CN-121980843-A - Roadway high-prestress end anchor support calculation method based on finite element virtual anchor element

CN121980843ACN 121980843 ACN121980843 ACN 121980843ACN-121980843-A

Abstract

The invention relates to the technical field of geotechnical engineering numerical simulation and underground engineering support, and discloses a roadway high-prestress end anchor support calculation method based on a finite element virtual anchor element, which comprises the steps of constructing an independent grid and dividing an anchor rod into an end anchor section, a free section and a tray section; the method comprises the steps of constructing geometric coupling by introducing double Lagrangian multipliers based on a virtual work principle, establishing a rigidity equation of a dimension-reducing coupling system through variable replacement, respectively defining a nonlinear bonding sliding model, zero rigidity contact and locking constraint for each section, converting prestress into initial strain, constructing a tray surface pressure dynamic feedback mechanism reflecting the increase of axial force caused by expansion of surrounding rock, assembling a global tangential rigidity matrix, solving a nonlinear equilibrium equation by utilizing a Newton-Lafson algorithm, and inverting the axial force and the shear stress. The invention realizes grid independence, characterizes the segmental differential mechanical behavior and the prestress dynamic coupling evolution, and effectively solves the problem that the traditional numerical simulation is difficult to reflect the real supporting mechanism.

Inventors

GAO FUQIANG
WANG SHOUGUANG
KANG HONGPU
LIU WENJU
LIU XIAOMIN

Assignees

中煤科工开采研究院有限公司

Dates

Publication Date: 20260505
Application Date: 20251218

Claims (10)

1. The roadway high-prestress end anchor supporting and calculating method based on the finite element virtual anchor element is characterized by comprising the following steps of: S1, constructing an anchor rod finite element grid and a surrounding rock finite element grid with mutually independent spatial positions, and dividing anchor rod nodes into an end anchor segment node set, a free segment node set and a tray segment node set according to the axial coordinates of anchor rod nodes, end anchoring length parameters and anchor rod effective length parameters; s2, constructing an independent stiffness equation of the anchor rod and the surrounding rock based on a virtual work principle, introducing a double Lagrangian multiplier to construct a geometric coupling relation, eliminating the freedom degree of the anchor rod through variable substitution, and constructing a dimension-reducing coupling system stiffness equation with core variables of surrounding rock node displacement and local relative displacement; s3, defining a nonlinear bonding sliding constitutive model for the end anchor section node set, defining zero-stiffness contact constraint for the free section node set, defining unidirectional normal support and tangential locking constraint for the tray section node set, converting preset locking prestress into initial axial strain of an anchor rod unit, and constructing a tray surface pressure dynamic feedback mechanism reflecting the increase of the anchor rod shaft force caused by expansion deformation of surrounding rock; S4, assembling a global tangential stiffness matrix comprising a system foundation elastic stiffness matrix and a full-system contact tangential stiffness matrix, solving a total nonlinear incremental balance equation by utilizing a Newton-Lapherson iterative algorithm, and inverting and calculating the anchor rod shaft force distribution and the interface shear stress distribution according to the converged system state.
2. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchor according to claim 1, wherein in step S1, the step of dividing the anchor rod node into an end anchor segment node set, a free segment node set and a tray segment node set specifically comprises: drawing anchor rod nodes positioned in the range from the bottom of the hole to the anchoring length of the end part into the end anchor section node set; scribing anchor rod nodes which are positioned outside the end anchoring length and are not equal to the effective length of the anchor rod into the free section node set; And (3) scribing anchor rod nodes with axial coordinates equal to the effective length of the anchor rods into the tray segment node sets.
3. The method for calculating the roadway high-prestress end anchor support based on the finite element virtual anchor according to claim 1, wherein in the step S2, the steps of introducing double lagrangian multipliers to construct a geometric coupling relation and constructing a rigidity equation of a dimension-reducing coupling system through variable substitution specifically comprise: the geometrical coupling relation is constructed by defining a relative displacement function of the anchor rod and surrounding rock and utilizing a biorthogonal basis function to conduct interpolation dispersion on contact stress; and constructing a geometric coupling matrix, and projecting the displacement field mapping of the surrounding rock node into equivalent displacement at the anchor rod node position by using the geometric coupling matrix, so as to execute the variable substitution.
4. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchor as recited in claim 3, wherein in step S2, the step of establishing a dimension-reduction coupling system stiffness equation further specifically comprises: Defining a system state vector of the coupling system stiffness equation to be composed of only surrounding rock node displacement vectors and local relative displacement vectors; and constructing a tangential stiffness matrix comprising the reinforced surrounding rock stiffness matrix, an anchor rod stiffness matrix projected under a local contact coordinate system and a mechanical coupling term between surrounding rock deformation and interface sliding.
5. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchors according to claim 1, wherein in step S3, the step of defining a nonlinear bond slip constitutive model for the end anchor segment node set specifically includes: Applying radial deformation coordination constraint in the normal direction by adopting a penalty function method; An evolution equation of interfacial shear stress as a function of tangential slip is defined in the tangential direction to describe the overall process shear behavior including elastic loading, nonlinear strengthening, peak softening, and residual friction.
6. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchors according to claim 1, wherein in step S3, zero-stiffness contact constraint is defined for the free segment node set, and unidirectional normal support and tangential locking constraint is defined for the tray segment node set, comprising the following steps: Setting a local contact residual force vector and a local tangential stiffness matrix to be zero for the free section node set, and allowing the anchor rod to independently displace relative to surrounding rock in the axial direction and the radial direction; for the tray segment node set, determining a contact state by utilizing a Herveledy step function in a normal direction, applying a high-rigidity support constraint, and applying a static friction locking constraint in a tangential direction.
7. The method for calculating the roadway high-prestress end anchor support based on the finite element virtual anchor according to claim 1, wherein in the step S3, the step of constructing a dynamic feedback mechanism of the surface pressure of the tray reflecting the increase of the axial force of the anchor rod caused by the expansion deformation of the surrounding rock specifically comprises the following steps: setting the initial axial strain to be a negative value for representing the shrinkage trend without external force balance; In the iteration process, the anchor rod node displacement is updated according to the current surrounding rock node displacement, the real dynamic axial stress after the initial strain is superimposed is calculated through the linear elastic constitutive relation of the anchor rod unit, and the node unbalanced force generated by the real dynamic axial stress is mapped into the dynamic equivalent surface pressure load acting on the surrounding rock surface.
8. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchors according to claim 1, wherein in step S4, the step of assembling a global tangential stiffness matrix including a system base elastic stiffness matrix and a full system contact tangential stiffness matrix specifically includes: superposing the system basic elastic stiffness matrix which is kept constant and the full-system contact tangent stiffness matrix which is updated along with the iteration step; Wherein the full system contact tangential stiffness matrix has a piecewise diagonal characteristic, there are non-zero elements only at the degrees of freedom positions corresponding to the local relative displacements, and the assembling step comprises updating tangential stiffness values only in accordance with the current tangential relative displacement.
9. The method for calculating roadway high-prestress end anchor support based on finite element virtual anchor according to claim 1, wherein in step S4, the step of solving the overall nonlinear incremental balance equation by using newton-raphson iterative algorithm specifically comprises: calculating the current system state increment by solving a linear equation set, updating the total displacement vector of the system, reconstructing an internal force vector and updating the total residual force vector; and judging that the system converges when the norm of the total residual force vector and the displacement correction norm simultaneously meet the preset tolerance.
10. The method for calculating the roadway high-prestress end anchor support based on the finite element virtual anchor according to claim 1, wherein in the step S4, the step of calculating the anchor axis force distribution and the interface shear stress distribution according to the converged system state inversion specifically comprises: Reconstructing global node displacement of the anchor rod by utilizing the geometric coupling relation and the converged surrounding rock node displacement and the local relative displacement; calculating the axial tension of the anchor rod unit based on the anchor rod global node displacement and the initial axial strain; And calculating the interfacial shear stress based on the converged tangential relative displacement and the nonlinear bond sliding constitutive model.

Description

Roadway high-prestress end anchor support calculation method based on finite element virtual anchor element Technical Field The invention relates to the technical field of geotechnical engineering numerical simulation and underground engineering support, in particular to a roadway high-prestress end anchor support calculation method based on finite element virtual anchor elements. Background The high prestress end anchor support is a main form of coal mine roadway surrounding rock control. In order to optimize the support design, numerical simulation methods are widely used. However, the prior art simulation techniques still have drawbacks in dealing with such complex support problems: Firstly, when an anchoring model is built by the existing finite element method, surrounding rock grid nodes are required to be strictly matched with anchor rod paths or embedded units depending on grids are adopted. The pretreatment modeling is extremely complicated, the spatial decoupling of the anchor rod and the surrounding rock cannot be realized, and in addition, when the large-scale three-dimensional nonlinearity problem is calculated, the calculation efficiency is low and the convergence is poor due to strong grid dependence. Secondly, the existing mechanical model often adopts full-length bonding or even spring assumption, and cannot distinguish the sectional structural characteristics of end anchor rod end anchoring, middle free and tail tray locking. The simplification process ignores nonlinear sliding and softening of the end anchor section, friction-free stretching of the free section and strong locking effect of the tray, so that a progressive failure mechanism of the support structure in a complex environment cannot be truly reflected. Finally, it is difficult to accurately simulate the dynamic coupling mechanism under the action of high prestressing force in the prior art. The prestress is generally simplified into constant static load or simple constraint, the process that the surface pressure of the tray dynamically evolves along with the expansion deformation of the surrounding rock is ignored, the closed loop feedback effect that the axial force is increased due to the deformation of the surrounding rock can not be captured, the surface pressure of the tray is further increased, the deformation is reversely restrained, and the active constraint effect of the high prestress support is difficult to quantitatively analyze. Disclosure of Invention Aiming at the defects of the prior art, the invention provides a roadway high-prestress end anchor supporting calculation method based on a finite element virtual anchor, which solves the problems that grid independence and convergence are poor, an end anchor progressive failure mechanism cannot be accurately simulated and a high-prestress active supporting effect is difficult to quantify in large-scale three-dimensional calculation in the prior art. In order to achieve the purpose, the invention provides a roadway high-prestress end anchor support calculation method based on finite element virtual anchor elements, which comprises the steps of constructing an anchor rod finite element grid and a surrounding rock finite element grid. The anchor rod finite element grids and the surrounding rock finite element grids are mutually independent in space position. And dividing the anchor rod node into an end anchor section node set, a free section node set and a tray section node set according to the axial coordinate of the anchor rod node, the end anchor length parameter and the anchor rod effective length parameter. The method is based on the virtual work principle to construct an independent stiffness equation of the anchor rod and the surrounding rock, and introduces a double Lagrangian multiplier to construct a geometric coupling relation. And the freedom degree of the anchor rod is eliminated through variable replacement, and a dimension-reducing coupling system stiffness equation with core variables of surrounding rock node displacement and local relative displacement is established. And defining a nonlinear bonding slip constitutive model for the end anchor section node set, defining zero-stiffness contact constraint for the free section node set, and defining unidirectional normal support and tangential locking constraint for the tray section node set. And converting the preset locking prestress into the initial axial strain of the anchor rod unit, and constructing a tray surface pressure dynamic feedback mechanism reflecting the increase of the anchor rod shaft force caused by the expansion deformation of the surrounding rock. And finally, assembling a global tangential stiffness matrix comprising a system foundation elastic stiffness matrix and a full-system contact tangential stiffness matrix, solving a total nonlinear incremental balance equation by utilizing a Newton-Lapherson iterative algorithm, and inverting and calculating the axial force distribution and t