Instability Mode and Movement Characteristics of Dangerous Rock Body in Steep Rock Slope

The cutting relationship and development degree of structural plane control the instability mode and scale of rock slope. The trajectory of rock mass after instability is an important basis for the design of dangerous rock prevention. The back slope of a residential area was investigated in this paper. Based on the survey data of the field structure surfaces, the possible instability mode of the slope rock mass was analyzed by using the stereographic projection method. The shear strength parameters of the rock mass were inverted through the investigation of dangerous rock mass. Finally, ANSYS/LS-DYNA was used to simulate the dangerous rock mass motion trajectory. This study provides a reference for the analysis of the instability process of single rock.

Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate

This paper investigates the origin of flow-induced instabilities and their sensitivities in a flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linear stability and sensitivity problem is formulated in the Eulerian frame by considering the geometric nonlinearity arising from the rotational motion of the cylinder which is not present in the stationary or purely translating stability methodology. This nonlinearity needs careful and consistent treatment in the linearised problem particularly when considering the Eulerian frame or reference adopted in this study that is not so widely considered. Two types of instabilities arising from the fluid–structure interaction are found. The first type of instabilities is the stationary symmetry breaking mode, which was well reported in previous studies. This instability exhibits a strong correlation with the length of the recirculation zone. A detailed analysis of the instability mode and its sensitivity reveals the importance of the flow near the tip region of the plate for the generation and control of this instability mode. The second type is an oscillatory torsional flapping mode, which has not been well reported. This instability typically emerges when the length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode, it is not so closely correlated with the length of the recirculation zone. The sensitivity analysis however also reveals the crucial role played by the flow near the tip region in this instability. Finally, it is found that many physical features of this instability are reminiscent of those of the flapping (or flutter instability) observed in a flow over a flexible plate or a flag, suggesting that these instabilities share the same physical origin.

Radius ratio dependency of the instability of fully compressible convection in rapidly rotating spherical shells

Based on the fully compressible Navier–Stokes equations, the linear stability of thermal convection in rapidly rotating spherical shells of various radius ratios $\eta$ is studied for a wide range of Taylor number $Ta$ , Prandtl number $Pr$ and the number of density scale height $N_\rho$ . Besides the classical inertial mode and columnar mode, which are widely studied by the Boussinesq approximation and anelastic approximation, the quasi-geostrophic compressible mode is also identified in a wide range of $N_\rho$ and $Pr$ for all $\eta$ considered, and this mode mainly occurs in the convection with relatively small $Pr$ and large $N_\rho$ . The instability processes are classified into five categories. In general, for the specified wavenumber $m$ , the parameter space ( $Pr, N_\rho$ ) of the fifth category, in which the base state loses stability via the quasi-geostrophic compressible mode and remains unstable, shrinks as $\eta$ increases. The asymptotic scaling behaviours of the critical Rayleigh numbers $Ra_c$ and corresponding wavenumbers $m_c$ to $Ta$ are found at different $\eta$ for the same instability mode. As $\eta$ increases, the flow stability is strengthened. Furthermore, the linearized perturbation equations and Reynolds–Orr equation are employed to quantitatively analyse the mechanical mechanisms and flow instability mechanisms of different modes. In the quasi-geostrophic compressible mode, the time-derivative term of disturbance density in the continuity equation and the diffusion term of disturbance temperature in the energy equation are found to be critical, while in the columnar and inertial modes, they can generally be ignored. Because the time-derivative term of the disturbance density in the continuity equation cannot be ignored, the anelastic approximation fails to capture the instability mode in the small- $Pr$ and large- $N_\rho$ system, where convection onset is dominated by the quasi-geostrophic compressible mode. However, all the modes are primarily governed by the balance between the Coriolis force and the pressure gradient, based on the momentum equation. Physically, the most important difference between the quasi-geostrophic compressible mode and the columnar mode is the role played by the disturbance pressure. The disturbance pressure performs negative work for the former mode, which appears to stabilize the flow, while it destabilizes the flow for the latter mode. As $\eta$ increases, in the former mode the relative work performed by the disturbance pressure increases and in the latter mode decreases.

The structure of self-sustained instability, transition and turbulence in the separating boundary layer under an internal solitary wave of depression

<p>The development of the separated bottom boundary layer (BBL) in the footprint of a large-amplitude ISW of depression is examined using high-accuracy/resolution implicit Large Eddy Simulation. The talk will focus on a single relatively idealized case of a large-amplitude ISW propagating against an oncoming barotropic current with its own, initially laminar, BBL under the inevitable restriction of laboratory-scale Reynolds number. Significant discussion will be dedicated to the non-trivial computational cost of setting up and conducting the above simulation, within long domains and over long-integration times, in a high-performance-computing environment. Results will focus on documenting the full downstream evolution of the structure of the separated BBL development. Particular emphasis will be placed on the existence of a three-dimensional global instability mode, at the core of the separation bubble where typically one might assume two-dimensional dynamics. The particular instability mode is spontaneously excited and is considered responsible for the self-sustained nature of the resulting near-bed turbulent wake in the lee of the ISW. Fundamental mean BBL flow metrics will then be presented along with a short discussion for potential for particulate resuspension. The talk will close with a discussion of the relevance of the existing flow configuration to both the laboratory and ocean, in light of recent measurements in the NW Australian Shelf.<br><br></p>

Analysis of Instability Mode and Limit Support Pressure of Shallow Tunnel Face in Sands

The stability analysis of the tunnel face is not only essential for guaranteeing the safe construction of urban shallow tunnels, but also directly affecting the influence degree of tunnel construction on nearby structures. The primary concerns in the stability analysis of the tunnel face are the instability mode of surrounding rocks and the limit support pressure on the tunnel face. In this paper, face stability of shallow tunnels in sands was conducted using a symmetrical model test. The ground surface settlement, support pressure on the tunnel face and progressive instability modes of sands at tunnel face are measured by using an LVDT (Linear Variable Differential Transformer) displacement sensor, high-precision pressure sensor and high-definition digital camera, respectively. The test results indicate that the shear failure band appears in sands in front of the tunnel face and develops from the tunnel invert to the tunnel crown. The upper sands undergo stress redistribution, and the pressure arch appears with initial form of “ellipsoid”, then of the “pyramid”. Moreover, the support pressure on the tunnel face experiences four stages, namely, rapid decline stage, the minimum stage, slowly raises stage and stable stage during tunnel excavation. The research results of this paper will provide theoretical support for the reasonable value of the support pressure on the tunnel face in practical engineering.

Study on the Ultimate Supporting Force of Shield Excavation Face Based on Anisotropic Strength Theory

The determination of the ultimate supporting force of the shield excavation face is an important problem to be solved in shield construction. Considering that the tunnel burial depth ratio has a significant effect on the instability mode of the excavation face, the classic “wedge-prism” limit equilibrium model is improved. Based on the rotation effect of principal stress axis, the Casagrande anisotropic strength equation is introduced into the modified limit equilibrium model of “wedge-prism”, and then the limit equilibrium solution of the ultimate supporting force of shield excavation face in anisotropic soil is deduced. Finally, the influence of each calculation parameter on the ultimate supporting force is analyzed by examples. The research results show that the results of the modified “wedge-prism” calculation model proposed in this paper are slightly larger than those of the centrifugal test. If the influence of the instability mode of excavation face and the anisotropy of soil strength on ultimate supporting force of the shield excavation face is not taken into account, the calculation result will be unsafe. The limit supporting force of shield tunnel excavation surface has a simple linear relationship with the anisotropy ratio. When the anisotropy ratio is greater than 1, the ultimate supporting force of shield excavation face decreases first and then tends to be stable with an increase in the buried depth ratio. When the anisotropy ratio is less than 1, the law is reversed. The more obvious the anisotropy of soil strength, the greater the rate of change of ultimate supporting force. The limit supporting force of the shield excavation face decreases linearly with the exertion of loosening earth pressure, linearly decreases with the increase in soil cohesion, and decreases nonlinearly with the increase in the angle of internal friction in soil. The relevant conclusions will provide theoretical guidance for controlling the reasonable chamber pressure of shield tunneling, and ensure the safety of construction.