Studies On Crack Problem In Gravity Dam Heel Based On Extended Finite Element Method

Cracks in concrete gravity dam heel are usually subjected to high head pressure,which intensifies the crack propagation,which exacerbates crack propagation and is extremely detrimental to dam safety.Considering the hydraulic pressure load on the fracture surface of dam heel,and carrying out the crack propagation analysis of the gravity dam heel,it is of great engineering significance to improve dam operation management and safety assessment.Extended finite element method is a numerical method with unique advantages in the analysis of discontinuous problems.The displacement field can be constructed by selecting different enhancement functions to meet the needs of specific problems,so that the form of the approximation function is independent of the meshing and the mesh reconstruction in the crack propagation is avoided.In this paper,the extended finite element method is used to simulate the crack of gravity dam heel considering the hydraulic pressure of fracture surface.The main research contents are as follows:(1)The basic principle of extended finite element method based on fracture mechanics is studied.The governing equation of extended finite element method for hydraulic fracturing analysis is derived.The calculation method of stress intensity factor and dynamic stress intensity factor considering hydraulic load on fracture surface are researched and realized by numerical simulation.The applicability and effectiveness of the calculation method are proved by comparing the subsequent simulation results with the literature conclusions.(2)A mathematical model of crack in gravity dam heel under the action of hydraulic pressure on fracture surface is constructed based on the extended finite element method.The model is used to calculate the influence of the water pressure distribution on fracture surface,the elastic modulus ratio of the bedrock and the concrete dam and the initial crack length on the dam crack under the hydrostatic pressure.The results show that the stress intensity factors K_?and K_?of crack tip increase gradually with the increase of the initial crack length and the elastic modulus ratio of the bedrock and the concrete dam.The crack gradually spread to the dam foundation surface.The influence of the distribution of water pressure on fracture surface on the stress intensity factor can not be ignored.When the water pressure distribution pattern of the fracture surface is uniform distribution,linear distribution and secondary distribution,the crack stress intensity factor K?gradually decreases,and K?gradually increases.And the crack gradually extends to the rock foundation.(3)Dynamic expansion analysis of cracks in gravity dam heel is carried out by using extended finite element method and Newmark implicit time integral.A mathematical model of seismic fracture of crack in dam heel of gravity dam considering the effect of water pressure on fracture surface is established.The crack propagation path,the time-history variation of equivalent stress intensity factor and the peak value of dynamic stress intensity factor are calculated by using the model.The calculation results show that the crack extension length decreases gradually with the increase of elastic modulus ratio of the bedrock and the concrete dam.The crack propagation length is gradually reduced when the water pressure distribution pattern of the fracture surface is uniform,linear and secondary.The initial length of the crack and the water pressure distribution form of the fracture surface have no obvious influence on the fluctuation period of the equivalent stress intensity factor.But the fluctuation period of equivalent stress intensity factor decreases with the increase of elastic modulus ratio between dam foundation and dam body.The influence of the elastic modulus ratio of dam foundation to dam body,the initial crack length and the water pressure distribution form of the fracture surface on the peak value of the dynamic stress intensity factor can not be ignored and should be paid enough attention in the dam operation management and safety assessment.