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Based on our previous study, we developed ground motion prediction equations (GMPEs) with two site proxies, that is, with one GMPE using the site period (TS, four times the travel time of shear waves down to the bedrock) and the other one using a pseudosite period (TVS30, four times the travel time of shear waves down to 30 m depth). We used two reasonably simple site-effect models based on TS or TVS30, and each site model has four parameters with each parameter having a physical meaning and miming the theoretical process in site amplification calculations. We found that only the linear magnitude terms in the site class (SC) model from our previous study need to be modified to accommodate the change in the site response parameters, suggesting that the source effect interacts with the site effect. At short periods up to about 0.3 s, the performances of these site models are largely similar. However, at spectral periods over 0.3 s, the performances of these site models are strikingly different, and the rank of the three models in the site model performance is (from the best to the worst) TS, SC, and TVS30 site models. It is a surprise that the SC model with four classes can be better than the TVS30 site model, which does not account for the effect of the soil or rock layers between the 30 m and the bedrock depth. These results may mean that the inclusion of these deep soil layers is more important than the limitations of using a simple step function for the SC model. The GMPE using TS presented in this study improved the prediction accuracy significantly, especially for sites with TS over 0.3 s at spectral periods over 0.3 s. The GMPE using TS in this study can be used whenever TS is available.

A large dataset from earthquakes up to the end of 2012 with a reliable earthquake tectonic category was used to develop a ground motion prediction equation (GMPE) for the vertical strong motions from the subduction interface earthquakes in Japan. Guided by the increase in the maximum log likelihood of the regression model, a minor extension on the maximum usable period was applied so that more records can be used at long spectral periods. A bilinear magnitude scaling function hinged at a moment magnitude (Mw) of 7.1 was adopted, and the scaling rate for events with Mw>7.1 is less than that for the other events. Site period-based site classes were used as the site parameter without a nonlinear site term. We used two datasets with the first dataset including strong-motion records from large events at stations with inferred site classes, and these records were removed in the second dataset so that all sites have a measured shear wave velocity profile down to the engineering bedrock. We found that excluding these records from sites with inferred site classes improved the model fit significantly. We modeled the effect of volcanic zones using the slant distance passing a set of volcanic zones. We also found that the between-site standard deviations for the vertical component in this study were generally less than those for the horizontal component at nearly all spectral periods. The total model standard deviations from this study are generally less than or similar to those from the GMPEs for the vertical ground motions for other earthquake categories. The distributions of between-site residuals with site period or TVS30 (120/VS30 in m/s) are not significantly biased, suggesting that the site term coefficients can be interpolated between that site class terms if a continuous predicted spectrum with site period or TVS30 is required.

We present a set of ground-motion prediction equations for the horizontal components of the strong-motion records from shallow-crustal and upper-mantle earthquakes in Japan. We used a reasonably large dataset from earthquakes with a moment magnitude (Mw) over 4.9 and a reliable earthquake category determined by the tectonic location of earthquakes up to the end of 2012. The modeling of source and site effects in this study is similar to that by Zhao, Zhou, et al. (2016); a two-segmented model for the magnitude scaling function hinged at Mw 7.1 and site-period-based site classes were used as the site effect proxy that accounts for the effect of the nonlinear soil response. We used two types of multisegmented geometric attenuation functions with the distance break points based on the distributions of within-event residuals versus source distance. We found that the geometric attenuation functions with three distance break points (70, 130, and 220 km) for the shallow-crustal earthquakes and with two distance break points (90 and 150 km) for the upper-mantle events improved the model performance significantly. The first two break points for the shallow-crustal events are similar to those for the attenuation of the Fourier spectrum due to Moho reflection, but the corresponding coefficients between these spectra differ significantly. For the upper-mantle events, the geometric attenuation coefficient is somewhat surprisingly close to −1.0 for the first segment, 0.0 for the second segment, and −0.5 for the third segment at many periods, because these values are close to the classic attenuation rates of the Fourier spectrum for shallow-crustal events but having different distance break points. Moho reflection is not usually present in the ground motions from deep events, and we can only provide a plausible explanation; a future study is warranted for a theoretical explanation.

A general sliding block model for calculating permanent displacement of slope is presented. Ground shaking can be applied to base or block in a direction horizontal or parallel to the inclined plane, with or without a simultaneous vertical component of ground motion, and the azimuth of the examined slope can be considered in the model. The effects of the application of excitation, the vertical component of ground motions, and the slope azimuth on earthquake-induced permanent displacements of near-fault seismic slopes are investigated using the model. The results indicate that: (1) The application of excitation has significant influence on the permanent displacements. (2) The influence of the vertical component of ground motion on the permanent displacement depends more on the phase synchronization of the horizontal and vertical components than on the amplitude. (3) The computed displacements are found to be very sensitive to the azimuth of the slope.

This article presents a nonlinear site amplification model for ground-motion prediction equations (GMPEs), using site period as site-effect proxy based on the measured shear-wave velocity profiles of selected KiK-net and K-NET sites in Japan. This model was derived using 1D equivalent-linear site-response analysis for a total of 516 measured soil-site shear-wave velocity profiles subjected to a total of 912 components of rock-site records. The modulus reduction and damping curves for each soil layer were assigned based on the soil-type description for a particular layer. The site period and site impedance ratio affect both the linear and nonlinear parts of this study, and were used as the site parameters in the 1D amplification model. A large impedance ratio enhances the amplification ratios when the site responds elastically and enhances the nonlinear response when the site develops a significant nonlinear response. The effects of moment magnitude and source distance on the linear part of the 1D amplification model were also incorporated in the model. To implement the 1D amplification model into GMPEs, a model adjustment is required to match the GMPE amplification ratio at weak motion and to retain the nonlinear amplification ratio at the strong motion of the 1D model. The two-step adjustment method by Zhao, Hu, et al. (2015) was adopted in this study with significant modifications. It is not possible to obtain a credible second-step adjustment parameter using the GMPEs dataset only. We proposed three methods for calculating the scale factors. Method 1 is a constant angle in a 30°–60° range for all spectral periods; method 2 was based on the GMPE dataset and 1-D model parameters; and method 3 was based on the strong-motion records used for the 1D site modeling. A simple second-step adjustment factor leads to smoothing amplification ratios and soil-site spectrum.

In this manuscript we present a nonlinear site amplification model for ground-motion prediction equations (GMPEs) in Japan, using a site period-based site class and a site impedance ratio as site parameters. We used a large number of shear-wave velocity profiles from the Kiban-Kyoshin network (KiK-net) and the Kyoshin network (K-NET) to construct the one-dimensional (1D) numerical models. The strong-motion records from rock-sites in Japan with different earthquake categories and taken from the Pacific Earthquake Engineering Research Center dataset were used in this study. We fit a set of 1D site amplification models using the spectral amplification ratios derived from 1D equivalent linear analyses. Parameters of site impedance ratios for both linear and nonlinear site response were included in the 1D model. The 1D model could be implemented into GMPEs using a new proposed adjustment method. The adjusted site amplification ratios retain the nonlinear characteristics of the 1D model for strong motions and match the linear amplification ratio in GMPE for weak motions. The nonlinearity of the present site model is reasonably similar to that of the historical models, and the present site model could satisfactorily capture the nonlinear site response in empirical data.

A ground-motion prediction equation for the vertical ground motions from the western and the southwestern parts of China (referred to as SWC) is presented in this study. Based on the Xing and Zhao (2021) study, the Zhao et al. (2017) model (referred to as ZHAO2017) for the shallow crustal earthquakes in Japan was used as the reference model. We used a bilinear magnitude-scaling function hinged at a moment magnitude (Mw) of 7.1. The magnitude-scaling rate for events with Mw>7.1 was determined by records from the SWC dataset and the large events in the Pacific Earthquake Engineering Research Center Next Generation Attenuation-West2 dataset. Site classes (SCs) were used as the site response proxy. All other parameters were derived from the SWC dataset only. The magnitude-scaling rates for events with Mw≤7.1 in this study are larger than in the ZHAO2017 model at most periods. The absolute values of the geometric attenuation rates are larger, and the absolute values of the anelastic attenuation rates are smaller than in the ZHAO2017 model. The between-event standard deviations are smaller than in the ZHAO2017 model at short periods, and the within-event standard deviations are larger than in the ZHAO2017 model at all periods. The differences in the between-site standard deviations vary significantly from one SC to another. We also find that the between-event and within-event residuals are almost independent of magnitude and source distance. The response spectrum attenuates less rapidly than in the ZHAO2017 model at distances less than 30 km.

Currently, the dynamic behavior of high-speed long-runout landslides triggered by earthquakes remains unclear due to the complexity of such phenomena. Degradation in the shear strength of rock masses is considered a primary factor contributing to the high velocities and long runout distances of these landslides. In this study, the strength degradation induced by changes in rock joint morphology is analyzed considering a numerical model of the Donghekou landslide, by using discontinuous deformation analysis (DDA). First, an exponential joint roughness degradation function (i.e., JRCm) that depends on displacement is incorporated with the nonlinear Barton–Bandis (B–B) shear strength criterion, and this modified B–B criterion is combined with the DDA. Moreover, a virtual joint is introduced in the DDA to model the propagation of cracks in intact rock masses, in order to simulate the dynamic phenomenon of earthquake-induced landslides. Subsequently, this improved DDA (IDDA) is validated via simulations of a shear test and a sliding block over an inclined plane. Finally, the IDDA is employed to simulate the Donghekou landslide, which was induced by the 2008 Wenchuan earthquake in China. Furthermore, the entire dynamic process of the landslide, including crack propagation, instability, initiation, and motion, is depicted. The simulated deposit patterns obtained via the IDDA are in good agreement with the results of field investigations. The simulation results also prove that the IDDA can reflect key movement behaviors of Donghekou landslide and that the degradation of rock joints significantly influences the long runout distance and high velocity of sliding mass.

This study evaluated the source, path, and site effects of the vertical ground motions from the western and the southwestern parts of China (referred to as SWC hereafter) using 2403 records from 449 earthquakes, including the records from the 2008 Mw 7.9 Wenchuan earthquake and its aftershocks. Only 677 records are from 73 mainshocks, and 259 events do not have a known focal mechanism. There is a large magnitude gap in the dataset, for example, there is only one event between Mw 6.3 and Mw 7.8. The average numbers of records per recording station and per earthquake are small, and many sites do not have a measured shear-wave velocity profile. These shortcomings make it difficult to develop a robust ground-motion prediction equation (GMPE) without adding overseas data or using a reference GMPE developed from a large dataset. We compared the SWC dataset with five recent GMPEs, three based on the Next Generation Attenuation-West2 dataset, one based on Europe and the Middle East, and one based on the shallow-crustal and upper-mantle earthquakes in Japan. We decomposed the total residuals for each model into constant term, between-event, and within-event residuals and calculated the corresponding standard deviations. The maximum log likelihood and the standard deviations suggest that, among the five GMPEs, the Zhao et al. (2017) model without the normal-fault term may be the most suitable GMPE for a probabilistic seismic hazard study in the SWC region. Correction functions based on simple magnitude, path, and site effect parameters were used to correct the residuals and to obtain the leftover between- and within-event standard deviations. These standard deviations appear to suggest that the GMPE from Zhao et al. (2017) without a normal-fault term may be the most suitable reference GMPE for developing a new GMPE for the SWC region.

Ground-motion prediction equations (GMPEs) for the horizontal and vertical spectral accelerations (SAs) from the offshore area off the Sagami Bay is presented in this article. To compare the ground motions on the seafloor with those at onshore sites, an onshore GMPE was derived for the onshore stations adjacent to the offshore sites and including those in the Kanto basin sites. The offshore dataset includes 738 three-component records, and the onshore dataset includes 3775 records; both datasets are derived from the same set of 233 earthquakes selected for this study. The local site conditions of the offshore sites are investigated by implementing the mean horizontal-to-vertical response spectral ratios because soil condition data are unavailable. Individual site correction terms are used for the offshore sites due to differences among the site conditions, whereas site-class terms are used for the onshore sites based on the travel-time-averaged shear-wave velocity to 30 m (VS30). A comparison between the offshore and onshore models shows that the horizontal SAs for the whole periods and vertical SAs for moderate and long periods of the offshore motions are considerably larger than those of the onshore motions due to the deep deposition layer comprising soft sediment blanketing the seafloor; the vertical SAs of the offshore motions are slightly smaller than those of the onshore motions at short spectral periods. The inconsistency of the vertical motions at short periods may be due to the combined effect of the deposition layer and water layer. However, the vertical site amplification for short periods is independent of the water depth, and the reason of high-frequency deficiency in vertical components need further investigation.

We present a damping modification factor (DMF) model for the total acceleration spectrum from subduction slab earthquakes. The model can be used for scaling a 5% damped design spectrum not associated with a particular earthquake that occurred in a subduction slab. The DMF model uses site-period-based site classes as the site-effect proxy. DMF models were constructed based on the spectrum for 13 damping ratios and 34 spectral periods; the DMF values can be calculated for any damping ratio between 1% and 30% and at any spectral period between 0.03 and 5.0 s. At moderately long and long spectral periods, the DMF values for acceleration spectrum are similar to or less than those for the displacement spectrum for a damping ratio of less than 5%, whereas the DMF values for the acceleration spectrum are similar to or larger than those for the displacement spectrum when the damping ratio is more than 5%. The standard deviations for acceleration and displacement spectra are similar at short or moderately short spectral periods, but those for the acceleration spectrum are about twice those for the displacement spectrum at long spectral periods. All standard deviations decrease linearly with increasing damping ratios in the logarithm scale when the damping ratio is less than 5% and increase linearly with increasing damping ratios in a logarithm scale for the other damping ratios. A set of simple functions for calculating various standard deviations is presented. The spectra from the Zhao, Jiang, et al. (2016) study for slab events scaled by the DMF values for other damping ratios vary smoothly with spectral period and have a trough at short spectral periods for a large event, a short distance, and high damping ratios. The relatively large between-event and within-site standard deviations are from the source and path effects.

This article presents a damping modification factor (DMF) model without source and path parameters for subduction interface earthquakes in Japan using a similar dataset as the one used in the Zhao, Liang, et al. (2016) study. Site effect was modeled by site classes based on site periods. DMF models were constructed using the spectra for 13 damping ratios at 34 spectral periods. The DMF values can be calculated in a damping ratio range of 1%–30% and in a spectral period range of 0.03–5.0 s. The effect of damping ratios was modeled by a simple quadratic function of the damping ratios in the logarithm scale, and the effect of the spectral period was modeled by a simple fourth-order polynomial of the spectral period also in the logarithm scale. The DMF value is 1.0 at a spectral period of ≤0.02 s . At long periods >5.0 s, the DMFs for different damping ratios appear to converge to 1.0, satisfying the condition of constant displacement spectrum at long periods. For an extrapolation to >5.0 s for a damping ratio 5%, DMF=1.0 can be selected when DMF>1.0. For a damping ratio 5%, all standard deviations increase linearly with increasing damping ratios in the logarithm scale. A smoothed displacement spectrum useful for engineering designs can be obtained by scaling the spectrum from Zhao, Liang, et al. (2016). The DMF values from this study are close to those of the published models at some spectral periods. The residual distribution suggests that DMFs are functions of earthquake source and path parameters.

A damping modification factor (DMF) model without source and path parameters is presented in this article for subduction slab earthquakes in Japan, using a similar dataset in the Zhao, Jiang, et al. (2016) study. Site classes based on site periods were used as the site-effect proxy. DMF models were derived from spectra of 13 damping ratios and 34 spectral periods, and the DMF can be calculated for any damping ratio between 1% and 30% and at any spectral period between 0.03 and 5.0 s. A simple fourth-order polynomial for the logarithm of the spectral periods and a simple quadratic function of the logarithm of damping ratios were used to model the effects of spectral periods and damping ratios, respectively. The model satisfies boundary conditions that require the DMF values equal to 1.0 at very short spectral periods; at long spectral periods, the DMFs for different damping ratios appear to converge to 1.0 to satisfy the constant displacement spectrum at long periods. Model standard deviations are smaller than those for the ground-motion prediction equations. All standard deviations vary linearly with the increasing logarithm of damping ratios. The DMFs presented in this study combined with the spectrum from the Zhao, Jiang, et al. (2016) study produce smoothed displacement spectrum that may be used for engineering designs. In a spectral period range of 0.2–3.0 s, the DMF values from this study are close to those by Daneshvar et al. (2016), but, at short periods, the difference is significant. The residual distribution suggests that DMFs also depend on earthquake source and path parameters. The model presented in this article does not include the effect of source and path variables so that this model can be used to scale a 5% damped spectrum without a known magnitude and a source distance.

Damping modification factors (DMFs) are important for estimating the response spectrum for the design of structures with different damping ratios. This study investigated the effects of earthquake source parameters (magnitude, source depth, and source categories), source distance (the closest distance from a site to a fault plane for large earthquakes and hypocentral distance for the other events), and site conditions on DMFs for the displacement and acceleration response spectra of the horizontal components of the records from Japan. This study used a total of 14,713 strong‐motion records from the KiK‐net and K‐NET to compare the DMFs from three earthquake category groups, namely shallow crustal and upper mantle, subduction interface, and subduction slab earthquakes. Statistical tests were carried out to determine whether the DMFs from these three types of earthquakes differ significantly from each other. The test results show that, between each pair of the three types of earthquakes, the DMFs for both displacement and acceleration response spectra differ significantly in terms of statistical tests and practically for engineering applications at many spectral periods, with the largest difference over 40%. The effects of earthquake category and site conditions for acceleration spectrum are similar to those of the displacement spectrum at short periods up to about 0.3 s but are much larger than those of the displacement spectrum at long spectral periods. The effects of magnitude and earthquake depth are also significant. Therefore, separate DMF models for the response spectrum of the horizontal component should be derived for each type of earthquake and should account for the effects of earthquake source and path parameters and site conditions.

This study aims at identifying ground‐motion prediction equations (GMPEs) derived from large overseas datasets that may be used for the southwestern part of China (SWC) with or without modifications, identifying the source of misfits and shedding some light on the differences of physical parameters among the three regions, that is, California, Japan, and SWC region. To achieve these objectives, correction functions of physical parameters were added to six GMPEs, including two Next Generation Attenuation‐West (NGA‐West) GMPEs, two NGA‐West2 GMPEs, a GMPE from China, and the GMPE for the shallow crustal and upper‐mantle earthquakes in Japan. The correction coefficients were determined by a reasonably large dataset, including the records from the 2008 Mw 7.9 Wenchuan earthquake. However, the data distribution with respect to magnitude is relatively poor and may not be suitable to develop a GMPE based on this dataset only. If the overall correction coefficients for a GMPE are the smallest, this GMPE will be considered as the best GMPE for the SWC data. We found that not all GMPEs can be modified to achieve the same goodness‐of‐fit level; the magnitude scaling rates from most GMPEs differ significantly from those of this dataset, especially at moderately long and long spectral periods; and the aftershock effect does not make a significant and consistent difference. We also found that three GMPEs do not model the site effect well either; the attenuation rates for the SWC region may be similar to those in California and for the shallow crust in Japan; and the magnitude scaling rate and the site class effect in the SWC region are similar to those in Japan. If an overseas GMPE is used for the SWC region, the GMPEs by Zhao, Zhou, et al. (2016) without the normal‐fault term and Abrahamson and Silva (2008) with or without modifications are recommended.

Edge-to-edge is the most common form of contact in a two-dimensional joint block system. Discontinuous deformation analysis (DDA) is a powerful tool for handling block systems and treats an edge-to-edge contact as two vertex-to-edge contacts with a couple of normal and shear springs at the extremes of the contact segment. However, this method is unsuitable for evaluating the tensile failure of a joint under asymmetrical tension conditions, even though it can simplify the contact type and increase computational efficiency. This is mainly because the distributed forces at an edge-to-edge contact are simplified as two couples of concentrated forces. To solve this problem, this paper proposes incorporating a multi-spring edge-to-edge contact model with DDA. In the model, several contact pairs with normal and shear springs on an edge-to-edge contact are set to simulate the distributed forces. Several benchmark tests were performed to demonstrate the discrepancy between the original and improved DDAs. The results revealed that the latter more accurately models the stress distribution across the edge-to-edge contact, providing a more reasonable acceleration required to topple a series of blocks resting on an inclined stepped base.

Edge-to-edge contact is a fundamental contact type in blocky systems. In two-dimensional discontinuous deformation analysis (2D DDA, and hereinafter DDA for short), an edge-to-edge contact is transformed into two separated vertex-to-edge contacts by applying two pairs of concentrated springs. Although this simplification facilitates the DDA algorithm, it is not always sufficiently accurate and can even yield irregular results. To solve this problem, a distributed-spring contact model (DSCM) that exerts distributed instead of concentrated forces on contact edges is proposed in this paper for the edge-to-edge contact in DDA. Submatrices for the force matrix and stiffness matrix are obtained by minimizing the potential energy of the distributed contact forces and are incorporated into an improved DDA (I-DDA) code. Four examples are evaluated to illustrate the validations and advantages of the I-DDA. The first example is a single square impacting on a base block. Deformation of the contact area is evaluated by comparison with the theoretical deformation solution, and the results calculated by the I-DDA show better agreement with the analytical solution than the original DDA (O-DDA). The second example is an impact validation, proving that the I-DDA is more adaptable to discrete systems containing blocks of different sizes. Then an example and an experiment about block rebounding are provided, demonstrating that the errors in rotation and rebounding exhibited in the O-DDA results are avoided when using the I-DDA, indicating that the I-DDA provides more realistic solutions. The results of this study suggest that the proposed I-DDA incorporating the DSCM is quite accurate and capable of improving calculation accuracy compared to the O-DDA.

The acceleration records at some liquefied sand deposits exhibit a distinctive spiky waveform, characterized by strong amplification and high-frequency components. A comprehensive constitutive model was used to analyze the mechanism of such spiky acceleration responses. An idealized single-degree-of-freedom (SDF) system was constructed, in which the force-displacement relation of the spring follows the stress-strain behavior of saturated sand during undrained shearing. The SDF system demonstrated that the spikes are directly related to the strain-hardening behavior of sand during post-liquefaction cyclic shearing. Furthermore, there exists a threshold shear strain length, which is in accordance with the limited amplitude of the fluid-like shear strain generated at instantaneous zero effective stress state during the post-liquefaction stage. The spiky acceleration can only occur when the cyclic shear strain exceeds the threshold shear strain length. It is also revealed that the time intervals between the acceleration spikes increase gradually along with the continuation of shaking because the threshold shear strain length increases gradually and then more time is needed to generate larger shear strain to cause strain hardening. Records at the Kushiro Port site and Port Island site during past earthquakes are simulated through the fully coupled method to validate the presented mechanism.

How to incorporate near-fault directivity effect into the ground motion prediction equations (GMPEs) is an active research topic in recent years. Many studies demonstrated that the directivity could amplify the spectral accelerations (S a) in a range close to the pulse period (T p). This study intends to propose a new empirical narrowband model for including such effects. The ratio of the S a from the original ground motions to the S a from the residual ground motions is employed to quantify this amplification effects, under the assumption that the S a from the residual ground motions are well predicted by the non-directivity-included GMPEs. Differing from previous models that suggested the amplified S a arise in a smooth bell-shaped pattern, the proposed model assumes that the peak amplification occurs as a plateau in the intermediate range. This plateau, having a constant ordinate of about 3.31, starts and ends at the period of 0.75 and 1.09 times the T p, respectively; while in the other ranges the amplification decreases away from the two sides of this plateau. To further simplify the proposed model, two additional controlling periods are derived to determine the period range with significant amplification effects. Then the proposed model is expressed in the form of a piecewise function comprising five line segments. Finally, it is concluded that the non-directivity-included GMPEs, when multiplying the proposed model, can reasonably approximate the S a of the original ground motions in the statistical sense within the T p-related range.

A series of three dimensional (3D) shaking table tests were carried out to investigate the mechanism and effect of seismic measures of mountain tunnel using a scaled model based on a real tunnel. Key technical details of the experiment, including similarity relations, seismic measures simulation, boundary conditions, sensor layout, modeling methods, and ground motion input were presented. Main seismic measures, including reinforcing surrounding rock with anchors, increasing lining flexibility with steel wire mesh, and installing seismic isolation layer between reinforced surrounding rock and tunnel lining, were investigated in this study. Experiment results show that: (1) adding a layer of steel wire mesh in the tunnel lining can improve the flexibility and seismic performance and also may effectively prevent radial cracks from crossing the lining; (2) installing a geofoam isolation layer between the reinforced surrounding rock and the tunnel lining reduces dynamic earth pressure by 70–90% for the lining without a seismic isolation layer; (3) the flexible joints can effectively avoid global failures of tunnel lining for they reduce dynamic strain and bending force in the tunnel lining and decrease the seismic energy transmission along the lining in axial direction; (4) reinforcing surrounding rock with anchors significantly reduces dynamic earth pressure and strain of the lining by about 50%. In addition, the length of seismic reinforcement for general mountain tunnel portal is recommended to be 50 m from the tunnel portal along the axial direction.

In this article, ground‐motion prediction equations (GMPEs) based on the horizontal components of the strong‐motion records from shallow crustal and upper‐mantle earthquakes in Japan are presented. We assembled a large dataset from earthquakes with a moment magnitude ( M w) over 4.9 and a reliable earthquake category (the tectonic location of earthquakes) up to the end of 2012. The GMPEs were based on a set of simple geometric attenuation functions. A bilinear magnitude‐scaling function hinged at M w 7.1 was adopted, with the scaling rates for large events being much smaller than those for the smaller events. Site classes based on site period were used as site terms, and nonlinear site terms were included. We modeled the effect of volcanic zones using an anelastic attenuation coefficient applied to a horizontal portion of the seismic‐wave travel distance within volcanic zones. Most strong‐motion records in our dataset are from stations with a measured shear‐wave velocity profile down to engineering bedrock. A small number of records are from stations with inferred site classes using the response spectral ratio of the horizontal‐to‐vertical components or geologic description of the surface soil layers. We tested the effect of site information quality by comparing the goodness‐of‐fit parameters from the model with and without the sites with inferred site classes. Our results suggest that the site information quality made a significant difference for spectral periods over 0.7 s, that is, the exclusion of sites with inferred site classes improves the model fit significantly. The within‐event residuals were approximately separated into within‐site and between‐site components, and the corresponding standard deviations were calculated. The approximate separation allows for the possibility of adopting different standard deviations for different site classes in a probabilistic seismic‐hazard analysis if desired. Online Material: References for fault rupture plane models, earthquake records and volcanic zones information, illustration of site information quality effect, standard deviations for between‐event, within‐event, between‐site and within‐site residual, and the distribution of between‐event and within‐event residuals.

The frequency content of strong ground motions from subduction slab earthquakes differs significantly from that of ground motions produced by other categories (tectonic locations: shallow crustal, upper mantle, and subduction interface) of earthquakes in subduction zones. In the last two decades, a large number of records from subduction slab events have been obtained in Japan. We present a ground‐motion prediction equation (GMPE) for this category of earthquakes. We used a large dataset from reliably identified slab events up to the end of 2012. The GMPEs were based on a set of simple geometric attenuation functions, site classes were used as site terms, and nonlinear site amplification ratios were adopted. A bilinear magnitude‐scaling function was adopted for large earthquakes with moment magnitude M w≥7.1, with the scaling rates for large events being much smaller than for the smaller events. A magnitude‐squared term was used for events with M w

Establishing a set of ground‐motion prediction equations (GMPEs) for Japan requires earthquake source categories in the dataset. Earthquakes are typically divided into three groups: shallow crustal events that occur in the Earth’s crust, subduction interface events that occur at the interface between the crust or mantle and the subducting plate, and the subduction slab events that occur within the subducting plate. In the present study, we compared the hypocentral locations published in the catalogs of the International Seismological Centre/Engdahl–van der Hilst–Buland (ISC‐EHB; Engdahl et al. , 1998), the Japan Meteorological Agency (JMA), and the National Earthquake Information Center (NEIC) of the U.S. Geological Survey (USGS). The hypocentral location for the same earthquake varies significantly from one catalog to another. We used the subduction interface model from the USGS, Slab 1.0, to help guide the classification. We designed four classification schemes using locations from these three catalogs. We then fitted a set of random effects models to the strong‐motion dataset from these earthquakes to assess the merits of the classification schemes. Our results showed that using ISC‐EHB locations for events before 2005, and then using the preference order of catalogs as (1) JMA locations with high precision levels, (2) ISC‐EHB, and (3) NEIC (excluding the events with a fixed depth) for events since 2005, together with some conditions for subduction interface events, produced the best GMPEs in terms of the maximum log likelihood. We also found that having a separate group for the earthquakes above the subduction interface, but with a depth over 25 km, improved the goodness of fit of the GMPEs. Online Material: Figures of azimuthal‐dependent distance shift of epicenters between catalogs, and between‐event and within‐event residuals.

This paper studies the run-out of earthquake-induced landslides. There are more than 20 mechanical models to explain long run-out of rapid landslides including some earthquake-induced landslides. However, notably few of them considered the effect of seismic loading on the run-out of landslides. In a previous study, we have proposed a model, which is called the multiplex acceleration model (MAM), to interpret the long run-out mechanism, and a shaking-table test has been performed to verify the MAM. Because the previous MAM is a conceptual model and only a single stone has been examined under sine waves by the shaking-table test, the MAM needs to be extended and further verified. In this paper, the MAM was extended by introducing the movement change that was induced by the so-called trampoline effect of earthquake loading, and the latest practical numerical simulation program, discontinuous deformation analysis (DDA), was used to verify the mobility of earthquake-induced landslides. After a conceptual landslide model was used to verify the effect of seismic loading on the mobility, the Donghekou landslide, which was a typical long run-out landslide that was induced by the 2008 Wenchuan earthquake, was analyzed. The results show that: the seismic loading could be one of the factors that could eventually help increase the run-out of landslides.

Nonlinear site models are an important part of ground‐motion prediction equations (GMPEs) and can be constructed in a number of ways. If numerous soil‐site strong‐motion records contain the effect of strong nonlinear soil response, the parameters for the nonlinear model can be a part of the regression parameters for GMPEs. It is also possible to derive nonlinear site models by numerical simulation. However, the number of strong‐motion records from Japan that contain the effect of strong nonlinear soil response is still too small to derive nonlinear site terms. We present a model of nonlinear site terms using site class as the site parameter in GMPEs based on a 1D equivalent linear model. The 1D model was constructed based on the shear‐wave velocity profiles from the KiK‐net strong‐motion stations with a wide range of site periods, soil depth, and impedance ratios. The rock‐site strong‐motion records were from different earthquake categories in Japan and the Pacific Earthquake Engineering Research Center dataset. Those records had a wide range of earthquake magnitudes, source distances, and peak ground accelerations. A random effects regression model was fitted to the calculated spectral amplification ratios, accounting for the effect of site impedance ratios, earthquake magnitudes, and source distances of the rock‐site records. We also designed a method to adjust the 1D model so it can be used in a GMPE, accounting for the fact that a 1D model is an overly simplistic assumption for many real strong‐motion recording stations in many parts of the world. Online Material: Tables of nonlinear site model parameters.

This paper extends the discontinuous deformation analysis (DDA) by using an additional evaluation of edge-to-edge contact, with the aim that it can be used to accurately model the failure behaviour of joints dominated by both cohesion and interface friction angle. The original DDA can deal well with the effects of interface friction angle. However, when cohesion exists, DDA results often show an inscrutable behaviour, i.e. a slope may be unstable even if the cohesion is much greater than the theoretical value required for its critical stability. After many detailed investigations and validations, joint contact treatment was found to be the key reason why the original DDA cannot simulate the cohesive material accurately, in which every edge-to-edge contact is treated as two vertex-to-edge contacts that may have different contact states associated with different cohesion treatments. In order to solve this problem, an additional contact type determination process for an edge-to-edge contact was added into the original computer code to avoid the unreasonable situation when two contact states exist in one joint. Several examples were performed to illustrate the accuracy of the modified code and a real landslide case was analysed by using the improved DDA to estimate the shear strength on the interface. Our results show that the improved DDA can simulate the failure of cohesive-frictional material accurately.

Impact force evaluation of rock landslides acted on structures is important to the hazard prevention. This paper presents a numerical method to estimate the impact force on structures. An impact force model for the contact force on the given boundary, rather than the resultant force at the center of gravity is presented and incorporated into Discontinuous Deformation Analysis (DDA). The accuracy is verified by comparing simulation results with both analytical and experimental results. A case is then carried out to study the impact force of sliding mass acting on structures, showing the applicability and capability of the presented method.

V S 30 , the shear‐wave travel time averaged soil shear‐wave velocity of the top 30 m, has been used to represent site effects in many recent ground‐motion prediction equations (GMPEs). However, while V S 30 has been found to be a reasonable parameter to represent site effects in some studies, other studies provide contradictory evidence. In the present study, a systematic comparison between the predictive capabilities of these two site‐effect parameters is carried out using a large ground‐motion dataset from Japan. The basis of the adopted approach is to compare the standard deviations and amplitudes of amplification ratios in empirically modeling site effects by using either site period ( T S , four times the shear‐wave travel time from the bedrock to the ground surface) or V S 30 . The site effects modeled specifically include site amplification ratios between surface and borehole records from KiK‐net, in addition to the site‐effect terms from a GMPE. For KiK‐net data, T S is determined to be a better predictive parameter than V S 30 for soil sites with T S >0.6 s, while the two parameters lead to a similar variability in amplification ratios for sites with T S V S 30 and T S are statistically equal for all site classes at most periods, while V S 30 leads to smaller variability than T S at some spectral periods. The conflict between the KiK‐net surface–borehole records, and the results from the GMPE is likely to be a result of large variability in the GMPE, containing source‐, path‐, and site‐variability, as compared with the reduced variability in the surface–borehole KiK‐net data pairs. Although V S 30 and T S lead to statistically similar standard deviations for the data from a GMPE, T S still leads to better median amplification ratios than V S 30 .

A revised empirical model has been developed for predicting liquefaction-induced lateral spreading displacement (LD) as a function of both response spectral acceleration derived from strong-motion attenuation models and geotechnical parameters from Youd’s LD data set (Youd website). This revised model is different from the model of Zhang and Zhao, which overcame some drawbacks of earlier models for predicting lateral spreading and was primarily used in Japan and the western U.S. The revised model can potentially be applied anywhere if ground shaking (in terms of 5% damped acceleration or displacement response spectra) can be estimated using local strong-motion attenuation relationships. The revised model is examined using data from Japan and the western U.S. and applied to Turkey and New Zealand, where the ground shaking is estimated using appropriate strong-motion attenuation relationships for each region. The accuracy of the revised model is evaluated by comparing its predicted lateral displacements with those measured in actual earthquakes. The results show that the revised model can account for the effects of local seismicity on lateral spreading displacements and is comparable with existing prediction models.

A moment magnitude (Mw) 6.2 earthquake struck beneath the outer suburbs of Christchurch, New Zealand's second largest city, on 22 February 2011 local time. The Christchurch earthquake was the deadliest in New Zealand since the 1931 Mw 7.8 Hawkes Bay earthquake and the most expensive in New Zealand's recorded history. The effects of the earthquake on the region's population and infrastructure were severe including 181 fatalities, widespread building damage, liquefaction and landslides. The Christchurch earthquake was an aftershock of the Mw 7.1 Darfield Earthquake of September 2010, occurring towards the eastern edge of the aftershock zone. This was a low recurrence earthquake for New Zealand and occurred on a fault unrecognised prior to the Darfield event. Geodetic and seismological source models show that oblique-reverse slip occurred along a northeast–southwest-striking fault dipping southeast at c. 69°, with maximum slip at 3–4 km depth. Ground motions during the earthquake were unusually large at near-source distances for an earthquake of its size, registering up to 2.2 g (vertical) and 1.7 g (horizontal) near the epicentre and up to 0.8 g (vertical) and 0.7 g (horizontal) in the city centre. Acceleration response spectra exceeded 2500 yr building design codes and estimates based on standard New Zealand models. The earthquake was associated with high apparent stress indicative of a strong fault. Furthermore, rupture in an updip direction towards Christchurch likely led to strong directivity effects in the city. Site effects including long period amplification and near-surface effects also contributed to the severity of ground motions.

Magnitude‐scaling rates (MSRs; the rates of increase in predicted response spectra with increasing moment magnitude) are evaluated for three ground‐motion prediction equations for response spectra from subduction interface earthquakes, including two empirical models developed for data from Japan and a model based on synthetic records generated by using a stochastic finite‐fault model. MSRs vary significantly among the three models, and the difference between the two empirical models is unacceptably large. A set of 2100 strong‐motion records from subduction interface events with a magnitude of 6.5 or larger from Japan, including the 11 March 2011 magnitude 9 earthquake, were compiled. The earthquakes were grouped according to magnitude, so that the magnitude spread in each group is less than 0.2 magnitude units. Each earthquake group was treated as a single event with magnitude equal to the average magnitude for the group. A simple attenuation model was fitted to the normalized and grouped data. The model has a constant term for each earthquake group to represent the effect of magnitude. Three separate functions of magnitude (a linear model for events with a magnitude greater than 7, a bilinear model, and a curved model) were then fitted to the constants, and MSRs were derived from these functions. At short periods, the derived MSRs are only a fraction of those from two of the three attenuation models. At spectral periods greater than 0.5 s, the derived MSRs are between about 1/3 and 1/2 of those of the two empirical models but are closer to those based on a set of synthetic records.

We have evaluated the magnitude-scaling rates (MSRs, the rate of increase in the predicted spectrum with increasing moment magnitude) of five modern ground-motion prediction equations (GMPEs) for response spectra, including four Next Generation Attenuation (NGA) models and a model developed for data from Japan. We have found that MSRs for crustal earthquakes with a moment magnitude over 7 vary significantly among the five models, by a factor of 2–3 for some cases. The variation of MSRs among the four NGA models is alarmingly large, considering that they were derived from largely the same dataset and used the same site parameters. We have selected 641 strong-motion records from shallow crustal earthquakes with a moment magnitude over 7 from the NGA dataset and 69 from the 2008 Wenchuan, China, earthquake with a moment magnitude of 7.9, all within a short distance of 200 km from the fault rupture plane. To illustrate the extreme extent of magnitude scaling, we have fitted an attenuation model without a magnitude term to this dataset, based on an observation that an increase in one moment magnitude unit is related to an increase in fault length by a factor of 5–10, a significant increase in shaking duration, which cannot be fully accounted for by response spectra, and limited or no increase in ground-motion amplitude. The statistical analyses of the results indeed suggest that a zero magnitude scaling at spectral periods over 0.6 s may be reasonable for our dataset, while the required apparent magnitude scaling at short periods may be due to other factors such as stress drop, a parameter that is not used in any of the models considered. We will provide some plausible explanations for the possible zero magnitude scaling that can be considered as the lower limit of the uncertain magnitude-scaling rate.

To estimate the near-fault inelastic response spectra, the accuracy of six existing strength reduction factors (R) proposed by different investigators were evaluated by using a suite of near-fault earthquake records with directivity-induced pulses. In the evaluation, the force-deformation relationship is modelled by elastic-perfectly plastic, bilinear and stiffness degrading models, and two site conditions, rock and soil, are considered. The R-value ratio (ratio of the R value obtained from the existing R-expressions (or the R-µ-T relationships) to that from inelastic analyses) is used as a measurement parameter. Results show that the R-expressions proposed by Ordaz & Perez-Rocha are the most suitable for near-fault ground motions, followed by the Newmark & Hall and the Berrill et al. relationships. Based on an analysis using the near-fault ground motion dataset, new expressions of R that consider the effects of site conditions are presented and verified.

The great 2008 Wenchuan earthquake (12 May 2008) with a moment magnitude of 7.9 and a surface-wave magnitude of 8.0 in Shichuan, China, caused unprecedented loss of human life and widespread severe damage to many types of structures. Thirty-two strong-motion records were obtained within a source distance of 300 km, and three near-source records were obtained within a source distance of 20 km. We present the preliminary results on the characteristics of the near-source records and the strong-motion aspects of this great earthquake. This earthquake may be divided into four subevents, according to the rupture time history and the final slip distribution. Three of the four subevents have large surface fault displacement, and we consider the subevents that generated the three near-source records as surface-rupture earthquakes, supported by the comparisons made to records from other surface-rupture or buried-fault earthquakes. One station recorded strong ground motions from two subevents in two well-separated time windows, and this allows us to examine the effect of earthquake parameters for each of the subevents. We find that, in the spectral period range of 0.5–2 s, the response spectra of the near-source records from the Wenchuan earthquake are significantly less than those of buried-fault earthquakes, such as the 1989 Loma Prieta earthquake and the 1994 Northridge earthquake that have a much smaller moment magnitude than the Wenchuan earthquake. In the fault-normal direction the displacement spectra at long period for the closest station are similar to those of the Lucerne record from the 1992 Landers earthquake but significantly smaller than those of the TCU052 and TCU068 records from the 1999 Chi-Chi, Taiwan, earthquake. At short and intermediate period, the near-source spectra are much larger than the design spectra in the previous version of the Chinese design code for the heavily damaged area, but they are comparable at long spectral periods.

We compared response spectra from the M w 7.9 2008 Wenchuan earthquake with five modern ground-motion prediction equations (GMPEs). Ninety-three strong-motion records within 300 km of the fault plane were selected for comparison with the GMPE models of Zhao, Zhang et al. (2006), Abrahamson and Silva (2008), Boore and Atkinson (2008), Campbell and Bozorgnia (2008) and Chiou and Youngs (2008) for spectral periods up to 5.0 s. The site class of the recording stations used for the Zhao, Zhang et al. (2006) model was inferred from response spectral ratios of the horizontal and vertical components (H/V) computed from the strong-motion records in moving and overlapping time windows. The average shear-wave velocity of the top 30 m ( V S 30) was only available for two stations. V S 30 was extrapolated from the average of the top 20 m ( V S 20) when possible and inferred from the H/V response spectral ratios when necessary. The average predictions of all models were acceptable. The Zhao, Zhang et al. (2006) model gave the best predictions for peak ground acceleration and short spectral periods, especially up to 100 km of the source distance. All Next Generation Attenuation (NGA) models predicted the recorded spectra very well for periods of 0.5–1.0 s and at 5.0 s. The Chiou and Youngs (2008) model gave the best overall predictions. The standard deviations of all attenuation models were similar at a 5% significance level. However, differences between spectra estimated by various NGA models were statistically and practically significant, with the largest difference between the average predictions being nearly a factor of 1.4 at the 0.1-s period and 2.3 at the 5.0-s period for data within a source distance of 100 km. Although one earthquake did not produce median ground motions that the GMPEs are designed to predict, such a large difference represents a challenge for empirical models when estimating spectra from very large crustal earthquakes.

Earthquake loadings standard NZS 1170.5:2004 has introduced new provisions for the design of building parts and non-structural components. The provisions include factors to define peak floor acceleration up the height of a building, and acceleration response amplifications for components that are quite different from overseas counterparts. In this study, acceleration demands on non-structural components located in ductile frame buildings are analysed under earthquake records from crustal and slab events, for design levels representing ultimate limit state and serviceability limit state. A floor response spectra approach is used to study the demands on non-structural components. It is noted that the peak floor acceleration demands with respect to that of the ground are not amplified up the height of the building to the extent suggested in NZS provisions. The floor response spectra show peaks near the modal periods of the building indicating higher demands on the components with periods closer to the building period. However, NZS provisions fail to include this effect, since the spectral response amplification is defined independent of building period. Spectral demands exceed the NZS provisions at the fundamental periods of the buildings, more significantly at serviceability conditions, indicating potential failure of non-structural components with periods close to the building periods. Following the analytical observations from the buildings considered in this study it is clear that the design provisions for non-structural components should be linked to the structural response for specific performance levels rather than the ‘life-safety’ performance level only that is currently adopted in the New Zealand design standard.

Our previous studies show that site effects (amplification of rock motions), source and path effects are coupled when response spectra are used to characterize the amplification ratios for a soil site modelled as nonlinear or elastic. The coupling is referred to as a “side effect” of using response spectral amplification ratios. In the present study we use a suite of rock site records, well distributed with respect to magnitude and source distance, from crustal, subduction interface and slab earthquakes to evaluate the response spectral amplification ratio for soft soil sites. We compare these side-effects for ground motions generated by three types of earthquakes, and we find that, at periods much shorter or much longer than the natural period of a soil site modelled as elastic, the average amplification ratios with respect to rock site ground motions from three types of earthquakes are moderately different and are very similar for other spectral periods. These differences are not statistically significant because of the moderately large scatter of the amplification ratios. However, the extent of magnitude- and source-distance-dependence of amplification ratios differs significantly. After the effects of magnitude and source distance on the amplification ratios are accounted for, the differences in amplification ratios between crustal and subduction earthquake records are very large in some particular combinations of source distance and magnitude range. These findings may have potential impact in establishing design spectra for soft soil sites using strong motion attenuation models or numerical modelling.

Attenuation models derived from recorded ground motions are still important elements of probabilistic seismic hazard studies. Engineers use empirical attenuation models to derive the displacement demand for a site of interest from an earthquake at a given location. Many attenuation models have been published for different parts of the world and for different types of earthquakes. Most models have a simple function of constant or magnitude-dependent geometric spreading, and seldom consider well-known seismological effects such as Moho reflection for shallow crustal earthquakes, multiple travel paths and constructive interference for subduction earthquakes, and special characteristics of volcano zones. The reason for not accounting for such effects may be the desire for simplicity in the attenuation functional forms for engineering applications and a lack of records from which to reliably identify these effects quantitatively. In this article, a large set of strong-motion records obtained from dense recording networks in Japan is used to derive geometric attenuation functional form and a possible manner to model the effect of volcanic zones. A liberal approach is taken to introduce a relatively large number of parameters that can account for known seismological effects while retaining a fairly simple attenuation functional form, based on analyses of residuals from simple models similar to those published previously. Preliminary results are reported here, together with the proposed geometric attenuation function forms and plausible explanation of the physical process that leads to the proposed geometric attenuation functions. The proposed model shows a large increase in the maximum likelihood from the random effects methodology, the elimination of bias in the distribution of residuals with respect to source distance, and much improved fitting for well-recorded earthquakes.

We investigate a special type of variability in response spectral amplification ratios computed from numerical “engineering” models for a soft soil site. The engineering models are defined by shallow soil layers over “engineering” bedrock with a shear-wave velocity over 600–700 m/s and the model is subjected to vertical propagating shear waves. The variability, perhaps unique in earthquake engineering, is a result of the “perfectly accurate” computational procedure. For example, an engineering soil site model, subjected to two rock site records or the two horizontal components of a rock site record, produces different response spectral amplification ratios. We use a large number of strong-motion records from “engineering” rock sites, with a reasonably balanced distribution with respect to magnitude and source distance, generated by subduction earthquakes in Japan, to investigate the nature of the variability. In order to avoid any approximation in removing the effect of soil nonlinear response, we use a simple model, a single horizontal soil layer over a bedrock, modelled as elastic. We then demonstrate that a similar type of variability observed in the one- or two-dimensional nonlinear soil models is caused by the nature of response spectral amplification ratios, not a direct result of soil nonlinear response. Examination of variability reveals that the average of response spectral amplification ratios systematically depends on both earthquake magnitude and source distance. We find that, at periods much longer than the site natural periods of the soil sites, the scatter of the amplification ratios decreases with increasing magnitude and source distance. These findings may have a potential impact in establishing design spectra for soft soil sites using strong-motion attenuation models or dynamic numerical modelling.

In current ground-motion models, the uncertainty in predicted ground motion is usually modeled with a lognormal distribution. One consequence of this is that predicted ground motions do not have an upper limit. In reality, however, there probably exist physical conditions that limit the ground motion. Applying the usual uncertainty distribution in probabilistic seismic hazard analysis may lead to ground-motion estimates that are unrealistically large, especially at the low annual probabilities considered for important structures, such as dams or nuclear reactors. A recently proposed statistical procedure to compare the actual and expected numbers of predicted spectral accelerations exceeding a given value gives clear results when applied to a ground-motion model developed for Japan from a very large strong-motion data set. It shows that, for increasingly large spectral accelerations, the actual number of exceedances becomes progressively less than the expected number of exceedances. The pattern of this discrepancy depends on the site class and the earthquake tectonic category. These results suggest that assuming a normal distribution for the prediction errors of an attenuation model (empirical ground-motion prediction equation) is likely to result in overestimation of the extreme values of spectral accelerations.

In order to determine the effect of geometry on the ground response of 2-dimensional (2-D) basins filled with soils that can develop nonlinear response, we use three basin models with width/depth ratios 3, 6 and 10. The three basins are subjected to a suite of rock site records with various magnitudes and source distances. We compute response spectral amplification ratios at four locations on the surface of the 2-D basins, and determine the average variation of the amplification ratios with respect to excitation spectra, for peak ground acceleration (PGA) and 3 spectral periods of 0.2, 0.5, 1 s. Similarly, we compute the average response spectral amplification ratios for two 1-dimensional (1-D) nonlinear models, one having the soil profile at the basin centre and the other having a soil profile at half the depth of the basin. From the relationship between the average amplification ratios and excitation spectra, we determine the cross-over point in terms of excitation spectral values that separate the amplification range from the deamplification range. Our results show that the cross-over point varies significantly from one location to another on the ground surface and from one basin to another, in a range of 0.3–1.1g for PGA. The effects of basin geometry are very strong at weak and moderate excitation, but decrease with increasing excitation spectra in a significant portion around the basin centre. Our results provide some justification for using 1-D models for 2-D basins with a width/depth ratio ⩾6 if the soil site is subjected to strong ground shaking.

There is considerable interest in the credibility of probabilities of exceedance estimated by ground-motion models for very high accelerations. A common statistical approach to this problem has been to examine the upper-tail shape of the distribution of residuals between recorded data and the model for evidence of suppression of high residuals. In this study, a more direct method is suggested, in which the actual number of times given accelerations are exceeded is compared to the expected numbers in strong-motion data sets. The method is illustrated by application to New Zealand and Japan models for peak ground acceleration (PGA). For the Japan model, which is based on a particularly large data set, the ratio of actual to expected number declines in a statistically significant and regular fashion from about 1 at 0.3g to about 0.15 at 1.0g. If these results are indicative of ground-motion models in general, the implications for probabilistic seismic hazard analyses may be far reaching. The method and results have particular importance for the analysis of seismic hazard at sites of critical facilities where strong ground motions with very long return periods may be of interest.

A very useful tool for the preliminary design of structures is the elastic demand spectrum that can be used in the capacity spectrum method. A pseudo-acceleration relationship has to be assumed when constructing a demand spectrum. This assumption results in large errors for long period structures with large damping ratios and the conventional demand spectra require a substitute elastic structure. In the present study, the conventional demand spectra are extended to bi-linear models. Pseudo-acceleration is still assumed but results in acceptably small errors, when a constant viscous damping coefficient for a single-degree-of-freedom (SDF) structure is calculated from the tangent stiffness and the damping ratio is set at 5% in both elastic and yield phases. For nonlinear structures, tangent stiffness dependency of damping force could be acceptable because energy absorption is primarily the result of structural nonlinear deformation. To extend the conventional demand spectra to a bi-linear model, effective p...

A spectral acceleration attenuation model for Japan is presented in the present study. The data set includes a very large number of strong ground-motion records up to the 2003 Off Tokach main and aftershocks. Site class terms, instead of individual site correction terms, are used. The site classes of recording stations are from a recent study on site classification for strong-motion recording stations in Japan according to a classification scheme that has been used in Japanese engineering design. The use of site class terms enables tectonic source-type effects to be identified and accounted for in the present model. The effects of a faulting mechanism for crustal earthquakes also are accounted for. For crustal and interface earthquakes, a simple form of an attenuation model (with respect to distance) is able to capture the main strong-motion characteristics and achieves unbiased estimates. For subduction slab events, a simple distance modification factor is employed to achieve plausible and unbiased predictions. The effects of source depth, tectonic source type, and faulting mechanism of crustal earthquakes are significant. The need for magnitude- squared terms is evaluated, and the use of magnitude-squared terms reduces the interevent error further.