Downhole Array Sites Research Articles

Application of non-stationary shear-wave velocity randomization approach to predict 1D seismic site response and its variability at two downhole array recordings

Accounting for uncertainties in seismic site response is crucial to improving the performance of one-dimensional (1D) ground response analyses (GRAs) at downhole array recording sites. In addition to site effects, uncertainties in 1D-GRAs can also be contributed from the seismic source and/or path. Though often representing not more than one percent of the distance (path) from the source, site conditions are known to have an enormous influence on ground shaking. In this study, we focus on the site shear-wave velocity (VS) structure, which is the main ingredient for estimating the variability of site response. As such, VS can manifest aleatory uncertainties related to the effects of small-scale spatial heterogeneities within the near surface, thus VS can substantially modify ground shaking during earthquakes. We apply a novel VS randomization approach to propagate the small-scale heterogeneities of VS to estimate seismic site response within a non-stationary probabilistic framework. The randomization approach generates samples of VS profiles that are used to perform several 1D-GRAs and obtain an averaged site response and related variability. The proposed method is implemented on data recorded at two downhole array sites with different subsurface soil conditions: a soft soil site on Treasure Island (California, United States of America) and a rock outcrop site in Cadarache (South-East France). We show that synthetic surface-to-borehole transfer functions from 1D-GRAs provide an acceptable fit to the empirical transfer functions from low-motion earthquake records and succeed in reproducing most of the site-specific seismic response variability. The remaining mismatch between transfer functions is likely due to insufficient precision on the seismic bedrock and the impedance contrast. The variability in site response is discussed with emphasis on the role of VS small-scale heterogeneities, attenuation, and input motion incidence angle in ground motion variability for the site and soil conditions at both locations.

Multi‐input integrative neural network for soil seismic response modeling at KiK‐net downhole array sites

AbstractPrediction of the soil seismic response is of primary importance for geotechnical earthquake engineering. Conventional physics‐based models such as the finite element method (FEM) often face challenges due to inherent model assumptions and uncertainties of model parameters. Furthermore, these physics‐based models require significant computational resources, particularly when simulating seismic responses across numerous soil sites. In this study, a multi‐ input integrative neural network is developed for predicting soil seismic response based on the recorded data from a large number of downhole array sites. Ground motions, seismic event information, and wave velocity structures of the sites are utilized as input data in the proposed neural network, enabling the model to adapt to various site conditions. Comparative assessments against state‐of‐the‐art FEM models demonstrate that the proposed models exhibit superior prediction performance with increased efficiency. Furthermore, the pre‐training technique, a transfer learning method, is employed to predict the seismic response at new stations. By fine‐tuning the pre‐trained model derived from the extensive dataset with limited recorded data from new stations, high‐precision seismic response predictions can be realized, illustrating the adaptability and efficacy of the proposed approach in data‐scarce conditions.

Novel techniques for in situ estimation of shear-wave velocity and damping ratio through MASW testing part II: a Monte Carlo algorithm for the joint inversion of phase velocity and phase attenuation

SUMMARY This paper deals with in situ characterization of the small-strain shear-wave velocity VS and damping ratio DS from an advanced interpretation of Multi-channel Analysis of Surface Waves (MASW) surveys. A new approach based on extracting Rayleigh wave data using the CFDBFa method has been discussed in the companion paper. This paper focuses on mapping the experimental Rayleigh wave phase velocity and attenuation into profiles of VS and DS versus depth, which is achieved through a joint inversion procedure. The joint inversion of phase velocity and attenuation data utilizes a newly developed Monte Carlo global search algorithm, which implements a smart sampling procedure. This scheme exploits the scaling properties of the solution of the Rayleigh eigenvalue problem to modify the trial earth models and improve the matching with the experimental data. Thus, a reliable result can be achieved with a limited number of trial ground models. The proposed algorithm is applied to the inversion of synthetic data and of experimental data collected at the Garner Valley Downhole Array site, as described in the companion paper. In general, inverted soil models exhibit well-defined VS profiles, whereas DS profiles are affected by larger uncertainties. Greater uncertainty in the inverted DS profiles is a direct result of higher variability in the experimental attenuation data, the limited wavelength range at which reliable values of attenuation parameters can be retrieved, and the sensitivity of attenuation data to both DS and VS. Nonetheless, the resulting inverted earth models agree well with alternative in situ estimates and geological data. The results stress the feasibility of retrieving both stiffness and attenuation parameters from active-source MASW testing and the effectiveness of extracting in situ damping ratio estimates from surface wave data.

Two-dimensional Ground Response Analyses at the Delaney Park Downhole Array Site

Two-dimensional Ground Response Analyses at the Delaney Park Downhole Array Site

Subsurface imaging dataset acquired at the Garner Valley Downhole Array site using a dense network of three-component nodal stations

There is a growing need to characterize the engineering material properties of the shallow subsurface in three dimensions for advanced engineering analyses. However, imaging the near-surface in three dimensions at spatial resolutions required for such purposes remains in its infancy and requires further study before it can be adopted into practice. To enable and accelerate research in this area, we present a large subsurface imaging data set acquired using a dense network of three-component (3C) nodal stations acquired in 2019 at the Garner Valley Downhole Array (GVDA) site. Acquisition of this data set involved the deployment of 196 stations positioned on a 14 × 14 grid with a 5 m spacing. The array was used to acquire active-source data generated by a vibroseis truck and an instrumented sledgehammer, and passive-wavefield data containing ambient noise. The active-source acquisition included 66 vibroseis and 209 instrumented sledgehammer source locations. Multiple source impacts were recorded at each source location to enable stacking of the recorded signals. The active-source recordings are provided in terms of both raw, uncorrected units of counts and corrected engineering units of meters per second. For each source impact, the force output from the vibroseis or instrumented sledgehammer was recorded and is provided in both raw counts and engineering units of kilonewtons. The passive-wavefield data include 28 h of ambient noise recorded over two nighttime deployments. The data set is shown to be useful for active-source and passive-wavefield three-dimensional imaging and other subsurface characterization techniques, which include horizontal-to-vertical spectral ratios (HVSRs), multichannel analysis of surface waves (MASW), and microtremor array measurements (MAM).

Soil seismic response modeling of KiK-net downhole array sites with CNN and LSTM networks

Accurate prediction of soil seismic response is necessary for geotechnical engineering. The conventional physics-based models such as the finite element method (FEM) usually fail to obtain accurate predictions due to the model assumption and parameter uncertainties. And the physics-based models are computationally expensive. This study proposes deep learning models to develop data-driven surrogate models for the prediction of soil seismic response based on the recorded ground motions from KiK-net downhole array sites. Two kinds of advanced neural networks, convolution neural network (CNN) and long short-term memory (LSTM) neural network, are applied in this framework respectively. These models do not rely on any prior knowledge about the soil site. The performance of the deep learning models is demonstrated through both numerical and recorded examples. Compared with the state-of-art FEM models, the proposed models could achieve better prediction performance with higher efficiency. The average prediction error is reduced by more than 40% in time domain and 30% in frequency domain. Even though great variability exists during the propagation of seismic in the reality, the models can still get satisfactory predictions.

A numerical separation method for incident wave of ground motion in time domain

Distinguishing incident wave in the downhole records is meaningful when assessing the amplification factor of site effect. A time-domain numerical separation method for incident wave is presented in this article. It can be applied in nonlinear case under strong motion because its formulation is based on the fundamental theory of particle motion behavior at the zero-stiffness interface during the propagation and reflection of body wave. The practicability of the proposed approach is verified on a two-layered idealized model site. Considering the Garner Valley Downhole Array site as a test case, the properties of soil characteristics are approximated on the basis of previous studies. The numerical reproductions of coseismic temporal changes by using two measured ground motions with different intensities are satisfactory, meanwhile the incident waves within motion of borehole records are recognized by utilizing the proposed method. The comparisons of outcrop and borehole responses suggest that the pseudoresonances can be observed in the latter, while the shapes of the former gradually resemble the latter with the increase in depth, due to the energy dissipation in the process of wave propagation. The discrepancy of site response under the ground motions of different intensities is remarkable in the considered frequency range.

Engineering site response analysis of Anchorage, Alaska, using site amplifications and random vibration theory

Earthquake records collected at dense arrays of strong-motion stations are often utilized in microzonation studies to evaluate the changes in site response due to variability in site conditions across a region. These studies typically begin with calculating Fourier spectral amplification(s) and then transition to performing engineering site response analyses. It has proven difficult to utilize Fourier spectral amplification(s) to define the appropriate elastic response spectr(um)/(a) for a site or sites. This is because, first, the ground motions recorded at these strong-motion stations have lower intensity and hence do not show the nonlinear site effects observed during higher-intensity earthquakes and, second, Fourier and response spectral amplitudes measure different aspects of ground motions. The strong-motion stations in Anchorage, Alaska, have been recording earthquakes in the region for the last three decades. This study utilizes a database of 95 events from 2004 to 2019 to calculate Fourier spectral amplifications at 35 stations using the generalized inversion technique (GIT). Estimated response spectra have been evaluated at each site by applying those Fourier spectral amplifications to a response spectrum of a reference station through random vibration theory (RVT). Correction factors are also applied within the approach to account for nonlinear site effects. This RVT-based approach is tested using ground motions recorded during the MW 7.1 2018 Anchorage Earthquake, and close matches between measured and predicted response spectra are found. The method is then compared with site response analyses using a calibrated 1D equivalent linear (EQL) model of the Delaney Park Downhole Array site. Estimated spectra using the RVT-based approach are, finally, compared with those using Next Generation Attenuation Subduction (NGA-Sub) and NGA-West2 ground-motion models. The proposed method provides a coherent and straightforward way to use GIT-derived Fourier spectral amplifications to directly estimate site-specific response spectra, accounting for nonlinear site effects and without requiring engineering characterization of subsurface soil conditions.

An H/V geostatistical approach for building pseudo-3D Vs models to account for spatial variability in ground response analyses Part II: Application to 1D analyses at two downhole array sites

Common procedures used to account for spatial variability of shear wave velocity (Vs) in one-dimensional (1D) ground response analyses (GRAs), such as stochastic randomization of Vs or increasing small-strain damping, have been shown to improve seismic site response predictions relative to 1D GRAs where no attempts are made to account for spatial variability. However, even after attempting to account for spatial variability using common procedures, 1D GRAs often still yield results that are different than ground motions recorded at many downhole array sites. When 1D predictions differ from observations, the site is typically considered to be too spatially variable to effectively use 1D GRAs. While there is no doubt that some sites are indeed too variable for 1D GRAs, it is also possible that simple 1D analyses could still be effectively used at many sites if spatial variability is accounted for through a more rational, site-specific approach. In this study, an H/V geostatistical approach for building pseudo-3D Vs models is implemented to account for spatial variability in 1D GRAs. The geostatistical approach is used to generate a uniform grid of Vs profiles that have been scaled to match fundamental site frequency estimates from horizontal-to-vertical spectral ratio (H/V) noise measurements. In this article, 1D GRAs are performed for each grid point and the results are statistically combined to reflect the average site response and its variability. This 1D application is demonstrated at the Treasure Island and Delaney Park Downhole Array sites, where it is shown to produce superior fits to the small-strain recorded site response relative to existing approaches used to account for spatial variability in 1D GRAs. Using the proposed approach, we also investigate the lateral area that is likely influencing site response at each site and show that it could extend to significant distances (as much as 1 km) from the boreholes.

An H/V geostatistical approach for building pseudo-3D Vs models to account for spatial variability in ground response analyses Part I: Model development

Many recent studies have shown that we are generally unable to accurately replicate recorded ground motions at most borehole array sites using available subsurface geotechnical information and one-dimensional (1D) ground response analyses (GRAs). When 1D GRAs fail to accurately predict recorded site response, the site is often considered too complex to be effectively modeled as 1D. While three-dimensional (3D) numerical GRAs are possible and believed to be more accurate, there is rarely a 3D subsurface model available for these analyses. The lack of affordable and reliable site characterization methods to quantify spatial variability in subsurface conditions, particularly regarding shear wave velocity (Vs) measurements needed for GRAs, has pushed researchers to adopt stochastic approaches, such as Vs randomization and spatially correlated random fields. However, these stochastically generated models require the assumption of generic, or guessed, input parameters, introducing significant uncertainties into the site response predictions. This article describes a new geostatistical approach that can be used for building pseudo-3D Vs models as a means to rationally account for spatial variability in GRAs, increase model accuracy, and reduce uncertainty. Importantly, it requires only a single measured Vs profile and a number of simple, cost-effective, horizontal-to-vertical spectral ratio (H/V) noise measurements. Using Gaussian geostatistical regression, irregularly sampled estimates of fundamental site frequency from H/V measurements ( f0,H/V) are used to generate a uniform grid of f0,H/V across the site with accompanying Vs profiles that have been scaled to match each f0,H/V value, thereby producing a pseudo-3D Vs model. This approach is demonstrated at the Treasure Island and Delaney Park Downhole Array sites (TIDA and DPDA, respectively). While the pseudo-3D Vs models can be used to incorporate spatial variability into 1D, two-dimensional (2D), or 3D GRAs, their implementation in 1D GRAs at TIDA and DPDA is discussed in a companion paper.

Deterministic ground motion simulations with shallow crust nonlinearity at Garner Valley in Southern California

AbstractWe present deterministic ground motion simulations that account for the cyclic multiaxial response of sediments in the shallow crust. We use the Garner Valley in Southern California as a test case. The multiaxial constitutive model is based on the bounding surface plasticity theory in terms of total stress and is implemented in a high‐performance computing finite‐element parallel code. A major advantage of this model is the small number of free parameters that need to be calibrated given a shear modulus reduction curve and the ultimate soil strength. This, in turn, makes the model suitable for regional‐scale simulations, where geotechnical data in the shallow crust are scarce. In this paper, we first describe a series of numerical experiments designed to verify the model implementation. This is followed by a series of idealized large‐scale simulations in a 35 26 4.5 km domain that encompasses the Garner Valley downhole array site, which is an instrumented and well‐characterized site in Southern California. Material properties were extracted from the Southern California Earthquake Center Community velocity model, CVM‐S4.26, considering its optional geotechnical layer, while the modulus reduction curves and soil strength were selected empirically to constrain the nonlinear soil model parameters. Our nonlinear simulations suggest that peak ground displacements within the valley increase relative to the linear case, while peak ground accelerations can increase or decrease, depending on the frequency content of the excitation. The comparisons of our simulations against hybrid three‐dimensional–one‐dimensional site response analyses suggest the inadequacy of the latter to capture the complexity of fully three‐dimensional simulations.

The Importance of Distinguishing Pseudoresonances and Outcrop Resonances in Downhole Array Data

ABSTRACTThis short note examines the downgoing wave effect and the appearance of pseudoresonances in downhole array data. It is demonstrated that pseudoresonances, distinct from the resonances associated with outcrop conditions, occur for sites with a shallow velocity contrast (VC) or with little to no VC. An approach is outlined to distinguish pseudoresonances from outcrop resonances using the theoretical 1D transfer functions for within and outcrop boundary conditions, as well as the horizontal-to-vertical spectral ratio. This approach is applied to hypothetical shear-wave velocity profiles, as well as three downhole array sites. We establish the importance of distinguishing pseudoresonances from outcrop resonances when using downhole array data to evaluate the accuracy of the 1D site response. For the example downhole array sites shown, the pseudoresonances are not captured well by 1D analysis, whereas the outcrop resonances are captured well. We propose that when evaluating the accuracy of 1D site-response analysis using downhole array data, the comparisons of the empirical and theoretical responses only consider the frequency range associated with outcrop resonances.

Taxonomy for evaluating the site-specific applicability of one-dimensional ground response analysis

Because one-dimensional (1D) ground response analysis remains the state-of-practice for geotechnical earthquake engineering, one crucial task is to identify whether the response of a site can be modeled well by 1D analysis. In this study, ground response analyses incorporating 1D transfer functions (TF) and the H/V Spectral Ratio (HVSR) technique are carried out for 34 downhole array sites and used to develop a taxonomy that assesses the suitability of 1D analysis for a site. The empirical HVSR is used to identify the first-mode resonant frequency of the site, and the within and outcrop TF are used to distinguish true outcrop-resonances from pseudo-resonances. The taxonomy is focused on capturing outcrop-resonances rather than pseudo-resonances because pseudo-resonances are an artifact of downhole array sites and are not present in the outcropping analysis of non-downhole array sites. Using the proposed taxonomy, 69% of the sites are considered suitable for 1D analysis, which is a much larger percentage than found in other studies. This more favorable result is a direct result of considering only true-resonances in the assessment of 1D applicability. This taxonomy system is developed using downhole array data but it can be applied to any site (even non-downhole array sites) in which the empirical HVSR curve and shear wave velocity profile are measured, making it easily applied in engineering practice.

A methodology for estimation of site-specific nonlinear dynamic soil behaviour using vertical downhole arrays

System identification (SI) techniques have been widely used in Geotechnical Engineering to understand the characteristics of soils. In this study, system identification techniques with and without using a constitutive model were examined using three downhole array sites in California, US. Shear wave velocities (VS) and maximum shear moduli (Gmax) of soils were obtained using SI techniques without using a constitutive model and low-amplitude earthquake records. Average shear moduli and average damping ratios of soil layers were estimated through SI technique using a linear constitutive model and relatively high amplitude records. Finally, a practical methodology was proposed for predicting site-specific shear modulus degradation (G/Gmax) and damping curves (ξ) using nonlinear constitutive models and high amplitude earthquake data recorded in some arrays. The proposed methodology predicts site-specific dynamic characteristics by using the recorded earthquake data and iterating the reference strain (γr) in the nonlinear constitutive model. From the results, it can be inferred that average shear modulus values estimated using the linear constitutive model might not predict the dynamic soil behaviour properly for high amplitude earthquakes. However, the acceleration time histories obtained using the site-specific G/Gmax and ξ curves predicted by the proposed methodology using nonlinear constitutive model were in good agreement with the recorded acceleration data.

Selection of representative shear modulus reduction and damping curves for rock, gravel and sand sites from the KiK-Net downhole array

Representative computation of ground response parameters requires accurate information about nonlinear dynamic behavior of the soil column, commonly incorporated in site response analysis through shear modulus reduction and damping curves which are functions of the strain level. Most site response studies are carried out by considering a set of existing shear modulus and damping curves, without knowing its suitability for the in situ soil type. In this study, an attempt has been made to identify suitable shear modulus and damping curves for soil grouped into different classes viz. sand, gravel and rock. Soil profiles of sites having surface and bedrock motion recordings are selected from the KiK-Net downhole array database and equivalent linear and total stress nonlinear site response analysis has been carried out by varying the shear modulus and damping curves for different sites. Estimated surface response spectra for each set of shear modulus and damping curves are compared with the observed response spectra at each site, and a detailed analysis is made to find out which set of curves gives a best match with the recorded data. Based on this study, representative property curves for rock, gravel and sand are suggested, which could be used for further site response studies in the region. This study shows that only a set of shear modulus and damping curves ensure a compatible spectrum with the recorded data from the KiK-Net downhole array sites, among the many available shear modulus and damping curves in the literature.

A source-synchronous filter for uncorrelated receiver traces from a swept-frequency seismic source

We have developed a novel algorithm to reduce noise in signals obtained from swept-frequency sources by removing out-of-band external noise sources and distortion caused from unwanted harmonics. The algorithm is designed to condition nonstationary signals for which traditional frequency-domain methods for removing noise have been less effective. The source synchronous filter (SSF) is a time-varying narrow band filter, which is synchronized with the frequency of the source signal at all times. Because the bandwidth of the filter needs to account for the source-to-receiver propagation delay and the sweep rate, SSF works best with slow sweep rates and moveout-adjusted waveforms to compensate for source-receiver delays. The SSF algorithm was applied to data collected during a field test at the University of California Santa Barbara’s Garner Valley downhole array site in Southern California. At the site, a 45 kN shaker was mounted on top of a one-story structure and swept from 0 to 10 Hz and back over 60 s (producing useful seismic waves greater than 1.6 Hz). The seismic data were captured with small accelerometer and geophone arrays and with a distributed acoustic sensing array, which is a fiber-optic-based technique for the monitoring of elastic waves. The result of the application of SSF on the field data is a set of undistorted and uncorrelated traces that can be used in different applications, such as measuring phase velocities of surface waves or applying convolution operations with the encoder source function to obtain traveltimes. The results from the SSF were used with a visual phase alignment tool to facilitate developing dispersion curves and as a prefilter to improve the interpretation of the data.

Reply to "Comment on 'Comparison of Time Series and Random-Vibration Theory Site-Response Methods' by V. Graizer"

We appreciate the comments of Graizer (2013) and agree that the accuracy of all site‐response methods should be evaluated with respect to recordings from downhole array sites. However, the goal of our study was not to evaluate the absolute accuracy of a specific method of site‐response analysis, but rather to evaluate two approaches to the same method of site‐response analysis. Namely, we aimed to evaluate the random‐vibration theory (RVT) and time‐series (TS) approaches to equivalent‐linear site‐response analysis using frequency‐domain transfer functions. Because these two types of analysis use the same algorithm to model wave propagation, we felt that the most insight would be gained by comparing the RVT and TS results to each other rather than with downhole recordings. When evaluating site‐response methods with downhole recordings the comparisons are influenced by several factors, including the quality of the site characterization, the applicability of the 1D assumptions and boundary conditions, and these factors would potentially obscure understanding the differences between RVT and TS analyses. Nonetheless, we feel that the results presented in Graizer (2013) regarding the Treasure Island site complement and reinforce the conclusions from Kottke and Rathje (2013). In particular, the results support the need for a correction to the ground‐motion duration for RVT motions computed at the surface of soil sites. The dynamic response of a soil deposit will change the duration of shaking. This effect is modeled in current ground‐motion prediction equations for duration (e.g., Bommer et al. , 2009) and it is clearly shown by the recorded motions from the Treasure Island downhole array. Qualitatively, figure 2 in Graizer (2013) reveals a significant increase in duration between the motions at 122 m depth and at the surface. Quantitatively, one may compute the significant duration ( D 5–75, defined as the time interval between the occurrence of 5% and 75% …

Site- and ground motion-dependent nonlinear effects in seismological model predictions

We investigate the empirical relationship between site response nonlinearity, soil properties, and ground motion characteristics, as a first step to enable efficient integration of nonlinear analyses in broadband ground motion simulations. For this purpose, we use 24 downhole array sites with detailed geotechnical information and subject the profiles to broadband ground motion synthetics. We quantify the extent of soil nonlinearity in site-specific response analyses by estimating the divergence between linear and nonlinear ground surface predictions. We show that the parameters controlling the nonlinear response are V S 30 (weighted averaged shear wave velocity in the top 30 m of the soil profile), the site amplification at the fundamental frequency (Amp), the peak ground acceleration (PGA), and the frequency index (FI), a quantitative measure we define to characterize how well the incident motion can “see” the near-surface soil layers. Using the synthetic results, we quantitatively describe the error introduced in ground motion predictions when nonlinear effects are not accounted for, and show that the error is both site and ground motion dependent. Our study indicates that to characterize the susceptibility of a soil profile to nonlinear effects, V S 30 should be complemented with measures of the soil–rock impedance contrast, as well as measures of the ground motion intensity and frequency content.

Site- and Motion-Dependent Parametric Uncertainty of Site-Response Analyses in Earthquake Simulations

We investigate the propagation of uncertainty in site-response analyses from the soil model parameters to the ground surface motion at three downhole array sites in the Los Angeles (LA) Basin. For this purpose, we develop realistic stochastic models of elastic and nonlinear dynamic soil properties using extensive site-specific and generic geotechnical data on the variability of soil properties. We also generate synthetic ground motions using a finite source dynamic rupture model over a wide range of magnitudes and distances and use this statistically significant number of ground motions in the analysis. For each of the three sites, we evaluate the effects of soil parameter uncertainty as a function of the seismic input intensity and frequency content. We show that the frequency range, where the ground-motion variability due to soil parameter uncertainty is maximized, is a function of both the site and the seismogram characteristics. We compare our results with previously published studies and show that different soil models, statistical descriptions of soil parameters, or ground-motion scenarios may yield substantial differences in the estimated site-response scatter. We conclude that the effects of nonlinear soil property uncertainties on the ground-motion variability strongly depend on the seismic motion intensity, and this dependency is more pronounced for soft soil profiles. By contrast, the effects of velocity profile uncertainties are less intensity dependent and more sensitive to the velocity impedance in the near surface that governs the maximum site amplification.

A hypoplastic model for site response analysis

Site response analyses must take into account the nonlinear behavior of soils. This is typically achieved using an equivalent linear approach or using numerical analyses with an appropriate constitutive model. In this work a family of hypoplastic models is proposed for use in site response analyses. These nonlinear models use a rate-type tensorial equation and are capable of reproducing plastic deformation of soils for cyclic loading under both drained and undrained conditions. A methodology for the calibration of hypoplastic parameter for dynamic loading is proposed. The hypoplastic constitutive models are implemented in a finite element code and the site response of the Lotung downhole array site is used to validate the use of hypoplastic models for site response analysis. The hypoplastic models reproduce accurately site response at the Lotung site. The advantages and disadvantages of the hypoplastic models compared to other models are discussed.