Application of Hyperstatic Reaction Method for Designing of Tunnel Permanent Lining, Part II: 3D Numerical Modelling

Underground structures often have abrupt changes in structural stiffness or ground conditions such as junctions of tunnels, tunnel portal in slopes, and niches in road tunnels. At these locations, stiffness differences may subject the structure to differential movements and generate stress concentrations. Because of adversity in these issues, they need a three dimensional analysis. This paper proposes a numerical approach to the hyperstatic reaction method (HRM) for three dimensional analysis of permanent tunnel linings. In this paper, three dimensional numerical modelling is performed by considering hyperstatic reaction concepts. Designing is done for Manjil-Rudabar freeway project, Tunnel No. 2. The numerical analyses performed for Operational Design Earthquake (ODE) and Maximum Design Earthquake (MDE) loading conditions. Then interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. The numerical results show that although more axial forces are created in tunnel lining for ODE condition, but the points in the P-M diagrams are located in the furthest distance to the diagram border (tunnel supporting system); because of less bending moment in this condition. Therefore, the safety factor in ODE condition is more than MDE condition. This numerical processing presented that the HRM is a proper, fast, and practical method for tunnel designers

Application of Hyperstatic Reaction Method for Designing of Tunnel Permanent Lining, Part I: 2D Numerical Modelling

The increase of bored tunnels in the entire world has raised the question how to design the tunnel structure in an efficient way. This paper proposes a numerical approach to the Hyperstatic Reaction Method (HRM) for analysing permanent tunnel linings. The permanent tunnel lining is known as main structure of tunnel maintenance during the time. The HRM is one of the analysis methods for tunnel lining in long term. In this paper, two dimensional numerical modelling is performed by considering hyperstatic reaction concepts. Loading is done after the calculation of long term loads, and ground reaction is simulated by springs. Designing is done for Manjil-Rudabar freeway project, Tunnel No. 2. The numerical analyses were performed for Operational Design Earthquake (ODE) and Maximum Design Earthquake (MDE) loading conditions. A new simplified approach is used for considering the effect of earthquake loading on the tunnel lining. Then, an interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. The thickness of tunnel lining and armature are calculated for three sections based on induced forces in tunnel lining. These forces were different in every section according to the load combinations, rock mechanics properties, lining properties, and overburden.  The numerical results showed that the forces in tunnel lining for MDE condition is approximately 50% more than ODE condition in earthquake loading. This numerical processing presented that the HRM is a proper, fast, and practical method for designing and analysing the tunnel lining

Scaling Geological Fracture Network from a Micro to a Macro Scale

Characterizing fracture systems at various scales, modeling fracture distributions, and clarifying scale relations that correlate total fracture systems are of paramount importance in geology, mining, civil engineering, and petroleum engineering. In this paper, the conditions of fracture network geometry are investigated in a field scale (about 100 m) and a core sample scale (several centimeters). To achieve this purpose, field surveys and coring of rock outcrops were performed in the Asmari Formation of Iran. Fractures were manually sampled from rock outcrops on the field scale while micro-fractures were surveyed using CT-scan images of core samples on a small scale. To compare the fracture network geometry, two perspectives of fractal dimensions and orientation of fractures were used. The results showed that the fractal dimension has the same value in both field and core scales and the orientation of the fractures is similar in both scales. Therefore, it can be claimed that in the Asmari Formation of Iran the structure of the fracture network is similar in two studied scales

Geomechanical key parameters of the process of hydraulic fracturing propagation in fractured medium

International audienceHydraulic Fracturing (HF) is a well-stimulation technique that creates fractures in rock formations through the injection of hydraulically pressurized fluid. Because of the interaction between HF and Natural Fractures (NFs), this process in fractured reservoirs is different from conventional reservoirs. This paper focuses mainly on three effects including anisotropy in the reservoir, strength parameters of discontinuities, and fracture density on HF propagation process using a numerical simulation of Discrete Element Method (DEM). To achieve this aim, a comprehensive study was performed with considering different situations of in situ stress, the presence of a joint set, and different fracture network density in numerical models. The analysis results showed that these factors play a crucial role in HF propagation process. It also was indicated that HF propagation path is not always along the maximum principal stress direction. The results of the numerical models displayed that the affected area under HF treatment is decreased with increasing the strength parameters of natural fracture and decreasing fracture intensity

A 3D numerical modeling of polyethylene buried pipes affected by fault movement

The large and sustainable deformations of ground and fault movement are the most serious threats for buried pipelines. Heavy damages resulting from the rupture of buried pipes have caused many researchers analyze this issue in the recent years. In this study, the impact of fault movement on the buried polyethylene pipes was investigated. Initially, numerical results were validated based on the fault test results. The fault movement was simulated using Finite Difference Method (FDM). The numerical results were in good agreement with the experimental results. Next, a sensitivity analysis was performed for various parameters of buried depth, the angle of fault, and the fault vertical displacement. The results showed that axial forces and bending moments in the pipe enhance by increasing each of these parameters. It was also observed that the induced horizontal and vertical displacements exceed the tolerance of connections and they will be disrupted at the location of fault movement. Keywords: Polyethylene buried pipes, Fault movement, Numerical modeling, FD

Determination of the Fractal Dimension of the Fracture Network System Using Image Processing Technique

Fractal dimension (FD) is a critical parameter in the characterization of a rock fracture network system. This parameter represents the distribution pattern of fractures in rock media. Moreover, it can be used for the modeling of fracture networks when the spatial distribution of fractures is described by the distribution of power law. The main objective of this research is to propose an automatic method to determine the rock mass FD in MATLAB using digital image processing techniques. This method not only accelerates analysis and reduces human error, but also eliminates the access limitation to a rock face. In the proposed method, the intensity of image brightness is corrected using the histogram equalization process and applying smoothing filters to the image followed by revealing the edges using the Canny edge detection algorithm. In the next step, FD is calculated in the program using the box-counting method, which is applied randomly to the pixels detected as fractures. This algorithm was implemented in different geological images to calculate their FDs. The FD of the images was determined using a simple Canny edge detection algorithm, a manual calculation method, and an indirect approach based on spectral decay rate. The results showed that the proposed method is a reliable and fast approach for calculating FD in fractured geological media

Discrete Element Simulation of Interaction between Hydraulic Fracturing and a Single Natural Fracture

Hydraulic fracturing (HF) treatment is performed to enhance the productivity in the fractured reservoirs. During this process, the interaction between HF and natural fracture (NF) plays a critical role by making it possible to predict fracture geometry and reservoir production. In this paper, interaction modes between HF and NF are simulated using the discrete element method (DEM) and effective parameters on the interaction mechanisms are investigated. The numerical results also are compared with different analytical methods and experimental results. The results showed that HF generally tends to cross the NF at an angle of more than 45° and a moderate differential stress (greater than 5 MPa), and the opening mode is dominated at an angle of fewer than 45°. Two effects of changing in the interaction mode and NF opening were also found by changing the strength parameters of NF. Interaction mode was changed by increasing the friction coefficient, while by increasing the cohesion of NF it was less opened under a constant injection pressure