Free Wobble of the Triaxial Earth: Theory and Comparisons with International Earth Rotation Service (IERS) Data

Earth’s free wobble is often referred to as the Euler wobble (for the rigid case) or the Chandler wobble for the real case. In this study, we investigate the theory of the free wobble of the triaxial Earth and demonstrate that: (1) the Euler period should actually be expressed by the complete elliptic integral of first kind, and (2) the trace of the free polar motion is elliptic, with the orientations of its semi-minor and major axes being approximately parallel to the Earth’s principal axes A and B, respectively. Numerical calculations show that, due to the triaxiality of the Earth, the spin rate ω ₃ fluctuates with the semi-Euler/Chandler period, although its amplitude (about 10⁻¹⁹ rad/s) is rather small and beyond the present measurement accuracy; the tilt of the instantaneous spin axis (or the amplitude of the free wobble), θ, has a fluctuation whose amplitude is around 0.34 milli-arcsecond (mas), which could be detected by present observations. Thus, we conclude that the Earth’s triaxial nature has little impact on ω ₃, but has an influence on the polar motion which should not be ignored. On the other hand, our study shows that there is a mechanism of frequency–amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and period of the Chandler wobble. We compare the theoretical polar parameters (m ₁, m ₂) with the observed values for the Chandler components obtained from the data EOP (IERS) C 04, and find that they coincide with each other quite well, especially for recent years. In addition, a polar wander towards 76.7°W, which is in agreement with previous results given by other scientists, is also obtained.     

Effect of coherent noise on single-station direction of arrival estimation

Polarization analysis of multi-component seismic data is used in both exploration seismology and earthquake seismology. In single-station polarization processing, it is generally assumed that any noise present in the window of analysis is incoherent, i.e., does not correlate between components. This assumption is often violated in practice because several overlapping seismic events may be present in the data. The additional arrival(s) to that of interest can be viewed as coherent noise. This paper quantifies the error because of coherent noise interference. We first give a general theoretical analysis of the problem. A simple mathematical wavelet is then used to obtain a closed-form solution to the principal direction estimated for a transient incident signal superposed with a time-shifted, unequal amplitude version of itself, arriving at an arbitrary angle to the first wavelet. The effects of relative amplitude, arrival angle, and the time delay of the two wavelets on directional estimates are investigated. Even for small differences in angle of arrival, there may be significant error (>10°) in the azimuth estimate.     

Simulation of torsional shear test results with neuro-fuzzy control system

In the first part of this study, a series of stress-controlled hollow cylinder cyclic torsional triaxial shear tests were conducted on loose to medium dense saturated samples of clean Toyoura sand to investigate its liquefaction behavior. A uniform cyclic sinusoidal loading at a 0.1 Hz frequency was applied to air-pluviated samples where confining pressure and relative density was varied. Cyclic shear stress–strain changes, the number of cycles to reach liquefaction and pore pressure variations were recorded. Results indicate that the liquefaction resistances of uniform sands are significantly affected by the method of sample preparation and initial conditions.     

Consolidation of inelastic clays under rectangular cyclic loading

This paper presents a semi-analytical solution for one dimensional consolidation problem of inelastic clays under cyclic loading considering the effect of the change of the consolidation coefficient of the soil layer. Due to change of the consolidation coefficient, and time-dependant loading, Terzaghi's theory would not be applicable in cyclic conditions. In this research, a method based on the time variable exchange along with the superimposing rule is employed to overcome these shortcomings. Changes in the consolidation coefficient are applied in the solution by modifying the loading and unloading durations introducing a Virtual Time. Based on the superimposing rule a set of continuous static loads in specified times are used instead of the cyclic load in the transformed time space. Each full cycle of loading is replaced by a pair of static loads with different signs. Based on the Terzaghi's theory the pore-water pressure distribution and the degree of consolidation are calculated for each static load and the results are superimposed. A set of laboratory consolidation tests under cyclic load and numerical analysis are performed in order to verify the presented method. The numerical solution and laboratory tests results showed the accuracy of the presented method.     

Unified modeling of flow liquefaction and cyclic mobility

Flow liquefaction and cyclic mobility are two different phenomena that are encountered during strong earthquakes. Flow liquefaction is associated with the contractive behavior of loose granular materials and cyclic mobility is associated with the dilative response of both loose and dense granular materials at low confining stresses. These two types of response pertain to the same material and therefore should be modeled in a consistent manner. Whether a soil in a given state exhibits contractive or dilative behavior is dependent on its dilatancy, d=d_v^p/d_q^p. A form of the dilatancy d=d(η,ψ,C) is proposed, where η=q/p is the stress ratio, and ψ and C denote the internal state variables and the intrinsic properties, respectively. It has been shown that such a state-dependent dilatancy is effective in describing both the contractive and dilative behavior. This allows the soil behavior associated with flow liquefaction and cyclic mobility during earthquakes to be modeled in a unified way.     

卸荷状态下岩爆岩石变形破裂机制的实验岩石力学研究

岩爆是高地应力区地下工程中常见的一种卸荷破坏地质灾害现象。本文按照地下洞室开挖过程中围岩的实际受力状态,采用卸荷三轴试验方法,探讨了岩爆岩石的变形破坏特征和岩爆形成力学机制问题。     

On the Investigations of Resilient Modulus of Residual Tropical Gravel Lateritic Soils from Senegal (West Africa)

Investigations on the mechanical behavior of compacted gravel lateritic soils have been the subject of several studies. Used as road materials, soils tests were mainly performed using standard tests. Static loads as unconfined compression test (UCT) remain the only engineering approach used. Alternative testing techniques can be chosen as supplementary tests for characterizing pavement materials. These researches were conducted so as to determine the response of these particular and problematic soils in its compacted form with road traffic loads. This paper presents the results of research conducted to investigate the effect of the soil compacity on the resilient modulus of lateritic soils. The influence of the percentage of cement added so as to stabilize each sample at the optimum modified proctor (OPM) State was also determined. Soil big specimens of around 180 mm diameter (with length to diameter aspect ratio of 2:1) were prepared according to the standard procedure described by AASHTO T 307 and then were subjected to repeated load triaxial tests. The models used, analyzed and developed in this paper are mainly the Andrei and the Uzan–Witczak universal model. Test results showed that the specimen compacity has no significant influence on the resilient modulus of the investigated gravel lateritic soils. Soil specimens with variation of the percentage of cement added exhibited the highest resilient modulus values while the specimens with variation of the compacity exhibited the lowest values. The resilient modulus variation seems to be independent of the level of stress.     

在三轴压缩下大理岩循环加载实验的初步研究

在围压10、50、100和200MPa,应变率5×10^-5/s和室温条件下,采用山东掖县大理岩岩样,在800t高温高压伺服三轴流变仪上进行了连续加载和循环加载实验.对岩样的残余强度和弹性模量的变化等问题进行了初步研究.得出:在低围压下（<100MPa）,残余强度与超过极限强度后的循环加载次数有关;超过极限强度后加载弹性模量随着非弹性应变的增加而减小,并趋于一个极限值.在高围压下（≥100MPa）,残余强度几乎与超过极限强度后的循环加载次数无关;超过极限强度或者产生应变强化后加载弹性模量几乎不随非弹性应变的增加而减小.     

液化判别的应力法与刚度法之比较

应力法和刚度法是判别土层液化的两种重要方法。本文在简要介绍判别原理的基础上,对两者作了比较,並结合工程实例和饱和标准砂样进行了对比。在相同的条件下,两种方法分析所得的抗液化安全系数是不相同的。本文提出的结论,就如何正确应用这二种方法提供了依据。     

Morphological expression of bedforms formed by supercritical sediment density flows on four fjord‐lake deltas of the south‐eastern Canadian Shield (Eastern Canada)

High‐resolution swath bathymetry data collected in fjord‐lakes Pentecôte, Walker and Pasteur (eastern Québec, Canada) allowed imaging in great detail the deltas of four rivers in order to understand the factors controlling the formation and downslope evolution of bedforms present on their slopes. The morphometry and morphology of 199 bedforms reflect the behaviour of sediment density flows. The shape of the bedforms, mostly crescentic, and the relationships between their morphological properties indicate that they were formed by supercritical density flows and that they are cyclic steps. The crescentic shape suggests an upslope migration while the aspect ratios and increasing wavelengths with distance from the shore (and decreasing slopes) are compatible with a cyclic step origin. At the rollover point, the acceleration of the density flows on steep slopes produces tightly spaced hydraulic jumps and favours short wavelength and symmetrical bedforms. Further downslope, decreasing slopes and increasing specific discharge increase the wavelength and asymmetry of the bedforms. The wavelength and asymmetry are increased because density flows require longer distances to become supercritical again on lower slopes after each successive hydraulic jump. Bedform morphometry and morphology are used to reconstruct density flow behaviour downslope. Froude numbers are high near the rollover point and gradually decrease downslope as the slope becomes gentler. Conversely, the specific discharge and flow depth are low near the rollover point and gradually increase downslope as the flow either erodes sediments or becomes more dilute due to sediment deposition and water entrainment. The supercritical density flows are believed to be triggered mainly by hyperpycnal flows but some evidence of delta‐front slope failures is also observed. The differences in delta morphology and bedform development between the four deltas are linked to basin morphology and watershed hydrology, but also mainly to the fjord heritage of the lakes that allowed the focusing of sediment at the delta front.