Elastic consolidation around a deep circular tunnel

A method of analysis is presented for the consilidation of a linear elastic soil due to the cutting of a long and deep circular tunnel. Solutions have been obtained for the time dependent displacements and stress changes occurring in the soil surrounding the tunnel opening.     

Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves

Potential function and complex function in the elliptic coordinate system are employed to solve the problem of scattering harmonic plane waves by multiple elliptic cavities in water saturated soil medium. The steady state Biot’s dynamic equations of poroelasticity are uncoupled into Helmholtz equations via given potentials. The stresses and pore water pressures are obtained by using complex functions in elliptic coordinates with certain boundary conditions. Finally, the dynamic stresses for the case of two interacting elliptic cavities are obtained and discussed in details via a numerical example.     

Viscoplastic creep of rocks around a lined tunnel

A rock-support analysis is done assuming that the rock behaves elastic/viscoplastically while the support can be any kind of nonlinear support. The case of circular tunnels is considered and the formulation of the mathematical problem is discussed. Furthermore, the creep of rock around a tunnel with nonlinear supports (called “yieldable” or “self-adapting” supports) to limit the closure of the tunnel is studied. It is shown that the ultimate ground reaction is not unique since it depends on the loading history such as excavation layout and support design. For relatively small pressures exerted by the support, it is shown that the onset of failure by dilatancy can be determined. Two kinds of solutions are given: a simplified approximate one, which is easy to apply and with which the qualitative discussion of the solution is simple and revealing, and a more rigorous general elaborate numerical solution obtained by using computer programs.     

Scattering of long waves around a circular island mounted on a conical shoal

Scattering of simple harmonic long waves by a cylindrical island mounted on a conical shoal in an otherwise open sea of constant depth is solved analytically based on the shallow-water wave (long-wave) theory. The new analytical solution not only confirms some conclusions and conjectures previously drawn from purely numerical studies, such as those showing how the slope of the shoal affects the amplification of the ocean waves around the coastline of islands, but also provides another useful check for numerical model developers.     

Internal waves around a disturbance in a fluid with arbitrary stratification and background shear flow

A three-dimensional ray theory is presented for calculating the phase configuration of internal waves around a moving disturbance in a flow with arbitrary stratification and background shear. The theory is applied to two-dimensional stratified shear flows which have been produced in the laboratory and good agreement is shown between the theoretical and experimental phase configurations. Good agreement is also shown when caustics and critical levels are present. This paper includes the wave systems arising from a combined translation and oscillatory motion of a source and it shows how distinct systems of waves arise from each, type of motion under different background conditions. This paper shows that for two-dimensional steady wave systems the critical level is at a well defined height which is independent of wavenumber but in three dimensions the critical height can in general vary with wavenumber.     

Diffraction of torsional elastic waves by a peripheral edge crack around a spherical cavity

This paper deals with the problem of finding the stress distribution in the neighborhood of a peripheral edge crack in a spherical cavity. The crack is excited by a torsional standing wave.The problem is solved by using integral transforms and is reduced to the solution of a singular integral equation. The solution of this equation is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically.     

Determination of the soil pressure distribution around a cone penetrometer

The objective of this paper was to investigate the pressure distribution around a cone penetrometer using a pressure sensing mat under laboratory conditions. The investigation was conducted under (1) constrained conditions using cylindrical split pipe molds and (2) unconstrained conditions using a soil box. These tests were conducted in Capay clay and Yolo loam soil containing two different moisture conditions and two compaction levels.In the constrained tests, a maximum radial pressure of 111 kPa was observed in the Capay clay soil with 3.4–4.3% d.b. moisture content and three blows of compaction (cone index value of 2040 kPa) when using the 41 mm diameter split pipe mold. These pressure levels decreased to 82 and 22 kPa, respectively, when 65 and 88 mm diameter molds were used. In both the Capay clay and Yolo loam tests, the average radial pressure and average cone index values showed similar trends.In the unconstrained tests, a maximum pressure of 9.0 kPa was observed in the Capay clay with 4.5% d.b. moisture content and three blows of compaction (cone index value of 550 kPa) at a horizontal distance of 25.4 mm from the vertical axis of the cone penetrometer and minimum pressure levels in the range of 0.2–0.3 kPa when the horizontal distance of the penetrometer was in the range of 56.8–66 mm. The pressure levels are much smaller than the ones obtained in the constrained tests and may suggest that the pressure distribution under field conditions is small at a distance of 25.4 mm or higher from the tip of the cone.The experimental data were statistically analyzed to identify significant factors. The results of the analysis for the constrained test indicated that the mold diameter and number of blows significantly increased the pressure readings within the soil mass. Increasing the mold diameter led to a decrease in the average radial pressure and increasing the number of blows contributed to an increase in the average radial pressure. In the unconstrained test, the average radial pressure distribution at a given point were significantly influenced by the horizontal distance of the point from the vertical axis passing through the center of the penetrometer shaft, soil type, and soil moisture content. Higher pressure values were obtained in the Capay clay tests compared to the Yolo loam tests. In all cases, the pressure levels were greater for the drier soil than for the moist soil.     

The phase configuration of the waves around an accelerating disturbance in a rotating stratified fluid

Ray theory is extended to consider the case of an accelerating disturbance which is producing waves in a rotating stratified fluid. Starting from the equations of motion, dispersion relations are derived for surface gravity waves, capillary waves, Rossby waves and internal-inertial waves. The wave system is studied in each case for the problem of a body starting impulsively from rest and for a body starting from rest and moving with constant acceleration.     

Diffraction of solitary water waves around three-dimensional floating bodies

By using the matched asymptotic expansion method and the idea of edge layer, a mathematic model for describing the interaction between weakly nonlinear shallow-water waves and three-dimensional floating bodies is formed in the paper. As a numerical example, the diffraction of a solitary wave around a vertically floating circular cylinder has been investigated and the results are presented. The present method can further be extended to the study of wave diffraction around floating bodies of general shape. The project is supported by the National Natural Science Foundation of China.     

Centered simple waves for the two-dimensional pseudo-steady isothermal ?ow around a convex corner

The two-dimensional(2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.     

Uniform approximation to surface gravity waves around a breakwater on water of variable depth

The linear surface gravity wavefield around a breakwater and on water of varying depth is described by a uniform asymptotic representation. The scattering of not necessarily irrotational wave packets generated by sources at arbitrary distance from the breakwater can be treated with the technique here expounded.     

Shear-horizontal (SH) surface waves propagating around stratified piezoelectric cylinders

Theoretical results describing the properties of SH (shear-horizontal) surface waves propagating around piezoelectric cylinders with superimposed layers are presented. Mode orthogonality, virial theorem and equality between group and energy velocities are proved. Integral formulas for the energy velocity are much more compact than the differential expressions for the group velocity, and this provides a convenient way for computing the latter. The results obtained are illustrated by numerical calculations and graphs for a set of typical cylindrical waveguides.     

Photoelastic simulation of the stress wave field around a tunnel in an anisotropic rock mass subject to shock load

The stress wave field around a tunnel in an anisotropic medium subject to shock load is analyzed using the dynamic photoelastic method. The influence of various factors on the distribution and magnitude of boundary stresses around the tunnel are studied by simulating the deformation process. The time dependence of the dynamic stress concentration factor on the tunnel walls is established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 122–125, August 2006.     

爆炸作用下土体隧道衬砌结构的动力响应

为了找出爆炸动力作用下的隧道衬砌结构薄弱部位和力学规律,建立了土体隧道动力分析整体有限元模型;利用显式动力有限元程序Ansys/Ls-dyna进行了数值模拟,探讨了土体隧道衬砌结构在爆炸作用下不同部位的时间历程曲线;分析了爆炸作用下土体隧道衬砌结构的动力响应。结果显示:隧道衬砌结构肩部在x、y方向的位移都较大;隧道衬砌结构顶部在y方向的位移较大;隧道衬砌结构顶部、肩部的加速度峰值最大并且加速度曲线均出现了两次或多次峰值。这反映了爆炸冲击波有比较强烈的多次反射;各部位压力时程曲线波动较大,按照肩部、顶部、胯部、底部、腰部的顺序先后到达峰值;顶部和肩部σx峰值最大,顶部和底部σy峰值最大,顶部、肩部、底部τmax峰值最大。顶部和肩部出现最大拉应力说明爆炸对拱顶拱肩损伤较大,隧道衬砌结构将会最先在这两处发生破坏。     

Computation of free surface waves around an arbitrary body by a Navier-Stokes solver using the psuedocompressibility technique

A Navier-Stokes equation solver is developed for computing free surface wave and viscous flow around an arbitrary body, in which a free surface model is introduced into the pseudocompressibility solution. The governing equations are classified in a vectorial form, with primitive variables, and a block diagonal system is generated by the discretization of an implicit factorization method. A moving grid system fitted to both the free surface and body surface is generated by an effective cubic spline fitting technique. Two zero-equation turbulence models, namely the Cebeci-Smith model and the Baldwin-Lomax model, are used for turbulent calculations. Numerical simulations are carried out for the free surface viscous flows generated by a submerged hydrofoil and a ship model. Computed results are in reasonable agreement with measurements.     

爆破地震波作用下城市隧道结构动力响应的敏感性

选取纵波作为研究对象,采用波函数展开法,推导了无限弹性介质中复合衬砌结构隧道在爆破地震波作用下动力响应问题的解析解,结合南京红山南路隧道群开挖工程开展了隧道结构动应力集中因数的敏感性分析,并通过曲线拟合分别得到了隧道围岩及内衬环向动应力集中因数随隧道结构动力学及几何参数变化的回归方程。分析结果表明:隧道围岩和二次衬砌层的弹性模量及围岩泊松比对考察点处环向动应力的影响较大,而初期支护层弹性模量的影响几乎可以忽略不计;衬砌层厚度变化对围岩环向动应力的影响要远大于内衬,在隧道施工设计时可以通过增加衬砌层的厚度平衡隧道结构的受力状态,但增加初期支护层的效果不如二次衬砌层。     

Elastic waves in a turbulent fluid

It is shown that a turbulent flow can support elastic waves for which the fluctuating stress is essentially proportional to the strain field. These fluctuations are described by a hyperbolic system and hence they do not decay away from a solid boundary. Their behaviour is also consistent with Taylor's frozen field hypothesis that turbulent fluctuations are advected with the local mean flow speed.     

Effect of imperfect bonding on axisymmetric elastodynamic response of a lined circular tunnel in poroelastic soil due to a moving ring load

A two-dimensional elasticity analysis for steady-state axisymmetric dynamic response of an arbitrarily thick elastic homogeneous hollow cylinder of infinite length, which is imperfectly bonded to the surrounding fluid-saturated permeable formation, subject to an axially moving ring load, is presented. The problem solution is derived by using Biot’s dynamic theory of poroelasticity in conjunction with double Fourier transformation with respect to time (frequency) and axial coordinate (axial wave number). The analytical results are illustrated with numerical examples in which a concrete tunnel lining of uniform wall thickness is imperfectly bonded to a surrounding water-saturated poroelastic formation of soft/stiff frame characteristic. Numerical solutions for the radial shell mid-plane and formation displacements are calculated by analytical (numerical) inversion of the Fourier transformation with respect to the frequency (axial wave number). Primary attention is focused on the influence of bonding condition at the liner/soil interface, formation material type, and load velocity on the system’s dynamic response. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.