Horizontal Ground Displacements Research Articles

Sustainable construction and quality of improved columns with three types of water-cement ratios on deep mixing method in Saga Lowland, Kyushu, Japan

In this study, we investigated the application of the deep mixing method (DMM) to cohesive soil in the Saga Lowland of Kyushu, Japan. The study focused on examining three types of water-cement ratio (W/C) conditions, with a constant addition of cement-based binder (C). Due to the soft clay nature of the Saga Lowland, frequent ground settlement and deformation occur, necessitating measures to prevent adverse effects on the surrounding environment. The objective of this research is to provide a valuable approach to optimizing the quality of the improved columns while minimizing ground displacement in an environmentally considerate manner. In Saga Lowland, it is common to fix the W/C ratio at 1.0 and vary the cement content. Through experimental construction for improved columns on the field, the study confirmed that W/C values of 0.5, 1.0, and 1.5 influence the quality of the improved structure. A higher W/C value of 1.5 resulted in a more fluid cement slurry due to a higher injection rate (IR = 23.9%), as evidenced by statistical analysis revealing higher average unconfined compressive strength ( qu¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{{q }_{u}}$$\\end{document}), and a lower coefficient of variation (CV). The defective rate of 10% (qudr) from the design standard strength shows that values are lowest for Case 2, followed by Case 3 and then Case 1. Comparing the values of Case 2 and Case 3, it is observed that in Case 3, with a higher W/C, the CV is lower.. Regarding horizontal ground displacement (Sh), Case 3 exhibited a Sh value of 2.0 to 6.5 mm, significantly lower than Saga prefecture standards (20 mm). This outcome is attributed to reduced viscosity during mixing, leading to improved fluidity and minimal lateral displacement of the soil–cement columns (which often results in lateral ground uplift). Even though with a higher W/C = 1.5, the implementation cost remains the same, but the constructed structure would be of higher quality and smaller displacement, with the overall structure corresponding to the standard quality. The study includes the specific geotechnical conditions of the Saga Lowland and the scope of experimentation. Nonetheless, in terms of the applicability and optimization of DMM in Saga Lowland, the findings provide practical guidance for engineers in selecting W/C ratio and IR during construction for future DMM implementations, thereby contributing to the development of long-lasting infrastructure and sustainable societal development.

A unified empirical method for predicting both vertical and horizontal ground displacements induced by tunnel excavation

An empirical model for describing the soil movements induced by tunneling is proposed, then the mathematical relationship between horizontal displacement and vertical displacement is obtained. By analyzing 25 sets of data from field engineering and 35 sets of data from model tests, the formula for the maximum settlement Sv, max( z) is optimized to adapt to different ground conditions. The Modified Gaussian function is developed by introducing the existing width coefficient of the settlement trough i( z) and the optimized Sv, max( z) to describe the surface and subsurface vertical displacement. Subsequently, the formula for the horizontal displacement is derived based on the Modified Gaussian function. H( z) representing the position of the oriented point of the soil movement is a variable in the formula for horizontal displacement. Based on measured results, a logarithmic function and a quadratic polynomial function are proposed to describe the variation of H( z) with depth in the clay stratum and sand stratum, respectively. Then, the rationality of the proposed method is validated by 4 sets of in-situ data and 4 sets of test data. Finally, the implementation process of the proposed method is illustrated, and the inversion results of the ground displacement field in Beijing Metro Line 12 are presented.

A Comprehensive Review on Mining Subsidence and its Geo-environmental Impact

Over the course of several decades, subsidence has exerted a notable impact on the mining sector. The preponderance of subsidence occurrences is evident within coal mines. Remote sensing and Geographic Information Systems (GIS) have emerged as principal instruments for the evaluation and characterization of subsidence phenomena. The manifestation of mininginduced subsidence engenders concerns encompassing roof collapse, infrastructural damage, and the formidable challenge of preserving human lives. The repercussions of mining-related subsidence extend to indigenous flora and subterranean water reservoirs. This phenomenon critically impedes the sustainable advancement of mining zones, precipitates the depletion of natural reservoirs, and engenders a host of ecological and environmental predicaments that cast an adverse influence on socio-economic dynamics. Within mining contexts, subsidence manifests as both vertical and horizontal ground displacement, presenting as fissures, depressions, troughs, and sinkholes. The present article furnishes a comparative discourse on diverse methodologies harnessed for the assessment of mining-induced subsidence. The scholarly community has employed a repertoire of eight predominant techniques, as delineated in the conclusive remarks of this study. Over the bygone two decades, considerable strides have been taken, enabling the deployment of sophisticated paradigms, such as remote sensing and GIS, Light Detection and Ranging (LiDAR), and Differential Interferometric Synthetic Aperture Radar (DiNSAR), for the identification and quantification of land subsidence phenomena.

Combination of kinematic and inertial loads acting on monopile founda-tions for offshore wind turbines

Due to a growing number of offshore wind farm projects in seismic areas, existing design procedures for slender piles under seismic loading need to be revised to allow for the design of larger and stockier monopiles. This study illustrates how advanced finite element analyses can be used to investigate the combination of seismic loads and may thus inform standard design procedures commonly adopted in practice. In standard design methods, a soil-pile foundation system is represented by a simplified beam-on-nonlinear-springs model [1]. Earthquake loads acting on this system can be decomposed into inertial forces, which originate from the acceleration of a superstructure mass, and kinematic loads due to ground displacements caused by the propagation of seismic waves. Inertial loads are typically derived from modified acceleration spectra which account for the difference between the pile head movement and the soil displacement in the free-field [2, 3, 4]. Maximum displacement profiles can be obtained from site response analyses of the free-field soil column. The distribution of pile bending moments and internal forces can thus be found by superposition of the two loads. However, unless numerical time-domain analyses are carried out, it is not evident whether these components are acting simultaneously on the pile. In the design of long and slender piles, a common assumption is that inertial and kinematic loads may be considered separately, as the former tend to affect only the near-surface zones while the latter dominate at larger depths [2]. However, their combined effect on a far less flexible monopile exhibiting rotational mechanisms is not yet understood, neither is the influence of soil liquefaction triggered by the seismic ground shaking. Experiments on pile groups presented in the literature suggest a dependence of the phase angle on the ratio between the fundamental frequency of the soil deposit and the superstructure [5]. The analogous scenarios are illustrated for a monopile-supported wind turbine in Figure 1.
 The turbine is considered as a single-degree-of-freedom system with the mass off the rotor nacelle assembly lumped together and located at hub height. The time history of the inertial force acting at hub height (), as well as the horizontal ground displacement at surface level (), are schematically shown in Figure 1(b) for a very stiff soil. In this case, the fundamental period of the soil deposit () is significantly lower than that of the superstructure (), which causes the response of the turbine system to act out of phase with the ground movement by 180°. For a soft soil deposit with much higher fundamental period than the turbine (Figure 1(c)), the kinematic and inertial loads are expected to act in phase.
 To investigate the combination of seismic loads acting on a monopile foundation in the time-domain, advanced numerical analyses are carried out on three-dimensional Finite Element models. Soil layers with widely different material properties are considered, including stiff marine clays and liquefiable sands with varying relative densities. The uni-directional motion records adopted as base excitations are sufficiently strong to induce large lateral ground movements and impose significant kinematic loads on the foundation. Through the of use of appropriate constitutive models in a hydro-mechanically coupled formulation, the response of the turbine sub-structure system is simulated while accounting for the degradation of stiffness in the surrounding soil and significant rises in excess pore pressures in the sand layers. An intensely nonlinear material behaviour typically leads to a shift of the fundamental frequency of the deposit [6], which can be deduced from the amplification of accelerations at various depths, with high frequencies dominating in the stiff soil layers and low frequencies in the soft liquefied sand. For a stiff soil deposit prior to liquefaction, local extrema in pile displacements at mudline level are therefore expected to act out of phase with the inertial force resulting from the acceleration of the rotor nacelle assembly at the turbine tower top (Case ). As the stiffness diminishes in a soft or fully liquefied ground, pile and free-field ground displacements are expected to move in-phase with the inertial load, as is characteristic for cases where the period of the soil deposit exceeds that of the superstructure (Case ). This change in behaviour highlights the influence of soil stiffness degradation and extensive ground liquefaction on the combination of seismic soil-structure interaction effects in the time-domain, which can be captured by advanced numerical methods.

A new technical pathway for extracting high accuracy surface deformation information in coal mining areas using UAV LiDAR data: An example from the Yushen mining area in western China

Western China is the world’s major coal-producing area, accounting for 1/3 of global coal production. Large-scale underground coal mining has led to serious ground deformation that has unique spatial and temporal characteristics. However, there are obvious engineering limitations to using GNSS, InSAR, and other common measurement techniques for monitoring mining subsidence. In recent years, researchers have attempted to use UAV LiDAR to monitor subsidence in mining areas. Point clouds are obtained through periodic ground scanning. Surface subsidence information is extracted through the filtering, modeling, and superposition processes. Conventional point cloud processing usually produces subsidence models that are too noisy and only provide information on surface subsidence. This means that it is unable to capture the horizontal ground displacement accompanying subsidence in mining areas, which hinders the practical application of this technology. A local flat point extraction (LFPE) algorithm based on geomorphic features is proposed. The algorithm extracts flat surface point clouds from the scan data and calculates the precise subsidence value of the ground by superposition to facilitate deformation monitoring. The obtained subsidence volume is spatially interpolated based on the unique spatial distribution characteristics of the mining subsidence basin to generate the initial surface subsidence model. By denoising this model, we can obtain a fine surface subsidence model that avoids significant noise caused by non-ground point clouds participating in modeling and superposition in common processing methods. On this basis, we successfully extracted the horizontal displacement information accompanying subsidence by employing sub-pixel correlation using the surface feature images before and after subsidence. The proposed technical pathway was validated by applying it to a coal mining subsidence area in the Yushen mining area in western China. Results demonstrate that, compared to conventional treatments, the proposed subsidence modeling method using laser scanning point clouds improves monitoring accuracy by over 50% while also obtaining the necessary horizontal displacement information for engineering requirements. These findings confirm the efficiency and accuracy of the proposed method for acquiring 3D surface deformation in mining areas.

Role of Nonlinearity in the Soil in Earthquake-Resistant Design of Structures

The nonlinearity of the soil may considerably affect the response of structures subjected to seismic events. This paper aims to show under which circumstances geometry, soil, and earthquake-type; the nonlinearity is important. A simple model based on a 1D shear column was developed to calculate the maximum shear strain (γ) in the soil subjected to earthquake excitation. It was found that γ is a function of peak ground acceleration PGA and the maximum horizontal ground displacement (∆). EC8 provides an expression for calculating ∆ that is independent of the soil thickness. It was found that this expression is conservative for shallow layers and underestimates γ for thick ones, as a result, improvements have been suggested. By performing several time history analyses, simple formulas are developed which enable the designer to assess when nonlinearity must be taken into account. Four curves based on soil thickness and peak ground acceleration have been introduced for different soil types (A, B, C, and D) using a limit value of γ = 10–4. These curves show that depending on the soil depth, the threshold acceleration of nonlinear soil behavior is around 0.48, 0.36, 0.29, and 0.10 m/s2 for soil types A, B, C, and D, respectively. Obviously, nonlinear analysis must be performed for shallow soil layers under moderate seismicity.

Prediction of lateral spreading displacement using conditional Generative Adversarial Network (cGAN)

Lateral spreading is the most pervasive type of earthquake-induced ground deformation, which can cause considerable damage to engineered structures and lifelines. There are several factors, such as soil properties and ground motion characteristics that affect the liquefaction induced lateral spread. This inherent complexity and nonlinear relationship between the variables make it difficult to predict lateral spread with high accuracy. There are several empirical and machine learning models developed to predict lateral spread. In this study, a conditional generative adversarial network (cGAN) is developed to predict the horizontal ground displacements. A ten-fold cross validation is used to assess the model performance. The average accuracy of the model for both free face and ground slope conditions are found to be 82% and 68%, respectively. Shapley additive explanations-based sensitivity analysis was carried out to identify the important parameters that influence the lateral displacement.

Ground Displacements Estimation through GNSS and Geometric Leveling: A Geological Interpretation of the 2016–2017 Seismic Sequence in Central Italy

Between August 2016 and January 2017, a very energetic seismic sequence induced substantial horizontal and vertical ground displacements in the Central Italian Apennines. After this event, the Italian Military Geographical Institute (IGM), owner and manager of the Italian geodetic networks, executed several topographic surveys in the earthquake area in order to update the coordinates of vertices belonging to the IGM95 geodetic network. The measurements began in the areas where the most significant deformation occurred: the localities of Amatrice and Accumoli, in the Rieti Province, and the area covering Norcia and Castelluccio, in the Province of Perugia, all the way to Visso (Province of Macerata). The activities described in this paper focused on the updated measurement of the IGM95 network points through GNSS and the restatement of extensive parts of the high precision geometric lines that were levelled until reaching stable zones. This unprecedented amount of data was used for a new geological interpretation of the seismic sequence, which confirms some of the previous hypotheses of the scientific community. In the analyzed territory, the latest estimate of the geodetic position points has allowed for an accurate determination of the east and the north and of the altitude components of the displacement induced by the earthquake through a comparison with the previous coordinates. The results confirm that the seismicity was induced by normal faults system activity. Still, they also indicate the possible influence of a significant regional thrust that conditioned the propagation of the seismicity in the area. The obtained maps of the displacement are coherent with other geodetic works and with a rupture propagation driven by the documented geotectonic structure.

Effect of Liquefaction Induced Lateral Spreading on Seismic Performance of Pile Foundations

Seismically active areas are vulnerable to liquefaction, and the influence of liquefaction on pile foundations is very severe. Study of pile-supported buildings in liquefiable soils requires consideration of soil-pile interaction and evaluation of the interaction resulting from movement of soil surrounding the pile. This paper presents the results of three-dimensional finite difference analyses conducted to understand the effect of liquefiable soils on the seismic performance of piles and pile groups embedded in stratified soil deposits using the numerical tool FLAC3D. A comparative study has been conducted on the performance of pile foundations on level ground and sloping ground. The soil model consists of a non-liquefiable, slightly cemented sand layer at the top and bottom and a liquefiable Nevada sand layer in between. This stratified ground is subjected to 1940 El Centro, 2001 Bhuj (India) earthquake ground motions, and harmonic motion of 0.3g acceleration. Parametric studies have been carried out by changing the ground slope from 0° to 10° to understand the effects of sloping ground on pile group response. The results indicate that the maximum bending moments occur at boundaries between liquefiable and non-liquefiable layers, and that the bending moment increases with an increase in slope angle. The presence of a pile cap prevents horizontal ground displacements at ground level. Further, it is also observed that the displacements of pile groups under sloping ground are in excess of those on level ground due to lateral spreading. Doi: 10.28991/CEJ-SP2021-07-05 Full Text: PDF

Mindlin solution on ground deformation caused by the trench excavation during installation of concrete diaphragm wall panels

Concrete diaphragm walls (CDWs) are widely used as support of deep excavation in soft ground in urban areas. Ground deformation occurs during the excavation of trenches for the installation of the CDW panels due to ground stress release. This paper investigates the ground deformation during slurry trenching using Mindlin solution. The pressure of slurry used to protect the trench stability during excavation is simulated as a triangularly distributed load on the trench walls, the soil stress state is solved using Mindlin solution, and the horizontal and vertical ground displacement are obtained through integral transformation of ground strain. The rationality of the solution is verified through comparison between the analytical solution and field measurement. Sensitivity analyses are performed on soil elastic modulus, Poisson's ratio, trench excavation depth and panel length. Simplified formulation is proposed for the prediction of horizontal ground deformation. The impact of excavation stages and adjacent panels on the ground deformation is explored. The study finds that the Mindlin solution is able to provide an approximate solution on the ground deformation during slurry trenching, and the simplified formulation can be used to provide a fast estimate of the horizontal ground movement in engineering practice.

Numerical evaluation of the ground response induced by dewatering in a multi-aquifer system

This study presents a numerical investigation of dewatering-induced settlement and wall deflection during pumping tests in Tianjin, China. Based on the measured groundwater head and building settlement during the pumping test, a three-dimensional liquid–solid coupling model is established by using the finite element method (FEM). The void ratio, hydraulic conductivity, and elastic modulus of each layer are back-calculated through the numerical model. The groundwater drawdown, seepage field, ground settlement, horizontal ground displacement, and diaphragm wall lateral deflection are analyzed using the FEM model. The simulated results demonstrate that (i) the maximum ground settlement outside of the excavation reaches to 82 mm due to the leakage effect of aquitards; (ii) large horizontal displacement occurs in the soil during the pumping test with a maximum value of 28.3 mm, and the installation of the diaphragm wall in the aquifer can reduce the horizontal displacement of the ground; (iii) long-term pumping causes a large lateral deflection of the diaphragm wall, and a maximum value of 23.2 mm occurs at the layer where the screens of the wells are located; and (iv) long-term large-scale pumping should be avoided before excavation.

Conditional Ground-Motion Models for Horizontal Peak Ground Displacement for Active Crustal Regions

ABSTRACTGround-motion models (GMMs) are developed for peak ground displacement (PGD) and for bandlimited PGD based on strong-motion data that has been filtered as part of standard processing and the total PGD that includes the tectonic deformation as well as the vibratory ground motion. For the bandlimited PGD, we develop conditional ground-motion models (CGMMs) using subsets of the Pacific Earthquake Engineering Research Center Next Generation Attenuation-West2 Project (NGA-W2) database and the National Center for Research on Earthquake Engineering Taiwan Senior Seismic Hazard Analysis Committee level 3 project database. The CGMM approach includes the observed pseudospectral acceleration (PSA(T)) as an input parameter in addition to magnitude and distance. The period of the PSA(T) is used as an input parameter; it is magnitude dependent and is based on the period for which there is the highest correlation between the ln(PGD) and ln(PSA(T)). Two CGMMs are developed: a global model based on the NGA-W2 data and a region-specific model for Taiwan. The conditional PGD models are combined with traditional GMMs for PSA(T) values to develop GMMs for both the median and standard deviation of PGD without the dependence on PSA. A second set of PGD GMMs are developed to correct for two factors: the effect of the high-pass filtering from standard record processing and the stronger large magnitude (M>6.5) scaling due to tectonic deformation. For magnitudes greater than 7, the PGD values from the total PGD GMMs are 2–5 times larger than the bandlimited PGD values based on the strong-motion data sets, but the increase is at very long periods. The appropriate PGD model to use, bandlimited PGD or total PGD, depends on the period range of interest for the specific engineering application.

Ground Deformation Characteristics Induced by Mechanized Shield Twin Tunnelling along Curved Alignments

This paper investigates the ground deformation characteristics induced by mechanized shield twin tunnelling along curved alignments by adopting the nonlinear three-dimensional (3D) finite element method (FEM). The performance of the adopted FEM is demonstrated to be satisfactory by comparing the numerical analysis results with the field monitoring data in a typical case history and with the predicted results generated by a modified version of the Peck’s empirical Gaussian formula. It has been found that the tunnelling-induced transverse ground surface settlement troughs and the distributions of the subsurface horizontal and vertical ground displacements are mostly similar in both form and magnitude for the considered various radii of curvature of tunnel alignment including 50 m, 100 m, 150 m, 200 m, 250 m, 300 m, 400 m, and infinity (i.e., straight-line tunnel). Considering the variational characteristics of the ground deformations with the magnitude of the radius of curvature, the radius of curvature of 100 m can be regarded as a critical tunnel alignment radius of curvature controlling the transformation of the curved tunnelling-induced ground deformational behaviors. For the benefit of geotechnical engineers interested in curved tunnelling with a small radius of curvature, a discussion of the technologies for reducing the overexcavation and improving the accuracy of tunnel lining segment installation is also presented.

Narrowbandness of seismic ground displacement on a broader area of the lithosphere and importance on base motion in isolated structures

Power spectral density of horizontal ground displacement of large and recent events in earthquake-prone Latin America is analyzed. The results confirm -in a larger region of the world- that strong motion horizontal displacement is a narrowband process, which was previously demonstrated solely on a very limited area: the State of California. Nonetheless, those limited and previous results proved to be important in seismic base isolation; particularly, in the solution of the problem of large displacements at the structure base. This is a current problem for which more expensive techniques than passive control are presently being implemented, as active or hybrid control; therefore, it is emphasized that a solution exists within simple base isolation, and it is based on ground displacement narrowbandness.

Direct least squares and derivative-free optimisation techniques for determining mine-induced horizontal ground displacement

Direct least squares and derivative-free optimisation techniques for determining mine-induced horizontal ground displacement

Reliability assessment of the performance of granular column in the nonuniform liquefiable ground to mitigate the liquefaction-induced ground deformation

ABSTRACT Granular columns have been widely used to mitigate the liquefaction-induced ground deformation. The increment in lateral stress due to densification, shear reinforcement, and drainage capacity of granular columns are believed to increase the liquefaction resistance of the ground. However, several case histories and recent research development exhibited the limitations of the effectiveness of granular columns under strong earthquakes. Besides, the mechanism of shear reinforcement governed by granular columns is poorly understood. Moreover, the spatial nonuniformity of the ground should be considered for a reliable engineering assessment of the performance of granular columns. A series of three-dimensional nonlinear stochastic analyses are carried out using the OpenSees framework with PDMY02 elasto-plastic soil constitutive model to map the reliability of the performance of equally-spaced granular columns. Soil variability is implemented with stochastic realizations of overburden and energy-corrected, equivalent clean sand, (N1)60cs values using spatially correlated Gaussian random field. The reliability of the performance of granular column is assessed based on the stochastic distributions of average surface settlement and horizontal ground displacement associated with the degree of confidence. The implications of cumulative absolute velocity, Arias Intensity and peak acceleration of different ground motions on the efficacy of the granular column are also discussed.

Semianalytical Solutions for Abutment Piles Under Combined Active and Passive Loading

Abstract Abutment piles in soft ground are always subjected to both active loads from upper structures and passive loads from horizontal soft ground displacements; however, theoretical solutions fo...

Investigation of the Horizontal Displacement of Ground Surface Due to Longwall Mining

Underground longwall mining results in both vertical and horizontal ground displacements. Although major studies have been conducted to evaluate vertical displacement component (subsidence), the overall examination of the horizontal displacement of the ground surface has been limited. In this study, investigations were conducted to evaluate the behavior of horizontal ground displacement due to longwall mining. As the magnitude and direction of horizontal ground displacement depend on the surface topography, both flat and rugged terrains were considered in the study. A correlation was developed between horizontal ground displacement and other site and displacement parameters by studying subsidence data of a mined area in the State of Wyoming as well as data collected from other underground mines in other mining regions. Based on the results, in flat grounds, the induced horizontal ground displacements are essentially perpendicular to the subsidence contours with the maximum value typically between 0.20 and 0.35 of the maximum subsidence. An empirical correlation was suggested to determine the horizontal ground displacement using ground subsidence data. For rugged terrains, correlations of the measured horizontal displacements were difficult to find but appear to be related to induced slope instability. Based on these findings, these displacements are directed down slope and have a greater magnitude than the displacements determined in flat terrains.

Omori-like slow decay (p\u2009

We infer the postseismic deformation mechanisms following the 2011 Tohoku megathrust earthquake via an analysis of onshore geodetic observations. We focus on the temporal decay characteristics of postseismic deformation using continuous time-series data at time scales that span many orders of magnitude by means of high-rate GNSS data. Our analysis indicates Omori-like power-law decay of the horizontal ground displacement rates, with p-value (0.69) that is significantly smaller than that of the aftershock occurrence (~ 1). This slow decay implies a (non-Maxwellian) viscoelastic relaxation mechanism other than afterslip since immediately after the mainshock, which is inferred using only onshore geodetic data. Spatial distribution of the Omori parameters implies that the postseismic deformation will continue over 100 years in a down-dip area of the northern part of the mainshock fault. The decay characteristics of vertical displacement rates are also almost Omori-like, but data deviation from the fitting line several 100 days after the mainshock might reflect the change of the dominant mechanism of the postseismic deformation. This multi-time scale geodetic approach will provide important constraints for future viscoelastic models of Earth’s interior.

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.