Upper Bound Limit Analysis Of Three-dimensional Stability Of Hole-wall With Slurry Support

In the process of drilling,the stability of borehole wall is a key issue which has been widely existed and paid much attention to.At present,the two-dimensional analysis method is mainly used in the theoretical analysis of the hole-wall stability.The influence of the aperture size and the circumferential squeezing action of the soil around the hole wall is ignored.The hole diameter with respect to the drilling depth is much smaller,and the three-dimensional effect is more significant.The stability of hole-wall is a typical three-dimensional mechanical problem.How to effectively and reliably evaluate the stability of hole-wall in the process of drilling and excavation and to guide practical engineering is an urgent problem to be solved by engineers and technicians.In this paper,based on the upper bound limit method,the limit analysis method of the three-dimensional stability of the hole-wall is proposed by a series of upper bound solutions and example analysis.At the same time,the finite element analysis method is used to realize the three-dimensional numerical simulation of the drilling and excavation process.The main research work and results are as follows:(1)The three-dimensional translational failure mechanism was established,and the external power and internal energy dissipation of the three-dimensional instability mechanism were calculated.According to the principle of energy,the formula for calculating the critical depth of drilling hole is deduced.The formula takes borehole radius,borehole depth,tangential force,mud weight,soil weight and soil shear strength into consideration.(2)Combined with the strength reduction method,the upper bound solution of the three-dimensional stability factor of the hole-wall was derived.The 3D stability of the hole-wall is transformed into a nonlinear programming problem.The minimum upper bound solution of the three-dimensional stability coefficient of the hole-wall is obtained according to the nonlinear optimization function in MATLAB.Through whether to consider the three-dimensional analysis results under the tangential force,and the comparative analysis with the two-dimensional analysis results,it shows that it is necessary to consider the tangential force in the three-dimensional stability analysis of the hole-wall.(3)When the aperture tends to infinity,the three-dimensional analysis of the hole-wall stability in this paper can be converted into two-dimensional analysis.A numerical example is given to compare the results of the three-dimensional stability analysis of the borehole wall with those of the previous studies.It shows that the existing studies are conservative in the stability analysis of the hole wall.The method in this paper can fully consider the influence of the hole size and the self-stability of the soil around the hole-wall.(4)Through the finite element analysis method,a three-dimensional numerical simulation of the drilling and excavation process was carried out,and the tangential stress change of the soil around the hole-wall after the drilling was analyzed.The critical depth and the three-dimensional stability coefficient of the hole-wall were obtained.The rationality of the method is further verified by comparing the calculated results with the numerical simulation results.Through a series of variable parameter analysis,the influence of soil shear strength,mud weight,hole diameter and hole depth on the stability of hole-wall is analyzed.