An Analytical Method For Mechanical Analysis Of Rockbolts In An Arbitrary Hole-shaped Tunnel

The excavation and support of underground tunnels has always been an important and difficult problem in the field of geotechnical and underground engineering.During the construction of underground engineering,the excavation of the tunnel will cause deformation and stress concentration of the surrounding rock.In the engineering practice,rockbolts and linings are generally used to support the surrounding rock to improve the stress distribution and limit the excessive deformation.There are many factors affecting the effect of tunnel support,such as the primitive in-situ stress,the mechanical parameters of the surrounding rock and the rockbolts,the geometric parameters of the tunnel and the rockbolts,the pre-tightening force of the rockbolts,etc.In order to achieve better supporting effect,it is necessary to analyze the axial force of the rockbolts under different layout schemes and the stress field and displacement field of the rock mass after excavation and support of the cavern.In this paper,the interaction problem between rockbolts and surrounding rock in deep underground tunnel is simplified to a plane strain problem with multiple pairs of concentrated forces in an infinite domain with one hole.For an infinite domain containing an arbitrary hole-shaped tunnel with a concentrated force load is applied at any point in the domain,using the complex variable function method,mapping the research domain to the unit circle outer domain on the image plane by conformal transformation,and combining The Cauchy integral solution method,this paper has obtained the exact analytical solution of the stress field and the displacement field of the problem,and further obtained the stress and displacement expressions of the multiple pairs of concentrated forces in the domain according to the superposition principle of the elastic mechanics.Based on the above displacement expression and the simplification,this paper has established the displacement coordination condition between the rockbolts and surrounding rock,by solving the corresponding system of linear equations,the results gives the axial force of the rockbolts under the condition of no pre-tightening force and pre-tightening force,which provides a theoretical basis for the optimum design of the rockbolt supporting.Taking the straight wall semi-circular arch tunnel as an example,the influence of lateral pressure coefficient,elastic modulus ratio of rockbolt to surrounding rock,length of rockbolt and pre-tightening force on the size and distribution of the axial force of rockbolts is quantitatively analyzed,then the effect of rockbolts on the stress state of surrounding rock under different layout schemes is further compared,and the optimization method of the tunnel bolt arrangement is proposed.