Study On Static And Dynamic Fracture Behavior Of Cracked Rock Mass Based On Field-enriched Finite Element Method

Rock masses are subjected to external forces,such as complex tectonic stress,resulting in many natural joints and fissures.These internal defects are dominant factors affecting the stability and security of geotechnical engineering,which has attracted great attention in the field of geotechnical engineering.In this paper,a novel numerical method,namely field-enriched finite element method(FE-FEM),is proposed,which connects fracture mechanics with continuous damage mechanics to simulate the fracture evolution process and failure mechanism of rock masses.More specifically,the damage variable is employed to distinguish the broken zone and unbroken zone of rock masses,and the mechanical equilibrium equation of damaged material is established.In addition to the displacement field,a damage field is introduced to degrade the stiffness in the constitutive model through the degradation function,equivalent to discrete cracks and affecting the distribution of displacement field.According to the specific research problems,the appropriate fracture criteria can be selected to determine the crack propagation.The “exponential distance weighting method” is employed to calculate the damage field,and two kinds of searching strategies are proposed to track the smeared crack zone,namely box and circular domain searching strategies,to complete the enrichment of the damage field.Neither a description of crack through the level set,nor the enrichment functions adopted to deal with various crack problems is needed in the proposed numerical method,which greatly improves the programming efficiency;spurious cracks are not easy to appear at the loading point,reducing the sensitivity of damage evolution.In this paper,the field-enriched finite element method is adopted to study the fracture evolution mechanism of cracked rock masses under static and dynamic loads.The following studies have been carried out:(1)Benchmark examples are employed to verify the ability of the FE-FEM in dealing with I-and II-modes cracks,and the study of parameter convergence is conducted to explore the influence of different model parameters on the numerical results.Through the numerical tests of diagonally loaded square plate and pre-cracked disc in radial compressive loading,the ability of the proposed field-enriched finite element method to handle the propagation evolution of mixed-mode cracks in different specimen configurations is validated.The effects of geometry and loading conditions of three SCB test configurations on crack paths and fracture parameters are investigated.(2)An intersection strategy to deal with three different types of coalescence is proposed,and a prediction-and-correction algorithm is also proposed to solve the problem of competitive propagation of complex cracks.Taking two horizontal offset cracks as an example,the correctness of the proposed intersection strategy is verified,the interaction mechanism between cracks is investigated,and the influence of crack offset distance on fracture parameters and crack propagation paths is analyzed.Numerical simulations are carried out for multiple cracks,and the propagation patterns of multiple cracks are studied to verify the effectiveness of the proposed prediction-and-correction algorithm.In addition,the evolution processes of complex cross cracks are numerically simulated to verify that the proposed numerical method can effectively solve the problem of complex cross crack propagation without special treatment for the intersection points.(3)The fracture problem of rock-like materials with pre-existing cracks under uniaxial compression is studied.Considering the maximum circumferential stress criterion as the only fracture criterion,wing crack as the dominant crack propagation pattern can be captured.Combined with the maximum circumferential stress criterion and Mohr-Coulomb criterion,the initiation and propagation of both wing crack and secondary crack can be captured.The uniaxial compression numerical test of rock-like specimens with multiple cracks is also carried out,and the complex crack propagation and coalescence patterns are observed,which verifies the excellent ability of the field-enriched finite element method in simulating multiple crack propagation and coalescence under compressive load.(4)A field-enriched finite element dynamic framework is developed,two kinds of cracks are considered: stationary cracks and moving cracks,the corresponding calculation formulas of dynamic stress intensity factors are introduced for these two kinds of cracks,and numerical experiments are carried out for stationary cracks and moving cracks,respectively.For stationary cracks,the dynamic fracture parameters of different test configurations,different crack arrangements and different loading conditions are calculated,and the dynamic information is investigated.Numerical examples are adopted to verify the ability of the dynamic FE-FEM method to deal with dynamic fracture problems.(5)The perfect matching layer(PML)absorption boundary is introduced in the field-enriched finite element method.By comparing the two numerical models with and without the perfect matching layer,the necessity of adopting the absorption boundary and the absorption effect of the perfect matching layer on dynamic waves are demonstrated.In this numerical framework,the crack propagation evolution in the surrounding rock around tunnel and the fracture evolution pattern of cracked rock slope under dynamic loads are numerically investigated.