A numerical study to investigate the influence of surface roughness and boundary condition on the shear behaviour of rock joints

Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures.

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NUMERICAL STUDY OF THE INTERACTION BETWEEN POSITIVE AND NEGATIVE MASS OBJECTS IN GENERAL RELATIVITY

International Journal of Modern Physics D ◽

10.1142/s0218271812500617 ◽

2012 ◽

Vol 21 (07) ◽

pp. 1250061 ◽

Cited By ~ 2

Author(s):

ZHOUJIAN CAO

Keyword(s):

Boundary Condition ◽

General Relativity ◽

Numerical Study ◽

Naked Singularity ◽

Newtonian Limit ◽

Computational Domain ◽

Positive Mass ◽

Negative Mass ◽

Mass Particle ◽

Causal Property

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

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Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank

Journal of Fluid Mechanics ◽

10.1017/s0022112089003095 ◽

1989 ◽

Vol 209 ◽

pp. 249-263 ◽

Cited By ~ 10

Author(s):

Lev Shemer ◽

Eliezer Kit

Keyword(s):

Boundary Condition ◽

Parametric Excitation ◽

Wave Breaking ◽

Model Equation ◽

Numerical Study ◽

Parametrically Excited ◽

Numerical Studies ◽

Scaling Procedure ◽

Long Time ◽

Cross Waves

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.

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Numerical Study on Influence of Joint Characters on Rock Mechanical Parameters

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.201-203.2909 ◽

2011 ◽

Vol 201-203 ◽

pp. 2909-2912

Author(s):

Yan Feng Feng ◽

Tian Hong Yang ◽

Hua Wei ◽

Hua Guo Gao ◽

Jiu Hong Wei

Keyword(s):

Rock Mass ◽

Compression Strength ◽

Numerical Study ◽

Process Analysis ◽

Failure Process ◽

Deformation Modulus ◽

Rock Joints ◽

Structured Surfaces ◽

Trace Length ◽

The Impact

Rock mass is the syntheses composed of kinds of structure and structured surfaces. The joint characters is influencing and controlling the rock mass strength, deformation characteristics and rock mass engineering instability failure in a great degree. Through using the RFPA2D software, which is a kind of material failure process analysis numerical methods based on finite element stress analysis and statistical damage theory, the uniaxial compression tests on numerical model are carried, the impact of the trace length of rock joints and the fault throws on rock mechanics parameters are studied. The results showed that with the gradual increase of trace length,compression strength decreased gradually and its rate of variation getting smaller and smaller, the deformation modulus decreased but the rate of variation larger and larger; with the fault throws increasing, the compression strength first increases and then decreases, when the fault throw is equal to the trace length, the deformation modulus is the largest. When the joint trace length is less than the fault throw, the rate of the deformation modulus is greater than that of trace length, but the deformation modulus was not of regular change.

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