A new constitutive law for the nonlinear normal deformation of rock joints under normal load

In view of the deviation of the fitting results of the classical exponential model and the hyperbolic model （the BB model） from several experiment data during intermediate stress period, a new constitutive model for the nonlinear normal deformation of rock joints under normal monotonous load is established with flexibility-deformation method. First of all, basic laws of the deformation of joints under normal monotonous load are discussed, based on which three basic conditions which the complete constitutive equation for rock joints under normal load should meet are put forward. The analysis of the modified normal con- stitutive model on stress-deformation curve shows that the general exponential model and the improved hyperbolic model are not complete in math theory. Flexibility-deformation monotone decreasing curve lying between flexibility-deformation curve of the classical exponential model and the BB model is chosen, which meets basic conditions of normal deformation mentioned before, then a new normal deformation constitutive model of rock joints containing three parameters is established. Two main forms of flexibility-deformation curve are analyzed and specific math formulas of the two forms are deduced. Then the range of the parameters in the g-δ model and the g-2 model and the correlative influence factor in geology are preliminarily discussed. Referring to different experiment data, the validating analysis of the g-δ model and the g-γ model shows that the g-2 model can be applied to both the mated joints and unmated joints. Besides, experiment data can be better fit with the g-2 model with respect to the BB model, the classical exponential model and the logarithm model.

A new apparatus for investigating stress,deformation and seepage coupling properties of rock fractures

A true triaxial apparatus which is composed of three units was presented.The apparatus allows for investigations on deformation and seepage behaviors of a single rock fracture subjected to lateral stress and normal stress.The first unit has three jacks which can apply loads independently in three orthogonal directions.The second unit is used to supply water inflow,control seepage pressure and measure flow velocity in real time.The third unit is for measuring the normal deformation of rock fractures.Some tests for investigating the normal deformation and seepage behaviors of rock fractures subjected to normal and lateral loads on hard granite specimens with an artificial persistent fracture,were introduced.The results show that both the normal deformation and the hydraulic conductivity are influenced not only by the normal stress but also by the lateral stress.It is also shown that the aperture and the hydraulic conductivity decrease with the increasing normal stress but increase with the increasing lateral stress and both the aperture and the hydraulic conductivity obey exponential relationships with the normal stress and the lateral stress.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.