Seismic Site Response Analysis Research Articles

Probabilistic seismic demand models for circular tunnels subjected to transversal seismic load

This paper proposes convenient probabilistic models to estimate the seismic demands of circular tunnels to transversal seismic load. The uncertainties in the earthquake intensity, seismic load, and calculation methods are fully considered. Peak ground velocity PGV is selected as an essential earthquake intensity parameter because it is more correlated with the earthquake damage of underground structures, and a probabilistic model of PGV is proposed. Because the seismic response of tunnel linings is highly correlated with the free-field ground deformation, the maximum free field shear strain gmax is selected as the seismic load parameter. A probabilistic model of gmax is developed based on a series of seismic site response analyses. PGV plays a key role in the estimation of gmax. The analytical methods have been proposed to estimate the seismic response of tunnels. However, the results are usually biased, and the underlying uncertainties have not been well studied. To obtained unbiased seismic response estimates and capture the uncertainties in the calculation methods, the probabilistic seismic demand models are constructed by developing correction terms to the analytical method. The maximum moment Mmax, thrust Tmax, and diametric distortion Δd/dmax of the tunnel lining are considered. A pseudo-static analysis approach is used to simulate the seismic response of tunnels, and Bayesian updating is used for the model optimization and parameter estimation. The results of this paper can be used in the seismic design and reliability analysis of circular tunnels.

Site-Specific Ground Response Analysis using the Geotechnical Dataset in Moderate Seismicity Region

An understanding of the soil response to dynamic waves from the earthquakes is an important aspect of engineering safety measures against tremors. This research presents the equivalent linear site response analysis of the Miri district by using a geotechnical dataset. The main objective of this paper is to study the amplification factor for the district of Miri. Analysis of site response is critical in determining the earthquake risk and harm allocation during earthquakes. The standard penetration test ‘N’ value (SPT-N) has been used in this study. A specific soil-type relationship has been used between shear wave velocity and SPT-N value to produce profiles of shear wave velocity in each borehole site in the Miri district. For all SPT-N borehole sites, site response parameters were interpolated to produce site response maps and shear wave velocity maps in the geographical information system (GIS) environment. The research showed that the Malaysian national annex to Eurocode 8 (MNA-EC8) site class C, D and E are dominant in the Miri district. Due to the inadequacy of records of input ground motions of low-to-moderate seismicity regions, this research used an earthquake record from other locations well-matched from a target response spectrum with similar characteristics obtained from the Pacific Earthquake Engineering Research Center (PEER) online database (PEER NGA). The equivalent linear method (EQL) using DEEPSOIL is an extensively researched numeric technique that is used for assessment of site response. From the results, it has been found that the amplification ratio varies from 2.1 to 4.79 and it suggests that it is vital to study the site effect in the seismic hazard assessment of the Miri district. The work also emphasizes the relationship between seismic microzonation and site response analysis in order to reduce the adverse effects of earthquakes in Miri city by planning a proper land use.

A fully coupled flow deformation model for seismic site response analyses of liquefiable marine sediments

This paper presents a fully coupled flow deformation model to characterize the nonlinear seismic site response of liquefiable marine sediments, considering the ocean wave environment. Emphasis is placed on extending a simplified soil hysteresis model for the effective stress analysis of nonlinear site seismic response. The proposed model addresses the limitations of existing one-dimensional (1D) hyperbolic soil models to simultaneously capture the 3D hysteretic stress–strain behavior and the accumulated volumetric deformation of soil skeleton. The volume strain formulation of soil skeleton is included in the Biot's volumetric compatibility equation as the source term for excess pore water pressure buildup. The proposed method is implemented into an explicit time matching finite difference analysis platform, and validated against the recordings of the KSRH10 site for North–South (NS) direction of KiK-net borehole arrays in Japan. Finally, the influences of ocean wave loading upon the seismic wave propagation behavior in liquefiable marine sediments are examined with reference to the Bohai Strait site condition, China. The obtained results indicate that the ocean wave environment has significant effect on the nonlinear seismic site response of liquefiable seabed at shallow depth.

Defining the Boundary Conditions for Seismic Response Analysis—A Practical Review of Some Widely-Used Codes

The first step for learning any calculation code for seismic response analysis is an adequate understanding of how to properly set the boundary conditions and the properties of the soil model at the initial stage, i.e., before the shaking event. To pursue this aim, nine different computer codes suitable for seismic response analyses of soil profiles have been reviewed. An ideal twenty-meter soil column with visco-elastic linear behavior, subjected to a pulse-like input motion, has been reproduced with the different codes with the scope to practically show the differences and peculiarities of each of them. In the definition of the soil properties in the small-strain range, special attention has been devoted to the definition of the damping ratio, usually defined in non-linear codes as viscous damping according to the Rayleigh formulation. This simple one-dimensional exercise has been considered as a useful benchmark for verifying the rightness of the application of the boundary conditions and setting the initial soil properties. The same analysis can be easily reproduced by beginner users and, therefore, constitutes a starting point in the learning phase of new and/or more sophisticated 2D and 3D calculation codes for seismic site response analysis.

Localized stationary seismic waves predicted using a nonlinear gradient elasticity model

This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behavior is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend) as well as localized stationary waves are found by analyzing the obtained ordinary differential equation in the phase portrait and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.

Modelling the 2D seismic response of the Kutch basin on the Indian Subcontinent

The Kutch region in India experienced one of the largest intraplate earthquakes on January 26, 2001, with approximately 20,000 fatalities. Although strong motion recordings from the aftershocks in this region indicate basin effects, no detailed numerical studies on the effect of the basin on the ground surface motion in this region have been reported. In the present study, we conduct a 2D non-linear seismic site response analysis of a shallow triangular basin model with various bedrock slopes using the finite difference method to examine the behaviour observed in the Kutch basin. The spatial amplification pattern of the ground motion in the basin with a bedrock slope 10⁰ accords with the recorded ground motion data. The developed basin model is tested with different earthquake motions recorded at various basins across the world. We then develop the amplification factors with respect to the rock outcrop for the peak ground motion parameters and Arias Intensity. Significant amplification is observed at the basin centre and the region between the centre and the edge. The frequency content of the surface motion shifts from a narrow to a broad spectrum from the edge towards the basin centre.

A homogenization approach to estimate the shear modulus of spatially variable soil materials

Engineers often use seismic site response analyses to evaluate the propagation of seismic waves through a soil deposit. These analyses have traditionally relied on dynamic properties (e.g., the maximum shear modulus, Gmax, and shear modulus reduction curves G/Gmax) measured on homogeneous soil specimens. However, soil properties are not uniform, and it is common to see variabilities at different scales. This study uses physical models with controlled variability to evaluate the Gmax and G/Gmax in heterogeneous soil samples to reflect the effects of soil variability. We used a 3D soil printer to create heterogeneous soil models of 20x20x20 cm that match target random field simulations generated by spatially varying the liquid limit on clayey-type soils. The models were used to sample cylindrical specimens, then tested in a torsional shear rheometer to measure Gmax and G/Gmax. The results show that Gmax and the G/Gmax curves are affected by the internal specimen variability, particularly by the coefficient of variation (COV) in the underlain random fields. Using the experimental results, we also show that the Hill [1] approach for estimating properties of composite materials provides a good estimation for the experimentally measured G/Gmax curves in a heterogeneous soil media, especially in specimens with low to medium variability. Finally, we evaluated the performance of the homogenization bounding theory of Hashin and Shtrikman [2], also formulated for composite materials, on estimating Gmax. We find that the Gmax of specimens with low and medium variability can be reasonably estimated using the upper bound. In contrast, samples with high variability are better estimated using the lower bound.

Evaluation of Uncertainties in Site Response Analysis of Deep Soil Profiles in South Carolina Coastal Plain

ABSTRACTThe South Carolina Coastal Plain consists of deep soil sediments over basement bedrock. The depth of basement bedrock varies from being present at the surface to a depth of more than 1200 m at the southern tip of the state. A large variation exists in the thickness of the sediment, which impacts the seismic site response analyses of the Coastal Plain, particularly in areas where the availability of deep shear-wave velocity profiles is limited. This study evaluates the impact of variations in the shear-wave velocity profiles for two sites in the South Carolina Coastal Plain. The shear-wave velocity profiles were measured using different geophysical methods, including a combined multichannel analysis of surface waves and microtremor array measurement (MASW-MAM) method and P–S suspension logging. The equivalent-linear site response analyses were conducted by applying a synthetic earthquake motion at the depth of the B–C boundary (a depth of competent rock in which the shear-wave velocity is 760 m/s). The results are presented in terms of the amplification factor and its standard deviation. Results show that the average shear-wave velocity at the first 30 m (VS30), the shear-wave velocity contrast at the interface of the base layer and the B–C boundary, and the depth to the B–C boundary have a significant impact on the amplification factor and its variability, particularly for the amplification factor at periods higher than 0.1 s. The MASW-MAM method provided significantly lower VS30 values than the P–S suspension logging method at one of the two sites. Consequently, an additional peak in the amplification factor was observed for the site that had a low VS30, and the corresponding period was close to the resonant period of the loose, surface deposit.

Dynamic site response analysis in the face of uncertainty–an approach based on response surface method

AbstractAlthough advanced modeling techniques such as the finite element method (FEM) have been used successfully in dynamic site response analysis, the high computational expense has hindered the incorporation of input parameter uncertainty in such analysis. Thus, when the variation of the peak ground acceleration (PGA) at the ground surface, which is the outcome of the site response analysis, has to be evaluated in the face of uncertainty, a surrogate model such as Response Surface Method (RSM) model is often used in lieu of the FEM model. In this paper, the RSM surrogate model was implemented in the context of seismic site response analysis to evaluate the variation (or uncertainty) of the PGA due to the propagation of input parameter uncertainty. The engineering implication of the variation of the surface PGA is significant as this knowledge is required for such tasks as reliability analysis of soil liquefaction and probabilistic seismic risk analysis. To derive the RSM model specifically for a site response analysis, a parametric study of the dynamic site responses using FEM code ABAQUS with the modified Davidenkov soil constitutive model implemented as a user‐defined material subroutine is first conducted. The input parameters, including the soil profile, soil properties, and input ground motion, in a typical dynamic site response analysis are then characterized and screened for their suitability to be included in the RSM model. For a given site response problem in the face of uncertainty, representative “samples” are taken for site response analysis using ABAQUS, and the analyses are carried out and finally the response surface is constructed using the outcomes of the ABAQUS numerical experimentations. The accuracy of the developed RSM model is then validated using the results of ABAQUS on cases not used in the development of the RSM model. Once the RSM model is deemed satisfactory, the reliability‐based formulation for evaluating the mean and standard deviation of the surface PGA is established. Example is provided to illustrate the RSM approach for dynamic site response analysis in the face of input parameter uncertainty.

Probabilistic seismic hazard assessment and site analyses of Arusha International Conference Centre (AICC), Arusha, Tanzania

This work presents the evaluation of earthquake resistance of the Arusha International ConferenceCentre (AICC) complex, in Tanzania. The evaluation included probabilistic seismic hazardanalysis (PSHA) and site response analysis. Seismic sources considered to constitute a seismichazard in this study were randomly occurring seismicity located within five tectonic provincesaround the site. For each province the seismic hazard is based on a cursory analysis of earthquakedata from compiled ESARSWG bulletins and temporary deployed networks within the NorthTanzania Divergence (NTD). Bedrock response signal together with the information of materialcharacteristics from boreholes around the AICC site were used in analysis of site response. PSHAresults indicated uniform hazard spectra values of 0.15, 0.2 and 0.27 g for return periods of 475,975 and 2475 years, respectively. The surface ground response results indicated a maximumamplification factor of 3.7 and a spectral response of 4.5 g for a wave period of 0.6 sec thatmatches the natural frequency of the 6-7 storey buildings of the AICC complex. It is thisresonance effect on the buildings that is assumed to have caused intense shaking in the earthquakeof December 5th 2005 from Lake Tanganyika.
 Keywords: Probabilistic seismic hazard analysis; Arusha International Conference Centre; EastAfrican Rift System; Uniform hazard spectra; Site effect.

Influence of site conditions on seismic design parameters for foundations as determined via nonlinear site response analysis

Site conditions, including geotechnical properties and the geological setting, influence the near-surface response of strata subjected to seismic excitation. The geotechnical parameters required for the design of foundations include mass density (ρ), damping ratio (βs), shear wave velocity (Vs), and soil shear modulus (Gs). The values of the last three parameters are sensitive to the level of nonlinear strain induced in the strata due to seismic ground motion. In this study, the effect of variations in soil properties, such as plasticity index (PI), effective stress (σ′), over consolidation ratio (OCR), impedance contrast ratio (ICR) between the bedrock and the overlying strata, and depth of soil strata over bedrock (H), on seismic design parameters (βs, Vs, and Gs) was investigated for National Earthquake Hazards Reduction Program (NEHRP) site classes C and D, through 1D nonlinear seismic site response analysis. The Morris one-at-a-time (OAT) sensitivity analysis indicated that βs, Vs, and Gs were significantly influenced by variations in PI, while ICR affected βs more than it affected Vs and Gs. However, the influence of H on these parameters was less significant. It was also found that variations in soil properties influenced seismic design parameters in soil type D more significantly than in soil type C. Predictive relationships for βs, Vs, and Gs were derived based on the 1D seismic site response analysis and sensitivity analysis results. The βs, Vs, and Gs values obtained from the analysis were compared with the corresponding values in NEHRP to determine the similarities and differences between the two sets of values. The need to incorporate PI and ICR in the metrics for determining βs, Vs, and Gs for the seismic design of foundations was highlighted.

Stress-independent parameters for stress-strain relationship and damping in nonlinear one-dimensional seismic site response analysis

The modulus reduction and damping curves represent the nonlinear behavior of soil under cyclic load. In the literature, those curves were produced from lab tests of soil at particular confining stresses. This study developed a set of parameters that can be used to normalize the modulus reduction and damping curves to be stress-independent. The proposed formulations for the stress-independent parameters were implemented in the finite element code SRAP and validated through producing shear modulus reduction and damping curves that match the existed ones. Nonlinear 1D seismic site response analyses were conducted for centrifuge experiments to verify the developed computer code. Comparisons of the analysis results between SRAP and another computer code were presented in terms of maximum and minimum displacement, peak ground acceleration, maximum shear strain profiles, and response spectra.
 Keywords:
 backbone curve; hysteretic damping; dynamic soil model; stress-independent parameters; finite element method; nonlinear 1D seismic site response analysis.

SANISAND-MSf: a sand plasticity model with memory surface and semifluidised state

A new constitutive model for sand is formulated by incorporating two new constitutive ingredients into the platform of a reference critical state compatible bounding surface plasticity model with kinematic hardening, in order to address primarily the undrained cyclic response. The first ingredient is a memory surface for more precisely controlling stiffness affecting the plastic deviatoric and volumetric strains and ensuing excess pore pressure development in the pre-liquefaction stage. The second ingredient is the concept of a semifluidised state and the related formulation of stiffness and dilatancy degradation, aiming at modelling large shear strain development in the post-liquefaction stage. In parallel, a modified flow rule aimed at providing a better description of non-proportional monotonic and cyclic loading is introduced. With a single set of constants, for which a detailed calibration procedure is provided, this new model successfully simulates undrained cyclic torsional and triaxial tests with different cyclic stress ratios, separately for the pre- and post-liquefaction stages, as well as liquefaction strength curves based on [Formula: see text] and shear strain criteria for initial liquefaction. The successful reproduction of the sand element response under undrained cyclic shearing contributes to future applications in realistic and thorough seismic site response analysis.

Seismic microzonation of Sarpol-e-zahab after Mw 7.3 2017 Iran earthquake: 1D-equivalent linear approach

The impacts of Iran’s recent and destructive earthquake of Mw 7.3 November 12 2017, and its important subsequent events are investigated at Sarpol-e-zahab by means of 1D-equivalent linear site response analyses. Local damages at Sarpol-e-zahab highlighted the role of seismic microzonation in seismic risk reduction and damage prevention plans for future events. Hence, the main goals of this study are set to provide maps for amplification factors and shaking levels of the city as well as validating design-basis earthquake loads for buildings and structures of the national code of IRSt2800. This is achieved by deconvolution of the strong motions recorded by ISMN-SPZ as the closest station to the epicenter of Mw 7.3 earthquake and finding the two horizontal bedrock motions and subsequently, convolution of the horizontal bedrock motions to find the ground motions at 38 points across the city. The results of seismic site response analyses have provided very instructive information for rehabilitation of the existing buildings and future constructions as well as seismic vulnerability assessment of buildings during earthquakes. Furthermore, it provides an unprecedented research in Iran of a complete seismic microzonation at urban scale after an earthquake and a successful application of seismic microzonation at urban area with inadequate number of strong motion recording stations.

Stochastic approach to study the site response in presence of shear wave velocity inversion: Application to seismic microzonation studies in Italy

One of the most important controlling parameters of the seismic site response in terms of earthquake ground motions modification is the shear wave velocity (Vs) profile of the subsoil, that generally increases with depth because of geological age, cementation and overburden stress. There exist, however, geological settings where the velocity profile is characterized by inversions, when a stiffer layer (exhibiting higher Vs) overlies a softer one (with a lower Vs). When referring to the Italian territory, these conditions are widespread and require specific seismic site response analyses, both for structures and infrastructures design and for land planning.The aim of the present work is to study the effect of Vs inversion on seismic site response in recurrent Italian geological domains for application in seismic microzonation studies, i.e., at the miunicipality scale.Firstly, the most common Italian geological domains characterized by inversion of Vs profiles are identified. Afterwards, one-dimensional subsoil columns representative of each identified geological domain are defined, based on Italian database of the seismic microzonation. In the end, based on the subsoil models defined at previous steps, numerical simulations of 1D site response are performed, in order to evaluate the influence of Vs inversion on ground shaking in terms of shear strain profiles and acceleration response spectra at the ground surface. To take into account the variability in the input parameters, stochastic 1D analyses are carried out via Monte Carlo method assuming assigned statistical distribution for Vs profiles and nonlinear variation curves of the normalized shear modulus and the damping ratio with the shear strain.

Effect of bedrock stiffness and thickness on numerical simulation of seismic site response. Italian case studies

Evaluation of bedrock stiffness and thickness effect on ground motion modification represent a key-issue in the perspective of seismic risk reduction policy, since the maximum depth of site prospection generally does not extend down to the stiff bedrock location. Site conditions were identified from the Italian database of seismic microzonation studies. Simplified and realistic numerical models were adopted, i.e. extended down to the soft and stiff bedrock, respectively, in order to perform seismic site response analyses. Results indicate that simplified numerical model provides a quantification of the surface ground motion modification with an error generally equal to ±10% with respect to the realistic model. Hence, the evaluation of seismic performance of sites based on simplified numerical models represents a support tool for seismic risk management at large area.

Influence of trapped soft/stiff soil layer in seismic site response analysis

As the ground response analysis serves an integral part of site specific seismic hazard study to obtain design ground motion, a proper and accurate estimation should be of prime importance. The paper presents a study on the effect of trapped soft and stiff soil layer on equivalent linear ground response analysis implemented in computer program STRATA. For this purpose, the concept of normally stiff and inversely stiff soil profiles have been introduced. The study clearly indicates the higher impact of a trapped soft soil layer profile, i.e., inversely stiff soil profile with soft layer, in comparison with trapped stiff layer profile, i.e., inversely stiff profile with stiff layer. For low to moderate ground motions, as the depth of the trapped soft layer increases, peak amplification and peak frequency reduces, and for high intensity input ground motion, significant reduction only in the peak frequencies is observed. On the other hand, as the depth of trapped stiff soil layer increases the outcome of ground response analysis remain quite similar. Peak transfer function, peak frequency, peak spectral ratio and peak spectral acceleration are found to exhibit a COV ≤ 60 to 100% for all combinations of IS-Soft profiles, whereas, IS-Stiff profiles exhibit a maximum COV ≤ 15 to 25% for all the considered input ground motions. Computed normalized-root mean square error (Norm-RMSE) values also clearly indicate the higher deviations in the ground response analysis for different combinations of trapped soft soil profiles, from that of normally stiff profile, whereas, trapped stiff layer profiles show lower deviations in the Norm-RMSE values. The profiles with trapped soft layer exhibit a Norm-RMSE value ≤0.8, whereas, trapped stiff layer profiles exhibit a Norm-RMSE value ≤0.2, which clearly demonstrate the large deviations in the outcome of ground response analysis in case of trapped soft layer profiles.

Nonlinearity and strength in 1D site response analyses: a simple constitutive approach

When performing seismic site response analyses in the design practice, one of the main issues consists in finding a compromise between the limited availability of site-specific experimental data to characterise the cyclic soil behaviour and the necessity of a proper constitutive representation of such behaviour, including nonlinearity, hysteresis and strength. This paper presents a new constitutive approach for 1D nonlinear soil models, capable of describing such features with a simple and easy to calibrate constitutive equation, requiring the definition of few parameters, all derived from conventional field and laboratory data. The main element of novelty in the proposed approach consists in recognizing that the soil shear strength is a key ingredient not only to limit the maximum shear stress that the soil can experience at large strains, but also to describe the dependence of the nonlinear soil properties on mean effective stress and plasticity index, as observed in the medium strain range. Based on a thorough comparison with laboratory data, it is shown that the proposed model provides a very good description of the soil behaviour, in the whole strain range. Its application in site response analyses is further validated on centrifuge data and verified against other nonlinear constitutive soil models. Finally, using a well-characterised site in Italy as reference, it is demonstrated that an erroneous prediction of the soil shear strength can lead to a misinterpretation of the amplification phenomena within the soil deposit, together with a possible gross underestimation of the actual surface acceleration.

1D seismic site response analysis for a soil deposit at Baoding city

Based on 1D equivalent linear method, the effect of a soil deposit at Baoding city on wave propagation was analysized. Firstly, probabilistic seismic hazard analysis (PSHA) was performed, and the peak accelartion and response spectrum of outcrop with exposure rate over 63%, 10% and 2% in 50 years are obtained; secondly, the artificial earthquake ground motions used as input motion of soil deposit were synthesized; lastly, 1D equivalent linear analysis was performed to evaluate the effect of soil deposit on wave propagation. Results show that soil deposit has a great influence on wave propagation. The intensity of input motion also plays an important role on the properities of seismic ground motion.

Evaluation of the seismic site response in randomized velocity profiles using a statistical model with Monte Carlo simulations

Abstract Uncertainty associated with the soil properties inevitably affects the seismic ground response, which is unable to be properly assessed using a deterministic seismic site response analysis. In this paper, an attempt has been made to investigate the possible impact of the shear-wave velocity ( V s ) variation on the predicted ground motions using a real site in Italy. A statistically-based randomization model is adopted to describe the uncertainty of the V s profiles for various scenarios. The equivalent-linear method combined with the direct Monte Carlo simulation is employed to perform the stochastic seismic site response analysis. The results are presented in terms of amplification function ( AF ), spectral acceleration ( S a ), fundamental frequency ( f 0 ) and amplification factor ( F a ). The mean and standard deviation of these four factors are evaluated for a wide range of shear-wave velocity variations, interlayer correlations, and input motion intensities. This study also explores the accuracy of adopting truncated bounds as an approximate process of preventing the generation of unrealistic soil profiles. The results show that the variability of the predicted ground motion is significant in some situations and can be decreased by reducing the shear-wave velocity uncertainty.