams and non-structural elements (infill walls, etc.). (Full Text)
Drosos V., Gerolymos N., Gazetas G. (2012). “Constitutive Model for Soil Amplification of Ground Shaking : Parameter, calibration, comparison, validation.” Soil Dynamics and Earthquake Engineering, Vol. 42, pp. 255-274.
A phenomenological constitutive model developed by Gerolymos and Gazetas (2005) for the one-dimensional nonlinear ground response analysis of soil deposits is modified, calibrated, and verified in this paper. The small number of parameters renders the model easily implemented, yet powerful, able of efficiently reproducing the nonlinear hysteretic behavior of various soils and simultaneously generating realistic shear modulus reduction and damping ratio curves. Model is calibrated against three sets of widely-used published G-γ / ξ-γ curves and a library of parameter values is assembled for utilization of the new model to analyze 1-D seismic soil response problems. The model and the explicit finite–difference code for the integration of the wave equations necessary to obtain the dynamic response of soil deposits are then validated against more sophisticated constitutive models and numerical tools, and experimental data from centrifuge tests. The sufficiently close agreement of calculated results and experimental measurements gives confidence for the use of the proposed model. (Full Text)
Drosos V., Georgarakos P., Loli M., Zarzouras O., Anastasopoulos I., Gazetas G. (2012). “Soil–Foundation–Structure Interaction with Mobilization of Bearing Capacity : An Experimental Study.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 138(11), pp.1369-1386.
While the current seismic design practice accepts yielding of structural members and nonlinear behaviour of the superstructure, at the same time it does not allow plastic deformation of foundation. However, recent earthquakes and modern research findings have shown that limited nonlinear foundation response may not be always unavoidable or detrimental. This paper presents an experimental study on the role of nonlinear foundation response on the performance of a structure–footing system. A typical bridge pier supported on shallow footings and founded on dense sand is tested on the shaking table. Three different footings characterized by distinctively different safety factors against vertical load FSV are examined under six ground motions of various intensities. The experimental findings show that the nonlinear foundation response neither unavoidable is, nor detrimental for the overall system performance. An “under designed” (according to current seismic codes) foundation transfers to the superstructure quite lower straining compared to a conventionally designed foundation. The increased residual settlements and rotations of the foundation experienced as compensation do not jeopardize the stability of the structure. (Full Text)
Gelagoti F., Kourkoulis R., Anastasopoulos I., Gazetas G. (2012), “Rocking Isolated Frame Structures: Margins of Safety against Toppling Collapse and Simplified Design Approach”, Soil Dynamics and Earthquake Engineering, Vol. 62(1), pp.87-102, 2012.
This paper aims to explore the limitations associated with the design of “rocking-isolated”frame structures. According to this emerging seismic design concept, instead of over-designing the isolated footings of a frame (as entrenched in current capacity–design principles), the latter are under-designed with the intention to limit the seismic loads transmitted to the superstructure. An idealized 2-storey frame is utilized as an illustrative example, to investigate the key factors affecting foundation design. Nonlinear FE analysis is employed to study the seismic performance of the rocking-isolatedframe. After investigating the margins of safetyagainsttopplingcollapse, a simplified procedure is developed to estimate the minimum acceptable footing width Bmin, without recourse to sophisticated (and time consuming) numerical analyses. It is shown that adequate margins of safetyagainsttopplingcollapse may be achieved, if the toppling displacement capacity of the frameδtopl (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand δdem. With respect to the capacity, the use of an appropriate “equivalent” rigid-body is suggested, and shown to yield a conservative estimate of δtopl. The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SDmax is proposed as a conservative measure of δdem. The validity and limitations of such approximation are investigated for a rigid-block on rigid-base, utilizing rigorous analytical solutions from the bibliography; and for the frame structure on nonlinear soil, by conducting comprehensive nonlinear dynamic time history analyses. In all cases examined, the simplifiedSDmaxapproach is shown to yield reasonably conservative estimates. (Full Text)
Sapountzakis E.J., and Kampitsis A.E.(2012). “A BEM Approach for Inelastic Analysis of Beam-Foundation Systems under Cyclic Loading”, CMES, Vol. 87(2), pp. 97-127.
In this paper a Boundary Element Method (BEM) is developed for the inelastic analysis of beams of arbitrarily shaped constant cross section having at least one axis of symmetry, resting on nonlinear inelastic foundation. The beam is subjected to arbitrarily distributed or concentrated vertical cyclic loading along its length, while its edges are subjected to the most general boundary conditions. A displacement based formulation is developed and inelastic redistribution is modelled through a distributed plasticity model exploiting material constitutive laws and numerical integration over the cross sections. An incremental-iterative solution strategy is adopted to resolve both the plastic part of stress resultants and the foundation reaction along with an efficient iterative process to integrate the inelastic rate equations. The arising boundary value problem is solved employing BEM. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. (Full Text)
Vassiliou M. and Makris N. (2012). “Analysis of the rocking response of rigid blocks standing free on a seismically isolated base”, Earthquake Engineering & Structural Dynamics, Vol. 41(2), pp. 177–196.
This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free- standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. (Full Text)
Kampas G. and Makris Ν. (2012). “Transverse versus Longitudinal Eigenperiods of Multispan Seismic Isolated Bridges”, Journal of Structural Engineering, 138(2), pp. 193–204.
This paper is motivated from the wider need in system identification studies to identify and interpret the Eigenvalues of seismically isolated bridges from field measurements. The paper examines the transverse Eigen values of multispan bridges which are isolated in both transverse and longitudinal directions at all supports including all center piers and end abutments. The paper shows that regardless of the value of the longitudinal isolation period of the deck, the length of the bridge, and the number of spans, the first transverse (isolation) period is always longer than the longitudinal isolation period of the deck. This result cannot be captured with the limiting idealization of a beam on continuously distributed springs (beam on a Winkler foundation) which yields the opposite result of the first transverse period always being shorter than the longitudinal isolation period. This fundamental difference between the response of a flexural beam supported on distinct, equally spaced springs and that of a beam supported on continuously distributed springs has not received the attention it deserves in the literature of structural mechanics-dynamics. Finally, the paper shows that the first normalized transverse Eigenperiod of any finite-span isolated deck follows a single master curve and the solutions from all configurations are self-similar and are not dependent on the longitudinal isolation period or on whether the deck is isolated on elastomeric or spherical-sliding bearings. (Full Text)
Smyrou, E., Tasiopoulou, P., Bal, I.E. and Gazetas, G. (2011). “Ground Motions Versus Geotechnical and Structural Damage in the Christchurch February 2011 Earthquake,” Seismological Research Letters, Vol. 82(6), pp. 882-892.
The Mw = 6.3 Christchurch earthquake was a surprising and unusual event which occurred in an unknown fault that had already been awakened by the September 2010 stronger earthquake, and it had a strong thrust component and a steeply dipping plane. This paper has attempted to identify quantifiable parameters that could provide better insight to seismologists and engineers who try to systematically investigate the reasons behind the structural and soil failures that occurred in the February shaking. (Full Text)
Loli M., Anastasopoulos I., Bransby M.F, Ahmed W., Gazetas G. (2011). ” Caisson Foundations Subjected to Reverse Fault Rupture: Centrifuge Testing and Numerical Analysis.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 137(10), pp. 914-925.
Numerous failures induced by surface faulting have been witnessed in recent large magnitude (M > 7) earthquakes, demonstrating the need to account for tectonic deformation in seismic design. Thanks to their usually-high rigidity, embedded (e.g. caisson) foundations may divert the fault rupture, thus leading to favourable performance, where surface or piled foundations may fail. This paper presents a series of centrifuge model tests undertaken to investigate the response of caisson foundations embedded in a cohesionless soil stratum, the base of which is subjected to reverse faulting. The interplay between the propagating fault rupture and the caisson is elucidated, focusing on the role of the location of the outcropping rupture relative to the caisson. The rigid-body of the caisson is shown to cause diversion and/or bifurcation of the shear localisation, which is forced to develop preferentially around the edges of the caisson. The observed failure pattern and the consequent caisson response depend strongly on the exact caisson position relative to the fault. Three dimensional FE modelling was employed and validated through comparison with centrifuge test results. The numerical method is shown to capture the general interaction mechanisms, showing satisfactory (if not always perfect) agreement with experiments. The validated numerical method is then employed in a parametric investigation, providing further insight into the different possible modes of foundation response. (Full Text)
Garini E., Gazetas G., Anastasopoulos I. (2011), “Asymmetric ‘Newmark’ Sliding Caused by Motions Containing Severe ‘Directivity’ and ‘Fling’ Pulses”, Géotechnique, Vol. 61(9), pp. 733–756.
Sliding of a rigid mass supported on an inclined seismically-shaking plane serves as a conceptual and computational model for a variety of problems in geotechnical earthquake engineering. A series of parametric analyses are presented in the paper using as excitation numerous near–fault–recorded severe ground motions and idealised wavelets, bearing the effects of ‘forward-directivity’ and ‘fling-step’. Using as key parameters the angle β of the sloping plane (mimicking the sliding surface), as well as the frequency content, intensity, nature, and polarity of the excitation, the paper aims at developing a deeper insight into the mechanics of the asymmetric sliding process and the role of key parameters of the excitation. It is shown that ‘directivity’ and ‘fling’ affected motions containing long-period acceleration pulses and large velocity steps, are particularly “destructive” for the examined systems. The amount of accumulating slip on a steep slope is particularly sensitive to reversal of the polarity of excitation. With some special ground motions, in particular (such as the Sakarya and Yarimca accelerograms, both recorded 3 km from the surface expression of the North Anatolian Fault that ruptured in the 1999 Kocaeli earthquake), what might at first glance appear elusively as “small details” in the record may turn out to exert a profound influence on the magnitude of slippage ― far outweighing the effects of peak acceleration, peak velocity, and Arias Intensity. The results are compiled in both dimensionless and dimensional charts, and compared with classical charts from the literature. Finally, it is shown that no convincingly robust correlation could exist between accumulated slip and the Arias Intensity of excitation. (Full Text)
Loli M., Bransby M.F, Anastasopoulos I., Gazetas G. (2011). ” Interaction of Caisson Foundations with a Seismically Rupturing Normal Fault : Centrifuge Testing versus Numerical Simulation.” Geoetchnique, Vol. 62(1),pp. 29–43.
Dramatic failures have occurred in recent earthquakes due to the interplay of surface structures with outcropping fault ruptures, highlighting the need to account for fault induced loading in seismic design. Current research into the mechanisms of fault rupture–foundation–structure interaction has revealed a potentially favourable role of caissons in comparison to other foundation types. This paper explores the mechanisms of normal fault rupture interaction with caisson foundations, with an integrated approach using both experiments and analysis. A series of centrifuge model tests were first conducted to study the response of a square (in plan) caisson foundation of dimensions 5 m x 5 m x 10 m, founded on a 15 m thick layer of dry dense sand. Nonlinear 3-D numerical simulation of the problem was then developed and adequately validated against centrifuge test results. Depending on its position relative to the fault, the caisson is found to interact with the fault rupture, sometimes modifying spectacularly the free field rupture path. Acting as a kinematic constraint, the caisson “forces” the rupture to divert on either one, or both, of its sides. The numerical study was extended to gain further insight into the effect of the exact position of the caisson relative to the fault outcrop. Different mechanisms taking place for different caisson positions are identified, and their effect on the response of the system is discussed.
Anastasopoulos I., Gelagoti F., Kourkoulis R., Gazetas G.(2011), “Simplified Constitutive model for Simulation of Cyclic Response of Shallow Foundations: Validation against Laboratory Tests”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 137(12), pp. 1168-1154.
The nonlinear response of shallow foundations has been studied experimentally and analytically. However, the engineering community is not yet convinced on the applicability of such concepts in practice. A key prerequisite is the ability to realistically model such effects. Although several sophisticated constitutive models are readily available in the literature, their use in practice is limited, because : (i) they typically require extensive soil testing for calibration ; (ii) as they are implemented in highly specialized numerical codes, they are usually restricted to simple superstructures ; and (iii) in most cases, they can only be applied by numerical analysis specialists. Attempting to overcome some of these difficulties, this paper develops a simplified but fairly comprehensive constitutive model for analysis of cyclic response of shallow foundations. Based on a kinematic hardening constitutive model with Von Mises failure criterion (readily available in commercial finite element codes), the model is made “pressure-sensitive” and capable of reproducing both the low-strain stiffness and the ultimate resistance of clays and sands. Encoded in ABAQUS through a simple user subroutine, the model is validated against : (a) U.C. Davis centrifuge tests of shallow footings on clays under cyclic loading, and (b) large-scale tests of a square footing on dense and loose sand under cyclic loading, conducted in the European Laboratory for Structural Analysis for the TRISEE project. The performance of the model is shown to be quite satisfactory, while discrepancies between theory and experiment are discussed, and potential culprits are identified. Requiring calibration of two parameters only, and being easily implemented in commercial FE codes, the model is believed to provide a practically applicable engineering solution. (Full Text)
Kourkoulis R., Gelagoti F., Anastasopoulos I., Gazetas G. (2011), “Slope Stabilizing Piles and Pile-Groups: Parametric Study and Design Insights”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 137(7), pp. 663–677.
This paper exploits a hybrid method for analysis and design of slope stabilizing piles, which was developed in a preceding paper by the authors [Kourkoulis et al., 2010]. The aim of this paper is to derive insights on the factors influencing the response of piles and pile−groups. Axis‐to‐axis pile spacing, S, thickness of stable soil mass, Hu, depth, Le, of pile embedment, pile diameter, D, and pile group configuration are the addressed problems parameters. It is shown that S = 4D is the most costeffective pile spacing, since it is the largest spacing that can still generate soil arching between the piles. Soil inhomogeneity (in terms of shear stiffness) was found to be unimportant, since the response is mainly affected by the strength of the unstable soil layer. For relatively small pile embedment, pile response is dominated by rigid‐body rotation, without substantial flexural distortion: “short pile” mode of failure. In such a case, the structural capacity of the pile cannot be exploited, and such a design will not be economical. The critical embedment depth to achieve fixity conditions at the base of the pile is found to range from 0.7Hu to 1.5Hu depending on the relative strength of the unstable ground compared to that of the stable ground (i.e. the soil below the sliding plane). An example of dimensionless Design Charts is presented for piles embedded in rock. Results are presented for two characteristic slenderness ratios and several pile spacings. It is concluded that single piles would generally be inadequate for stabilizing deep landslides, while capped pile groups invoking framing action may offer an efficient solution. (Full Text)
Kampas G. and Makris N. (2011) “Modal Identification of Freeway Overcrossings with Soil- Structure Interaction: A case study”, Structural Control and Health Monitoring, DOI: 10.1002/stc.494
This paper is concerned with a widely studied problem—that of the identification of the modal characteristics of freeway overcrossings and other bridges, which response is interacting with their approaching embankments and their foundation. The study implements a sophisticated parameter estimation method known as the prediction error method and examines in detail the sensitivity of the modal characteristics (frequency and damping) of the bridge when the input signals are taken at the free field, at the approaching embankments and pile caps, and on the abutments and the pile caps. The findings of this case study on the Meloland Road Overcrossing with the prediction error method are compared with the results from past system identification studies and the results from finite element analyses, which examined in depth the contribution of the approaching embankments in the bridge response. The study concludes that despite the appreciable energy dissipation capability of the approaching embankments the concrete bridge structure, while interacting mechanically with the embankments, remains small. (Full Text)
Sapountzakis E.J., Kampitsis A.E. (2011), “Nonlinear Response of Shear Deformable Beams on Tensionless Nonlinear Viscoelastic Foundation under Moving Loads”, Journal of Sound and Vibration, Vol. 330, pp. 5410 -5426.
In this paper, a boundary element method is developed for the nonlinear dynamic analysis of beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on nonlinear three-parameter viscoelastic foundation, undergoing moderate large deflections under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy and the range of applications of the developed method. (Full Text)
E.J. Sapountzakis, A.E. Kampitsis (2011), “Nonlinear Analysis of Shear Deformable Beam-Columns Partially Supported on Tensionless Three-Parameter Foundation”, Archive of Applied Mechanics, pp. 1-19, doi:10.1007/s00419-011-0521-4.
In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless three parameter foundation, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy and the range of applications of the developed method. (Full Text)
Makris N., Vassiliou M.F. (2011), “The existence of “complete similarities” in the response of seismic isolated structures subjected to pulse like ground motions and their implications in analysis”, Earthquake Engineering and Structural Dynamics, 40, pp. 1103–1121.
In this paper the seismic response of isolated structures supported on bearings with bilinear and trilinear behavior is revisited with dimensional analysis in an effort to better understand the relative significance of the various parameters that control the mechanical behavior of isolation systems. An isolation system that consists of lead rubber bearings or of single concave spherical sliding bearings exhibits bilinear behavior; whereas, when a double concave configuration is used the behavior is trilinear. For the case of bilinear behavior it is well known that the value of the normalized yield displacement is immaterial to the response of the isolated superstructure–or, in mathematical terms, that the response of the bilinear oscillator exhibits a complete similarity in the dimensionless yield displacement. Similarly, for the case of trilinear behavior the paper shows that the presence of the intermediate slope is immaterial to the peak response of most isolated structures–a finding that shows that the response of the trilinear oscillator exhibits a complete similarity in the difference between the coefficients of friction along the two sliding surfaces as well as in the ratio of the intermediate to the final slope. This finding implies that even when the coefficient of friction of the two sliding surfaces are different, the response of isolated structures for most practical configurations can be computed with confidence by replacing the double concave spherical bearings with single concave spherical bearings with an effective radius of curvature and an effective coefficient of friction. (Full Text)
Sapountzakis E.J., Kampitsis A.E. (2010), “Nonlinear Dynamic Analysis of Timoshenko Beam-Columns Partially Supported on Tensionless Winkler Foundation”, Computers and Structures, Vol.88(21–22), pp. 1206–1219
In this paper, a boundary element method is developed for the nonlinear dynamic analysis of beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless winkler foundation, undergoing moderate large deflections under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the analog equation method, a bem based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified newton raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy and the range of applications of the developed method. (Full Text)
Sapountzakis E.J., Kampitsis A.E. (2010), “Nonlinear Analysis of Shear Deformable Beam-Columns Partially Supported on Tensionless Winkler Foundation”, International Journal οf Engineering, Science And Technology, Vol.2, No.4, pp. 31-53.
In this paper, a boundary element method is developed for the nonlinear analysis of shear deformable beam-columns of arbitrary doubly symmetric simply or multiply connected constant cross section, partially supported on tensionless Winkler foundation, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member as well as the shear forces along the span induced by the applied axial loading. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy and the range of applications of the developed method. (Full Text)
Kourkoulis R., Anastasopoulos I., Gelagoti F., Gazetas G. (2010), “Interaction of Foundation−Structure Systems with seismically precarious Slopes : Numerical Analysis with Strain Softening Constitutive Model”, Soil Dynamics & Earthquake Engineering, Vol. 30(12), pp. 1430–1445.
This paper studies the combined effects of earthquake-triggered landslides and ground shaking on foundation-structure systems founded near slope crests. Plane-strain nonlinear finite element dynamic analyses are performed. The soil constitutive model is calibrated against published data to simulate the (post-peak) softening behavior of soil during a seismic event and under the action of gravitational forces. The plastic shear zones and the yield accelerations obtained from our dynamic analyses are shown to be consistent with the slip surfaces and the seismic coefficients obtained by classical pseudostatic limiting equilibrium and limit analysis methods. The foundation and frame columns and beams are modeled as flexural beam elements, while the possibility of sliding and detachment (separation) between the foundation and the underlying soil is considered through the use of special frictional gap elements. The effects of foundation type (isolated footings versus a rigid raft) on the position of the sliding surface, on the foundation total and differential displacements, and on the distress of the foundation slab and superstructure columns, are explored parametrically. It is shown that a frame structure founded on a properly designed raft could survive the combined effects of slop failure and ground shaking, even if the latter is the result of a strong base excitation amplified by thesoil layer and slope topography. (Full Text)
Gelagoti F., Kourkoulis R., Anastasopoulos I., Tazoh T., Gazetas G. (2010), “Seismic Wave Propagation in a very soft Alluvial Valley : Sensitivity to Ground Motion Details and Soil Nonlinearity, Generation of Parasitic Vertical Component”, Bulletin of the Seismological Society of America, Vol. 100(6), pp. 3035-3054.
This paper explores the sensitivity of 2D wave effects to crucial problem parameters, such as the frequency content of the base motion, its details, and soil non-linearity. A numerical study is conducted, utilizing a shallow soft valley as a test case. It is shown that wave focusing effects near valley edges and surface waves generated at valley corners are responsible for substantial aggravation (AG) of the seismic motion. With high-frequency seismic excitation, 1D soil amplification is prevailing at the central part of the valley, while 2D phenomena are localized near the edges. For low-frequency seismic excitation, wave focusing effects are overshadowed by laterally propagating surface waves, leading to a shift in the location of maximum AG towards the valley center. If the response is elastic, the details of the seismic excitation do not seem to play any role on the focusing effects at valley edges, but make a substantial difference at the valley center, where surface waves are dominant. The increase of damping mainly affects the propagation of surface waves, reducing AG at the valley center, but does not appear to have any appreciable effect at the valley edges. Soil nonlinearity may modify the 2D valley response significantly. For idealized single-pulse seismic excitations, AG at the valley center is reduced with increasing nonlinearity. Quite remarkably, for real multi-cycle seismic excitations AG at the valley edges may increase with soil nonlinearity. In contrast to the vertical component of an incident seismic motion, which is largely the result of P-waves and is usually of too high frequency to pose a serious threat to structures, the valley-generated parasitic vertical component could be detrimental to structures : being a direct result of 2D wave reflections/refractions, it is well correlated and with essentially the same dominant periods as the horizontal component. (Full Text)
Anastasopoulos I., Antonakos G., Gazetas G. (2010), “Slab Foundations subjected to Thrust Faulting : Parametric Analysis and Simplified Design Method”, Soil Dynamics & Earthquake Engineering, Vol. 30(10), pp. 912–924.
Motivated by recent case histories of faulting–induced damage to structures (Chi-Chi 1999, Wenchuan 2008), this paper applies a thoroughly validated finite element analysis methodology to study the response of slab foundations subjected to thrust faulting. A parametric study is conducted, investigating the effect of key response parameters. It is shown that the stressing of the foundation, and consequently of the superstructure, stems mainly from loss of support. Depending on the geometry, loss of support takes place either under the edges or under the middle of the foundation, generating hogging or sagging deformation, respectively. Increasing the weight of the structure and/or decreasing soil stiffness leads to less stressing of the foundation. Surprisingly, even when the fault rupture emerges beyond the structure, completely avoiding the foundation, substantial foundation distress may still be generated. Exploiting the results of the parametric study, a simplified design method is developed, calling for conventional static analysis of a slab on Winkler supports, “simulating” the fault rupture by removing Winkler springs from equivalent area(s) of loss of support. The latter can be estimated with the help of design charts, further facilitating its use in practice. The proposed simplified method should not be viewed as a general design tool, but as a first idea of a practical solution to the investigated problem. (Full Text)
Anastasopoulos Ι., Georgarakos T., Georgiannou V, Drosos V., Kourkoulis R.. (2010), “Seismic Performance of Bar-Mat Reinforced-Soil Retaining Wall: Shaking Table Testing versus Numerical Analysis with Modified Kinematic Hardening Constitutive Model”, Soil Dynamics & Earthquake Engineering, Vol. 30(10), pp. 1089–1105.
Reinforced-soil retaining structures possess inherent flexibility, and are believed to be insensitive to earthquake shaking. In fact, several such structures have successfully survived destructive earthquakes (Northridge 1994, Kobe 1995, Kocaeli 1999, and Chi-Chi 1999). This paper investigates experimentally and theoretically the seismic performance of a typical bar-mat retaining wall. First, a series of reduced- scale shaking table tests are conducted, using a variety of seismic excitations (real records and artificial multi-cycle motions). Then, the problem is analyzed numerically employing the finite element method. A modified kinematic hardening constitutive model is developed and encoded in ABAQUS through a user-defined subroutine. After calibrating the model parameters through laboratory element testing, the retaining walls are analyzed at model scale, assuming model parameters appropriate for very small confining pressures. After validating the numerical analysis through comparisons with shaking table test results, the problem is re-analyzed at prototype scale assuming model parameters for standard confining pressures. The results of shaking table testing are thus indirectly ‘‘converted’’(extrapolated) to real scale. It is shown that: (a) for medium intensity motions (typical of Ms ≈ 6 earthquakes) the response is ‘‘quasi-elastic’’, and the permanent lateral displacement in reality could not exceed a few centimeters; (b) for larger intensity motions (typical of Ms ≈ 6.5–7 earthquakes) bearing the effects of forward rupture directivity or having a large number of strong motion cycles, plastic deformation accumulates and the permanent displacement is of the order of 10–15 cm (at prototype scale); and (c) a large number of strong motion cycles (N>30) of un realistically large amplitude (A ≈1.0 g) is required to activate a failure wedge behind the region of reinforced soil. Overall, the performance of the bar-mat reinforced-soil walls investigated in this paper is totally acceptable for realistic levels of seismic excitation. (Full Text)
Anastasopoulos I., Gazetas G., Loli M., Apostolou M, Gerolymos N. (2009), “Soil Failure can be used for Earthquake Protection of Structures”, Bulletin of Earthquake Engineering, Vol. 8, No.2, pp. 309-326.
A new seismic design philosophy is illuminated, taking advantage of soil “failure” to protect the superstructure. Instead of over-designing the foundation to ensure that the loading stemming from the structural inertia can be “safely” transmitted onto the soil (as with conventional capacity design), and then reinforce the superstructure to avoid collapse, why not do exactly the opposite by intentionally under-designing the foundation to act as a “safety valve” ? The need for this “reversal” stems from the uncertainty in predicting the actual earthquake motion, and the necessity of developing new more rational and economically efficient earthquake protection solutions. A simple but realistic bridge structure is used as an example to illustrate the effectiveness of the new approach. Two alternatives are compared : one complying with conventional capacity design, with over-designed foundation so that plastic “hinging” develops in the superstructure ; the other following the new design philosophy, with under-designed foundation, “inviting” the plastic “hinge” into the soil. Static “pushover” analyses reveal that the ductility capacity of the new design concept is an order of magnitude larger than of the conventional design : the advantage of “utilising” progressive soil failure. The seismic performance of the two alternatives is investigated through nonlinear dynamic time history analyses, using an ensemble of 29 real accelerograms. It is shown that the performance of both alternatives is totally acceptable for moderate intensity earthquakes, not exceeding the design limits. For large intensity earthquakes, exceeding the design limits, the performance of the new design scheme is proven advantageous, not only avoiding collapse but hardly suffering any inelastic structural deformation. It may however experience increased residual settlement and rotation : a price to pay that must be properly assessed in design. (Full Text)