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
Random field generators serve as a tool to model heterogeneous media for applications in hydrocarbon recovery and groundwater
flow. Random fields with a power-law variogram structure, also termed fractional Brownian motion (fBm) fields, are of interest
to study scale dependent heterogeneity effects on one-phase and two-phase flow. We show that such fields generated by the
spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. To illustrate
this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose
a new method to generate fBm fields that introduces weighting functions into the spectral method. It leads to a flexible and
efficient algorithm. The flexibility permits an optimal choice of summation points (that is points in frequency space at which
the weighting function is calculated) specific for the autocovariance structure of the field. As an illustration of the method,
comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields are presented.
For power-law semivariograms, the proposed spectral method with a cylindrical distribution of the summation points gives optimal
results. 相似文献