In a micromechanics framework, the main issue is the relationship between the microscale variables and the macroscale variables. These variables are used to describe either the statics or kinematics of the system. The relationships can be classified in two ways, namely, the “averaging” relationships and the “tracking” relationships. The averaging relationships express the macroscale variable as an averaging of the microscale variables; for example, the stress as a function of contact forces. The “tracking” relationships express the microscale variable as a function of the macroscale variables; for example, the contact force at a given orientation as a function of the stress. Based on fundamental premises, a unique averaging relationship exists for either the statics or the kinematics case. However, it is generally impossible to have a unique expression of the “tracking” relationship because they are generally derived with certain assumptions. In this paper, we will present expressions of the “tracking” based on three different approaches, namely, (1) energy conservation principle, (2) representation theory, and (3) indirect scheme. The assumptions used in each approach are discussed. The results are compared among the three approaches as well as that obtained from the Discrete Element Method (DEM). 相似文献
Vertical seismic compressional- and shear-wave (P-and S-wave) profiles were collected from three shallow boreholes in sediment of the upper Mississippi embayment. The site of the 60-m hole at Shelby Forest, Tennessee, is on bluffs forming the eastern edge of the Mississippi alluvial plain. The bluffs are composed of Pleistocene loess, Pliocene-Pleistocene alluvial clay and sand deposits, and Tertiary deltaic-marine sediment. The 36-m hole at Marked Tree, Arkansas, and the 27-m hole at Risco, Missouri, are in Holocene Mississippi river floodplain sand, silt, and gravel deposits. At each site, impulsive P- and S-waves were generated by man-made sources at the surface while a three-component geophone was locked downhole at 0.91-m intervals.
Consistent with their very similar geology, the two floodplain locations have nearly identical S-wave velocity (VS) profiles. The lowest VS values are about 130 m s−1, and the highest values are about 300 m s−1 at these sites. The shear-wave velocity profile at Shelby Forest is very similar within the Pleistocene loess (12 m thick); in deeper, older material, VS exceeds 400 m s−1.
At Marked Tree, and at Risco, the compressional-wave velocity (VP) values above the water table are as low as about 230 m s−1, and rise to about 1.9 km s−1 below the water table. At Shelby Forest, VP values in the unsaturated loess are as low as 302 m s−1. VP values below the water table are about 1.8 km s−1. For the two floodplain sites, the VP/VS ratio increases rapidly across the water table depth. For the Shelby Forest site, the largest increase in the VP/VS ratio occurs at 20-m depth, the boundary between the Pliocene-Pleistocene clay and sand deposits and the Eocene shallow-marine clay and silt deposits.
Until recently, seismic velocity data for the embayment basin came from eartquake studies, crustal-scale seismic refraction and reflection profiles, sonic logs, and from analysis of dispersed earthquake surface waves. Since 1991, seismic data for shallow sediment obtained from reflection, refraction, crosshole and downhole techniques have been obtained for sites at the northern end of the embayment basin. The present borehole data, however, are measured from sites representative of large areas in the Mississippi embayment. Therefore, they fill a gap in information needed for modeling the response of the embayment to destructive seismic shaking. 相似文献
—A new, yet simple, method using the asperity model to estimate ground motion in the near-source regime for probabilistic seismic hazard analyses is proposed in this study. This near-source model differs from conventional empirical attenuation equations. It correlates peak ground motions with the local contributing source in terms of the static stress drop released non-uniformly on the causative fault plane rather than with the whole seismic source in terms of magnitude. Here the model is simplified such that ground motions at a rock or firm soil site near extended vertical strike-slip faults are dominated by direct shear waves. The proposed model is tested by comparing its predictions with strong ground motion observations from the 1979 Imperial Valley and the 1984 Morgan Hill earthquakes. The results have revealed that ground motions in the near-source region can be adequately predicted using the asperity model with appropriate calibration factors. The directivity effect of ground motion in the near-source region is negligible for high-frequency accelerations. The cut-off frequency (?max?) at a site is an important parameter in the near-source region. Higher values of ?max yield higher estimates of peak ground accelerations. For high-frequency structures, ?max should be carefully estimated. In the near- source region both non-uniform and uniform source models can produce non-stationary high-frequency ground motions. Peak motions may not be caused by the nearest sections of the fault (even if the uniform source model is considered). 相似文献
It has been observed that the field biodegradation rates for soluble hydrocarbon plumes are significantly smaller than the
aerobic rates observed in the laboratory. It is believed that this difference is related to the fact that in the field oxygen
and hydrocarbon must be mixed before the biodegradation reaction can occur, and that the effective degradation rate is controlled
by the actual, not mean, concentrations of oxygen and hydrocarbon. In this work, we present a conceptual model of oxygen-mixing
limited biodegradation, which indicates that the effective degradation rate should depend on the cross correlation between
the oxygen and hydrocarbon concentration fluctuations. This is followed by a development of a rigorous, field-scale model. 相似文献