Cavity In Half-space Research Articles

Scattering of SH waves by a scalene triangular hill with a shallow cavity in half-space

Scattering of SH waves by a scalene triangular hill with a shallow cavity in half-space

Scattering of SH waves by a non-symmetrical V-shaped canyon with a shallow cavity in half-space

Both surface motion and hole stress concentration have always been concerned in engineering design. In this paper, a theoretical approach is used to study the scattering problem of circular cavities under a non-symmetrical V-shaped canyon. The wave displacement function is obtained by solving the Helmholtz equation that meets the zero-stress boundary conditions by adopting the method of separation of variables and the symmetric method. Based on the complex function method, multi-polar coordinate method and region-matching technique, algebraic equations are established at relevant conditions, which include auxiliary and free boundary conditions. Then, according to sample statistics, a least-square method is used instead of the Fourier expansion method to solve the undetermined coefficients of the algebraic equations by discrete boundary. Numerical results show that the theoretical method is verified valid by the finite element method and the reduced model, and the displacement of the free surface and the stress of the circular cavity are related to the shape of the canyon, the position of the circular cavity, the direction of the incident wave and the frequency content of the excitation.

Analytical solution to the SH wave scattering problem caused by a circular cavity in a half space with inhomogeneous modulus

In this work, the scattering problem of SH wave caused by circular cavity in half space with inhomogeneous shear modulus is solved. The shear modulus is assumed to vary in two dimensions. Based on the complex function theory and conformal mapping technique, the analytical expressions of the displacement field and stress field in half space are obtained. The unknown coefficient is determined according to the boundary condition. The numerical results show that the inhomogeneous parameters, the reference wave number, and the buried depth of the cavity have obvious effects on the displacement amplitude of the horizontal surface and the stress concentration around the circular cavity.

Upper and lower bound solutions for pressure-controlled cylindrical and spherical cavity expansion in semi-infinite soil

Previous cavity expansion analyses are all performed in infinite soil. However, cavity expansion problem in half space (or semi-infinite soil) is also required in geotechnical engineering (tunneling and compaction grouting). New upper and lower bound solutions are derived for expanded spherical and cylindrical cavities in half space of Tresca soil based on the method of finite element limit analysis in this paper. Two types of case, namely homogenous soil and non-homogenous soil with undrained strength linearly increased with depth, are consider in the analysis. Simple empirical closed-form equations are then proposed for predicting the limit cavity expansion pressure through nonlinear regression analysis. The present solutions provide theoretical reference for the corresponding geotechnical engineering problems such as tunneling and compaction grouting.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.

Diffraction of plane SH waves by a semi-circular cavity in half-space

This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.

Scattering of SH Wave by an Interacting Mode III Crack and a Circular Cavity in Half Space

Scattering of SH wave by an elastic half space with a circular cavity and a crack in any position and direction is studied with Green’s function, complex function and multi-polar coordinate method. First, a suitable Green’s function is constructed, which is the fundamental solution of the displacement field for a half space with a circular cavity impacted by an out-plane harmonic line source loading at an arbitrary point in half space. Then a crack in any position and direction is constructed by means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular cavity and crack, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. According to numerical examples, the influences of different parameters on DSIF are discussed.

Scattering of SH-wave by multiple circular cavities in half space

In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circular cavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave function and method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for case with two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.