An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

THE DETERMINATION OF AN EQUIVALENT ELASTIC MODULUS FOR BODIES WITH CRACKS BY BOUNDARY ELEMENT METHOD

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.

Flexural rigidity of honeycomb consisting of hexagonal cells

In this study,the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated.It is found that the honeycomb bending can not be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation because the moments acting on the inclined cell wall are different for in-plane deformation and bending deformation.Based on the fact that the inclined wall is twisted under the condition of the rotation angle in both connection edges being zero,a theoretical technique for calculating the flexural rigidity of honeycombs is proposed,and the validity of the present analysis is demonstrated by numerical results obtained by BFM.

Analytical modeling and vibration analysis of fiber reinforced composite hexagon honeycomb sandwich cylindrical-spherical combined shells

This study analyzes and predicts the vibration characteristics of fiberreinforced composite sandwich(FRCS)cylindrical-spherical(CS)combined shells with hexagon honeycomb core(HHC)for the first time based on an analytical model developed,which makes good use of the advantage of the first-order shear deformation theory(FSDT),the multi-segment decomposition technique,the virtual spring technology,the Jacobi-Ritz approach,and the transfer function method.The equivalent material properties of HHC are firstly determined by the modified Gibson’s formula,and the related energy equations are derived for the HHC-FRCS-CS combined shells,from which the fundamental frequencies,the mode shapes,and the forced vibration responses are solved.The current model is verified through the discussion of convergence and comparative analysis with the associated published literature and finite element(FE)results.The effects of geometric parameters of HHC on the dynamic property of the structure are further investigated with the verified model.It reveals that the vibration suppression capability can be greatly enhanced by reducing the ratio of HHC thickness to total thickness and the ratio of wall thickness of honeycomb cell to overall radius,and by increasing the ratio of length of honeycomb cell to overall radius and honeycomb characteristic angle of HHC.

A LINEAR DYNAMIC MODEL DESCRIBING LYMPH CIRCULATION

The lymph circulation plays an important role in interstitial fluid balance, protein transport, and immune system. However, its mechanism is poorly understood, and associated pathologies are mostly untreatable. By following Sungawa＇s method of discussing the heart output, a hemodynamic model of lymph circulation was set up. The model was used to demonstrate how the lymphatic fluid formation, investigate the relationship between the lymph flow rate QL and physiological parameters, and explore how local massage influences QL Computer simulation results show that QL is linearly proportional to the interstitial fluid pressure P~, which is similar to experimental observations. Comparing the simulated value of QL during the massage of different frequency with the experimental data from Ikomi shows that they are identical, which indicates that the presented model is rational to explain the mechanism of massage treatment in traditional Chinese medicine （TCM）.