Geotechnical Earthquake Engineering and Soil Dynamics V: Numerical Modeling and Soil Structure Interaction

Catastrophic infrastructure failures frequently are frequently caused by the dynamic interaction of soil and water. Earthquake induced liquefaction, high-water induced levee failures, bridge scour, and rainstorm-induced slides are all examples of such phenomena involving various time and space scales. In many cases, engineering techniques for predicting onset of failures are available and widely used in practice, but there is a dearth of tools available for more general consideration of post-failure behavior. Modeling behavior up to and beyond the point of failure is complicated by the fact that the overall material response involves complex interactions between solid and liquid phases and transitions from solid behavior to sediment transport. Frameworks designed for use in either solid-only or fluid-only contexts are not capable of tracking the significant phenomena throughout a given event history. The early work of Biot, and subsequent adoption of mixture theories, facilitated the development of coupled finite element applications capable of representing the response of saturated and partially saturated soils. This together with the development of constitutive models capable of representing the contractive and dilative response of soils enhanced the predictive capabilities of liquefaction and lateral spreading in the context of a deforming soil/water domain. However, these advancements are limited to moderately small deformations and situations where the fluid and solid domains coexist in a smeared domain. Advances in experimental work at multiple scales create an opportunity to revisit and expand existing constitutive models to incorporate fabric information at the micro-scale and provide physical data to validate computational models at the macro-scale. Meshless techniques like SPH and MPM help mitigate mesh distortion at large deformation providing suitable techniques for lateral spreading and other phenomena like debris flow where mixing and separation is relevant. This paper reviews a few of these aspects indicating trends, opportunities and challenges, and ventures into the prospects of future liquefaction simulation.

Modulus reduction and damping curves are commonly used as input parameters in site response analyses. Until very recently, constitutive models for nonlinear site response analysis could not accurately capture both the desired modulus reduction and damping behavior due to flaws in the assumed functional form for the backbone curve, and/or flaws in the unload-reload relationship. New relationships that solve these issues have recently been proposed, however, they are restricted to defining the in-plane stress-strain relationship for a single plane of shear, and are therefore only appropriate for 1D site response. This paper presents a multi-axial generalization of one of these 1D models, enabling its use in 2D and 3D site response. The 1D model is first briefly described, followed by the multi-axial generalization in terms of stress and strain invariants. The modulus reduction and damping curves are defined in terms of stress ratios rather than shear strains, which allows the model to better capture changes in confining pressure during undrained loading. An example is presented to illustrate fundamental differences in multi-axial versus 1D loading.

This paper proposes a modified uniaxial Bouc-Wen model to evaluate reaction force-displacement backbone curve for transverse lateral pipe-cohesionless soil interaction. The model is capable of representing the nonlinearity and the smooth transition zone of the curve. Using unscented Kalman filter, the model parameter $\mathrm{\kappa }$ that controls the smoothness of transition zone is derived, on the basis of results from high-fidelity validated finite element analyses. $\mathrm{\kappa }$ is larger in loose sand compared to that in dense sand, implying a smoother transition zone of the curve for loose sand. There is a slight change of $\mathrm{\kappa }$ with pipe burial depth in case of dense sand, while the change is clearer and larger in loose sand. The variation of $\mathrm{\kappa }$ is related to the "passive-wedge" and "plow-through" failure mode of soil. The model is subsequently implemented in a series of soil-pipe interaction configurations, and the reaction force-deformation curves are found in good agreement with experimental data.

A modified bounding surface plastic sand model for geotechnical earthquake engineering application is developed to capture essential soil dynamic characteristics. The modification is upon the simple critical state compatible, bounding surface theory based, and fabric-dilatancy related sand plasticity model (DM04 model) introduced by Dafalias and Manzari (2004). By revising some formula without destroying the conciseness of the original DM04 model, the modifications improve the matches between the simulated results and various laboratory or field observations with various initial and loading conditions. The modified model switches all void-ratio related formula, including the elastic modulus, plastic hardening modulus, and critical state, to be relative density related. The modified model embraces an easier calibration procedure in terms of in situ data, such as normalized blow counts instead of experimental data in the laboratory. The modified model retains the general 3D formulation, considering Lode angle effect, and thus can be used for general 3D boundary value problems. The modified model preserves the feature that one set of model constants is used to simulate different responses with different initial relative densities and initial stress states.

This paper presents the analysis of the contractive behavior of saturated sand deposits subjected to biaxial seismic excitation. The analysis is performed on reduced scale centrifuge models of soil deposits. The models were instrumented with dense arrays of accelerometers and pore pressure transducers in order to capture the soil response under seismic excitation. Shear stresses and shear strains are estimated based on the recorded accelerations. A multi-yield surface constitutive model is used to infer the shear-volume behavior of the soil based on the acceleration and pore pressure response. The analysis offers insight into the coupled two-directional response of soil deposits.

Evaluating the hydrodynamic effects within a fluid-filled tank during seismic loading is critical for safe design of large fluid-filled tanks. Ideally, a three-dimensional (3-D) numerical model is required to fully capture the dynamic interactions among tank and its support structures, the stored fluid, and foundation soils. However, simulations using a 3-D model may not always be feasible due to project constraints (i.e., costs and schedule) and modeling complexity. This paper presents a case study where an equivalent 2-D tank model was used to capture its 3-D dynamic behaviors so that it can be analyzed using the more-readily available 2-D finite difference computer program FLAC. The cylindrical tank with conical base was modeled using an equivalent 2-D “compression-tension braced frame system” to capture the 3-D tank’s ring stiffness. A lumped mass-spring model was also used to represent the hydrodynamic sloshing and impulsive loadings of the stored fluid, and the stiffness of shear walls and secant pile walls on the perimeter of the below-grade reinforced concrete support structure were included in the model. Non-linear plasticity models were utilized to model the non-linear behaviors of the foundation soils, including the PM4SAND effective-stress soil model for the liquefiable soils to estimate the excess pore-water pressure generation under cyclic loading and initiation of liquefaction. The dynamic soil-structure-fluid interaction analysis was performed using seven earthquake motions, selected to represent the design earthquakes for the project. The results show that the simplified 2-D modeling approach using equivalent 3-D structural stiffness can reasonably capture the dynamic responses of this complex fluid-tank system.

The increase of urban population in seismic areas and the lack of urban planning have caused the occupancy of hazardous zones around most cities in Latin America. Some dwellings in these settlements are located on terraces on steep hills supported by pircas (dry stone retaining walls). Seismic vulnerability analysis of these structures becomes a crucial step to assess the level of damage generated in possible events, and to propose alternatives for risk reduction and prevention. This analysis was conducted through a numerical model based on the discrete element method (DEM), three typologies of pircas where modelled according to a statistical analysis carried out in the case study. Damage state was defined taking into account the maximum displacement response. According to the lateral seismic acceleration in the out of plane direction, four states of damage were defined: slight, moderate, extensive, and complete. Seismic vulnerability curve represents the relationship between the structural damage of pircas and the seismic acceleration. The obtained curve showed that during frequent earthquakes pircas would be in extensive damage, while for occasional earthquakes almost all typologies of pircas would be in complete damage.

A centrifuge experiment was performed modeling seismic site performance under 1D horizontal earthquake shaking in a saturated and layered soil profile, including a loose layer of Ottawa sand. The results were used to evaluate the predictive capabilities of two classes of soil constitutive models (multi-yield and bounding surface) and two numerical platforms (OpenSees and FLAC) used by three different teams. The models were independently calibrated using the same set of monotonic and cyclic triaxial tests as well as the larger boundary value problem modeled in centrifuge. Despite differences in calibration methodologies and priorities among three modelers, the results showed that small element tests and centrifuge experiments do not always lead to the same calibrated soil parameters. Although current numerical platforms and constitutive models were capable of reproducing many aspects of seismic site response observed in centrifuge, they still need improvements to capture volumetric strains in free-field conditions.

The focus of this study is to verify the capabilities of a constitutive model to mimic a wide range of monotonic and cyclic multi-directional stress paths in clays. The generalized elasto-plastic constitutive formulation of the model enables to describe stress-strain response, accumulation of permanent deformations, and excess pore pressure in monotonic and multi-directional cyclic loading. The model is calibrated based on the experimental database on the Gulf of Mexico clay developed at Texas A&M, including the constant rate strain (CRS) consolidation as well as monotonic triaxial tests. Capabilities of the calibrated model to predict the cyclic multi-directional stress paths are then evaluated through comparison with the results of cyclic, circular, and figure 8 multi-directional simple shear tests as a part of the Gulf of Mexico clay experimental database. We also used the extensive database for Boston blue clay (BBC) to calibrate model constants and verify its capabilities to mimic the monotonic and cyclic response of lower plasticity clays. The model proves successful to predict a wide range of complicated cyclic multi-directional stress paths for clays.

Liquefaction is a phenomenon usually observed in saturated granular soils when subjected to monotonic or cyclic shearing under constrained volumetric conditions. Liquefaction is usually associated with a loss of mean effective stress due to generation of excess pore pressure during the shearing of soil. In this process the particles reduce, or in the extreme case may lose, contact with each other. This nearly contact-free state is known as “semi-fluidized regime”. In this state, the soil behaves almost like a viscous fluid, but the properties and origins of this response are not well understood. This study presents a series of numerical simulations using discrete element method (DEM) to model the constant volume cyclic shearing of three granular assemblies with different packing fractions. The variations of the stress-strain response and the corresponding coordination number for each sample are tracked when the semi-fluidized regime is achieved. The results show the semi-fluidized regime in all of these assemblies regardless their packing fraction. This micro-mechanics based approach to the analysis can elaborate on the variations of the coordination number, mean effective stress, and developed shear strains before and after entering such regime.

Recent computational models create a large amount of data, which can be hard to analyze. In this paper, we demonstrate the power of employing data analytics techniques to characterize soil behavior during liquefaction. We used simple simulation output aggregated over several locations along the depth of the deposit. Available were five simulated quantities (shear strain, acceleration, coordination number, pore pressure, change in volume) and we added four change features (direction and magnitude of change of the quantity). We then performed data mining using conventional analytics methods (clustering using k-means with k = 5 and principal components analysis). The clustering visualization showed that a visible break started to propagate downward on the onset of liquefaction through all depth locations. Using this scheme, we were able to build cluster profiles that generate new insights by visualizing details of the transformation process of the soil from a solid state to a liquefied state.

The mean squared deviation between acceleration time histories (of soil-system test replicas) is expressed as a unique aggregate of three discrepancy measures associated with shape, phase, and frequency-shift. The shape-measure quantifies the deviations associated with dissimilarities in form and amplitude. The phase-measure estimates the deviations associated with differences in phase angle. The frequency-shift-measure quantifies the deviations associated with differences in frequency components. These measures were used to assess the discrepancies among six replicas of a centrifuge experiment of a liquefiable soil tested at six different facilities. A sensitivity analysis was thereafter used to assess the effects of input motion discrepancies on a liquefiable soil response. The conducted analysis showed that the acceleration response of the analyzed soil is more sensitive to discrepancies in input motion frequency than in phase or amplitude.

Understanding evolution of microstructure in granular soils can provide significant insights into constitutive modeling of soil liquefaction. By tracing all particle movement, the discrete element modeling (DEM) quantifies the microstructure of a granular assemblage using a variety of fabric indices, such as the numbers of contacts, orientation of contact normal, as well as particles, and voids distribution. The DEM simulations revealed significant change in particle-void fabric to a strongly anisotropic state after initiation of liquefaction. Large flow deformations in the post-liquefaction stage were found to be closely correlated to the evolving particle-void fabric. In addition, fabric evolution in soil packings was also investigated under a variety of multi-directional loading paths. Interestingly, the contact-based fabric ultimately becomes almost identical for all oval and circular loading. The discrete element modeling provides insightful observation that links microscopic fabric evolution to macroscopic cyclic behavior of soils, which is instrumental for developing micromechanically based constitutive models.

Loose saturated sands when subjected to seismic loading develop high excessive pore water pressures eventually leading to liquefaction of the soil. The deep vibration compaction method includes densification of loose sands by means of shear deformation processes imparted by horizontal vibrations of vibrator probe. In order to study the feasibility of deep vibration compaction for liquefaction mitigation, a numerical model is created in the finite element framework. The methodology consisted on performing FE simulations using non-linear coupled hypoplastic model based on the u-p formulation for sand behavior at three different stages: i) analysis of seismic response and liquefaction susceptibility of untreated loose saturated sands using Lagrangian finite elements (FE); ii) simulation of the deep-vibration process by using a coupled Lagrangian-Eulerian (CLE) FE; iii) post-liquefaction susceptibility analysis of improved sands using the Lagrangian FE.

Seismic energy (mechanical energy) is dissipated around and within the SSI system, mostly in the form of heat, during irreversible dissipative processes. Energy dissipation in soil structure interaction (SSI) system is related to inelastic behavior of materials (soil, rock, structural components, energy dissipation devices), viscous coupling between solid and fluid phases, frictional dissipation in contact zones, and seismic energy radiation. Based on principles of thermodynamics, an energy dissipation analysis framework for elastic-plastic materials is proposed. A common misconception of plastic dissipation and plastic work is addressed and corrected using proper formulation of thermomechanics. The nature and computation approach of plastic free energy in solid and structural element is discussed. The proposed methodology is illustrated through several finite element (FE) simulations. It is shown that the consideration of plastic free energy is necessary to correctly evaluate energy dissipation in elastic-plastic solid and structural elements. Results of energy analysis indicates that the different between plastic work and plastic dissipation could be significant, and the ratio between them evolves with time thus should not be assumed constant.

This paper presents results from effective stress analyses on four Christchurch sites under the shaking induced by the 22 February 2011 Christchurch earthquake. The four sites have similar characteristics in terms of critical layers but differ significantly with regard to the composition of soils within the top 10 m of the deposit, with the main distinctive feature being either vertical continuity or discontinuity of liquefiable materials. These differences are reflected in varying levels of severity of surface liquefaction manifestation observed at the four sites during the 2010–2011 Canterbury earthquakes. In contrast to the CPT-based simplified liquefaction triggering evaluation which predicts liquefaction of the shallow critical layer for all four sites, the effective stress analyses effectively explain their different performance during the February 2011 earthquake. In particular, the effective stress analyses predict different combinations of depth–thickness–severity of liquefaction between the four sites and demonstrate that system response effects related to dynamic cross-interaction between different layers in the deposit and pore water redistribution and water flow play a predominant role on the occurrence and severity of liquefaction at a given depth. Findings from this study emphasize the need to consider system–response of deposits when evaluating liquefaction and its damage potential.

In this work the capabilities of the ISA-hypoplasticity model for the simulation of a sandy material are carefully analyzed. The ISA-hypoplasticity model is based on the hypoplastic model by von Wolfferdorff (1996), extended by the intergranular strain anisotropy (ISA) concept by Fuentes and Triantafyllidis (2015). The model is able to simulate monotonic and cyclic loading, and has been recently modified to consider the cyclic mobility effect. Within this work, a calibration procedure has been conducted to determine the material parameters of Ottawa F65 sand and a set of experiments showing monotonic and cyclic loading has been simulated. This work is embedded within the liquefaction experiments and analysis projects (LEAP), which seeks to assess and improve the current numerical tools for prediction and evaluation of soil liquefaction phenomena.

This paper provides a review of the different methodologies for the fragility assessment of critical transportation infrastructure subjected to earthquake excitations with emphasis placed on geotechnical effects. Available approaches to fragility analysis are summarized, along with the main parameters and limitations. Additionally, definitions of damage are synthesized for the individual transportation assets and subsequently the definition of system of assets (SoA) is introduced. Numerical fragility curves are developed for a representative SoA subjected to seismic excitations. The paper concludes with the gaps in the area of fragility analysis and the needs for future development.

Fragility-based seismic performance assessment and design procedures are being refined and adopted for many civil structures. With recent advances in computational capabilities as well as broad improvements in ground motion characterization and inelastic modeling of structural and geotechnical systems, large-scale direct models for underground structures—e.g., tunnels, water reservoirs, etc.—can now be devised with relative ease and deployed in engineering practice. In this study, we present a fragility-based seismic performance assessment of a large buried water reservoir. We use existing documents/codes to define the performance criteria and develop fragility functions through a probabilistic seismic demand analysis (PSDA) procedure. The analyses incorporate inelastic/nonlinear behavior of soils and structural components, and account for uncertainties in the expected ground motions. The seismic performance assessment methodology presented herein can be applied to other large underground reservoirs.

Understanding the dynamic properties of soils, i.e., damping and shear modulus, and predicting their behavior under earthquake loading are of paramount importance. The damping ratio is a significant parameter in design and is relatively difficult to predict. It often requires following tedious procedures and solving equations with many unknown factors to determine the damping behavior. In this paper, current models and approaches to predict material damping are briefly summarized. A general equation to predict the material damping of clay, utilizing Amir-Faryar et al. 2016’s universal damping model, is proposed as a function of the plasticity index of clay. The general equation will be useful for design engineers in predicting the damping behaviors of cohesive soils for their site response analysis, when the only known property for the clay is the plasticity index. A simplified damping model form characterized by three coefficients was derived from the general equation for clay to predict the material damping.

This paper presents the implementation, validation, and application of the PM4Sand model (version 3) formulated by Boulanger and Ziotopoulou (2015) in the PLAXIS finite element code. The model can be used for modelling geotechnical earthquake engineering applications, especially in the case liquefaction is likely to occur. The PM4Sand model represents an improvement of the elasto-plastic, stress ratio controlled, bounding surface plasticity model for sands formulated by Dafalias and Manzari (2004). The two-dimensional version has been implemented in PLAXIS and compared to the original implementation by Boulanger and Ziotopoulou (2015). The original implementation has been used in explicit finite difference simulations which can be sensitive to the size of the returned stress increment, based on the chosen time step size and loading rate. Therefore, the user needs to evaluate the sensitivity of the solution with respect to the chosen time step sizes. On the contrary, in the finite element method used here, the default time step together with the sub-stepping used at the constitutive model level provide a robust solution independent of the size of the returned stress increment.

Ground shaking during earthquakes can be a prominent cause of strength loss in loose saturated soils. In some cases, uncontrolled pore pressure build-up and liquefaction may occur with a time lag with respect to strong ground motion, especially when the time-dependent properties of the soil interact with the constraints brought by undrained and/or partially drained conditions. Here a rate-dependent law based on the critical state theory has been used to replicate the cyclic response of sand by taking into account density effects. The model equations have been inspected to define indices of delayed undrained instability. Then, the model has been calibrated by considering laboratory tests for both monotonic and cyclic undrained loading on loose Hostun sand. Numerical simulations of undrained creep stages following cyclic loading have been performed to illustrate the transition from stable to unstable creep as a function of the number of cycles, thus providing a conceptual framework to evaluate the risk of delayed flow liquefaction in loose sandy deposits.

In this study, the analysis of the seismic response of a soil-retaining wall system is performed based on a three-dimensional microscale framework utilizing the discrete element method (DEM). The proposed method is employed to investigate the seismic response of gravity-type retaining walls with three degrees of freedom. In the simulation, the granular soil deposit is idealized as a collection of spherical soil particles; the retaining wall is simulated as a rigid block composed of clumped particles to yield the physical characteristics of a typical retaining wall. The computational model captured some of the dynamic characteristics typically observed from the response of retaining walls. For instance, time histories of the resultant lateral thrust on the wall show that its magnitude varies as the wall moves relative to the backfill and its location changes as well.

This paper proposes a new formulation of governing equation of three phase medium, consisting of solid skeleton, gas, and water through a generalized fluid vector and validation with leaking test. The proposed generalized fluid vector consists of generalized degrees of freedom in pore pressures; one for gas, other for water, in case of two degrees of freedom. This fluid vector can be further generalized to take into account the multiple degrees of freedom of pore pressures, such as mixtures of oil, water, air, natural gasses, etc. The use of the generalized fluid vector allows the apparently a simpler formulation of the governing equations dealing with three or larger number of phases of materials. The simpler formulation in mathematical terms reduces to and coincides with that of two phase medium and thus has significant advantages when the complexities in pore filling materials are increased. Example analysis of this formation for validation is performed based on a 1D leaking test of a partially saturated soil column. In overall, the computed results are consistent with those of the previous bench marking test and numerical study, and thus confirm the applicability of the proposed formulation of partially saturated soil.

A series of full-scale dynamic vibration tests and cyclic lateral tests are to be performed on a single pipe pile and a 2×2 pile group as part of an ongoing research project. The parallelized boundary element method (BEM) code BEASSI was modified and used to predict the three-dimensional vibration response of the pile group with account of the layered soil profile including material damping and radiation damping in the viscoelastic system. The concept of the disturbed-zone model for pile groups is employed to account for pile installation effects, soil inhomogeneity, and stress- and strain-dependent modulus and damping in the near-field, while simultaneously capturing three-dimensional wave propagation and rigorously accounting for radiation damping in the far-field. To acquire accurate soil profiles as input to the analyses, a comprehensive site investigation was recently conducted, including seismic cone penetration testing with pore pressure measurement (SCPTu), standard penetration testing (SPT), and Shelby tube sampling. In the present paper, the acceleration sensor responses from SCPT tests at various depths are analyzed by the cross-correlation method to obtain shear wave velocity profiles, and the results are compared to those by the arrival time and cross-over methods, as well as empirical correlations to CPT tip resistance and sleeve friction. Material damping in the soil is also estimated from the SCPT data by the spectral ratio slope (SRS) method, which aims to minimize effects of radiation damping. The BEM program is then used with the resulting shear wave velocity profiles to calculate impedance functions in the frequency domain, which explicitly quantify the three-dimensional interaction between all the piles in the group. A general formulation based on the sub-structuring method is employed to analyze the dynamic response of pile groups using the impedance functions to obtain accelerance functions of the pile cap in vertical and coupled lateral-rocking vibration modes for validation. The findings demonstrate the accuracy and stability of the cross-correlation method for estimating shear-wave velocity from SCPT data, and an average minimum material damping ratio of 2.6% by the SRS method for the clay soils encountered. The impedance functions of the pile group indicate strong frequency-dependent dynamic soil-pile-soil interaction for the case examined. Results of this study will aid development of the proposed disturbed-zone continuum models, and provide insights into future physical pile group tests.

Numerical noise, in the form of high frequency acceleration spikes, may become a major obstacle to the prediction of peak seismic ground acceleration and short period spectral accelerations. This problem is examined herein for the special case of liquefiable sites, where noise effects become more pronounced. It is shown that the acceleration spikes are not related to the numerical solution algorithm and to problem-specific modelling assumptions, but are associated to the abrupt changes in soil stiffness which occur during loading reversals, after the onset of soil liquefaction. The use of Rayleigh damping may moderate noise effects only in cases of low cyclic shear strain amplitude, as in the case of dry soil profiles. For liquefiable sites, where cyclic strains become large, numerical noise may be effectively eliminated by filtering separately the pre- and the post-liquefaction segments of the predicted acceleration time-histories, using different low-pass filters.

A simplified method accounting for nonlinear soil-pile interactions of laterally loaded piles is proposed in order to simulate dynamic behavior of structures with pile foundations in liquefiable ground by using two-dimensional (2D) effective stress finite element (FE) analysis. The method is a kind of Winkler foundation model with nonlinear interaction springs, connecting between nodes of beam elements and corresponding soil elements in 2D model. We develop a system to specify automatically and objectively the material properties of the nonlinear interaction springs in effective stress analysis program of “FLIP ROSE 2D”. Pile behaviors in existing large scaled experiments in the static or dynamic manner are assessed using the program in which the proposed method is incorporated. The results indicate that for the specific case considered here the proposed method provides a reasonable accuracy in spite of its simplicity. It suggests that proposed method is applicable to practical 2D FE analysis to assess the earthquake responses of pile foundations during soil liquefaction.

Guardrails, consisting of soil-embedded piles tied with a rail, are safety barriers that are installed along highways to shield errant motorists from roadside hazards and to minimize the risk of serious injuries. Soil resistance plays a crucial role in the way that guardrails perform when impacted by vehicles. Although the consequences of guardrail system failures are tragic, little is known on the dynamic impact characteristics of soil and soil-pile interaction under impact loading. Thus, research was conducted to investigate the load-deflection behavior of a single pile under impact through dynamic large-scale component testing and numerical simulation using LS-DYNA. Baseline dynamic tests were performed on a steel W6x16 pile embedded in crushed limestone soil impacted by a surrogate bogie vehicle. Test results were used to develop a simplified numerical model of soil-pile system when impacted by a vehicle. The validated model was then compared to full-scale crash test data. The proposed soil modeling method accurately represented soil and pile behavior in component tests and full-scale vehicle crash tests.

The replacement of an existing pump station located near San Francisco’s Mission Bay neighborhood was designed for seismic loading using response spectrum analysis and equivalent lateral force procedures per ASCE 7. However, the seismic performance of the pump station was also assessed as part of a suite of structure-soil-structure-interaction (SSSI) analyses looking at its potential impact on an existing wet weather transport/storage box (T/S box) located approximately 1.5 m to the north. These SSSI analyses explicitly included the new pump station, the T/S box, and the soil domain with bedrock-propagated ground motions. Comparison of the results from the simplified code-based analyses and the SSSI analyses provide a useful check on the validity of both methods. In addition, the suite of SSSI analyses shed light on the key factors influencing the seismic interaction between these embedded structures.

This study presents an output-only model inversion method to jointly estimate the model parameters and foundation input motions in structural models. The model inversion is based on Bayesian finite element model updating using the measured seismic response of the structure. The model parameters to be estimated consist of parameters characterizing the structural model, dynamic soil springs (to account for inertial soil structure interaction effects), and Rayleigh damping. We use the recorded response of the Millikan Library building to the 2002 Yorba Linda earthquake for validation study, in which the recorded structural responses are used to update the structural model resting on soil springs and dashpots. This study is a step forward towards developing model inversion methods that can be used with seismic response of real-world buildings to identify the Rayleigh damping and dynamic soil springs parameters.

A number of linear-elastic solutions have been dedicated to resolve the problem of earth pressures on a rigid wall overlying rigid bedrock, among which, the classic solutions have been provided by Matsuo and Ohara (1960), Wood (1973), and Veletsos and Younan (1994). Wood's solution is mathematically involved (it requires evaluation of a double infinite sum) and the other two involve severe simplifying assumptions. An approximation procedure is presented to develop easy-to-evaluate estimates for the lateral earth thrust on rigid retaining walls under quasi-static loading. The procedure is based on the estimation of soil kinematic variables in the vicinity of the wall, from which strains, stresses, and total thrust are obtained. While the procedure is presented for quasi-static loading of a rigid wall overlaying rigid bedrock, this novel approach could be used to account for other complex effects that have been cumbersome to include in state-of-the art earth pressures procedures, such as dynamic loading, soil non-linear behavior, and wall compliance.

Measurement of the distribution and magnitude of static and dynamic earth pressures resulting from geostatic and applied stresses is essential to the design and performance of many civil engineering-type structures involving soil-structure interaction. Seismic soil pressures recorded on a vertical flexible hollow shaft with model scale dimensions of 0.8 m square and 7.0 m in height are compared with predictions from elastic-based analytical approaches found in current literature. The vertical shafts were part of an underground structure system, placed in a laminar soil box, and embedded in a two-layer soil stratigraphy. Two directional ground motions were applied via shake table testing at the E-Defense facility in Japan. Pressure measurements were recorded using recently developed pressure sensors and details pertaining to the design, fabrication, and calibration of the sensor are discussed. Despite of the uncommon geometry of the vertical shaft systems, elastic based methods were able to predict the response reasonably well, in some cases capturing both, pressure magnitudes and pressure distribution.

Because of soil-foundation-structure interaction (SFSI), the measured foundation motion (FM) diverges from the free-field motion (FFM). In the substructure SFSI analysis, a motion for a massless rigid foundation is defined as the foundation input motion (FIM), which cannot be physically measured. This paper describes a set of seismic centrifuge experiments to compare the FM motions in single foundations with responses closer to FIM. Three tests were performed on a soil-foundation-structure model (SFSM), a steel foundation model (SFM), and an acrylic foundation model (AFM). Results show that FM in SFSM is different from the ones in single foundation models and in a frequency range around the flexible base natural frequency of the structure. While the lateral component of FM in SFSM is smaller than those of SFM and AFM, the rocking component is greater. Therefore, using the measured FM instead of FIM specially in the translational direction would be non-conservative.

We report on snap-back testing of vertical 220 mm diameter steel tube piles driven into a stiff clay soil profile at a site to the north of Auckland in New Zealand. The site where the piles were installed was investigated with CPT and dilatometer measurements and shear wave velocity profiles were obtained through geophysical testing. The piles were subject to gradually increasing lateral loads prior to snap-back release which provided information about the static lateral load behaviour of the piles. We present three damping curves: (i) as a function of the lateral displacement at snap-back, (ii) when the cyclic displacement amplitude is 1% or a little less than the pile shaft diameter, and (iii) when the cyclic displacement amplitude is 0.2% or less than the pile shaft diameter. The fact that these curves are different indicates that damping under lateral pile head vibration cannot be charactised by a single value for the equivalent viscous damping ratio. However, we suggest that if working within in a displacement based design framework how it might be possible to decide on a representative value for the damping parameter. We modelled the inertial dynamic response of the piles with the finite element software OpenSeesPL which gives 3D dynamic modelling of pile-soil interaction, allows for nonlinear stress-strain behaviour of the soil, and prevents tensile stresses in the soil near the pile shaft. The nonlinear finite element analyses indicate that after many snap-back releases the stiffness of the soil adjacent to pile shaft is much degraded. Reasonable modelling of snap releases from small pull-back forces was achieved but for large pull-back forces, after many snap releases from smaller forces, the frequency of the response was matched only with a large reduction in the soil stiffness, but the damping in the computed response was considerably less than for the measured values.

The seismic earth pressure increment is typically computed using either pseudo-static limit equilibrium methods or elastic wave equation analyses of the interaction between a retaining structure and backfill material, yet current interpretations of the two methods provide conflicting recommendations. The focus of this study is to compare the seismic earth pressure increment computed using the two methods. This approach is demonstrated by subjecting an initially uniform prototype site selected from standard site classifications to harmonic excitation in one-dimensional equivalent linear analyses. Then, the seismic earth pressure resultant for a rigid wall is computed using the two methods. The limit equilibrium approach utilizes the acceleration records from the equivalent linear analysis to compute a seismic coefficient, whereas the elastic solution incorporates the reduced modulus and damping from the final iteration of the analysis, as well as the relative displacement records. The results presented herein corroborate the findings of recent centrifuge experiments and associated analyses.

Engineering procedures for predicting ground failure potential typically express seismic demands in the form of shear stresses. In soil materials underlying foundations, referred to here as ‘foundation soils’, dynamic stress demands result from wave propagation associated with site response in combination with demands associated with soil-structure interaction (SSI). Numerous post-earthquake field investigations and centrifuge modeling studies have provided evidence for local ground failure beneath foundations that appears to have been influenced by SSI-related demands. Here we present procedures for analyzing SSI-related stress demands. The procedures consist of dynamic stress bulbs evaluated from simulations performed using the boundary element method. The stress bulbs represent dynamic stresses normalized by suitable parameters representing load amplitude, frequency, and problem geometry. We illustrate the normalization procedure and provide example results for the case of a vertical surface line load.

The pseudo-static approach has been conventionally applied for the design of gravity type quay walls. In this method, the seismic coefficient (k_h), expressed in terms of acceleration due to gravity, is used to convert the real dynamic behavior to an equivalent pseudo-static inertial force for seismic analysis and design. Therefore, the calculation of an appropriate k_h considering frequency characteristics of input earthquake is critical for representing the real dynamic behavior. However, the definitions of k_h, which is used for simplified analysis in Korea, focus only on convenience, and the frequency characteristics of input earthquake are not reflected in the k_h definitions. This paper evaluates the influences of the frequency characteristics of input earthquake on k_h by initially reviewing the k_h definitions in the existing codes of Japan for port structures and then by performing two dynamic centrifuge tests on caisson gravity quay walls of different earthquake input motions (Ofunato, Hachinohe). A review of the existing codes and guidelines has shown that the k_h values are estimated differently according to the frequency characteristics of input earthquake. On the other hand, based on the centrifuge tests, it was found that the permanent displacements of wall are larger when long-period-dominant earthquake is applied.

Deep foundations supporting skewed bridges and flyovers may need to resist torsional loads induced by seismic loading. To facilitate the serviceability and ultimate limit state design of a geometrically-variable deep foundation subjected to torsion in multi-layered soils, a software package, TorPILE, is developed using a finite difference model (FDM) framework. Simplified, pressure- and state-dependent nonlinear torsional load transfer models relating the unit torsional resistance to the magnitude of relative displacement are developed using available interface shear tests and torsional load test data. The soil-structure interface behavior is simulated using hyperbolic displacement-hardening model for granular and plastic fine-grained soils that exhibit a contractive response and a displacement-softening model for granular soils with dilatant response. The FDM methodology, as well as the proposed torsional load transfer models, is validated by comparing the torsional responses of deep foundations predicted by TorPILE with the centrifuge test data reported in the literature. Parametric studies investigating the role of various design parameters, including the dimensions of deep foundations and soil properties, are conducted.

Rocking shallow foundations may act as a good mechanism for base isolation that limits the seismic force to the superstructure during strong seismic events; however, a lack of comprehensive field investigation might have limited the use of rocking foundation. This paper presented a field study of a rocking shallow foundation resting on a natural soil deposits in Alberta, Canada. The foundation system consisted of a 1.5 m by 1.0 m concrete footing, column, and deck to simulate a prototype bridge system. A geotechnical investigation was carried out to determine soil conditions before and after the experiments. The footing was subjected to slow cyclic loading which consists of 4 to 5 packets of which each contain 3 to 4 cycles of similar displacement amplitude. The drift ratio was increased to a maximum of 5%. The estimated factors of safety against bearing failure ranges from 4 to 22. Nonlinear behaviour of the foundations and underlying soil was evident; changes in the physical and mechanical properties of underlying soils were characterized. Energy dissipation, residual settlement, and stiffness degradation observed in the tests were discussed.

Results of a centrifuge test on a pile-supported wharf were used to investigate the time-, depth-, and row-dependent nature of kinematic and inertial loading on wharf piles in sloping rockfill. P-y models were calibrated against recorded bending moments in different piles and different depths. It was found that full kinematic demands and full superstructure inertia should be combined to estimate bending moments at pile head and shallow depths (less than 10 diameters below the ground surface). On the contrary, it was found that applying full kinematic demands alone was adequate to estimate pile bending moments at large depths (greater than 10 diameters deep).

An interactive web application has been developed to compute seismic earth pressure. The application employs an expanded form of Rankine’s classic earth pressure solution. The application computes seismic active earth pressure behind rigid walls supporting c–φ backfill considering both wall inclination and backfill slope. The lateral earth pressure formulation is based on Rankine’s conjugate stress concept. The developed expression can be used for the static and pseudo-static seismic analyses of c–φ backfill. The results based on the proposed formulations are found to be identical to those computed with the Mononobe-Okabe method for cohesionless soils, provided the same wall friction angle is employed. For c–φ soils, the formulation yields comparable results to available solutions for cases where a comparison is feasible. The application eliminates the need for design charts, since it can accommodate any set of user-defined kinematically admissible design parameters.

The USGS reports that between the years 1973–2008, there was an average of 21 earthquakes of magnitude three and larger in the central and eastern United States. The rate has increased dramatically to over 600 magnitude M_w=3 and larger earthquakes in 2014 and over 1000 in 2015. Per USGS data through August 2016, over 500 magnitude M_w=3 and larger earthquakes had occurred in 2016. The documented increased seismicity has raised concerns from the public and owners, operators, and investors of wind power plants in areas of increased induced seismicity such as portions of Oklahoma, Kansas, and northern Texas. The concerns for wind power plants due to induced seismicity typically include potential effects on the foundations, blades, towers, and other turbine components. Seismic effects are a typical consideration for design of all wind turbines and associated wind power plant components but seismicity has historically not been a controlling factor for the central United States. However, with increased occurrence of earthquakes, a better understanding of the characteristics of the earthquakes and potential impact on wind power plants is necessary. Methods to account for the increased rate of earthquake occurrence are being developed by the USGS to better characterize the hazards due to induced seismicity and will likely be incorporated into future design standards. This paper presents a review of ground motions based on available induced seismicity earthquake records and results of time domain simulations for reference 1.5 MW and 5 MW turbine models to investigate effects on foundation loads. In addition, the study includes evaluation of effects of generic subsurface conditions typically encountered at wind power plants on ground motions and response spectra. A comparison of response spectra developed from earthquake records due to induced seismicity and typical building code spectra for the region provides insight into potential impact of increased seismicity on wind power plants and associated infrastructure.

Rocking behavior of shallow foundations for bridge piers has emerged as an effective method to reduce the seismic load on the superstructure. The design philosophy that uses the rocking behavior of shallow foundation during an earthquake is called “rocking foundation”. Previous studies on rocking foundation have focused on the verification of rocking effect to reduce the seismic load. Nevertheless, the rocking foundation is not used in practice due to the lack of understanding on the mechanism of rocking behavior. In this study, slow cyclic tests were performed using a geotechnical centrifuge with different slenderness ratios of structures to investigate the rocking mechanism of shallow foundation. From the variations of the pressure below the shallow foundation, “soil rounding” phenomenon was observed. In addition, the soil rounding effect, the key mechanism of rocking foundation, was described in two parts. Before yielding, a relation between overturning moment in the shallow foundation and the cyclic load direction was observed. The overturning moment converged to the ultimate moment capacity of shallow foundation after yielding. Therefore, the rocking mechanism of the shallow foundation was investigated using the soil rounding phenomena.

Settlement and tilt of structures due to liquefaction have resulted in significant losses in past earthquakes. Recent research by the authors employed numerical modeling to identify the parameters that have the most influence on the settlement of shallow-founded structures. We extend this analysis to determine the key parameters for predicting the residual tilt of structures. In addition to the density, thickness, and depth of the layer of liquefiable sand, we find that many of the parameters that are significant predictors of near-surface deviatoric settlements are also strongly correlated to residual tilt—in particular, the size of the foundation and its bearing pressure. However, the inertial properties of the structure (e.g., mass and effective height) are more influential on tilt than settlement. We also explore how the relative influence of these parameters is affected by ground shaking intensity, and evaluate the efficiency and sufficiency of several intensity measures in predicting tilt. We find that cumulative absolute velocity ($CAV$) and cumulative absolute velocity above a 5 cm/s² threshold ($CA{V}_5$) are the most efficient single IMs for predicting tilt, and that adding peak ground velocity ($PGV$) or peak incremental ground velocity ($V_{gi}$) increases efficiency slightly. In general, soil-foundation-structure systems that have higher expected values of settlement at a given level of shaking are also more susceptible to residual tilt. These insights provide the basis for the development of a probabilistic model for evaluating the potential residual tilt of shallow-founded structures.

Empirical equations to predict ground motions during construction operations have been suggested by various researchers. These empirical correlations were developed after measuring particle velocities on the ground surface during pile installation or other construction activities. When waves travel through the soil and away from the impact source, energy is lost due to material and geometric damping, respectively. This paper presents an overview of existing wave attenuation formulas for man-made induced vibrations. The authors collected ground motion measurements from impact pile driving by installing sensors at varying depths and very close to driven piles. A conventional line array of surface sensors was also used. Attenuation curves developed from records of both surface and in-depth sensors are presented.

Offshore wind farms that are constructed in seismic active areas have high requirements for their foundation designs. The earthquake induced soil liquefaction may cause severe damage to the whole structure and consequently influence the operation of wind turbines. Monopile foundation has been widely used currently, and based on this type of foundation, an innovative foundation is proposed. The concept of hybrid monopile-friction wheel foundation is a combination of a monopile and a gravity base, which is regarded as an improved and reinforced design of the original monopile. A series of centrifuge tests was performed to investigate the seismic response of the hybrid foundation system in sandy soil. Two types of hybrid monopile-friction wheel foundations, which contain solid wheel or gravel wheel, were tested, and the results were compared with the original monopile foundation. Accelerations, pore water pressure ratios, and settlements were recorded to illustrate the results. Each tested model exhibited distinct behaviors during the earthquake. It was found that the friction wheel further reinforced the foundation soil, and the liquefaction tendency is lower. The results validate this new concept of offshore wind hybrid foundation systems.

In this paper, seismic bearing capacity of a surface strip footing, placed at the edge of a soil slope is computed by using the lower bound finite elements limit analysis technique. Non-associated flow rule is assumed to be applicable for soil mass to consider the effect of dilation on the bearing capacity of footing. The variation of bearing capacity factors N_c and N_γ with slope angle (β), soil friction angle (ϕ), dilative coefficient (η), and horizontal seismic acceleration coefficient (k_h) are presented graphically. It is observed that the value of N_c and N_γ reduce with an increase in the value of slope angle and horizontal seismic acceleration coefficient. Whereas, with an increase in the magnitude of ϕ, and η, N_c and N_γ increase quite considerably. The effect is found to be more pronounced in the case of N_γ. The stress contours during the yielding of soil are also plotted for few cases.

Lifeline structures which are employed worldwide for the conveyance of water, sewage, oil, natural gas, and other material, gets uplifted during an earthquake due to the liquefaction of the soil in which they are buried. From the damages observed from the past earthquakes, it can be seen that many of these lifeline structures lie in the region with high liquefaction potential and large ground displacement. Therefore, there exists a need to understand the uplift mechanism of an underground structure during an earthquake. In this study, the uplift mechanism of a 5 m diameter underground structure buried at a depth of 1.1 times the diameter of the structure from the surface in a 16 m deep potentially liquefiable soil as reported in Chian et al. (2014) is analyzed using a finite difference program FLAC3D. The soil model with the dynamic boundaries is subjected to sinusoidal motion applied at the base of the model. The cyclic behavior of the soil represented by Finn-model involves the dynamic pore pressure generation from the volumetric strain induced by the seismic excitation. The results obtained emphasizing the pore pressure response at different level of the structure was compared with the centrifuge model and 2D numerical analysis results published by Chian et al. (2014). It was found that the results obtained from the three dimensional analysis using Finn-model gives slightly higher results as obtained from the two dimensional analysis using the Wang model.

The Winkler method is often adopted for the evaluation of the seismic response of retaining walls, and several closed form solutions in the literature present values for Winkler stiffness intensity (i.e., stiffness per unit area of wall) for certain simplified conditions. A common assumption in these solutions is that the wall is a rigid body. This paper presents an extensive parametric analysis of Winkler stiffness intensity for flexible elastic walls retaining inhomogeneous elastic soil. The finite element software framework OpenSees is used in the DesignSafe cyberinfrastructure to perform the analyses. The wall is cantilevered from a fixed base and its flexural stiffness is varied relative to the soil stiffness to cover a reasonable range. Pseudo-static excitation is applied to soil elements using horizontal body forces, producing variable wall and soil displacements. The Winkler stiffness intensity is then computed based on (i) the horizontal stress mobilized at the soil-wall interface, and (ii) the difference in displacement between the wall and the soil in the free-field. Results show that both wall flexibility and soil inhomogeneity significantly influence the Winkler stiffness intensity. In particular, the Winkler stiffness intensity for flexible walls can be up to three times greater than the values computed for rigid walls due to shear stresses mobilized at the wall-soil interface as the wall rotates due to flexure. This result indicates that Winkler stiffness intensity is not a fundamental soil parameter, and that values must be carefully selected to account for boundary conditions.