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Analysis of the geological conditions of high-altitude and low-temperature stope slopes and the study of grade division are the basis for the evaluation of slope stability. Based on the engineering background of the eastern slope of the Preparatory iron mine in Hejing County, Xinjiang, we comprehensively analyse and summarize the factors that affect the geological conditions of high-altitude and cold slopes and finally determine nine geological conditions that affect the index parameters. Based on a back-propagation (BP) neural network algorithm, we establish an applicable network model to analyse the geological conditions of slopes in cold areas. The model is applied to the eastern slope to analyse and classify the geological conditions of the high-altitude and low-temperature slopes. The research results show that the skarn rock layer in the eastern slope is in a stable state and not prone to landslides, and its corresponding geological condition is Grade I, meanwhile, the monzonite porphyry rock layer is in a relatively stable state, with a potential for landslides and a corresponding geological condition Grade II. The marble rock layer is in a generally stable state, there is the possibility of landslide accidents, and the corresponding geological condition level is Grade III. The limestone rock layer is in an unstable state and prone to landslide accidents, it has a corresponding geology condition Grade IV. Therefore, the eastern slope can be divided into different geological condition regions: Zone I, Zone II, Zone III, and Zone IV, and the corresponding geological condition levels for these are Grade I, Grade II, Grade III, and Grade IV. These results may provide a basis for the stability evaluation of high altitudes and cold slopes.

The acoustic response has many important roles in seismic exploration and nondestructive testing. It enables the development of fracture classification and sizing. In this paper, we combined Hudson’s effective medium scheme and finite-difference time-domain modeling method to simulate acoustic wave propagation in fractured media. Fractures are represented by discrete fracture networks, allowing for a state-of-the-art representation of natural fracture networks by a negative Exponential Law length distribution. The propagation of acoustic waves that are emitted by a point source and reflected from a fractured area in a 2D digital rock model are examined numerically with the purpose of developing an acoustic inference of fracture properties. In these fractured models, we vary the number and mean length of fractures to explore the relation between internal structure of rock and acoustic wave field characters. The modeling results indicate that acoustic wave field is more sensitive to the fracture number than to the mean of the fracture length. Moreover, a fracture-dependent attenuation analysis of the reflection records of discrete stochastic fractured models is obtained. The frequency- and time- dependent attenuation profiles feature two parts in frequency, (1) fracture-to-background at lower frequencies and (2) fracture-to-fracture at higher frequencies. Our results indicate that accounting for attenuation effects may not only allow for improving estimation of fracture number, but also provide information about geometrical characteristics of length distribution. Such an approach can be used to estimate nature fracture network properties with given acoustic records.

This study proposes an approach to identify earthquake-induced site liquefaction and/or nonlinearity from Hilbert–Huang–Transformation- or HHT-based data analysis of seismic motion recordings. The proposed approach fully utilizes unique features of the HHT method in characterizing instantaneous frequency and damping as well as temporal-frequency motion from the recordings, so as to single out and quantify liquefaction- and/or nonlinear-soil-related nonlinear phenomena shown in the recordings. With post-earthquake, site investigation as a reference, this study shows that the proposed approach is effective in characterizing site nonlinearity, quantifying nonlinear influences in site amplification, and diagnosing site liquefaction. Major results from this study are listed below.1. Predominant instantaneous frequency of earthquake motion is defined as the frequency with the largest amplitude in Hilbert amplitude spectra of the motion at a time instant, and subsequently used together with other motion features for identifying site liquefaction conditions. Analysis of 29 sets of seismic recordings with different liquefaction conditions shows that the proposed approach is more effective in detecting site liquefaction than other Fourier-based methods.2. HHT-based site amplification is defined as the ratio of marginal Hilbert amplitude spectra, similar to the Fourier-based one that is the ratio of Fourier amplitude spectra. The HHT-based site amplification can be used for effectively quantifying site nonlinearity in terms of frequency downshift in the low-frequency range and amplification-reduction factor in intermediate-frequency range in comparison with the Fourier-based one.3. Instantaneous damping, and Hilbert and marginal Hilbert damping spectra are defined in way similar to instantaneous frequency, and Hilbert and marginal Hilbert amplitude spectra, respectively. Consequently, the HHT-based site damping is found as the difference of marginal Hilbert damping spectra, which can be used as an alternative, complementary index to measure influences of site nonlinearity in seismic ground responses.

This study proposes an approach for estimating the damping factor of non-linear soil and its role in seismic wave responses at soil sites from earthquake recordings. In particular, the paper first reviews the Fourier-based approach to characterizing the dynamic features of soil sites in seismic ground motion and shows the deficiencies for assessing non-linear site amplification and damping. It then offers an alternative approach, i.e., the Hilbert–Huang transform (HHT) for non-linear and non-stationary data process, in addressing the non-linearity issues. This study focuses on discerning the signature of non-linear site damping from the general non-linear features in the motion that are typically shown in the frequency-dependent site amplification. As a result, the study proposes an HHT-based approach to estimate site damping with non-linear soil from earthquake recordings and to measure the influences in the motion at soil sites. With the use of recordings from the mainshock and aftershock of the 2001 Nisqually earthquakes, this study shows that the proposed approach is able to assess appropriately the site damping that can be used to estimate the influences of soil damping in non-linear site responses.

In this article we use empirical mode decomposition (EMD) to charac- terize the 1994 Northridge, California, earthquake records and investigate the sig- natures carried over from the source rupture process. Comparison of the current study results with existing source inverse solutions that use traditional data processing suggests that the EMD-based characterization contains information that sheds light on aspects of the earthquake rupture process. We first summarize the fundamentals of the EMD and illustrate its features through the analysis of a hypothetical and a real record. Typically, the Northridge strong-motion records are decomposed into eight or nine intrinsic mode functions (IMF's), each of which emphasizes a different oscillation mode with different amplitude and frequency content. The first IMF has the highest-frequency content; frequency content decreases with an increase in IMF component. With the aid of a finite-fault inversion method, we then examine aspects of the source of the 1994 Northridge earthquake that are reflected in the second to fifth IMF components. This study shows that the second IMF is predominantly wave motion generated near the hypocenter, with high-frequency content that might be related to a large stress drop associated with the initiation of the earthquake. As one progresses from the second to the fifth IMF component, there is a general migration of the source region away from the hypocenter with associated longer-period signals as the rupture propagates. This study suggests that the different IMF components carry information on the earthquake rupture process that is expressed in their different frequency bands.

A generalized earthquake-wave-motion model is established in this study, which considers 3D random heterogeneous media, together with existing models for sources and realistic geological profiles for sedimentary basins and irregular topography. The model can be used not only to examine the influences of random heterogeneous media, but also to explore the multiple interactions of source, site (irregularity and/or heterogeneity), and wave interference on spatial variations of ground motion. Specifically, the earth is modeled as a layered half-space with 3D weak-random heterogeneity media. Seismic waves are generated by a shear-dislocation source buried in one of the layers and then propagated through the modeled earth medium. A first-order perturbation approach together with wave propagation theory is used to solve the problem at hand for wave motion response, which is found as the superposition of the mean and scattered wave responses. The mean wave response is obtained as a wave-motion solution for a layered half-space without heterogeneity subjected to a buried seismic dislocation source. The scattered wave field is obtained as a wave-motion solution for the same layered half-space without heterogeneity subjected to virtual distributed body forces that mathematically replace the heterogeneity. The explicit expressions for the responses in both mean and scattered wave fields are derived in this study. A computational procedure for the wave-motion responses is also presented in detail.

State of the art in modeling, synthetics, statistical estimation, and engineering applications of strong ground motion is reported in this paper. In particular, models for earthquake wave motion are presented, in which uncertainties both in the earth medium and the seismic source are taken into consideration. These models can be used to synthesize realistic strong earthquake ground motion, specifically near-field ground motion which is quite often not well recorded in real earthquakes. Statistical estimation techniques are also presented so that the characteristics of spatially-correlated earthquake motion can be captured and consequently used in investigating the seismic response of such large scale structures as pipelines and long-span bridges. Finally, applications of synthesized strong ground motion in a variety of engineering fields are provided. Numerical examples are shown for illustration.

The stochastic dynamic response of the 310 m tall Nanjing TV tower in Nanjing, China under turbulent wind is analysed. The turbulent wind speed consists of mean and fluctuating components. The spatial variation of the mean wind speed follows a power law. The fluctuating component is idealized as a stochastic process which is non-white in time and space. Hence, the spatial variation of the fluctuating component along the height of the tower is taken into consideration. The interaction between wind and structure is also accounted for in the analysis. Assuming that the wind direction is slightly off the direction normal to one side of the TV tower (the x-direction), the vibration in the x-direction is induced primarily by the drag force due to the x-component turbulent wind speed, while the y-direction vibration perpendicular to the x-direction is generated primarily by the lift force exerted by vortex shedding resulting from the turbulent wind as well as by the drag force due to the y-component of turbulent wind speed. With the aid of the spectral representation method for numerical simulation of the fluctuating component of wind speed, the static and random vibration response of the TV tower is found for each simulated turbulent wind input. The response trajectories of the TV tower at specific heights are also derived. These results provide fundamentally important input information for the vibration control analysis of the TV tower with passive and/or active mass dampers.

This study presents system identification of ten-story Millikan Library in Pasadena, California with a pair of the Yorba Linda earthquake of September 3, 2002. The fundamental of the proposed approach is based on wave features of generalized impulse and frequency response function (GIRF or GFRF), i.e., wave response at one structural response location to an impulsive motion at another reference location in time and frequency domains respectively. With a pair of seismic recordings at the two locations, GIRF/GFRF is obtainable. With a continuous-discrete model for the structure, a closed-form solution of GFRF, and subsequent GIRF with Fourier transformation of GFRF, can also be found in terms of structural physical properties above the impulse location. Matching the two sets of GIRF/GFRF from recordings and the model helps identify system parameters such as wave velocity or shear modulus.

A discrete wave number approach in conjunction with a propagator-based formalism is used to synthesize the Loma Prieta earthquake ground motion at both the near and the far field, taking into account all kinds of seismic waves (body and surface). A bilaterally propagating shear slip over a rectangular fault is used to describe the seismic source mechanism, while the earth model is based on geological profiles of the Santa Cruz mountain area and consists of three layers overlaying a half-space. The synthesized ground motion is first compared with actual records from the Loma Prieta earthquake and the agreement between the two is found to be satisfactory, as far as magnitude, duration and essential wave form characteristics are concerned. Then, ground motions are synthesized and plotted at a dense grid of observer locations over a large area around the epicenter, at different time instants. Using such plots, it is possible to study the generation ana propagation of different kinds of seismic waves, the spatial variability of ground motion, as well as the development of the permanent gound deformation.

A model for earthquake ground motion is developed using principles of geophysics and stochastics in a sequence of two papers. In the first paper, the earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is modeled as a concentrated seismic moment located within one of the layers. The partial differential equations for the seismic motion in each layer are solved using a Fourier finite-Hankel transformation approach, and solutions in terms of state vectors of displacements and forces are converted to wave vectors composed of up-going and down-going waves. Transmission and reflection matrices are obtained for each layer, for each layer-to-layer interface, and for the free ground-surface boundary to characterize their roles in transmitting and reflecting a wave motion. The use of these matrices allows the numerical calculation to be channeled in the directions of wave propagation, resulting in better numerical accuracy. An example is included for illustration.

An earthquake model is developed, in which the earth is idealized as horizontally stratified layers and the seismic source as propagating dislocation along a line. The line source is further discretized into point sources at equal intervals, and the times at which seismic signals are emitted from the source points are assumed to be Poisson events. The strengths of individual sources are assumed to be independent and identically distributed random variables. A generalized version of the random-pulse-train theory is then used to compute the mean and covariance functions of the ground motion at one site, and the cross-covariance function at two sites. The covariance and cross-covariance functions are converted to the evolutionary spectral density and cross-evolutionary density of the ground motion, which are useful in the computation of the statistics of structural response to earthquake excitations.. Numerical examples are given for illustration.