Rock Stress Around Noncircular Tunnel: a New Simple Mathematical Method

2017 ◽  
Vol 9 (6) ◽  
pp. 1330-1346 ◽  
Author(s):  
Wenlong Shen ◽  
Xiangyu Wang ◽  
Jianbiao Bai ◽  
Wenfeng Li ◽  
Yang Yu
Keyword(s):  
Mathematical Method ◽  
Horizontal Stress ◽  
Rock Stress ◽  
Stress Monitoring ◽  
Change Rate ◽  
Mechanical Boundary Condition ◽  
Vertical Boundary ◽  
Horizontal Boundary ◽  
Boundary Load ◽  
Rectangular Tunnel

AbstractA new simple mathematical method has been proposed to predict rock stress around a noncircular tunnel and the method is calibrated and validated with a numerical model. It can be found that the tunnel shapes and polar angles affect the applicable zone of the theoretical model significantly and the applicable zone of a rectangular tunnel was obtained using this method. The method can be used to predict the values of the concentrated stress, and to analyze the change rate of rock stress and back to calculate the mechanical boundary condition in the applicable zone. The results of the stress change rate indicate that the horizontal stress is negatively related to the vertical boundary load and positively related to the horizontal boundary load. The vertical stress is negatively related to the horizontal boundary load and positively related to the vertical boundary load. These findings can be used to explain the evolution of the vertical increment in stress obtained with field-based borehole stress monitoring.

scholarly journals Model Experimental Study on Stress Transfer and Redistribution in a Clay Landslide under Surcharge Load

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Heng-Jun Hou ◽  
Bo Wang ◽  
Quan-Xiang Deng ◽  
Zheng-Wei Zhu ◽  
Feng Xiao
Keyword(s):  
Slip Surface ◽  
Process Analysis ◽  
Stress Transfer ◽  
Horizontal Stress ◽  
Vertical Stress ◽  
Transfer Efficiency ◽  
Stress Monitoring ◽  
Stress Growth ◽  
Stress Variation ◽  
Two Stages

Stress transfer and redistribution always accompany with the evolution of landslides. However, previous literature studies have mainly focused on stages of stress variation, and far too little attention has been paid to detailed transfer and redistribution process analysis on stress variation. In this paper, a large-scale clay model slope with masonry slide bed and prefabricated cambered slip surface was constructed. Earth pressure cells were embedded into slip mass to monitor vertical and horizontal stresses in different parts of the test soils under the set load sequence. Stress transfer efficiency (STE) indicators based on qualified stress monitoring datasets (tested by Shapiro-Wilk method) were established to quantify the stress transfer process. Staged development of stress inside the clay slope was analyzed through extracting slopes of stress curves and limit loads. The stress redistribution process was analyzed using STE and deflection of stress isolines derived from numerical simulation. Moreover, to study the influence of loading position on stress variation, geometry partitioning has also been discussed. Results showed that vertical and horizontal stresses had different growth trends on both sides of 80 kN and 60 kN, respectively. Horizontal stress growth has two stages; vertical stress growth has two stages in soils close to slope surface and shear outlet, while there are three stages in other soils. Vertical stress transfer efficiency (VSTE) and horizontal stress transfer efficiency (HSTE) are recommended to quantify stress transfer and redistribution process. Based on VSTEs and HSTEs, the slip mass could be partitioned into three parts: loading zone, transfer zone, and free zone. Deflecting amplitudes of stress isolines were in consistency with the results revealed by STEs.

scholarly journals Fractal Characterization of Complex Hydraulic Fractures in Oil Shale via Topology

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1123
Author(s):  
Qiang He ◽  
Bo He ◽  
Fengxia Li ◽  
Aiping Shi ◽  
Jiang Chen ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Stress Ratio ◽  
Fractal Theory ◽  
Horizontal Stress ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fluid Viscosity ◽  
Fracture Networks ◽  
Change Rate ◽  
Complex Fracture

The formation of complex fracture networks through the fracturing technology is a crucial operation used to improve the production capacity of tight gas/oil. In this study, physical simulation experiments of hydraulic fracturing were conducted with a true triaxial test system on cubic shale oil samples from the Yanchang Formation, China. The fractures were scanned by CT both before and after the experiments and then reconstructed in 3D. The complexity of fracture networks was investigated quantitatively by the fractal theory with topology. Finally, the effect of the horizontal stress ratio, fluid viscosity, and natural fractures on the complexity of the fracture networks was discussed. The results indicate that the method based on fractal theory and topology can effectively characterize the complexity of the fracture network. The change rates of the fractal dimension (K) are 0.45–3.64%, and the fractal dimensions (DNH) of the 3D fracture network after fracturing are 1.9522–2.1837, the number of connections per branch after fracturing (CB) are 1.57–2.0. The change rate of the fractal dimension and the horizontal stress ratio are negatively correlated. However, the change rate of the fractal dimension first increases and then decreases under increasing fluid viscosities, and a transition occurs at a fluid viscosity of 5.0 mPa·s. Whether under different horizontal stress ratios or fluid viscosities, the complexity of the fracture networks after fracturing can be divided into four levels according to DNH and CB. Complex fracture networks are more easily formed under a lower horizontal stress ratio and a relatively low fluid viscosity. A fracturing fluid viscosity that is too low or too high limits the formation of a fracture network.

Linear Discriminatory Analysis: A Patient Classifying for Research and Production Control

1971 ◽  
Vol 10 (02) ◽  
pp. 96-102 ◽  
Author(s):  
B. HALLEN ◽  
P. HALL ◽  
H. SELANDER
Keyword(s):  
Mathematical Method ◽  
Medical Information ◽  
Production Control ◽  
Human Ability ◽  
Discriminatory Analysis

Administrative and medical information about the patient forms, in each case, a pattern, the complexity of which increases as the number of data grows. Even when the data are 4—5 in number, the human ability to recognize and distinguish between different patterns begins to fail, A mathematical method (linear discriminatory analysis) has been worked out. This system of analysis appears to provide opportunities of placing patients with the same or similar patterns in classes which are diagnostically, prognostically or therapeutically homogeneous.

Mathematical Method to Unfolding Couplings

2019 ◽  
Vol 17 (17) ◽  
pp. 63-64
Author(s):  
Carmen Popa ◽  
Ivona Petre ◽  
Ruxandra-Elena Bratu
Keyword(s):  
Mathematical Method ◽  
Mathematical Methods ◽  
Intersection Curves ◽  
Four Cylinders

AbstractThe purpose of this paper is to establish the intersection curves between cylinders, using Mathematica program. The equations curves which are inferred by mathematical methods are introduced in this program. This paper takes into discussion the case of four cylinders.

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