Peak Ground Displacement Research Articles

Earthquake Magnitude Scaling Using Peak Ground Velocity Derived from High-Rate GNSS Observations

AbstractRapid response to destructive tsunami and seismic events requires rapid determination of the earthquake magnitude. We propose a new method that employs peak ground velocities (PGVs) derived from Global Navigation Satellite System (GNSS) data to estimate earthquake magnitudes. With a total of 1434 records from 22 events as the constraints, we perform the regression and obtain a PGV scaling law for magnitude determination. The advantage of the new method is that the PGVs are extracted from the GNSS velocity waveforms, which can be easily computed using broadcast GNSS ephemeris. In contrast, the peak ground displacement (PGD) depends on a sophisticated high-precision GNSS-processing subject to external correction data, realization of which cannot be kept robust constantly, especially in real time. The results show that the PGV magnitudes agree with reported moment magnitudes with mean absolute deviation of 0.26 magnitude units for the 22 events and also agree well with the PGD magnitude. We further demonstrate that GNSS-derived PGV and the modified Mercalli intensity values can be consistent with their counterparts from the U.S. Geological Survey ShakeMap products and therefore the GNSS-derived PGVs have the potential to be included in the ShakeMap as a complementary constraint, especially in areas with sparse seismic station coverage for large earthquake.

Magnitude Calculation without Saturation from Strong-Motion Waveforms

ABSTRACTAfter destructive earthquakes, it is a challenge to estimate magnitude rapidly and accurately for dissemination to emergency responders and the public. Here, we propose criteria to calculate peak ground displacement (PGD) from strong-motion records, which can be used to calculate unsaturated event magnitude. Using collocated strong-motion and Global Navigation Satellite Systems observations of five major earthquakes in Japan, we demonstrate the effectiveness and accuracy of our strategy. Our results show that, with the right filtering criteria, PGD estimated from strong-motion acceleration waveforms is consistent with geodetic estimates. The methodology, however, does not allow for calculation of reliable estimates of coseismic deformation or other ground displacement metrics. We demonstrate a simulated real-time magnitude estimation that suggests it is feasible to generate an unsaturated magnitude estimate in real time from near-field strong-motion records. These findings have important implications for early warning and emergency response in seismically active areas, especially where real-time strong-motion data are more widely available than geodetic measurements.

Seismic Hazard Assessment for Thuong Tan-Tan My Quarries (Vietnam)

This paper presents the seismic hazard assessment for Thuong Tan-Tan My quarries in Di An commune, Binh Duong province, Vietnam. Combination methods of gravity and magneto-telluric were used to estimate the dip angle and the width of the seismic source. The highest water column of 160 m will cause direct stress on the reservoir bottom with a maximum value of 1535.600 kPa and Coulomb stress of 68.693 kPa (at a depth of 2 km). The typical components of natural earthquake hazard (Mn.max = 5.0, depth of 10 km) in Thuong Tan - Tan My reservoir have the following values: peak ground acceleration PGA = 0.073 g ÷ 0.212 g; peak ground velocity PGV = 2.662 cm/s ÷ 7.984 cm/s; peak ground displacement PGD = 0.706 cm ÷ 1.918 cm at 10% probability of exceedance in 50 years. The typical components of triggered earthquake hazard (Mtr.max = 3.5, depth of 6 km) in Thuong Tan - Tan My reservoir have the following values: peak ground acceleration PGA = 0.024 g ÷ 0.172 g; peak ground velocity PGV = 0 ÷ 5.484 cm/s; peak ground displacement PGD = 0.061 cm ÷ 0.461 cm at 10% probability of exceedance in 50 years.

Identifying Optimal Intensity Measures for Predicting Damage Potential of Mainshock–Aftershock Sequences

Large earthquakes are followed by a sequence of aftershocks. Therefore, a reasonable prediction of damage potential caused by mainshock (MS)–aftershock (AS) sequences is important in seismic risk assessment. This paper comprehensively examines the interdependence between earthquake intensity measures (IMs) and structural damage under MS–AS sequences to identify optimal IMs for predicting the MS–AS damage potential. To do this, four categories of IMs are considered to represent the characteristics of a specific MS–AS sequence, including mainshock IMs, aftershock IMs (i.e., IMMS and IMAS, respectively), and two newly proposed IMs through taking an entire MS–AS sequence as one nominal ground motion (i.e., IM1MS–AS), or determining the ratio of IMAS to IMMS (i.e., IM2MS–AS), respectively. The single-degree-of-freedom systems with varying hysteretic behaviors are subjected to 662 real MS–AS sequences to estimate structural damage in terms the Park–Ang damage index. The intensities in terms of IMMS, IMAS, and IM1MS–AS are correlated with the accumulative damage of structures (i.e., DI1MS–AS). Moreover, the ratio (i.e., DI2MS–AS) of the AS-induced damage increment to the MS-induced damage is related to IM2MS–AS. The results show that IM2MS–AS exhibits significantly better performance than IMMS, IMAS, and IM1MS–AS for predicting the MS–AS damage potential, due to its high interdependence with DI2MS–AS. Among the considered 22 classic IMs, Arias intensity, root-square velocity, and peak ground displacement are respectively the optimal acceleration-, velocity-, and displacement-related IMs to formulate IM2MS–AS. Finally, two empirical equations are proposed to predict the correlations between IM2MS–AS and DI2MS–AS in the entire structural period range.

Investigation of the relationship between intensity measures and engineering demand parameters of cable-stayed bridges using intra-plate earthquakes

PurposeThe purpose of the study is to investigate and reveal this relationship of various engineering demand parameters (EDPs) of this structural type and intensity measures (IMs) under intra-plate earthquakes.Design/methodology/approachThe nonlinear finite element model used was calibrated first to the existing results of the shaking table test to verify the modeling technique.FindingsThis paper investigated the relationship between intensity measures and various engineering demand parameters of cable-stayed bridges using intra-plate earthquakes. The correlation analysis and Pearson coefficient are used to study the correlation between EDPs and IMs. The results showed that peak ground velocity (PGV)/peak ground acceleration, peak ground displacement and root-mean-square of displacement showed weak correlation with IMs. PGV, sustained maximum velocity, a peak value of spectral velocity, A95 parameter, Housner intensity and spectral acceleration at the fundamental period, the spectral velocity at the fundamental period and spectral displacement at the fundamental period were determined to be better predictors for various EDPs.Originality/valueThis paper investigated the correlation between the intensity measures of intra-plate earthquakes with the seismic responses of a typical long-span cable-stayed bridge in China. The nonlinear finite element model used was calibrated to the existing results of the shaking table test to verify the modeling technique. In total, 104 selected ground motions were applied to the calibrated model, and the responses of various components of the bridge were obtained. This study proposed PGV as the optimal IM.

High-rate GPS positioning for tracing anthropogenic seismic activity: The 29 January 2019 mining tremor in Legnica- Głogów Copper District, Poland

High-rate GNSS observations are usually studied in relation to earthquake analysis and structural monitoring. Most of the previous research on short-term dynamic deformations has been limited to natural earthquakes with magnitudes exceeding 5 and amplitudes equal to several dozen centimetres. High-frequency position monitoring via GNSS stations is particularly important in mining areas due to the need to monitor mining damages. On 29 January 2019 (12:53:44 UTC), an M3.7 event occurred in the area of Legnica-Głogów Copper District.This study presents GPS-derived displacement analysis in relation to seismological data. Station position time series were determined by double differencing and Precise Point Positioning. The peak ground displacement was 2–14 mm. The correlation coefficients between GPS and seismological displacement time series reached 0.92. A statistical evaluation of GPS displacement time series was carried out to detect an event using only GPS observations.

Scaling earthquake magnitude in real time with high-rate GNSS peak ground displacement from variometric approach

Peak ground displacement (PGD) derived from high-rate Global Navigation Satellite System (GNSS) can be used to determine, i.e., the estimate or scale the earthquake magnitude in real time without magnitude saturation experienced by seismic sensors at large earthquakes. Compared with relative positioning or Precise Point Positioning (PPP), the variometric approach can calculate station velocity using the broadcast ephemeris and avoiding estimating phase ambiguities. By integration, velocities can be translated into displacements. However, an inaccurate broadcast ephemeris might cause integrated displacements to show nonlinear drifts. Recently developed real-time orbit and clock products used by real-time PPP have higher accuracy and can also be employed by the variometric approach. We evaluate the performance of the variometric approach on magnitude scaling using high-rate GNSS data collected during the 2019 Mw 7.1 Ridgecrest earthquake, the 2016 Mw 7.8 New Zealand earthquake, and the 2017 Mw 6.5 Jiuzhaigou earthquake. The results indicate that a spatial filter cannot correct nonlinear drifts of integrated displacements completely and scaled magnitudes are not stable when the broadcast ephemeris is used. While using the Centre National d’Etudes Spatiales (CNES) real-time ephemeris, we find both the spatial filter and linear filter can correct drifts well and scaled magnitudes have the same accuracy as those of PPP. While comparing different GNSS systems, we find that BDS is superior to GPS and GLONASS in the case of the Jiuzhaigou earthquake because BDS has a better satellite geometry in this region. Compared with single GPS, multi-GNSS can improve satellite geometry and provide more precise seismic displacements when broadcast ephemeris and low sampling precise clocks are used by the variometric method.

Development of earthquake early warning system for Kachchh, Gujarat, in India using τc and Pd

Development of earthquake early warning system (EEWS) is in advanced stage in different parts of the world including India. The success of EEWS for mitigating seismic risk and saving human lives has been well documented in Mexico, Japan, and Taiwan, where the alert is issued to the public. Taking advantage of the recorded ground motion data from the network of Institute of Seismological Research (ISR), India, with magnitude range 3.0–5.2, we investigated correlations between various ground motion parameters like peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), Pa, Pv, Pd, and τc.Three- to 5-s time windows are considered to measure Pa, Pv, Pd, and τc from the vertical component of the waveforms. Linear regression analysis is performed at various time steps (3- to 5-s time interval). The results show that considering 4- and 5-s windows exhibits good relationships compared with the 3-s window, which shows more scattering. These empirical relationships using τc and M as well as Pd and M are very helpful in determining the earthquake magnitude and subsequently taking steps toward risk assessment.

Spectral acceleration matching procedure with respect to normalization approach

This study aimed at proposing a new ground motion scaling method for precise spectral matching between the response accelerations and the standard design spectrum regarding the normalization procedure. In this method, the dispersion in acceleration and displacement responses were decreased significantly. Moreover, 11 parameters were used for normalizing response accelerations, including peak ground acceleration, peak ground velocity, peak ground displacement, Arias intensity, Housner intensity, cumulative absolute velocity, maximum incremental velocity, energy index, acceleration spectrum intensity, velocity spectrum intensity, and specific energy density. Three sets of non-pulse-like, near-field pulse-like and non-pulse-like long-duration ground motions were taken into account to investigate the effect of earthquake characteristics on normalizing parameters. Hence, by performing sensitivity analysis, suitable parameters were determined for normalizing response accelerations. Statistical results illustrated that normalizing response accelerations to acceleration spectrum intensity, Housner intensity, and peak ground displacement led to minimum dispersion at acceleration-sensitive, velocity-sensitive, and displacement-sensitive regions, respectively. Moreover, the results showed that suitable normalizing parameters could be determined considering the period of vibration. It was concluded that normalizing response accelerations and scaling of them could lead to appropriate spectral matching and low dispersion. Finally, drift dispersion for four, eight, and twelve-story steel special concentrically braced frame structures under nonlinear fiber-element time-history analysis was evaluated carefully. The results indicated that the inter-story drift dispersion decreased acceptably in all structures.

Application of high-rate GPS for earthquake rapid response and modelling: a case in the 2019 Mw 7.1 Ridgecrest earthquake

SUMMARYThe 2019 Mw 7.1 Ridgecrest earthquake opens an opportunity to investigate how soon we can produce a reliable fault geometry and subsequently a robust source model based on high-rate Global Positioning System (GPS) data. In this study, we conduct peak ground displacement (PGD) magnitude scaling, real-time centroid moment tensor (CMT) calculation and rapid kinematic slip inversion. We conclude that a four-station PGD warning with a magnitude of Mw 7.03 can be issued at 24 s after initiation of the rupture. Fast CMT inversion can initially recover the correct nodal planes at 30 s. The kinematic slip model reveals that the Mw 7.1 earthquake is a predominant dextral strike-slip event with both normal and thrust components resolved. The earthquake shows a bilateral rupture with a low propagation speed of ∼2.1 km s−1 and a slip maxima of ∼4 m. The total moment is 5.18 × 1019 N m (Mw 7.11). We further suggest that a reasonable source model will be available in a simulated real-time mode within 30 s after the earthquake occurring, without using full high-rate GPS waveforms. This research highlights the significance of high-rate GPS for rapid earthquake response and modelling of kinematic rupture, which is also generalized by the hypothetical real-time GPS analysis for the 2016 Mw 7.8 Kaikoura earthquake and the 2010 Mw 7.2 El Mayor-Cucapah earthquake.

Simulation Study on Seismic Response of Ground Surface Above an Underground Longwall Goaf

The dynamic varied elastic modulus and damping coefficient of underground goaf are most important factors which describes the goaf absorption ability on seismic wave energy. This numerical simulation study have focused on the effect of goaf area on earthquake-wave propagation and seismic response on the ground surface in a coal mine area. The laboratory measurements were carried out by 135 porous samples cases consisting rocks and coal particles 0.12–0.25 mm in size to estimate the dynamic elastic modulus and damping coefficient of the fragmented rock masses. In this simulation, a new model on damping coefficient of longitudinal and transverse waves has been presented in considering rock size (D), effective stress (σe), porosity (φ) and compaction time (t). The empirical correlation between the damping coefficient and effective stress (depth) as well as the compaction time of the goaf area has been derived and used for each goaf and strata grid blocks in the simulation. The results showed that the peak ground acceleration (PGA) above the goaf area exhibits 9–20% reduction compared to that of unexcavated condition (original coal seam), and around 10–35% seismic energy is trapped in the goaf area as goaf varied from 100 to 700 m. In the meantime, the peak ground displacement (PGD) is amplified up to seven times for the goaf depth ranging from 100 to 700 m compared to that of the unexcavated condition. Both PGA and PGD above goaf area are smaller than those above the undisturbed coal seam.

Database of rocking shallow foundation performance: Dynamic shaking

Several experimental studies have shown that rocking shallow foundations have beneficial seismic performance features: recentering and energy dissipation with little damage. A new publicly available database, “FoRDy” (Foundation Rocking—Dynamic), summarizes the results of dynamic physical model tests of single-degree-of-freedom-like structures supported on rocking foundations. It contains data from five centrifuge and three 1- g shaking table test series that were conducted at experimental facilities in the United States, Greece, and Japan. The database includes 200 model “case histories” that span a wide range of model sizes, soil and structure properties, and seismic excitations. It is compiled as the first step toward building a comprehensive dynamic rocking foundation database, and it has the potential to grow in the future. To illustrate its usefulness, the data are used to show example correlations between the peak drift ratio demand and selected ground motion intensity measures. The results suggest that peak ground velocity (PGV), peak ground displacement (PGD), and the geometric mean of the linear spectral displacement over the period range of 0.2–3 times the initial natural period predict the peak drift ratio response reliably.

Evaluation of Earthquake Magnitude Estimation and Event Detection Thresholds for Real-Time GNSS Networks: Examples from Recent Events Captured by the Network of the Americas

Abstract Several studies have shown that real-time (RT) Global Navigation Satellite Systems (GNSS) measurements can provide an estimate of an earthquake’s moment magnitude (Mw) using scaling laws that relate peak ground displacements (PGDs) and hypocentral distance with Mw. In this study, we use data from GNSS stations operated by UNAVCO as part of the National Science Foundation Geodetic Facility for the Advancement of Geoscience (GAGE) that comprises the Network of the Americas (NOTA) to show that precise point positioning (PPP) solutions distributed in RT during five recent earthquakes could be used to calculate Mw rapidly and reliably. We analyze solutions distributed by UNAVCO during the 8 September 2017 Mw 8.2 Tehuantepec, Mexico, 10 January 2018 Mw 7.5 Great Swan Island, Honduras, 23 January 2018 Mw 7.9 Gulf of Alaska earthquake, and the 4 July 2019 Mw 6.4 and 6 July 2019 Mw 7.1 Ridgecrest, California, earthquakes. We find that RT-GNSS Mw estimates consistent with Advanced National Seismic System Comprehensive Earthquake Catalog values are available tens of seconds to a few minutes after the event origin time. The speed with which an estimate is available is dependent on the proximity to the epicenter of the closest NOTA stations. The results demonstrate that RT-GNSS networks could be used to mitigate the problem of magnitude saturation observed in seismic-based earthquake early warning (EEW) systems. RT-GNSS effectively expands the spectrum of events for which a seismic EEW system can provide accurate warnings of impending ground shaking and provides an independent verification of seismically derived magnitudes. We also analyze the RT-PPP solutions from more than 800 RT-GNSS stations to determine the ambient-noise levels of each NOTA station and combine that with PGD magnitude scaling laws to construct regional network sensitivity maps for the NOTA network. Such maps may be used to determine “blind spots” or regions of lower sensitivity in RT-GNSS networks under consideration for EEW.

The Influence of Surface Topography on the Weak Ground Shaking in Kathmandu Valley during the 2015 Gorkha Earthquake, Nepal.

It remains elusive why there was only weak and limited ground shaking in Kathmandu valley during the 25 April 2015 Mw 7.8 Gorkha, Nepal, earthquake. Our spectral element numerical simulations show that, during this earthquake, surface topography restricted the propagation of seismic energy into the valley. The mountains diverted the incoming seismic wave mostly to the eastern and western margins of the valley. As a result, we find de-amplification of peak ground displacement in most of the valley interior. Modeling of alternative earthquake scenarios of the same magnitude occurring at different locations shows that these will affect the Kathmandu valley much more strongly, up to 2–3 times more, than the 2015 Gorkha earthquake did. This indicates that surface topography contributed to the reduced seismic shaking for this specific earthquake and lessened the earthquake impact within the valley.

Dynamic-response characteristics and deformation evolution of loess slopes under seismic loads

The Loess Plateau is one of the most seismically and geologically active regions in China. The related catastrophic earthquakes and geological disasters have caused more than 1.4 million deaths in the plateau. In this study, the slopes on the edge of the loess tableland in Pingliang City, Gansu Province—the core area of the Loess Plateau—are investigated. Based on large-scale shaking-table model tests and discrete-element numerical simulation—particle flow code (PFC 2D), the dynamic-response characteristics and deformation evolution process of fissured and non-fissured loess slopes under different seismic loads are studied. The test results show that with increasing seismic load input, the peak ground displacement (PGD) of the loess slopes increases gradually with increasing slope height. For the two types of slopes, the acceleration amplification effects in the slope with horizontal direction load are larger than those of the vertical direction load. The amplification factor of the peak ground acceleration (PGA) at the shoulder of the fissured slope is significantly larger than that of the non-fissured slope. According to the numerical simulation results of the fissured slope, when the seismic load is small, the bond-failures are distributed densely in the initial fissured structural plane and at the model bottom. Regarding the non-fissured slope, the bond-failures in the slope are mainly distributed at the bottom of the model. With increasing acceleration amplitude, the number of bond-failures in the slopes increases rapidly. When the input load increases to 0.40 g, two potential slip surfaces occur in the shallow surface of the fissured slope and a potential slip surface appears at the back edge of the non-fissured slope.

Optimal intensity measures for probabilistic seismic demand models of a cable-stayed bridge based on generalized linear regression models

Seismic intensity measures (IMs) play an important role in predicting the seismic responses of structures subjected to strong earthquakes. This paper proposes a general procedure to identify the optimal IMs for a long span cable-stayed bridge subjected to far-field and near-fault ground motions based on generalized linear regression models. Firstly, the generalized linear regression models, such as ordinary least squares (OLS), ridge regression and Lasso regression are presented. Secondly, the three dimensional numerical model of the bridge is generated in the OpenSees platform. Thirdly, 22 IMs are considered, and 160 ground motions from four site conditions are selected to excite the bridge in longitudinal and transverse directions separately. Then, the optimal IMs are determined by Lasso regression, which is an extended version of OLS, and the quadratic polynomial regression model is adopted to establish the probabilistic seismic demand models of the bridge. The numerical results reveal that peak ground velocity (PGV) can be selected as the optimal IM if only one IM is considered in the seismic demand models. However, PGV has a poor predictive ability for the seismic responses in the transverse direction. Hence, PGV, peak ground displacement (PGD), root-mean-square of velocity (VRMS), specific energy density (SED), velocity spectrum intensity (VSI) and Fajfar intensity (FI) are selected as the optimal IMs by Lasso regression, and they are correlated with velocity except for PGD. The identified six IMs together can significantly increase the fitting ability of the models.

Scaling of Peak Ground Displacement with Seismic Moment above the Mexican Subduction Thrust

AbstractWe use accelerograms, seismograms, and data from sparse continuous Global Positioning System (GPS) and campaign-mode GPS stations, deployed along the Pacific coast of Mexico, to study scaling of horizontal peak ground displacement (PGD) with seismic moment (M0) in the epicentral zone above the Mexican subduction thrust. The thrust interface is located at a depth of ∼25 km below the coast. We select recordings with (S–P) time ≤5.9 s (R≤46 km) and reduce the amplitudes to (S–P) time of 3.2 s (R = 25 km). The dataset consists of 58 events and covers a M0 range of 1013–1021 N·m. We find that the double integration of accelerograms, using piecewise linear detrending schemes, leads to sufficiently accurate estimation of PGD to study the scaling relation. The sparse data for great earthquakes are complemented with theoretical static displacement computed using the model of Okada (1992). For earthquakes with M0≤1.26×1018 N·m (Mw≤6.0) the point-source, far-field approximation holds, and the PGD data follows theoretically expected M02/3 scaling. For great earthquakes (M0>1.26×1021 N·m; Mw>8.0), static offset (which is approximately equivalent to PGD) scales as M01/3. About two-thirds of the observed PGD data fall within a factor of 0.67 and 1.5 of the relation given above. The relationship may be useful in earthquake engineering as well as for rapid estimation of magnitude for early tsunami alert.

Some principles of generating seismic input for calculating structures

In this paper different models of seismic input are analyzed. The most essential characteristics of seismic effects are peak ground acceleration, peak ground velocity, peak ground displacement, Arias intensity, cumulative absolute velocity, seismic energy density, harmonic coefficient κ, pseudo spectral kinematic characteristics, root-mean-square peak kinematic characteristics, plastic forces work and damage spectrum. The influence of seismic impulse on characteristics of seismic input is studied. A.A. Dolgaya’s and L.N. Dmitrovskaya’s models with seismic impulse are compared. L.N. Dmitrovskaya’s model allows to reach estimated values of energy characteristics of seismic input with the smallest deviation. When generating such processes, it is important to take into account both the properties of real actions and the limiting state of the calculated structure. The considered models of seismic inputs should be applied in the following cases: a) in case of designing mass construction projects when it is not possible to get a package of design accelerograms, b) in typical designing when the design object can be located on sites with different seismic and geological conditions, c) at early stages of designing important objects when the package of design accelerograms is not available yet but it is necessary to make technical solutions.

Real-Time High-Rate GNSS Displacements: Performance Demonstration during the 2019 Ridgecrest, California, Earthquakes

AbstractTraditional real-time (RT) seismology has relied on inertial sensors to characterize ground motions and earthquake sources, particularly for hazards applications such as warning systems. In the past decade, a revolution in high-rate, RT Global Navigation Satellite Systems (GNSS) displacement has provided a new source of data to augment traditional measurement devices. The Ridgecrest, California, earthquake sequence in 2019 provided one of the most complete recordings of RT-GNSS displacements to date, helping aid in an initial source characterization over the first few days. In this article, we analyze and make available the archived RT displacement streams and compare their performance to postprocessed results, which we also provide. We find good agreement for all stations showing a noticeable signal. This demonstrates that simple modeling in RT, such as peak ground displacement scaling, would be practically identical to postprocessed results. Similarly, we find good agreement across the full spectral range, from the coseismic offsets (∼0 Hz) to the Nyquist frequency. We also find low latency between the measurement acquisition at the field site and the position calculation at the data center. In aggregate, the performance during the Ridgecrest earthquakes is strong evidence of the viability and usefulness of RT-GNSS as a monitoring tool.

Effect of peak ground parameters on the nonlinear seismic response of long lined tunnels

The response mechanism of tunnels under earthquake loads is a critical issue in tunnels located in seismically active regions. This study aims to investigate the seismic response and damage sensitivity of tunnels under earthquake motions with different peak ground acceleration, velocity and displacement (PGA, PGV and PGD). Based on the design acceleration response spectrum (ARS), four groups of total 40 artificial accelerograms are synthesized with specified PGA, PGV and PGD. In addition, for considering the wave travelling effect on the tunnel axial response, an obliquely incident method for P waves is developed by using the equivalent nodal force method. Then, the nonlinear response of tunnels subjected to artificial accelerograms with different incident angles are simulated, respectively. The numerical results indicate that the PGV and PGA have accretion effect on the seismic response of the tunnel. However, the impact of PGD on the tunnel earthquake response is less evident. The PGV has obvious incremental effect on the dynamic response of tunnels subjected to earthquake P waves with large incident angles. Compared with PGV, the PGA intends to increase the response of tunnels significantly under P waves with small incident angles. Thus, it is important to take the PGA and PGV into account during seismic analysis and design for tunnels.