Multi-field Coupling Material Point Method And Its Application In Rock Fracturing Simulation

Under the background of promoting the western development in the new era and the "30·60" dual carbon goal,the complex engineering environmental conditions have posed severe challenges to the design and construction of rock engineering,and the huge pressure of carbon reduction tasks has also promoted the continuous technological innovation and upgrading of the geological and mineral industry,all of which are inseparable from the theoretical basis of rock mechanics.This involves not only the cracking and failure process of rock,but also a series of complex multi-physical field processes including flow,solid,heat,chemistry,even mass transfer and phase transformation.Therefore,it is necessary to develop numerical methods related to rock fracturing and multi-physical coupling as soon as possible.However,the limitation of continuity hypothesis in the simulation of rock cracking and failure still makes it difficult to solve such complex discontinuous problems.For the simulation of rock multi-field coupling,the grid-like method still faces great challenges in the field of fluid-structure coupling.The material point method has the dual properties of grid and particle,which is not constrained by grid in rock cracking and failure problem,and is suitable for simulating fluid and solid at the same time.Therefore,it has great potential in solving the above problems.Material point method is still in its preliminary stage of development today,however,for complex rock cracking and multi-field coupling simulation research is very limited and very incomplete.Therefore,the material point method is further improved and extended in this paper,so that it can play its own advantages in the above problems and be applied to more complex rock mechanics,the specific contents and achievements are as follows:(1)Based on the basic principle of the traditional material point method,the Drucker-Prager yield criterion commonly used in rock mechanics was introduced into the material point method,so as to build a complete material point method calculation process,and develop the material point method calculation program on the Matlab platform.The program includes data input,node mapping,momentum updated,stress updated,and data output five different functions of the subroutine,can realize the explicit solution to dynamic problems,and after three examples of the cohesiveless soil collapse,fluid leak,and rock under uniaxial compression test,the applicability and accuracy of the program in different scenarios are verified.(2)On the basis of the basic material point method,the extended material point method is proposed by introducing the crack description method,phantom node segmentation algorithm,multi-crack contact algorithm and particle interaction integral method.The algorithm can accurately track the crack surface,divide the discontinuous velocity field around any complex crack,simulate the frictional contact between multiple intersecting crack surfaces,and predict the crack propagation.Four numerical examples were used to verify the correctness of the above four methods,and the uniaxial compression tests of rock specimens with two prefabricated cracks were simulated,and three crack propagation modes including wing crack propagation,shear crack propagation and wing crack propagation with prefabricated crack were achieved.(3)On the basis of material point space discretization and explicit time integration of the basic heat transfer equation,the temperature field and strain field under the unified framework of material point method are solved.And the coupling between temperature field and strain field is realized by calculating temperature strain,then puts forward the thermo-mechanical coupling material point method,the algorithm can realize the calculation of thermal stress,and the calculation of contact thermal conductivity between discontinuous surfaces can be realized.Three numerical examples were used to verify the accuracy of the thermo-mechanical coupled material point method,and the simulation of cryogenic fracturing test was carried out.It was found that the cracks exhibit approximately equal spacing and periodic and hierarchical distribution due to the interaction between cracks during crack initiation and propagation.(4)The mass conservation and momentum conservation equations of solid and liquid phase were solved separately by using the double-point material point method,and then the fluid-structure coupling material point method was proposed.By introducing porosity gradient and smoothing function,the method could simulate the fluid-structure interaction in porous media and cracks at the same time.The correctness of the fluid-structure coupling material point method is verified by two examples of fluid-structure coupling in porous media with and without fractures,and the method is applied to the hydraulic fracturing simulation of single and multiple fractures,and the crack propagation law in hydraulic fracturing process is analyzed.(5)On the basis of double points material point method,using the local equilibrium hypothesis,the energy conservation equation of solid and liquid phase was added,realizing the simulation of heat transfer and heat exchange between fluid and solid,and then puts forward the flow-thermal coupling material point method,this method can simulate fluid-thermal coupling in porous media and cracks simultaneously.Through two numerical examples of fluid thermal coupling in porous media with and without cracks,the results verify the accuracy of the fluid-thermal coupling material point method,at the same time the method was applied to the problem of hot dry rock geothermal reservoir simulation,it was found that increasing the convective heat transfer coefficient between fluid and solid in thermal reservoir rock plays a significant role in improving the efficiency of geothermal exploitation.(6)Combined with the above basic principles of thermal-mechanical coupled material point method,fluid-structure coupled material point method and fluid-thermal coupled material point method,the multi-field coupled material point method is proposed.This method can realize the coupling of fluid-solid-thermal fields,and the sensible heat capacity method is adopted in this method,the phase function is coupled with other physical fields,so the coupling simulation of pore fluid phase transformation process can be realized.Through the two examples of phase change heat transfer and frost heave,the correctness of the proposed method was verified,and a case of frost heaving of rock is successfully simulated by multi-field coupled material point method,the different stages of rock deformation during frost heave are analyzed.