Stabilization of Deep Roadways in Weak Rocks Using the System of Two-level Rock Bolts

Large rock mass deformation around deep roadways in the weak rocks was a significantproblem in mining activities in Vietnam and other countries. The excavation of roadways leads to highreleasing stress, which exceeds the peak strength of spalling surrounding rock and causes it to enter thepost-failure stage. Tensile failures then initiate and develop around the roadways, which causes thefragmentation, dilation, and separation of surrounding rock. The capacity of the primary support systemis low, which results in a severe contraction in the whole section of roadways, which requires findingsolutions to prevent the deformation of rock mass around roadways and technical solutions fromstabilizing for deep roadways. To stability analysis of roadways can be applied analytical, experimental,semi-experimental, and numerical methods. This paper introduces the prevention mechanism of largedeformation of rock mass around roadways using 2-level rock bolts. The research results show that usingthe system of two-level rock bolts can reduce the values of tensile stress on the boundary of roadwaysrange from 10 to 15% compared with only one. The importance of the total displacement of rock mass onthe boundary of roadways will be reduced from 3.47 to 13.85% using six long cable bolts.

FORMATION OF CRUSHING ZONE AT THE LEVEL OF TAMPING IN THE CONDITIONS OF MASS EXPLOSIONS

The purpose of the work is to study the sequence of formation of the fracture zone in the area of the array above the ends of the system of adjacent charges in connection with the technological parameters of their mutual location. The task of works is the analytically substantiate the dependence of the value of the undamaged area of the array at the level of the bottomhole on the parameters of the system of downhole charges, taking into account the phenomenon of the edge effect. Research results. Data on the dimentions of the part of the massif in the lborewhole that does not participate in the mass deformation motion of the rock during the formation of adjacent downhole funnels are obtained. It is assumed that this area between adjacent charges is the source of the oversized fraction. Originality. The process of formation of the destroyed zone in space above the end of the boreholeis considered step by step: generation of the shock wave front, the symmetry of which is close to spherical, formation of the loosenning funnel system in the second stage, which does not adjacent charges of the total front of the stress wave from the explosion of downhole charges detonated from their bottom. Behind him moves the deformation front of a complex structure. It is assumed that this front in the system of two adjacent charges acquires a shape similar to a vertical wedge inverted by the base towards the free surface. The expected result of such a step-by-step deformation process is the desired degree of crushing of the rock mass at the level of the tamping. Conclusions and practical implications. Theoretically and calculatedly obtained and recommended rational parameters of the location of the system of well charges of limited length to reduce the size of the non-destructive region of the rock mass at the level of the tamping, which improves the design of mass explosions in mountain slopes.

Supersymmetry breaking deformations and phase transitions in five dimensions

We analyze a recently proposed supersymmetry breaking mass deformation of the E1 superconformal fixed point in five dimensions which, at weak gauge coupling, leads to pure SU(2) Yang-Mills and which was conjectured to lead to an interacting CFT at strong coupling. We provide an explicit geometric construction of the deformation using brane-web techniques and show that for large enough gauge coupling a global symmetry is spontaneously broken and the theory enters a new phase which, at infinite coupling, displays an instability. The Yang-Mills and the symmetry broken phases are separated by a phase transition. Depending on the structure of the potential, this can be first or second order.

On the compactification of 5d theories to 4d

We study general properties of the mapping between 5d and 4d superconformal field theories (SCFTs) under both twisted circle compactification and tuning of local relevant deformation and CB moduli. After elucidating in generality when a 5d SCFT reduces to a 4d one, we identify nearly all $$ \mathcal{N} $$ N = 1 5d SCFT parents of rank-2 4d$$ \mathcal{N} $$ N = 2 SCFTs. We then use this result to map out the mass deformation trajectories among the rank-2 theories in 4d. This can be done by first understanding the mass deformations of the 5d$$ \mathcal{N} $$ N = 1 SCFTs and then map them to 4d. The former task can be easily achieved by exploiting the fact that the 5d parent theories can be obtained as the strong coupling limit of Lagrangian theories, and the latter by understanding the behavior under compactification. Finally we identify a set of general criteria that 4d moduli spaces of vacua have to satisfy when the corresponding SCFTs are related by mass deformations and check that all our RG-flows satisfy them. Many of the mass deformations we find are not visible from the corresponding complex integrable systems.

SU(N) q-Toda equations from mass deformed ABJM theory

It is known that the partition functions of the U(N)k × U(N + M)−k ABJM theory satisfy a set of bilinear relations, which, written in the grand partition function, was recently found to be the q-Painlevé III3 equation. In this paper we have suggested that a similar bilinear relation holds for the ABJM theory with $$ \mathcal{N} $$ N = 6 preserving mass deformation for an arbitrary complex value of mass parameter, to which we have provided several non-trivial checks by using the exact values of the partition function for various N, k, M and the mass parameter. For particular choices of the mass parameters labeled by integers ν, a as m1 = m2 = −πi(ν − 2a)/ν, the bilinear relation corresponds to the q-deformation of the affine SU(ν) Toda equation in τ-form.

Flavor symmetry of 5d SCFTs. Part II. Applications

In Part I of this series of papers, we described a general method for determining the flavor symmetry of any 5d SCFT which can be constructed by integrating out BPS particles from some 6d SCFT compactified on a circle. In this part, we apply the method to explicitly determine the flavor symmetry of those 5d SCFTs which reduce, upon a mass deformation, to some 5d$$ \mathcal{N} $$ N = 1 gauge theory carrying a simple gauge algebra. In these cases, the flavor symmetry of the 5d gauge theory is often enhanced at the conformal point. We use our method to determine this enhancement.