A borehole stability study by newly designed laboratory tests on thick-walled hollow cylinders

At several mineral exploration drilling sites in Australia, weakly consolidated formations mainly consistof sand particles that are poorly bonded by cementing agents such as clay, iron oxide cement or calcite.These formations are being encountered when drilling boreholes to the depth of up to 2 0 0 m. To studythe behaviour of these materials, thick-walled hollow cylinder （TWHC） and solid cylindrical syntheticspecimens were designed and prepared by adding Portland cement and water to sand grains. The effectsof different parameters such as water and cement contents, grain size distribution and mixture curingtime on the characteristics of the samples were studied to identify the mixture closely resembling theformation at the drilling site. The Hoek triaxia! cell was modified to allow the visual monitoring of graindebonding and borehole breakout processes during the laboratory tests. The results showed the significanceof real-time visual monitoring in determining the initiation of the borehole breakout. The sizescaleeffect study on TWHC specimens revealed that with the increasing borehole size, the ductility ofthe specimen decreases, however, the axial and lateral stiffnesses of the TWHC specimen remain unchanged.Under different confining pressures the lateral strain at the initiation point of boreholebreakout is considerably lower in a larger size borehole （2 0 mm） compared to that in a smaller one（10 mm）. Also, it was observed that the level of peak strength increment in TWHC specimens decreaseswith the increasing confining pressure.

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development.In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle(α) reduces the strength of the generalized shear stress and shear strain curves.Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient(b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Simulation on flow, heat transfer and stress characteristics of large-diameter thick-walled gas cylinders in quenching process under different water spray volumes

Cooling strength is one of the important factors affecting microstructure and properties of gas cylinders during quenching process,and reasonable water spray volume can effectively improve the quality of gas cylinders and reduce production costs.To find the optimal water spray parameters,a fluid-solid coupling model with three-phase flow was established in consideration of water-vapor conversion.The inner and outer walls of gas cylinder with the dimensions of d914 mm×38 mm×12000 mm were quenched using multi-nozzle water spray system.The internal pressure,average heat transfer coefficient(have)and stress of the gas cylinder under different water spray volumes during quenching process were studied.Finally,the mathematical model was experimentally verified.The results show that both the internal pressure and have increase along with the increase of spray volume.The internal pressure increases slowly first and then rapidly,but have increases rapidly first and then slowly.To satisfy hardenability of gas cylinders,the minimum spray volume should not be less than 40 m^3/(h·m).The results of stress indicate that water spray quenching will not cause deformation of bottle body in the range of water volume from 40 to 290 m^3/(h·m).

Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.

Reduction of the residual stresses in cold expanded thick-walled cylinders by plastic compression

We suppose that in order to maintain high accuracy of holes and to lower residual stresses after cold expansion of thick-walled cylinders, which undergo cross-section plastic deformation, it is necessary to perform axial plastic compression and subsequent cold expansion with small interferences. To test this hypothesis, we studied hoop, radial and axial residual stresses in cylinders made of carbon steel AISI 1050 with hole diameter of 5 mm, outer diameter of 15 mm and length of 30 mm by Sachs method as well as accuracy of expanded holes. It is found that double cold expansion with total interference equal to 5.1% generates hoop residual stresses with largest absolute value equal to 284 MPa and ensures high holes accuracy(IT7). After plastic compression with strain equal to 0.5 and 1% the mentioned stresses reduced to 120 and 75 MPa respectively,and accuracy of the holes reduced as well. Subsequent cold expansion with small interference equal to 0.9% helps to restore holes accuracy(IT7)gained by double cold expansion and ensure that absolute value of hoop residual stresses(177 MPa) is lower compared to double cold expansion.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Ringlike failure experiment of thick-walled limestone cylinder specimens in triaxial unloading tests

In order to study the failure of surrounding rock under high in situ stress in deep underground engineering projects, disturbed by excavation unloading, we carried out triaxial unloading experiments using thickwalled cylinder specimens on a TATW-2000 rock servo-controlled triaxial testing machine in a laboratory. The specimens were made of limestone material, taken from Tongshan county, Xuzhou city, Jiangsu province, China. In our experiments, rock deformation and failure behavior was studied through loading and unloading of inner hole pressure of thick-walled cylinder specimens. At first, the axial stress, confining pressure and inner pressure were increased simultaneously to a specified designed state of stress. Then, keeping the axial stress and confining pressure stable, the pressure on the inner hole was decreased until the specimen was fractured. When the inner pressure was released completely but the specimen did not fracture, the confining pressure was decreased subsequently until complete failure occurred. Our experimental results suggest that traces of major circular ringlike fractures with a number of radial cracks often appear in thick cylinder walls. This type of ringlike failure phenomenon, similar to intermittent zonal fracturing characteristics of deep exploitation, has, so far, not been published. Our experimental results show that rock deformation and failure behavior of thick-walled limestone cylinders vary under different stress paths between loading and unloading. Tensile failure and orderly failure surfaces occur under unloading conditions while irregular damaged rock blocks are produced during loading failure. This type of triaxial unloading experiment provides for new research methodology and approach for thorough investigations on intermittent zonal fracturing in deep underground excavations.

ANALYTICAL SOLUTION OF AXIAL SYMMETRICAL WALL TEMPERATURE DISTRIBUTION FOR HOLLOW CYLINDER

Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.

Analysis of a functionally graded piezothermoelastic hollow cylinder

A long thick-walled hollow cylinder of piezothermoelastic materials was studied in this work. The gradient prop- erty of the piezoelectric parameter g31 was taken into account. The theory of elasticity was applied to obtain the exact solutions of the cylinder subjected simultaneously to thermal and electric loadings. As an application, these solutions have been success- fully used to study the inverse problems of the material. For comparison, numerical results have been carried out for both graded and double-layered cylinders.

Mechanism of the excitation of single pure mode L（0, 2） and its interaction with the defect in a hollow cylinder

Guided elastic waves have a great potential in pipe inspection as an efficient and low-cost nondestructive evaluation （NDE） technique, among which the wave of mode L（0, 2） receives a lot of attention because this mode is the fastest mode in a weakly dispersive region of frequency to minimize dispersion effects over a long distance and sensitive to the defects distributed circumferentially. Though many experimental and numerical researches have already been carried out about the excitation of L（0, 2） and its interaction with the defect in a hollow cylinder, its excitation mechanism has not been clarified yet. In this paper based on the transient response solution of the hollow cylinder, derived by the method of eigenfunction expansion, the theory about the exciting mechanism of mode L（0, 2） is advanced and the effects of the spatial distribution, vibration frequency and direction of the external force on the excitation are discussed. And the pure mode L（0, 2） is excited successfully under the parameters obtained through theoretical analysis. Furthermore, its interactions with some kinds of defects in hollow cylinders are simulated with the method of finite element analysis （FEA） and the results agree well with those obtained by other researchers.

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young＇s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson＇s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.

Conventional triaxial compression on hollow cylinders of sandstone with various fillings: Relationship of surrounding rock with support

The interaction of surrounding rock with a support system in deep underground tunnels has attracted extensive interest from researchers.However,the effect of high axial stress on tunnel stability has not been fully considered.In this study,compression tests with and without confining pressure were conducted on solid specimens and hollow cylinder specimens filled with aluminium,lead,and polymethyl methacrylate(PMMA)to investigate the strength,deformation and failure characteristics of circular roadways subjected to high axial stress.The influence of the three-dimensional stress on the surrounding rock supported with different stiffness was studied.The results indicate that the strength and peak strain of hollow cylinders filled with PMMA are higher than those of hollow cylinders filled with aluminium or lead,indicating that flexible retaining is beneficial for roadway stability.The results obtained in this paper can contribute to better understanding the support failure of a buried roadway subjected to high axial stress and thus to analyzing and evaluating roadway stability.

Dynamic responses of a multilayer piezoelectric hollow cylinder under electric potential excitation

The dynamic responses of a multilayer piezoelectric infinite hollow cylinder under electric potential excitation were obtained. The method of superposition was used to divide the solution into two parts, the part satisfying the mechanical boundary conditions and continuity conditions was first obtained by solving a system of linear equations; the other part was obtained by the separation of variables method. The present method is suitable for a multilayer piezoelectric infinite hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric electric excitation. Dynamic responses of stress and electric potential are finally presented and analyzed.

Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.

ELASTODYNAMIC SOLUTION OF A NON-HOMOGENEOUS ORTHOTROPIC HOLLOW CYLINDER

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.

A novel specimen preparation method for TJ-1 lunar soil simulant in hollow cylinder apparatus

Conventional methods for hollow cylinder apparatus （HCA） specimen preparation are not applicable for T J-1 lunar soil simulant due to its wide particle size distribution. A novel method to prepare uniform T J-1 specimen for HCA tests is put forward. The method is a combination of the multi-layering dry-rodding method and a new under-compaction criterion in the multi-layer with under-compaction method （UCM）. In the novel method, the specimen is prepared with 5 layers by dry-rodding and the UCM is used to determine the height after each layer is compacted. The density uniformity of specimen is evaluated by the freezing method to find out the best under-compaction criterion. Two HCA specimens with the same target density are prepared by the novel method and examined in the tests of pure rotation of the principal stresses. Their conformable mechanical behaviors ascertain the effectiveness of the method to produce uniform and reproducible HCA specimens. Four groups of HCA tests are carried out to investigate the anisotropic and non-coaxial behaviors of TJ-I lunar soil simulant. The results indicate that the principal stress direction, the deviator stress ratio, the stress level and the coefficient of the intermediate principal stress significantly influence the strength and deformation properties of T J-1 lunar soil simulant.

Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating

In this article, a formulation for a hollow cylinder reinforced with an electroelastic layer is investigated. The hollow cylinder and its electro-elastic coating are under the Saint-Venant torsional loading. First, the solution to the problem containing a Volterra-type screw dislocation is obtained by using the Fourier transform. The problem is then reduced to a set of Cauchy singular integral equations by the distributed dislocation method. Finally, several examples are presented to show the effect of the electro-elastic coating on the reduction of the stress intensity factors at the crack tips.

TRANSIENT THERMAL STRESSES IN AN ORTHOTROPIC HOLLOW CYLINDER FOR AXISYMMETRIC PROBLEMS

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder,one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only.However,additional mathematical difficulties should be encountered and a different solution procedure should be developed.By the separation of variables,the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time,which can be solved efficiently and quickly by the interpolation method.The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads.Numerical comparison is made to show the effect of the axial strain on the displacements and stresses.

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.