Study On The Cracking Process Of Rock Using The Extended Finite Element Method

Lots of engineering practices of shale gas, oil, coal-bed methane show that the production is closely related to the propagation and coalescence of fractures inside rock mass. The fracture network provides channels for oil and gas to flow, so the more developed the fracture network is, the more productive the oil and gas will be. On the other hand, the failure of some rock mass is related to initiation, propagation and coalescence of fractures. In consequence, study on the initiation, propagation, branching and coalescence process of fractures has an important significance to the design and construction of oil and gas engineering and rock mass engineering.The extended finite element method was proposed by professor Belytschko in 1999. This method is based on the conventional finite element method which needs cracks to be coincident with mesh lines and fine mesh in the vicinity of the crack tip. These defects are overcomed by the extended finite element method In this dissertation, by using the extended finite element method, some problems related to the cracking process of rock, such as initiation, propagation, and coalescence of fractures, frictional cracks, orthotropic rock mass, fractures at the interface between different type of rocks, and fluid-solid coupling problem are studied systematically and deeply. To effectively simulate the complicated cracking process of rock, some new criteria, algorithms and models are proposed. The main innovative points of this dissertation are as follows:(1) The weighted average of maximum principal tensile stress criterion is proposed and used as a criterion of crack propagation in the extended finite element method. The control parameter a of the shape of the weighted function is suggested to be 1. The comparison with other criteria shows that the maximum circumferential tensile stress criteria, the maximum energy release rate criteria, the minimum strain energy density criterion could result in a zigzag crack path when |KII / KI| is relatively large. On the contrary, crack path predicted by the criterion proposed in the article is smooth and matches well with actual situation.(2) A computational method is presented according to the displacement characteristics of the frictional crack surfaces, in which the displacement in x and y direction are connected through the crack angle. The shear stiffness ktt of the crack surfaces can be obtained by a shearing test. The stiffness matrix of crack surface in the global coordinate will be ready after a coordinate transformation, then assemble the matrix into the global stiffness matrix to figure out the shear displacements of crack surfaces. By adopting this method, iterative calculation of classical contact algorithm can be avoided, and calculation time can also be reduced.(3) Initiation criteria of shearing crack and tensile crack in orthotropic rock are introduced. In this article, strength parameters are assumed to be distributed by a trigonometric function with respect to the angle between the fracture surface and the bedding plane. On this basis, a shear failure factor Fs and a tensile failure factor Ft are defined. For the shearing crack, the corresponding rupture angle of the potential failure surface should lead to a result that Fs is maximal and Fs31. Besides, for the tensile crack, the corresponding rupture angle of the potential failure surface should lead to a result that Ft is minimal and Ft￡ -1.(4) A new enrichment scheme of the crack tip nodes is proposed. All enrichment nodes are enriched by the Heaviside enrichment function, and then to smoothly vanish the Heaviside enrichment to zero at the crack tip, a smooth function in terms of crack local tip Cartesian coordinate tipx* and the local truncation length of the crack ls is given by tip1 cos( /) 2spx l*é -ù? ?. In the proposed enrichment scheme, only two additional degrees of freedom are added at each enrichment node. Besides, the derivation is avoided when calculating shape function derivatives B. Therefore, the calculation time is considerably reduced.(5) After the contrast of mechanisms between hydraulic fracturing and rock blasting, two different numerical simulation models are presented based on the extended finite element method. For the hydraulic fracturing, the Reynolds equation, which is adopted to represent the flowing process of fracturing fluid in the fracture, is discretized by using Galerkin finite element method, and then the coupled equations are solved by the Picard fixed-point iteration method. However, for the rock blasting, turbulent flow equation of high pressure gas inside the fracture is discretized in both time domain and space domain by taking the finite difference method, and the pressure change of the detonation gas is calculated by the JWL equation of state. The reliability of numerical simulation models is verified by means of cases study.(6) A two-dimensional simulation program of rock failure process is developed based on the extended finite element method and numerical models introduced in this dissertation. This program has comprehensive features, simple interface and parallel calculating ability, and is available for the simulation of rock sample indoor tests, rock mass excavation, hydraulic fracturing, rock blasting and other cracking process of rock and rock mass.