Effect of property anisotropy of a rock mass on its stressed state and length of the plastic region of an excavated seam

The solution of the mixed problem of the theory of elasticity for a half plane modeling the stress-strain state of an anisotropic rock mass during the excavation of a seam is constructed. The results of numerical investigation of the length of the neardrift plastic zone of the seam being excavated as a function of the anisotropy of its plastic properties are given. Diagrams showing the stress distribution in the mass are presented.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 38–43, 1987.     

The stress state of rock with an excavation and load-removing slits

We propose a method of determining the stress state of an anisotropic rock with an excavation, including the case in which there are load-removing slits extending to the surface. In cross section the excavation can have an arbitrary curvilinear outline. The rocks have any rectilinear anisotropy, and may have planes of elastic symmetry with an arbitrary inclination to the horizontal plane. The method is based on solving the two-dimensional problem of the theory of elasticity of an anisotropic body using generalized complex potentials, conformal mappings, and the method of least squares. The problem is reduced to solving a system of linear algebraic equations in the unknowns that occur in the complex potentials. We carry out detailed numerical studies on the distribution of stresses and lowering their concentration around the excavation by setting up a system of load-removing slits. The proposed method of studying the stress state of rocks around an excavation both with and without slits and makes it possible not only to establish the zone of high stress concentration, but also to choose the optimal combination and location of load-removing slits. Its application by specialists in the coal industry will make it possible to establish the stability of excavations taking account of their geometric parameters and the depth, length, and location of the load-removing slits, and the physico-mechanical characteristics of the rock. Five figures. One table. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 28–35.     

Modeling of strip mine excavations as dislocations in elastic rock

We propose a new model of excavation in rock based on Volterra dislocations. We develop a software package for determining the stressdeformed state in modeling excavations as dislocations, on the basis of which we study the qualitative properties of the vertical stress field of a solid problem of elasticity theory. Four figures.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 85–91.     

Analytical stress and displacement around non-circular tunnels in semi-infinite ground

The construction of non-circular tunnels at shallow depths is becoming increasingly common to efficiently use excavation space. However, the stress concentration and ground movement are probably much greater around shallow non-circular tunnels than around deep ones; the greater stress and ground movement have significant negative effects on tunnel stability and the safety of nearby structures. This study provides a methodology for obtaining the analytical solutions of ground response induced by non-circular tunnel excavation. The surcharge loadings and gravity induced initial stresses, as well as the internal forces due to liners, are considered in the derivation.Using the Schwartz alternating method combined with complex variable theory, a series of two types of problems on simply connected domain, i.e., a non-circular hole in an infinite plane and a half-plane without holes, is in turn successfully solved. Convergent and accurate analytical solutions are finally achieved by superposing the solutions in all the alternating iterations. The analytical solutions exhibit a close agreement with the numerical results, except for the horizontal displacement along the line near the ground surface. Finally, a parametric study is performed for the elliptical/square tunnel subjected to infinite surcharge loadings.The proposed analytical solutions have great value for the conceptual understanding of the mechanical behavior of non-circular tunnels and for verifying the numerical models. Moreover, an alternative approach is provided for the preliminary designs of future shallow tunnels excavated in rock or medium/stiff clay.     

隧洞围岩应力复变函数分析法中的解析函数求解

利用复变函数理论进行地下任意开挖断面隧洞围岩应力分析的前提,是根据围岩应力边界条件方程推导出两个解析函数．从Harnack定理出发,将隧洞围岩应力边界条件方程转化成积分方程;把Laurent级数有限项表示的映射函数引入积分方程中,将以任意开挖断面为边界条件的解析函数求解转化成以单位圆周线为边界条件的求解问题．对积分方程中各被积函数在讨论域内的解析性进行了分析,在此基础上利用留数理论求解了方程中各项积分值,并获得了用来表示任意开挖断面隧道围岩应力的两个解析函数通式．给出了圆形和椭圆形隧道的两个解析函数求解算例,所获得的结果与文献中的结果一致．利用留数理论推导出的两个解析函数通式,适用于任意开挖断面隧洞的围岩应力解析解的计算,且计算过程更为简单,计算结果更为精确．     

基于曲梁弹性理论的弯曲覆岩变形及应力分析

引入适用于极坐标下曲梁的位移函数,通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上,采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后,采用数值计算方法,分析了煤层开采后弯曲覆岩的位移和应力分布特征,结果表明:1)煤层开采后弯曲覆岩产生下沉变形;弯曲岩层环向位移既有拉伸也有压缩.2)离开切眼不远处径向应力将达到峰值,径向应力由内边界向外逐渐增大;工作面后方不远处环向应力将达到峰值,环向应力较容易引起压缩破断;离开切眼不远处剪应力将达到峰值,对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考.     

A study of the cavities that form in dynamic phenomena in coal mines

We give a classification of the cavities formed by sudden subsidences in the Donbass mines as functions of their shape. We propose a method of computing the maximal extent of the zone of fracture of coal in the direction perpendicular to the face line of the excavation. It is shown that the parameters that characterize the dimensions and location of the cavities that form in actual subsidences in drifts do not exceed the theoretical values obtained from the mathematical model of the process of sudden extrusion. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 98–104.     

Hyperelliptic components of the moduli spaces of quadratic differentials with prescribed singularities

Moduli spaces of quadratic differentials with prescribed singularities are not necessarily connected. We describe here all cases when they have a special hyperelliptic connected component. We announce the general classification theorem: up to the four exceptional cases in low dimensional stratum, any stratum of meromorphic quadratic differentials is either connected, or has exactly two connected components. In this last case, one component is hyperelliptic, the other not.     

基于系统识别方法的围岩弹性模量及水平地应力反演分析

利用有限元软件建立隧道开挖正演模型,基于新奥法隧道施工现场实测围岩收敛数据,采用灵敏度分析建立了参数调整算法,利用系统识别方法对隧道围岩弹性模量及水平地应力进行了反演分析,并讨论了初始值的影响.结果表明,系统识别反演分析法具有自适应能力强、反演分析过程收敛计算稳定性好和计算速度快等优点,在隧道及地下工程领域具有广阔的应用前景.     

A simplified method of computing the process of opening of a parachute

We propose a simplified method of determining the integral characteristics of the opening of a parachute which makes it possible to compute the maximal stress on a parachute and the trajectory parameters of the motion of the load in the region of the opening of the parachute, and to determine the size of the portion of the canopy at the time of maximal stress.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 38–41.     

The stress-strain state of anisotropic rock

We use integrals of Cauchy type and the complex potentials of S. G. Lekhnitskii to solve the problem of the stress-strain state of a piecewise-homogeneous anisotropic rock during the working of a horizontal seam of mineral. We study the stress distribution in the deloaded zones. Three figures, 1 table. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 81–86.     

考虑底部隆起的浅埋隧道围岩压力计算分析

针对浅埋隧道开挖后底部隆起变形现象,应用极限分析上限法构造了考虑底部隆起变形的围岩压力计算模型,结合线性Mohr-Coulomb准则等推导出极限围岩压力的理论表达式。通过约束条件将围岩压力的计算转化为数学中的最优化问题,编制程序进行了优化计算。将计算结果与工程实测数据及文献计算结果进行了对比,验证了当前方法的可靠性。同时,指出在运用极限分析法处理浅埋隧道围岩压力问题过程中应将隧道底部一同考虑,对隧道底部支护会对整个围岩压力产生影响,有助于隧道结构的整体稳定。研究可以为浅埋隧道的开挖、支护提供一定的理论指导.     

Notes on the peripheral volume of hyperbolic 3‐manifolds

We consider orientable hyperbolic 3‐manifolds with either non‐empty compact geodesic boundary, or some toric cusps, or both. For any such M we analyze what portion of the volume of M can be recovered by inserting in M boundary collars and cusp neighbourhoods with disjoint embedded interiors. Our main result is that this portion can only be maximal in some combinatorially extremal configurations. The techniques we employ are very elementary but the result is in our opinion of some interest.     

Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Certain Sums of Squares of Vector Fields

We consider an operator P which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form σ is not constant on Char P. Moreover the Hamilton foliation of the non-symplectic stratum of the Poisson-Treves stratification for P consists of closed curves in a ring-shaped open set around the origin. We prove that then P is analytic hypoelliptic on that open set. And we note explicitly that the local Gevrey hypoellipticity for P is G ^k+1 and that this is sharp.      

Bi-Lipschitz Sufficiency of Jets

We give some theorems of bi-Lipschitz or C ¹ sufficiency of jets which are expressed by means of transversality with respect to some strata of a stratification satisfying the (L) condition of T. Mostowski. This enables us to prove that the number of metric types of intersection of smooth transversals to a stratum of an (a) regular stratification of a subanalytic set is finite.     

基于模糊灰色新陈代谢FGM(1,1)模型预测及应用探讨

巷道围岩变形是煤矿开采普遍存在的问题,巷道开挖过程中围岩会出现破裂现象.主要探讨模糊灰色系统的深部巷道围岩变形预测模型及应用,通过分析模糊数学理论、灰色理论,给出模糊灰色系统预测新陈代谢模型.     

On love waves in a stratified hypoelastic solid with material boundary

Transverse surface waves in a half-space covered with a stratum of a different material are investigated in the context of hypoelasticity of grade zero, taking into account the surface stress effects on the boundary. It is found that the wave motion is possible and that unlike in the corresponding problem with classical boundary, the variation of amplitude in the stratum may be either periodic or exponential. When the amplitude in the stratum is periodic, the motion is similar to that in a stratum bounded on both sides by very deep layers of different elastic or hypoelastic materials.     

Consolidation of a poroelastic sphere: Numerical investigations of Cryer's problem

In geomechanics the consolidation of a fluid-saturated soil is of great interest and many theories have been proposed in the recent years. A special case is the consolidation problem in a porous, fluid-saturated sphere under drainage and hydrostatic pressure. For this configuration Cryer [2] discussed the special effect of pore pressure response. We increase the complexity of the classical approach, taking into account a modified sphere with an undrained layer. This modification is an expansion of the original problem towards more realistic situations of a poroelastic rock which contains a heterogeneity (modified Cryer problem). It results in nearly effective drainage for the heterogeneity and significant differences in momentary stress state. The interaction between the skeleton and the pore fluid of the porous sphere is implemented numerically with Biot's theory of linear consolidation in an u _s-p-formulation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parametrization of the varieties of symmetrizers for operators in finite-dimensional vector spaces

We determine the space that parametrizes the cone of symmetrizers of a semisimple operator with real spectrum in a finite-dimensional vector space. It is proved that the set that determines the cone of symmetrizers is parametrized by the portion of the unit sphere of the vector space lying the first octant.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 1–3.     

Minimal sets for flows on moduli space

LetS be a compact orientable surface, letQ be the moduli space of quadratic differentials onS and letM be a stratum inQ. We explicitly describe the minimal sets for the (Teichmüller) horocycle flow onM and onQ, and show that these correspond to horizontal cylindrical decompositions ofS.