scholarly journals Study on the Influence of Tectonic Stress on Stability of Horseshoe-Shaped Tunnels

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xin Lv ◽  
Shuzhi Wang ◽  
Yu Qiu ◽  
Xiangxin Liu
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Tectonic Stress ◽  
Structural Stress ◽  
Deformation Characteristics ◽  
Complex Function Theory ◽  
Tunnel Stability ◽  
Deformation State ◽  
Stress Environment ◽  
The Stability

While the tunnel is in the high tectonic stress environment and surrounding rock of tunnel has the characteristics of soft texture and stronger expansion, the preference of tunnel shape is horseshoe. An elastic-plastic model is analyzed by complex function theory in accordance with the deformation characteristics of a horseshoe-shaped tunnel in an engineering site. The numerical model of the tunnel is built by FLAC3D, and the influence of the magnitude and direction of structural stress on the horseshoe-shaped tunnel is studied in detail. Finally, the security support of the tunnel is discussed. Results show that the stress concentration phenomenon is easily focused on the left, right, and bottom sides of the tunnel; these places should therefore be the focus of attention of tunnel stability analysis. The magnitude and direction of tectonic stress greatly affect the stability of the horseshoe-shaped tunnel. Similarly, the magnitude of tectonic stress can significantly affect the deformation state of the tunnel. The direction of tectonic stress mainly reflects the orientation of the tunnel. In addition, the orientation of the tunnel should be arranged along the maximum direction of principal stress.

scholarly journals Interpolation in Fréchet spaces with an application to complex function theory

1993 ◽  
Vol 4 (1) ◽  
pp. 17-26
Author(s):  
Jean Paul Calvi
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Fréchet Spaces ◽  
Complex Function Theory

Complex Function Theory

2021 ◽  
pp. 516-521
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Complex Function Theory

RESEARCH ON COMPLEX FUNCTION THEORY

1963 ◽  
Author(s):  
P. B. Kennedy
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Complex Function Theory

The beginnings of complex function theory

1991 ◽  
pp. 90-107
Author(s):  
Helmut Koch
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Complex Function Theory

Riemann and Complex Function Theory

2021 ◽  
pp. 153-158
Author(s):  
Jeremy Gray
Keyword(s):  
Function Theory ◽  
Complex Function ◽  
Complex Function Theory

The Topological Nature of Two Noguchi Theorems on Sequences of Holomorphic Mappings Between Complex Spaces

1995 ◽  
Vol 47 (6) ◽  
pp. 1240-1252
Author(s):  
James E. Joseph ◽  
Myung H. Kwack
Keyword(s):  
Function Theory ◽  
Riemann Sphere ◽  
Complex Function ◽  
Holomorphic Extension ◽  
Holomorphic Mappings ◽  
Classical Theorem ◽  
Complex Function Theory ◽  
Topological Methods ◽  
Complex Spaces ◽  
Picard Theorem

AbstractLet C,D,D* be, respectively, the complex plane, {z ∈ C : |z| < 1}, and D — {0}. If P1(C) is the Riemann sphere, the Big Picard theorem states that if ƒ:D* → P1(C) is holomorphic and P1(C) → ƒ(D*) n a s more than two elements, then ƒ has a holomorphic extension . Under certain assumptions on M, A and X ⊂ Y, combined efforts of Kiernan, Kobayashi and Kwack extended the theorem to all holomorphic ƒ: M → A → X. Relying on these results, measure theoretic theorems of Lelong and Wirtinger, and other properties of complex spaces, Noguchi proved in this context that if ƒ: M → A → X and ƒn: M → A → X are holomorphic for each n and ƒn → ƒ, then . In this paper we show that all of these theorems may be significantly generalized and improved by purely topological methods. We also apply our results to present a topological generalization of a classical theorem of Vitali from one variable complex function theory.

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