Field-enriched Finite Element Method For Simulating Crack Propagation And Its Application In Geotechnical Engineering

Studying the crack propagation mechanism has certain theoretical guiding significance not only for structural protection in geotechnical engineering,but also for artificially increasing crack network density in the process of oil and gas development to improve oil and gas production.To better explain the process of crack propagation,researchers have continuously proposed various numerical models.Among the numerous numerical methods,extended finite element method and phase field method are two representative numerical methods in discrete crack method and diffusion crack method,respectively.Due to the robustness of simulation results and the completeness of related theories,extended finite element method and phase field method have been widely used to solve the problem of crack fracture.However,the extended finite element method and the phase field method also have their own shortcomings in some simulation cases.For example,the extended finite element method is difficult to characterize branched cracks,crossed cracks and complex crack networks due to the limitation of level set function.When the phase field method is used to simulate the propagation of compression-shear crack in rock materials,it is difficult to get the results matching with the experiment.Based on the above background,combining the characteristics of extended finite element method and phase field method,this paper puts forward a new numerical method called field-enriched finite element method,and applies it to solve several common fracture problems in geotechnical engineering.The research work of this paper is mainly focuses on the following aspects.(1)Firstly,the field-enriched finite element method is proposed to simulate the crack propagation process: in the field-enriched finite element method,the field variables are used to show the crack and characterize the influence of the existence of the crack on the solution model,and the crack initiation and propagation process are predicted by the fracture criterion.At the same time,it can effectively avoid the process of re-meshing and using level set function in crack propagation simulation,and it is easy to realize the representation of complex cracks.The advantages of field-enriched finite element method such as high calculation efficiency,high calculation accuracy and easy implementation are explained theoretically and verified by some numerical examples.Then,the relevant factors affecting the convergence of the simulation results obtained by field-enriched finite element method are studied.Finally,from the perspective of displacement field,stress field and energy conservation,it is proved that it is feasible to approximately replace discrete crack in finite element method with crack represented by field variables.(2)The maximum tensile stress criterion,Mohr-Coulomb criterion and maximum tangential stress criterion are introduced into the calculation frame of field-enriched finite element method.On this basis,the failure process of rock samples with different hole numbers,fractured rock samples under different loading conditions and rock samples with cracks and holes is simulated.According to the different crack generation mechanisms,the coalescence modes of different types of cracks are proposed,and the influence of the geometric position of prefabricated crack distribution on the crack coalescence mode is obtained.(3)The field-enriched finite element model of orthotropic and functionally graded materials is proposed,and the change influence of mechanical parameters with direction and position coordinates is considered.By comparing the simulation results of crack propagation path in constant stiffness composite thin plate,variable stiffness composite thin plate and functionally graded material samples with those of other methods,the validity and accuracy of the model are verified.(4)The field-enriched finite element model of interface crack is proposed.The interaction integral is divided into three types to calibrate the crack tip stress intensity factors in different stages of interfacial crack propagation.The traditional F-criterion is improved,and it is used to predict the interface crack propagation path.The field-enriched finite element model of interface crack is verified from three aspects:stress intensity factor,crack initiation angle and propagation path.(5)The field-enriched finite element method is extended to the three-dimensional situation,the constitutive equation of three-dimensional field-enriched finite element method is established,the three-dimensional interaction integral form is deduced,the enriched mode of field-variables in the three-dimensional model is proposed,the algorithm of three-dimensional crack propagation process is developed,and the three-dimensional crack propagation process under different load types is simulated.(6)By considering the effect of body force in the governing equation,the field-enriched finite element method is applied to engineering case analysis.Through the simulation of slope instability failure and concrete dam cracking process and the analysis of tunnel chamber stability,it is proved that the different types of field-enriched finite element method models proposed in the previous chapters of this paper have the ability to analyze and solve practical problems in engineering.