displacement discontinuity method

In nature, rocks contain non persistent joints and in rock slope stability analyses it is assumed that discontinuity is persistent, while stress intensity is centralized attips of non-persistent joints and this stress intensity affects the size and orientation of joint growth in rock and also stability of structures created in it such as rock slope. Fracture mechanics is a science that discusses the probability of joints growth and also fracture propagation path. The development of this science provides the possibility of using actual non persistent joints modeling in rock slope stability as well as controlling mechanical behavior of discontinuities especially in crack tips. By creating rock slopes and changing the matrix of regional stress, intensity of stress occurs in joints tips. If this stress overcomes strength parameters of the joint, it will grow and joint propagation will result. One type of failure that occurs in rocky environments due to crack propagation is toppling whose analysis is one of the most difficult problems in aeromechanics. The aim of this study is to model joint propagation by using the principles of rock fracture mechanics, growth and publication ofnon -persistent and random joints in rock slope with potential of toppling failure. An acceptable numerical method for joint propagation modeling that is boundary element method as displacement discontinuity method (DDM) was selected. As a case study tectonic block IV-2 of Choghart open pit mine was selected and3D geometrical model by random disk method by 3DGMMathematica program was simulated and also 2D cross section was prepared. The amount and direction of joint propagation were calculated by applying boundary conditions, in-situ stresses and stiffness matrix. The mechanical model was created according to geomechanical characteristics reported in stability analysis of this wall. Length of linear elements in joints was considered 3m and propagation step applied was 0.2 over the joint length and the model was run typically in four stages of crack growth. Obtained geometrical model contains early and propagation joints can be used in softwares that geometrical model of joints is essential I analysis but the propagation of joint is not available. So the program code can be used as a complementary method for analysis method as key-groups method and distinct element method (UDEC) to analyze the jointed rock mass

Fracturing of rock structures occurs usually under mixed mode I-II loading. The determination of the complete fracture toughness envelopes (KI-KII) for rocks is essential since it may serve as a fracture criterion for crack initiation under mixed mode I-II loadings. A number of methods have been developed to determine the fracture toughness of these modes using different specimen configuration. The Brazilian disk specimens with a central crack is proposed by many researchers for investigating modes I, II, and mixed fracture toughness in brittle materials. In this study, the numerical program (2DFPM) was developed based on the boundary element method (displacement discontinuity method) for studying the fracture propagation on Central Straight through Crack Brazilian Disk (CSCBD) specimens. In-order to enhance the capability and accuracy of the numerical program, special elements (crack tip, and quadratic element) were used. The validity of the program was verified by different analytical and numerical results. The results from numerical analysis show that the inclination angle of the crack with respect to the diametrical load and the crack length have the most important impact on the SIFs (Stress Intensity factor) and fracture propagation path.

Hydraulic Fracturing method was developed to increase the productivity of low permeability reservoirs. In this method، it is very important to predict the hydraulic fracturing geometry to ensure a safe and optimum design. Hydraulic fracture propagation is affected from natural discontinuities (fault، joint…) in fractured reservoirs. In this study، the interaction of hydraulic fracture with natural fractures and consequently the fracture propagation and variation of fluid pressure inside the hydraulic fracture is studied numerically. The numerical program (2DFPM) was developed based on combination of boundary element method (displacement discontinuity method (DDM)) and finite difference method (FDM). The validity of the numerical program was verified by KGD model. Different conditions of hydraulic and natural fracture interaction are modeled and the effect of natural fracture on distribution of fluid pressure profile along the hydraulic fracture length is studied. The results show that the interaction condition and injection parameters of fluid have more influence on the hydraulic fracturing method.

In the jointed rock masses such as rock slopes، the joints considered as cracks in which their tips are the weak points for fracture initiation. Some of the numerical codes for the stability analysis of jointed rock masses have considered only blocks movement on the surfaces of the existing fractures. The tips of these rock joints may act as the fracture creation points and some new discontinuities containing high stress intensity points or plasticity situation may develop. The purpose of this research is to simulate the stable or unstable crack propagation mechanism in the rock bridge area and the cracks coalescence phenomena until the blocks can be created in the fractured rock slopes using linear elastic fracture mechanics (LEFM) theories. Thus، combining the displacement discontinuity based indirect boundary element method (called the higher order displacement discontinuity method) with the maximum tangential stress criterion and programming it by Mathematica software has been used for the crack analysis in this study. The fracture types or modes of fracturing predicted and the crack propagation and cracks coalescence estimated in the rock bridge area for several examples of typical rock slopes. After cracks propagation and coalescence، blocks velocity and shear displacement on new discontinuities obtained as high stress concentration points or plastic mode zones using a distinct element method (UDEC).

Hydraulic fracturing as a method for reservoir stimulation depends on the properties of the media that fracture propagates in it. The elastic properties of layers greatly affect the geometry and propagation of hydraulic fractures. In this research study، the hydraulic fracturing propagation in multi-layered media (stiff and soft) with different elastic properties is investigated. Therefore، boundary element method based on the displacement discontinuity formulation is presented to solve general problems of hydraulic fracturing propagation in layered formations. The crack tip element and a higher order boundary displacement collocation technique are used to increase the accuracy of the method (2DFPM) in modeling of non-homogenous media. The stress intensity factor and tensile stress near the crack tip under different elastic modulus are evaluated to study the hydraulic fracture propagation. Related to the position of the fracture with interface (vertical، intersect and parallel) these factors have different values and finally، they control the fracture propagation. In comparison between the width of fractures in soft and stiff layers، the study displays that the fracture width in soft layers is greater than width of fracture in stiff layers.