Excess Stress Model Research Articles

Estimating the static shear stiffness of joints by wave attenuation

Recent studies on the shear behavior of joints demonstrated that the joint seismic stiffness value measured using seismic wave propagation is different from the static stiffness values determined by static stress-displacement measurements. Several experimental studies on mated fractures quantified this difference and revealed that the seismic stiffness is almost two to eight times larger than the static one. However, the underlying physical mechanisms responsible for this discrepancy are still poorly understood. In this study, the difference between the seismic and static shear stiffnesses was attributed to the frequency dependence of joint stiffness. A velocity discontinuity model composed of Hooke and Newton elements was used to interpret experimentally collected shear waves transmitted through a rock joint to predict the static shear stiffness at different strain levels. Specifically, the rate-independent stiffness of this model was associated with joint deformation responses at low frequencies, providing an estimation of the static stiffness. Existing experimental results support that the excess stress model enables the estimation of the values of static stiffnesses of rough joints, as indicated by a simple shear wave transmission experiment. Moreover, the results indicate that strain rate effects and frequency effects are intrinsically related.

An excess stress model for capturing rate-dependent compressive behavior of rock joint and its validation and applications

The deformational and mechanical behavior of rock masses is determined by discontinuities at different scales, e.g., rock joints. The discontinuous rock masses are often subjected to dynamic loads, e.g. blasts and earthquakes. Therefore, understanding dynamic response of rock joints is crucial. However, the dynamic compressive characteristics of rock joints have not been well understood yet. In this study, an excess stress model, employing the mechanical conceptual models based on the Hooke, the modified Saint Venant and the Newton elements, was developed. It is capable of capturing the nonlinear compressive processes of joints at different loading rates. This new model was validated by the comparison between model predictions and laboratory measurements obtained at loading rates ranging from approximately 200 GPa/s to 600 GPa/s. It was found that certain of rate-dependent compressive characteristics of rough joints can be successfully quantified with the proposed joint model. Compressive strength can be approximately predicted on the assumption that the peak-stress displacement is independent of the loading rate. Both the peak-stress secant stiffness and tangent stiffness predicted by the new joint model increase linearly with the loading rate. The wave energy dissipation at joints calculated by the proposed model decreases with increasing loading rate. Based on this model, the underlying mechanisms responsible for loading rate effects were related to the rate-dependency of crack propagation. Two hypotheses have been proposed: 1)the amount of cracking decreases with the increase of loading rate before the peak stress, causing ‘apparent’ hardening effects; 2) crack propagation velocity is relatively steady under static/quasi-static conditions, but becomes increasingly unstable when the loading rate is higher than the critical transition value. The present findings potentially provide a mechanically sound frame for the rate-dependent characteristics of joints, and have important implications for explicating the rate-dependent phenomena of fracturing, such as crack branching and fracture smoothening.

Deriving Parameters of a Fundamental Detachment Model for Cohesive Soils from Flume and Jet Erosion Tests

Abstract. The erosion rate of cohesive soils is commonly quantified using the excess shear stress model, which is dependent on two major soil parameters: the critical shear stress (I„ c ) and the erodibility coefficient (k d ). A submerged jet test (jet erosion test, or JET) is one method that has been developed for measuring these parameters. The disadvantage of using the excess shear stress model is that parameters I„ c and k d change according to erosion conditions, such as soil structure, soil orientation, type of clay, presence of roots, and seepage forces. A more mechanistically based detachment model, called the Wilson model, is proposed in this article for modeling the erosion rate of soils using hydraulic analysis of a JET. The general framework of the Wilson model is based on two soil parameters (b 0 and b 1 ). The objectives of this study were to: (1) develop methods of analysis of the JET to determine parameters b 0 and b 1 for the Wilson model in a similar fashion to the previous methodology developed for open-channel flow, and (2) compare the excess stress model parameter (k d ) and the Wilson model parameters (b 0 and b 1 ) determined from the flume tests and JETs for two cohesive soils. Flume tests, treated as the standard test method, and original and “mini” JETs were conducted on two soils to independently measure the excess shear stress model parameter (k d ) and the Wilson model parameters (b 0 and b 1 ). Soil samples of two cohesive soils (silty sand and clayey sand soils) were packed in a soil box for the flume tests and the JETs at water contents ranging from 8.7% to 18.1%. No statistically significant differences were observed for the excess shear stress model parameter (k d ) and for the Wilson model parameters (b 0 and b 1 ) when determined from the flume tests and JET devices, except for b 1 with the original JET. The Wilson model is advantageous in being a more mechanistic, fundamentally based erosion equation as compared to the excess shear stress model. The Wilson model can be used in place of the excess shear stress model with parameters that can be estimated using existing JET techniques.

Strain and critical layer thickness analysis of carbon-doped GaAs

We have calculated the lattice constant, strain, and critical layer thickness of heavily carbon (C)-doped GaAs epilayers as a function of hole concentration. The lattice constant of C-doped GaAs epilayers decreased with increasing hole concentration due to strain by carbon incorporation where carbon has a smaller covalent radii than gallium and arsenic. We also have discussed the relationship between hole concentration and critical layer thickness ( L c ) by the excess stress and Matthews-Blakeslee model. We have calculated not only for the pure case but also 10% compensated case. In compensated epilayers the carbon atoms exist not only on the arsenic sites but also on the gallium sites. As we compared the experimental data of C-doped GaAs with the calculated results, the excess stress model is more agreeable than the Matthews-Blakeslee model. The excess stress, at which surface cross hatching could be seen from the surface, was σ exc μ = 0.0021 for pure case and 0.0024 for 10% compensated case. Thus we could identify these excess stresses as the critical excess stresses for C-doped GaAs epilayers.

Characteristics of heavily carbon-doped GaAs by LPMOCVD and critical layer thickness

The carbon-doping characteristics of GaAs epilayers have been investigated by varying the growth parameters - V/III ratio and growth temperature. We have obtained the highest 1.4 × 10 20 cm -3 hole concentration with hole mobility 42 cm 2/V·s without using intentional doping source gases. The carbon incorporation increased with increasing growth temperature up to the critical temperature and above this temperature the carbon incorporation decreased. This critical temperature depends on input TMG flow rate. The peak energy of the PL intensity distribution was shifted to lower energy (red shift) and the full width at half maximum (FWHM) increased with increasing hole concentration. The (400) diffraction peak of the carbon-doped GaAs epilayer was split from the substrate GaAs peak. The split angle was 191.25 arc for the carbon-doped GaAs with 9 × 10 19 cm -3 hole concentration. We also have discussed the relationship between carbon-doping concentration and critical layer thickness ( L C ) by an excess stress model. The excess stress at which partial strain relief became observable was σ exc / μ = 0.0021. Thus we identified this excess stress as the critical excess stress for carbon-doped GaAs epilayers. If the excess stress was greater than this, the epilayers showed the surface cross-hatching.

Raman and X-ray diffraction study of relaxation in Si–Si1–xGex strained-layer superlattices

We report a study of the relaxation of Si–Si1–xGex strained single layers and superlattices by Raman scattering spectroscopy, double crystal X-ray diffraction, and transmission and scanning electron microscopy. Samples of various dimensions and compositions were produced by molecular beam epitaxy at a growth temperature of 500 ± 30 °C. The thermal stability of the various specimens was investigated by annealing experiments at temperatures between 600 and 900 °C. Considerable deterioration of the crystal quality and progressive relaxation were observed in some of the samples. Relaxation occurred through formation of misfit dislocations at the first Si–Si1–xGex interface and these caused threading dislocations to form within the epilayer. The degradation of the superlattice interfaces on annealing is correlated with a sharp decrease in the acoustic mode Raman intensities. Strain values perpendicular to the growth direction as a function of annealing temperature are obtained from a kinematical simulation of the X-ray rocking curves. These results are compared with the frequency shifts of the longitudinal optical phonons in the Raman spectra. The results obtained for the critical layer thicknesses versus x are consistent with the excess stress model of Tsao and co-workers.