Direct scaling of residual displacements for bilinear and pinching oscillators

The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.

Analytical solutions for the restraint effect of isolation piles against tunneling-induced vertical ground displacements

This paper presents a simplified elastic continuum method for calculating the restraint effect of isolation piles on tunneling-induced vertical ground displacement,which can consider not only the relative sliding of the pile‒soil interface but also the pile rowesoil interaction.The proposed method is verified by comparisons with existing theoretical methods,including the boundary element method and the elastic foundation method.The results reveal the restraining mechanism of the isolation piles on vertical ground displacements due to tunneling,i.e.the positive and negative restraint effects exerted by the isolation piles jointly drive the ground vertical displacement along the depth direction from the original tunneling-induced nonlinear variation situation to a relatively uniform situation.The results also indicate that the stiffness of the pile‒soil interface,including the pile shaft‒surrounding soil interface and pile tip-supporting soil interface,describes the strength of the pile‒soil interaction.The pile rows can confine the vertical ground displacement caused by the tunnel excavation to the inner side of the isolation piles and effectively prevent the vertical ground displacement from expanding further toward the outer side of the isolation piles.

Vertical and horizontal displacements of a reservoir slope due to slope aging effect,rainfall,and reservoir water

Landslides are common hazards in reservoir areas and significantly affect dam operation and human lives.For the prevention and management of landslides,accurate assessment of the factors influencing their generation is essential.This study evaluated the key external factors influencing horizontal and vertical displacements of Luobogang Reservoir Slope in Hanyuan County,China.Displacements had been monitored by a surface-displacement-monitoring system consisting of 118 GPS stations during 2012-2015.To identify the external driving factors,their influence zones,and slope responses,we analyzed 32 months of displacement measurements and other multi-source datasets using the empirical orthogonal function.Overall,the results show that slope aging effect,rainfall,and reservoir water levels are three main driving factors.For horizontal displacement,aging effect is the most critical factor and predominantly affects the edges of landslides,the gob cave,and the public building zones.The secondary factor is the reservoir water level,which mainly acts on the boundary between the slope and reservoir water surface.The closer the slope zone is to the reservoir water,the more significant the impact is.Regarding vertical displacement,the most important factor is rainfall.The vertical displacement caused by rainfall accounts for 56.76% of the total vertical displacements.However,rainfall induces elastic displacements that generally cause less damage to the slope.The secondary factor is aging effect,and the vertical displacement caused by aging effect accounts for 9.42%.However,seven individual zones are highly affected by slope aging effect,which is consistent with the distribution of public buildings.

PATH-INDEPENDENT J-INTEGRAL AND ITS DUAL FORM IN ELASTIC-PLASTIC SOLIDS WITH FINITE DISPLACEMENTS

In this paper, based on energy variational principles of elastic-plastic solids, the path-independent J-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whose testification is given there after.

The coseismic displacements of the 2013 Lushan Mw6.6 earthquake determined using continuous global positioning system measurements

Based on Continuous GPS （CGPS） observation data of the Crustal Movement Observation Network of China （CMONOC） and the Sichuan Continuous Operational Reference System （ SCCORS）, we calculated the horizontal coseismic displacements of CGPS sites caused by the 2013 Lushan Mw 6.6 earthquake. The resuits indicate that the horizontal coseismic deformations of CGPS stations are consistent with thrust-compression rupture. Furthermore, the sites closest to the epicenter underwent significant coseismic displacements. Three network stations exhibited displacements greater than 9 mm （ the largest is 20.9 mm at SCTQ） , while the others were displaced approximately 1 -4 mm.

Annual Fluctuations and Displacements of Inter Tropical Convergence Zone (ITCZ) within the Range of Atlantic Ocean-India

Inter Tropical Convergence Zone (ITCZ) is one of the major systems in making the general circulation of atmosphere. Many climatologists believe that the starting point of the general circulation of atmosphere is from this system. It seems that the annual displacement of this system is coordinated with the sun. In this study we have tried to investigate the annual and seasonal displacement of this system within the range of Middle East, especially within the range of longitude of Iran in a long period of time (statistical period of 66 years). This is the first study in the field of ITCZ monthly and annual long-term changes in Iran. In this study, not only his exact position on Africa and South West Asia ITCZ is determined, it also shows the change in the period of 66 years. These results can also be used on regional climate changes. For this purpose topographic and surface level pressure maps are 1000 and 850 hpa and they were approximately extracted monthly for 12 months of the year from 1948 to 2013 and also they were extracted from the National Oceanic and Atmospheric Ad-ministration Site in America within the range of 30°west to 110°east, and they were extracted by using the flow map of location (ITCZ). Due to the sudden displacement in the ITCZ bar path in the two seasons of summer and winter, on the Middle East region, the direct impact of this displacement on sudden changes of seasons, the start and end of untimely rains, its impacts on agricultural products and water recourses of the country so all these reasons are essential that this phenomenon should be studied carefully. Studies have shown that ITCZ is not a coordinated solar system and its displacement is not coordinate with the apparent annual displacement of the sun. October is the only month of ITCZ that within the range of 10 northern degrees in all the ranges of longitude 20°west to 110°east has an approximate orbital shape. In 6 months of the year (from November to April) (ITCZ) within the range of 30°east or 110°east, it is entirely located in the Southern Hemisphere and on the contrary in 5 months from May to September (ITCZ) within the range of 30°east to 110°east, it is entirely located in the Northern Hemisphere. And in this period, ITCZ has its highest Northern movement on the Earth. So that at the foot of the Himalayas it moves to 30°north. Within the range of Africa, ITCZ never enters the Southern Hemisphere at any time of the year. And the interesting phenomenon of severe refraction in the way of ITCZ, during the cold period, is within the range of Ethiopia and ITCZ has approximately redirected for Meridian and enters the Southern Hemisphere.

Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.

Probabilistic analysis of tunnel displacements based on correlative recognition of rock mass parameters

Displacement is vital in the evaluations of tunnel excavation processes,as well as in determining the postexcavation stability of surrounding rock masses.The prediction of tunnel displacement is a complex problem because of the uncertainties of rock mass properties.Meanwhile,the variation and the correlation relationship of geotechnical material properties have been gradually recognized by researchers in recent years.In this paper,a novel probabilistic method is proposed to estimate the uncertainties of rock mass properties and tunnel displacement,which integrated multivariate distribution function and a relevance vector machine(RVM).The multivariate distribution function is used to establish the probability model of related random variables.RVM is coupled with the numerical simulation methods to construct the nonlinear relationship between tunnel displacements and rock mass parameters,which avoided a large number of numerical simulations.Also,the residual rock mass parameters are taken into account to reflect the brittleness of deeply buried rock mass.Then,based on the proposed method,the uncertainty of displacement in a deep tunnel of CJPL-II laboratory are analyzed and compared with the in-situ measurements.It is found that the predicted tunnel displacements by the RVM model closely match with the measured ones.The correlations of parameters have significant impacts on the uncertainty results.The uncertainty of tunnel displacement decreases while the reliability of the tunnel increases with the increases of the negative correlations among rock mass parameters.When compared to the deterministic method,the proposed approach is more rational and scientific,and also conformed to rock engineering practices.

Ground Surface Ruptures and Near-Fault,Large-Scale Displacements Caused by the Wenchuan Ms8.0 Earthquake Derived from Pixel Offset Tracking on Synthetic Aperture Radar Images

The 12 May 2008 Wenchuan Ms8.0 earthquake produced surface displacements along the causative fault, the Yingxiu-Beichuan Fault, which are up to several meters near the fault. Because of the large gradient, satellite synthetic aperture radar （SAR） interferometric data are strongly incoherent; the usual SAR interferometry method does not allow such displacements to be measured. In the present study, we employed another approach, the technique based on pixel offset tracking, to solve this problem. The used image data of six tracks are from the Advanced Land Observing Satellite, Phased Array type L-band Synthetic Aperture Radar （ALOS/PALSAR） dataset of Japan. The results show that the entire surface rupture belt is 238 km long, extending almost linearly in a direction of 42°north-east. It is offset left laterally by a north-west-striking fault at Xiaoyudong, and turns at Gaochuan, where the rupture belt shifts toward the south by 5 km, largely keeping the original trend. In terms of the features of the rupture traces, the rupture belt can be divided into five sections and three types. Among them, the Beichuan-Chaping and Hongkou-Yingxiu sections are relatively complex, with large widths and variable traces along the trend. The Pingtong-Nanba and Qingping-Jingtang sections appear uniform, characterized by straight traces and small widths. West of Yingxiu, the rupture traces are not clear. North of the rupture belt, surface displacements are 2.95 m on average, mostly 2-3.5 m, with 7-9 m the maximum near Beichuan. South of the rupture belt, the average displacement is 1.75 m, dominated by 1-2 m, with 3-4 m at a few sites. In the north, the displacements in the radar line of sight are of subsidence, and in the south, they are uplifted, in accordance with a right-slip motion that moves the northern wall of the fault to the east, and the southern wall to the west, respectively. Along the Guanxian-Jiangyou Fault, there is a uplift zone in the radar line of sight, which is 66 km long, 1.5-6 km wide, and has vertical displacements of approximately 2 m, but no observable rupture traces.

Double Beams to Measure Three-dimensional Rigid Body Displacements

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Co- and post-seismic vertical displacements of Wenchuan Ms8.0 earthquake near Beichuan

Co- and post-seismic vertical displacements of the Wenchuan earthquake derived from two measurements in 2008 and 2010 along two partly-damaged leveling lines near the epicenter show the following features： Co-seismic displacement at Beichuan-Yingxiu fault was as large as 4. 711 m near Beichuan, where the maximum observed fault offset was 5.1 m. In contrast, the observed co-seismic offset of the Qingchuan fault in Pingwu County was only 0. 064 m. During 2008 - 2010, the post-seismic displacement rate was 5 - 27 mm/a near Beichuan-Yingxiu fault in Beichuan area, 20.6 mrn/a at Jiangyou-Guangyuan fault near Dakang, and only 0.2 - 1.3 mm/a at Qingehuan fault near Gucheng.

Development of a preliminary slope stability calculation method based on internal horizontal displacements

This paper proposes a horizontal displacement-based approach to determine the potential slip surface of the slope. Firstly, a group of in-situ inclinometers with an appropriate spacing in the horizontal direction is located in the model slope.The equation of horizontal displacement with time for each in-situ inclinometer is fitted during the whole simulation process. Furthermore, the intersection of each inclinometer with potential slip surface is determined by using an optimization model. The slip surface can be obtained by using least square fitting method. Finally, the feasibility and accuracy of the method are validated by a series of numerical simulations. It is noted that the optimization model taking the maximum value of displacement increment gradient as an objective has higher accuracy when compared with other optimization models. This method employed in this study provides a preliminary approach to determine the real-time slope stability based on displacement, which can also be measured by using conventional instruments on site.

Detecting Droughts in Southwest China from GPS Vertical Position Displacements

The solid Earth responds elastically to terrestrial water storage(TWS)changes.Here global positioning system(GPS)vertical position data at 31 stations from the crustal movement observation network of China(CMONOC)from August 2010 to December 2016 are used to detect droughts in Southwest China.Monthly GPS vertical position displacements respond negatively to precipitation changes and TWS changes observed by gravity recovery and climate experiments(GRACE)as well as river water level variations.GPS vertical position anomalies(the non-seasonal term)are well correlated negatively(correlations of about-0.70)with the commonly used meteorological composite index(CI)in China and the GRACE drought severity index(GRACE-DSI),but less correlated with the standardized precipitation evapotranspiration index(SPEI).Compared to CI,GPS vertical position anomalies have the advantage of detecting droughts caused by abrupt precipitation deficits in a short time.GRACE-DSI is less accurate in drought monitoring for some periods due to the missing data,while the severity of abrupt precipitation absent in some cases can be overestimated from SPEI with big variability.This study shows the reliability and advantages of GPS data in drought monitoring.

Line-integral representations for extended displacements, stresses,and interaction energy of arbitrary dislocation loops in transversely isotropic magneto-electro-elastic bimaterials

In addition to the hexagonal crystals of class 6 mm, many piezoelectric materials （e.g., BaTiO3）, piezomagnetic materials （e.g., CoFe2O4）, and multiferroic com-posite materials （e.g., BaTiO3-CoFe2O4 composites） also exhibit symmetry of transverse isotropy after poling, with the isotropic plane perpendicular to the poling direction. In this paper, simple and elegant line-integral expressions are derived for extended displace-ments, extended stresses, self-energy, and interaction energy of arbitrarily shaped, three-dimensional （3D） dislocation loops with a constant extended Burgers vector in trans-versely isotropic magneto-electro-elastic （MEE） bimaterials （i.e., joined half-spaces）. The derived solutions can also be simply reduced to those expressions for piezoelectric, piezo-magnetic, or purely elastic materials. Several numerical examples are given to show both the multi-field coupling effect and the interface/surface effect in transversely isotropic MEE materials.

Experimental Study of Shrinkage Displacements of Points on Injection Molded Parts

The existing research on shrinkage of the injection molded plastic part mainly focuses on various shrinkage ratios of the part dimensions,and the relevant experimental studies belong to mere dimension measurement after demoulding.Obviously,measuring after the plastic part is demoulded from the cavity can not offer shrinkage displacements of points on the plastic part.However,shrinkage displacements of points on an injection molded plastic part are essential for exposing the inner relation among shrinkage ratios of various dimensions of the part.So visualization of the in-mold plastic part which can indicate the location relationship between the part and the cavity is needed.In this paper,a visual injection mold was fabricated by adopting the half mold structure and light transmission manner.With the visual mold,in-mold shrinkage images of injection molded plastic parts were photographed after the plastic part stayed in the injection mold for 24 h.By means of digital image processing of the in-mold shrinkage images,the experimental data of shrinkage displacements of points on injection molded parts were researched.From the experimental data,it is found that shrinkage directions of points on an injection molded part are related with both positions of the gate and of the part centroid,and either the gate or the centroid will exert more influence on the shrinkage direction of some point which is closer.Furthermore,some point at the later filled area has more shrinkage distance than the point at the earlier filled area.Combination of shrinkage directions and shrinkage distances of points on an injection molded part determine shrinkage ratios for various dimensions of the part,and shrinkage directions are more influential to shrinkage ratios of dimensions.This experimental research of shrinkage displacements offers a unique approach to understand the shrinkage principles of injection molded parts.

Analysis of dynamical response to large deformation of piles with initial displacements

In this paper, a nonlinear mathematical model for analyzing dynamical response to the large deformation of piles with initial displacements is firstly established with the arc-coordinate, and it is a set of nonlinear integral-differential equa- tions, in which, the Winkeler model is used to simulate the resistance of the soil to the pile. Secondly, a set of new auxiliary functions are introduced. The differential-integral equations are transformed into a set of nonlinear differential equations, and the differential quadrature method （DQM） and the finite difference method （FDM） are applied to discretize the set of nonlinear equations in the spatial and time domains, respectively. Then, the Newton-Raphson method is used to solve the set of discretization algebraic equations at each time step. Finally, numerical examples are presented, and the dynamical re- sponses to the deformation of piles, including configuration, bending moment and shear force, are graphically illuminated. In calculation, two types of initial displacements and dynamical loads are applied, and the effects of parameters on the dynamical responses of piles are analyzed in detail.

Coseismic displacements and inospheric changes of the 2013 Ms7. 0 Lushan earthquake from GPS measurements

By inverting GPS data recorded at stations of the Crustal Movement Observation Network of China （CMONOC） near the 2013 Lushan Ms7.0 earthquake, we found a horizontal displacement of 22 mm at a site about 32 kin SW of the epicenter and vertical displacements of as much as 12.4 mm at several sites. The vertical displacements were generally uplift on the west side of the nearby Longmenshan fault zone and subsidence on the east side. We also found coseismic ionospheric disturbances about 0.5 to 0.9 TECU in amplitude that lasted for about one hour.

Occasional Forces and Displacements of Longitudinally Coupled Ballastless Jointless Turnout on Bridges

For the longitudinally coupled baUastless turnout on Leida bridge on Wuhan-Guangzhou passenger dedicated line （PDL） in China, a turnout （cross over）-track slab-bridge deck-pier integrated finite element model was established, in which two No. 18 jointless turnouts with movable frogs in form of crossover, longitudinally coupled ballastless track, bridges and piers were regarded as one system. Based on this model, the additional forces and displacement regularities of turnouts, track slab, bridges and piers under occasional loading were analyzed, and the effect of occasional loading position was researched. The results show that slab breaking is more influential on the longitudinal force and deformation of the whole system than rail breaking, that slab breaking on one line could deteriorate both the slab force on another line and the forces exerted on the piers and fastener components, and that a great slab force at the left end of the continuous bridge expansion joint should be particularly avoided in design.

Stability analysis of the moving interface in piston- and non-piston-like displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axisymmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.

Velocities and Displacements of Shrapnel and a Shock Wave during Blast

It is important to minimize the destruction of defense works when blasted. In our opinion, information in the available literature is very deficient. We now present our research results on better and simpler formulas for calculating the velocities and displacements of shrapnel and a shock wave; these formulas are indispensable for understanding the destruction of blast. Formulas now available in China are too complicated. In this paper, we derive Equation （ 13 ） as the formula for calculating the velocity of shrapnel and Equation （ 18 ） as that for calculating the velocity of a shock wave. We used the test data of Denver Research Institute, as reported in Reference 4, as numerical example and found that our Equations （13） and （18） give calculated results that agree well with their test data in two respects： （ 1 ） both test data and our calculations show that at first a shock wave is ahead of shrapnel, then their displacements are equal, and finaUy shrapnel is ahead of the shock wave; （2） when the displacements of shrapnel and shock wave are equal, the time is 0. 34 s according to test data and 0. 31 s according to our calculations.